Kalman
Filter:
One-dimensional using linearized soil moisture forecasting equations, ignoring infiltration, evaporation, and transpiration.
A linearization of the observation operator (relating surface soil moisture to the model surface excess, root-zone excess, and catchment deficit prognostics) using a Taylor series expansion.
Specifics:
Standard
Kalman Filter Forecasting Equations:
States: Xn+1/n=AXn/n
+ Un+(wn)
Covariance: Σn+1/n = AnΣn/nAT+Qn
Observation
Equation
Z=HXn + (v)
Updating
Equations:
States: Xn+1/n+1=Xn+1/n+Kn+1 (Zn+1-Hn+1Xn+1/n)
Covariance: Σn+1/n+1 = (I-Kn+1Hn+1)Σn+1/n