Revising the ensemble-based Kalman filter covariance for the retrieval of deep-layer soil moisture

However, it remains a challenging issue to provide good estimates of soil moisture in the deep layers, because the error correlation between the surface and deep layers is low and hence is easily influenced by the physically limited range of soil moisture, probably resulting in a large noise-to-signal ratio.

Furthermore, the temporally correlated errors between the surface and deep layers and the nonlinearity of the system make the retrieval even more difficult. To tackle these problems, a revised ensemble-based Kalman filter covariance method is proposed by constraining error covariance estimates in deep layers in two ways: 1) explicitly using the error covariance at the previous time step and 2) limiting the increase of the soil moisture error correlation with the increase of the vertical distance between the two layers.