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Emulating the Adaptation of Wind Fields to Complex Terrain with Deep Learning

Emulating the Adaptation of Wind Fields to Complex Terrain with Deep Learning JANUARY 2023 L E T O U M EL I N ET A L . 1 a a b,c d d LOUIS LE TOUMELIN , ISABELLE GOUTTEVIN, NORA HELBIG, CLOVIS GALIEZ, MATHIS ROUX, AND FATIMA KARBOU Université Grenoble Alpes, Université de Toulouse, Météo-France, CNRS, CNRM, Centre d’Études de la Neige, Grenoble, France WSL Institute for Snow and Avalanche Research SLF, Davos, Switzerland Eastern Switzerland University of Applied Sciences, Rapperswil, Switzerland Université Grenoble Alpes, CNRS, Grenoble Institute of Engineering, Jean Kuntzmann Laboratory, Grenoble, France (Manuscript received 19 May 2022, in final form 14 October 2022) ABSTRACT: Estimating the impact of wind-driven snow transport requires modeling wind fields with a lower grid spac- ing than the spacing on the order of 1 or a few kilometers used in the current numerical weather prediction (NWP) systems. In this context, we introduce a new strategy to downscale wind fields from NWP systems to decametric scales, using high- resolution (30 m) topographic information. Our method (named “DEVINE”) is leveraged on a convolutional neural net- work (CNN), trained to replicate the behavior of the complex atmospheric model ARPS, and was previously run on a large number (7279) of synthetic Gaussian topographies under controlled weather conditions. A 10-fold cross validation reveals that our CNN is able to accurately emulate the behavior of ARPS (mean absolute error for wind speed 5 0.16 m s ). We then apply DEVINE to real cases in the Alps, that is, downscaling wind fields forecast by the AROME NWP system using information from real alpine topographies. DEVINE proved able to reproduce main features of wind fields in complex terrain (acceleration on ridges, leeward deceleration, and deviations around obstacles). Furthermore, an evaluation on quality-checked observations acquired at 61 sites in the French Alps reveals improved behavior of the downscaled winds (AROME wind speed mean bias is reduced by 27% with DEVINE), especially at the most elevated and exposed stations. Wind direction is, however, only slightly modified. Hence, despite some current limitations in- herited from the ARPS simulations setup, DEVINE appears to be an efficient downscaling tool whose minimalist ar- chitecture, low input data requirements (NWP wind fields and high-resolution topography), and competitive computing times may be attractive for operational applications. SIGNIFICANCE STATEMENT: Wind largely influences the spatial distribution of snow in mountains, with direct consequences on hydrology and avalanche hazard. Most operational models predicting wind in complex terrain use a grid spacing on the order of several kilometers, too coarse to represent the real patterns of mountain winds. We intro- duce a novel method based on deep learning to increase this spatial resolution while maintaining acceptable computa- tional costs. Our method mimics the behavior of a complex model that is able to represent part of the complexity of mountain winds by using topographic information only. We compared our results with observations collected in com- plex terrain and showed that our model improves the representation of winds, notably at the most elevated and ex- posed observation stations. KEYWORDS: Snow; Wind; Artificial intelligence; Data science; Deep learning; Machine learning 1. Introduction importance for human activities, with consequences in terms of flood hazard, hydropower management, and more gener- The transport of snow particles by the wind, hereinafter re- ally water resource management (Lehning 2013; Jorg- ¨ Hess ferred to as drifting snow, is a key process for understanding et al. 2015; Vionnet et al. 2020). At the scale of a mountain the spatial distribution of mountain snowpacks (Mott et al. slope, drifting snow is also influencing the evolution of ava- 2018). Drifting snow redistributes both falling hydrometeors lanche hazard (Schweizer et al. 2003; Lehning et al. 2000), before they reach the surface and snow originating from the thus impacting the safety of infrastructures and people. surface through mechanisms of ablation and deposition. As In addition to its influence on snow preferential deposition, the mountain snowpack acts as a major freshwater reservoir wind fields are the major driving factor of snow erosion over during winter and spring in continental areas, its spatial distri- snow-covered areas (Xie et al. 2021). Topography has a strong bution prior to and during the melting periods is of high influence on wind fields, first influencing the motion of large- scale air masses (Wanner and Furger 1990), and second intro- ducing a strong spatial variability in wind fields at a very local scale (Lewis et al. 2008; Sharples et al. 2010; Butler et al. Supplemental information related to this paper is available at the Journals Online website: https://doi.org/10.1175/AIES-D-22- 2015). Dynamic modifications of incoming flows, often re- 0034.s1. ferred to as terrain-forced flows (Whiteman 2000), occur when air masses interact locally with topography. The most noticeable features of terrain-forced flows are speedup on Corresponding author: Louis Le Toumelin, louis.letoumelin@ gmail.com mountain crests, accelerations across gaps and passes, or DOI: 10.1175/AIES-D-22-0034.1 e220034 Ó 2023 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses). 2 AR TI F I C I A L I N T E LLI G E N C E F O R T H E E AR TH S Y S T E M S VOLUME 2 changes in wind direction with channeling in topographic de- et al. (2020) similarly used CNN to downscale wind fields but pressions and around obstacles (Whiteman 2000). at a larger spatial scale, capturing physical processes that influ- Mountain wind fields commonly present a high variability ence the motion of synoptic air masses. at a local scale (,100 m) (Mott et al. 2018), intrinsically lim- In this study, we leverage on a combination of simulations iting the benefit of numerical weather prediction systems obtained with a complex atmospheric model and deep learning (NWP), which generally operate with a horizontal grid spac- methods to tackle the issue of wind downscaling in complex ter- ing above 1 km (e.g., Baldauf et al. 2011; Seity et al. 2011; rain. We proceed as follows: we use a high number of existing Kehler et al. 2016; Pickering et al. 2020). Furthermore, basic atmospheric model simulations performed with the Advanced interpolation methods (i.e., linear, polynomial), when ap- Regional Prediction System (ARPS) atmospheric model, all ob- plied to synoptic winds provided by NWP models, do not ac- tained under controlled atmospheric conditions over a set of curately represent the complex reality of mountain winds synthetic Gaussian topographies (Helbig et al. 2017). Using (Wagenbrenner et al. 2016). Consequently, dynamic down- those simulations, we derive a link between coarse-scale wind scaling methods are often used to infer the behavior of fields (such as winds provided by an NWP), topography, and mountain winds at a local scale (Raderschall et al. 2008; high-resolution wind fields through a parameterization, in a Mott and Lehning 2010; Vionnet et al. 2014). These meth- manner similar to statistical downscaling. However, in our case, ods rely on complex atmospheric models to handle coarse- the statistical relationship is automatically determined using an scale signal, and to generate high-resolution wind fields. artificial intelligence model and, more specifically, a CNN. They solve equations of state describing the flow, including its interaction with the terrain and more generally the representa- 2. Data tion of various physical processes that most directly determine a. ARPS simulations the large spatial variability of wind fields in complex terrain (Mott and Lehning 2010). The counterpart of this complexity 1) ARPS CONFIGURATION lies in large computing requirements, hence restricting the use ARPS is an atmospheric model that solves the nonhydro- of the method to small domains and/or limited time scales static and compressible Navier–Stokes equations. A detailed (Mott and Lehning 2010; Vionnet et al. 2014). Therefore, mod- description of the model implementation can be found in els with relatively low complexity have been developed and (Xue et al. 2000, 2001). Notably, the model is able to repre- provide a good trade-off in terms of physical complexity versus sent several features of terrain-forced flow such as speedup numerical costs (Forthofer et al. 2014; Vionnet et al. 2021). on crests, sheltering, separation, recirculation, topographic Statistical parameterizations using topographic information channeling (Raderschall et al. 2008), and thermally driven have also been largely used to bridge the gap between coarse- scale-resolution wind fields provided by NWP models and the winds such as valley breezes (Anquetin et al. 1998). high-resolution forcings required by small-scale applications Helbig et al. (2017) performed individual simulations with and, notably, drifting snow models (Liston and Elder 2006; ARPS on synthetic topographies derived from isotropic and Helbig et al. 2017; Winstral et al. 2017). Such downscaling stationary Gaussian random fields (GRF). GRF are stochas- methods identify parameters expected to capture the effect tic processes, that have been identified as a good proxy for of topography on the wind fields and then apply statistical real topographies, particularly in their ability to approxi- operations to transform the coarse-scale signal into a dis- mate real slope distributions (Helbig and Lowe 2012)and tributed signal at a higher target resolution. The choice of have already been successfully used to develop topo- accurate parameters relies both on the identification of graphic parameterizations (Helbig and Lo ¨we 2012, 2014; dominant physical processes at a local scale (e.g., sheltering, Helbig et al. 2017). In this study, we make use of ARPS exposition, channeling) and their formulation through a simulations performed on individual Gaussian topogra- mathematical expression (using, e.g., curvature, slope, and phies (Helbig et al. 2017). Each simulation covers a rectan- Laplacian). For example, the MicroMet model (Liston and gle of 79 3 69 pixels with a horizontal resolution of 30 m. Elder 2006) identified slope, terrain slope azimuth, and cur- Notably, a broad range of topographic characteristics was vature as relevant parameters to account for the effect of achieved by selecting nine combinations of the two charac- local topography on wind fields, whereas Winstral et al. (2017) teristic length scales: the typical width j [200–1000 m; see modeled sheltering/exposure of locations to wind using the Eq. (1)] and typical height s (88–364 m) of topographic DEM terrain parameter Sx (Winstral et al. 2002;see section 3a)and features, for 5 spatial mean square slopes m (198–368)within a the topographic position index (TPI; Weiss 2001). Comple- topography: mentarily, Helbig et al. (2017) identified the local Laplacian from terrain elevations and squared slope as valuable parame- 2 3 s DEM j 5 : (1) ters to downscale wind speeds. Recently, new statistical ap- proaches have emerged to downscale wind fields in complex terrain (Bonavita et al. 2021). Notably, Dujardin and Lehning Each combination of j, s generated 200 realizations, re- DEM (2022) proposed an architecture based on convolutional neural sulting in a total of 9000 topographies [for more technical de- network (CNN) to process both topographic information and tails see Table 2 in Helbig et al. (2017)]. About 80% of the NWP data in order to perform pointwise predictions of wind topographies (7279) resulted in usable simulated wind fields fields in the Swiss Alps at high resolution (,100 m). Hohlein and were used in this study. JANUARY 2023 L E T O U M EL I N ET A L . 3 FIG.1. (a)–(c) Maps featuring examples of Gaussian topographies, and (d)–(f) surface winds from the ARPS first layer on these topog- raphies. The ARPS first layer has a mean elevation above ground of 2.95 m. These three simulations, as labeled, exemplify topography and model output couples that constitute our training database. For these ARPS simulations, constant initial atmospheric The speed of the wind outputs (three-dimensional outputs, 2 2 2 conditions were chosen. Notably, all simulations were initial- speed computed using u 1 y 1 w ) are distributed follow- ized with a constant wind profile, initially oriented from left ing Fig. 2a. As noted in Helbig et al. (2017), the mean wind speed simulated by ARPS is always slightly less than 3 m s , to right (wind coming from the west) with a speed of 3 m s . the speed that served as initialization. Notably, the steeper The atmospheric stability was fixed as neutral (as frequently the mean slope, the lower the mean wind speed. This behav- observed during drifting snow episodes) and radiation effects ior exemplifies the mean drag exerted by the topography were neglected (Helbig et al. 2017). Thermally driven flows on the flow and the associated loss of momentum, which is were neglected to solely represent the interaction between intensified on rougher terrain. Oppositely, the distribution large-scale flow and topography. The total integration time tails highlight more frequent intense wind speeds on steep was limited to 30 s (with an integration time step of 0.1 s), pro- topographies. We note that ARPS simulates accelerations hibiting the dominance of turbulence in the outputs, and re- up to 4 times the initial wind speed and reductions to almost stricting the simulated flow to the resultant of the adaptation null wind speeds. of a mean flow to local topography (Raderschall et al. 2008; ARPS simulated wind fields deviated from the direction of Mott and Lehning 2010). In all simulations, the surface was the input wind (west) in both directions according to Fig. 2b. representative of uniform snow-covered areas, with an aero- Counterclockwise and clockwise deviations are equally rep- dynamic roughness length of 0.01 m. We give an example of resented in our dataset and range from 08 to 828. The distri- three ARPS simulations, encompassing different mean slopes bution of angular deviations is centered on zero for each (308,108, and 368) and j (400 and 800 m), and their associated category of mean slope and deviations introduced by ARPS topography in Fig. 1 (see also the same figure with normal- are generally low. Such deviations can be representative of ized axis in section S.6 and Fig. S4 in the online supplemental flow deflections around obstacles, alignment of the flow on material). Notably, we observe accelerations on peaks (red ar- ridges and more generally encompass an adaptation of the rows) and deceleration windward and leeward (blue arrows). flow to local topography. The formation of turbulent struc- The intensity of the modifications of the high-resolution wind tures was deliberately prevented in the ARPS simulations differs with mean slope and j, the largest modulations occur- used here as training dataset: the ARPS wind fields thus do ring on the steepest topographies. not describe more complex behaviors of mountain winds, such as turbulent recirculation or extremely strong devia- 2) CHARACTERISTICS OF THE SIMULATIONS tions (e.g., barrier jets), which are generally epitomized by We describe in this section the characteristics of ARPS higher angular deviations (Raderschall et al. 2008; Sharples wind outputs (Fig. 2), which constitute our training database. et al. 2010; Whiteman 2000). Similar to the situation with 4 AR TI F I C I A L I N T E LLI G E N C E F O R T H E E AR TH S Y S T E M S VOLUME 2 Mean slope [°] (a) (b) Wind speed [m/s] Angular deviation from West [°] FIG. 2. (a) Wind speed and (b) angular deviation distributions as simulated by ARPS on the 7279 Gaussian topogra- phies. Such winds constitute the training dataset used to fit the CNN of the DEVINE model. wind speeds, we observe that the most intense wind direc- and climate observations {Glacier, an Observatory of the Climate tion modifications from the input wind occur on the steepest [les Glacier, un Observatoire du Climat (GLACIOCLIM)]} mean slopes. network. Three other ones are located at Col du Lac Blanc (latitude 5 45.128,longitude 5 6.118; elevation 5 2720 m) in the b. AROME simulations Grandes Rousses massif and belong to a high-mountain meteo- AROME is a limited-area NWP system used by Meteo- rological observatory dedicated to drifting snow and snow– France (Seity et al. 2011). It provides short-term forecasts of atmosphere interactions (Vionnet et al. 2017; Guyomarc’het al. atmospheric fields since 2008, over a domain encompassing 2019). The61sites cover thewhole French Alps and a largevari- the French Alps. Benefiting from its high horizontal resolu- ety of terrain, with some stations being located on flat surfaces, tion (1300 m) and complex physics and dynamics, the model other on slopes, and some on exposed terrain (e.g., Aiguille du has gained interest for mountain meteorology and snow sci- Midi: latitude 5 45.878,longitude 5 6.888; elevation 5 3845 m). ences, progressively bridging the gap with coarser atmo- The observation stations are mainly located in nonforested areas spheric products currently used to force snow models over and are mostly snow covered during the winter seasons. the French mountain ranges (Quéno et al. 2016; Vernay Wind observations are commonly subject to measurement et al. 2022; Gouttevin et al. 2023). AROME solves the errors (DeGaetano 1997), particularly when collected in a nonhydrostatic fully compressible Euler equations system challenging mountainous environment. These measurement using hybrid pressure terrain-following coordinates. Nota- errors can be of diverse nature and occur at different steps bly, AROME uses a subgrid parameterization to describe during the data collection process (Lucio-Eceiza et al. 2018a). the influence of unresolved orography on wind fields, via an A striking example of wind sensor dysfunction in mountain effective roughness length described in Georgelin et al. terrain is null and constant wind speed observations for (1994). We used here 10-m AROME wind fields initialized several consecutive hours due to the accretion of ice on the from the 0000 UTC analysis, from which we extracted daily sensor. Because our data come from different networks, forecasts between 0000 UTC 1 7 h and 0000 UTC 1 30 h at their quality is unequal. Thus, we homogenized the quality an hourly resolution. This way, we reconstructed continuous standard of our dataset by applying a quality check, deeply time series of gridded wind fields over the French Alps for a inspired by Lucio-Eceiza et al. (2018a,b). These authors period of interest extending from 1 August 2017 to 31 May proposed a series of sequential tests designed to detect suspicious wind observations. We adapted the quality pro- cess of Lucio-Eceiza et al. (2018a,b) to fitthe specificities c. Observations of our dataset by selecting the most relevant tests and Hourly observations of wind speed and direction have eventually introducing some modifications, as listed in sec- been collected and quality-checked in order to evaluate tion S.1 in the online supplemental material. We refer to the downscaling scheme over real alpine topographies. A Lucio-Eceiza et al. (2018a,b) for the evaluation of the qual- total of 61 automatic weather stations (AWS) acquiring ity process. wind measurements have been selected in the French Alps (Fig. 3). Most of them are part of Meteo-France operational 3. Method observational network. Three stations: Vallot observatory This paper’s method is organized as follows: we first build a (latitude 5 45.838, longitude 5 6.858;elevation 5 4360 m), Argentieres glacier (latitude 5 45.968,longitude 5 6.978; statistical model by notably fitting a CNN to ARPS simula- elevation 5 2434 m), and Saint-Sorlin glacier (latitude 5 45.178, tions. Then we use this statistical model to downscale wind longitude 5 6.178;elevation 5 2720 m) are part of the glacier fields from the AROME NWP system in the French Alps. JANUARY 2023 L E T O U M EL I N ET A L . 