Data assimilation for estimating the terrestrial water budget using a constrained ensemble Kalman filter

A procedure is developed to incorporate equality constraints in Kalman filters, including the ensemble Kalman filter (EnKF), and is referred to as the constrained ensemble Kalman filter (CEnKF). The constraint is carried out as a two-step filtering approach, with the first step being the standard (ensemble) Kalman filter. The second step is the constraint step carried out by another Kalman filter that optimally redistributes any imbalance from the first step. The CEnKF is implemented over a 75 000 km₂ domain in the southern Great Plains region of the United States, using the terrestrial water balance as the constraint. The observations, consisting of gridded fields of the upper two soil moisture layers from the Oklahoma Mesonet system, Atmospheric Radiation Measurement Program Cloud and Radiation Testbed (ARM-CART) energy balance Bowen ratio (EBBR) latent heat estimates, and U.S. Geological Survey (USGS) streamflow from unregulated basins, are assimilated into the Variable Infiltration Capacity (VIC) land surface model. The water balance was applied at the domain scale, and estimates of the water balance components for the domain are updated from the data assimilation step so as to assure closure.