Explanation and Probabilistic Prediction of Hydrological Signatures with Statistical Boosting Algorithms

Abstract

Hydrological signatures, i.e., statistical features of streamflow time series, are used to characterize the hydrology of a region. A relevant problem is the prediction of hydrological signatures in ungauged regions using the attributes obtained from remote sensing measurements at ungauged and gauged regions together with estimated hydrological signatures from gauged regions. The relevant framework is formulated as a regression problem, where the attributes are the predictor variables and the hydrological signatures are the dependent variables. Here we aim to provide probabilistic predictions of hydrological signatures using statistical boosting in a regression setting. We predict 12 hydrological signatures using 28 attributes in 667 basins in the contiguous US. We provide formal assessment of probabilistic predictions using quantile scores. We also exploit the statistical boosting properties with respect to the interpretability of derived models. It is shown that probabilistic predictions at quantile levels 2.5% and 97.5% using linear models as base learners exhibit better performance compared to more flexible boosting models that use both linear models and stumps (i.e., one-level decision trees). On the contrary, boosting models that use both linear models and stumps perform better than boosting with linear models when used for point predictions. Moreover, it is shown that climatic indices and topographic characteristics are the most important attributes for predicting hydrological signatures.

The Drying Regimes of Non‐Perennial Rivers and Streams

“…Category Climate Land/water use Physiography slowly through time compared to climate, we observed seasonal patterns in drying event type (Figure 3), and previous studies have shown that climate is the most important factor in predicting mean annual no flow occurrence (Hammond et al, 2021;Tyralis et al, 2021).…”

“…The dominant importance of land cover/use and physiography relative to climate is surprising, given that land cover/use and physiography change relatively PRICE ET AL. slowly through time compared to climate, observed seasonal patterns in drying event type (Figure 3), and previous studies have that climate is the most important factor in predicting mean annual no flow occurrence (Hammond et al, 2021;Tyralis et al, 2021).…”

“…To confirm our results, random forests using conditional inference trees as well as random forests using hydrologic signatures as the response variable were constructed and resulted in similar behavior (Figures and ). The dominant importance of land cover/use and physiography relative to climate is surprising, given that land cover/use and physiography change relatively slowly through time compared to climate, we observed seasonal patterns in drying event type (Figure 3), and previous studies have shown that climate is the most important factor in predicting mean annual no flow occurrence (Hammond et al., 2021; Tyralis et al., 2021).…”

Quantile-Based Hydrological Modelling

“…The quantile loss function can substitute the squared error function (or its equivalents) in hydrological models tailored to deliver forecasts; therefore, one can directly obtain quantile forecasts using a single model or post-process quantile simulation in the data assimilation procedure. Finally, similar methodological themes to those proposed in this work, including several ones for issuing point [90] and probabilistic [91] predictions of hydrological signatures, could be provided by exclusively using hydrological models instead of relying on data driven-ones. Other similar themes for improved quantile-based predictions are those combining multiple hydrological models and more [30].…”

Probabilistic Water Demand Forecasting Using Quantile Regression Algorithms

“…More precisely, Tyralis, Papacharalampous, Langousis, et al. (2021) have compared boosting with linear models as base learners and boosting with a combination of linear models and stumps as base learners (Bühlmann & Hothorn, 2007; Hofner et al., 2014; Hothorn et al., 2020) in probabilistically predicting −in quantile regression settings− mean daily discharge, 5% flow quantile, 95% flow quantile, baseflow index, average duration of high‐flow events, frequency of high‐flow days, average duration of low flow events, frequency of low‐flow days, runoff ratio, streamflow precipitation elasticity, slope of the flow duration curve and mean half‐flow date in 667 catchments in the contiguous United States. They have found that the former boosting algorithm performs better than the latter in predicting signature quantiles at levels 2.5% and 97.5%, while the opposite holds for the prediction of the median.…”