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Pedo-transfer functions (PTFs) relate soil/landscape static properties to a wide range of model inputs (e.g., soil hydraulic parameters) that are essential to soil hydrological modeling. Combining PTFs and hydrological models is a powerful strategy allowing the use of soil/landscape static properties for the generalization of large-scale modeling. However, since the spatial scales of soil hydraulic parameters required for model inputs and soil/landscape static properties are often not identical, cross-scale transfer is required, which can be a significant source of errors. Here, we investigate uncertainties in cross-scale transfer and develop an approach that avoids them. The proposed method uses the convolutional neural network (CNN) as a cross-scale transfer approach to directly map soil/landscape static properties to soil hydraulic parameters across different spatial scales. The proposed CNN approach is applied under two different estimation strategies to invert the hydraulic parameters of a soil-water balance model and subsequently the quality of the parameters is assessed. Both synthetical and real-world results around the conterminous United States indicate that in general the employed end-to-end strategy is superior to the two-step strategy. The CNN-based integrated model successfully reduces potential errors in cross-scale transfer and can be applied to other areas lacking information on hydraulic parameters or observations. The proposed method can be extended to improve parameter estimation in earth system models and enhance our understanding of key hydrological processes.

Pedo‐transfer functions (PTFs) relate soil/landscape static properties to a wide range of model inputs (e.g., soil hydraulic parameters) that are essential to soil hydrological modeling. Combining PTFs and hydrological models is a powerful strategy allowing the use of soil/landscape static properties for the generalization of large‐scale modeling. However, since the spatial scales of soil hydraulic parameters required for model inputs and soil/landscape static properties are often not identical, cross‐scale transfer is required, which can be a significant source of errors. Here, we investigate uncertainties in cross‐scale transfer and develop an approach that avoids them. The proposed method uses the convolutional neural network (CNN) as a cross‐scale transfer approach to directly map soil/landscape static properties to soil hydraulic parameters across different spatial scales. The proposed CNN approach is applied under two different estimation strategies to invert the hydraulic parameters of a soil‐water balance model and subsequently the quality of the parameters is assessed. Both synthetical and real‐world results around the conterminous United States indicate that in general the employed end‐to‐end strategy is superior to the two‐step strategy. The CNN‐based integrated model successfully reduces potential errors in cross‐scale transfer and can be applied to other areas lacking information on hydraulic parameters or observations. The proposed method can be extended to improve parameter estimation in earth system models and enhance our understanding of key hydrological processes.

Numerical simulation of unsaturated soil hydrology relies on calibrated soil hydraulic parameters, which are subject to uncertainty due to imperfect information during the inverse modelling. This study investigates the effectiveness of reducing parameter uncertainty using the recently developed Rosetta 3 pedotransfer function. The GLUE method was employed for numerical modeling using the Darcy-Richards equation under two strategies for sampling Mualem-van Genuchten (MvG) parameters: the first uses conventional random generation of MvG parameters (GLUE-random), while the second adopts Rosetta 3 to transfer soil particle composition to MvG parameter (GLUE-Rosetta). Both approaches were used for inverse modeling of 9 typical soils, each with a recommended parameter set defined as true values and associated soil moisture dynamics as observations. The posterior parameters selected with both GLUE-random and GLUE-Rosetta show an equifinality phenomenon. GLUE-random fails to provide well-constrained posterior parameters to recover the pre-defined true values, and its posterior results of soil water characteristic curve (SWCC) and soil hydraulic conductivity function (HCF) are poorly constrained. In contrast, GLUE-Rosetta significantly improves the accuracy of the inversely-estimated soil hydraulic parameters, and the ensemble of posterior SWCC and HCF also encompasses the predefined true curves. The results demonstrate the effectiveness of using Rosetta 3 to reduce the dimensionality of the optimization problem, which results in reliable estimation of soil hydraulic parameters and soil particle compositions. Moreover, GLUE-Rosetta outperforms GLUE-random in predicting soil moisture dynamics under different rainfall intensities. Overall, it is recommended to integrate Rosetta 3 with existing optimization tools to reduce the uncertainty of soil parameters and support more reliable modeling of unsaturated soil hydrology.

