Water Flow Model Research Articles

A Numerical Simulation of Moisture Reduction in Fine Soil Subgrade with Wicking Geotextiles.

A new wicking geotextile is proposed to control the water content of fine-grained soil subgrade. By comparing the spatial distribution of volumetric water content and matric suction before and after the installation of the wicking geotextile, the effectiveness of the geotextile in controlling the subgrade humidity is evaluated. Firstly, the hydraulic parameters of the wicking geotextile are obtained through laboratory tests using a pressure plate apparatus. Then, a numerical model for water flow in the subgrade is established using COMSOL to obtain the spatial distribution characteristics of humidity in the subgrade under different groundwater levels (2~8 m). The results show the wicking geotextile exhibits strong hydrophilicity, low water retention, and high horizontal permeability. Compared to the subgrade without geotextile, the water content of the soil above the geotextile decreases significantly by 7.6~9.6% at groundwater levels of 4~8m, while the saturation decreases by 18.3~23.0%, and the matric suction increases by 2~2.3 times. The wicking fabric functions as an effective drainage material to serve as a capillary barrier in the cross-plane direction and an effective drainage tunnel to transport water in the in-plane direction. The dynamic resilient modulus of the subgrade increases by 23.2~43.6%. The wicking geotextile effectively absorbs and drains weakly bound water in unsaturated soil due to the matric suction difference and its horizontal drainage capacity to improve the bearing capacity of the subgrade. It suggests that using wicking geotextile for drainage and reinforcement in fine-grained soil subgrades with groundwater levels ranging from 4 to 8 m is beneficial.

Assessment of the Impacts of Rainfall Characteristics and Land Use Pattern on Runoff Accumulation in the Hulu River Basin, China

Climate change causes the river basin water cycle disorders, and rainfall characteristics frequently result in flood disasters. This study aims to simulate and assess the response behavior of basin floods under the influence of rainfall characteristics and land use changes in the Hulu River basin using a 2D hydrological and hydraulic GAST (GPU Accelerated Surface Water Flow and Transport Model). The peak flow rate and water depth during floods were examined by simulating the evolution process of basin floods and related hydraulic elements under the independent effects of various rainfall characteristics or land use and further simulating the response results of basin floods under the combined effects of rainfall characteristics and land use. The seven scenarios were set to quantify the degree of influence that land use and rainfall characteristics have on the basin flood process based on examining changes in land use and rainfall characteristics in the research area. The results from different rainfall characteristics scenarios depicted that as the rainfall return period is shorter, the peak flow rate is higher, and the peak flow rate is lower as the return period is prolonged. Under different rainfall characteristics, the peak flow rate in scenario R8 is 41.30%, 40.00%, and 34.51% higher than the uniform distribution of rainfall, while water depth is decreased by 0.55%, increased by 4.96% and 2.92% as compared to the uniform distribution of rainfall. While under different land use scenarios, it is observed that the change in land use has increased 2.7% in cultivated land and 1.1% in woodland. In addition, the interactive effect of different rainfall characteristics and land use it can be seen that the scenario with the greatest reduction in flood risk due to rainfall characteristics and land use is RL2-4, representing a 12.55% decrease in peak flow and a 37.69% decrease in peak water depth. In this scenario, the rainfall is heavier in the southeast and northwest regions and lighter in the northeast and southwest regions. The land use type is characterized by reforestation and the return of cultivated land to forests. The changes in rainfall distribution and the increase in grassland contribute to the decrease in flood threat. Future research in the erodible parts of the Hulu River basin, planning for water resources, and soil and water conservation can all benefit from the study’s conclusions.

