Assessing wind fields at a local scale in mountainous terrain has long been a scientific challenge, partly because of the complex interaction between large-scale flows and local topography. Traditionally, the operational applications that require high-resolution wind forcings rely on downscaled outputs of numerical weather prediction systems. Downscaling models either proceed from a function that links large-scale wind fields to local observations (hence including a corrective step) or use operations that account for local-scale processes, through statistics or dynamical simulations and without prior knowledge of large-scale modeling errors. This work presents a strategy to first correct and then downscale the wind fields of the numerical weather prediction model AROME (Application of Research to Operations at Mesoscale) operating at 1300 m grid spacing by using a modular architecture composed of two artificial neural networks and the DEVINE downscaling model. We show that our method is able to first correct the wind direction and speed from the large-scale model (1300 m) and then accurately downscale it to a local scale (30 m) by using the DEVINE downscaling model. The innovative aspect of our method lies in its optimization scheme that accounts for the downscaling step in the computations of the corrections of the coarse-scale wind fields. This modular architecture yields competitive results without suppressing the versatility of the DEVINE downscaling model, which remains unbounded to any wind observations.

Understanding the declination of synoptic winds at a local scale in complex terrain is crucial for a wide range of applications, including assessing the dispersion of pollutants, predicting wildfire spread, and evaluating wind energy potential

Wind field variability at a local scale in mountains is largely driven by two factors: terrain forced flow, which refers to the direct impact of topography on large-scale winds, and thermally driven flows, which result from local temperature gradients caused by terrain inhomogeneity and variable shading

Many applications rely on the ability of numerical weather prediction (NWP) systems to model synoptic-scale wind fields above mountains

Several methods have emerged to adapt the wind fields provided by NWP systems (in this work referred to as “large scale”) to a local scale. Statistical downscaling is a family of methods that adapt large-scale information, such as NWP outputs, to local-scale specificities using statistical operations. Another approach, dynamical downscaling, relies on models to directly simulate atmospheric and surface processes at a higher resolution. A large variety of statistical downscaling methods can be found in the literature: e.g.,

Conversely, other downscaling methods restrict their use to the modeling or parameterization of local-scale processes only, without any optimization based on observations. These methods may improve evaluation metrics through the added value of the representation of missing processes; however, they do not compensate for systematic errors in large-scale modeling and hardly compete in terms of evaluation metrics with methods including a corrective step. However, their use is not restricted to any specific NWP or to any specific geographic area. A large array of the aforementioned models can be found in the literature, ranging from simple statistical relationships

Consequently, systematic errors originating from the NWP large-scale inputs can eventually be transferred and amplified through DEVINE. These errors can have a variety of origins, like missing or imperfect parameterizations, overly coarse model topography, and errors due to the assimilation procedure. Furthermore, the use of a downscaling model also makes it difficult to determine the origin of the modeling errors: whether the downscaling model accurately or inaccurately simulates local-scale processes or whether error compensations between the large-scale forcing and the downscaling model scramble the evaluation. However, even though error attribution is complex, identifying typical weather and topographic situations where inputs or downscaled data are incorrect is more accessible, notably thanks to deep learning.

As an illustration,

In this context, we design and present a strategy, based on deep learning, that corrects NWP input wind fields upstream of the DEVINE downscaling method. Indeed, the correction is made before the downscaling step, but the effect of downscaling is accounted for in the optimization of the neural networks' parameters that are responsible for the correction. In turn, most errors affecting the coarse-scale wind fields are corrected without affecting the spatial extrapolation capabilities of the downscaling model and diminishing the associated performances. By scrutinizing a set of variables including many variables that can influence air motion (e.g., temperature, humidity, boundary layer height) and advanced topographic metrics, the artificial neural networks developed for this correction optimize NWP wind speed and direction before calling the downscaling model. With this modular architecture, we provide an end-to-end chain including downscaling and model output statistics, which permits us to boost the evaluation performances of the DEVINE downscaling model.