Stability analysis of unsaturated landslide deposits requires reliable estimates of soil moisture and pore water pressure. However, modeled soil moisture and pore water pressure contain substantial uncertainties due to imperfect information on soil hydraulic properties. Due to the relatively high dimensionality, commonly used parameter optimization strategies can be significantly affected by equifinality problems. This study investigates the effectiveness of reducing parameter estimation dimensionality using soil pedo-transfer functions. Specifically, we first estimated soil hydraulic parameters using the traditional Generalized Likelihood Uncertainty Estimation (GLUE) method, with parameters randomly drawn from the entire space (refer to as GLUE-random). In a second strategy, we use the Rosetta 3 pedotransfer function to constrain soil hydraulic parameters (refer to as GLUE-Rosetta). The two methods were tested in a typical landslide deposit with in-situ measured soil moisture dynamics for inverse modeling. The GLUE-random estimated soil hydraulic parameters contained substantial uncertainties –resulting in poorly constrained soil water retention curves (SWCC) and hydraulic conductivity functions (HCF). As a result, the uncertainty bands of pore water pressure and slope stability can cross values with several orders of magnitudes. In contrast, GLUE-Rosetta provided well-constrained SWCC and HCF, which significantly reduce the uncertainties in pore water pressure and slope stability estimates. These results suggest that the Rosetta 3 pedotransfer function can significantly improve the reliability of soil hydraulic parameters by reducing the dimensionality of the optimization problem and high-quality prior information of soil hydraulic properties. In conclusion, Rosetta 3 can enhance the reliability of soil parameters estimates and the reliability of subsurface hydrology, which may benefit the development of landslide early-warning systems.

Hydro-pedotransfer functions (PTFs) relate easy-to-measure and readily available soil information to soil hydraulic properties for applications in a wide range of process-based and empirical models, thereby enabling the assessment of soil hydraulic effects on hydrological, biogeochemical, and ecological processes. At least more than four decades of research have been invested to derive such relationships. However, while models, methods, data storage capacity, and computational efficiency have advanced, there are fundamental concerns related to the scope and adequacy of current PTFs, particularly when applied to parameterize models used at the field scale and beyond. Most of the PTF development process has focused on refining and advancing the regression methods, while fundamental aspects have remained largely unconsidered. Most system settings are not captured by existing PTFs, which have been built mostly for agricultural soils in temperate climates. Thus. existing PTFs largely ignorie how parent material, vegetation, land use, and climate affect processes that shape soil hydraulic properties. The PTFs used to parameterise the Richards-Richardson equation are mostly limited to predicting parameters of the van Genuchten-Mualem soil hydraulic functions, despite sufficient evidence demonstrating their shortcomings. Another fundamental issue relates to the diverging scales of derivation and application, whereby PTFs are derived based on laboratory measurements while being often applied at field to regional scales. Scaling, modulation, and constraining strategies exist to alleviate some of these shortcomings in the mismatch between scales. These aspects are addressed here in a joint effort by the members of the International Soil Modelling Consortium (ISMC) Pedotransfer Functions Working Group with the aim to systematise PTF research and provide a roadmap guiding both PTF development and use.

Soil hydrological processes (SHP) support ecosystems, modulate the impact of climate change on terrestrial systems and control feedback mechanisms between water, energy and biogeochemical cycles. However, land-use changes and extreme events are increasingly impacting these processes. In this Review, we describe SHP across scales and examine their links with soil properties, ecosystem processes and climate. Soil structure influences SHP such as infiltration, soil water redistribution and root water uptake on small scales. On local scales, SHP are driven by root water uptake, vegetation and groundwater dynamics. Regionally, SHP are impacted by extreme events such as droughts, floods, heatwaves and land-use change; however, antecedent and current SHP partially determine the broader effects of extreme events. Emerging technologies such as wireless and automated sensing, soil moisture observation through novel synthetic aperture radars satellites, big data analysis and machine learning approaches offer unique opportunities to advance soil hydrology. These advances, in tandem with the inclusion of more key soil types and properties in models, will be pivotal in predicting the role of SHP during global change.

