Flow-dependent large-scale blending for limited-area ensemble assimilation

Limited-area models (LAMs) often suffer from degradation in their representation of large-scale features compared to that of global models (GMs) due to the restricted domain size and limited observational coverage. To address this, we propose a novel flow-dependent large-scale blending (LSB) method for LAM data assimilation (DA). LSB methods incorporate large-scale information from a GM into the LAM DA system using scale-dependent weights. Our approach, termed as nested EnVar, extends the previously proposed static variational LSB method (nested 3DVar) to an ensemble-based framework. Unlike static LSB methods, nested EnVar simultaneously assimilates both observational and large-scale GM information into LAM forecasts with dynamically adjusting the weight given to GM information based on its estimated flow-dependent uncertainty. 

Through idealized assimilation experiments using a nested system of simplified chaotic models with a single spatial dimension, we demonstrate that nested EnVar effectively reduces large-scale errors in LAM DA as existing LSB methods, and offers better forecasts than GM downscaling. Compared to both traditional DA and other LSB methods, nested EnVar provides more accurate analyses and forecasts when dealing with dense and unevenly distributed observations. By dynamically accounting for GM uncertainty, nested EnVar improves the stability and accuracy of the analysis across scales. 

Our findings suggest that nested EnVar offers a promising alternative to traditional LSB methods for high-resolution simulations of complex, hierarchically structured phenomena. This novel approach has the potential to enhance the effectiveness of high-resolution LAM DA for spatially localized convective-scale observations.