Water retention curve (WRC) and hydraulic conductivity function (HCF) are essential information to model the movement of water in the soil using the Richardson-Richards equation (RRE). Although laboratory measurement methods of WRC and HCF have been well established, the lab-based WRC and HCF can not be used to model soil moisture dynamics in the field because of the scale mismatch. Therefore, it is necessary to derive the inverse solution of the RRE and estimate WRC and HCF from field measurement data. We are proposing a physics-informed neural networks (PINNs) framework to obtain the inverse solution of the RRE and estimate WRC and HCF from only volumetric water content measurements. The PINNs was constructed using three feedforward neural networks, two of which were constrained to be monotonic functions to reflect the monotonicity of WRC and HCF. The PINNs was trained using noisy synthetic volumetric water content data derived from the simulation of soil moisture dynamics for three soils with distinct textures. The PINNs could reconstruct the true soil moisture dynamics from the noisy data. As for WRC, the PINN could not precisely determine the WRCs. However, it was shown that the PINNs could estimate the HCFs from only the noisy volumetric water content data without specifying initial and boundary conditions and assuming any information about the HCF (e.g., saturated hydraulic conductivity). Additionally, we showed that the PINNs framework could be used to estimate soil water flux density with a broader range of estimation than the currently available methods.

Potential evapotranspiration (ETp), defined as the amount of water that would be lost by evaporation and transpiration from an area in the absence of water limitation, is an import hydrometeorological variable. Accurate estimation ETp is critical for a wide range of applications including predictions of, irrigation water requirement, groundwater recharge, stream discharge, drought and wildfires. Long-term change in ETp is considered an indicator of the impact of climate change on ecosystem functioning. A wide range of physically-based and empirical models have been developed to estimate ETp. These methods can be explained in terms of their complexity data requirements. The most complex and demanding models (e.g., Penmann-Montheith) require measurements of radiation, temperature, windspeed, and vapor pressure and have been shown to provide very close approximation of physically measured ET from unstressed systems. On the other extreme, the simplest models require only temperature data (e.g., Thornthwaite, 1948) and are the most commonly implemented. However, without site-specific calibration, methods that depend solely on temperature achieve only modest accuracy. Here we present a machine-learning (ML) approaches that utilize hourly and sub-hourly temperature records to produce predictions that are comparable with the more complex methods that require full meteorological datasets. Specifically, we show that ML algorithms can learn the patterns of temperature fluctuations that are related to attenuation of potential solar radiation. We anticipate the approach developed here will be valuable for estimation of historical ETp as well as for short-term forecasting using temperature forecasts.