Research papersA generalized Gaussian distribution based uncertainty sampling approach and its application in actual evapotranspiration assimilation

- Uncertainties of state variables are sampled by generalized Gaussian distribution.
- A common assimilation equation is derived with the outlined sampling method.
- Assimilated actual evapotranspiration and state variables agree with in-situ values.

It is extremely important for ensemble based actual evapotranspiration assimilation (AETA) to accurately sample the uncertainties. Traditionally, the perturbing ensemble is sampled from one prescribed multivariate normal distribution (MND). However, MND is under-represented in capturing the non-MND uncertainties caused by the nonlinear integration of land surface models while these hypernormal uncertainties can be better characterized by generalized Gaussian distribution (GGD) which takes MND as the special case. In this paper, one novel GGD based uncertainty sampling approach is outlined to create one hypernormal ensemble for the purpose of better improving land surface models with observation. With this sampling method, various assimilation methods can be tested in a common equation form. Experimental results on Noah LSM show that the outlined method is more powerful than MND in reducing the misfit between model forecasts and observations in terms of actual evapotranspiration, skin temperature, and soil moisture/ temperature in the 1st layer, and also indicate that the energy and water balances constrain ensemble based assimilation to simultaneously optimize all state and diagnostic variables. Overall evaluation expounds that the outlined approach is a better alternative than the traditional MND method for seizing assimilation uncertainties, and it can serve as a useful tool for optimizing hydrological models with data assimilation.