Information relating to errors in evapotranspiration (ET) products, including satellite-derived ET products, is critical to their application but often challenging to obtain, with a limited number of flux towers available for the sufficient validation of measurements. Triple collocation (TC) methods can assess the inherent uncertainties of the above ET products using just three independent variables as a triplet input. However, both the severity with which the variables in the triplet violate the assumptions of zero error correlations and the corresponding impact on the error estimation are unknown. This study proposed a cross-correlation analysis approach to discover the optimal triplet of satellite-derived ET products with regard to providing the most reliable error estimation. All possible triple collocation solutions for the same product were first evaluated by the extended triple collocation (ETC), among which the optimum was selected based on the correlation between ETC-based and in-situ-based error metrics, and correspondingly, a statistic experiment based on ranked triplets demonstrated how the optimal triplet was valid for all pixels of the product. Six popular products (MOD16, PML_V2, GLASS, SSEBop, ERA5, and GLEAM) that were produced between 2003 to 2018 and which cover China’s mainland were chosen for the experiment, in which the error estimates were compared with measurements from 23 in-situ flux towers. The findings suggest that (1) there exists an optimal triplet in which a product as an input of TC with other collocating inputs together violate TC assumptions the least; (2) the error characteristics of the six ET products varied significantly across China, with GLASS performing the best (median error: 0.1 mm/day), followed by GLEAM, ERA5, and MOD16 (median errors below 0.2 mm/day), while PML_V2 and SSEBop had slightly higher median errors (0.24 mm/day and 0.27 mm/day, respectively); and (3) removing seasonal variations in ET signals has a substantial impact on enhancing the accuracy of error estimations.

In recent years, remote sensing data have revealed considerable potential in unraveling crucial information regarding water balance dynamics due to their unique spatiotemporal distribution characteristics, thereby advancing multi-objective optimization algorithms in hydrological model parameter calibration. However, existing optimization frameworks based on the Soil and Water Assessment Tool (SWAT) primarily focus on single-objective or multiple-objective (i.e., two or three objective functions), lacking an open, efficient, and flexible framework to integrate many-objective (i.e., four or more objective functions) optimization algorithms to satisfy the growing demands of complex hydrological systems. This study addresses this gap by designing and implementing a multi-objective optimization framework, Py-SWAT-U-NSGA-III, which integrates the Unified Non-dominated Sorting Genetic Algorithm III (U-NSGA-III). Built on the SWAT model, this framework supports a broad range of optimization problems, from single- to many-objective. Developed within a Python environment, the SWAT model modules are integrated with the Pymoo library to construct a U-NSGA-III algorithm-based optimization framework. This framework accommodates various calibration schemes, including multi-site, multi-variable, and multi-objective functions. Additionally, it incorporates sensitivity analysis and post-processing modules to shed insights into model behavior and evaluate optimization results. The framework supports multi-core parallel processing to enhance efficiency. The framework was tested in the Meijiang River Basin in southern China, using daily streamflow data and Penman–Monteith–Leuning Version 2 (PML-V2(China)) remote sensing evapotranspiration (ET) data for sensitivity analysis and parallel efficiency evaluation. Three case studies demonstrated its effectiveness in optimizing complex hydrological models, with multi-core processing achieving a speedup of up to 8.95 despite I/O bottlenecks. Py-SWAT-U-NSGA-III provides an open, efficient, and flexible tool for the hydrological community that strives to facilitate the application and advancement of multi-objective optimization in hydrological modeling.

Modern hydrological modeling frequently incorporates global remote sensing or reanalysis products for multivariate calibration. Although these datasets significantly contribute to model accuracy, the inherent uncertainties in the datasets and multivariate calibration present challenges in the modeling process. To address this issue, this study introduces an adaptive, process-wise fitting framework for the iterative multivariate calibration of hydrological models using global remote sensing and reanalysis products. A distinctive feature is the “kinship” concept, which defines the relationship between model parameters and hydrological processes, highlighting their impacts and connectivity within a directed graph. The framework subsequently develops an enhanced particle swarm optimization (PSO) algorithm for stepwise calibration of hydrological processes. This algorithm introduces a learning rate that reflects the parameter’s kinship to the calibrated hydrological process, facilitating efficient exploration in search of suitable parameter values. This approach maximizes the performance of the calibrated process while ensuring a balance with other processes. To ease the impact of inherent uncertainties in the datasets, the Extended Triple Collocation (ETC) method, operating independently of ground truth data, is integrated into the framework to assess the simulation of the calibrated process using remote sensing products with inherent data uncertainty. This proposed approach was implemented with the SWAT model in both arid and humid basins. Five calibration schemes were designed and evaluated through a comprehensive comparison of their performance in three repeated experiments. The results highlight that this approach not only improved the accuracy of ET simulation across sub-basins but also enhanced the precision of streamflow at gauge stations, concurrently reducing parameter uncertainty. This approach significantly advances our understanding of hydrological processes, demonstrating the potential for both theoretical and practical applications in hydrology.