Surrogate modeling for unsaturated infiltration via the physics and equality-constrained artificial neural networks

Machine learning(ML)provides a new surrogate method for investigating groundwater flow dynamics in unsaturated soils.Traditional pure data-driven methods(e.g.deep neural network,DNN)can provide rapid predictions,but they do require sufficient on-site data for accurate training,and lack interpretability to the physical processes within the data.In this paper,we provide a physics and equalityconstrained artificial neural network(PECANN),to derive unsaturated infiltration solutions with a small amount of initial and boundary data.PECANN takes the physics-informed neural network(PINN)as a foundation,encodes the unsaturated infiltration physical laws(i.e.Richards equation,RE)into the loss function,and uses the augmented Lagrangian method to constrain the learning process of the solutions of RE by adding stronger penalty for the initial and boundary conditions.Four unsaturated infiltration cases are designed to test the training performance of PECANN,i.e.one-dimensional(1D)steady-state unsaturated infiltration,1D transient-state infiltration,two-dimensional(2D)transient-state infiltration,and 1D coupled unsaturated infiltration and deformation.The predicted results of PECANN are compared with the finite difference solutions or analytical solutions.The results indicate that PECANN can accurately capture the variations of pressure head during the unsaturated infiltration,and present higher precision and robustness than DNN and PINN.It is also revealed that PECANN can achieve the same accuracy as the finite difference method with fewer initial and boundary training data.Additionally,we investigate the effect of the hyperparameters of PECANN on solving RE problem.PECANN provides an effective tool for simulating unsaturated infiltration.

Infiltration,runoff,and slope stability behaviors of infinite slope with macropores based on an improved Green–Ampt model

Infiltration–runoff–slope instability mechanism of macropore slope under heavy rainfall is unclear.This paper studied its instability mechanism with an improved Green–Ampt(GA)model considering the dual-porosity(i.e.,matrix and macropore)and ponding condition,and proposed the infiltration equations,infiltration–runoff coupled model,and safety factor calculation method.Results show that the infiltration processes of macropore slope can be divided into three stages,and the proposed model is rational by a comparative analysis.The wetting front depth of the traditional unsaturated slope is 17.2%larger than that of the macropore slope in the early rainfall stage and 27%smaller than that of the macropore slope in the late rainfall stage.Then,macropores benefit the slope stability in the early rainfall but not in the latter.Macropore flow does not occur initially but becomes pronounced with increasing rainfall duration.The equal depth of the wetting front in the two domains is regarded as the onset criteria of macropore flow.Parameter analysis shows that macropore flow is delayed by increasing proportion of macropore domain(ω_(f)),whereas promoted by increasing ratio of saturated permeability coefficients between the two domains(μ).The increasing trend of ponding depth is sharp at first and then grows slowly.Finally,when rainfall duration is less than 3 h,ωf andμhave no significant effect on the safety factor,whereas it decreases with increasingωf and increases with increasingμunder longer duration(≥3 h).With the increase ofω_(f),the slope maximum instability time advances by 10.5 h,and with the increase ofμ,the slope maximum instability time delays by 3.1 h.

Estimation and inter-comparison of infiltration models in the agricultural area of the Mitidja Plain, Algeria

Infiltration is an important part of the hydrological cycle, and it is one of the main abstractions accounted for in the rainfall-runoff modeling. The main purpose of this study is to compare the infiltration models that were used to assess the infiltration rate of the Mitidja Plain in Algeria. Field infiltration tests were conducted at 40 different sites using a double ring infiltrometer. Five statistical comparison criteria including root mean squared error(RMSE), normalized root mean squared error(NRMSE), coefficient of correlation(CC), Nash-Sutcliffe efficiency(NSE), and Kling-Gupta efficiency(KGE) were used to determine the best performing infiltration model and to confirm anomalies between predicted and observed values. Then we evaluated performance of five models(i.e., the Philip model, Kostiakov model, Modified Kostiakov model, Novel model, and Horton model) in simulating the infiltration process based on the adjusted performance parameters cited above. Results indicated that the Novel model had the best simulated water infiltration process in the Mitidja Plain in Algeria. However, the Philip model was the weakest to simulate the infiltration process. The conclusion of this study can be useful for estimating infiltration rate at various sites using a Novel model when measured infiltration data are not available and are useful for planning and managing water resources in the study area.

