Watershed Parameters Research Articles

Enhancing machine learning models for total organic carbon prediction by integrating geospatial parameters in river watersheds

This study utilizes machine learning (ML) algorithms to develop a robust total organic carbon (TOC) prediction model for river waters in the Geumho River sub-basins, South Korea, considering both non-rain and rain events. The model incorporates geospatial parameters such as land use, slope, flow rate, and basic water quality metrics including biochemical oxygen demand (BOD), chemical oxygen demand (COD), total nitrogen (TN), total phosphorus (TP), and suspended solids (SS). A key aspect of this research is examining how land use information enhances the model's predictive accuracy. We compared two ML algorithms—extreme gradient boosting (XGBoost) and deep neural networks (DNN)—with a traditional multiple linear regression (MLR) approach. XGBoost outperformed the others, achieving an R2 value between 0.61 and 0.68 in the test dataset and demonstrating significant improvement during rain events with an R2 of 0.77 when including land use data. In contrast, this enhancement was not observed with the MLR model. Feature importance analysis using Shapley values highlighted COD as the primary predictor for non-rain events, while during rain events, COD, TP, TN, SS and agricultural land collectively influenced TOC levels. This study significantly advances understanding of TOC variability across different land use scenarios in river systems and underscores the importance of integrating geospatial and water quality parameters to enhance TOC prediction, particularly during rain events. This methodology provides a valuable framework for developing river management strategies and monitoring long-term TOC trends, especially in scenarios with gaps in essential monitoring data.

Dissolved Iron and Organic Matter in Boreal Rivers across a South–North Transect

Iron (Fe) is one of the main nutrients present in dissolved, suspended, and colloidal states in river water. Predicting the composition and size of dissolved Fe compounds is crucial for assessing water quality. In this stud, we used a combination of physical methods (filtration), chemical techniques (ion exchange chromatography), and thermodynamic modeling (Visual MINTEQ) to characterize dissolved Fe speciation in boreal organic-rich rivers across a sizable south–north transect. We chose contrasting rivers with a predominance of either allochthonous or autochthonous organic compounds. We found that the dissolved organic matter (DOM) in the studied rivers varies in molecular weights and the degree of humification. Regardless of the climate parameters of the river watershed, the dominant status of dissolved Fe during the summer low-water period was essentially colloidal and dominated by anionic complexes of the type [MeL]n−.

Land use effects on spatiotemporal variations of dissolved organic matter fluorescence and water quality parameters in watersheds, and their interrelationships

Fluorescence spectroscopy has demonstrated its potential for assessing organic matter (OM) –related water quality (WQ) and identifying anthropogenically driven pollution sources within watersheds. This study involves a comparison of spatial variations in general WQ parameters and dissolved organic matter (DOM) fluorescence characteristics between two adjacent watersheds characterized by disparate land uses (i.e., urban and agricultural). The investigation encompasses both rain and non-rain events to evaluate the diagnostic utility of DOM fluorescence in monitoring WQ fluctuations. In the urban watershed, variations were predominantly influenced by wastewater effluents, leading to noticeable changes exclusively downstream from sewage treatment facilities, regardless of distinct hydrological conditions. In contrast, the agricultural watershed exhibited more extensive spatial variations, suggesting a prevalence of non-point source pollution stemming from agricultural and livestock activities. The humic-like fluorescent components (C1 and C2) exhibited a robust positive correlation with total organic carbon (TOC), unaffected by varying hydrological conditions and catchment land use. Conversely, the assessment of nutrient levels utilizing the protein-like component (C3) was considerably influenced by catchment land use. A stronger positive correlation between C3 and total nitrogen (TN) was observed in the urban watershed compared to the agricultural watershed. Moreover, the fluorescence index (FI) demonstrated a substantial positive relationship with TN in both watersheds, indicating the dominance of microbial sources in nitrogen pollution for both watersheds. No significant differences were found in the variation trends of WQ and DOM fluorescence between non-rain and rain events. This study emphasizes that catchment land use plays a pivotal role in influencing the associations between fluorescence indices and WQ parameters. Our findings validate the robust potential for replacing conventional WQ parameters with DOM fluorescence indices in watersheds characterized by distinct land uses.

