The anisotropy and directional variation of spatial attributes is one of the most important challenges in spatial estimation of environmental features. This problem received a suitable response in the realm of stochastic modeling using directional variography; however, there is not any specific solution in the field of deterministic methods. In this research, Moving Least Square (MLS) and Moving Inverse Distance Weighting (MIDW) have been used to assess a moving domain as the remedy; although, there has been no research on the spatial estimation with the MLS method. The methods are evaluated in three case studies, (I) using anisotropic piezometric head data from the Wolfcamp aquifer in Texas, (II) long-term annual average precipitation measurements in Namak Lake Watershed (NLW) located in the central part of Iran, and (III) estimation of annual precipitation with remote-sensing products, TRMM, in NLW as well. To achieve the best performance of the methods, parameters have been optimized using the modified version of shuffled complex evolutionary method. Assessment of statistical metrics, Taylor Diagram, and numerical results showed that spatial interpolation using MIDW and MLS revealed better results, with an improvement of 45.3% on average in terms of Root Mean Square Error (RMSE), in comparison with original IDW as the benchmark evaluation approach. This shows the power of moving data partitioning on the performance of deterministic estimators. Additionally, MLS was more effective than MIDW with an average of 0.55, 10.53, and 17.19% reduction in RMSE of case I, II, and III, respectively.

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The importance of optimization of rain gauge stations locations is critical given that rainfall data is central to various water-related studies. As rainfall data has vagueness in nature, fuzzy set theory can describe uncertainties existing in rainfall data. In this paper, we develop a framework to rainfall network design that combines fuzzy concepts and a deterministic spatial interpolation method known as Fuzzy Inverse Distance Weighted (FIDW). It addresses two important issues: (1) the assessment of two types of fuzzy mathematical approaches known as Fuzzy Standard IDW (FS-IDW) and Fuzzy Modified IDW (FM-IDW); (2) the comparison of the FIDW with spatial and spatiotemporal network designs using Ordinary Kriging (OK), known as OK-S and OK-ST, respectively. We consider four objective functions (OF): interval-based Estimation Error Variance Types 1 and 2 (EEVT1, EEVT2), Mean Square Error (MSE) and Coefficient of Determination (R²). Four scenarios of number of removed stations including 5, 10, 15 and 20 are also analysed via statistical indicators. Firstly, the FIDW parameters (power and radius) are optimized for each OF. Then, we resort to a Genetic Algorithm (GA) to solve these OFs. Percentage of similarity between optimal removed station in both FIDW methods (FS-IDW and FM-IDW) is higher than OK-ST method. Between FIDW methods, FM-IDW yields better results. Statistical results of four removed stations (5, 10, 15 and 20 rain gauge stations) show that the highest variation in estimation accuracy is from 5 to 20 removed stations which belongs to EEVT1 OF and is around 30%.

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Evapotranspiration (ET) is one of the most important factors controlling hydrologic, agricultural, and weather cycles. It also converts a large portion of rainfall into vapor, being known as the largest water flux from the earth into the atmosphere. Since ET is affected by many factors, such as land surface characteristics and climatic conditions, it undergoes considerable spatiotemporal variations, particularly at the watershed scale. Hence, to obtain a more accurate estimation of ET, it is required to identify homogenous and uniform regions, each represented by a meteorological station. In this study, three scenarios were proposed in order to identify homogenous regions to estimate ET based on METRIC method, and the scenarios were tested in Sefidrood Watershed in the north of Iran. The first scenario included only vegetation factor with one representative station for the entire case study watershed and ignored diverse conditions affecting ET across the watershed. The second scenario incorporated not only the vegetation factor but also the altitudinal variations of the watershed. In the second scenario, the watershed was divided into two distinct altitudinal sections, each with a representative station with a specific influenced area, with ET being estimated separately for each section. Finally, the third scenario incorporated the altitudinal and climatic variations. The results indicated that the second scenario performed better than two other scenarios in ET estimation. In other words, altitude and vegetation strongly influenced spatial and temporal distributions of ET, leading to considerable variations of it in the watershed.