Evaluating Model Effectiveness for Soil Infiltration Attribute: Comparison of Green-Ampt, Horton and Modified Green-Ampt Infiltration Models

Soil infiltration is a very important concept in hydrology as well as irrigation, which plays a vital role in estimating surface runoff and groundwater recharge. It is a complicated process that varies with numerous factors. Accurate estimation of soil infiltration is required for future irrigation, and many other purposes. To estimate the infiltration process, there are numerous models. The majority of them have some presumptions, a unique calculation method, and some limitations. The purpose of the paper was to assess the model’s performance for a similar hypothetical scenario involving soil infiltration. It compared the infiltration rate, runoff rate, and incremental infiltration versus time for three different infiltration models: the Green-Ampt model (GA), the Horton model and the Modified Green-Ampt (MGA) model. A spreadsheet was used to calculate the Horton model, and HYDROL-INF (V 5.03) was used to simulate the other two models. Among those three models, the MGA model outperformed those three models, while the GA model produced greater infiltration rate than rainfall, which was insensible. The study showed that the MGA model, which provides useful infiltration predictions, outperformed the other two infiltration models. Since the Horton model does not consider ponding conditions, it is only applicable when the effective rainfall intensity exceeds the final infiltration capacity. Moreover, the GA model’s initial infiltration rate is irrational because it disregards the intensity of the rainfall. The results of this study will assist in selecting the most accurate method for estimating soil infiltration for agricultural purposes.

Stability analysis of unsaturated soil slope during rainfall infiltration using coupled liquid-gas-solid three-phase model

Generally, most soil slope failures are induced by rainfall infiltration, a process that involves interactions between the liquid phase, gas phase,and solid skeleton in an unsaturated soil slope. In this study, a loosely coupled liquid-gas-solid three-phase model, linking two numerical codes,TOUGH2/EOS3, which is used for water-air two-phase flow analysis, and FLAC^(3D), which is used for mechanical analysis, was established. The model was validated through a documented water drainage experiment over a sandy column and a comparison of the results with measured data and simulated results from other researchers. The proposed model was used to investigate the features of water-air two-phase flow and stress fields in an unsaturated soil slope during rainfall infiltration. The slope stability analysis was then performed based on the simulated water-air two-phase seepage and stress fields on a given slip surface. The results show that the safety factor for the given slip surface decreases first, then increases, and later decreases until the rainfall stops. Subsequently, a sudden rise occurs. After that, the safety factor decreases continually and reaches its lowest value, and then increases slowly to a steady value. The lowest value does not occur when the rainfall stops, indicating a delayed effect of the safety factor. The variations of the safety factor for the given slip surface are therefore caused by a combination of pore-air pressure, matric suction, normal stress, and net normal stress.

Stability analysis of an unsaturated soil slope considering rainfall infiltration based on the Green-Ampt model

Based on the principle of saturated infiltration and the Green-Ampt model,an unsaturated infiltration model for a soil slope surface was established for either constant moisture content,or depth-varying moisture content and the slope.Infiltration parameters in the partially saturated slope were revealed under sustained rainfall.Through analysis of the variation of initial moisture content in the slope,the ponding time,infiltration depth,and infiltration rate were deduced for an unsaturated soil slope subject to rainfall infiltration.There is no ponded water on the surface of the slope under sustained low-intensity rainfall.The results show that the infiltration parameters of an unsaturated slope are influenced by the initial moisture content and the wetting front saturation,the soil cohesion and rainfall intensity under sustained rainfall.More short-term slope failures can occur with the decrease of cohesion of the soil of the slope.The ponding time and infiltration depth differ considering constant or different initial moisture content respectively in the soil slope.Then,best-fit curves of the infiltration rate,ponding time,and infiltration depth to the wetting front saturation were obtained with constant or different initial moisture contents.And the slope failure time is roughly uniform when subject to a rainfall intensity I>5 mm/h.