Lithological controls of the Mg isotope composition of the Lena River across seasons and its impact on the annual isotope flux to the Arctic Ocean

Given the importance of permafrost regions in providing the major elements to the Arctic Ocean, and the vulnerability of these regions to ongoing climate change due to permafrost thaw and landscape modifications, assessing the magnitude and characterizing the factors governing isotope compositions in river waters across seasons and space is of high priority.Towards identifying possible environmental controlling factors (climate, vegetation, rock lithology) and quantifying annual fluxes of dissolved Mg isotopic signatures in large Arctic rivers located in the continuous permafrost zone, here we measured hydrochemical and Mg isotope compositions of the Lena River main channel and its various tributaries over different seasons of the year. In general, we did not find evidence of any statistically significant (p < 0.05) correlation between δ26Mg and main physico-geographical parameters of the river watersheds (temperature, permafrost, type of vegetation). The exception is the decrease in riverine δ26Mg values that was accompanied by an increase in the carbonate rock proportion in the watershed, whereas an opposite trend was observed for the abundance of terrigenous and silicate rocks. An incontestable control of dolomite rocks on Mg isotope signature in the Lena River was also supported by decreasing δ26Mg values with increasing Dissolved Inorganic Carbon (DIC) concentration, as also observed for other Artic River basins. This relationship was mostly pronounced during the high-flow period, when secondary Mg silicate formation in soils and underground waters and so the terrestrial uptake of Mg were the lowest. In the Lena River main channel, the lowest δ26Mg values (−1.5 ± 0.05 ‰) were observed during autumn-winter (September to March), probably reflecting a dominant role of underground reservoirs and subsurface soil weathering of isotopically light Precambrian dolomites.The mean δ26Mg values of the Lena River during two months of spring (−1.02 to −1.28 ‰), 4 months of summer baseflow (−1.30 ‰) and 6 months of winter yields a mean discharge-weighted annual value of −1.26 ± 0.05 ‰. This number coincides with the value of summer baseflow reported in earlier works. Therefore, like in the recently studied Yenisey River basin, the Mg isotope signature of the Lena River water likely stems from a mixture of carbonate (−2.0 ≥ δ26Mg ≥ −2.5 ‰) and silicate (0 ≥ δ26Mg ≥ −0.2 ‰) rocks in its watershed. We also argue that the discharge-weighted mean annual isotopic signature of an element in the Artic rivers can be reasonably approximated by a single sampling campaign during summer baseflow. This allows cost-effective assessment of mean riverine isotopic signatures of other elements in both small and large rivers to the Arctic Ocean.

Development of Synthetic Unit Hydrographs Using Spatial Proximity Regionalization for the Makiling Forest Reserve, Philippines

There is a dearth of streamflow data in the Philippines to generate hydrographs needed for flood forecasting and water resources assessment. A method of generating and calibrating synthetic hydrographs using model simulations and spatial proximity regionalization is presented. Synthetic unit hydrographs of four storm events in the gauged watershed of Makiling Forest Reserve were generated using Soil Conservation Service Unit Hydrograph, Clark Unit Hydrograph, and Snyder’s Unit Hydrograph methods. The generated synthetic hydrographs for each runoff modeling technique were calibrated with the actual hydrographs of the watershed. Snyder’s Unit Hydrograph model results were the most acceptable based on the Nash-Sutcliffe Efficiency, Index of Volumetric Fit, and Relative Error of Peak Flow. The weighted values of the calibrated watershed parameters computed using spatial proximity regionalization technique and the hyetographs derived from the Rainfall Intensity Duration Frequency Curve of the University of the Philippines Los Baños-National Agrometeorological Station were used to generate the synthetic unit hydrographs for three neighboring ungauged watersheds at 2-, 5-, 10-, 15-, 20-, 25-, 50, 100-year return periods. Total runoff volume, the magnitude of peak flows, and time to peak derived from the generated hydrographs can be used in watershed planning, water resources management, flood forecasting and the design of various water control structures.

Investigation of the Water Basins of Kalafgan District with GIS Analysis

The rapid and unpredictable growth of the population, the development of cultivation, and the lack of surface and underground water management have caused problems in the irrigation and hydrological system in Kalafgan city. In this region, the lack of sufficient water diversion dams and the canalization system, at the same time as the rapid development of cultivation and agriculture, have caused problems for the residents of this city. To solve the water shortage, there is a need to increase the number of water diversion dams, manage surface water, and determine and identify water sources and drainage patterns. Determining and stabilizing the location construction of suitable dams and channels in the regional study is determined by using a geographic information system. One of the effective sciences in the field of earth and environmental science studies is the use of geographic information systems, which is very useful in the accurate estimation of hydrometric parameters of watersheds. In this research, as an example of hydrometric studies of the water basins of Kalafgan city in the geographic information system, the digital elevation model (DEM) has been used with the help of geographic information system software for the studied basin.