5 FIG. 3. Locations of observation stations (colored triangles) used for model evaluation. The colors of the observation sites indicate their elevation ranges. The small application domain used later in Fig. 6 is outlined in blue, and the larger domain that is used later in Fig. 7 is outlined in red and magnified in the zoom. a. Topographic descriptors Sx 5 (z 2 z )/d , where |tan[(z 2 z )/d ]| 5 max |tan[(z 2 j i ij j i ij k k z )/d ]|, with x being the cell of interest and k being the index i ik i In this study we make use of several parameters describing of any pixel located in a zone starting from x and extending the topography and derived from digital elevation models toward a direction defined by the incoming wind direction, (DEMs), all with a 30-m horizontal resolution dx. Here, we within a 308 window and a 300-m maximum distance from x . describe these parameters shortly with references: the TPI Last, d indicates the distance between x and x . In summary, ij i j (Weiss 2001) compares the elevation of a DEM pixel with the positive values for Sx indicate sheltering for x , that is, how mean elevation of the neighboring pixels given a fixed radius. much x is protected from incoming wind within a 300-m ra- The radius is equal to 500 m in our study, and consequently dius, whereas negative Sx values quantify exposure. TPI and the TPI parameter is oriented toward the detection of topo- Sx are thus computed using information from neighboring graphic peaks/bowls on the slope scale. The Sx parameter pixels within a given radius and thus integrate information (Winstral et al. 2002), is a direction-dependent parameter and from areas located within a few hundreds of meters to charac- quantifies how sheltered or exposed a pixel is within a given radius [here 300 m, as in Winstral et al. (2017)]. In detail, terize each DEM pixel. In contrast, the discrete Laplacian Df: f (x 1 dx, y) 1 f(x 2 dx, y) 1 f(x, y 1 dx) 1 f(x, y 2 dx) 2 4f(x, y) D(fx, y) 5 , (2) dx which aims at detecting local peaks and bowls in topographic for pattern recognition among spatialized data. Fully convolu- maps, and the squared slope, referred to as slope and com- tional neural networks (FCN) are a specific type of CNN, pro- puted following Helbig et al. (2017), only consider nearest- posing an end-to-end solution relying on convolutional and neighbor pixels in addition to the cell of interest and hence pooling layers without any use of dense networks, making provide very local topographic information. We use these them an efficient solution for gridded predictions. Convolu- four parameters to characterize alpine and Gaussian topogra- tional layers consist of convolving a filter (i.e., a matrix with a phies in sections 4 and 5. predetermined size) to input data so as to detect spatial pat- terns. The product of convolutions goes through pooling b. Fully convolutional neural networks layers that reduce their spatial resolution. Repeating both op- CNN are a specific kind of neural network that benefits the erations hence permits us to encode spatial features with a use of convolution operations on tensors and are well suited high level of abstraction. In FCN, encoding operations can be 6 AR TI F I C I A L I N T E LLI G E N C E F O R T H E E AR TH S Y S T E M S VOLUME 2 FIG.4.Workflow of the downscaling model DEVINE. Both preprocessing operations (labeled A–E) and postprocessing opera- tions (labeled F) are required before and after calling the CNN for predictions. In detail, label A corresponds to the selection of wind fields in the form of gridded outputs provided by an NWP system. This grid is interpolated (label B), and the following opera- tions are done pixelwise: DEM data around each pixel are first selected (label C), then rotated with respect to the initial wind direc- tion provided by the NWP system, and finally cropped (label E) to match the CNN input size. The CNN is then called and outputs high-resolution maps of wind fields. Within the CNN, the following standard operations are used: normalization, padding maps with zeros (“ZeroPadding”), convolutions (“Conv.”), dropout connection (“Dropout,” only during training), maximum pooling op- eration (“MaxPooling”), concatenations (“Concat.”), cropping map borders (“Cropping”), and increasing the size of a matrix by re- peating its rows and columns (“UpSampling2D”). Small numbers next to each layer represent the number of features maps. The scaled outputs of the CNN go through an activation layer to ensure that plausible values are produced. Wind patches are ultimately rotated back and placed on the high-resolution grid to constitute a continuous map of wind fields (label F). followed by a decoding stage, where convolutions are mixed performance are investigated using 10-fold cross validation. with spatial interpolations of the encoded signal, to sequentially Cross validation consists of randomly partitioning our data- increase the spatial resolution. The Unet architecture has been base into “training” data (90% of the data) and “test” data introduced in 2015 (Ronneberger et al. 2015) and constitutes a (the remaining 10%), which permits us to fit the CNN on the specific type of FCN frequently used for meteorological applica- first group and evaluate its performance on the second group. tions (Trebing et al. 2021; Ferna ´ndez and Mehrkanoon 2021). For a more robust evaluation, the process is repeated 10 times In Unet (Fig. 4), encoding and decoding stages are connected by rolling over 10 random training/test splits. Furthermore, we through concatenation operations, which makes it possible to extracted validation data from the training data (i.e., 10% of transfer high-resolution information to lower-resolution infor- the remaining 90% among the 10 folds) to follow a validation mation within the model architecture. Indeed, data in the first loss (mean absolute error on validation data) during training. layers of the Unet have not been through almost any pooling We sequentially reduced the learning rate when the loss reached operation. Hence, this “raw” (or moderately encoded) infor- aplateau (“reduce on plateau”), and eventually stopped the mation from the encoding stage is used to complement en- learning process (“early stopping”) whenever the validation loss coded and processed information from the decoding stage. stopped decreasing for 15 epochs (“patience”). This approach, Such an operation is also frequently referred to as “skip con- coupled with the fact that after validation the CNN outputs are nection” (Lagerquist et al. 2021). evaluated on an independent test set, aims at limiting the risk of Here, two-dimensional topographic maps are fed into a overfitting the training set. In our specific case, hyperparameter Unet architecture. The model then outputs three features tuning did not prove crucial to converge toward an efficient maps, each one of them representing a component of the CNN architecture, as the training statistics highlighted a low wind vector. To determine the appropriate filters used in sensibility to the different hyperparameters. We adopted a the convolutional layers, the Unet is fitted during a training shallower version of the initially published Unet with only step using Gaussian topographies as inputs and ARPS simu- two additional layers corresponding to dropout connections, lationsaslabels (see section 1). Model architecture and added to limit overfitting during the training phase. The selected JANUARY 2023 L E T O U M EL I N ET A L . 7 hyperparameters are summarized in section S.4 and Table S.1 in outputted by the CNN [UV ;Eq. (3)] using AROME wind cnn the online supplemental material. speed [UV ;Eq. (3)], as CNN outputs are only valid for AROME an input speed of 3 m s [UV ;Eq. (3) and section 2a]: initARPS c. DEVINE downscaling model UV cnn Several preprocessing and postprocessing steps are required UV 5 UV 3 : (3) scaling AROME UV initARPS before and after calling the CNN in order to generate high- resolution wind predictions on real topographies (Fig. 4). Their We discuss the implication of this assumption in section 5. combination with the CNN forms a full downscaling scheme Given that we extrapolate results obtained on a set of Gaussian that we named Downscaling Wind Fields in Complex Terrain topographies under controlled atmospheric conditions to the with Deep Learning, Applications for Nivology and Associated very vast diversity of real topographies and atmospheric condi- Challenges [Descente d’Echelle de Vent par Méthodes d’Ap- tions (section 5a), we introduced a custom activation layer using prentissage Profond, Application pour la Nivologie et ses En- a modified arctan function g that eventually curbs predicted un- jeux (DEVINE)]. realistic large wind speeds at extreme locations to plausible First, the initial NWP gridded outputs (Fig. 4:label A) wind speeds: are upsampled using bilinear interpolation (using a factor of 2) (Fig. 4: label B). This step is necessary to ensure that g(x) 5 a arctan(x/a): (4) the initial NWP signal is (i) dense enough to produce continu- ous wind fields at 30-m spatial resolution, and (ii) smoothly This function does not act as a bias corrective term, but densified before calling the Unet, so that the final high- rather as a safety guard: we defined a maximum acceptable resolution maps produced are not affected by chesslike mean speed in our model (60 m s ), which is above the patterns. First, the initial NWP gridded outputs (Fig. 4: maximum observed speed in our historical observational da- label A) are interpolated using bilinear interpolation and taset (36 m s ) and scaled the parameter a (538.2) so that an interpolation rate of two (the dimensions of the inter- the g limit in positive infinity is equal to 60. The choice of the polated grid are twice the original dimensions) (Fig. 4: function arctan is motivated by the shape of the function g label B). Two reasons justify the use of interpolation: (monotonically increasing and progressively departing from the firstly since the outputs of our CNN are of predetermined 1–1 line for speeds above 20 m s ; see section S.5 and Fig. S3 size (79 3 69 pixels), we have to ensure that predicted in the online supplemental material). Following these proper- maps (around each NWP pixel) are sufficiently large to be ties, g has an almost null impact on downscaled wind speeds juxtaposed one next to each other without introducing any lower than 20 m s (i.e., most of the time) and starts lowering hole in the final downscaled map. In our case, the grid speeds for outputs larger than .20 m s .Hence, g limits the spacing configuration (DEM 5 30 m; NWP 5 1300 m) en- simulation of unrealistic wind speeds that could potentially be sures having no holes in the final maps. But for applica- obtained when particularly high NWP wind speeds are associ- tions with, for example, another NWP system of coarser ated with the highest accelerations, generally obtained on the grid spacing, an initial interpolation of the NWP grid may most exposed locations in real topographies. be used to ensure spatial continuity. Second the use of in- In the final step of the DEVINE model, the downscaled terpolation is motivated by the necessity to reduce chess- pixels generated by the CNN are rotated back to their original board-like patterns. Such patterns appear at the NWP gridcell position (Fig. 4: label F), in the opposite direction of the first boundaries when downscaling gridded data (Winstral et al. rotation (Fig. 4: label D), and assembled to reconstruct a con- 2017; Dujardin and Lehning 2022); see section 5c. They can be tinuous regularly spaced grid of wind predictions, with a hori- largely diminished by downscaling an interpolated map, that is, zontal grid spacing of 30 m. CNN outputs can overlap one on downscaling a higher-resolution grid where the transition be- each other and are thus cropped (patch size 5 23 pixels) to avoid overlapping areas in the final predictions. tween wind values of two neighboring grid points is less abrupt than in the original grid. Then, each interpolated NWP pixel is downscaled sequentially as described hereinafter. For each in- 4. Results terpolated NWP pixel, high-resolution topography patches sur- a. Performance at emulating ARPS rounding the pixel are first extracted (patches of size 140 3 140 pixels, Fig. 4: label C) and then rotated with respect to the We first assess the performance of the CNN at emulating NWP wind direction so that the rotated direction is from the ARPS on synthetic topographies on the test datasets, using west (Fig. 4: label D), similar to the ARPS simulations. The ro- 10-fold cross validation (Fig. 5 and Table 1). We computed the tated patches of topography are then cropped (to 79 3 69 pixel error between all predicted maps and corresponding labels pix- size), normalized using their mean value and the standard de- elwise and categorized the CNN errors (i.e., the difference be- viation of the Gaussian topographies used during the training tween modeled and observed value, definedat eachtime step) phase, and then go through the CNN (Fig. 4: label E), which in terms of topographic characteristics (TPI, Sx, Laplacian, and produces three maps corresponding to the three components slope) to interpret the results encapsulated in integrated met- of wind speed. Horizontal wind speed and direction are then rics. Each TPI, Sx, Laplacian, and slope values are sorted ac- computed from wind components. This step eventually in- cording to their position in their respective distribution using volves a linear scaling [UV ;Eq. (3)] applied to the speeds the0.25quantile q , 0.5 quantile q , and 0.75 quantile q .We scaling 25 50 75 8 AR TI F I C I A L I N T E LLI G E N C E F O R T H E E AR TH S Y S T E M S VOLUME 2 (a) (b) (c) (d) (g) (e) (f) (h) TPI [m] Sx [rad] Slope [°] FIG. 5. Performance (errors) of the CNN at reproducing ARPS behavior on Gaussian topographies, using a 10-fold cross validation. All of the statistics presented have been acquired using test data (i.e., data not used during the training phase) and explored using parameters describing the topography (TPI, Sx, Laplacian, and slope). All parameters are categorized in four classes according to the quantiles of the parameter distribution (q , q ,and q ). Each boxplot has been computed using approximately 10 million samples. 25 50 75 observe that all errors on the test groups are centered on 0, sug- fact that the largest wind speeds and angular deviations are also gesting that the CNN is able to produce unbiased estimations observed on the most complex terrain: when relative errors of ARPS wind fields. Errors are relatively low: boxplots suggest (i.e., errors at each time steps divided by ARPS wind speed) that most of the speed errors are lower than 0.25 m s ,with a are considered, the performances of the CNN are more bal- mean absolute error of 0.16 m s (5% of the initial wind speed; anced among all topographic classes (see section S.2 and Table 1). Similarly, most of wind direction errors range be- Fig. S1 in the online supplemental material). We note that tween 25and 5 .More specifically, we observe that the pixels the meridional component of the wind presents lower errors corresponding to the most complex terrain (i.e., steepest slopes than the zonal component (Table 1), also in line with stron- or tails of the parameter distributions) lead to larger errors, sug- ger zonal wind speeds due to ARPS initial conditions (wind gesting the difficulty to capture wind behavior in the most ex- coming from the west). Last, we analyzed the spatial loca- treme terrains (Fig. 5). However, this could be explained by the tion of the errors and observed that most errors are located TABLE 1. Performance of the Unet model at emulating ARPS on Gaussian topographies, using a 10-fold cross validation. All the statistics presented have been acquired using test data (i.e., data not used during the training phase); U, V, and W respectively refer 2 2 to the zonal, meridional, and vertical component of wind speed; UV designates the horizontal wind speed ( U 1 V ); and UVW is 2 2 2 the three-dimensional wind speed ( U 1 V 1 W ). Also, AE refers to absolute error and r is the Pearson correlation coefficient. 21 21 21 21 21 U (m s ) V (m s ) W (m s )UV(ms ) UVW (m s ) Wind direction (8) Mean bias ,0.01 ,0.01 ,0.01 ,0.01 ,0.01 } Mean AE 0.15 0.13 0.06 0.16 0.16 3 q25 AE 0.04 0.04 0.01 0.04 0.04 1 q50 AE 0.10 0.08 0.03 0.10 0.10 2 q75 AE 0.19 0.17 0.08 0.20 0.21 3 r 0.96 0.94 0.99 0.96 0.95 } Speed error Direction error [m/s] [°] JANUARY 2023 L E T O U M EL I N ET A L . 