Applicability of five models to simulate water infiltration into soil with added biochar

As a soil amendment, biochar can reduce soil bulk density, increase soil porosity, and alter soil aggregates and thus affect the infiltration. Researchers have proposed and revised several theoretical models to describe the process of soil infiltration. Although these models have been successfully used to evaluate the soil infiltration in different scenarios in agricultural fields, little effort has been devoted to assess their performances in arid and semi-arid soils after the addition of biochar. A laboratory experiment was performed to study the infiltration characteristics of two typical Loess Plateau soils at three particle sizes（2–1, 1–0.25, and 〈0.25 mm） and five biochar application amounts（0, 10, 50, 100, and 150 g/kg）. The performance of five models（i.e., the Philip model, Kostiakov model, Mezencev model, USDA-NRCS model, and Horton model） in simulating the infiltration process was then evaluated based on the adjusted coefficient of determination and a reduced Chi-Square test. Results indicated that the Horton model best simulated the water-infiltration process in an aeolian sandy soil with added biochar. However, the Mezencev model best simulated the infiltration process in a loamy clay soil（Eum-Orthic Anthrosol）. The three-parameter model, i.e., Mezencev and Horton models can better describe the relationship between cumulative infiltration and infiltration time. In conclusion, biochar reduced the soil infiltration capacity of the aeolian sandy soil and increased that of the Eum-Orthic Anthrosol.

Identification and validation of a pyroptosis-related prognostic model for colorectal cancer based on bulk and single-cell RNA sequencing data

BACKGROUND Pyroptosis impacts the development of malignant tumors,yet its role in colorectal cancer(CRC)prognosis remains uncertain.AIM To assess the prognostic significance of pyroptosis-related genes and their association with CRC immune infiltration.METHODS Gene expression data were obtained from The Cancer Genome Atlas(TCGA)and single-cell RNA sequencing dataset GSE178341 from the Gene Expression Omnibus(GEO).Pyroptosis-related gene expression in cell clusters was analyzed,and enrichment analysis was conducted.A pyroptosis-related risk model was developed using the LASSO regression algorithm,with prediction accuracy assessed through K-M and receiver operating characteristic analyses.A nomo-gram predicting survival was created,and the correlation between the risk model and immune infiltration was analyzed using CIBERSORTx calculations.Finally,the differential expression of the 8 prognostic genes between CRC and normal samples was verified by analyzing TCGA-COADREAD data from the UCSC database.RESULTS An effective pyroptosis-related risk model was constructed using 8 genes-CHMP2B,SDHB,BST2,UBE2D2,GJA1,AIM2,PDCD6IP,and SEZ6L2(P<0.05).Seven of these genes exhibited differential expression between CRC and normal samples based on TCGA database analysis(P<0.05).Patients with higher risk scores demonstrated increased death risk and reduced overall survival(P<0.05).Significant differences in immune infiltration were observed between low-and high-risk groups,correlating with pyroptosis-related gene expression.CONCLUSION We developed a pyroptosis-related prognostic model for CRC,affirming its correlation with immune infiltration.This model may prove useful for CRC prognostic evaluation.

Application of isotopic information for estimating parameters in Philip infiltration model

Minimizing parameter uncertainty is crucial in the application of hydrologic models.Isotopic information in various hydrologic components of the water cycle can expand our knowledge of the dynamics of water flow in the system,provide additional information for parameter estimation,and improve parameter identifiability.This study combined the Philip infiltration model with an isotopic mixing model using an isotopic mass balance approach for estimating parameters in the Philip infiltration model.Two approaches to parameter estimation were compared:(a) using isotopic information to determine the soil water transmission and then hydrologic information to estimate the soil sorptivity,and(b) using hydrologic information to determine the soil water transmission and the soil sorptivity.Results of parameter estimation were verified through a rainfall infiltration experiment in a laboratory under rainfall with constant isotopic compositions and uniform initial soil water content conditions.Experimental results showed that approach(a),using isotopic and hydrologic information,estimated the soil water transmission in the Philip infiltration model in a manner that matched measured values well.The results of parameter estimation of approach(a) were better than those of approach(b).It was also found that the analytical precision of hydrogen and oxygen stable isotopes had a significant effect on parameter estimation using isotopic information.