Development of Infiltration Map Using Geographical Information System Based on Ground Test in Cisadane Watershed Indonesia

Infiltration is one of the watershed parameters that are essential for integrated water resources management. Infiltration can be measured directly by a ground test such as using a double infiltrometer. But for the very large watersheds, the ground test methods take a lot of time, require a lot of skilled manpower, and cost. Geographical information systems (GIS) and remote sensing applications have been developed and used in various fields such as water resources, and produce good and fairly accurate results. The present study aims to develop an infiltration map based on a limited point of survey using GIS. This study uses the Cisadane watershed in Indonesia as the case study with an area of 154547 ha. Furthermore, it will be compared with the potential recharge zone map that has been generated from previous research. The resulting map of infiltration generated by GIS with a limited point of the survey is quite close to the potential recharge zone map using the weighted method with watershed physical and hydrological factors.

Wild Rice Lakes in Comparison to Mapped Surficial Sands in Minnesota

Several recent studies have considered the distribution of wild rice (Zizania palustris) compared to a variety of physical and watershed parameters. However, the distribution of wild rice has not been systematically compared to the surficial geology. In this study, a relatively comprehensive list of identified wild rice lakes in Minnesota was compared to the mapped areas of surficial sands. Wild rice is significantly more likely to occur on basins which are within or adjacent to mapped surficial sands. Statewide, an odds ratio of 2.1. indicates that a given lake within the mapped surficial sands has more than twice the odds of wild rice occurrence than a lake outside of the mapped surficial sands. The correlation observed here between mapped surficial sands and wild rice presence suggests that a groundwater-surface water interaction may have more widespread importance for sustaining wild rice populations than previously considered.

Wild Rice Lakes in Comparison to Mapped Surficial Sands in Minnesota

Several recent studies have considered the distribution of wild rice (Zizania palustris) compared to a variety of physical and watershed parameters. However, the distribution of wild rice has not been systematically compared to the surficial geology. In this study, a relatively comprehensive list of identified wild rice lakes in Minnesota was compared to the mapped areas of surficial sands. Wild rice is significantly more likely to occur on basins which are within or adjacent to mapped surficial sands. Statewide, an odds ratio of 2.1. indicates that a given lake within the mapped surficial sands has more than twice the odds of wild rice occurrence than a lake outside of the mapped surficial sands. The correlation observed here between mapped surficial sands and wild rice presence suggests that a groundwater-surface water interaction may have more widespread importance for sustaining wild rice populations than previously considered.

Hydrological status of the Dagu River Basin and management suggestions based on soil and water assessment tool multi-station calibration

Soil and water assessment tool (SWAT) model was used to calculate the runoff, nitrogen and phosphorus emissions in the Dagu River Basin from 2002 to 2012 and provided preliminary suggestions on environmental protection measures. Calibration on hydrological watershed parameters was obtained from data obtained from multiple representative stations. Cluster analysis was used to group all stations, and the parameters of different representative stations were applied to the entire geographical area to reflect the hydrological conditions of the basin. Additionally, the spatiotemporal changes and pollution source characteristics of nitrogen and phosphorus were analyzed. Anthropogenic sources—chemical fertilizer loss and livestock breeding—accounted for 49.9–29.6% of total nitrogen (TN) and 41.4% and 40.3% of total phosphorus (TP), respectively. Non-point sources accounted for 85.8% of the TN and 89.4% of the TP. Six landscape management practices were set up to evaluate the reduction effect on non-point source pollution loads, and comprehensive measures were proposed to reduce TN (TP) by ~ 70%. According to water quality model, the response relationship between river control and nutrient distribution in Jiaozhou Bay is calculated. Based on the findings, we propose an optimal control scheme for non-point source pollution in the Dagu River Basin and other similar basins.

