Lumped conceptual hydrologic model applied to small catchments in the semi-arid area of the north Mexico
In a co-operative programme between CENID RASPA (Centro National de Investigación Disciplinaria - Relación Agua, Suelo, Planta y Atmosfera, México) and IRD (formerly ORSTOM, France), seven small dams were equipped for hydrological measurements in an extensive breeding system, the ranch Atotonilco, located in a semi-arid area of northern Mexico. The main aim of the equipment was to follow the surface water in the water supply system of the ranch (ESTRADA AVALOS, 1999). In order to analyse the role of the seven small dams, it was necessary to understand the hydrological conditions of their filling and emptying. Also, manual and automatic rain gauges were installed on small experimental watersheds (0.15 to 5 km2) and on the ranch (450 km2), and in addition evaporation pans and a floating pan were placed on the banks of a few dams and in a reservoir (THIEBAUX, 2000). The aim of this paper is to present the overall conceptual hydrological model used to calculate runoff in the small catchments in the Atotonilco ranch, considering that it was necessary to utilise the rainfall intensities to explain the surface runoff. Hydrological observations were made from 1996 to 1998 on the Atotonilco ranch. Spatial analysis of the rainfall demonstrated the existence of several types of storms: those with a small extension (17 km2), with a middle extension (160 km2) or with a great extension (more than 450 km2). The average distance between two isohyets with a deviation of 10 mm varied from 2 to 3 km. In this semi-arid area, obtaining rainfall measurements of good precision requires a dense rain gauge network. On the small catchment scale it was necessary to put three or four rain gauges in each river basin. On the scale of small catchments, the analysis of the relationship between the amount of rainfall and surface runoff showed that rainfall intensity explained very clearly the surface runoff. This led us to the construction of a lumped model using the following criteria: - rainfall intensity limit of surface runoff (IL), with a time step of 30 min, - forward rainfall index (IK), - useful rainfall (PUIL), sum of the depths of rainfall with intensities higher than the limit value of IL. Experimental measures without runoff and with surface runoff have been used to describe the variation of the rainfall intensity limit of the surface runoff (IL), which decreases exponentially with increasing forward rainfall index (IK). This index IK is defined as the sum of the previous rainfall andthe previous index, which decreases in an exponential manner with the time interval ?t expressed in days (and partial days) between two successive showers (LINSLEY et al., 1949). The interval dt, which defines the rainfall intensity, depends on the time of concentration in the small catchments. On the Atotonilco ranch, the correlations between rainfall intensities for different intervals and surface runoff demonstrated that a 30-min interval provided the best results. However, we did not obtain significant correlations between surface runoff and different values of the exponential decreasing coefficient of IL as a function of IK (a). Considering the results obtained by ESTRADA AVALOS (1999) on the scale of experimental plots (60 m2), we have chosen the value a ?=0.1 day-1. This value increases IK during the rainy season when increasing soil moisture and grass cover growth, but these two factors have opposite effects on the surface runoff.Two parameters define the quadratic relationships between the useful depth of rainfall and the surface runoff: the parabolic increasing coefficient (E) and the position coefficient (F). It is possible to determine the position coefficient F with the value of the useful rainfall (PUIL0) which gives a null value to the depth of surface runoff. Using the observations collected from 1996-1998, we demonstrated that the position coefficient F decreased linearly with an increasing forward rainfall index IK. In addition, the parabolic increasing coefficient E was constant in the same basin, except when the storms were spaced less than 24 h apart and when the grass cover was low at the beginning of the rainfall season (1996). In these two cases, the runoff aptitude of the watersheds was clearly greater resulting in a higher E coefficient, which was sometimes too high for a parabolic relationship. It would be better to extrapolate above the limit value of PUIL taking into consideration that the additional runoff is equal to the additional useful rainfall. In order to validate the calibration of this model we used the criterion of NASH and SUTCLIFFE (1970). This criterion was calculated only for the year of 1996 but for two scenarios: the first scenario considered the parameter F as a constant and the second scenario allowed for a linear decrease of this parameter with the forward rainfall index IK. The results demonstrated that it was always better to use, for the position parameter F, a linearly decreasing relationship with the index IK. The relationships defined for the seven experimental catchments in the Atotonilco ranch were used to calculate long daily chronic inflows into the little dams (ESTRADA AVALOS, 1999). The hydrological parameters were also mixed with the natural characteristics of the small catchments in order to perform a principal components analysis of the relationships between hydrological parameters and natural criteria. Rules for the transposition of the parameters of this quadratic model on the Atotonilco ranch were established using the results of the analysis.