Use of Kostiakov’s Infiltration Model on Michael Okpara University of Agriculture, Umudike Soils, Southeastern, Nigeria

The main purpose of this study is to obtain the water infiltration parameters of the soils of Michael Okpara University of Agriculture, Umudike. This could be used in simulating infiltration for these soils when designing irrigation projects, thereby saving time and cost of field measurement. Field measurements of infiltration were first made using a double ring infiltrometer. The test lasted for 180 mins in each location. Infiltration values ranged from 0.03 cm/min to 0.1 cm/min. The highest value was obtained in the Forest Block. Kostiakov’s infiltration model was then applied on the field data in order to determine the soils’ infiltration parameters and equations. The model empirical constants or parameters obtained were “m” and “n”. For “m” the values were: 0.53 for the soil of Forest Block, 0.42 for Poultry block, 0.50 for P.G. block, 0.41 for the soils of Staff School and Guest House. The corresponding “n” values were: 1.37, 1.12, 0.37, 1.79, and 1.38. Infiltration equations: 0.4It1.38, 0.4lt1.79, 0.42t1.12, and 0.53t1.37 were determined for the locations. These were used to simulate data which were evaluated by comparing them with the field data. The two data sets showed closed relationships. This implied that the model could be used to simulate water infiltration during irrigation projects in the farms of Michael Okpara University of Agriculture, Umudike.

Comparison and Estimation of Four Infiltration Models

Infiltration is an important component of the hydrological cycle. It provides soil moisture in the vadose zone to support plant growth. This study was conducted to compare the validity of four infiltration models with measured values from the double ring infiltrometer. The parameters of the four models compared were estimated using the linear regression analysis. The C.C was used to show the performance of the predictability of the models. The RMSE, MAE and MBE were employed to check the anomalies between the predicted and the observed values. The results showed that, average values of the C.C ranged from 0.9294 - 0.9852. The average values of the RMSE were 4.0033, &minus;17.489, 11.2400 and 49.8448;MAE were 3.1341, 15.9802, 10.6525, and 61.4736;and MBE were 0.0786, 9.5755, 0.0007 and 47.0204 for Philip, Horton, Green Ampt and Kostiakov respectively for the wetland soils. Statistical results also from the Fisher’s multiple comparison test show that the mean infiltration rate estimated from the Green Ampt’s, Philip’s and Horton’s model was not significantly different (p > 0.05) from the observed. The results indicated that the Kostiakov’s model had the highest deviations as it overestimated the measured data in all the plots. Comparison of the statistical parameters C.C, RMSE, MAE, and MBE for the four models indicates that the Philip’s model agreed well with the measured data and therefore, performed better than the Green Ampt’s, Horton’s and Kostiakov’s models respectively in that order for Besease wetland soils. Estimation of infiltration rate by the Philip’s model is important in the design of irrigation schemes and scheduling. Therefore, in the absence of measured infiltration data, the Philip’s model could be used to produce infiltration information for inland valley bottom soils that exhibit similar characteristic as Besease wetland soils.

Observation and modeling on irregular purple soil water infiltration process

The infiltration process is a critical link between surface water and groundwater. In this research, a specific device to observe infiltration processes in homogeneous and heterogeneous soils with triangular and inverted triangular profiles was designed, and the Green-Ampt model was employed for the process simulation. The results indicate that(1) the wetting front in coarse texture soils transports faster than in fine texture soils;(2) for the homogeneous case, the wetting front in triangularshaped soils transports faster than the inverted triangular type, but the triangular-shaped soils show a lower infiltration rate;(3) in the initial step, the wetting front in triangular-shaped soils shows higher transport speed, but depicts lower speed with increase in the time;(4) both the wetting front and infiltration rate show a significant exponential relation with the time. From these findings, an empirical model was developed which agrees well with the observed data and provides a useful method for this field of soil research.