Estimating surface runoff using the curve number method in an ungauged watershed in Jalisco, Mexico evaluating its morphometric parameters

The surface runoff was estimated using the curve number (CN) method for different storm events and it was associated with the morphometric parameters of an ungauged watershed in Jalisco, México. The land use and land cover map from 2019 was derived from the unsupervised classification of a Sentinel-2 image at 10 m resolution. The morphometric analysis revealed that the study area is dominated by areas of gentle slope and moderate to high permeability with dense vegetation and low relief. It is a well-drained watershed with low flood potentiality as well as a groundwater potential zone. About 69% of the study area corresponds to natural cover with tropical dry forest and evergreen forest as the most representative classes. A total of 77 storm events were identified from 2013 to 2019, with runoffs that ranged from 0.05 to 227.2 Mm3. September and October were the months with the most intense rainfall and, therefore, the months with the highest runoff volume. The average runoff was 14.52 Mm3, corresponding to an average runoff coefficient of 12.86%. Together, the methods used here provide useful results for delineating conservation strategies at the watershed level.

GIS preprocessing for rainfall-runoff modeling using HEC-HMS in Nekkor watershed (Al-Hoceima, Northern Morocco)

All Discharge data are among the most critical factors that must be considered when evaluating the management of water resources in a watershed. Simulation of rainfall-runoff is therefore an important element in assessing the impacts of serious flooding. In the present study, rainfall-runoff in the Nekkor watershed in Al Hoceima province was simulated using GIS, remote sensing and the Hydrologic Engineering Center Hydrologic Modeling System (HEC-HMS) model. The applicability, capacity and suitability of this model for rainfall runoff in the watershed were examined. The watershed parameters were generated using (HEC-GeoHMS) and ArcGIS. The model was calibrated using a daily data set that occurred in the watershed between 2003 and 2007, the validation period was from 2009 to 2012. Model performance was evaluated using a variety of different statistical indices to study the response and impact of rainfall-runoff. Model parameters were changed and calibration was performed using the Soil Conservation Service Curve Number loss method. Consistent and satisfactory performance in terms of peak discharge, total flood volume, timing of peak discharge and overall hydrograph adjustment effect was found. The determination coefficient (R2) for the validation period reached 0.73 versus 0.71 for the calibration period. The root mean square error (RMSE) is within the acceptable range. The relative bias (RE) demonstrates an overestimation in the calibration period and an underestimation in the validation period in the peak flows. These results will help decision makers to better manage water resources in this watershed and mitigate flood risks.

Watershed Delineation and Morphometric Analysis Using Gis and Remote Sensing

A watershed is a territory from which many rivers and streams drain into a common reservoir. The first step in reaping the benefits of watersheds is identifying them and determining how much water they supply. Important watershed parameters may be defined and calculated using a Geographic Information System (GIS). The city of Chittoor in the Indian state of Andhra Pradesh is being investigated here. The Google Earth engine is used to create a LULC map (land use land cover), and USGS Earth Explorer is used to gather DEM data to define watersheds to better understand the study area’s landscape. Watershed boundaries and morphometric parameters are presented in the current study.

Application of Head Loss Coefficient for Surcharge Straight Path Manhole to Improve the Accuracy of Urban Inundation Analysis

Currently, adopted runoff analysis models focus on the characteristic factors of watersheds and neglect the analysis of the flow in conduits. Additionally, the usually employed XP-SWMM modeling package generally underestimates the flood area because it considers manholes as nodes and does not consider local head losses according to the shape and size of the nodes. Therefore, it is a necessity to consider the loss coefficient in surcharge manholes to improve inundation and runoff analysis methods. This study aims at improving the accuracy of discharge analysis before analyzing the storage and runoff reduction effects of storage facilities. Hydraulic experiments were conducted according to the changes in discharge and manhole shapes. We show that the flood area increases as the overflow discharge at manhole increases due to the application of the head loss coefficient. We demonstrate a concordance rate ≥95% between results and observed flood area when accurate input data (from the parameters of the target watershed) and the head loss coefficient (from hydraulic experiments) are applied. Therefore, we demonstrate that the result of our 2D inundation analysis, considering the head loss coefficient in surcharge manhole, can be used as basic data for accurately identifying urban flood risk areas.