In this study, we used forecasts from the AROME NWP system as inputs to our new downscaling strategy. We rely on forecasts from AROME for both large-scale wind fields and other atmospheric variables used in the corrective step. Our models also make use of high-resolution topographical information (30 m). Quality-controlled wind observations acquired over a large network of automatic weather stations (AWSs) are used for model training (training set) and evaluation (test set). We finally compared the performance of our models to the operational analysis of the AROME system.

The AROME NWP system embeds a limited-area model, notably run by Météo-France for short-term weather forecasting operations. It simulates the state of the atmosphere and the surface over a European domain including the French Alps, the Pyrenees and Corsica. The model solves the non-hydrostatic fully compressible Euler equations by using a semi-Lagrangian and semi-implicit numerical solver and by including a spectral representation of several prognostic variables

AROME analyses are produced every UTC hour, whereas the model is also run in forecast mode every 3 h. For this study, we built two different products from the aforementioned cycles. Firstly, we built a continuous time series by extracting

Input variables used in

Architecture, hyperparameters and loss functions used in Neural Network and Neural Network+DEVINE.

We gathered hourly wind field observations from AWSs originating from different observation networks in Switzerland and France in order to train and evaluate our models (Fig.

In situ observation stations used to train the model (218 blue dots) and evaluate the model (55 red dots). All the stations are located in Switzerland and France. Train–test partitioning was performed using a stratified sampling method described in Sect.

Since most of the wind observations used in this study were obtained in complex terrain and frequently under challenging meteorological conditions, we applied a quality-check procedure to our observational dataset, inspired by

Since the local topography has a large impact on wind fields, several topographic parameters are used as input variables for the corrective strategy so as to capture the dominant local features of the topography. Among the selected parameters, the

Artificial neural networks (ANNs) are a specific type of machine-learning model. They are composed of interconnected units called neurons, which hold floating-point values, all organized into different layers. In a layer, neurons transmit the information received from the previous layer's neurons to the next layer's neurons. Communication consists first of an affine modification of each neuron value using weights (slope parameters) and biases (intercepts). Then, all neuron-modified values are summed and pass through a nonlinear activation function which produces the next layer's neuron input values. Finally, the first layer holds the raw inputs, while the last layer holds the predicted values. All weights and biases are typically initialized using random values and are then modified using optimization algorithms based on gradient descent methods. Such methods are based on the computation of the gradient of a loss function between the neural network output and the expected output with respect to the network weights and biases. Weights and biases are then optimized in the opposite direction of the gradient in order to minimize the loss. By replicating this strategy a large number of times over a large number of samples, artificial neural networks can learn complex patterns that link the training inputs to the training target outputs. Finally, we note the existence of different hyperparameters, which consist of parameters that are not weights and biases (e.g., the number of neurons and the number of layers). These parameters are not learned during the training process but are rather fixed independently.

DEVINE is a downscaling model based on a U-Net convolutional neural network

The model presented in this study corresponds to an extension of the DEVINE model. It consists of the addition of two ANNs that process large-scale NWP data and local-scale topographic data prior to the use of the DEVINE downscaling model. More precisely, a first neural network is designed to compute an additive correction for the NWP wind direction (

As

In order to adapt the weights and biases of the ANNs, we adopted a sequential approach. First, we optimized

Scheme of the new model architecture. The architecture is composed of two artificial neural networks (ANNs) in addition to the DEVINE downscaling model. The first ANN predicts wind direction (orange,

Two loss functions were selected for training

For

Deep-learning applications commonly involve the use of a training set for model optimization and a test set for model evaluation. Many studies

The spatial split involved a stratified selection process that resulted in the selection of 55 AWS sites from the 273 sites available in the Alps. We first identified six topographic and geographic descriptors for the AWS locations, calculated as described in Sect.

