Can AROME-Austria Hybrid-3DEnVar improve the forecast of 2-meter temperature (T2m) in complex Alpine terrain?

An accurate forecast of T2m in complex terrain is essential for a wide range of economic and societal applications. However, improper assimilation of T2m observations can degrade forecast quality. 
The 3DVar scheme relies on a climatological error covariance matrix, which can produce unrealistic analysis increments and consequently inaccurate forecasts, particularly over sloped terrain. For example, an observation from a valley station may still generate increments at the mountaintop, even though the valley observation does not adequately represent the atmospheric conditions at the mountaintop. In contrast, 3DEnVar utilizes flow-dependent error covariances that are representative of the recent atmospheric flow regime. Hybrid-3DEnVar, on the other hand, employs an error covariance with 50\% weight assigned to the climatological covariance matrix and 50\% to the flow-dependent covariance matrix. Hybrid-3DEnVar has been tested in AROME-Austria and improved the initial conditions of AROME-Austria compared to 3DVar.  
Our study compares the T2m forecast of  Hybrid-3DEnVar against the operational 3DVar scheme of AROME-Austria in complex terrain.
For this purpose, we utilize the convective-scale limited-area ensemble forecast system (C-LAEF) Alpe Adria based on the numerical weather prediction model AROME, which operates at a horizontal grid space of 1 km. The 32-member ensemble of C-LAEF Alpe Adria (with a 1 km horizontal resolution) provides the flow-dependent error covariances. 
We conduct three sets of data denial experiments in which we run a 3-hourly assimilation cycle over 10 days, once with all observations and once with the T2m measurements removed. The first set of experiments uses 3DVar, the second 3DEnVar, and the third Hybrid-3DEnVar. We present first-guess departure statistics and forecast verification for T2m over the Alpine terrain.