Data Assimilation of Lightning using 1D+3D/4D WRF Var Assimilation Schemes with Non-Linear Observation Operators

NASA's launch of the GOES-R Lightning Mapper (GLM) in 2015 will provide continuous, full disc, high resolution total lightning (IC + CG) data. The data will be available at a horizontal resolution of approximately 9 km. Compared to other types of data, the assimilation of lightning data into operational numerical models has received relatively little attention. Previous efforts of lightning assimilation mostly have employed nudging.

This paper will describe the implementation of 1D+3D/4D Var assimilation schemes of existing ground-based WTLN (Worldwide Total Lightning Network) lightning observations using non-linear observation operators in the incremental WRFDA system. To mimic the expected output of GLM, the WTLN data were used to generate lightning super-observations characterized by flash rates/81 km2/20 min.

A major difficulty associated with variational approaches is the complexity of the observation operator that defines the model equivalent of lightning. We use Convective Available Potential Energy (CAPE) as a proxy between lightning data and model variables. This operator is highly nonlinear. Marecal and Mahfouf (2003) have shown that nonlinearities can prevent direct assimilation of rainfall rates in the ECMWF 4D-VAR (using the incremental formulation proposed by Courtier et al. (1994)) from being successful. Using data from the 2011 Tuscaloosa, AL tornado outbreak, we have proved that the direct assimilation of lightning data into the WRF 3D/4D - Var systems is limited due to this incremental approach. Severe threshold limits must be imposed on the innovation vectors to obtain an improved analysis.

We have implemented 1D+3D/4D Var schemes to assimilate lightning observations into the WRF model. Their use avoids innovation vector constrains from preventing the inclusion of a greater number of lightning observations Their use also minimizes the problem that nonlinearities in the moist convective scheme can introduce discontinuities in the cost function between inner and outer loops of the incremental 3-D/4-D VAR minimization.

The first part of this paper will describe the methodology and performance analysis of the 1D-Var retrieval scheme that adjusts the WRF temperature profiles closer to an observed value as in Mahfouf et al. (2005). The second part will show the positive impact of these 1D-Var pseudo – temperature observations on both model 3D/4D-Var WRF analyses and short-range forecasts for three cases - the Tuscaloosa tornado outbreak (April 27, 2011) with intense but localized lightning, a second severe storm outbreak with more widespread but less intense lightning (June 27, 2011), and a northeaster containing much less lightning.