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Water flow in partially saturated porous media is of importance in many disciplines such as hydrology, agriculture, environmental management or geotechnical engineering. A robust and accurate solution methodology applicable across the range of soils, initial and boundary conditions found in practice is difficult to identify. Three mass conservative iteration schemes for the approximation of the flow equation in partially saturated porous media are evaluated considering large contrasts in soil texture, initial moisture and boundary conditions typically found in real world application. The three schemes reviewed are the well established modified Picard algorithm (Celia-Scheme), and two promising approaches the L-Scheme and the Casulli-Scheme. A systematic variation of soil texture and initial moisture in an intense rainfall infiltration scenario is set up in order to consider the numerical challenges associated with high non-linearity. The present analysis provides insights into robustness and efficiency in solving variably saturated flow across the range of soils, initial and boundary conditions found in practice. Casulli’s scheme, in particular, provides an acceptable compromise between robustness and execution duration even under the severest conditions investigated, while the other schemes sacrifice one for the sake of the other. The authors believe that advances in the development of numerical schemes for partly saturated flow require the kind of methodology presented here in combination with relevant benchmark problems in order to enable a fair evaluation and comparison of numerical techniques across the related disciplines.

A three‐dimensional variably saturated flow model was developed for assessing future global water resources and parameterized for groundwater pumping. We applied this model to an actual watershed to verify its validity as an Earth System Model. For global applicability, the parameterization method for multi‐layered groundwater pumping was developed and verified through comparison with observations and MODFLOW results. The parameterization proposed in this study is applicable even when multiple groundwater pumping wells are present within one horizontal computational grid and when the well spans multiple vertical grids. This method can be applied at the global scale without parameters such as the well radius, for which data may be difficult to obtain. The parameterization recreated seasonal and annual variations in the observed values. Furthermore, the results were comparable to those of MODFLOW. However, the calculation results were overestimated relative to the observed values. This overestimation was likely to be due to active groundwater pumping in the Central Valley before the start of the unsteady‐state calculation. Therefore, the groundwater level at the beginning of the unsteady‐state calculation was calculated using observed values, improving reproducibility. Furthermore, as observed groundwater levels are unlikely to be available at the global scale, steady‐state calculations were conducted over 15 and 60 years considering groundwater pumping. However, the results were not as reproducible as those obtained using observed groundwater levels. These results suggest that the groundwater level set at the beginning of the calculation is important for global‐scale groundwater flow calculation. Plain Language Summary Water resources are expected to become strained in the future due to climate change and population growth. The main focus of water resource assessments conducted to date has been on river water. Although groundwater is an important component of water resources, it has generally not been considered. This is largely due to the lack of groundwater models that can be applied at a global scale. Therefore, we developed a new groundwater model that was parameterized for groundwater pumping and validated in plains. The results of this study indicate that parameterization of groundwater pumping can produce reasonable results relative to observed values, and that the groundwater level set at the beginning of the calculation is important for the evaluation and prediction of global water resources. In particular, collection of observed groundwater levels or estimation of groundwater pumping are key steps toward more realistic prediction. Key Points A three‐dimensional variably saturated flow model for use as an Earth System Model was developed and parameterized for groundwater pumping The validation results reproduced observations to some extent and were comparable to those of MODFLOW in the Central Valley The results show that setting the groundwater level at the beginning of the unsteady‐state simulation is important for global‐scale

As water flow erodes bed sediment in a steep channel, a partly saturated debris flow, which has an unsaturated layer in its upper part, develops while interacting with a subsurface flow in the bed sediment; however, this interaction remains unclear. This study developed a numerical model that links the shallow water equation representing surface flows (i.e., fully and partly saturated, hyperconcentrated, and turbulent flows) with the depth-averaged Richards equation representing subsurface flows. The shallow water equation incorporates a new resistance equation, which accurately reproduces previous experimental results on steady uniform fully and partly saturated flows. The numerical model successfully replicated our experimental results on the evolution of a partly saturated flow. The sensitivity analysis of the numerical model demonstrated that the front velocity of a debris flow over the 4.0-m-thick bed is 28% smaller than that over the 0.6-m-thick bed and that over the unsaturated bed sediment is 22% smaller than that over bed sediment saturated through the entire layer. The decreases in front velocities are due to water seeping through the bed surface. Additionally, the analysis revealed that water infiltrating through a bed surface triggers the transition of a debris flow front from fully to partly saturated flow when the channel gradient ranges from 18 to 19°. We concluded that the interaction between the process of infiltration in the bed sediment and the development of a debris flow should be considered for accurate prediction of debris flow development processes in a steep channel.

