Les phénomènes météorologiques en montagne sont soumis à de nombreux facteurs d’influence tels que le relief ou l’altitude, et possèdent de ce fait une grande variabilité spatiale, qui rend l’hydrométéorologie des massifs particulièrement complexe. En conséquence, l’estimation des stocks de neige et des précipitations, primordiale pour les gestionnaires du parc hydroélectrique d’EDF restent encore aujourd’hui sujets à des incertitudes non négligeables. DTG cherche actuellement à développer des outils d’interpolations robustes, capable de fournir une valeur estimée fiable des précipitations en tout point des massifs montagneux, en s’appuyant sur le réseau DTG de mesure au sol des précipitations et de la neige.

La thèse menée actuellement au sein de l’équipe hydrologie de DTG a parmi ses objectifs, le développement d’un outil d’interpolation des précipitations en zones de montagne. Ce dernier permettrait à terme de progresser vers une vision spatialisée et cartographiée de la pluie et de la neige, mesurées sur les bassins versants faisant l’objet d’une prévision opérationnelle.

Pour développer ce modèle, une très vaste base de données a été constituée, regroupant des données françaises (DTG et Météo France) mais également suisses, italiennes et espagnoles.

Cet outil repose sur un Modèle Numérique de Terrain de maille de taille 1´1 km. Sur chaque pixel l’effet orographique, considéré comme prépondérant dans l’explication des précipitations en montagne, est modélisé par une relation linéaire reliant les précipitations à l’altitude. Cette relation s’appuie sur les points de mesure situés à proximité du pixel, dont le mode de sélection et de pondération conditionne la qualité des résultats.

L’utilisation de la validation croisée a permis d’évaluer le niveau de restitution du modèle sur les Alpes, les Pyrénées, et le Massif Central. On peut considérer les résultats comme très encourageant aux regards de ceux obtenus par d’autres méthodes (notamment AURELHY), ce qui est sans doute le fait du caractère résolument régional du mode de reconstitution des précipitations.

The estimation of snow storage and precipitation, essential for managing hydroelectric reservoirs of EDF, still remains subject to considerable uncertainties. EDF-DTG currently seeks to develop some tools for robust interpolations, able to provide a reliable estimate of precipitation and snow water equivalent at any point in mountainous areas. The developed tools are essentially based on the ground sensor network of DTG, which measures precipitations, snow depth and water equivalent over French mountains. In the long term, these tools should make it possible to progress towards a better spatial vision of the daily or “event” precipitation, as well as of the snow cover on the ground, based on measurements taken all over the basins requiring an operational hydrological forecast.

To develop this model, a very large database was collected for the main mountainous areas, gathering precipitation data from France but also Switzerland, Italy and Spain. This tool makes use of a Digital Elevation Model with a mesh of 1´1 km. Since the orographic effect is dominant in the explanation of precipitations in mountain, a linear relation is considered for each pixel to connect precipitation to elevation. This procedure takes into account a specific distance between the target pixel and the measurement points located in its vicinity, whose mode of selection and weighting conditions the quality of the results.

The use of a cross validation made it possible to evaluate the level of accuracy of the model for the Alps, the Pyrenees, and the Central mountains. One can regard the results as very encouraging taking into consideration those obtained by other methods, which is undoubtedly the fact of the local character of this mode of reconstitution.

The hydropower production concerns of EDF are essentially concentrated in the French mountainous areas. So our approach is developed for the Alps, the Pyrenees and the Massif Central, which are equipped with many hydroelectric facilities. We consider independently these three geographical sub-regions for which we have a DEM (Digital Elevation Model) with a 1 km mesh. The mapping of precipitation will be developed on this DEM, with this resolution scale.

The database is especially derived from the EDF’s network, centered on the EDF’s facilities. The EDF’s network is the densest and the highest network in the French mountainous areas (some stations are higher than 2000 m). This database is supplemented by series of Météo France, as well as Spanish, Italian and Swiss series, in order to limit border effects. The whole of the collected series are daily measurements.

