Télédétection du manteau neigeux et modélisation de la contribution des eaux de fonte des neiges aux débits des oueds du haut atlas de Marrakech

VI.5 Implementation and calibration of SRM

VI.5.1 Description of SRM

Among many snowmelt runoff models that use snow-cover information, the deterministic SRM is one of the most widely used models in both diagnostic (Rango & van Katwijk, 1990; Songweon et al., 2005), and prognostic modes (Rango & Martinec, 1979; Shafer et al., 1982; Martinec, 1985; Martinec & Rango, 1995; Rango & Martinec, 1997; Klaus, 1998; Jesko et al., 1999 ; Gomez, 2002; Thomas et al., 2008). It was first applied to small European basins in 1975 and since then has been successfully used in approximately 80 mountainous basins in 25 countries worldwide (Martinec, 1975; Martinec et al., 2005). SRM is a degree-day-based model for daily runoff simulations and forecasts in the mountainous areas in which snowmelt is the major runoff contributor (Rango & Martinec, 1981; Martinec et al., 2005; Mitchell & DeWalle, 1998). The degree-day method employed by the SRM model has been used in different ways for more than 60 years (Clyde, 1931; Collins, 1934), and Rodriguez (1994) points out that the SRM and the Hydrologiska Byrans Vattenbalansavdelning (HBV) model (Bergstrom, 1975) are the two most widely used models based on the degree-day method (Rango and Martinec, 1995).

Assuming that there is an 18h time lag between the meteorological inputs on day n and the resulting streamflow on day n+1, the SRM calculates the daily streamflow separately for each elevation band as follows ( Équation ýVI )

Équation ýVI-

In Équation ýVI Q_n+1 (m3/s), the daily average discharge on day n+1, is calculated as the sum of three quantities from the preceding day n:

Snowmelt calculated as the product of the degree-day factor a (cm/°C/d), the representative zonal degree-days (T+ ÄT) (°C day), the ratio S of the SCA to the total basin area A (km²), and the snowmelt runoff coefficient Cs;

Precipitation contributing to runoff (cm), calculated as the product of measured precipitation P and the rainfall runoff coefficient Cr;

Discharge on the previous day Q_n, weighted by the recession coefficient where x and y are two empirical parameters.

(T+ ÄT) represents the extrapolated degree day calculated at the hypsometric average elevation of the zone from the degree-days measured at the meteorological stations. The snowmelt and rainfall runoff coefficients Cs and Cr are defined, respectively, as those fractions of snowmelt and rainfall that become streamflow. The recession coefficient on day n+1, k_n+1, is defined, as the ratio of streamflow on day n+1 to that on day n when there is no input of runoff (see Équation ýVI ). The factor 10 000/86 400 converts cm km² / day to m³/s.

Équation ýVI is applied separately to each zone and the discharges are summed. In addition to the five parameters (Cs, a, Cr, x and y) and input data appearing in Équation ýVI , the other parameters are the critical temperature for melting (Tf) and for the snowfall/snowmelt partition (Tc), i.e. the temperatures above which snow starts melting and precipitation falls as snow (respectively).