Abstract
Abstract. This paper studies how to improve the accuracy of hydrologic models using machine-learning models as post-processors and presents possibilities to reduce the workload to create an accurate hydrologic model by removing the calibration step. It is often challenging to develop an accurate hydrologic model due to the time-consuming model calibration procedure and the nonstationarity of hydrologic data. Our findings show that the errors of hydrologic models are correlated with model inputs. Thus motivated, we propose a modeling-error-learning-based post-processor framework by leveraging this correlation to improve the accuracy of a hydrologic model. The key idea is to predict the differences (errors) between the observed values and the hydrologic model predictions by using machine-learning techniques. To tackle the nonstationarity issue of hydrologic data, a moving-window-based machine-learning approach is proposed to enhance the machine-learning error predictions by identifying the local stationarity of the data using a stationarity measure developed based on the Hilbert–Huang transform. Two hydrologic models, the Precipitation–Runoff Modeling System (PRMS) and the Hydrologic Modeling System (HEC-HMS), are used to evaluate the proposed framework. Two case studies are provided to exhibit the improved performance over the original model using multiple statistical metrics.
Highlights
1.1 MotivationHydrologic models are commonly used to simulate environmental systems, which help us to understand water systems and their responses to external stresses
We use the quantitative statistics to perform the statistical evaluation of modeling accuracy in the testing step: root mean square error (RMSE), percent bias (PBIAS), Nash–Sutcliffe efficiency (NSE), and coefficient of determination (CD)
As evaluated by using crossvalidation, we found the best scale factor α is 0.5, the best transformation parameter a is 0.0305, and b is 0.0605, where α is used in Eq (2); a and b are used in Eq (13)
Summary
Hydrologic models are commonly used to simulate environmental systems, which help us to understand water systems and their responses to external stresses. They are widely used in scientific research for physical process studies and environmental management for decision support and policymaking (Environmental Protection Agency, 2017). One of the most important criteria for model performance evaluations is prediction accuracy. A reliable model is able to capture the hydrologic features with robust and stable predictions. It is challenging to develop a reliable hydrologic model with low biases and variances. We aim to develop a post-processor framework, named MELPF, which is short for Modeling Error Learning based Post-Processor Framework, to improve the reliability of hydrologic models
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