By taking the soil moisture as a proxy in the modelling, a neural network is designed to capture those impact factors of soil water storage capacity and their nonlinear interaction implicitly without knowing the underlying soil hydrologic processes. An internal vector of the proposed neural network assimilates the soil moisture response to meteorological conditions and is regulated as the profile of the soil water storage capacity. Different from static single value indicators, the profile vector can describe the amount of water that a soil can hold under various moisture levels over a range of time periods. Moreover, the trained model can be deployed as an alternative to the expensive sensor networks for continuous soil moisture monitoring.
Soil moisture represents the water content of the soil, which is strongly affected by the storage and movement of water in the soil. Several indicators have been proposed to infer the ability of holding water in soil such as saturated water content and field capacity. However, these indicators are static measurements of the amount of water in the soil at a specific time. They do not take into account the variability in soil moisture and the changes in soil properties or climatic conditions over time. The same weaknesses are also shared in a soil water characteristic curve (SWCC), which represents a single snapshot of the soil’s water-holding capacity at a given point in time. Water storage capacity of soil, on the other hand, is not limited to a specific point in time. It describes the amount of water that a soil can hold under various moisture levels over a range of time periods. It takes soil dynamics into account as well as environmental factors, such as precipitation, evapotranspiration, etc.; thus, the modelling of water storage capacity becomes very complicated and difficult. For example, the space between soil particles can be filled with water as well as air, the physicochemical interactions between soil and water can alter the density of soil water, and the relationship between soil moisture and runoff responses can be nonlinear and is attributed to many factors such as topography, soil properties, vegetation, etc. 
. Many methods have been proposed to model the water storage capacity of soil from various perspectives, such as pore geometry 
, soil physical properties 
, initial wetness conditions 
, soil texture and organic matter 
, hydrological soil properties 
, etc. However, it is impossible to take all impact factors explicitly into account in a model.
Recently, the data-driven approach, which infers soil information directly from the data without considering the underlying physical processes, has become popular. The proposed neural network is based on LSTM, a type of recurrent neural network capable of capturing highly nonlinear relationships and handling long-term dependencies in sequential data. The neural network takes the meteorology data as predictor variables and the in situ soil moisture as target variables. Seven months of in situ soil moisture data from 10 capacitance-based sensors deployed on 10 experimental sites, together with corresponding meteorology data, are collected to build the models. The cell state vectors in the built LSTM models are then extracted out as the profiles of the soil water storage capacity for the 10 sensor sites.
2. Soil Hydrology Modelling
Water storage and drainage in soil are essential steps in the hydrologic cycle. Nachabe et al. 
introduced a model to estimate soil water storage capacity using observations of shallow water table fluctuations and soil moisture in shallow, sandy soil. However, the estimation requires the consideration of many impact factors explicitly such as encapsulated air, the capillary fringe, and soil texture heterogeneity. Sheikh et al. 
introduced a simple two-layer soil water balance model to predict soil moisture, which utilizes daily meteorological records, soil physical properties, basic crop characteristics, and topographical data. The root mean squared error of predicted soil moisture content for their experimental locations ranged from 0.011 to 0.065 cm3cm−3cm3cm−3
. Alves et al. 
suggested a model to predict the soil water characteristic curve based on pore-scale analysis and three-dimensional approximations of pore geometry using unit cells. The proposed model considers the effect of particle size and packing porosity on retention and provides reasonable results for drying SWCCs, offering a general approach that may be modified in the future.
In general, rainfall–runoff models are the standard tools used for investigating hydrological processes 
. Matteo 
reconstructed the SWCC with the Soil Water Characteristic software 
to understand the infiltration processes in unsaturated soils. Song and Wang 
conducted artificial rainfall–runoff experiments to investigate the nonlinear patterns of rainfall–runoff response. The study found that soil moisture data can provide valuable insights into the processes of runoff generation in hydrology. Singh et al. 
also revealed that soil moisture responses are influenced by a combination of storm properties and landscape characteristics, which in turn affect the relationship between soil moisture and runoff during storms.
3. Long Short-Term Memory Modelling
Long short-term memory (LSTM) is an artificial neural network for sequence modelling 
. Li et al. 
built a data-driven model with LSTM for streamflow prediction on a 15-minute scale using precipitation as the only input. Compared to the process-driven gridded surface subsurface hydrologic analysis (GSSHA) model, the data-driven model is clearly more efficient and robust in terms of prediction and calibration. Li et al. 
developed an attention-aware LSTM model for soil moisture and soil temperature prediction. They experimented with 1 day and 7 days flux tower data in a sequence for the soil moisture prediction and obtained the root mean squared errors of 10 experiment sites from 1.1781.178
at the lead time of 1 day. O and Orth 
trained an LSTM model to extrapolate daily soil moisture dynamics in space and in time, based on in situ data collected from more than 1000 stations across the globe. The daily meteorological time series and static features obtained from both reanalysis and remote sensing datasets were used as the inputs to the LSTM, and the adjusted in situ soil moisture measurements were used as the training targets. Fang and Shen 
trained LSTM with sequences of climatic forcings and physiographic attributes, such as soil properties and land cover attributes, and targetedthe Soil Moisture Active Passive (SMAP) L3 passive radiometer product for near-real-time forecasts of SMAP-based soil moisture.
Kratzert et al. 
pointed out that the internal cell states of LSTM can be interpreted as some kind of storage such as snow accumulation, soil water content, or groundwater storage. They trained a regional hydrological model using LSTM to investigate the potential of LSTM for simulating runoff from meteorological observations, and demonstrated that the evolution of a cell state in the LSTM matches the dynamics of the temperature as well as the understanding of snow accumulation and snow-melt. Lees et al. 
further investigated what information the LSTM captures about the hydrological system and argued that LSTMs can be used to gain an estimate of intermediate stores of water. In their study, it was shown that the state cell vector of the LSTM reflects known hydrological concepts such as soil water storage and snow processes, which are important for discharge generation.