The temporal split simply consisted of excluding the last year of data from the training set and excluding the first 2 years from the test set. Finally, we obtain 2 years of data at 218 sites for training and 1 other year at 55 other sites for evaluation.

In statistical modeling, interpretability methods give insights into the causes that lead a model to make a specific decision. Among these methods, partial dependence plots (PDPs) form an intuitive method giving insights into the isolated effect of a given variable on the model outputs. Their computation consists of iteratively fixing all instances of the studied input variable

Accumulated local effects (ALE) also permit us to study the influence of a given input variable on the model outputs. Unlike more common methods such as PDPs or feature importance ranking

Mean wind speed error of AROME forecasts versus observed wind speed (color) at all stations available (training and test) in the Alps. The results are categorized by

In addition, we observe that the

The 1-1 plots of simulated versus observed wind speed. The models are

Finally,

Wind roses of modeled wind directions for

In this section, we evaluate the performances of different wind products, including

We also observe (as expected) improved behavior of

Evaluation metrics obtained on the test dataset (Alps). MAE designates the mean absolute error, RMSE the root mean square error, and

We then scrutinized the model performances for wind speed with respect to elevation in Fig.

Wind direction absolute error

In terms of wind direction,

In this section, we analyze model performances with respect to forecast lead times (Fig.

Wind speed absolute error as a function of the forecast lead time

We obtain similar model rankings in terms of wind direction. Nevertheless, we observe that the

When modeling errors are interpreted with regards to the month of the year, we observe a peak in speed error during the winter months (Fig.

The design of an appropriate loss function was important for ultimately obtaining the best-performing model presented in this study. The function used to optimize

Plot of the observed quantiles versus the modeled quantiles for different models. A perfect simulation would present all quantiles along the 1-1 line (red). Each color refers to a single model, mse refers to Neural Network+DEVINE optimized using a mean square error loss function, and

When fitted using observation from the Alps, Neural Network+DEVINE yields poor evaluation metrics in terms of speed when evaluated against data from other mountain ranges but performs well when downscaling wind direction. We evaluate the ability of our models to correct and downscale

Evaluation metrics obtained by comparing simulation and observed data in other mountain ranges (Corsica and the Pyrenees) than the one used during training (Alps). No data from Corsica (18 AWSs) or the Pyrenees (21 AWSs) were used during training. MAE designates the mean absolute error, RMSE the root mean square error, and

To illustrate the added value of Neural Network+DEVINE compared to DEVINE alone, we selected a case study at a mountain observation station located near Piz Corvatsch in southwestern Switzerland (

Use case of Neural Network+DEVINE at Piz Corvatsch in Switzerland for 7 to 9 October 2019. Panel

Neural Network+DEVINE shows improved metrics when compared to

The modular architecture of Neural Network+DEVINE appears to us to be one of its greatest assets. Decoupling the spatial interpolation of wind fields (in DEVINE) from its correction (in Neural Network) makes the model robust to new NWP systems or NWP version evolutions. Indeed, if a new version of

Since we did not modify the DEVINE downscaling model in this study but only added upstream modifications related to coarse-scale wind fields, our new architecture inherits the pros and cons of the downscaling model concerning the local structures of simulated wind fields. On the one hand, using DEVINE favors the simulation of spatially consistent three-dimensional outputs at a local scale since DEVINE was built to replicate the structure of outputs provided by an atmospheric model

In addition to potential applications in wildfire spread modeling, wind energy forecast, wind energy potential assessment, pollutant dispersion evaluation, drifting-snow modeling, and avalanche hazard forecasting

Accumulated local effects (ALE) associated with each input variable of

Topographic parameters also have strong impacts on the speed outputs, particularly when this concerns the tails of the parameter distributions. Real elevation (elevation, Fig.

Finally, we observe that input variables related to the state of the atmosphere (green-shaded areas in Fig.