Our interpolation model of precipitations has been inspired by PRISM (Precipitation-elevation Regressions on Independent Slopes Model), a model developed by DALY et al. (1994) at Oregon State University for areas of average latitude with dominant orographic effect. This analytical model seeks to estimate monthly and annual precipitations on pixels of a DEM representing the domain at hand. The estimation is based on ground measurement, which provide an actual precipitation on some pixels of the DEM. Orographic precipitations are then analysed through a combination of climatological and statistical considerations, in order to estimate precipitations on all the non-instrumented pixels of the DEM.

Generally, precipitations increase with altitude, due to the orographic effect. The developed model tries to approach this relation between precipitations and altitude through a local linear approximation. We seek first for annual or seasonal precipitations P, a relation like:

Indeed the orographic gradient of precipitation A_z has significant variations with the place (X,Y) where the approximation is made, according for example with the mountainous area, the slope or the orientation considered. For example, the edges of a mountainous area correspond often to stronger gradients ("barrier" effect on the weather flow), and the inside to weaker gradients, because weather flows are well attenuated.
It is obviously impossible to obtain an analytical expression of the functions A_z and B, taking into account the very significant number of parameters brought into play, and of the complexity of the weather phenomena considered. The relation is thus discretized on the DEM, and the model propose a numerical expression of the precipitation estimated PE_ij in any point (i,j) of the DEM :

The goal of the model is to determine the coefficient a_ij and b_ij with local linear regression, on a judicious selection of a part of the measured precipitations PO_kl located around and closed to the pixel (i,j) considered.

A subset of neighbouring stations of proximity are selected in the vicinity of each pixel (i,j) on the DEM in order to estimate the coefficients a_ij and b_ij. The stations are selected according to a “crossing distance” d_3D that separates them from the target pixel. This “crossing distance” takes in consideration the horizontal Euclidian distance station-to-pixel, but also a vertical component related to the crossing of crests and valleys. An exhaustive definition of the “crossing distance” is given on the Figure 2.

A station is selected and considered as explanatory if the crossing distance, which separates it from the pixel, is lower than a fixed limit d_lim. When the station is selected, it receives a weight W, in order to give it more or less weight in the linear regression. The weight of the station is given by the entire part of the function f, the “bell of selection”.

The cross validation is used to estimate the quality of the interpolations of the model. Thus we have for each observed precipitation P_obs an interpolated precipitation P_int independently from P_obs. If n is the total number of observed and cross-validated precipitation, one is able to define these three coefficients, which quantify the quality of an interpolation:

The final objective is to reach the daily time step, in order to produce daily maps for the historical datas but also for every day in real time. The spatial density of the measurement network available on the French mountainous areas is very variable over the last fifty years. The 1957-1973 years seems to display a maximum of density. Today, the network has been reduced, and it appears unrealistic to generate precipitation maps using only the existing observations.
The introduction of guess fields is necessary. The idea is to use the daily structure of the precipitation field identified on a better-instrumented period, to try as well as possible a reconstitution of the current day by wrapping this structure on observed precipitations. A layer of residual kriging is then carried out to correct the variations between the observed point and their counterpart on the guess field:

In order to produce these guess fields, we are considering a classification into daily weather patterns. The classification retained is that established at EDF (PAQUET et al. 2006) because of it is used in other applications of EDF, and was developed specifically for the needs of DTG. This classification contains eight weather patterns identified by the shape of the 700 hPa and 1000 hPa geopotential fields:

It allows generating eight maps of inter-annual mean of precipitation for each weather pattern. These maps have a specific daily mean structure and can be used as a guess once scaled or distorted appropriately. Each day is associated with a weather pattern and the associated outline.

DALY Christopher, NEILSON Ronald P., PHILLIPS Donald L., A statistical-topographic model for mapping climatological precipitation over mountainous areas, Journal of Applied Meteorology, Vol. 33, 1994.

FREI Christoph, SCHÄR Christoph, A precipitation climatology of the alps from high-resolution rain-gauge observations, International Journal of climatology, Vol. 18, 1998.

GYALISTRAS D., Development an validation of high-resolution monthly gridded temperature and precipitation data set for Switzerland (1951-2000), Climate Research, Vol. 25, 2003.