Root distributions predict shrub–steppe responses to precipitation intensity

Abstract. Precipitation events are becoming more intense around the world, changing the way water moves through soils and plants. Plant rooting strategies that sustain water uptake under these conditions are likely to become more abundant (e.g., shrub encroachment). Yet, it remains difficult to predict species responses to climate change because we typically do not know where active roots are located or how much water they absorb. Here, we applied a water tracer experiment to describe forb, grass, and shrub root distributions. These measurements were made in 8 m by 8 m field shelters with low or high precipitation intensity. We used tracer uptake data in a soil water flow model to estimate how much water respective plant root tissues absorb over time. In low-precipitation-intensity plots, deep shrub roots were estimated to absorb the most water (93 mm yr−1) and shrubs had the greatest aboveground cover (27 %). Grass root distributions were estimated to absorb an intermediate amount of water (80 mm yr−1) and grasses had intermediate aboveground cover (18 %). Forb root distributions were estimated to absorb the least water (79 mm yr−1) and had the least aboveground cover (12 %). In high-precipitation-intensity plots, shrub and forb root distributions changed in ways that increased their water uptake relative to grasses, predicting the increased aboveground growth of shrubs and forbs in these plots. In short, water uptake caused by different rooting distributions predicted plant aboveground cover. Our results suggest that detailed descriptions of active plant root distributions can predict plant growth responses to climate change in arid and semi-arid ecosystems.

Using specularity content to evaluate eight geothermal heat flow maps of Totten Glacier

Abstract. Geothermal heat flow (GHF) is the dominant factor affecting the basal thermal regime of ice sheet dynamics. But it is poorly defined for the Antarctic ice sheet. We compare the basal thermal state of the Totten Glacier catchment as simulated by eight different GHF datasets. We use a basal energy and water flow model coupled with a 3D full-Stokes ice dynamics model to estimate the basal temperature, basal friction heat and basal melting rate. In addition to the location of subglacial lakes, we use specularity content of the airborne radar returns as a two-sided constraint to discriminate between local wet or dry basal conditions and compare the returns with the basal state simulations with different GHFs. Two medium magnitude GHF distribution maps derived from seismic modelling rank well at simulating both cold- and warm-bed regions, the GHFs from Shen et al. (2020) and Shapiro and Ritzwoller (2004). The best-fit simulated result shows that most of the inland bed area is frozen. Only the central inland subglacial canyon, co-located with high specularity content, reaches the pressure melting point consistently in all the eight GHFs. Modelled basal melting rates in the slow-flowing region are generally 0–5 mm yr−1 but with local maxima of 10 mm yr−1 at the central inland subglacial canyon. The fast-flowing grounded glaciers close to the Totten ice shelf are lubricating their bases with meltwater at rates of 10–400 mm yr−1.

Numerical modelling of flow and heat transport in closed mines. Case study Walsum drainage province in the Ruhr coal-mining area

High geothermal potential and multiple mine-water-based geothermal installations in Germany and other countries improve the relevance of detailed studies and modeling of promising sites. In this context, we developed a numerical model of water flow and heat transport in the Walsum mine drainage province in the west of the Ruhr coalmining area using the available data on geology, mining, water levels, pumping, and the temperatures of deep rocks and mine water. The model was validated by varying the parameters of groundwater recharge and hydraulic conductivity to achieve sufficient consistency with measured inflows and pumping rates from the central pumping facility located in the Walsum 2 shaft. The calculated mine water temperature of 30.3 ºC is close to the average of the measured temperature varied within the range of 29 – 33 ºC during the last years of mine maintenance. Using the numerical model, we evaluated the expected thermal capacity of a hypothetical open-loop circulation system and two closed-loop geothermal systems within the study area. The installation and operation of these systems would enable the generation of a thermal capacity from a few dozen kW to 1 MW sufficient for small-size to mid-size heat consumers with insignificant impact on the high thermal energy potential of the Walsum mine drainage province.

