# B6 - Parameter estimation using a data assimilation system for improved representation of clouds

*Principal investigator: Dr. Tijana Janjic-Pfander*

*Other researcher: Yvonne Ruckstuhl (PhD)*

For the transport of heat and moisture, for the build up of CAPE, and the initiation of convection, accurate surface fluxes as well as a proper parameterization of the boundary layer are required. Numerical weather prediction (NWP) models usually have limited skill in the boundary layer owing to errors in the land surface boundary conditions, surface fluxes and parameterization of vertical mixing. The calculation of surface fluxes and vertical mixing depends on very crude estimated parameters such as the roughness lengths and the turbulent length scale. Modest changes to these parameters can significantly affect the initialization and development of clouds in numerical models.

In this project, we intend to use data assimilation to objectively estimate relevant parameters and quantify their uncertainty. Our focus is on reducing uncertainty in the representation of the surface fluxes, with the goal of understanding what leads to more accurate representation of convective clouds in the non-hydrostatic, convection-permitting COSMO-DE model.

Ensemble data assimilation offers the possibility to estimate the NWP model parameters and their model error structure from observations. The parameter and state estimation can be done jointly by means of state space augmentation. Furthermore, the cumulative time-varying model error structure can be determined in the assimilation framework by estimating unknown properties of the model error covariance, for example, the variance and length scale.

However, two difficulties are associated with the estimation of model parameters and their error covariances. One is the strong nonlinear coupling between the parameters and model equations and the second is that the parameters are usually restricted to a certain value range. Due to these properties, a data assimilation method such as the EnKF that relies on Gaussian assumptions needs to be modified in order to be able to deal with probability density functions poorly approximated by the normal distribution. In a recent work we have shown that for state estimation the inclusion of constrained estimation can improve ensemble Kalman filter results even in cases of non-Gaussian error statistics. The new method is based on the ensemble Kalman filter algorithm and on quadratic programming. The solution of this hybrid algorithm exactly conserves linear equality and inequality constraints, thus maintaining non-negativity. This algorithm will be tested for parameter estimation together with other recently developed algorithms that use higher order moments, on a common test case designed for convective scale application.

Further, in this project we will develop an ensemble-based data assimilation algorithm that estimates parameters within the Km-scale Ensemble Data Assimilation (KENDA) system of DWD for the regional model COSMO-DE. Although the algorithm itself could be used for the estimation of any parameter in the numerical weather prediction model, we focus on parameters in surface and boundary layer schemes. Two issues that will be addressed are: (a) the methodology of the nonlinear parameter estimation problem within the ensemble Kalman filter framework, and (b) the effect of turbulence closure parameters on the representation of clouds. The results will be verified with Meteosat Second Generation visible (VIS) and near-infrared (NIR) satellite reflectance observations.