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To fully benefit from remotely sensed observations of the terrestrial water cycle, bias and random errors in these data sets need to be quantified. This paper presents a Bayesian hierarchical model that fuses monthly water balance data and estimates the corresponding data errors and error-corrected water balance components (precipitation, evaporation, river discharge, and water storage). The model combines monthly basin-scale water balance constraints with probabilistic data error models for each water balance variable. Each data error model includes parameters that are in turn treated as unknown random variables to reflect uncertainty in the errors. Errors in precipitation and evaporation data are parameterized as a function of multiple data sources, while errors in GRACE storage observations are described by a noisy sine wave model with parameters controlling the phase, amplitude, and randomness of the sine wave. Error parameters and water balance variables are estimated using a combination of Markov Chain Monte Carlo sampling and iterative smoothing. Application to semiarid river basins in Iran yields (a) significant reductions in evaporation uncertainty during water-stressed summers, (b) basin-specific timing and amplitude corrections of the GRACE water storage dynamics, and (c) posterior water balance estimates with average standard errors of 4–12 mm/month for water storage, 3.5–7 mm/month for precipitation, 2–6 mm/month for evaporation, and 0–2 mm/month for river discharge. The approach is readily extended to other data sets and other (gauged) basins around the world, possibly using customized data error models. The resulting error-filtered and bias-corrected water balance estimates can be used to evaluate hydrological models.

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Improving precipitation accuracy over a watershed is one of the highest priorities in water resources studies and management. Several global precipitation datasets are available for estimating precipitation over any region in the world. However, local or regional application of these datasets should account for and correct potential errors in the original products. This article presents a novel spatiotemporal calibration framework to improve the accuracy (bias and correlation) of global precipitation datasets in regional applications. The proposed methodology consists of two steps. First, gridded global precipitation datasets are regressed pointwise against rain gauge data. This yields downscaled and bias-corrected precipitation values at the point scale. Second, the resulting point-scale regression parameters are used to build a geostatistical model that predicts the regression parameters across the region of interest, allowing for bias-correcting the precipitation datasets at the regional scale. The framework is applied to the Urmia Lake Watershed in northwestern Iran. Eight global high-resolution monthly precipitation datasets (CHIRPS, ERA-5, IMERG, PERSIANN, PERSIANN-CCS, PERSIANN-CDR, TRMM and Terra) are evaluated and three downscaling approaches including linear, Q-Q and Linear Scaling (LS) regression methods are used to calibrate the precipitation datasets based on a regional network of rain gauge observations. Ordinary kriging is subsequently used to predict the regression parameters at ungauged locations. Out of all combinations (i.e., eight datasets and three methods), downscaled IMERG using linear and Q-Q regression methods showed the best performance in estimating the spatiotemporal variations of monthly precipitation across the watershed of interest. The original IMERG dataset overestimated the monthly precipitation by approximately 20% compared to the precipitation from rain gauges. After applying the proposed methodology in this article, the IMERG bias was reduced by 93%, with an additional 26% decrease in the RMSE.

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Accurate estimation of the spatial distribution of precipitation is crucial for hydrologic modeling. To achieve the realistic estimation of precipitation, developing a ground-based observatory system is a costly and time-consuming strategy compared with other solutions such as using a combination of satellite- and ground-based observations. In this paper, to improve the estimation accuracy of spatial precipitation variation, various linear regression methods were used that combine digital elevation model (DEM) data, rain gauge observations, and Tropical Rainfall Measuring Mission (TRMM) products. Specifically, fuzzy cluster-based linear regression (FCLR), local multiple linear regression using historical similarity (LMLR-HS), model tree (MT), and moving least squares (MLS) were used in the proposed methodology based on local data behavior. The results were compared with those obtained from multiple linear regression (MLR) methods including simple multiple linear regression (SMLR), robust multiple linear regression (RMLR), and generalized linear model (GLM) for monthly precipitation estimation. The study area was Namak Lake watershed, one of the largest watersheds in Iran. The results, estimated for wet and dry years (years 1999 and 2003, respectively), show superiority of local linear regression methods over the other linear methods. Based on the statistical metrics used for assessing the quality the results, FCLR and MLS outperformed other tested methods.

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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