9 1e6 (a) (b) D M 1e6 (c) D M FIG. 6. Downscaling AROME wind fields at Col du Lac Blanc using DEVINE for three specific dates: (a) 1100 UTC 7 Mar 2018, (b) 0900 UTC 6 Apr 2021, and (c) 0000 UTC 9 Apr 2021; M, L, and D correspond to three in situ wind obser- vations (Muzelle, Lac, and Dome stations), and A corresponds to the AROME forecast wind field. The x and y coordi- nates are expressed in Lambert 93 projection, i.e. EPSG 2154. Note that the left y axes are divided by 1 3 10 . on the margins of topography maps (see section S.3 and (A in Fig. 6; distance to the Lac station 5 148 m, and pixel ele- Fig. S2 in the online supplemental material). vation 5 2681 m) is first extracted for three dates (Fig. 6a: 1100 UTC 7 March 2018; Fig. 6b: 0900 UTC 6 April 2021; b. Case study: Application to a small domain Fig. 6c: 0000 UTC 9 April 2021) and then downscaled using We explore the behavior of DEVINE on real topographies DEVINE. We selected the dates using the following criteria: by first downscaling a single AROME grid cell surrounding (i) three distinct initial wind direction (respectively, west, the Col du Lac Blanc experimental site in the French Alps north, and east as simulated by AROME), (ii) different (Fig. 6). This observation site (see section 2c) is composed AROME speeds (#3, ’3, and $3m s ), (iii) AROME of three distinct AWS located between tens to a few hundreds of roughly in phase with local observations (speed error less than meters from each other. The Lac station (L in Fig. 6; elevation 5 8 2m s and direction error less than 90 ), and (iv) including 2720 m) and Muzelle (M in Fig. 6; elevation 2722 m) are one “close to training” condition, that is, a neutrally stratified both located along a north–south pass. The relative proxim- boundary layer (20.1 # observed Richardson number ≤ 0.1) ity of the two stations makes them subject to very similar lo- with an AROME speed close to 3 m s (Fig. 6c). cal wind conditions. On the contrary the Dome station (D in At 1100 UTC 7 March 2018, a west flux blows above the Fig. 6; elevation 5 2808 m) is located on a small hill, domi- massif, with AROME locally simulating a low wind speed nating the pass by 85 m in elevation. This station is more (1.4 m s ) with a west-southwest direction, (2438). DEVINE subject to the influence of the hill on the local flow and is downscales the AROME signal and increases the speed on D more exposed (TPI at Dome 5 164 m, TPI at Muzelle 5 (2 m s ). The flow is decelerated on both the windward and 224 m, and TPI at Lac 5227 m). In our case study, infor- the leeward areas, but it is almost unchanged when compared 21 21 mation from the nearest interpolated AROME grid point with AROME at M and L (1.3 m s at L and 1.4 m s at M; Wind speed [m/s] Wind speed [m/s] Wind speed [m/s] 10 AR TI F I C I A L I N T E LLI G E N C E F O R T H E E AR TH S Y S T E M S VOLUME 2 model). DEVINE acceleration patterns at D are consistent the modeling of drifting snow, as, for example, the zones of with the observations (observed wind speed at D 5 2m s ), deceleration simulated in Fig. 6 could potentially favor flux but the model fails to fully capture deceleration at M and L convergence and hence shape drifting snow deposition (respectively, 1 and 0.4 m s for the observations). In terms (Vionnet et al. 2021). Further work might use more dense of direction, the observed wind aligns perpendicularly to the observation networks such as in Taylor and Teunissen topographic barrier at D (2858, observation), a feature par- (1987), Butler et al. (2015),and Wagenbrenner et al. (2016) tially captured by DEVINE (2538; model). The model then to better characterize the spatial variability of DEVINE suggests a small deviation of the flow toward the north of the wind fields. pass (2278; model), which is slightly confirmed by observation c. Case study: Application to a large domain at M (2578; observation). However, L suggests an orientation of the flow toward the south of the pass (3038; observation), The DEVINE architecture can also be deployed on larger but the direction observation is acquired for an almost null domains than Fig. 6 to downscale wind fields provided by wind speed (0.4 m s ; observation). gridded outputs of an NWP (Fig. 7). We selected a 40 km On the second example (Fig. 6b; 0900 UTC 6 April 2021), by 30 km domain in the French Alps (Fig. 7a), and down- the synoptic conditions indicate a flux from the north above scaled AROME wind forecast at 1500 UTC 11 July 2019 the western French Alps, and AROME locally forecasts a (Figs. 7b–d). For this specific date, the dominant wind direc- 27 wind direction (north-northeast) characterized by larger tion was from the west with maximum AROME speeds speeds (5.5 m s ). DEVINE accelerates AROME wind at reaching 7.7 m s . Figure 7 shows the initial AROME wind D(6.8 m s ; model), and across the pass at L and M (6.9 with a 1300-m horizontal resolution (green/yellow arrows) 21 21 and 7 m s ). The observed speed is larger at D (5.8 m s ; and the downscaled speeds at 30-m horizontal resolution observation) than at L and M (respectively, 4.1 and 4.6 m s ; (violet/orange color). We observe strong modifications of speeds observation). Interestingly, the acceleration at the pass, cap- on this domain (maximum downscaled speed 5 16.2 m s ). tured by DEVINE but not retrieved in the observation at this Highest downscaled wind speeds appear on clear lines in specific date, is a well-known behavior of wind fields at M and Fig. 7b, which mostly correspond to mountains ridges and sum- L, where drifting snow measuring devices have been specifi- mits as identified in Fig. 7a. Oppositely, dark violet areas corre- cally installed to monitor wind driven processes. In terms of di- spond to low wind speeds as simulated by DEVINE and are rection, DEVINE suggests almost no deviation at D, L and M often in phase with low AROME speeds (small arrows), sug- (338,198,and 188; model), a pattern not confirmed at L (648; gesting that even if DEVINE modifies the AROME signal, it observation). The explanation of this divergence can also be still respects important features provided by the NWP system retrieved in the observation acquisition process, because the (areas of high wind speeds vs areas of low wind speeds). quality control flagged as suspicious the direction observation Thus, even though DEVINE has been fitted to simulations per- at L for this specificdate. formed assuming certain weather conditions and is not able to On the third and final case (0000 UTC 9 April 2021), synoptic reproduce some processes of mountain winds at a local scale conditions feature a flux from the south with AROME simulat- (recirculation areas, thermally driven flows, etc.), the larger- ing a wind speed 5 2.4 m s and a wind direction 5 1308 scale wind fields simulated by AROME, which can be obtained (southeast). As in Figs. 6a and 6b, observations suggest stronger 21 under all types of weather conditions, can be used to drive the winds at D (3.4 m s ; observation) than L and M and this vari- 21 downscaling model. Accelerations and decelerations lie in the ability is captured by DEVINE (3.7 m s at D; model). This range of accelerations/decelerations as simulated by ARPS on could be interpreted by the incidence of the incoming synoptic synthetic topographies (section 2). We also observe strong accel- wind forecast by AROME, which is rather perpendicular to erations with DEVINE on the Grandes Rousses massif (Fig. 7a; the hill around D. AROME speeds are almost unmodified by 21 white ellipse) and on the Aiguille d’Arves massif (Fig. 7a;red DEVINE at M and L (respectively, 2.4 and 2.4 m s ; model), ellipse), which are both oriented toward a north–south axis a pattern confirmed by the observation at M and L (2.4 m s (thus perpendicular to the dominant synoptic wind on 11 July at M and 2.6 m s at L; observations). DEVINE agrees with 2019). Oppositely, the north of the Ecrin massif (Fig. 7a;black AROME direction without introducing any important direc- ellipse) is oriented east–west, along the main wind direction, tional shift at D, M, and L (respectively, 1268,1438, and 1448). and DEVINE does not suggest any strong acceleration on this Oppositely, the observations suggest a flow from the south more complex and higher massif. Thus, we draw the conclusion and a tendency to align along the pass at M and L (respec- that on this example DEVINE is able not only to detect ridges tively, 1638,2088, and 1618 at D). In this example, a small dif- and complex terrain but also to interpret the incidence angle be- ference in both speed and direction occurs between M and L, tween AROME wind fields and topographic features. We also which might highlight very local phenomena and more gener- observe angular deviations with respect to the AROME initial ally the spatial variability of wind speed at scales below 30 m direction (Fig. 7c; red and blue colors). These deviations mainly in complex terrain. lie in the range of ARPS deviations on Gaussian topogra- All the above examples illustrate how DEVINE produces ac- phies (deviations from AROME direction up to 818 on this celerations and decelerations with respect to the underlying to- pographic features, and how zones of accelerations/deceleration specific case study). The presence of red features (counter- and their relative intensity are a function of the AROME wind clockwise deviations) in Fig. 7 next to blue features (clock- direction that served as initialization. This is of high interest for wise deviations) suggests local circumventions of the flow JANUARY 2023 L E T O U M EL I N ET A L . 11 AROME wind speed [m/s] Angle between DEVINE and (a) Elevation [m] DEVINE wind speed [m/s] (c) (b) AROME wind fields [°] 0 km 18km Zoom (d) (e) 18 km 0 km FIG. 7. (a) Topography of an alpine domain and wind field simulations at 1500 UTC 11 Jul 2019, with (b) AROME (colored arrows) and DEVINE wind speed (color shading) on the domain, (c) AROME (colored arrows) and DEVINE angular deviations from AROME (color shading) on the domain, and (d) topography and DEVINE wind speeds projected on a vertical west–east transect, with (e) an en- largement of the area within the red-outlined box in (d). On this transect, the bases of the arrows locate the associated wind field. AROME wind fields are two-dimensional 10-m wind fields, whereas DEVINE wind fields also incorporate a vertical dimension. around topographic obstacles and channeling within valleys. supporting our above hypothesis. Conversely, some low ob- Last, we projected in Fig. 7d DEVINE 3D wind fields on an served wind speeds are overestimated by DEVINE. Further 18 km west–east transect (see the black horizontal bar in analyses show that the overestimation of low wind speeds by Figs. 7a–c). We observe on this transect accelerations DEVINE is, among other factors, imputable to the behav- (larger arrows) on peaks and changes in the vertical compo- ior of the model at a few exposed observation stations, nent of the wind field, which generally tend to follow the such as the Aiguille du Midi station (TPI 5 288 m). These terrain and to be oriented with respect to topographic fea- behaviors are discussed in section 5a. tures. From a modeling perspective, topography imposes A quantile-to-quantile analysis complements the compari- surface conditions that force the wind speed to orient fol- son of model wind speeds with in situ observations and indi- lowing the terrain. cates that the observed wind distribution is better captured by DEVINE than by AROME (Fig. 8c). The underestimation of d. Performance on real topographies high wind speeds in AROME is reflected by a departure from When compared with in situ observations collected at the the 1–1line in Fig. 8c for high quantiles. As partially observed 61 observation sites in the French Alps, AROME wind fields in Fig. 8b, high wind speeds are better captured by DEVINE, are characterized by a negative speed bias for high wind which is reflected by a better representation of the highest speeds (.10 m s )(Fig. 8a). This behavior has already been wind speed quantiles. However, as previously pointed out in documented (Vionnet et al. 2016; Gouttevin et al. 2023) and Fig. 8b the overestimation of low wind speeds contributes to might be to some extent explained by the 1.3-km horizontal simulating larger speeds and hence to obtain a better match grid spacing of the model that fails to capture wind accelera- on the 1–1 plot with DEVINE than with AROME in Fig. 8c. tions on ridges and speed variability due to subkilometric var- Further analysis reveals that DEVINE reduces wind speed iations of elevation. For lower wind speeds (,10 m s ), mean biases at most of the observation stations, whereas di- AROME is closer to the observations. The departure of the rection is only slightly affected. In Fig. 9, wind speed errors points from the 1–1 line for high wind speeds in Fig. 8a have first been normalized by the observed wind speed and is partly corrected by DEVINE downscaling (Fig. 8b), then categorized by TPI. Only speeds above 1 m s are Elevation [m] 12 AR TI F I C I A L I N T E LLI G E N C E F O R T H E E AR TH S Y S T E M S VOLUME 2 AROME DEVINE (a) (b) Observed wind speed [m/s] (c) Observed wind speed quantiles [m/s] FIG.8.(a) AROME 1–1 plot (modeled vs observed hourly values), (b) DEVINE 1–1 plot, and (c) quantile–quantile plot (each point being a quantile in the respective distributions, both discretized in 10 000 quantiles). In (a)–(c), the red line represents the 1–1 line. The color bar in (b) represents data density for (a) and (b). considered in this process. Error normalization is preferred in modifications are brought by DEVINE: the maximum modifi- our case as generally elevated stations are characterized by cation in direction introduced by DEVINE, at the 61 stations, stronger winds and consequently larger errors, thus scram- is equal to 378. We link this to the fact that (i) our CNN is fitted bling the interpretation when compared with stations located on ARPS model outputs where wind direction is generally only at lower elevations that are less prone to strong winds. slightly modified by topography (Fig. 2a) and (ii) the largest DEVINE reduces speed median errors among half of the TPI wind direction modifications are expected on the most complex classes, with a notable improvement for the most exposed sta- terrain (Fig. 2a), which corresponds to areas not necessarily tions, characterized by the largest TPI (q , TPI), where the equipped with AWS (section 5). negative speed mean bias is reduced by 66%. Among the 61 ob- We finally investigate the errors of DEVINE when com- servation stations, DEVINE significantly reduces wind speed pared with AROME, in a seasonal and diurnal perspective mean bias at 37 stations (dependent Student’s t test at a 95% (Fig. 10). This is done by considering the difference in the confidence interval, using Bonferroni method for multiple- normalized absolute error (defined as the absolute value of comparison correction), a feature concerning 58% of the sta- the error at each time step divided by the observed speed) of tions located above 1500 m. We also notice that correlation in both wind products, categorized into three distinct groups speed signals is only slightly improved with DEVINE (0.56 for based on the observed wind speed. The evolution of the nor- AROME vs 0.58 for DEVINE; Table 2). However, Fig. 9b indi- malized absolute error confirms that DEVINE mostly im- cates that errors in direction are almost unchanged between proves forecast for higher wind speeds (Fig. 10). Lowest wind AROME and DEVINE (average change in direction error less speeds are generally characterized by an increased absolute than 18). Furthermore, we observe that AROME can be af- error with DEVINE (brown color in Fig. 10), and wind speeds fected by strong direction errors (.908), for which only small above3m s are on the contrary characterized by a Modeled wind speed [m/s] Modeled wind speed quantiles [m/s] Densiity JANUARY 2023 L E T O U M EL I N ET A L . 13 (a) (b) Wind speed error / observed wind speed Wind direction error [] [°] FIG. 9. Performances in wind (a) speed and (b) direction of AROME and DEVINE on real topographies with respect to in situ observations (for observed wind speed $ 1m s ). Results are clustered by TPI according to the quantiles of the TPI distribution (q 5215 m, q 5 3m, and q 5 32 m). 