A Mechanistic Model for Simulation of Carbendazim and Chlorothalonil Transport through a Two-Stage Vertical Flow Constructed Wetland

A mechanistic model was developed to simulate one-dimensional pesticide transport in two-stage vertical flow constructed wetland. The two pesticides taken under study were carbendazim and chlorothalonil. The water flow patterns within the constructed wetland were simulated using the Richards equation. Water content and vertical flux, which are the outputs of the substrate water flow model, were used to calculate the substrate moisture-related parameters and advection term in the solute transport model. The governing solute transport equation took into account a total of six processes: advection, molecular diffusion, dispersion, adsorption to the solid surface, degradation and volatilization. A total of 14 simulation cases, corresponding with available experimental data, were used to calibrate the model, followed by further simulations with standardized influent pesticide concentrations. The simulations indicated that the constructed wetland reached a steady state of pesticide removal after 7 days of operation. Two distinct water flow patterns emerged under saturated and unsaturated conditions. The patterns observed while varying the hydraulic loading rates were similar for each individual saturation condition. Two-factor ANOVA of the simulated data further revealed that the carbendazim and chlorothalonil removal was dependent on the hydraulic loading rates, but it was independent of the influent pesticide concentration. Analysis of the simulated pesticide removal showed that degradation emerged as the predominant removal process over time for both the pesticides. The model developed in this study can be an important tool for the design and construction of treatment wetlands for pesticide removal from wastewater.

From global glacier modeling to catchment hydrology: bridging the gap with the WaSiM-OGGM coupling scheme

Coupled glacio-hydrological models have recently become a valuable method for predicting the hydrological response of catchments in mountainous regions under a changing climate. While hydrological models focus mostly on processes of the non-glacierized part of the catchment with a relatively simple glacier representation, the latest generation of standalone (global) glacier models tend to describe glacier processes more accurately by using new global datasets and explicitly modeling ice-flow dynamics. Yet, to the authors' knowledge, existing catchment-scale coupled glacio-hydrological models either do not include these most recent advances in glacier modeling or are simply not available to other users. By making use of the capabilities of the free, distributed, physically-based Water Flow and Balance Simulation Model (WaSiM) and the Open Global Glacier Model (OGGM), a coupling scheme is developed to bridge the gap between global glacier representation and local catchment hydrology. The WaSiM-OGGM coupling scheme is used to further assess the impacts under future climates on the glaciological and hydrological processes in the Gepatschalm catchment (Austria), by considering a combination of three climate projections under the Representative Concentration Pathways (RCP) 2.6, 4.5, and 8.5. Additionally, the results are compared to the original WaSiM model with the integrated Volume-Area (VA) scaling approach for modeling glaciers. Although both models (WaSiM with VA scaling and WaSiM-OGGM coupling scheme) perform very similar during the historical simulations (1971–2010), large discrepancies arise when looking into the future (2011–2100). In terms of runoff, the VA scaling model suggests a reduction of the mean monthly peak between 10–19%, whereas a reduction of 26–41% is computed by the coupling scheme. Similarly, results suggest that glaciers will continuously retreat until 2100. By the end of the century, between 20–43% of the 2010 glacier area will remain according to the VA scaling model, but only 1–23% is expected to remain with the coupling scheme. The results from the WaSiM-OGGM coupling scheme raises awareness of including more sophisticated glacier evolution models when performing hydrological simulations at the catchment scale in the future. As the WaSiM-OGGM coupling scheme is released as open-source software, it is accessible to any interested modeler with limited or even no glacier knowledge.

Three-dimensional X-ray imaging of macropore flow

Macropores are known to be important pathways for the rapid transport of water, solutes and colloids in soil. Nevertheless, we still know very little about how the topology and geometry of macropore networks govern water flow configurations and velocities in natural soil. In this study, we aimed at gaining more insight into macropore flow by using X-ray tomography to quantify air–water distributions in the macropore networks of undisturbed topsoil and subsoil columns of a clay soil at varying steady-state flow rates. We observed that while large fractions of the macropore network remained air-filled, the air phase only became entrapped when the irrigation rate was very close to the saturated hydraulic conductivity of the soil. The data enabled us to parameterize a kinematic wave model for water flow following the approach proposed in Jarvis et al. (2017a). Follow-up experiments would be required to evaluate whether these kinematic wave parameters derived by X-ray imaging match with those obtained from outflow measurements. We found that quantitative X-ray imaging of macropore flow through soils still remains a challenging task. We recommend that future experiments are conducted on smaller soil samples to improve image resolution and minimize experimental time spans as well as X-ray image noise and illumination bias. Such experiments could also include 3-D tracer imaging to identify the imaged macropore networks transporting most of the water (i.e. the backbone) at varying steady irrigation rates.

