Modelling the hydrology of small granitic catchments in the Sahel with parsimony
Abstract:
Abstract:This work aims at proposing a parsimonious modelling approach to describe the hydrology of the granitic basement exorheic context in the Sahel. Niger, as the rest of West African Sahel, roughly shows two markedly different behaviors: (i) endorheic zones are found in the sedimentary context as can be encountered on the left bank side of the Niger river while (ii) exorheic zones are found on the right bank where granitic basement is only covered by a thin layer of sandy soil. In the whole area, the hydrology is generally considered to be controlled by the top layer of soil, especially within crusted areas which were the focus of numerous studies. The hortonian runoff always proved to be the dominant process in this region.
Within the AMMA-CATCH experimental network, two small experimental watersheds (5-6 ha) were equipped in the Mele Haoussa (MH) area in NE Niger where granite outcrops are seen. One of the two catchments (MH1) was cultivated and the other one (MH2) was not. The basins were composed by a mosaic of six identified surface features (SF), fallow, cultivated field and four different crust types. Hydraulic conductivity was measured with disk infiltrometers forced to produce a one-dimensional flow within a cylinder softly pushed vertically into the soil and two mini-tensiometers. Runoff plots (5x2 m2) were replicated three times on each SF to characterize the hydrological response in each case. Both catchments were also equipped with two recording rain gauges and a concrete Venturi station with a recording stream gauge at the outlet. The experiment was run from 2011 to 2013. Topsoil (0-5 cm) water content for each SF was measured manually with capacitive probes at least on a daily basis so that the initial water content for each rain event was known.
To obtain the catchments cartography, low altitude flights were performed and high-resolution photos were taken at regular space intervals. Using the Arc-GIS © software, 173 (MH1) and 166 (MH2) polygonal plots (Figure) were then defined with a given SF attributed to each of them according to optical characteristics. The correspondence was later checked by field local observations and very few corrections were needed.
The modelling approach aimed at reproducing the hydrogram associated to each rain event with only three parameters, two of which spatially distributed and one global for the basin. Infiltration was described by the two-parameter Green-Ampt equation. The hydraulic conductivitiy values for each SF were measured at the point scale and considered constant in time except for that of cultivated fields which was dependent on elapsed time and amount of received rain after tillage and thus varying on a wide range of values: from 170 mm.h-1 right after tillage down to 20 mm.h-1 after 100 mm of received rain and even 10 mm.h-1 after 180 mm rain). Two tillage operations were carried out during the rainy season. Minimum spatial average value (10 mm.h-1) was found for ERO crusts and maximum was found for cultivated sites (40 mm.h-1). Fallow had an intermediate value of 20 mm.h-1. Spatial standard deviation varied between 20 and 70%., within the usual range of spatial variability for this variable.
The second distributed parameter was the wetting front suction head of the Green-Ampt equation. Values were fitted for each SF by using a point-scale Green-Ampt iterative scheme (15 s time increment) with the natural rain events and by trying to obtain a runoff volume as closed as possible to that measured on the runoff plots. For each SF, there was one solution value allowing to reproduce very nicely the measured volumes. Wetting front suction head values were very low in all cases, which is typical for sandy soils and implies a quick stabilization of the infiltration flux to values very close to the hydraulic conductivity. This was confirmed with the fact that measured runoff volumes were almost not sensitive to the initial water content. Finally, runoff volumes allowed to calculate, for the corresponding SF, a mean runoff coefficient through the year that was found consistent with hydraulic conductivity values (i.e. high runoff coefficients were found on SF with a high conductivity value and inversely). Runoff coefficient values ranged between 25% for cultivated sites and 63% for ERO crusts. Spatial standard deviation was only between 2% and 20%.
Based on the Green-Ampt calculated runoff volumes, catchment outlet hydrograms were obtained by adding the contributions of all the identified local plots (Figure). Each plot was considered concentrated on its centre of gravity (COG) and the minimal distance between the COG and the stream was calculated. When a plot was crossed through by the stream network, it was divided into two half-plots with a distinct COG for each half to avoid an effect of distance underestimation. For each plot, the runoff per unit area was produced by applying the iterative Green-Ampt scheme at the COG and was then multiplied by the plot area to obtain a runoff volume. Thus, total catchment runoff was obtained by using a spatial distribution of six measured hydraulic conductivity values and six wetting front suction head values calibrated for each SF at a scale (10 m2) very much smaller than that of the basin (5-6 ha).
