Physics-constrained Gaussian process regression for soil moisture dynamics

Li, He; Zhang, Qiuru; Shi, Liangsheng; Wang, Yakun; Wang, Lijun; Hu, Xiaolong; Huang, Kai

doi:10.1016/j.jhydrol.2022.128779

Cited by 3 publications

(3 citation statements)

References 68 publications

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“…Therefore, more practical numerical solutions which can adapt to a variety of complex initial and boundary conditions (Cui & Zhu, 2018; Mao et al., 2018; Zhang et al., 2016), use more flexible forms of soil and water parameter models (Vanderborght et al., 2017), and also provide better performance for unsteady flows that are difficult with analytical solutions (Cui & Zhu, 2018) are gradually being investigated and developed. However, although the accuracy and reliability of the numerical solution method are sufficiently validated, the uncertainty of the model structure and the demanding requirements on the parameters of the hydraulic and soil characteristic curves limit its application to SM prediction problems (Gupta et al., 2012; He et al., 2022; Pagès et al., 2012).…”

Section: Introductionmentioning

confidence: 99%

“…Kornelsen and Coulibaly (2014) used HYDRUS-1D to generate a large number of physically meaningful samples and added them to the training set as real data. He et al (2022) used the variance of the Gaussian process prediction to characterize the uncertainty of the model and, based on this, assigned different weights to the PM and machine learning and thus obtained a weighted average of fused results of the two methods, achieving a combination of the two models. However, on the one hand these studies tend to use simpler structured machine learning methods and are less involved in deep learning methods with more complex structures, better fitting abilities, and more representativeness; on the other hand, these studies focus on artificially expanding the data in the training set for the combined framework of physical mechanisms and data-driven methods or implementing physical mechanisms embedded in machine learning from a statistical point of view.…”

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confidence: 99%

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A Deep Learning Approach Based on Physical Constraints for Predicting Soil Moisture in Unsaturated Zones

Wang,

et al. 2023

Water Resources Research

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Water transport in the unsaturated zone is an important part of the hydrological cycle and is the link between the atmosphere‒soil‐groundwater for material and energy transport. The accurate prediction of soil moisture (SM) is essential for the rational exploitation of water resources. Data‐driven deep learning methods are widely used in many fields; however, the lack of physical mechanisms limits their application in hydrological fields, especially for SM prediction in unsaturated zones. To solve this problem, this study proposes a new deep learning method that introduces the water balance principle, Richard's equation, and SM boundary conditions as constraints to construct the new loss function that guides the training process of deep learning, called physics‐informed deep learning (PIDL). In tests consisting of a large number of data sets acquired from in situ observation sites in the field, PIDL exhibits higher accuracy than ordinary deep learning (long short‐term memory) and physical models, with 51.03% and 53.46% reduction in root mean square error of SM prediction, respectively. PIDL performance significantly improved in predicting scenarios that are difficult for ordinary deep learning to handle, such as sparse data sets, extreme values, and mutated values. In addition, PIDL maintains high accuracy over a longer prediction period. The addition of physical mechanisms allows deep learning to mine patterns not only from the data itself but also from a priori physical theoretical knowledge for guidance, and this hybrid modeling approach can also be generalized to prediction problems in other hydrological domains.

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Section: Introductionmentioning

confidence: 99%

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confidence: 99%

A Deep Learning Approach Based on Physical Constraints for Predicting Soil Moisture in Unsaturated Zones

Wang,

et al. 2023

Water Resources Research

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“…The temporal dynamics of soil moisture are typically considered as a stochastic process, which is mainly driven by stochastic precipitation events [6,7]. Lots of investigations into temporal variations and the time stability of soil moisture with different ecosystems or under different climate conditions were carried out through ground or remote sensing-based data [8][9][10][11][12][13]. Stochastic soil moisture dynamic models were developed for different conditions of soil, topography, and vegetation [14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Spatial and Temporal Variations in Soil Moisture for a Tamarisk Stand under Groundwater Control in a Hyper-Arid Region

Yi,

Luo,

Wang

et al. 2023

Water

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In hyper-arid regions, soil moisture’s role in ecohydrological processes can differ significantly from that in arid or semi-arid ecosystems. We investigated the spatial–temporal dynamics of soil moisture and its relationship with groundwater depths in a 200 m × 300 m phreatophytic tamarisk stand in the lower basin of the Tarim River, a hyper-arid zone in China. Soil moisture profiles, from the surface to the water table, were derived using drilling and oven-drying techniques. Over a three-year period, the soil moisture at multiple depths was continuously monitored in a specific plot using nine frequency domain reflectometry (FDR) sensors. Our results indicate a correlation between horizontal variations in soil moisture and groundwater depths (GWDs). Nevertheless, anomalies in this correlation were observed. Variations in horizontal soil moisture were strongly influenced by the clay content in the soil, with finer soils retaining more moisture. Despite varying GWDs, soil moisture profiles remained consistent, with no distinct correlation between them. Soil moisture exhibited stability across layers, with noticeable changes only adjacent to the water table. These results imply that in hyper-arid environments, soil texture primarily governs soil moisture distribution. However, the limited spatial and temporal scopes in our dataset, constrained by the region’s inhospitable conditions, necessitate further investigation. Future work should prioritize amalgamating diverse data sources to devise a region-specific soil moisture model for in-depth analysis of hyper-arid regions.

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A Review of Root Zone Soil Moisture Estimation Methods Based on Remote Sensing

Li,

Sun,

Zhao

2023

Remote Sensing

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Root zone soil moisture (RZSM) controls vegetation transpiration and hydraulic distribution processes and plays a key role in energy and water exchange between land surface and atmosphere; hence, accurate estimation of RZSM is crucial for agricultural irrigation management practices. Traditional methods to measure soil moisture at stations are laborious and spatially uneven, making it difficult to obtain soil moisture data on a large scale. Remote sensing techniques can provide soil moisture in a large-scale range, but they can only provide surface soil moisture (SSM) with a depth of approximately 5–10 cm. In order to obtain a large range of soil moisture for deeper soil layers, especially the crop root zone with a depth of about 100–200 cm, numerous methods based on remote sensing inversion have been proposed. This paper analyzes and summarizes the research progress of remote sensing-based RZSM estimation methods in the past few decades and classifies these methods into four categories: empirical methods, semi-empirical methods, physics-based methods, and machine learning methods. Then, the advantages and disadvantages of various methods are outlined. Additionally an outlook on the future development of RZSM estimation methods is made and discussed.

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Physics-constrained Gaussian process regression for soil moisture dynamics

Cited by 3 publications

References 68 publications

A Deep Learning Approach Based on Physical Constraints for Predicting Soil Moisture in Unsaturated Zones

A Deep Learning Approach Based on Physical Constraints for Predicting Soil Moisture in Unsaturated Zones

Spatial and Temporal Variations in Soil Moisture for a Tamarisk Stand under Groundwater Control in a Hyper-Arid Region

A Review of Root Zone Soil Moisture Estimation Methods Based on Remote Sensing

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