Modeling Water Flow in Variably Saturated Porous Soils and Alluvial Sediments

The sustainable exploitation of groundwater resources is a multifaceted and complex problem, which is controlled, among many other factors and processes, by water flow in porous soils and sediments. Modeling water flow in unsaturated, non-deformable porous media is commonly based on a partial differential equation, which translates the mass conservation principle into mathematical terms. Such an equation assumes that the variation of the volumetric water content (θ) in the medium is balanced by the net flux of water flow, i.e., the divergence of specific discharge, if source/sink terms are negligible. Specific discharge is in turn related to the matric potential (h), through the non-linear Darcy–Buckingham law. The resulting equation can be rewritten in different ways, in order to express it as a partial differential equation where a single physical quantity is considered to be a dependent variable. Namely, the most common instances are the Fokker–Planck Equation (for θ), and the Richards Equation (for h). The other two forms can be given for generalized matric flux potential (Φ) and for hydraulic conductivity (K). The latter two cases are shown to limit the non-linearity to multiplicative terms for an exponential K-to-h relationship. Different types of boundary conditions are examined for the four different formalisms. Moreover, remarks given on the physico-mathematical properties of the relationships between K, h, and θ could be useful for further theoretical and practical studies.

HAM-based analysis of nonlinear convection of two-layer water and air-TiO2 flow model in a vertical channel

This article investigates the nonlinear convection transport of heat transfer in a nanoparticle laden two-layer flow in a vertical channel under the additional effects of magneto hydrodynamic (MHD) and radiation. Water and compressed air are chosen as the fluids in two-layer flow. This type of flow is commonly seen in the transportation of oil and gas in pipelines, therefore, correct understanding of flow dynamics including convective transport phenomenon, layers interaction, and graphical interpretation of flow variables is important for better designing of equipments. Titanium dioxide ( Ti O 2 ) nanoparticles are added into the air to magnify the transport mechanism. The mathematical model incorporating buoyancy, nonlinear convection, MHD, viscous dissipation, and radiation effects is presented in the form of nonlinear Ordinary Differential Equation (ODE’s). Then utilizing homotopy analysis method, these interconnected differential equations are resolved. A visual illustration shows how different physical factors affect fluid rate and temperature. Tabulated values of Nusselt number at both walls are presented to discuss the numerical data of convection and found that it decreases toward the left boundary but rises toward the right wall by increasing Eckert number and Prandtl number. The results of this two-layer flow will help in understanding this complex flow which has practical applications in various engineering processes and further enhance the scientific knowledge related to multilayer problems.

A 1D-2D dynamic bidirectional coupling model for high-resolution simulation of urban water environments based on GPU acceleration techniques

Urban water pollution is an important issue of global concern. An integrated model that can be employed to efficiently and accurately simulate the whole system of urban surfaces, underground drainage systems and river and lake water environments is an important tool for comprehensively treating urban water pollution. Therefore, we developed a 1D-2D dynamic bidirectional coupling model for high-resolution simulation of the entire urban water environment (GAST-GCSE) comprising the graphics processing unit (GPU)-accelerated surface water flow and transport (GAST) model and the storm water management model (SWMM). The SWMM and GAST model were used for coupled simulation of hydrological and hydrodynamic quantities and water quality in 1D and 2D regions, respectively. The time steps of the two models are the same. Compute Unified Device Architecture (CUDA) parallel architecture programming and advanced model algorithms were adopted to improve the simulation accuracy and efficiency of the GAST model. The two models were dynamically coupled by calling the dynamic link library (DLL) in the SWMM and adding external functions. Two test cases were considered to verify the performance of the proposed model. The results showed that the proposed model provides high simulation accuracy. Compared with the results obtained by commercial software and theoretical values, the relative errors of the water quantity and water quality simulation results were less than 3%. The whole water environment of the main urban area of Changzhi city in North China was evaluated by the GAST-GCSE model, and the simulation results were compared with monitoring data and pure SWMM simulation results. The simulation errors at three waterlogging points were less than 14%, and the Nash efficiency coefficients (NSE) of the NH4+-N concentration in the three river sections were 0.77, 0.56 and 0.64, respectively. Notably, the model needed only 4.39 h to simulate rainfall production and confluence on a 2D surface, a river flood in complex terrain and its accompanying pollutant evolution process involving 3,849,428 cells over 4 h. This study provides new insights, ideas and tools for urban water environment simulation and change mechanism study.

