This study evaluates the steepest descent algorithm as a tool for root mean square (RMS) error optimization in geodetic reference systems to improve the integrity of transformation. With an initial RMS error estimate of 0.01830m, the negative gradient direction was applied through the steepest optimization leading to a final RMS error estimate of 0.00051m. Using the exact line search mode with a one-point step size of 0.1, we achieved the minimum values in less than sixty iterations, regardless of the slow convergence rate of the steepest descent algorithm.
The Congo River basin in west-central Africa Traditional machine learning algorithms are recently being replaced by integrated learning techniques in pattern recognitions and predictions. These updated tools (or techniques), which attempt to explore higher dimensions and uncover hidden patterns in considerably non-linear datasets are the new normal in small, medium and large dataset even in higher orders. This study investigates the performance of a convolution-based support vector machine in hydrological analysis to optimize forecast of terrestrial water storage anomalies (TWSA). The linear, polynomial, and radial basis function (RBF) kernels were explored in reconstructing the three variants of TWSA obtained from the Gravity Recovery and Climate Experiment (GRACE) level 3 products. Using the original input training datasets, we built and trained the convolution-neural network (CNN) which is composed of convolution and fully connected layers, and was integrated into the traditional support vector machine (SVM). The network was trained with twenty-two (22) datasets. The original predictor datasets are composed of hydrological fluxes (HF), climate indices (CI), and sea surface temperature (SST) datasets whose influence on GRACE-TWSA was analyzed in the body of our work. Our results show that the polynomial-kernel based on the convolution-based support vector machine (CSVM) outperformed the other regression models in the reconstruction of all variants of TWSA. The high accuracy achieved using the CSVM demonstrates its promising potential to fill the gaps in the missing GRACE observations through its refined reconstruction capabilities. In this study, (i) SST variants or components (e.g., those of east tropical Atlantic) were leading predictors of TWSA, (ii) increasing polynomial order does not increase accuracy in all polynomial kernel operations, especially in cases of severe non-linearity between predictors and predictands, (iii) for the RBF kernels, intermediate gamma values ranging from 0.05 to 0.5 are ideal for climatic analysis, as very small or very large gamma values will either behave like a linear model or over fit, respectively, and (iv) overall, the polynomial kernels reconstructed and predicted TWSA better than the other kernels. The other conventional machine learning procedures used to compare the fit of the CSVM show significant insight for future TWSA reconstruction processes. Their robustness can be explored by varying the independent variables fed into the machine learning framework and tuning their hyper-parameters to result in better fitting index, which promises to be much more useful than traditional learning methods.
Abstract The coarse spatial resolution of the Gravity Recovery and Climate Experiment (GRACE) dataset has limited its application in local water resource management and accounting. Despite efforts to improve GRACE spatial resolution, achieving high resolution downscaled grids that correspond to local hydrological behaviour and patterns is still limited. To overcome this issue, we propose a novel statistical downscaling approach to improve the spatial resolution of GRACE-terrestrial water storage changes (ΔTWS) using precipitation, evapotranspiration (ET), and runoff data from the Australian Water Outlook. These water budget components drive changes in the GRACE water column in much of the global land area. Here, the GRACE dataset is downscaled from the original resolution of 1.0° × 1.0° to 0.05° × 0.05° over a large hydro-geologic basin in northern Australia (the Cambrian Limestone Aquifer—CLA), capturing sub- grid heterogeneity in ΔTWS of the region. The downscaled results are validated using data from 12 in-situ groundwater monitoring stations and water budget estimates of the CLA’s land water storage changes from April 2002 to June 2017. The change in water storage over time (ds/dt) estimated from the water budget model was weakly correlated (r = 0.34) with the downscaled GRACE ΔTWS. The weak relationship was attributed to the possible uncertainties inherent in the ET datasets used in the water budget, particularly during the summer months. Our proposed methodology provides an opportunity to improve freshwater reporting using GRACE and enhances the feasibility of downscaling efforts for other hydrological data to strengthen local-scale applications.
Abstract The Gnangara groundwater system is a highly productive water resource in southwestern Australia. However, it is considered one of the most vulnerable groundwater systems to climate change, due to consistent declines in precipitation and recharge, and regional climate models project further declines into the future. This study introduces a new framework underpinned by machine learning techniques to provide reliable estimates of precipitation‐based recharge over the whole Perth Basin (including the Gnangara system). By combining estimates of baseflow, groundwater evaporation, and extraction, groundwater recharge was estimated over the Perth (testing site) and Gnangara (calibration site) systems using downscaled Groundwater Storage Anomalies (GWSA) from the Gravity Recovery and Climate Experiment (GRACE) mission. The random forest regression (RFR) model was used to downscale the spatial resolution of GRACE to 0.05° (approx. 5 km), providing estimable signals over the relatively small calibration site (∼2,200 km 2 ) in order to discern any meaningful signals from the original GRACE resolution. Our study reveals that downscaled signals from GRACE can be used to provide precipitation‐based recharge estimates for groundwater systems accurately. However, the growing impacts of climate change, which has led to sporadic precipitation patterns over Western Australia, can limit the efficiency of satellite remote sensing methods in estimating recharge, especially in deep and complex aquifers.
