Data assimilation (DA) provides optimal combination of model simulation results with observed values. There are four sources of uncertainty for any DA: 1) inherent uncertainty from limitations of scientific knowledge, 2) data insufficiency, which is insufficient information content in target observations for history matching-constrained parameter selection, 3) observation or measurement error, and 4) model representation error. Null space sensitivity analysis is a technique to examine data sufficiency. Sensitivity is the variation in model solution values due to variability, or uncertainty, in one or more parameter values. Parameters are in the null space when their variation causes minimal change to history matching skill during assimilation. As a result, null space parameters can be set to any value, constrained only by professional judgement, to produce a best fit model. Null space parameters that generate significant changes to important model predictions are however diagnostic of data insufficiency. We present a new null space sensitivity analysis for the iterative ensemble smoother (iES) algorithm, which provides an ensemble method for DA, in PEST++. A fundamental advantage of iES is computational efficiency through efficient and empirical sampling of posterior parameter distributions. Our new method leverages uncertainty analysis post-assimilation rather than robust Monte Carlo sampling, which is computationally expensive, to determine empirical parameter sensitivity and maintain the computational advantages of iES. Sensitivity analysis is generated by an ensemble of models with insensitive parameters varying across the feasible range of parameter values and sensitive parameters fixed to best-fit model values. The case study application of the null space sensitivity analysis identified data insufficiency leading to limited decision support regarding the amount of groundwater storage in the system, and it demonstrated a more than 97% reduction in computational requirements relative to the Null Space Monte Carlo (NSMC) method.

Data assimilation (DA) is used to integrate artificial intelligence including machine learning (AI-ML) and process-based models to produce a dynamic operational water balance tool for groundwater management. The management tool is a three-step calculation. In the first step, a traditional process-based 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-based DA approach is the second step and generates updated storage volumes by combining a trained AI-ML model, providing replacement 'measurements' for missing observations, 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 based on AI-ML predictions. Pumping and recharge values are uncertain and unobserved in the study region and can be adjusted without contradicting measurements.