Estimating cumulative evapotranspiration using superconducting gravimeter data: a study in Buenos Aires Province, Argentina

ABSTRACT A new method for estimating cumulative evapotranspiration using superconducting gravimeter data is presented. Evapotranspiration is computed from the classical water balance equation using precipitation data, estimated runoff, and water storage assessed from temporal variations of gravity. The gravity-based methodology is applied to a study site located at the Argentinian–German Geodetic Observatory (AGGO) in the flatland area of Buenos Aires Province (Argentina), which houses the only superconducting gravimeter in South America. For the period from April 2017 to May 2018, the cumulative evapotranspiration is estimated at 710.7 ± 25.7 mm. Evapotranspiration values are successfully compared with estimates provided by three methods, based on the water balance equation using soil moisture data, the numerical modelling of water flow in the unsaturated zone and the MODIS product (MOD16A2). The analysis of evapotranspiration also allows us to identify a period of soil water stress which is validated by soil moisture measurements.

Validating coupled flow theory for bare‐soil evaporation under different boundary conditions

AbstractEvaporation from bare soil is an important hydrological process and part of the water and energy balance of terrestrial systems. Modeling bare‐soil evaporation is challenging, mainly due to nonlinear couplings among liquid water, water vapor, and heat fluxes. Model concepts of varying complexity have been proposed for predicting evaporative water and energy fluxes. Our aim was to test a standard model of coupled water, vapor, and heat flow in the soil using data from laboratory evaporation experiments under different boundary conditions. We conducted evaporation experiments with a sand and a silt loam soil and with three different atmospheric boundary conditions: (i) wind, (ii) wind and short‐wave radiation, and (iii) wind and intermittent short‐wave radiation. The packed soil columns were closed at the bottom (no water flux) and instrumented with temperature sensors, tensiometers, and relative humidity probes. We simulated the evaporation experiments with a coupled water, vapor, and heat flow model, which solves the surface energy balance and predicts the evaporation rate. The evaporation dynamics were predicted very well, in particular the onset of stage‐two evaporation and the evaporation rates during the stage. A continuous slow decrease of the measured evaporation rate during stage‐one could not be described with a constant aerodynamic resistance. Adding established soil resistance parametrizations to the model significantly degraded model performance. The use of a boundary‐layer resistance, which takes into account the effect of point sources of moisture, improved the prediction of evaporation rates for the sandy soil, but not for the silt loam.

Development of a water flow and nutrients concentration simulation model for cascade hydroponic systems

Development of a water flow and nutrients concentration simulation model for cascade hydroponic systems

Approximate Solutions for A Fractional Shallow Water Flow Model

This paper presents the solutions of fractional Drinfeld-Sokolov-Wilson (DSW) equations
 that occur in shallow water flow models using the residual power series method.
 The fractional derivatives and integrals are considered in the conformable sense. In
 addition, surface plots of the solutions are given. The solutions and results show that
 the present method is very efficient and effective due to the lack of a need for complex
 calculations and that the method also has a wide range of practicability in the resolution
 of partial differential fractional equations.