25 50 75 decreased error with DEVINE (green color in Fig. 10). It rather than forecast lead time hour, also suggesting an influ- is interesting to note that for wind speeds below 3 m s , ence of thermal processes. the largest increases in normalized absolute error occur between April and September, and between 0900 and 5. Discussion 1700 UTC. This tends to occur at periods of highest incom- a. Representativity of Gaussian topographies ing shortwave radiations and temperatures, suggesting some influence of thermal processes (section 5c). Oppositely, visi- The characteristics of Gaussian topographies accurately ap- ble improvements occur with DEVINE during nights of sum- proximate the mean characteristics of alpine topographies mer months where atmospheric stability could be closer to (Fig. 11). For every pixel of a digital elevation model covering neutral conditions than during afternoons of the same periods. the French Alps, thus including the observation sites that More generally, we observe that improvements/degradations served for model evaluation in section 4d, we computed the with DEVINE tend to be more linked with validity hour TPI, Sx (using a fixed direction of 2708), Laplacian, and slope. TABLE 2. Evaluation statistics of AROME and DEVINE when compared with 61 AWS located in the French Alps, in terms of wind speed and direction. DEVINE designates DEVINE performances when DEVINE is initialized by realistic AROME forecasts. AROME forecasts are here considered to be realistic when the speed error is less than 3 m s and the direction error is less than 308 (AROME ). Variable Metric AROME DEVINE AROME DEVINE c c Speed Mean bias (m s ) 20.33 20.24 20.29 20.17 r (}) 0.56 0.58 0.73 0.72 Mean AE (m s ) 1.40 1.37 1.06 1.07 q AE (m s ) 0.44 0.44 0.41 0.40 q AE (m s ) 0.98 0.96 0.91 0.89 q AE (m s ) 1.89 1.84 0.91 0.89 Direction Mean AE (8)58 57 14 14 q AE (8)18 17 7 6 q AE (8)43 41 14 13 q AE (8)88 87 14 13 75 14 AR TI F I C I A L I N T E LLI G E N C E F O R T H E E AR TH S Y S T E M S VOLUME 2 FIG. 10. Evolution of the mean of the normalized absolute error (nAE) for wind speed between AROME and DEVINE (nAE 2 DEVINE nAE ), categorized by hour of the day and month of the year (the mean of the nAE corresponds to the mean of the absolute value AROME of the error at each time step divided by the observed wind speed) (a) only considering observed wind speed between 1 and 3 m s ,(b) for 21 21 wind speeds between 3 and 7 m s , and (c) for wind speeds above 7 m s . Negative values correspond to improvements (green), and positive values correspond to degradations (brown). We then compare the results with the same parameters obtained (2012), who showed that Gaussian statistics outperformed on the Gaussian topographies forming our training dataset other statistical models when representing slopes of real (Fig. 11). We observe that for each parameter, the distribu- topographies in complex terrain. tion obtained on Gaussian topographies (yellow distribu- However, for individual pixels, some terrain parameters tion) overlaps most of the distribution obtained on real derived on the real alpine topographies are not encom- passed in the range of the same parameters derived on the topographies (green distribution) suggesting that, with re- spect to the chosen parameters, most of the alpine topo- Gaussian topographies. These correspond to pixels located graphic pixels are represented in our Gaussian topographies in extremely complex terrain. Notably, the tail of the distribu- dataset. This strengthens the results of Helbig and Low ¨ e tion of Laplacians [Df;Eq. (2)] computed on real topographies (a) (b) TPI [m] FIG. 11. Parameters computed for each point of a real digital elevation model (“real topographies”; green), only at sites with wind observations (“observation stations”; red), and on Gaussian topographies used in our training dataset (“Gaussian topographies”; orange): (a) TPI vs Sx and (b) Laplacian [Eq. (2)] vs slope. The Sx values are computed us- ing a wind direction of 2708; A indicates the Aiguille du midi station, and V indicates the Vallot station. Sx [rad] Slope [] JANUARY 2023 L E T O U M EL I N ET A L . 15 TABLE 3. DEVINE computing performances on a 1250-km domain presented in Fig. 7 (40.9 km by 30.5 km; horizontal resolution of 30 m). The computing time does not account for data loading overhead (loading DEM map, NWP gridded outputs, etc.). Note that because the downscaling operation is not sequential through time it can be easily parallelized across time by using different processing units. Name Value Domain Domain size 40.9 km by 30.5 km Horizontal resolution (input) 1300 m Initial interpolation rate 2 Horizontal resolution (interpolated) 650 m No. of interpolated NWP grid points to downscale 3072 Performance on CPU CPU model Intel Core i7-10610U CPU at 1.80 GHz No. of CPU 1 Prediction (downscaling 1 time step) 64 s Prediction (downscaling 24 time steps) 1461 s Performance on a GPU 1 CPU GPU model Nvidia Tesla V100 No. of GPU 1 Prediction (downscaling 1 time step) 14 s Prediction (downscaling 24 time steps) 97 s exhibits the largest discrepancies with respect to their Gaussian Such a low computational cost is also attributable to our counterparts. choice of limiting input channels of the CNN to topographic Most of the topographies surrounding the observation sta- maps only. As a consequence, DEVINE only requires mini- tions, however, have characteristics well represented in our mal inputs (i.e., topography and initial wind fields provided by Gaussian topographies (red dots in Fig. 11). We nevertheless an NWP system) to output downscaled wind predictions at a note that some extreme locations such as the Aiguille du Midi high resolution. Following the topographic nature of the se- (TPI 5 288 m, Sx 520.88 rad, Laplacian 520.039 m s , lected inputs, we observed that DEVINE is able to detect and slope 5 0.29) or the Vallot station (TPI 5 120 m, main features of terrain-forced flow, including the representa- Sx 520.3 rad, Laplacian 520.033 m , and slope 5 0.58) tion of acceleration on ridges, deceleration on leeward areas, flow deflections and moderate deviations around obstacles are localized on the tails of the distributions obtained on the Gaussian topographies. We note that DEVINE frequently (Figs. 6 and 7). It is worth noting that contrary to Dujardin overestimates low wind speeds at Aiguille du midi, suggest- and Lehning (2022), who reached state-of-the-art results using ing current limitations of our method on such extremely ex- a downscaling model also based on CNN, we did not used precomputed topographic parameters (TPI, aspect, etc.) as in- posed and complex terrain, for which only few information puts. Indeed, we converged to low errors on the test dataset can be derived from the training dataset. It would be ques- tionable that adding more complex topographies to our by simply using raw topographic maps. Three factors emerge training dataset would be beneficial for DEVINE since nu- to explain our choice to use raw topographic data as inputs versus preprocessed topographic data as in Dujardin and merical limitations and errors can arise when computing Lehning (2022): our training dataset encompasses more top- wind fields on very steep slopes with mesoscale models (e.g., ographies [7279 vs 261 for Dujardin and Lehning (2022)], our Lundquist et al. 2012). CNN learns topographic features related to Gaussian topog- raphies versus real topographies in Dujardin and Lehning b. Efficient downscaling by using a CNN with (2022) and as we only have one channel in input, feature de- reduced complexity tection is directly oriented toward topographic characteristics Wind downscaling with DEVINE is particularly useful as it whereas Dujardin and Lehning (2022) join topographic maps comes with a low computational cost, when compared with with many other atmospheric variables when constituting the much more computationally expensive atmospheric models input channels, which could eventually make the detection of such as ARPS. Here, we optimized the model implementation topographic characteristic less direct. using a strategy leveraged on the graphical processing unit The impact of high-resolution topography on wind fields is (GPU) only for raw CNN predictions plus computationally reflected in the evaluation statistics, including a decrease in expensive rotations and left other pre- and postprocessing op- the mean bias, a more moderate reduction in MAE and a erations (interpolation, normalization, final activation, etc.) slightly increasing correlation. We emphasize the fact that our for the CPU. As a result, it is possible to downscale AROME method is only based on an emulation of the atmospheric fields as presented in Fig. 7,in 14 s (Table 3). These perform- model ARPS and does not need to be calibrated with any ob- ances pave the way for the use of our method in time con- servation, in contrast to Pohl et al. (2006), Liston and Elder strained applications, for instance as a downscaling tool to (2006), Winstral et al. (2017), and Dujardin and Lehning reach decametric scales within operational forecasting sys- (2022). It highlights that DEVINE upsamples NWP wind tems in complex terrain. fields but does not explicitly involve a bias correction, as was 16 AR TI F I C I A L I N T E LLI G E N C E F O R T H E E AR TH S Y S T E M S VOLUME 2 done, for example, in Winstral et al. (2017) and Dujardin and As described in section 1, DEVINE exhibits features of a Lehning (2022). Thus, DEVINE is independent from the NWP mostly nonturbulent flow, including the absence of recircula- tion zones (Raderschall et al. 2008; Sharples et al. 2010), whose system providing the initial information. However, as the initial impact on snow deposition is important (Vionnet et al. 2021). errors of the NWP are not compensated with any calibration Avoiding the inclusion of turbulent features favors the devel- step, they can eventually be propagated (Wagenbrenner et al. opment of simple yet generalizable outputs and is in phase 2016) and amplified through DEVINE. For instance, we ob- with the choice of an initial speed of 3 m s in ARPS simula- serve that when the wind fields simulated byAROME arein tions, where the generation of turbulent eddies due to wind– phase with the observation, that is, a direction error less than topography interaction is probably low (Whiteman 2000). 308 and a speed error less than 3 m s ,DEVINE mean bias is Again, this assumption might not stand for higher speeds. even more reduced (Table 2). We underline that simultaneous occurrence of assumptions i, ii, iii, and iv in the atmosphere is probably rare. However, c. Limits of our approach even though DEVINE is limited in terms of physical processes Apart from error propagation due to the initial errors of it can represent at the slope scale, it proves to add value as a the NWP (section 5b), limitations on the most extreme alpine downscaling tool of NWP wind fields in all weather conditions terrain (section 5a), and even though the CNN reproduces (Table 2, Fig. 10). Furthermore, the NWP system driving particularly well the ARPS simulations, some errors remain DEVINE is not bound to these assumptions so that it provides when predicting wind on real topographies (section 4). In- a representation of all atmospheric situations, to the extent en- deed, for simplicity and computational efficiency, we pruned abled by its spatial resolution and inherent assumptions. DEVINE to a minimalist architecture. In particular this was Note that AROME uses a parameterization of the subgrid possible following the assumptions used in the setup of the topography following Georgelin et al. (1994). Consequently, ARPS model (Helbig et al. 2017). Inheriting the assumption high-resolution wind fields obtained using DEVINE have inter- of the ARPS configuration, DEVINE assumes (i) a neutral acted twice with the topography: a first time through AROME stratification of the atmosphere, (ii) an absence of thermal subgrid parameterization and a second time through DEVINE. This redundancy could contribute to errors in wind fields processes, (iii) mostly nonturbulent flow, and (iv) a linear be- estimations. havior between the wind flow obtained for a 3 m s initial Also note that AROME wind fields (arrows in Fig. 7) are speed and output obtained with any other speed. first interpolated to double the horizontal resolution and limit For DEVINE, the assumption i on the neutral stratification the establishment of chesslike patterns in the output signal of the atmosphere may explain the model’s limited ability to (section 3c). Chessboard-like patterns correspond to colored drastically change wind direction. The thermal stability of the squares in the downscaled signal: as (i) two neighbors in an atmosphere influences the motion of air masses in complex NWP grid can forecast different wind conditions and (ii) as terrain, and more particularly, is responsible for large devia- each (interpolated) NWP grid point is treated independently tions of stable and heavy air masses (Whiteman 2000) that from its neighbors by DEVINE, discontinuity can appear at tend to get around obstacles rather than above. Additionally, the border of each grid cell in the downscaled signal. Such assumption iii is responsible for the absence of small-scale tur- patterns progressively disappear by increasing the interpola- bulent eddies in DEVINE simulations and thus also explain tion rate, at the expense of more computing time. Ultimately, the model difficulty to simulate large modifications in wind we note that the impact of chesslike patterns on the down- direction. scaled signal could impact drifting snow modeling, a task that We also attribute increasing normalized errors observed in requires spatially coherent wind forcing for the computation Fig. 10, for the lowest wind speeds, to the absence of thermal of snow flux divergences. This impact still has to be quantified processes in DEVINE. Butler et al. (2015) and Sharples et al. through the evaluation of distributed snowpack simulations. (2010) indicated the prominence of along-slope and valley flows during spring/summer months, underlining that the in- 6. Summary and conclusions tensity of some thermal flows largely depends on seasonality. Interestingly, we observe that the largest degradations with DEVINE is a downscaling scheme based on deep learning, DEVINE occur for observed wind speeds less than 3 m s relying on a fully convolutional neural network (Unet-like), during days of spring and summer month. that downscales NWP gridded wind fields from a grid spacing Moreover, using additional ARPS simulations performed on the order of several kilometers to tens of meters using to- by Helbig et al. (2017) on a small group of the Gaussian top- pographical information only. This model has been fitted using ographies using a different initial wind speed (5 m s instead simulations obtained with the model ARPS on a set of 7279 of 3 m s ), we challenged our assumption iii on linearity. We Gaussian topographies. We demonstrated that the Unet archi- observed that the acceleration rates obtained with an initial tecture is performant on a cross-validation dataset to emulate speed of 3 m s are consistent with the acceleration rates ob- the behavior of ARPS on synthetic topographies. By evaluat- tained at 5 m s , thus suggesting that the assumption on line- ing our model using simulations performed on real topogra- arity holds (not shown). However, we can expect that a phies and by using quality-checked data from 61 observation nonlinear relation would arise with higher wind speeds, which stations in the French Alps, we showed that DEVINE partially is still to be benchmarked. improves AROME wind speed forecasts, and is able to reproduce JANUARY 2023 L E T O U M EL I N ET A L . 17 Butler, B. W., and Coauthors, 2015: High-resolution observations observed wind speed patterns, thus providing a numerically effi- of the near-surface wind field over an isolated mountain and cient alternative to complex atmospheric models for simulations in a steep river canyon. Atmos. Chem. Phys., 15, 3785–3801, of high-resolution wind fields. Most notably, DEVINE reduces https://doi.org/10.5194/acp-15-3785-2015. AROME mean bias, slightly reduces the absolute error, and in- DeGaetano, A. T., 1997: A quality-control routine for hourly wind creases the correlation. Moreover, DEVINE outputs are consis- observations. J. Atmos. Oceanic Technol., 14,308–317, https:// tent with the well-known influence of main topographic features doi.org/10.1175/1520-0426(1997)014,0308:AQCRFH.2.0.CO;2. (peaks, slopes, and ridges) on airflow at local scale. Our method is Dujardin, J., and M. Lehning, 2022: Wind-topo: Downscaling developed for snow-transport applications and therefore does not near-surface wind fields to high-resolution topography in account for some processes that may be controlling the wind pat- highly complex terrain with deep learning. Quart. J. Roy. terns at a local scale in other conditions like thermal stability and Meteor. Soc., 148, 1368–1388, https://doi.org/10.1002/qj.4265. thermal winds. Using transfer learning and additional model Ferna ´ndez, J. G., and S. Mehrkanoon, 2021: Broad-Unet: Multi- simulations could be of interest to complement current capabili- scale feature learning for nowcasting tasks. Neural Network, ties of DEVINE. This would probably require thousands of new 144,419–427, https://doi.org/10.1016/j.neunet.2021.08.036. Forthofer, J. M., B. W. Butler, and N. S. Wagenbrenner, 2014: A high-resolution simulations to be used as labels and may induce comparison of three approaches for simulating fine-scale sur- modifying DEVINE architecture. Additionally, we discussed the face winds in support of wildland fire management. Part I. influence of several factors that could restrict DEVINE appli- Model formulation and comparison against measurements. cability and conclude that future work might focus on an Int. J. Wildland Fire, 23,969–981, https://doi.org/10.1071/ indirect distributed evaluation of the downscaling model, WF12089. through the use, for example, of remotely sensed data and Georgelin, M., E. Richard, M. Petitdidier, and A. Druilhet, 1994: Im- drifting snow models. Moreover, we note that reducing the pact of subgrid-scale orography parameterization on the simula- initial biases of the NWP could limit error propagation when tion of orographic flows. Mon. Wea. Rev., 122, 1509–1522, https:// increasing the spatial resolution of wind fields using DEVINE. doi.org/10.1175/1520-0493(1994)122,1509:IOSSOP.2.0.CO;2. A comprehensive intercomparison exercise of state-of-the-art Gouttevin, I., V. Vionnet, Y. Seity, A. Boone, M. Lafaysse, Y. downscaling models could help to benchmark solutions for Deliot, and H. Merzisen, 2023: To the origin of a wintertime drifting snow applications. screen-level temperature bias at high altitude in a kilometric NWP model. J. Hydrometeor., 24,53–71, https://doi.org/10. 1175/JHM-D-21-0200.1. Acknowledgments. This research is supported by the Guyomarc’h, G., and Coauthors, 2019: A meteorological and French Meteorological Institute (Météo-France). The au- blowing snow data set (2000–2016) from a high-elevation al- thors thank the national observation service GLACIOCLIM pine site (Col du Lac Blanc, France, 2720 m a.s.l.). Earth Syst. (CNRS-INSU, OSUG, IRD, INRAE, and IPEV) for the Sci. Data, 11,57–69, https://doi.org/10.5194/essd-11-57-2019. data provided. The authors thank Eric Bazile, Yann Seity, Helbig,N., andH.Lowe, 2012: Shortwave radiation parameteriza- Hugo Merzisen, and Ange Haddjeri for the meaningful dis- tion scheme for subgrid topography. J. Geophys. Res., 117, cussions that helped to build the study. D03112, https://doi.org/10.1029/2011JD016465. }},and }}, 2014: Parameterization of the spatially averaged Data availability statement. AROME outputs and all AWS sky view factor in complex topography. J. Geophys. Res. data that are not otherwise mentioned below can be re- Atmos., 119,4616–4625, https://doi.org/10.1002/2013JD020892. quested online (https://donneespubliques.meteofrance.fr/). }}, R. Mott, A. Van Herwijnen, A. Winstral, and T. Jonas, 2017: Parameterizing surface wind speed over complex topog- Training data are available from norahelbig@gmail.com upon raphy. J. Geophys. Res. Atmos., 122, 651–667, https://doi.org/ request. 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Part I: 10.1007/s007030170027. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Artificial Intelligence for the Earth Systems American Meteorological Society