Development Of Unit Hydrograph Parameters Model Using Selected Watershed Parameters on Rivers in Central Sulawesi

Permasalahan utama dalam analisis debit berbasis hidrograf satuan adalah menetapkan metode yang paling sesuai untuk memperkirakan parameter hidrograf. Paper ini bertujuan merumuskan persamaan parameter hidrograf menggunakan lebih banyak jumlah parameter DAS terindikasi berkorelasi tinggi yang didasarkan pada data 8 DAS terukur di Provinsi Sulawesi Tengah, Indonesia. Sebanyak 12 parameter DAS yaitu luas DAS (A, km 2 ), panjang sungai utama (L, km), kemiringan sungai utama (S), panjang sungai utama sampai titik terdekat titik berat DAS (Lc, km), faktor bentuk DAS (FB), jumlah orde sungai (n), jumlah pertemuan sungai (JN), panjang sungai orde 1 (L1, km), panjang sungai semua orde (Lt, km), kerapatan drainase (D), jumlah ruas orde 1 (R1), dan jumlah ruas semua orde (Rt) digunakan untuk membangun 3 parameter utama hidrograf satuan yaitu waktu puncak (Tp, hour), debit puncak (Qp, m 3 /s) dan waktu dasar (Tb, hour). Analisis regresi linier diterapkan terhadap 12 parameter DAS tersebut untuk memformulasikan ketiga parameter hidrograf. Hasil kajian menunjukkan bahwa setidaknya 5 dari 12 parameter DAS yang diuji memperlihatkan pengaruh yang sangat besar pada ketiga parameter hidrograf dengan indikator RMSE yang sangat rendah: 0.019, 0.098, 0.014 secara berturut-turut untuk Tp, Qp, dan Tb. Rendahnya indikator RMSE mengindikasikan bahwa ketiga persamaan parameter hidrograf tersebut berkinerja sangat tinggi. Namun demikian, validasi pada DAS-DAS terukur lainnya masih harus dilakukan untuk dapat diapkikasikan pada skala DAS lebih luas dan beragam

Characterization of basaltic rock aquifer parameters using hydraulic parameters, Theis’s method and aquifer test software in the hard rock area of Buchakewadi watershed Maharashtra, India

The twelve wells were selected to carry out the various test, duration of pumping (min), maximum draw drown (m), duration of recovery (min), residual drawdown, and aquifer type in the basaltic rock aquifer parameters of Buchakewadi watershed. The source and flow of groundwater are essential concerns in hydrological systems that concern both spatially and temporally components of groundwater discharge and water supply problems. The content and temperature of groundwater flowing through an aquifer might change depending on the aquifer environment. As a result, hydrodynamic analyses can provide valuable information about a region's subsurface geology. The present research attempts of aquifer variables such as transmissivity (T) and storativity (S) estimation are significant for groundwater resource development and evaluation. There are numerous approaches for calculating precise aquifer characteristics (i.e., hydrograph analysis, pumping test, etc.). A most frequent in situ analysis is a well-pumping test, which accurately measures the decline and rise of groundwater levels. During an aquifer pumping test, to characterize aquifer properties in an undiscovered location to forecast the rate of depletion of the groundwater table/potentiometric surface. The shallow, weathering subsurface water accessible above the Deccan traps in an unconfined state is insufficient to satisfy the ever-increasing pressure on water supplies. Maharashtra is similarly dominated by hard rocks, whose rainfall susceptibility is limited by weathering and primary porosity, as is their volume to store and convey water. Based on the hydraulic parameters and Theis method, results are optimized. Aquifer mapping and pumping test results can be more important for solving problems such as water scarcity, nonpolluting water, health issues, and source of fresh water on the earth surface. However, the characterization of aquifer parameters should be significant role in the scientific planning and engineering practices.

Morphometric evaluation of Ranikhola watershed in Sikkim, India using geospatial technique

Morphological parameters are linked with the hydrological behaviour of the watershed. It helps to understand different basin characteristics. Characterization of quantitative morphology and river basin analysis is the way to implement proper river basin planning and management of soil and water conservation measures. In the present study, Cartosat-1 Digital Elevation Model (DEM) was used in Geographic Information System (GIS) environment to determine the morphometric parameters (stream length, stream order, stream frequency, bifurcation ratio, form factor, drainage density, circulatory ratio, etc.) of the Ranikhola watershed of Sikkim state, India. The slope of a major portion of the watershed area was found to be less than 30% (42 km2) and has a drainage density of 0.585 km-1. The lower value of drainage density in the watershed indicates a relatively lower streams frequency over the watershed. The elongation ratio, form factor, and circulatory ratio were estimated as 0.665, 0.347, and 0.510, respectively, which indicate that the watershed is elongated in shape, having gentle slopes and long flow paths. The relief ratio for the watershed was estimated to be 0.187, which indicates the watershed has a low elevation difference, low runoff, and high groundwater potential. This kind of morphometric analysis is required for the watershed characterization and helps to understand the hydrogeological behavior of the watershed.