Development of mechanistic-artificial intelligence model for simulation of numerical data of water flow in porous materials

Fluid dynamics of water flow through porous metallic media is significant for cooling and heating applications. The prediction of the velocity of fluid flowing inside the porous media could provide useful data for pressure drop calculations. This prediction is usually performed by a mathematical modeling approach like computational fluid dynamics (CFD). The computational method is a powerful means of precision calculation, although it could take more time and expenditure for more complex geometries or more complex fluid flow regimes. Artificial intelligence (AI) algorithms could learn and map CFD data under several conditions. AI algorithms could continue the prediction of physical data, saving computing time and performance. The present study focuses on CFD modeling of water flow inside a pipe filled with copper porous media. For the first time, the fuzzy bee algorithm (BAFIS) maps the generated CFD data to inlet velocities of 0.5, 0.7, 1.1, and 1.3 m/s. The BAFIS intelligence assessment for accurate convective flow prediction in porous media is not available in the literature. Additionally, the reliability of this method for missing CFD data prediction has not been considered yet. The results showed that the maximum intelligence (regression=0.97) is for a bee number of 140. Using the most intelligent BAFIS, the outlet velocity can be predicted by the artificial intelligence method for further nodes and inlet velocities without CFD modeling. BAFIS could precisely predict the outlet velocity for missing data with an inlet velocity of 0.91 m/s based on previously mapped data. A comparison was made between BAFIS and the fuzzy neural network (ANFIS) for CFD data predictions. The mean-square error and the root-mean-square error of ANFIS were slightly more than BAFIS (i.e., 0.1% and 3%, respectively).

Encoder–Decoder Convolutional Neural Networks for Flow Modeling in Unsaturated Porous Media: Forward and Inverse Approaches

The computational cost of approximating the Richards equation for water flow in unsaturated porous media is a major challenge, especially for tasks that require repetitive simulations. Data-driven modeling offers a faster and more efficient way to estimate soil moisture dynamics, significantly reducing computational costs. Typically, data-driven models use one-dimensional vectors to represent soil moisture at specific points or as a time series. However, an alternative approach is to use images that capture the distribution of porous media characteristics as input, allowing for the estimation of the two-dimensional soil moisture distribution using a single model. This approach, known as image-to-image regression, provides a more explicit consideration of heterogeneity in the porous domain but faces challenges due to increased input–output dimensionality. Deep neural networks (DNNs) provide a solution to tackle the challenge of high dimensionality. Particularly, encoder–decoder convolutional neural networks (ED-CNNs) are highly suitable for addressing this problem. In this study, we aim to assess the precision of ED-CNNs in predicting soil moisture distribution based on porous media characteristics and also investigate their effectiveness as an optimizer for inverse modeling. The study introduces several novelties, including the application of ED-CNNs to forward and inverse modeling of water flow in unsaturated porous media, performance evaluation using numerical model-generated and laboratory experimental data, and the incorporation of image stacking to account for transient moisture distribution. A drainage experiment conducted on a sandbox flow tank filled with monodisperse quartz sand was employed as the test case. Monte Carlo simulation with a numerical model was employed to generate data for training and validation of the ED-CNN. Additionally, the ED-CNN optimizer was validated using images obtained through non-intrusive photographic imaging. The results show that the developed ED-CNN model provides accurate approximations, addressing the high-dimensionality problem of image-to-image regression. The data-driven model predicted soil moisture with an R2 score of over 91%, while the ED-CNN optimizer achieved an R2 score of over 89%. The study highlights the potential of ED-CNNs as reliable and efficient tools for both forward and inverse modeling in the analysis of unsaturated flow.

Water Flow Modeling and Forecast in a Water Branch of Mexico City through ARIMA and Transfer Function Models for Anomaly Detection

Early identification of anomalies (such as leakages or sensor failures) in urban water distribution systems is critical to mitigating water scarcity in cities and is a challenge in water resource management. Several data-driven methods based on machine learning algorithms have been proposed in the literature for leakage detection in urban water distribution systems. Still, most of them are challenging to implement due to their complexity and requirements of vast amounts of reliable data for proper model generation. In addition, the required infrastructure and instrumentation to collect the data needed to train the models could be unaffordable. This paper presents the use and comparison of Autoregressive Integrated Moving Average models and Transfer Function models generated via the Box–Jenkins approach to modeling the water flow in water distribution systems for anomaly detection. The models were fit using water flow data from tanks operating in a branch of the water distribution system of Mexico City. The results showed that both methods helped select the best model type for each variable in the analyzed water branch, with Seasonal ARIMA models achieving a lower mean absolute percentage error than the fitted Transfer Function models. Furthermore, this methodology can be adjusted to different time windows to generate alerts at different rates and does not require a large sample size. The generated anomaly detection models could improve the efficiency of the water distribution system by detecting anomalies such as wrong measurements and water leakages.