Heterogeneity is a natural characteristic of aquifers, which has a profound influence on groundwater flow and solute transport. However, the heterogeneity in an aquifer is difficult to characterize and its impact on groundwater response to Earth tides remains insufficiently explored. A common heterogeneity in thick aquifers is the decrease in porosity and hydraulic conductivity with depth. In the present study, we present an analytical model that includes this particular heterogeneity in both the unsaturated and saturated zones to explore its impact on the tidal response. Our results reveal that, as the hydraulic conductivity decays with depth, the amplitude ratio of the tidal response increases and its phase shift decreases, and the impact of the capillary zone on tidal responses is primarily restricted to the shallow region of the aquifer. Neglecting the decay of conductivity in the previous models would result in underestimation of the amplitude ratio and overestimation of the phase shift. The solutions are applied to the field data to effectively estimate the decay in conductivity with depth. This study highlights the importance of considering aquifer heterogeneity in the analysis of the response of saturated and unsaturated flow to Earth tides. Key Points Decay in conductivity with depth causes an increase in amplitude ratio and a decrease in phase shift Influence of capillary zones on tidal responses is restricted to shallow aquifers due to decrease in conductivity with depth Homogeneous solutions estimate mean conductivity well with smaller decay rates of conductivity, but underestimate with larger decay rates

Low-Impact Developments (LIDs), like green roofs and bioretention cells, are vital for managing stormwater and reducing pollution. Amidst climate change, assessing both current and future LID systems is crucial. This study utilizes variably saturated flow modeling with the HYDRUS software (version 4.17) to analyze ten locations in Ontario, Canada, focusing on Toronto. Historical and projected climate data are used in flow modeling to assess long-term impacts. Future predicted storms, representing extreme precipitation events, derived from a regional climate model, were also used in the flow modeling. This enabled a comprehensive evaluation of LID performance under an evolving climate. A robust methodology is developed to analyze LID designs, exploring parameters like water inflow volumes, peak intensity, time delays, runoff dynamics, and ponding patterns. The findings indicate potential declines in LID performance attributed to rising water volumes, resulting in notable changes in infiltration for green roofs (100%) and bioretention facilities (50%) compared to historical conditions. Future climate predicted storms indicate reduced peak reductions and shorter time delays for green roofs, posing risks of flooding and erosion. Anticipated extreme precipitation is projected to increase ponding depths in bioretention facilities, resulting in untreated stormwater overflow and prolonged ponding times exceeding baseline conditions by up to 13 h at numerous Ontario locations.

Study of the saturated‐unsaturated flow in porous media is of interest in many branches of science and engineering. Among the various numerical simulation methods available, the finite difference method is advantageous because it offers simplicity of discretization. This method has been widely used for simulating saturated‐unsaturated flows. However, the simulation of geometrically complex flow domains requires the use of high‐resolution grids in conventional finite difference models because conventional finite difference discretization assumes an orthogonal coordinate system. This makes a finite difference model computationally less efficient than other numerical models that can treat nonorthogonal grids, such as the finite element model and finite volume model. To overcome this disadvantage, we use a coordinate transformation method and develop a multidimensional finite difference model for simulating saturated‐unsaturated flows; this model can treat nonorthogonal grids. The cross‐derivative terms derived by the coordinate transformation method are evaluated explicitly for ease of coding. Therefore, a 7 point stencil is used for implicit terms in the iterative calculation, as in the case of conventional finite difference models with an orthogonal grid. We assess the performance of the proposed model by carrying out test simulations. We then compare the simulation results with dense grid solutions in order to evaluate the numerical accuracy of the proposed model. To examine the performance of the proposed model, we draw a comparison between the simulation results obtained using the proposed model and the results obtained by using (1) a model in which all terms are considered fully implicitly, (2) a finite element model, and (3) a conventional finite difference model with a high‐resolution orthogonal grid.