Emulating the Adaptation of Wind Fields to Complex Terrain with Deep Learning

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JANUARY 2023 L E T O U M EL I N ET A L . 1 a a b,c d d LOUIS LE TOUMELIN , ISABELLE GOUTTEVIN, NORA HELBIG, CLOVIS GALIEZ, MATHIS ROUX, AND FATIMA KARBOU Université Grenoble Alpes, Université de Toulouse, Météo-France, CNRS, CNRM, Centre d’Études de la Neige, Grenoble, France WSL Institute for Snow and Avalanche Research SLF, Davos, Switzerland Eastern Switzerland University of Applied Sciences, Rapperswil, Switzerland Université Grenoble Alpes, CNRS, Grenoble Institute of Engineering, Jean Kuntzmann Laboratory, Grenoble, France (Manuscript received 19 May 2022, in final form 14 October 2022) ABSTRACT: Estimating the impact of wind-driven snow transport requires modeling wind fields with a lower grid spac- ing than the spacing on the order of 1 or a few kilometers used in the current numerical weather prediction (NWP) systems. In this context, we introduce a new strategy to downscale wind fields from NWP systems to decametric scales, using high- resolution (30 m) topographic information. Our method (named “DEVINE”) is leveraged on a convolutional neural net- work (CNN), trained to replicate the behavior of the complex atmospheric model ARPS, and was previously run on a large number (7279) of synthetic Gaussian topographies under controlled weather conditions. A 10-fold cross validation reveals that our CNN is able to accurately emulate the behavior of ARPS (mean absolute error for wind speed 5 0.16 m s ). We then apply DEVINE to real cases in the Alps, that is, downscaling wind fields forecast by the AROME NWP system using information from real alpine topographies. DEVINE proved able to reproduce main features of wind fields in complex terrain (acceleration on ridges, leeward deceleration, and deviations around obstacles). Furthermore, an evaluation on quality-checked observations acquired at 61 sites in the French Alps reveals improved behavior of the downscaled winds (AROME wind speed mean bias is reduced by 27% with DEVINE), especially at the most elevated and exposed stations. Wind direction is, however, only slightly modified. Hence, despite some current limitations in- herited from the ARPS simulations setup, DEVINE appears to be an efficient downscaling tool whose minimalist ar- chitecture, low input data requirements (NWP wind fields and high-resolution topography), and competitive computing times may be attractive for operational applications. SIGNIFICANCE STATEMENT: Wind largely influences the spatial distribution of snow in mountains, with direct consequences on hydrology and avalanche hazard. Most operational models predicting wind in complex terrain use a grid spacing on the order of several kilometers, too coarse to represent the real patterns of mountain winds. We intro- duce a novel method based on deep learning to increase this spatial resolution while maintaining acceptable computa- tional costs. Our method mimics the behavior of a complex model that is able to represent part of the complexity of mountain winds by using topographic information only. We compared our results with observations collected in com- plex terrain and showed that our model improves the representation of winds, notably at the most elevated and ex- posed observation stations. KEYWORDS: Snow; Wind; Artificial intelligence; Data science; Deep learning; Machine learning 1. Introduction importance for human activities, with consequences in terms of flood hazard, hydropower management, and more gener- The transport of snow particles by the wind, hereinafter re- ally water resource management (Lehning 2013; Jorg- ¨ Hess ferred to as drifting snow, is a key process for understanding et al. 2015; Vionnet et al. 2020). At the scale of a mountain the spatial distribution of mountain snowpacks (Mott et al. slope, drifting snow is also influencing the evolution of ava- 2018). Drifting snow redistributes both falling hydrometeors lanche hazard (Schweizer et al. 2003; Lehning et al. 2000), before they reach the surface and snow originating from the thus impacting the safety of infrastructures and people. surface through mechanisms of ablation and deposition. As In addition to its influence on snow preferential deposition, the mountain snowpack acts as a major freshwater reservoir wind fields are the major driving factor of snow erosion over during winter and spring in continental areas, its spatial distri- snow-covered areas (Xie et al. 2021). Topography has a strong bution prior to and during the melting periods is of high influence on wind fields, first influencing the motion of large- scale air masses (Wanner and Furger 1990), and second intro- ducing a strong spatial variability in wind fields at a very local scale (Lewis et al. 2008; Sharples et al. 2010; Butler et al. Supplemental information related to this paper is available at the Journals Online website: https://doi.org/10.1175/AIES-D-22- 2015). Dynamic modifications of incoming flows, often re- 0034.s1. ferred to as terrain-forced flows (Whiteman 2000), occur when air masses interact locally with topography. The most noticeable features of terrain-forced flows are speedup on Corresponding author: Louis Le Toumelin, louis.letoumelin@ gmail.com mountain crests, accelerations across gaps and passes, or DOI: 10.1175/AIES-D-22-0034.1 e220034 Ó 2023 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses). 2 AR TI F I C I A L I N T E LLI G E N C E F O R T H E E AR TH S Y S T E M S VOLUME 2 changes in wind direction with channeling in topographic de- et al. (2020) similarly used CNN to downscale wind fields but pressions and around obstacles (Whiteman 2000). at a larger spatial scale, capturing physical processes that influ- Mountain wind fields commonly present a high variability ence the motion of synoptic air masses. at a local scale (,100 m) (Mott et al. 2018), intrinsically lim- In this study, we leverage on a combination of simulations iting the benefit of numerical weather prediction systems obtained with a complex atmospheric model and deep learning (NWP), which generally operate with a horizontal grid spac- methods to tackle the issue of wind downscaling in complex ter- ing above 1 km (e.g., Baldauf et al. 2011; Seity et al. 2011; rain. We proceed as follows: we use a high number of existing Kehler et al. 2016; Pickering et al. 2020). Furthermore, basic atmospheric model simulations performed with the Advanced interpolation methods (i.e., linear, polynomial), when ap- Regional Prediction System (ARPS) atmospheric model, all ob- plied to synoptic winds provided by NWP models, do not ac- tained under controlled atmospheric conditions over a set of curately represent the complex reality of mountain winds synthetic Gaussian topographies (Helbig et al. 2017). Using (Wagenbrenner et al. 2016). Consequently, dynamic down- those simulations, we derive a link between coarse-scale wind scaling methods are often used to infer the behavior of fields (such as winds provided by an NWP), topography, and mountain winds at a local scale (Raderschall et al. 2008; high-resolution wind fields through a parameterization, in a Mott and Lehning 2010; Vionnet et al. 2014). These meth- manner similar to statistical downscaling. However, in our case, ods rely on complex atmospheric models to handle coarse- the statistical relationship is automatically determined using an scale signal, and to generate high-resolution wind fields. artificial intelligence model and, more specifically, a CNN. They solve equations of state describing the flow, including its interaction with the terrain and more generally the representa- 2. Data tion of various physical processes that most directly determine a. ARPS simulations the large spatial variability of wind fields in complex terrain (Mott and Lehning 2010). The counterpart of this complexity 1) ARPS CONFIGURATION lies in large computing requirements, hence restricting the use ARPS is an atmospheric model that solves the nonhydro- of the method to small domains and/or limited time scales static and compressible Navier–Stokes equations. A detailed (Mott and Lehning 2010; Vionnet et al. 2014). Therefore, mod- description of the model implementation can be found in els with relatively low complexity have been developed and (Xue et al. 2000, 2001). Notably, the model is able to repre- provide a good trade-off in terms of physical complexity versus sent several features of terrain-forced flow such as speedup numerical costs (Forthofer et al. 2014; Vionnet et al. 2021). on crests, sheltering, separation, recirculation, topographic Statistical parameterizations using topographic information channeling (Raderschall et al. 2008), and thermally driven have also been largely used to bridge the gap between coarse- scale-resolution wind fields provided by NWP models and the winds such as valley breezes (Anquetin et al. 1998). high-resolution forcings required by small-scale applications Helbig et al. (2017) performed individual simulations with and, notably, drifting snow models (Liston and Elder 2006; ARPS on synthetic topographies derived from isotropic and Helbig et al. 2017; Winstral et al. 2017). Such downscaling stationary Gaussian random fields (GRF). GRF are stochas- methods identify parameters expected to capture the effect tic processes, that have been identified as a good proxy for of topography on the wind fields and then apply statistical real topographies, particularly in their ability to approxi- operations to transform the coarse-scale signal into a dis- mate real slope distributions (Helbig and Lowe 2012)and tributed signal at a higher target resolution. The choice of have already been successfully used to develop topo- accurate parameters relies both on the identification of graphic parameterizations (Helbig and Lo ¨we 2012, 2014; dominant physical processes at a local scale (e.g., sheltering, Helbig et al. 2017). In this study, we make use of ARPS exposition, channeling) and their formulation through a simulations performed on individual Gaussian topogra- mathematical expression (using, e.g., curvature, slope, and phies (Helbig et al. 2017). Each simulation covers a rectan- Laplacian). For example, the MicroMet model (Liston and gle of 79 3 69 pixels with a horizontal resolution of 30 m. Elder 2006) identified slope, terrain slope azimuth, and cur- Notably, a broad range of topographic characteristics was vature as relevant parameters to account for the effect of achieved by selecting nine combinations of the two charac- local topography on wind fields, whereas Winstral et al. (2017) teristic length scales: the typical width j [200–1000 m; see modeled sheltering/exposure of locations to wind using the Eq. (1)] and typical height s (88–364 m) of topographic DEM terrain parameter Sx (Winstral et al. 2002;see section 3a)and features, for 5 spatial mean square slopes m (198–368)within a the topographic position index (TPI; Weiss 2001). Comple- topography: mentarily, Helbig et al. (2017) identified the local Laplacian from terrain elevations and squared slope as valuable parame- 2 3 s DEM j 5 : (1) ters to downscale wind speeds. Recently, new statistical ap- proaches have emerged to downscale wind fields in complex terrain (Bonavita et al. 2021). Notably, Dujardin and Lehning Each combination of j, s generated 200 realizations, re- DEM (2022) proposed an architecture based on convolutional neural sulting in a total of 9000 topographies [for more technical de- network (CNN) to process both topographic information and tails see Table 2 in Helbig et al. (2017)]. About 80% of the NWP data in order to perform pointwise predictions of wind topographies (7279) resulted in usable simulated wind fields fields in the Swiss Alps at high resolution (,100 m). Hohlein and were used in this study. JANUARY 2023 L E T O U M EL I N ET A L . 3 FIG.1. (a)–(c) Maps featuring examples of Gaussian topographies, and (d)–(f) surface winds from the ARPS first layer on these topog- raphies. The ARPS first layer has a mean elevation above ground of 2.95 m. These three simulations, as labeled, exemplify topography and model output couples that constitute our training database. For these ARPS simulations, constant initial atmospheric The speed of the wind outputs (three-dimensional outputs, 2 2 2 conditions were chosen. Notably, all simulations were initial- speed computed using u 1 y 1 w ) are distributed follow- ized with a constant wind profile, initially oriented from left ing Fig. 2a. As noted in Helbig et al. (2017), the mean wind speed simulated by ARPS is always slightly less than 3 m s , to right (wind coming from the west) with a speed of 3 m s . the speed that served as initialization. Notably, the steeper The atmospheric stability was fixed as neutral (as frequently the mean slope, the lower the mean wind speed. This behav- observed during drifting snow episodes) and radiation effects ior exemplifies the mean drag exerted by the topography were neglected (Helbig et al. 2017). Thermally driven flows on the flow and the associated loss of momentum, which is were neglected to solely represent the interaction between intensified on rougher terrain. Oppositely, the distribution large-scale flow and topography. The total integration time tails highlight more frequent intense wind speeds on steep was limited to 30 s (with an integration time step of 0.1 s), pro- topographies. We note that ARPS simulates accelerations hibiting the dominance of turbulence in the outputs, and re- up to 4 times the initial wind speed and reductions to almost stricting the simulated flow to the resultant of the adaptation null wind speeds. of a mean flow to local topography (Raderschall et al. 2008; ARPS simulated wind fields deviated from the direction of Mott and Lehning 2010). In all simulations, the surface was the input wind (west) in both directions according to Fig. 2b. representative of uniform snow-covered areas, with an aero- Counterclockwise and clockwise deviations are equally rep- dynamic roughness length of 0.01 m. We give an example of resented in our dataset and range from 08 to 828. The distri- three ARPS simulations, encompassing different mean slopes bution of angular deviations is centered on zero for each (308,108, and 368) and j (400 and 800 m), and their associated category of mean slope and deviations introduced by ARPS topography in Fig. 1 (see also the same figure with normal- are generally low. Such deviations can be representative of ized axis in section S.6 and Fig. S4 in the online supplemental flow deflections around obstacles, alignment of the flow on material). Notably, we observe accelerations on peaks (red ar- ridges and more generally encompass an adaptation of the rows) and deceleration windward and leeward (blue arrows). flow to local topography. The formation of turbulent struc- The intensity of the modifications of the high-resolution wind tures was deliberately prevented in the ARPS simulations differs with mean slope and j, the largest modulations occur- used here as training dataset: the ARPS wind fields thus do ring on the steepest topographies. not describe more complex behaviors of mountain winds, such as turbulent recirculation or extremely strong devia- 2) CHARACTERISTICS OF THE SIMULATIONS tions (e.g., barrier jets), which are generally epitomized by We describe in this section the characteristics of ARPS higher angular deviations (Raderschall et al. 2008; Sharples wind outputs (Fig. 2), which constitute our training database. et al. 2010; Whiteman 2000). Similar to the situation with 4 AR TI F I C I A L I N T E LLI G E N C E F O R T H E E AR TH S Y S T E M S VOLUME 2 Mean slope [°] (a) (b) Wind speed [m/s] Angular deviation from West [°] FIG. 2. (a) Wind speed and (b) angular deviation distributions as simulated by ARPS on the 7279 Gaussian topogra- phies. Such winds constitute the training dataset used to fit the CNN of the DEVINE model. wind speeds, we observe that the most intense wind direc- and climate observations {Glacier, an Observatory of the Climate tion modifications from the input wind occur on the steepest [les Glacier, un Observatoire du Climat (GLACIOCLIM)]} mean slopes. network. Three other ones are located at Col du Lac Blanc (latitude 5 45.128,longitude 5 6.118; elevation 5 2720 m) in the b. AROME simulations Grandes Rousses massif and belong to a high-mountain meteo- AROME is a limited-area NWP system used by Meteo- rological observatory dedicated to drifting snow and snow– France (Seity et al. 2011). It provides short-term forecasts of atmosphere interactions (Vionnet et al. 2017; Guyomarc’het al. atmospheric fields since 2008, over a domain encompassing 2019). The61sites cover thewhole French Alps and a largevari- the French Alps. Benefiting from its high horizontal resolu- ety of terrain, with some stations being located on flat surfaces, tion (1300 m) and complex physics and dynamics, the model other on slopes, and some on exposed terrain (e.g., Aiguille du has gained interest for mountain meteorology and snow sci- Midi: latitude 5 45.878,longitude 5 6.888; elevation 5 3845 m). ences, progressively bridging the gap with coarser atmo- The observation stations are mainly located in nonforested areas spheric products currently used to force snow models over and are mostly snow covered during the winter seasons. the French mountain ranges (Quéno et al. 2016; Vernay Wind observations are commonly subject to measurement et al. 2022; Gouttevin et al. 2023). AROME solves the errors (DeGaetano 1997), particularly when collected in a nonhydrostatic fully compressible Euler equations system challenging mountainous environment. These measurement using hybrid pressure terrain-following coordinates. Nota- errors can be of diverse nature and occur at different steps bly, AROME uses a subgrid parameterization to describe during the data collection process (Lucio-Eceiza et al. 2018a). the influence of unresolved orography on wind fields, via an A striking example of wind sensor dysfunction in mountain effective roughness length described in Georgelin et al. terrain is null and constant wind speed observations for (1994). We used here 10-m AROME wind fields initialized several consecutive hours due to the accretion of ice on the from the 0000 UTC analysis, from which we extracted daily sensor. Because our data come from different networks, forecasts between 0000 UTC 1 7 h and 0000 UTC 1 30 h at their quality is unequal. Thus, we homogenized the quality an hourly resolution. This way, we reconstructed continuous standard of our dataset by applying a quality check, deeply time series of gridded wind fields over the French Alps for a inspired by Lucio-Eceiza et al. (2018a,b). These authors period of interest extending from 1 August 2017 to 31 May proposed a series of sequential tests designed to detect suspicious wind observations. We adapted the quality pro- cess of Lucio-Eceiza et al. (2018a,b) to fitthe specificities c. Observations of our dataset by selecting the most relevant tests and Hourly observations of wind speed and direction have eventually introducing some modifications, as listed in sec- been collected and quality-checked in order to evaluate tion S.1 in the online supplemental material. We refer to the downscaling scheme over real alpine topographies. A Lucio-Eceiza et al. (2018a,b) for the evaluation of the qual- total of 61 automatic weather stations (AWS) acquiring ity process. wind measurements have been selected in the French Alps (Fig. 3). Most of them are part of Meteo-France operational 3. Method observational network. Three stations: Vallot observatory This paper’s method is organized as follows: we first build a (latitude 5 45.838, longitude 5 6.858;elevation 5 4360 m), Argentieres glacier (latitude 5 45.968,longitude 5 6.978; statistical model by notably fitting a CNN to ARPS simula- elevation 5 2434 m), and Saint-Sorlin glacier (latitude 5 45.178, tions. Then we use this statistical model to downscale wind longitude 5 6.178;elevation 5 2720 m) are part of the glacier fields from the AROME NWP system in the French Alps. JANUARY 2023 L E T O U M EL I N ET A L . 