Data worth analysis within a model-free data assimilation framework for soil moisture flow

Abstract. Conventional data worth (DW) analysis for soil water problems depends on physical dynamic models. The widespread occurrence of model structural errors and the strong nonlinearity of soil water flow may lead to biased or wrong worth assessment. By introducing the nonparametric data worth analysis (NP-DWA) framework coupled with the ensemble Kalman filter (EnKF), this real-world case study attempts to assess the worth of potential soil moisture observations regarding the reconstruction of fully data-driven soil water flow models prior to data gathering. The DW of real-time soil moisture observations after Gaussian process training and Kalman update was quantified with three representative information metrics, including the trace, Shannon entropy difference and relative entropy. The sequential NP-DWA framework was examined by a number of cases in terms of the variable of interest, spatial location, observation error, and prior data content. Our results indicated that, similarly to the traditional DW analysis based on physical models, the overall increasing trend of the DW from the sequential augmentation of additional observations within the NP-DWA framework was also susceptible to interruptions by localized surges due to never-experienced atmospheric conditions (i.e., rainfall events). The difference is that this biased DW in the former is caused by model structural errors triggered by contrasting scenarios, which is difficult to be compensated for by assimilating more prior data, while this performance degradation in the NP-DWA can be effectively alleviated by enriching training scenarios or the appropriate amplification of observational noise under extreme meteorological conditions. Nevertheless, a substantial expansion of the prior data content may cause an unexpected increase in the DW of future potential observations due to the possible introduction of ensuing observation noises. Hence, high-quality and representative small data may be a better choice than unfiltered big data. Compared with the observations in the surface layer with the strongest time variability, the soil water content in the middle layer robustly exhibited remarkable superiority in the construction of model-free soil moisture models. We also demonstrated that the DW assessment performance was jointly determined by 3C, i.e., the capacity of potential observation realizations to capture actual observations, the correlation of potential observations with the variables of interest and the choice of DW indicators. Direct mapping from regular meteorological data to soil water content within the NP-DWA mitigated the adverse effects of nonlinearity-related interference, which thus facilitated the identification of the soil moisture covariance matrix, especially the cross-covariance.

MATHEMATICAL MODELING OF WATER MOVEMENT DURING A DAM BREAK USING THE VOF METHOD

River valleys in mountainous areas are often subject to heavy rains and melting glaciers, resulting in the risk of mudflows and the destruction of hydraulic protective structures. In order to minimize the potential risk and negative outcomes of a disaster, both on an individual and environmental scale, it is crucial to possess essential information. This includes understanding the timing, location, and extent of flooding, as well as comprehending the force of water flow impact on protective structures. In the research, the numerical process of the movement of the water flow caused by the breakthrough of the dam is investigated. A two-dimensional numerical model of water flow during a dam break was constructed using the VOF method to describe the described process. With the help of the VOF method, the movement of the water surface is captured, while maintaining the law of conservation of mass. The mathematical model consists of Reynolds-averaged incompressible Navier-Stokes equations and includes the interphase equation. The turbulent k-e model was used to close the system of equations. The numerical algorithm used is PISO (Pressure-Implicit with Splitting of Operators). The obtained numerical results agree with the experimental data, indicating the developed algorithm’s reliability and accuracy. The results are presented as comparative graphs and images showing the contour of the free surface movement along the experimental reservoir. A numerical model that has been tested in this way can provide significant support in preventing the devastating consequences of a dam break and providing timely assistance during the evacuation of the population.