Sensitivity maps of drawdown observations on spatial hydraulic parameters are essential information for hydraulic tomographic analysis. It can guide us to design the optimal cross-hole pumping test strategy. In this study, we show how the sensitivity equation method can be employed to derive analytical sensitivity maps of drawdown observations on spatially variable hydraulic parameters during cross-hole pumping test in a two-dimensional, unbounded aquifer. Unlike previously used adjoint state method, the analytical solutions of the sensitivity maps are not in the forms of complex integration and the properties can be evaluated readily. Moreover, we provide discussions on the essess of adjoint method by comparing the derivation of the close-form solution via the sensitivity equation method and the adjoint equation method.

Soil moisture plays a critical role as an essential component of the global water resources by regulating mass and energy exchange between land surface and atmosphere. Quantification of these exchange processes requires accurate characterization and simulation of soil water movement. Physically-based models (PBMs) and machine learning methods (MLMs) can both be used in soil moisture simulation. However, their performances in soil water simulation have only been compared in a limited number of cases. Moreover, almost all of them are conducted in field studies each with fixed soil, initial condition, and boundary condition. Here, we developed three artificial neural network (ANN) frameworks, and made clearer and more systematic comparisons between them and a PBM—Ross numerical model solving Richards equation and parameter estimation using a data assimilation approach (iterative ensemble smoother, Ross-IES) in synthetic and real-world conditions. Compared with the ANNs, Ross-IES is more significantly affected by physical model uncertainties such as soil heterogeneity, initial and boundary conditions, while both methods are affected by observation noise. For Ross-IES, the errors from boundary conditions and hydraulic parameter conceptualization are found to be more prominent than that of observation noise and therefore are suggested to be identified first. Meanwhile, the ANNs have difficulty in simulating the peaks and troughs of the soil water time series as well as in situations where the soil moisture is constantly saturated. ANNs yield a superior simulation when the nonlinear relationship between the response variables and driving data is weak, while the performance of Ross-IES is governed by the prior soil hydraulic information. In addition, Ross-IES approach requires much higher computational cost than the ANNs. ANN-MS performs best among the three ANN-based machine learning models and demonstrates great data mining ability and robustness against overfitting.

Accurate measurements of soil moisture are essential for hydrological, agricultural and environmental sciences. Among many indirect measurement approaches, Frequency-Domain Reflectometry (FDR) soil moisture sensors are popular but are prone to be affected by many factors (e.g., temperature, bulk density, texture, mineralogy) at different installation sites. To avoid the enormous effort required for site-specific FDR calibration, we propose a calibration-free framework, in which a linear calibration model (that links FDR observation and true soil moisture) is incorporated. Based on the classical bias-blind methods using the ensemble Kalman filter (EnKF) and the iterative ensemble smoother (IES), two such bias-aware data assimilation methods are developed to simultaneously identify the unknown hydraulic and the linear calibration parameters based on uncalibrated FDR observations as well as meteorological data. We thoroughly discuss the effects of various factors (i.e., observation noise and number of observations, ensemble size, number of unknown parameters and two potential model errors) on their performances in the synthetic cases and make an application in a real-world case, besides comparing them with their previous versions simultaneously. In particular, the linear calibration model coupled with IES is more favored. From a pragmatic point of view, we demonstrate the usefulness of the proposed approaches in calibrating the FDR data in an online manner with easily-accessible meteorological data.

Sensitivity maps of drawdown observations on spatial hydraulic parameters are essential information for hydraulic tomographic analysis. It can guide us to design the optimal cross-hole pumping test strategy. In this study, we show how the sensitivity equation method can be employed to derive analytical sensitivity maps of drawdown observations on spatially variable hydraulic parameters during cross-hole pumping test in a two-dimensional, unbounded aquifer. Unlike previously used adjoint state method, the analytical solutions of the sensitivity maps are not in the forms of complex integration and the properties can be evaluated readily. Moreover, we provide discussions on the essess of adjoint method by comparing the derivation of the close-form solution via the sensitivity equation method and the adjoint equation method.