The use of pumped two-phase cooling to improve the thermal management of insulated gate bipolar transistor (IGBT) in rail transportation is a novel cooling technology. An experimental investigation on pumped two-phase cold plate of IGBT used in HXD1C locomotives was conducted at a mass flow rate of 0.1 kg/s–0.29 kg/s and a heat flux of 6.2 W/cm2, with R245fa as the working fluid. The experimental results showed that the base temperature nonuniformity can be controlled within 2.2 °C at flow rates of 0.14 kg/s and 0.19 kg/s, which is of great benefit to the reliability of IGBT. Based on well known correlations for saturated flow boiling in tubes, an analytical model was developed and compared with the experimental data. The model could predict the base temperature data within an error band of ±3 °C, as well as capture the trend of base temperature as a function of vapour quality and mass flow rate. The performance of the pumped two-phase cold plate of IGBT could be further improved with the aid of the developed model.

For the sustainable restoration of wet farm land degraded by the climate change-induced rise of ground water level (GWL) and soil salinity etc., the sheet pipe system is one of the most useful technologies which reduces cultivation obstacles due to the poor drainage by controlling the rapid drainage function and enabling farmers to produce profitable crops. This system is characterized mainly as a perforated polyethylene rolled-band sheet 180 mm in width and 1 mm thick which is drawn into the subsurface layer while transforming a drainage pipe with φ = 50 mm. The major advantage of this system is that since the sheet pipe is installed without trenching, the disturbance of land is minimized and the construction period can be shortened to about 1/4 (which reduces the cost approximately by 50%). In this study, by using the sheet pipe installed miniature-type model soil box, the drainage capacity of the sheet pipe was confirmed as being the same as the pipe-shaped standard drainage pipes. Based on the observations of the saturated–unsaturated flow and the maximum lowering rate of GWL was predicted. Finally, at the farm land wherein the free board of the adjoining canal was limited, the effectiveness of the sheet-pipe system was confirmed.

Subsurface transport of a sorbing contaminant is poorly understood and characterized. Here, a new semi-analytical saturated–unsaturated flow and transport model is coupled to a kinetic sorption algorithm to assess the impact of changes in the subsurface permeability architecture and flow rate on sorption characteristics. The model outputs reveal the pronounced effect of the rate of vertical decline in Ks on the frequency of occurrence and spatial distribution of subsurface sorption as well as the timing and rate of sorbing contaminants discharged into stream. Sorption potential is weakened with infiltration rate. The impact of infiltration rate on the decline in sorption potential becomes more accentuated as the degree of subsurface vertical heterogeneity in saturated hydraulic conductivity increases. Porosity pattern also impacts sorption characteristics; but its effects highly depend upon the degree of vertical heterogeneity in Ks. The results and methodology presented in this paper have potential implications for assessing water quality in integrated groundwater–surface water systems as well as designing remediation systems.

Through linearizing an implicit differencing scheme, several noniterative numerical solutions of Richards’ equation in different forms are derived here. Paniconi et al. ( Water Resources Research , 27 (6), 1147–1163, 1991) have developed a first-order accurate linearization of the head-based Richards’ equation (RE) and a second-order accurate linearization of the implicit-factored head-based RE. Considering other forms of RE, we propose a second-order accurate linearization of the moisture-based RE and a second-order accurate linearization of the mixed form RE combined with the primary variable switching technique. Extensive comparisons between the noniterative solutions are conducted through three numerical experiments. Their accuracies, efficiencies, and mass balance behaviors are analyzed. The results indicate that the first-order accurate scheme is not efficient compared to iterative models. The noniterative schemes of head-based RE suffer from the mass imbalance problem without iteration. The linearized moisture-based RE can obtain mass conservative, accurate results effectively, while it may confront numerical problems when the soil approaches saturation. Among these noniterative schemes, the linearized mixed form RE combined with the primary variable switching technique is superior in terms of accuracy, mass balance, and efficiency compared to traditional iterative methods.