Here, ALE appear to be useful for model interpretation and as a tool for input variable selection. Indeed, we can distinguish between three groups of input features of unequal importance within the model (topographic variables, wind-related variables, and other weather-related variables). This is partly supported by additional sensitivity tests that reveal a larger increase in the RMSE when removing the topographic variables (

This is of interest for the application of the Neural Network+DEVINE correction and downscaling strategy to a variety of products like reanalyses, as solely topographic or topographic plus basic atmospheric variables may be easier to access, retrieve, and process than a complex suite of ancillary weather variables not always available in the reanalysis archives.

Input variables of

Partial dependence plot (PDP) for each input variable of

Understanding the complex patterns that characterize wind in mountainous terrain is of great importance for several applications, with direct consequences for the environment and human societies. Despite years of continuous improvements, NWP models still rely on downscaling techniques to represent wind features at a local scale in mountains. Not only does the typical kilometer-scale spatial resolution limit their use for several applications, but NWP models are also affected by systematic errors linked to typical meteorological or topographic situations. In this study, we used a large network of observation stations to identify and understand

Aware of the aforementioned limits, here we designed a new postprocessing architecture, called Neural Network+DEVINE, with the purposes of both correcting

This hybrid architecture yields better integrated metrics (MAE, RMSE, mean bias, and correlation coefficient) compared to previous alternatives. The evaluation metrics show performances similar to

This new type of downscaling model greatly benefits from its modular architecture on several points. By making a distinction between correction and downscaling, our design adds flexibility to the different use cases of our model: it is now easy to either use the optimized version (Neural Network+DEVINE) or only rely on DEVINE downscaling models when required. Finally, the whole architecture permits us to output consistent three-dimensional wind fields previously corrected with wind observations. This is a direct consequence of relying on DEVINE for modeling winds at a local scale, an advantage that is counterbalanced by the fact that DEVINE limitations are also inherited by our new architecture.

This work also stresses the potential of deep-learning techniques for the correction of other near-surface atmospheric variables. The general architecture designed here, with a model tailored to correct large-scale errors followed by a more general downscaling scheme, could favorably be applied for the bias correction and downscaling of other variables like 2 m air temperature that similarly exhibit high spatial variations in complex terrain in relation to topographic and meteorological gradients.

Future work should include a generalization of our model to other forecast cycles. Indeed, here we only used forecasts initialized from the 00:00 LT analysis, making our model a proof of concept that needs to be generalized to other forecast cycles. Furthermore, our design adds up to a large array of existing solutions to downscale wind fields in complex terrain for which an intercomparison project is highly required. Such a project could include the use of dense observational networks to assess precisely the behavior of wind at a local scale. This exercise could help list the pros and cons of each method, often developed over different areas and targeting distinct end-user application cases, and reveal each method's value for operational applications. The wealth of near-surface observations to be acquired at high spatial resolution in the central European Alps within the TeamX campaign

The code used to build, train and evaluate the model is available at

AROME outputs and weather observations from Météo-France can be requested online (

The supplement related to this article is available online at:

LLT worked on the conceptualization; led the investigations; built, trained and evaluated the models; wrote the first draft; and designed the figures. IG worked on the conceptualization, supervision and investigation and helped to write the first draft. CG and NH worked on the conceptualization, provided guidance in scientific developments and helped to write the first draft.

The contact author has declared that none of the authors has any competing interests.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors.

The authors thank the national observation service GLACIOCLIM (CNRS-INSU, OSUG, IRD, INRAE, IPEV) for the data provided. The authors thank MeteoSwiss, the Swiss Federal Office of Meteorology and Climatology, for the services provided.

This research is supported by the French Meteorological Institute. Col du Lac Blanc is a part of IR OZCAR, GLACIOCLIM Observatory, and receives financial support from OSUG, LabEx OSUG@2020 (ANR10 LABX56), Météo-France, and INRAE.

This paper was edited by Pierre Tandeo and reviewed by two anonymous referees.

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