Calibration and validation of rainfall erosivity estimators for application in Rwanda

Abstract

Rainfall erosivity is one of the most important erosion factors in tropical humid areas including Rwanda. Its current application in erosion modelling is often restricted to the use of externally validated erosivity indices based on annual or monthly data, even though daily rainfall data have become more readily available. The present study aimed to calibrate and validate six different models predicting monthly and annual rainfall erosivity from daily, monthly and annual precipitation records. The reference dataset constituted mid-term average (1980–1989) monthly REI30 erosivities reported by Ryumugabe and Berding (1992) at five stations from mid and high altitude zones of Rwanda. The analysis is partly supported by data collected during a short-term field experiment with bare erosion plots at Tangata, located in the northern highlands of Rwanda. Rwanda’s mid altitude zone exhibits a bimodal rainfall erosivity, reflecting both short and long rains. Analysis of this reference dataset revealed moderate to strong linear relations of monthly rainfall erosivity to monthly rainfall amounts. The erosivity density, retrieved from the REI30 data, proved strongly variable by season, month and station. The field experiment showed a stronger correlation of event-based soil losses to rainfall amount times intensity than to rainfall amount. Since no unique rainfall amount threshold value for erosive rainfall events could be retrieved, total daily rainfall amount values were used for developing the erosivity models (estimators).Both regionally (all stations) and locally (one station) calibrated models were tested. At regional scale, estimators with a daily rainfall support performed best. The daily power function adopting monthly-calibrated coefficients (Model 1 by Richardson et al., 1983) proved most suited to capture the irregular patterns in erosivity densities, reported at most stations. In case only monthly rainfall data are available, the power function at monthly temporal resolution (model 4 by Wu, 1994) is to be recommended. Variable performances between stations are explained by the diversity in rainfall generators active at short distances in Rwanda west of Kigali. A local calibration of the selected models confirms the improved performance obtained with daily input data, even when monthly varying model coefficients are replaced by a seasonal function (Yu and Rosewell, 1996), except for Kigali. At this latter station, the power (Wu, 1994) and linear (model 3 by Moore, 1979 or Zhou et al., 1995) functions with monthly support perform best. At Gisenyi, a linear model 5 (Angulo-Martínez and Beguería, 2009) using rainfall amount and number of wet days in the month performs well. Differences in performance reflect the variable capacity of the different models to deal with either seasonal or irregular fluctuations in erosivity density, as well either outstanding or limited differences in erosivity between both rainfall seasons within Rwanda. This frequently leads to over- or underestimations of rainfall erosivity in one of the seasons. The models however perform very well when used to estimate annual erosivity. The monthly power model 4 distinctly outperformed all other models, even those at daily rainfall support, with a prediction quality that is slightly better than a linear regression based on the modified Fournier index (MFI), using all stations except for Kigali. This confirms the power of the MFI as a rainfall erosivity index, but also highlights the importance of this regional calibration within Rwanda and the need for at least two different regression equations.