Modeling of gas phase diffusion transport during chemical vapor infiltration process

In order to improve the uniformity of both the concentration of gaseous reagent and the deposition of matrix within micro pores during the chemical vapor infiltration (CVI) process, a calculation modeling of gas phase diffusion transport within micro pores was established. Taken CH 3SiCl 3 as precursor for depositing SiC as example, the diffusion coefficient, decomposing reaction rate, concentration within the reactor, and concentration distributing profiling of MTS within micro pore were accounted, respectively. The results indicate that, increasing the ratio of diffusion coefficient to decomposition rate constant of precursor MTS is propitious to decrease the densification gradient of parts, and decreasing the aspect ratio (L/D) of micro pore is favorable to make the concentration uniform within pores.

Optimization of the Conceptual Model of Green-Ampt Using Artificial Neural Network Model (ANN) and WMS to Estimate Infiltration Rate of Soil (Case Study: Kakasharaf Watershed, Khorram Abad, Iran)

Determination of the infiltration rate in a watershed is not easy and in empirical and theoretical point of view, it is important to access average value of infiltration. Infiltration models has main role in managing water sources. Therefore different types of models with various degrees of complexity were developed to reach this aim. Most of the estimating methods of soil infiltration are expensive and time consuming and these methods estimate infiltration with hypothesis of zero slope. One of the conceptual and physical models for estimating soil infiltration is Green-Ampt model which is similar to Richard model. This model uses slope factor in estimating infiltration and this is the power point of Green-Ampt model. In this research the empirical model of Green-Ampt was optimized with integrating artificial neural network model (ANN) and a model of geographical information system WMS to estimate the infiltration in Kakasharaf watershed. Results of the comparison between the output of this method and real value of infiltration in region (through multiple cylinders) showed that this method can estimate the infiltration rate of Kakasharaf watershed with low error and acceptable accuracy (Nash-Sutcliff performance coefficient 0.821, square error 0.216, correlation coefficient 0.905 and model error 0.024).

Modeling Water Infiltration and Solute Transfer in a Heterogeneous Vadose Zone as a Function of Entering Flow Rates

Due to its rapid movement, preferential flow (PF) in the vadose zone allows much faster contaminant transport, which may have a significant impact on ground-water quality. PF can occur in heterogeneous vadose zones and it strongly depends on hydric and hydraulic conditions like entering flow rates at surface. This study deals with the modeling of the establishment of PF, and related solute transfer during the infiltration phase in a strongly heterogeneous glaciofluvial deposit. This deposit is made of four contrasting lithofacies (sand, gravel, bimodal gravel and matrix-free gravel) and lies underneath an urban infiltration basin (Lyon, France). Previous studies have been carried out on this site and linked the regionalization of soil pollution with the lithological heterogeneity. But none of them clearly demonstrated how heterogeneity could impact flow and solute transfer and may explain such a regionalization. In this study, we model flow and solute transfer at the trench scale for both uniform and heterogeneous profiles in order to characterize the effect of lithological heterogeneity. In addition, such a modeling was performed for two different entering flow rates to depict the influence of condition at surface on PF. A key result is that heterogeneity clearly impacts unsaturated flow and solute transfer. Numerical modeling permitted pointing out the existence of PF paths associated with the sedimentary heterogeneity of the glaciofluvial deposit. For lower surface fluxes, the sand lens and matrix-free gravel were the sources of capillary barrier effects, leading to a funneled flow and a groundwater recharge characterized by earlier and more dispersed wetting fronts. Such a flow pattern enhances solutes transfer and reduces solute retention by soil. Thus, the effect of heterogeneity on solute transfer is significant, especially for the most reactive solutes.