5 FIG. 3. Locations of observation stations (colored triangles) used for model evaluation. The colors of the observation sites indicate their elevation ranges. The small application domain used later in Fig. 6 is outlined in blue, and the larger domain that is used later in Fig. 7 is outlined in red and magnified in the zoom. a. Topographic descriptors Sx 5 (z 2 z )/d , where |tan[(z 2 z )/d ]| 5 max |tan[(z 2 j i ij j i ij k k z )/d ]|, with x being the cell of interest and k being the index i ik i In this study we make use of several parameters describing of any pixel located in a zone starting from x and extending the topography and derived from digital elevation models toward a direction defined by the incoming wind direction, (DEMs), all with a 30-m horizontal resolution dx. Here, we within a 308 window and a 300-m maximum distance from x . describe these parameters shortly with references: the TPI Last, d indicates the distance between x and x . In summary, ij i j (Weiss 2001) compares the elevation of a DEM pixel with the positive values for Sx indicate sheltering for x , that is, how mean elevation of the neighboring pixels given a fixed radius. much x is protected from incoming wind within a 300-m ra- The radius is equal to 500 m in our study, and consequently dius, whereas negative Sx values quantify exposure. TPI and the TPI parameter is oriented toward the detection of topo- Sx are thus computed using information from neighboring graphic peaks/bowls on the slope scale. The Sx parameter pixels within a given radius and thus integrate information (Winstral et al. 2002), is a direction-dependent parameter and from areas located within a few hundreds of meters to charac- quantifies how sheltered or exposed a pixel is within a given radius [here 300 m, as in Winstral et al. (2017)]. In detail, terize each DEM pixel. In contrast, the discrete Laplacian Df: f (x 1 dx, y) 1 f(x 2 dx, y) 1 f(x, y 1 dx) 1 f(x, y 2 dx) 2 4f(x, y) D(fx, y) 5 , (2) dx which aims at detecting local peaks and bowls in topographic for pattern recognition among spatialized data. Fully convolu- maps, and the squared slope, referred to as slope and com- tional neural networks (FCN) are a specific type of CNN, pro- puted following Helbig et al. (2017), only consider nearest- posing an end-to-end solution relying on convolutional and neighbor pixels in addition to the cell of interest and hence pooling layers without any use of dense networks, making provide very local topographic information. We use these them an efficient solution for gridded predictions. Convolu- four parameters to characterize alpine and Gaussian topogra- tional layers consist of convolving a filter (i.e., a matrix with a phies in sections 4 and 5. predetermined size) to input data so as to detect spatial pat- terns. The product of convolutions goes through pooling b. Fully convolutional neural networks layers that reduce their spatial resolution. Repeating both op- CNN are a specific kind of neural network that benefits the erations hence permits us to encode spatial features with a use of convolution operations on tensors and are well suited high level of abstraction. In FCN, encoding operations can be 6 AR TI F I C I A L I N T E LLI G E N C E F O R T H E E AR TH S Y S T E M S VOLUME 2 FIG.4.Workflow of the downscaling model DEVINE. Both preprocessing operations (labeled A–E) and postprocessing opera- tions (labeled F) are required before and after calling the CNN for predictions. In detail, label A corresponds to the selection of wind fields in the form of gridded outputs provided by an NWP system. This grid is interpolated (label B), and the following opera- tions are done pixelwise: DEM data around each pixel are first selected (label C), then rotated with respect to the initial wind direc- tion provided by the NWP system, and finally cropped (label E) to match the CNN input size. The CNN is then called and outputs high-resolution maps of wind fields. Within the CNN, the following standard operations are used: normalization, padding maps with zeros (“ZeroPadding”), convolutions (“Conv.”), dropout connection (“Dropout,” only during training), maximum pooling op- eration (“MaxPooling”), concatenations (“Concat.”), cropping map borders (“Cropping”), and increasing the size of a matrix by re- peating its rows and columns (“UpSampling2D”). Small numbers next to each layer represent the number of features maps. The scaled outputs of the CNN go through an activation layer to ensure that plausible values are produced. Wind patches are ultimately rotated back and placed on the high-resolution grid to constitute a continuous map of wind fields (label F). followed by a decoding stage, where convolutions are mixed performance are investigated using 10-fold cross validation. with spatial interpolations of the encoded signal, to sequentially Cross validation consists of randomly partitioning our data- increase the spatial resolution. The Unet architecture has been base into “training” data (90% of the data) and “test” data introduced in 2015 (Ronneberger et al. 2015) and constitutes a (the remaining 10%), which permits us to fit the CNN on the specific type of FCN frequently used for meteorological applica- first group and evaluate its performance on the second group. tions (Trebing et al. 2021; Ferna ´ndez and Mehrkanoon 2021). For a more robust evaluation, the process is repeated 10 times In Unet (Fig. 4), encoding and decoding stages are connected by rolling over 10 random training/test splits. Furthermore, we through concatenation operations, which makes it possible to extracted validation data from the training data (i.e., 10% of transfer high-resolution information to lower-resolution infor- the remaining 90% among the 10 folds) to follow a validation mation within the model architecture. Indeed, data in the first loss (mean absolute error on validation data) during training. layers of the Unet have not been through almost any pooling We sequentially reduced the learning rate when the loss reached operation. Hence, this “raw” (or moderately encoded) infor- aplateau (“reduce on plateau”), and eventually stopped the mation from the encoding stage is used to complement en- learning process (“early stopping”) whenever the validation loss coded and processed information from the decoding stage. stopped decreasing for 15 epochs (“patience”). This approach, Such an operation is also frequently referred to as “skip con- coupled with the fact that after validation the CNN outputs are nection” (Lagerquist et al. 2021). evaluated on an independent test set, aims at limiting the risk of Here, two-dimensional topographic maps are fed into a overfitting the training set. In our specific case, hyperparameter Unet architecture. The model then outputs three features tuning did not prove crucial to converge toward an efficient maps, each one of them representing a component of the CNN architecture, as the training statistics highlighted a low wind vector. To determine the appropriate filters used in sensibility to the different hyperparameters. We adopted a the convolutional layers, the Unet is fitted during a training shallower version of the initially published Unet with only step using Gaussian topographies as inputs and ARPS simu- two additional layers corresponding to dropout connections, lationsaslabels (see section 1). Model architecture and added to limit overfitting during the training phase. The selected JANUARY 2023 L E T O U M EL I N ET A L . 7 hyperparameters are summarized in section S.4 and Table S.1 in outputted by the CNN [UV ;Eq. (3)] using AROME wind cnn the online supplemental material. speed [UV ;Eq. (3)], as CNN outputs are only valid for AROME an input speed of 3 m s [UV ;Eq. (3) and section 2a]: initARPS c. DEVINE downscaling model UV cnn Several preprocessing and postprocessing steps are required UV 5 UV 3 : (3) scaling AROME UV initARPS before and after calling the CNN in order to generate high- resolution wind predictions on real topographies (Fig. 4). Their We discuss the implication of this assumption in section 5. combination with the CNN forms a full downscaling scheme Given that we extrapolate results obtained on a set of Gaussian that we named Downscaling Wind Fields in Complex Terrain topographies under controlled atmospheric conditions to the with Deep Learning, Applications for Nivology and Associated very vast diversity of real topographies and atmospheric condi- Challenges [Descente d’Echelle de Vent par Méthodes d’Ap- tions (section 5a), we introduced a custom activation layer using prentissage Profond, Application pour la Nivologie et ses En- a modified arctan function g that eventually curbs predicted un- jeux (DEVINE)]. realistic large wind speeds at extreme locations to plausible First, the initial NWP gridded outputs (Fig. 4:label A) wind speeds: are upsampled using bilinear interpolation (using a factor of 2) (Fig. 4: label B). This step is necessary to ensure that g(x) 5 a arctan(x/a): (4) the initial NWP signal is (i) dense enough to produce continu- ous wind fields at 30-m spatial resolution, and (ii) smoothly This function does not act as a bias corrective term, but densified before calling the Unet, so that the final high- rather as a safety guard: we defined a maximum acceptable resolution maps produced are not affected by chesslike mean speed in our model (60 m s ), which is above the patterns. First, the initial NWP gridded outputs (Fig. 4: maximum observed speed in our historical observational da- label A) are interpolated using bilinear interpolation and taset (36 m s ) and scaled the parameter a (538.2) so that an interpolation rate of two (the dimensions of the inter- the g limit in positive infinity is equal to 60. The choice of the polated grid are twice the original dimensions) (Fig. 4: function arctan is motivated by the shape of the function g label B). Two reasons justify the use of interpolation: (monotonically increasing and progressively departing from the firstly since the outputs of our CNN are of predetermined 1–1 line for speeds above 20 m s ; see section S.5 and Fig. S3 size (79 3 69 pixels), we have to ensure that predicted in the online supplemental material). Following these proper- maps (around each NWP pixel) are sufficiently large to be ties, g has an almost null impact on downscaled wind speeds juxtaposed one next to each other without introducing any lower than 20 m s (i.e., most of the time) and starts lowering hole in the final downscaled map. In our case, the grid speeds for outputs larger than .20 m s .Hence, g limits the spacing configuration (DEM 5 30 m; NWP 5 1300 m) en- simulation of unrealistic wind speeds that could potentially be sures having no holes in the final maps. But for applica- obtained when particularly high NWP wind speeds are associ- tions with, for example, another NWP system of coarser ated with the highest accelerations, generally obtained on the grid spacing, an initial interpolation of the NWP grid may most exposed locations in real topographies. be used to ensure spatial continuity. Second the use of in- In the final step of the DEVINE model, the downscaled terpolation is motivated by the necessity to reduce chess- pixels generated by the CNN are rotated back to their original board-like patterns. Such patterns appear at the NWP gridcell position (Fig. 4: label F), in the opposite direction of the first boundaries when downscaling gridded data (Winstral et al. rotation (Fig. 4: label D), and assembled to reconstruct a con- 2017; Dujardin and Lehning 2022); see section 5c. They can be tinuous regularly spaced grid of wind predictions, with a hori- largely diminished by downscaling an interpolated map, that is, zontal grid spacing of 30 m. CNN outputs can overlap one on downscaling a higher-resolution grid where the transition be- each other and are thus cropped (patch size 5 23 pixels) to avoid overlapping areas in the final predictions. tween wind values of two neighboring grid points is less abrupt than in the original grid. Then, each interpolated NWP pixel is downscaled sequentially as described hereinafter. For each in- 4. Results terpolated NWP pixel, high-resolution topography patches sur- a. Performance at emulating ARPS rounding the pixel are first extracted (patches of size 140 3 140 pixels, Fig. 4: label C) and then rotated with respect to the We first assess the performance of the CNN at emulating NWP wind direction so that the rotated direction is from the ARPS on synthetic topographies on the test datasets, using west (Fig. 4: label D), similar to the ARPS simulations. The ro- 10-fold cross validation (Fig. 5 and Table 1). We computed the tated patches of topography are then cropped (to 79 3 69 pixel error between all predicted maps and corresponding labels pix- size), normalized using their mean value and the standard de- elwise and categorized the CNN errors (i.e., the difference be- viation of the Gaussian topographies used during the training tween modeled and observed value, definedat eachtime step) phase, and then go through the CNN (Fig. 4: label E), which in terms of topographic characteristics (TPI, Sx, Laplacian, and produces three maps corresponding to the three components slope) to interpret the results encapsulated in integrated met- of wind speed. Horizontal wind speed and direction are then rics. Each TPI, Sx, Laplacian, and slope values are sorted ac- computed from wind components. This step eventually in- cording to their position in their respective distribution using volves a linear scaling [UV ;Eq. (3)] applied to the speeds the0.25quantile q , 0.5 quantile q , and 0.75 quantile q .We scaling 25 50 75 8 AR TI F I C I A L I N T E LLI G E N C E F O R T H E E AR TH S Y S T E M S VOLUME 2 (a) (b) (c) (d) (g) (e) (f) (h) TPI [m] Sx [rad] Slope [°] FIG. 5. Performance (errors) of the CNN at reproducing ARPS behavior on Gaussian topographies, using a 10-fold cross validation. All of the statistics presented have been acquired using test data (i.e., data not used during the training phase) and explored using parameters describing the topography (TPI, Sx, Laplacian, and slope). All parameters are categorized in four classes according to the quantiles of the parameter distribution (q , q ,and q ). Each boxplot has been computed using approximately 10 million samples. 25 50 75 observe that all errors on the test groups are centered on 0, sug- fact that the largest wind speeds and angular deviations are also gesting that the CNN is able to produce unbiased estimations observed on the most complex terrain: when relative errors of ARPS wind fields. Errors are relatively low: boxplots suggest (i.e., errors at each time steps divided by ARPS wind speed) that most of the speed errors are lower than 0.25 m s ,with a are considered, the performances of the CNN are more bal- mean absolute error of 0.16 m s (5% of the initial wind speed; anced among all topographic classes (see section S.2 and Table 1). Similarly, most of wind direction errors range be- Fig. S1 in the online supplemental material). We note that tween 25and 5 .More specifically, we observe that the pixels the meridional component of the wind presents lower errors corresponding to the most complex terrain (i.e., steepest slopes than the zonal component (Table 1), also in line with stron- or tails of the parameter distributions) lead to larger errors, sug- ger zonal wind speeds due to ARPS initial conditions (wind gesting the difficulty to capture wind behavior in the most ex- coming from the west). Last, we analyzed the spatial loca- treme terrains (Fig. 5). However, this could be explained by the tion of the errors and observed that most errors are located TABLE 1. Performance of the Unet model at emulating ARPS on Gaussian topographies, using a 10-fold cross validation. All the statistics presented have been acquired using test data (i.e., data not used during the training phase); U, V, and W respectively refer 2 2 to the zonal, meridional, and vertical component of wind speed; UV designates the horizontal wind speed ( U 1 V ); and UVW is 2 2 2 the three-dimensional wind speed ( U 1 V 1 W ). Also, AE refers to absolute error and r is the Pearson correlation coefficient. 21 21 21 21 21 U (m s ) V (m s ) W (m s )UV(ms ) UVW (m s ) Wind direction (8) Mean bias ,0.01 ,0.01 ,0.01 ,0.01 ,0.01 } Mean AE 0.15 0.13 0.06 0.16 0.16 3 q25 AE 0.04 0.04 0.01 0.04 0.04 1 q50 AE 0.10 0.08 0.03 0.10 0.10 2 q75 AE 0.19 0.17 0.08 0.20 0.21 3 r 0.96 0.94 0.99 0.96 0.95 } Speed error Direction error [m/s] [°] JANUARY 2023 L E T O U M EL I N ET A L . 