To Study the Hydrological System and Watershed by Using Remote Sensing (RS) and Geographic Information System (GIS) in Kannad Taluka, Aurangabad District, MS, India

The current study in this research focuses on the importance of the digital elevation model (DEM) and satellite images to evaluate and interpret the relative parameters of watersheds in Kannad taluka, Aurangabad district, India. Watersheds in the area were identified and calculated using the SRTM DEM through ARCGIS 10.8 software. Kannad shows a first to fourth-order drainage network which is of dendritic type, which indicates a sign of the structural lack of control and homogeneity of the watersheds in Kannad taluka. The basin’s mean bifurcation ratio is found to be 1.47 which indicates that the drainage network pattern is not much influenced by geological structures. Based on the hydrological assessment on the watershed scale, the present study reveals that the SRTM DEM is the most accurate application compared to other techniques. As visual or manual identification and evaluation are difficult and may not provide a holistic view of watersheds, modern tools of RS and GIS were used to study the watershed of Kannad taluka. There was lack of published reports on watersheds by using the RS and GIS and work undertaken.

Assessment of correlation amongst physico-chemical, topographical, geological, lithological and soil type parameters for measuring water quality of Rawal watershed using remote sensing

Abstract The quality of water is traditionally assessed by the collection of physico-chemical parameters, i.e., pH, turbidity, dissolved oxygen of the water bodies. However, the variations in environmental factors may have an impact on the quality of water, as changes in these attributes may affect the water bodies. These factors include the topographical, geological, lithological and soil type parameters of the watershed. In this study, the relationship amongst the physico-chemical, topographical, geological, lithological and soil type parameters of the Rawal watershed was evaluated. The parameters included in the present study could be classified as follows: (a) water quality parameters (b) topographical parameters, (c) geological parameters, (d) lithological parameters, and (e) soil type parameters. Water quality parameters consisted of dissolved oxygen, pH, turbidity and temperature. The topographical parameters include the slope and aspect of the watershed while the lithological, geological and soil type parameters include the lithology, geology and soil type of the watershed. Pearson's correlation was used to determine the relationship amongst these different parameters. The results have revealed that the correlations of the topographical, lithological, geological parameters with the water quality parameters in the Rawal watershed for the monsoon seasons of June to August mostly have the same trend. Throughout the four-year time period, turbidity and temperature parameters had positive correlations with soil type (ranging 0.03–0.24), but however had weak correlation with geological and lithological parameters. Dissolved oxygen did not show any relationship with topographical and lithological parameters. The results for pH show that it has weak to fair positive correlations with topographical parameters. However, this analysis is based on the Landsat 8 images extracted for the monsoon seasons of the years 2017–2020, and to examine a more prominent impact of geographical or environmental factors on the physico-chemical features, a large dataset should be considered.

Performance optimization of the MGB hydrological model for multi-core and GPU architectures

Large-scale hydrological models simulate watershed processes with applications in water resources, climate change, land use, and forecast systems. The quality of the simulations mainly depends on calibrating optimal sets of watershed parameters, a time-consuming task that highly demands computational resources from repeated simulations. This work aims at performance optimizations on the MGB (“Modelo de Grandes Bacias”) hydrological model and the MOCOM-UA (Multi-Objective Complex Evolution) calibration method for two watersheds. The optimizations target state-of-the-art CPU/GPU systems, exploiting techniques that include AVX-512 vectorization, and multi-core (CPU) and many-core (GPU) parallelisms. Significant speedups of up to 20 × (CPU) were achieved for calibration, while the scalability analysis indicated 24 × (CPU) and 65 × (GPU) for simulations with larger problem sizes. The roofline analysis confirmed more effective use of the hardware resources, and the quantitative accuracy evaluation of the optimized implementations reached maximum relative errors of approximately 6% for discharges and objective functions.