Adjustment of Infiltration Models in Poorly Developed Soils

Infiltration is a fundamental component of the rainfall-runoff process. It was characterized through the adjustment and comparison of the Smith-Parlange, Green-Amptd, Philip, Horton and Kostiakov equations, using simulated rain in poorly developed soils from three geological formations and from different ages (Marino Fm., Mogotes Fm., quaternary cover). Trials with the rainfall simulator were run in piedmont areas west of the city of Mendoza. Adjustments were performed separately for each of the trials and globally for each surface cover. The adjustment was satisfactory when the observed and the simulated infiltration velocity curves were compared using lumped parameters. The Green-Amptd model exhibited the best behavior for the three covers, while the Smith-Parlange equation was the least accurate, al- though it had little dispersion in the prediction errors. The Kostiakov and Horton equations yielded satisfactory results in view of the fact that the development of the infiltration rate curve was simulated after the impoundment time was determined with the Green-Amptd formula. The Philip model is not consistent, with the exception of the results obtained for the Marino cover. In the post-calibration procedure the parameters showed no noticeable differences with respect to those obtained during calibration. In every case the relative squared error of the infiltration curve was very satisfactory, below 5%.

Estimation of Infiltration Models’ Parameters Using Regression Analysis in Irrigation Fields of Northern Ghana

The quantification of soil infiltration is necessary for the estimation of water accessibility in soils for plant growth and development. Field infiltration tests runs were conducted on agricultural soils in three irrigation sites of Northern Ghana. The field data were fitted into Green and Ampt, Kostiakov, Philip, Holtan, Soil Conservation Service and Horton infiltration models for the determination of the unknown model parameters. Regression analysis at 95% confidence level using GraphPad Prism 8. Laboratory and field data on infiltration were used for the model fitting and the unknown parameters were determined using the calibrated models. The k and n parameters of Kostiakov model at Bontanga study site were found to be k = 28.0027 and n = 0.5902, k = 17.0294 and n = 0.4504 for Golinga and k = 23.0356 and n = 0.6339 for Libga. For all the models, the coefficient of determination ranged from 0.7612 to 0.9876 indicating strong relationships. Only Holtan model gave different values at all the three study sites. The parameter GIa and ic of the Holtan model drawn from hydrologic soil group were the same at all the study sites because of the same vegetative cover and surface conditions. The study observed the values of the parameters to have influenced the models’ performance.

Comparative modeling of gas transport in isothermal chemical vapor infiltration process of C/SiC composites

Two comparative models taking into account of momentum, energy and mass transport coupled with chemical reaction kinetics were proposed to simulate gas transport in isothermal CVI reactor for fabrication of C/SiC composites. Convection in preform was neglected in one model where momentum transport in preform is neglected and mass transport in preform is dominated by diffusion. Whereas convection in preform was taken into account in the other model where momentum transport in preform is represented by BRINKMAN equations and mass transport in preform includes both diffusion and convection. The integrated models were solved by finite element method. The calculation results show that convection in preform have negligible effect on both velocity distribution and concentration distribution. The difference between MTS molarities in preform of the two models is less than 5×10-5, which indicates that ignorance of convection in preform is reasonable and acceptable for numerical simulation of ICVI process of C/SiC composites.

Comparison of models to predict air infiltration rate of buildings with different surrounding environments

The air infiltration rate of buildings strongly influences indoor environment and energy consumption.In this study,several traditional methods for determining the air infiltration rate were compared,and their accuracy in different scenarios was examined.Additionally,a method combining computational flow dynamics(CFD)with the Swami and Chandra(S-C)model was developed to predict the influence of the surrounding environment on the air infiltration rate.Two buildings in Dalian,China,were selected:one with a simple surrounding environment and the other with a complex surrounding environment;their air infiltration rates were measured.The test results were used to validate the accuracy of the air infiltration rate solution models in different urban environments.For the building with a simple environment,the difference between the simulation and experimental results was 0.86%–22.52%.For the building with a complex environment,this difference ranged from 17.42%to 159.28%.We found that most traditional models provide accurate results for buildings with simple surrounding and that the simulation results widely vary for buildings with complex surrounding.The results of the method of combining CFD with the S-C model were more accurate,and the relative error between the simulation and test results was 10.61%.The results indicate that the environment around the building should be fully considered when calculating the air infiltration rate.The results of this study can guide the application of methods of determining air infiltration rate.