Event-based flood estimation using a random forest algorithm for the regionalization in small catchments

Abstract

The hydrological cycle is a complex system, composed of multiple variables, which in most cases are not measured. This is one of the reasons why it is a challenge to have models that adequately represent the expected discharges. The PUB initiative reinforces the need on having models that capture the different catchment interactions and represent various catchment processes. These models are more robust and thus can be more reliable to transfer to the ungauged catchments. In recent years, the field of hydrological research has focused on understanding and explaining the different processes present in catchments. Nevertheless, few applications that include pre- cipitation, the main responsible of runoff change,are found.Further understanding of the temporal and spatial dependence of the meteorological event triggering the floods is needed. In this study, an analysis of the meteorological event triggering the floods was carried out. The concept of entropy was used to characterize the temporal distribution of precipitation. It was found that the precipitation temporal entropy is a better indicator of hydrograph shape than the duration or the intensity. Further, the geographical interdependence of the amount of precipitation and the temporal precipitation entropy causing the floods was described looking at the association of sta- tions triples. This suggested that, up until a given quantile, flood events are more likely caused by precipitation events of total coverage. However, for larger quantile values, it is observed that as the quantile increases the probability of observing joint occurrence in space decreases. The tem- poral distribution of precipitation events causing the floods showed to be more associated in space than the amount of precipitation triggering the floods. Nonetheless, this temporal distribu- tion is not constant over all flood events, what can be attributed to d ifferent flood mechanisms. The Antecedent Precipitation Index (API) was used to explain the soil moisture content. The em- pirical distribution of (API) at the time of a flood was compared with empirical distributions of unconditioned (API) data series. T o this end, the Wilcoxon statistic and the Kolmogorov -Smirnov distance were used to compare the empirical distributions. The re sults showed that the soil mois- ture triggering the floods is not an annual extreme, rather a value close to the monthly maximum (API). Further, it was observed that the longer memory of the catchment gives more information about the occurrence of the flood. Additionally, in order to estimate the catchment reaction at the time of a flood, a regiona lization of the flood wave hydrographs was carried out. T o this end, three methods of defining the simi- larity of the floods were considered. In all three methods, the similarity matrices were generated using the random forest algorithm. The novelty of this procedure was the use of a supervised random forest to describe the similarity of the floods events. It was supervised given that the algorithm was trained to estimate a target variable. The proximity matrix was obtained by calcu- lating the joint occurrence of floods in the random forest space. For evaluating the estimation the hydrograph peak and the time to peak were used. In all three methods, the same tendencies were observed, an overestimation of the peak and an underestimation of the time to peak. However, the bias was observed to be smaller when an ensemble of similarity matrices was used as com- pared to having a single similarity matrix. Moreover, an approach using an unsupervised random forest was compared to the supervised one. It was found that the unsupervised random forest yields larger estimation errors. Finally, to estimate the volume of the flood event a rainfall-runoff model was modified to represent the study region. The model chosen in this study was EPIC. The model was calibrated to be more representative of the study region. To this end, the estimation errors in the space of the model parameters were studied. This allowed to find the model parameters that can better represent the study area. The values obtained were considered reasonable. For example, it is observed that the longer memory of the catchment is more representative of the study catchments, which are the same results as when analyzing the meteorological phenomenon causing the floods. Further, the values obtained for the regional constant, parameter modifying the initial abstraction of the catchment, were found to be smaller than the original ones obtained for United States catchments, which agrees with other studies in European catchments.