9 1e6 (a) (b) D M 1e6 (c) D M FIG. 6. Downscaling AROME wind fields at Col du Lac Blanc using DEVINE for three specific dates: (a) 1100 UTC 7 Mar 2018, (b) 0900 UTC 6 Apr 2021, and (c) 0000 UTC 9 Apr 2021; M, L, and D correspond to three in situ wind obser- vations (Muzelle, Lac, and Dome stations), and A corresponds to the AROME forecast wind field. The x and y coordi- nates are expressed in Lambert 93 projection, i.e. EPSG 2154. Note that the left y axes are divided by 1 3 10 . on the margins of topography maps (see section S.3 and (A in Fig. 6; distance to the Lac station 5 148 m, and pixel ele- Fig. S2 in the online supplemental material). vation 5 2681 m) is first extracted for three dates (Fig. 6a: 1100 UTC 7 March 2018; Fig. 6b: 0900 UTC 6 April 2021; b. Case study: Application to a small domain Fig. 6c: 0000 UTC 9 April 2021) and then downscaled using We explore the behavior of DEVINE on real topographies DEVINE. We selected the dates using the following criteria: by first downscaling a single AROME grid cell surrounding (i) three distinct initial wind direction (respectively, west, the Col du Lac Blanc experimental site in the French Alps north, and east as simulated by AROME), (ii) different (Fig. 6). This observation site (see section 2c) is composed AROME speeds (#3, ’3, and $3m s ), (iii) AROME of three distinct AWS located between tens to a few hundreds of roughly in phase with local observations (speed error less than meters from each other. The Lac station (L in Fig. 6; elevation 5 8 2m s and direction error less than 90 ), and (iv) including 2720 m) and Muzelle (M in Fig. 6; elevation 2722 m) are one “close to training” condition, that is, a neutrally stratified both located along a north–south pass. The relative proxim- boundary layer (20.1 # observed Richardson number ≤ 0.1) ity of the two stations makes them subject to very similar lo- with an AROME speed close to 3 m s (Fig. 6c). cal wind conditions. On the contrary the Dome station (D in At 1100 UTC 7 March 2018, a west flux blows above the Fig. 6; elevation 5 2808 m) is located on a small hill, domi- massif, with AROME locally simulating a low wind speed nating the pass by 85 m in elevation. This station is more (1.4 m s ) with a west-southwest direction, (2438). DEVINE subject to the influence of the hill on the local flow and is downscales the AROME signal and increases the speed on D more exposed (TPI at Dome 5 164 m, TPI at Muzelle 5 (2 m s ). The flow is decelerated on both the windward and 224 m, and TPI at Lac 5227 m). In our case study, infor- the leeward areas, but it is almost unchanged when compared 21 21 mation from the nearest interpolated AROME grid point with AROME at M and L (1.3 m s at L and 1.4 m s at M; Wind speed [m/s] Wind speed [m/s] Wind speed [m/s] 10 AR TI F I C I A L I N T E LLI G E N C E F O R T H E E AR TH S Y S T E M S VOLUME 2 model). DEVINE acceleration patterns at D are consistent the modeling of drifting snow, as, for example, the zones of with the observations (observed wind speed at D 5 2m s ), deceleration simulated in Fig. 6 could potentially favor flux but the model fails to fully capture deceleration at M and L convergence and hence shape drifting snow deposition (respectively, 1 and 0.4 m s for the observations). In terms (Vionnet et al. 2021). Further work might use more dense of direction, the observed wind aligns perpendicularly to the observation networks such as in Taylor and Teunissen topographic barrier at D (2858, observation), a feature par- (1987), Butler et al. (2015),and Wagenbrenner et al. (2016) tially captured by DEVINE (2538; model). The model then to better characterize the spatial variability of DEVINE suggests a small deviation of the flow toward the north of the wind fields. pass (2278; model), which is slightly confirmed by observation c. Case study: Application to a large domain at M (2578; observation). However, L suggests an orientation of the flow toward the south of the pass (3038; observation), The DEVINE architecture can also be deployed on larger but the direction observation is acquired for an almost null domains than Fig. 6 to downscale wind fields provided by wind speed (0.4 m s ; observation). gridded outputs of an NWP (Fig. 7). We selected a 40 km On the second example (Fig. 6b; 0900 UTC 6 April 2021), by 30 km domain in the French Alps (Fig. 7a), and down- the synoptic conditions indicate a flux from the north above scaled AROME wind forecast at 1500 UTC 11 July 2019 the western French Alps, and AROME locally forecasts a (Figs. 7b–d). For this specific date, the dominant wind direc- 27 wind direction (north-northeast) characterized by larger tion was from the west with maximum AROME speeds speeds (5.5 m s ). DEVINE accelerates AROME wind at reaching 7.7 m s . Figure 7 shows the initial AROME wind D(6.8 m s ; model), and across the pass at L and M (6.9 with a 1300-m horizontal resolution (green/yellow arrows) 21 21 and 7 m s ). The observed speed is larger at D (5.8 m s ; and the downscaled speeds at 30-m horizontal resolution observation) than at L and M (respectively, 4.1 and 4.6 m s ; (violet/orange color). We observe strong modifications of speeds observation). Interestingly, the acceleration at the pass, cap- on this domain (maximum downscaled speed 5 16.2 m s ). tured by DEVINE but not retrieved in the observation at this Highest downscaled wind speeds appear on clear lines in specific date, is a well-known behavior of wind fields at M and Fig. 7b, which mostly correspond to mountains ridges and sum- L, where drifting snow measuring devices have been specifi- mits as identified in Fig. 7a. Oppositely, dark violet areas corre- cally installed to monitor wind driven processes. In terms of di- spond to low wind speeds as simulated by DEVINE and are rection, DEVINE suggests almost no deviation at D, L and M often in phase with low AROME speeds (small arrows), sug- (338,198,and 188; model), a pattern not confirmed at L (648; gesting that even if DEVINE modifies the AROME signal, it observation). The explanation of this divergence can also be still respects important features provided by the NWP system retrieved in the observation acquisition process, because the (areas of high wind speeds vs areas of low wind speeds). quality control flagged as suspicious the direction observation Thus, even though DEVINE has been fitted to simulations per- at L for this specificdate. formed assuming certain weather conditions and is not able to On the third and final case (0000 UTC 9 April 2021), synoptic reproduce some processes of mountain winds at a local scale conditions feature a flux from the south with AROME simulat- (recirculation areas, thermally driven flows, etc.), the larger- ing a wind speed 5 2.4 m s and a wind direction 5 1308 scale wind fields simulated by AROME, which can be obtained (southeast). As in Figs. 6a and 6b, observations suggest stronger 21 under all types of weather conditions, can be used to drive the winds at D (3.4 m s ; observation) than L and M and this vari- 21 downscaling model. Accelerations and decelerations lie in the ability is captured by DEVINE (3.7 m s at D; model). This range of accelerations/decelerations as simulated by ARPS on could be interpreted by the incidence of the incoming synoptic synthetic topographies (section 2). We also observe strong accel- wind forecast by AROME, which is rather perpendicular to erations with DEVINE on the Grandes Rousses massif (Fig. 7a; the hill around D. AROME speeds are almost unmodified by 21 white ellipse) and on the Aiguille d’Arves massif (Fig. 7a;red DEVINE at M and L (respectively, 2.4 and 2.4 m s ; model), ellipse), which are both oriented toward a north–south axis a pattern confirmed by the observation at M and L (2.4 m s (thus perpendicular to the dominant synoptic wind on 11 July at M and 2.6 m s at L; observations). DEVINE agrees with 2019). Oppositely, the north of the Ecrin massif (Fig. 7a;black AROME direction without introducing any important direc- ellipse) is oriented east–west, along the main wind direction, tional shift at D, M, and L (respectively, 1268,1438, and 1448). and DEVINE does not suggest any strong acceleration on this Oppositely, the observations suggest a flow from the south more complex and higher massif. Thus, we draw the conclusion and a tendency to align along the pass at M and L (respec- that on this example DEVINE is able not only to detect ridges tively, 1638,2088, and 1618 at D). In this example, a small dif- and complex terrain but also to interpret the incidence angle be- ference in both speed and direction occurs between M and L, tween AROME wind fields and topographic features. We also which might highlight very local phenomena and more gener- observe angular deviations with respect to the AROME initial ally the spatial variability of wind speed at scales below 30 m direction (Fig. 7c; red and blue colors). These deviations mainly in complex terrain. lie in the range of ARPS deviations on Gaussian topogra- All the above examples illustrate how DEVINE produces ac- phies (deviations from AROME direction up to 818 on this celerations and decelerations with respect to the underlying to- pographic features, and how zones of accelerations/deceleration specific case study). The presence of red features (counter- and their relative intensity are a function of the AROME wind clockwise deviations) in Fig. 7 next to blue features (clock- direction that served as initialization. This is of high interest for wise deviations) suggests local circumventions of the flow JANUARY 2023 L E T O U M EL I N ET A L . 11 AROME wind speed [m/s] Angle between DEVINE and (a) Elevation [m] DEVINE wind speed [m/s] (c) (b) AROME wind fields [°] 0 km 18km Zoom (d) (e) 18 km 0 km FIG. 7. (a) Topography of an alpine domain and wind field simulations at 1500 UTC 11 Jul 2019, with (b) AROME (colored arrows) and DEVINE wind speed (color shading) on the domain, (c) AROME (colored arrows) and DEVINE angular deviations from AROME (color shading) on the domain, and (d) topography and DEVINE wind speeds projected on a vertical west–east transect, with (e) an en- largement of the area within the red-outlined box in (d). On this transect, the bases of the arrows locate the associated wind field. AROME wind fields are two-dimensional 10-m wind fields, whereas DEVINE wind fields also incorporate a vertical dimension. around topographic obstacles and channeling within valleys. supporting our above hypothesis. Conversely, some low ob- Last, we projected in Fig. 7d DEVINE 3D wind fields on an served wind speeds are overestimated by DEVINE. Further 18 km west–east transect (see the black horizontal bar in analyses show that the overestimation of low wind speeds by Figs. 7a–c). We observe on this transect accelerations DEVINE is, among other factors, imputable to the behav- (larger arrows) on peaks and changes in the vertical compo- ior of the model at a few exposed observation stations, nent of the wind field, which generally tend to follow the such as the Aiguille du Midi station (TPI 5 288 m). These terrain and to be oriented with respect to topographic fea- behaviors are discussed in section 5a. tures. From a modeling perspective, topography imposes A quantile-to-quantile analysis complements the compari- surface conditions that force the wind speed to orient fol- son of model wind speeds with in situ observations and indi- lowing the terrain. cates that the observed wind distribution is better captured by DEVINE than by AROME (Fig. 8c). The underestimation of d. Performance on real topographies high wind speeds in AROME is reflected by a departure from When compared with in situ observations collected at the the 1–1line in Fig. 8c for high quantiles. As partially observed 61 observation sites in the French Alps, AROME wind fields in Fig. 8b, high wind speeds are better captured by DEVINE, are characterized by a negative speed bias for high wind which is reflected by a better representation of the highest speeds (.10 m s )(Fig. 8a). This behavior has already been wind speed quantiles. However, as previously pointed out in documented (Vionnet et al. 2016; Gouttevin et al. 2023) and Fig. 8b the overestimation of low wind speeds contributes to might be to some extent explained by the 1.3-km horizontal simulating larger speeds and hence to obtain a better match grid spacing of the model that fails to capture wind accelera- on the 1–1 plot with DEVINE than with AROME in Fig. 8c. tions on ridges and speed variability due to subkilometric var- Further analysis reveals that DEVINE reduces wind speed iations of elevation. For lower wind speeds (,10 m s ), mean biases at most of the observation stations, whereas di- AROME is closer to the observations. The departure of the rection is only slightly affected. In Fig. 9, wind speed errors points from the 1–1 line for high wind speeds in Fig. 8a have first been normalized by the observed wind speed and is partly corrected by DEVINE downscaling (Fig. 8b), then categorized by TPI. Only speeds above 1 m s are Elevation [m] 12 AR TI F I C I A L I N T E LLI G E N C E F O R T H E E AR TH S Y S T E M S VOLUME 2 AROME DEVINE (a) (b) Observed wind speed [m/s] (c) Observed wind speed quantiles [m/s] FIG.8.(a) AROME 1–1 plot (modeled vs observed hourly values), (b) DEVINE 1–1 plot, and (c) quantile–quantile plot (each point being a quantile in the respective distributions, both discretized in 10 000 quantiles). In (a)–(c), the red line represents the 1–1 line. The color bar in (b) represents data density for (a) and (b). considered in this process. Error normalization is preferred in modifications are brought by DEVINE: the maximum modifi- our case as generally elevated stations are characterized by cation in direction introduced by DEVINE, at the 61 stations, stronger winds and consequently larger errors, thus scram- is equal to 378. We link this to the fact that (i) our CNN is fitted bling the interpretation when compared with stations located on ARPS model outputs where wind direction is generally only at lower elevations that are less prone to strong winds. slightly modified by topography (Fig. 2a) and (ii) the largest DEVINE reduces speed median errors among half of the TPI wind direction modifications are expected on the most complex classes, with a notable improvement for the most exposed sta- terrain (Fig. 2a), which corresponds to areas not necessarily tions, characterized by the largest TPI (q , TPI), where the equipped with AWS (section 5). negative speed mean bias is reduced by 66%. Among the 61 ob- We finally investigate the errors of DEVINE when com- servation stations, DEVINE significantly reduces wind speed pared with AROME, in a seasonal and diurnal perspective mean bias at 37 stations (dependent Student’s t test at a 95% (Fig. 10). This is done by considering the difference in the confidence interval, using Bonferroni method for multiple- normalized absolute error (defined as the absolute value of comparison correction), a feature concerning 58% of the sta- the error at each time step divided by the observed speed) of tions located above 1500 m. We also notice that correlation in both wind products, categorized into three distinct groups speed signals is only slightly improved with DEVINE (0.56 for based on the observed wind speed. The evolution of the nor- AROME vs 0.58 for DEVINE; Table 2). However, Fig. 9b indi- malized absolute error confirms that DEVINE mostly im- cates that errors in direction are almost unchanged between proves forecast for higher wind speeds (Fig. 10). Lowest wind AROME and DEVINE (average change in direction error less speeds are generally characterized by an increased absolute than 18). Furthermore, we observe that AROME can be af- error with DEVINE (brown color in Fig. 10), and wind speeds fected by strong direction errors (.908), for which only small above3m s are on the contrary characterized by a Modeled wind speed [m/s] Modeled wind speed quantiles [m/s] Densiity JANUARY 2023 L E T O U M EL I N ET A L . 13 (a) (b) Wind speed error / observed wind speed Wind direction error [] [°] FIG. 9. Performances in wind (a) speed and (b) direction of AROME and DEVINE on real topographies with respect to in situ observations (for observed wind speed $ 1m s ). Results are clustered by TPI according to the quantiles of the TPI distribution (q 5215 m, q 5 3m, and q 5 32 m). 