Accurate measurements of soil moisture are essential for hydrological, agricultural and environmental sciences. Among many indirect measurement approaches, Frequency-Domain Reflectometry (FDR) soil moisture sensors are popular but are prone to be affected by many factors (e.g., temperature, bulk density, texture, mineralogy) at different installation sites. To avoid the enormous effort required for site-specific FDR calibration, we propose a calibration-free framework, in which a linear calibration model (that links FDR observation and true soil moisture) is incorporated. Based on the classical bias-blind methods using the ensemble Kalman filter (EnKF) and the iterative ensemble smoother (IES), two such bias-aware data assimilation methods are developed to simultaneously identify the unknown hydraulic and the linear calibration parameters based on uncalibrated FDR observations as well as meteorological data. We thoroughly discuss the effects of various factors (i.e., observation noise and number of observations, ensemble size, number of unknown parameters and two potential model errors) on their performances in the synthetic cases and make an application in a real-world case, besides comparing them with their previous versions simultaneously. In particular, the linear calibration model coupled with IES is more favored. From a pragmatic point of view, we demonstrate the usefulness of the proposed approaches in calibrating the FDR data in an online manner with easily-accessible meteorological data.

Soil moisture plays a critical role as an essential component of the global water resources by regulating mass and energy exchange between land surface and atmosphere. Quantification of these exchange processes requires accurate characterization and simulation of soil water movement. Physically-based models (PBMs) and machine learning methods (MLMs) can both be used in soil moisture simulation. However, their performances in soil water simulation have only been compared in a limited number of cases. Moreover, almost all of them are conducted in field studies each with fixed soil, initial condition, and boundary condition. Here, we developed three artificial neural network (ANN) frameworks, and made clearer and more systematic comparisons between them and a PBM—Ross numerical model solving Richards equation and parameter estimation using a data assimilation approach (iterative ensemble smoother, Ross-IES) in synthetic and real-world conditions. Compared with the ANNs, Ross-IES is more significantly affected by physical model uncertainties such as soil heterogeneity, initial and boundary conditions, while both methods are affected by observation noise. For Ross-IES, the errors from boundary conditions and hydraulic parameter conceptualization are found to be more prominent than that of observation noise and therefore are suggested to be identified first. Meanwhile, the ANNs have difficulty in simulating the peaks and troughs of the soil water time series as well as in situations where the soil moisture is constantly saturated. ANNs yield a superior simulation when the nonlinear relationship between the response variables and driving data is weak, while the performance of Ross-IES is governed by the prior soil hydraulic information. In addition, Ross-IES approach requires much higher computational cost than the ANNs. ANN-MS performs best among the three ANN-based machine learning models and demonstrates great data mining ability and robustness against overfitting.

Soil, through its various functions, plays a vital role in the Earth's ecosystems and provides multiple ecosystem services to humanity. Pedotransfer functions (PTFs) are simple to complex knowledge rules that relate available soil information to soil properties and variables that are needed to parameterize soil processes. In this paper, we review the existing PTFs and document the new generation of PTFs developed in the different disciplines of Earth system science. To meet the methodological challenges for a successful application in Earth system modeling, we emphasize that PTF development has to go hand in hand with suitable extrapolation and upscaling techniques such that the PTFs correctly represent the spatial heterogeneity of soils. PTFs should encompass the variability of the estimated soil property or process, in such a way that the estimation of parameters allows for validation and can also confidently provide for extrapolation and upscaling purposes capturing the spatial variation in soils. Most actively pursued recent developments are related to parameterizations of solute transport, heat exchange, soil respiration, and organic carbon content, root density, and vegetation water uptake. Further challenges are to be addressed in parameterization of soil erosivity and land use change impacts at multiple scales. We argue that a comprehensive set of PTFs can be applied throughout a wide range of disciplines of Earth system science, with emphasis on land surface models. Novel sensing techniques provide a true breakthrough for this, yet further improvements are necessary for methods to deal with uncertainty and to validate applications at global scale.