Resumen
A three-step data assimilation (DA) of deep learning (DL) predictions to a process-based water budget is developed and applied to produce an active, operational water balance for groundwater management. In the first step, an existing water budget model provides forward model predictions of aquifer storage from meteorological observations, estimates of pumping and diversion discharge, and estimates of recharge. A Kalman filter DA approach is the second step and generates updated storage volumes by combining a long short-term memory (LSTM) network, a DL method, and predicted ?measurements? with forward model predictions. The third ?correction? step uses modified recharge and pumping, adjusted to account for the difference between Kalman update storage and forward model predicted storage, in forward model re-simulation to approximate updated storage volume. Use of modified inputs in the correction provides a mass-conservative water budget framework that leverages DL predictions. LSTM predictor ?measurements? primarily represent missing observations due to missing or malfunctioning equipment. Pumping and recharge inputs are uncertain and unobserved in the study region and can be adjusted without contradicting measurements. Because DL requires clean and certain data for learning, a common-sense baseline facilitates interpretation of LSTM generalization skill and accounts for feature and outcome uncertainty when sufficient target data are available. DA, in contrast to DL, provides for explicit uncertainty analysis through an observation error model, which allows the integrated approach to address uncertainty impacts from an LSTM predictor developed from limited outcome observations.