home/Options_sensitivity_tests.md

@@ -31,4 +31,15 @@ and to SAFRAN’s extrapolation over higher altitudes where weather stations are
 
 ## Analogue days
 
-Then for the moment, we have presented a methodology that works to construct a forcing over the period common to both initial datasets (SAFRAN and CPRCM run). However, here we introduce another method based on analogue days, which would allow to extend the methodology to the full period covered by SAFRAN (1979-2014).
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+Then for the moment, we have presented a methodology that works to construct a forcing over the period common to both initial datasets (SAFRAN and CPRCM run). However, here we introduce another method based on analogue days, allowing us to extend the methodology to the full period covered by SAFRAN (1979-2014).
+
+So far we have been calculating a bias day by day, taking one day in SAFRAN and using it to rescale the same day in the CPRCM outputs. However, this method only allows to cover the common period for the two datasets (2000-2009). If we want to construct a forcing to run and test LSM performances, we need it to cover at least a period of 20 years, a period significant enough to include long-term climate variability and slower hydrological processes.
+We therefore introduce here a method that, if validated, would allow to extrapolate the methodology out of the common period between SAFRAN and the models’ runs.
+After having integrated the model values at the polygon level for each altitude class (bias by altitude), we calculate, for each SAFRAN’s day, each altitude class and for each variable, a spatial correlation between SAFRAN’s day and all the model’s days (correlation matrix).
+
+![Corr_SAF_Mod_vimage](uploads/7cbace56d9a0cf7822c4a391d07065c7/Corr_SAF_Mod_vimage.jpg "Illustration of a subset of the correlation matrix (from 01/01/2000 to 12/31/2000), for temperature. Spatial correlation day by day for the altitude class 0. The visible diagonal shows good correlation between one SAFRAN day and its matching day in the model. The full correlation matrix extends to 1979-2014 (SAFRAN) x 2000-2009 (Model).")
+
+Once we have the correlation matrix, instead of using the day in the model matching SAFRAN’s day temporally, we can instead look for the day in the model best matching SAFRAN spatially. For each SAFRAN day, through the correlation matrix, we identify the model day, across all years covered by the model run, in the same month (to be sure to match the season), with the best spatial correlation. We select the model day with the best average spatial correlation, considering the spatial correlation for precipitation and temperature over the first four altitude classes, which cover most of the area of interest and where SAFRAN’s data are probably most accurate. We call that selected model day the ”analogue day” corresponding to SAFRAN’s day. Then, to temporally and spatially disaggregated SAFRAN’s variables of a given day, instead of using the same day in the
+model, we instead use the ”analogue” day. The methodology is developed the same way except the bias and all the rest are calculated comparing SAFRAN’s day to the ”analogue” day in the model. The ”analogue” day is only selected once for each SAFRAN’s day and is the same for all variables, to keep the coherence between all atmospheric variables.
+
+This ”analogue” day method allows to extend the forcing construction outside of the common period. For each SAFRAN’s day before or after the period covered by the model run, there is a possibility to look for its best ”analogue” day in the period covered by the model, and therefore use that day to disaggregate at high-resolution for each of SAFRAN’s days. Applying that ”analogue” day method over the common period and comparing it to the ”day by day” method should allow to test and validate the method prior to extending it to outside of the common period.
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