25 50 75 decreased error with DEVINE (green color in Fig. 10). It rather than forecast lead time hour, also suggesting an influ- is interesting to note that for wind speeds below 3 m s , ence of thermal processes. the largest increases in normalized absolute error occur between April and September, and between 0900 and 5. Discussion 1700 UTC. This tends to occur at periods of highest incom- a. Representativity of Gaussian topographies ing shortwave radiations and temperatures, suggesting some influence of thermal processes (section 5c). Oppositely, visi- The characteristics of Gaussian topographies accurately ap- ble improvements occur with DEVINE during nights of sum- proximate the mean characteristics of alpine topographies mer months where atmospheric stability could be closer to (Fig. 11). For every pixel of a digital elevation model covering neutral conditions than during afternoons of the same periods. the French Alps, thus including the observation sites that More generally, we observe that improvements/degradations served for model evaluation in section 4d, we computed the with DEVINE tend to be more linked with validity hour TPI, Sx (using a fixed direction of 2708), Laplacian, and slope. TABLE 2. Evaluation statistics of AROME and DEVINE when compared with 61 AWS located in the French Alps, in terms of wind speed and direction. DEVINE designates DEVINE performances when DEVINE is initialized by realistic AROME forecasts. AROME forecasts are here considered to be realistic when the speed error is less than 3 m s and the direction error is less than 308 (AROME ). Variable Metric AROME DEVINE AROME DEVINE c c Speed Mean bias (m s ) 20.33 20.24 20.29 20.17 r (}) 0.56 0.58 0.73 0.72 Mean AE (m s ) 1.40 1.37 1.06 1.07 q AE (m s ) 0.44 0.44 0.41 0.40 q AE (m s ) 0.98 0.96 0.91 0.89 q AE (m s ) 1.89 1.84 0.91 0.89 Direction Mean AE (8)58 57 14 14 q AE (8)18 17 7 6 q AE (8)43 41 14 13 q AE (8)88 87 14 13 75 14 AR TI F I C I A L I N T E LLI G E N C E F O R T H E E AR TH S Y S T E M S VOLUME 2 FIG. 10. Evolution of the mean of the normalized absolute error (nAE) for wind speed between AROME and DEVINE (nAE 2 DEVINE nAE ), categorized by hour of the day and month of the year (the mean of the nAE corresponds to the mean of the absolute value AROME of the error at each time step divided by the observed wind speed) (a) only considering observed wind speed between 1 and 3 m s ,(b) for 21 21 wind speeds between 3 and 7 m s , and (c) for wind speeds above 7 m s . Negative values correspond to improvements (green), and positive values correspond to degradations (brown). We then compare the results with the same parameters obtained (2012), who showed that Gaussian statistics outperformed on the Gaussian topographies forming our training dataset other statistical models when representing slopes of real (Fig. 11). We observe that for each parameter, the distribu- topographies in complex terrain. tion obtained on Gaussian topographies (yellow distribu- However, for individual pixels, some terrain parameters tion) overlaps most of the distribution obtained on real derived on the real alpine topographies are not encom- passed in the range of the same parameters derived on the topographies (green distribution) suggesting that, with re- spect to the chosen parameters, most of the alpine topo- Gaussian topographies. These correspond to pixels located graphic pixels are represented in our Gaussian topographies in extremely complex terrain. Notably, the tail of the distribu- dataset. This strengthens the results of Helbig and Low ¨ e tion of Laplacians [Df;Eq. (2)] computed on real topographies (a) (b) TPI [m] FIG. 11. Parameters computed for each point of a real digital elevation model (“real topographies”; green), only at sites with wind observations (“observation stations”; red), and on Gaussian topographies used in our training dataset (“Gaussian topographies”; orange): (a) TPI vs Sx and (b) Laplacian [Eq. (2)] vs slope. The Sx values are computed us- ing a wind direction of 2708; A indicates the Aiguille du midi station, and V indicates the Vallot station. Sx [rad] Slope [] JANUARY 2023 L E T O U M EL I N ET A L . 15 TABLE 3. DEVINE computing performances on a 1250-km domain presented in Fig. 7 (40.9 km by 30.5 km; horizontal resolution of 30 m). The computing time does not account for data loading overhead (loading DEM map, NWP gridded outputs, etc.). Note that because the downscaling operation is not sequential through time it can be easily parallelized across time by using different processing units. Name Value Domain Domain size 40.9 km by 30.5 km Horizontal resolution (input) 1300 m Initial interpolation rate 2 Horizontal resolution (interpolated) 650 m No. of interpolated NWP grid points to downscale 3072 Performance on CPU CPU model Intel Core i7-10610U CPU at 1.80 GHz No. of CPU 1 Prediction (downscaling 1 time step) 64 s Prediction (downscaling 24 time steps) 1461 s Performance on a GPU 1 CPU GPU model Nvidia Tesla V100 No. of GPU 1 Prediction (downscaling 1 time step) 14 s Prediction (downscaling 24 time steps) 97 s exhibits the largest discrepancies with respect to their Gaussian Such a low computational cost is also attributable to our counterparts. choice of limiting input channels of the CNN to topographic Most of the topographies surrounding the observation sta- maps only. As a consequence, DEVINE only requires mini- tions, however, have characteristics well represented in our mal inputs (i.e., topography and initial wind fields provided by Gaussian topographies (red dots in Fig. 11). We nevertheless an NWP system) to output downscaled wind predictions at a note that some extreme locations such as the Aiguille du Midi high resolution. Following the topographic nature of the se- (TPI 5 288 m, Sx 520.88 rad, Laplacian 520.039 m s , lected inputs, we observed that DEVINE is able to detect and slope 5 0.29) or the Vallot station (TPI 5 120 m, main features of terrain-forced flow, including the representa- Sx 520.3 rad, Laplacian 520.033 m , and slope 5 0.58) tion of acceleration on ridges, deceleration on leeward areas, flow deflections and moderate deviations around obstacles are localized on the tails of the distributions obtained on the Gaussian topographies. We note that DEVINE frequently (Figs. 6 and 7). It is worth noting that contrary to Dujardin overestimates low wind speeds at Aiguille du midi, suggest- and Lehning (2022), who reached state-of-the-art results using ing current limitations of our method on such extremely ex- a downscaling model also based on CNN, we did not used precomputed topographic parameters (TPI, aspect, etc.) as in- posed and complex terrain, for which only few information puts. Indeed, we converged to low errors on the test dataset can be derived from the training dataset. It would be ques- tionable that adding more complex topographies to our by simply using raw topographic maps. Three factors emerge training dataset would be beneficial for DEVINE since nu- to explain our choice to use raw topographic data as inputs versus preprocessed topographic data as in Dujardin and merical limitations and errors can arise when computing Lehning (2022): our training dataset encompasses more top- wind fields on very steep slopes with mesoscale models (e.g., ographies [7279 vs 261 for Dujardin and Lehning (2022)], our Lundquist et al. 2012). CNN learns topographic features related to Gaussian topog- raphies versus real topographies in Dujardin and Lehning b. Efficient downscaling by using a CNN with (2022) and as we only have one channel in input, feature de- reduced complexity tection is directly oriented toward topographic characteristics Wind downscaling with DEVINE is particularly useful as it whereas Dujardin and Lehning (2022) join topographic maps comes with a low computational cost, when compared with with many other atmospheric variables when constituting the much more computationally expensive atmospheric models input channels, which could eventually make the detection of such as ARPS. Here, we optimized the model implementation topographic characteristic less direct. using a strategy leveraged on the graphical processing unit The impact of high-resolution topography on wind fields is (GPU) only for raw CNN predictions plus computationally reflected in the evaluation statistics, including a decrease in expensive rotations and left other pre- and postprocessing op- the mean bias, a more moderate reduction in MAE and a erations (interpolation, normalization, final activation, etc.) slightly increasing correlation. We emphasize the fact that our for the CPU. As a result, it is possible to downscale AROME method is only based on an emulation of the atmospheric fields as presented in Fig. 7,in 14 s (Table 3). These perform- model ARPS and does not need to be calibrated with any ob- ances pave the way for the use of our method in time con- servation, in contrast to Pohl et al. (2006), Liston and Elder strained applications, for instance as a downscaling tool to (2006), Winstral et al. (2017), and Dujardin and Lehning reach decametric scales within operational forecasting sys- (2022). It highlights that DEVINE upsamples NWP wind tems in complex terrain. fields but does not explicitly involve a bias correction, as was 16 AR TI F I C I A L I N T E LLI G E N C E F O R T H E E AR TH S Y S T E M S VOLUME 2 done, for example, in Winstral et al. (2017) and Dujardin and As described in section 1, DEVINE exhibits features of a Lehning (2022). Thus, DEVINE is independent from the NWP mostly nonturbulent flow, including the absence of recircula- tion zones (Raderschall et al. 2008; Sharples et al. 2010), whose system providing the initial information. However, as the initial impact on snow deposition is important (Vionnet et al. 2021). errors of the NWP are not compensated with any calibration Avoiding the inclusion of turbulent features favors the devel- step, they can eventually be propagated (Wagenbrenner et al. opment of simple yet generalizable outputs and is in phase 2016) and amplified through DEVINE. For instance, we ob- with the choice of an initial speed of 3 m s in ARPS simula- serve that when the wind fields simulated byAROME arein tions, where the generation of turbulent eddies due to wind– phase with the observation, that is, a direction error less than topography interaction is probably low (Whiteman 2000). 308 and a speed error less than 3 m s ,DEVINE mean bias is Again, this assumption might not stand for higher speeds. even more reduced (Table 2). We underline that simultaneous occurrence of assumptions i, ii, iii, and iv in the atmosphere is probably rare. However, c. Limits of our approach even though DEVINE is limited in terms of physical processes Apart from error propagation due to the initial errors of it can represent at the slope scale, it proves to add value as a the NWP (section 5b), limitations on the most extreme alpine downscaling tool of NWP wind fields in all weather conditions terrain (section 5a), and even though the CNN reproduces (Table 2, Fig. 10). Furthermore, the NWP system driving particularly well the ARPS simulations, some errors remain DEVINE is not bound to these assumptions so that it provides when predicting wind on real topographies (section 4). In- a representation of all atmospheric situations, to the extent en- deed, for simplicity and computational efficiency, we pruned abled by its spatial resolution and inherent assumptions. DEVINE to a minimalist architecture. In particular this was Note that AROME uses a parameterization of the subgrid possible following the assumptions used in the setup of the topography following Georgelin et al. (1994). Consequently, ARPS model (Helbig et al. 2017). Inheriting the assumption high-resolution wind fields obtained using DEVINE have inter- of the ARPS configuration, DEVINE assumes (i) a neutral acted twice with the topography: a first time through AROME stratification of the atmosphere, (ii) an absence of thermal subgrid parameterization and a second time through DEVINE. This redundancy could contribute to errors in wind fields processes, (iii) mostly nonturbulent flow, and (iv) a linear be- estimations. havior between the wind flow obtained for a 3 m s initial Also note that AROME wind fields (arrows in Fig. 7) are speed and output obtained with any other speed. first interpolated to double the horizontal resolution and limit For DEVINE, the assumption i on the neutral stratification the establishment of chesslike patterns in the output signal of the atmosphere may explain the model’s limited ability to (section 3c). Chessboard-like patterns correspond to colored drastically change wind direction. The thermal stability of the squares in the downscaled signal: as (i) two neighbors in an atmosphere influences the motion of air masses in complex NWP grid can forecast different wind conditions and (ii) as terrain, and more particularly, is responsible for large devia- each (interpolated) NWP grid point is treated independently tions of stable and heavy air masses (Whiteman 2000) that from its neighbors by DEVINE, discontinuity can appear at tend to get around obstacles rather than above. Additionally, the border of each grid cell in the downscaled signal. Such assumption iii is responsible for the absence of small-scale tur- patterns progressively disappear by increasing the interpola- bulent eddies in DEVINE simulations and thus also explain tion rate, at the expense of more computing time. Ultimately, the model difficulty to simulate large modifications in wind we note that the impact of chesslike patterns on the down- direction. scaled signal could impact drifting snow modeling, a task that We also attribute increasing normalized errors observed in requires spatially coherent wind forcing for the computation Fig. 10, for the lowest wind speeds, to the absence of thermal of snow flux divergences. This impact still has to be quantified processes in DEVINE. Butler et al. (2015) and Sharples et al. through the evaluation of distributed snowpack simulations. (2010) indicated the prominence of along-slope and valley flows during spring/summer months, underlining that the in- 6. Summary and conclusions tensity of some thermal flows largely depends on seasonality. Interestingly, we observe that the largest degradations with DEVINE is a downscaling scheme based on deep learning, DEVINE occur for observed wind speeds less than 3 m s relying on a fully convolutional neural network (Unet-like), during days of spring and summer month. that downscales NWP gridded wind fields from a grid spacing Moreover, using additional ARPS simulations performed on the order of several kilometers to tens of meters using to- by Helbig et al. (2017) on a small group of the Gaussian top- pographical information only. This model has been fitted using ographies using a different initial wind speed (5 m s instead simulations obtained with the model ARPS on a set of 7279 of 3 m s ), we challenged our assumption iii on linearity. We Gaussian topographies. We demonstrated that the Unet archi- observed that the acceleration rates obtained with an initial tecture is performant on a cross-validation dataset to emulate speed of 3 m s are consistent with the acceleration rates ob- the behavior of ARPS on synthetic topographies. By evaluat- tained at 5 m s , thus suggesting that the assumption on line- ing our model using simulations performed on real topogra- arity holds (not shown). However, we can expect that a phies and by using quality-checked data from 61 observation nonlinear relation would arise with higher wind speeds, which stations in the French Alps, we showed that DEVINE partially is still to be benchmarked. improves AROME wind speed forecasts, and is able to reproduce JANUARY 2023 L E T O U M EL I N ET A L . 17 Butler, B. W., and Coauthors, 2015: High-resolution observations observed wind speed patterns, thus providing a numerically effi- of the near-surface wind field over an isolated mountain and cient alternative to complex atmospheric models for simulations in a steep river canyon. Atmos. Chem. Phys., 15, 3785–3801, of high-resolution wind fields. Most notably, DEVINE reduces https://doi.org/10.5194/acp-15-3785-2015. AROME mean bias, slightly reduces the absolute error, and in- DeGaetano, A. T., 1997: A quality-control routine for hourly wind creases the correlation. Moreover, DEVINE outputs are consis- observations. J. Atmos. Oceanic Technol., 14,308–317, https:// tent with the well-known influence of main topographic features doi.org/10.1175/1520-0426(1997)014,0308:AQCRFH.2.0.CO;2. (peaks, slopes, and ridges) on airflow at local scale. Our method is Dujardin, J., and M. Lehning, 2022: Wind-topo: Downscaling developed for snow-transport applications and therefore does not near-surface wind fields to high-resolution topography in account for some processes that may be controlling the wind pat- highly complex terrain with deep learning. Quart. J. Roy. terns at a local scale in other conditions like thermal stability and Meteor. Soc., 148, 1368–1388, https://doi.org/10.1002/qj.4265. thermal winds. Using transfer learning and additional model Ferna ´ndez, J. G., and S. Mehrkanoon, 2021: Broad-Unet: Multi- simulations could be of interest to complement current capabili- scale feature learning for nowcasting tasks. Neural Network, ties of DEVINE. This would probably require thousands of new 144,419–427, https://doi.org/10.1016/j.neunet.2021.08.036. Forthofer, J. M., B. W. Butler, and N. S. Wagenbrenner, 2014: A high-resolution simulations to be used as labels and may induce comparison of three approaches for simulating fine-scale sur- modifying DEVINE architecture. Additionally, we discussed the face winds in support of wildland fire management. Part I. influence of several factors that could restrict DEVINE appli- Model formulation and comparison against measurements. cability and conclude that future work might focus on an Int. J. Wildland Fire, 23,969–981, https://doi.org/10.1071/ indirect distributed evaluation of the downscaling model, WF12089. through the use, for example, of remotely sensed data and Georgelin, M., E. Richard, M. Petitdidier, and A. Druilhet, 1994: Im- drifting snow models. Moreover, we note that reducing the pact of subgrid-scale orography parameterization on the simula- initial biases of the NWP could limit error propagation when tion of orographic flows. Mon. Wea. Rev., 122, 1509–1522, https:// increasing the spatial resolution of wind fields using DEVINE. doi.org/10.1175/1520-0493(1994)122,1509:IOSSOP.2.0.CO;2. A comprehensive intercomparison exercise of state-of-the-art Gouttevin, I., V. Vionnet, Y. Seity, A. Boone, M. Lafaysse, Y. downscaling models could help to benchmark solutions for Deliot, and H. Merzisen, 2023: To the origin of a wintertime drifting snow applications. screen-level temperature bias at high altitude in a kilometric NWP model. J. Hydrometeor., 24,53–71, https://doi.org/10. 1175/JHM-D-21-0200.1. Acknowledgments. This research is supported by the Guyomarc’h, G., and Coauthors, 2019: A meteorological and French Meteorological Institute (Météo-France). The au- blowing snow data set (2000–2016) from a high-elevation al- thors thank the national observation service GLACIOCLIM pine site (Col du Lac Blanc, France, 2720 m a.s.l.). Earth Syst. (CNRS-INSU, OSUG, IRD, INRAE, and IPEV) for the Sci. Data, 11,57–69, https://doi.org/10.5194/essd-11-57-2019. data provided. The authors thank Eric Bazile, Yann Seity, Helbig,N., andH.Lowe, 2012: Shortwave radiation parameteriza- Hugo Merzisen, and Ange Haddjeri for the meaningful dis- tion scheme for subgrid topography. J. Geophys. Res., 117, cussions that helped to build the study. D03112, https://doi.org/10.1029/2011JD016465. }},and }}, 2014: Parameterization of the spatially averaged Data availability statement. AROME outputs and all AWS sky view factor in complex topography. J. Geophys. Res. data that are not otherwise mentioned below can be re- Atmos., 119,4616–4625, https://doi.org/10.1002/2013JD020892. quested online (https://donneespubliques.meteofrance.fr/). }}, R. Mott, A. Van Herwijnen, A. Winstral, and T. Jonas, 2017: Parameterizing surface wind speed over complex topog- Training data are available from norahelbig@gmail.com upon raphy. J. Geophys. Res. Atmos., 122, 651–667, https://doi.org/ request. 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