À Trous Wavelet Based Four-Dimensional Evapotranspiration Assimilation

Generalized Gaussian distribution (GGD) can more accurately model the uncertainties involved in evapotranspiration assimilation than Normal distribution for ensemble based assimilation methods. In this paper, GGD derived perturbing samples are introduced to track the flow characteristics of the uncertainties in four-dimensional variational assimilation (4Dva) after the parameters of GGD are estimated from the coefficients of à trous wavelet transform (AWT) using global convergence method. For dissecting the contribution of the multiscale nature of the uncertainties on 4Dva, cost function is in advance converted with AWT from time domain to frequency domain by using wavelet profile as the constraint. Then, the unmatch of background field from model solution is approximated with a linear combination of the perturbing samples, with which the implicit optimization problem is transformed into an explicit one. Finally, assimilated variables are updated by executing multiscale Kalman filter in frequency domain. The outlined method avoids the tangent linear models required in 4Dva so that it can be easily implemented. Evapotranspiration assimilations in Noah prove that the outlined method performs much better than ensemble Kalman filter and 4Dva derived 4DLETKF when there are errors in background initial field or the forcing.