Actual evapotranspiration (ET_a) plays a crucial role in the water and energy cycles of the earth. An accurate estimate of the ET_a is essential for management of the water resources, agriculture, and irrigation, as well as research on atmospheric variations. Despite the importance of accurate ET_a values, estimating and mapping them remains challenging due to the physical and biological complexity of the ET process. As a novel approach for rapid and reliable estimation of ET_a, the present study develops automated deep learning (AutoDL) models that incorporate a metaheuristic optimization algorithm for image processing, architectural design, and hyperparameter tuning. The proposed AutoDL models integrate three different spatial and channel attention mechanisms, including a novel activated spatial attention mechanism (ASPAM), with the U-Net architecture. Bypassing the need for meteorological inputs, the proposed framework uses Moderate Resolution Imaging Spectrometer (MODIS) products and Digital Elevation Model (DEM) data as inputs. To evaluate the performance of the models, they are applied to three study areas in the United States with various climatic characteristics. According to the results, during the spring and summer, when the target values have higher certainty, the estimations are highly promising, with R² as high as 0.91 and MAPE as low as 6.40%. Furthermore, the proposed ASPAM module improves the accuracy of ET_a estimations compared to attention gate (AG) and squeeze and excitation (SE) attention modules. The results also indicate that the MODIS raw products and derived vegetation and water indices can predict ET_a within a reliable range of accuracy, with the addition of DEM data marginally enhancing the models' performance. The automatic workflow of this model makes it significantly easy to use, contributing to its applicability and generalizability for enhancing atmospheric research.

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Hydrological models are simplified imitations of natural and man-made water systems, and because of this simplification, always deal with inherent uncertainty. To develop more rigorous modeling procedures and to provide more reliable results, it is inevitable to consider and estimate this uncertainty. Although there are different approaches in the literature to assess the parametric uncertainty of hydrological models, their structures and results have rarely been compared systematically. In this research, two different approaches to analyze parametric uncertainty, namely direct and inverse methods are compared and contrasted. While the direct method employs a sampling simulation procedure to generate posterior distributions of parameters, the inverse method utilizes an optimization-based approach to optimize parameter sets of an interval-based hydrological model. Two different hydrological models and case studies are employed, and the models are set by two distinct mathematical operations of interval mathematics. Findings of this research show that while the choice of the interval mathematic method can affect the final results, generally, the inverse method cannot be counted on as a reliable tool to analyze the parametric uncertainty of hydrological models, and the direct method provides more accurate results.@en

Due to the complicated nature of environmental processes, consideration of uncertainty is an important part of environmental modelling. In this paper, a new variant of the machine learning-based method for residual estimation and parametric model uncertainty is presented. This method is based on the UNEEC-P (UNcertainty Estimation based on local Errors and Clustering–Parameter) method, but instead of multilayer perceptron uses a “fuzzified” version of the general regression neural network (GRNN). Two hydrological models are chosen and the proposed method is used to evaluate their parametric uncertainty. The approach can be classified as a hybrid uncertainty estimation method, and is compared to the group method of data handling (GMDH) and ordinary kriging with linear external drift (OKLED) methods. It is shown that, in terms of inherent complexity, measured by Akaike information criterion (AIC), the proposed fuzzy GRNN method has advantages over other techniques, while its accuracy is comparable. Statistical metrics on verification datasets demonstrate the capability and appropriate efficiency of the proposed method to estimate the uncertainty of environmental models.

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