No re-infiltration between plots was accounted for. Re-infiltration before catchment outlet was only considered in the sandy stream ("kori in haoussa"). Indeed, previous studies during the HAPEX-Sahel experiment led to estimate that, in sedimentary zones (Banizoumbou and Wankama sites), between 25% and 55% of the water was "lost" within the stream and thus did not reach the catchment outlet, which clearly explains the endorheism of these regions. To account for and estimate the stream re-infiltration within our granitic basins, manual soundings were made along the main stream to measure the bedrock depth. This was done all along the stream on cross-sections with a 10 m (MH1) or 15 m (MH2) interval. Section width was also measured. Finally, a simple trapezoidal integration from section to section led to estimate the volume of sand present in the stream at 143 m3 (MH1) and 171 m3(MH2). The measured sand porosity was 40% which allowed to convert the sand volume into a water storage volume for each catchment. When divided by the catchment area, these volumes only corresponded to 1 to 1.5 mm of rain.
Calculated basin runoff volumes where found closer to the measured values when the stream storage was accounted for than when it was not. Finally, correlation between measured and calculated runoff volumes led to an overestimation by 16% (MH1) and 8% (MH2) only, according to the regression line forced at the origin slope value. Note that the model had no calibrated parameter at the scale of application. This overestimation might be even reduced in future simulations when accounting for the whole stream network volume (these measurements will be done in a close future) and not only that of the main stream as was done in the presented study.
To obtain catchment hydrograms, surface flow must be modelled. In the interest of parsimony, a very simple constant and uniform water surface velocity was chosen. This also was the result of visual observations during runoff events. After trials and errors, the value of 0.05 m.s-1was chosen and led to a correct simulation of most runoff events, even for those with two well separated rain peaks (Figure). The stream water storage was modelled as a simple delaying reservoir: as long as it is not filled, no runoff water reaches the outlet; when filled, all supplementary runoff water reaches the basin outlet. No transfer time within the stream itself was considered as it would involve hydraulics modelling in opposition with the desired simplicity of the approach.
The lag time (duration between the first raindrop and the stream gauge response) was better reproduced when the stream water storage was considered than when it was ignored. It was slightly underestimated which is in accordance with the assumption of instantaneous water transfer from any point of the stream to the outlet made in the model. This only slight underestimation shows that the transfer time within the watershed –not within the stream - was here the limiting process.
Based on the set of measured runoff events, the basin average runoff coefficient was found to depend on the considered catchment but not to be dependent on the year (Table 1). 2013 events are not considered here due to modifications occurring within the basins.
According to both the measures and the model, only 3 mm of rain were sufficient to produce runoff at the outlet. Rain events having a smaller amount are totally lost in the stream. Compared to the 25-55% of annual runoff water re-infiltrating the stream in sedimentary areas, only 4% of annual runoff water in average was lost in the stream in our granitic basement basins. This is in obvious agreement with the endorheic vs. exorheic behavior of the sedimentary vs. granitic context.
|
2011 |
2012 |
MH1 |
0.29 |
0.28 |
MH2 |
0.42 |
0.41 |
Table 1. Catchment runoff coefficients averaged over the mentioned year.
The initial water content had no effect on the rain-outflow relation within the two catchments at both the plot scale and the basin scale. This is well consistent with the low values of wetting front suction head found adequate to the Green-Ampt infiltration in our soils. This is also consistent with the low capillary sorptivity values estimated through the analysis of transient flow from the disk infiltrometers. One of the consequences of this finding is that runoff production was linear with the duration of the rain but not linear with the rain intensity. Thus, the approximation consisting in applying a constant threshold to a hyetogram to calculate the runoff volume of a given event is a good approximation in this context. On the other hand, this means that rainfall intensities, not only volumes, are necessary to predict the runoff amounts in these regions.
Of course, our basins had a small surface and the next step of this study will certainly be the equipment of much larger experimental catchments in the same area. Nevertheless, hydraulic conductivity and wetting front suction head are not scale-dependent variables as long as measured with the same devices and the number of SF will probably remain at six or not many more. Also, as the catchment area increases, the mean distance between a given producing plot and the closer point of the stream network will not increase much. Thus, it is foreseen that the re-infiltration within the watersheds will, as well, not increase much. It is most probably within the hydrographic network itself that the re-infiltration will substantially increase, reducing the runoff coefficient. Consequently, at these larger scales, the stream hydraulics will have to be taken into account and modelled.