Three‐dimensional constrained variational analysis: Approach and application to analysis of atmospheric diabatic heating and derivative fields during an ARM SGP intensive observational period

Atmospheric vertical velocities and advective tendencies are essential large-scale forcing data to drive single-column models (SCMs), cloud-resolving models (CRMs), and large-eddy simulations (LESs). However, they cannot be directly measured from field measurements or easily calculated with great accuracy. In the Atmospheric Radiation Measurement Program (ARM), a constrained variational algorithm (1-D constrained variational analysis (1DCVA)) has been used to derive large-scale forcing data over a sounding network domain with the aid of flux measurements at the surface and top of the atmosphere (TOA). The 1DCVA algorithm is now extended into three dimensions (3DCVA) along with other improvements to calculate gridded large-scale forcing data, diabatic heating sources (Q1), and moisture sinks (Q2). Results are presented for a midlatitude cyclone case study on 3 March 2000 at the ARM Southern Great Plains site. These results are used to evaluate the diabatic heating fields in the available products such as Rapid Update Cycle, ERA-Interim, National Centers for Environmental Prediction Climate Forecast System Reanalysis, Modern-Era Retrospective Analysis for Research and Applications, Japanese 55-year Reanalysis, and North American Regional Reanalysis. We show that although the analysis/reanalysis generally captures the atmospheric state of the cyclone, their biases in the derivative terms (Q1 and Q2) at regional scale of a few hundred kilometers are large and all analyses/reanalyses tend to underestimate the subgrid-scale upward transport of moist static energy in the lower troposphere. The 3DCVA-gridded large-scale forcing data are physically consistent with the spatial distribution of surface and TOA measurements of radiation, precipitation, latent and sensible heat fluxes, and clouds that are better suited to force SCMs, CRMs, and LESs. Possible applications of the 3DCVA are discussed.