In large freshwater river basins across the globe, the composite influences of large-scale climatic processes and human activities (e.g., deforestation) on hydrological processes have been studied. However, the knowledge of these processes in this era of the Anthropocene in the understudied hydrologically pristine South Central African (SCA) region is limited. This study employs satellite observations of evapotranspiration (ET), precipitation and freshwater between 2002 and 2017 to explore the hydrological patterns of this region, which play a crucial role in global climatology. Multivariate methods, including the rotated principal component analysis (rPCA) were used to assess the relationship of terrestrial water storage (TWS) in response to climatic units (precipitation and ET). The use of the rPCA technique in assessing changes in TWS is warranted to provide more information on hydrological changes that are usually obscured by other dominant naturally-driven fluxes. Results show a low trend in vegetation transpiration due to deforestation around the Congo basin. Overall, the Congo (r2 = 76%) and Orange (r2 = 72%) River basins maintained an above-average consistency between precipitation and TWS throughout the study region and period. Consistent loss in freshwater is observed in the Zambezi (−9.9 ± 2.6 mm/year) and Okavango (−9.1 ± 2.5 mm/year) basins from 2002 to 2008. The Limpopo River basin is observed to have a 6% below average reduction in rainfall rates which contributed to its consistent loss in freshwater (−4.6 ± 3.2 mm/year) from 2006 to 2012.Using multi-linear regression and correlation analysis we show that ET contributes to the variability and distribution of TWS in the region. The relationship of ET with TWS (r = 0.5) and rainfall (r = 0.8) over SCA provides insight into the role of ET in regulating fluxes and the mechanisms that drive precipitation in the region. The moderate ET–TWS relationship also shows the effect of climate and anthropogenic influence in their interactions.
The Southern African region consists of ten countries including, Angola, Zambia, Malawi, Namibia, Botswana, Zimbabwe, Mozambique, South Africa, Lesotho, and Swaziland. Frequent drought episodes in the arid and semi-arid parts of the region suggest the impact of climate change and the need for a sustainable framework for groundwater level assessments. In this study, we developed a machine learning modelling framework based on the deep belief network (DBN) to predict the changes in monthly groundwater levels (CGWLs) at 1–5 month time scales for 27 groundwater wells over the southern Africa region. With a predictor dataset constituted by hydrological parameters, groundwater level estimates, and global climate indices, we ascertain the possibility of forecasting changes in groundwater levels (CGWL) up to 5-month lead times at most locations in the study region. Using the quantile regression technique, the strength of the DBN network at 90% and 95 % confidence levels were tested, and this helped to determine the accuracy of our forecasts at five months lead times over the four representative wells. Deep learning offers new capabilities in evaluating non-linear hydrological systems, including groundwater analysis. The re-injection procedure of the DBN network, which allows the prior CGWL estimates to serve as inputs for the next estimate was key in maintaining the forecast accuracy in the 4th and 5th month lead times. This was evidenced in the accuracy of the four representative wells (r = 0.91, 0.87, 0.81, 0.75), which formed part of the test samples in CGWL analysis. We also observed that the DBN is highly susceptible to local climate variables and global climate indices, which are important drivers of climate change, and can have strong impact on groundwater level fluctuations. Therefore, the DBN proved to be a robust algorithm in our general assessments of groundwater level fluctuations.
The coarse spatial resolution of the Gravity Recovery and Climate Experiment (GRACE) data has limited its application in the management of local-scale water resources. To address this limitation, we developed a new downscaling approach using predictors from regional and global hydrological models for a 15-year period (2002–2017) and tested it in the northern Great Artesian Basin, Australia. We used four different machine learning algorithms (support vector machine, partial least squares, gaussian process and random forest) to downscale the original GRACE estimate of 0.5° to a spatial grain size of 0.1° (global) and 0.05° (regional). This was based on precipitation, evapotranspiration and runoff estimates from the Famine Early Warning Systems Network Land Data Assimilation System (FLDAS) and Australian Water Outlook (AWO) hydrological models, respectively. The downscaled products were validated using 42 in-situ precipitation observations spread across the test region. We further evaluated which of the downscaled products best mimicked local-scale hydrology using a range of statistical metrics. Our results showed that regional hydrological models best characterized the dynamics of local scale hydrology (rainfall v. downscaled product), and the gaussian process regression algorithm made the best predictions for both models. The correlation coefficients for the raw values varied from 0.45 to 0.49 while that of the standardized values varied from 0.46 to 0.52 with the random forest model providing the best fitting for the regional-based products. The regional downscaling approach employed in this study may be readily integrated into local water resources planning programs.
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