Toward geostatistical unbiased predictions of flow duration curves at ungauged basins

Flow duration curves (FDCs) represent the percentage of time (or duration) during which a given streamflow is equaled or exceeded. Flow duration curves provide a rapid and direct response to the behavior of water resources in a basin. Thus, predicting FDCs is important in basins with little or no monitoring for both all-time and seasonal periods. The geostatistical approach for predicting FDCs at ungauged sites represents an advancement in this research topic. However, poor results have been observed, particularly overestimates (positive bias) for high durations, i.e., low flows. This study aims to predict FDCs in all-time and seasonal periods by using a geostatistical approach based on models, toward unbiased prediction. Streamflow data from 81 stream gauges made available by the Brazilian National Water Agency (ANA) have been used. These stations have a high spatial density and are well spread across the study area. To map the FDCs, and consequently, all their quantiles, the scale and shape parameters of the FDCs were modeled geostatistically. First, some basic assumptions for the FDC parameters such as data normality and spatial stationarity were verified. After an inference by the maximum likelihood method was performed to fit the geostatistical models and estimate the best model forms, we compared them with the benchmark models (i.e. regression models). Finally, the spatial interpolation was performed and the performance was assessed by a leave-one-out cross-validation. The geostatistical models yielded better fits and performance for mapping the FDCs than the regression models. Both the median of relative residuals for all-time and seasonal periods were unbiased for the entire duration. We suggest that the fixed effect modeling of the geostatistical models, associated with external drifts, led to this better and unbiased performance.

Automated summary

Flow duration curves (FDCs) provide important information on water resource behavior, geostatistical methods show advantages in predicting FDCs but need to avoid overestimation, especially for low flows.