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

Abstract

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 (Q 1 ), and moisture sinks (Q 2 ). 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 (Q 1 and Q 2 ) 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.

Large-scale vertical velocity, diabatic heating and drying profiles associated with seasonal and diurnal variations of convective systems observed in the GoAmazon2014/5 experiment

“…The upper-level heating and drying, lowerlevel cooling and moistening indicate that there are precipitating stratiform clouds in the upper level and evaporation of precipitation underneath. The negative Q 1 − Q 2 − Q rad in the lower level and the positive Q 1 − Q 2 − Q rad in the upper level are seen in both the COS and BOS case, which indicates lower-level divergence of h and upper-level convergence of h due to moist convective processes, consistent with Tang and Zhang (2015). The lower-level positive Q 1 −Q 2 −Q rad in the afternoon is mainly contributed by the vertical convergence of moisture by sub-grid eddies, similar to that in the LOS case.…”

“…This local circulation and the horizontal inhomogeneity of largescale vertical velocity, heating and moistening could be better studied using high-resolution 3-D gridded large-scale forcing data from the 3-D constrained variational analysis recently developed by Tang and Zhang (2015) and Tang et al (2016). This will be the subject of a future study.…”

Forcing Single‐Column Models Using High‐Resolution Model Simulations

“…The ability to separate the physics parameterization schemes from the dynamics is very useful, as most stochastic schemes assume that model error is due only to the parameterized physics. The usefulness of SCM forcing data that includes an estimate of subgrid variability has been demonstrated by Tang and Zhang () and Tang et al (), who consider subgrid variability in forcing fields derived from measurements at the Atmospheric Radiation Measurement Southern Great Plains site. In particular, they highlight the utility of such data sets for deriving and evaluating scale‐aware parameterization schemes, since the SCM forcing files can be specified across a range of resolutions (Tang et al, ).…”

“…New sophisticated methods have been developed to reduce errors in the large‐scale forcing (Zhang & Lin, ; Zhang et al, ), though the accuracy of the data can be limited by missing data and scale aliasing in the measurements. In addition, recent advances have seen the development of a three‐dimensional constrained variational analysis approach (Tang & Zhang, ), which enables the estimation of fine‐resolution SCM forcing data sets from observational data. The new technique enables the estimation of atmospheric profiles for a number of adjacent columns around suitable observational sites.…”

An ensemble constrained variational analysis of atmospheric forcing data and its application to evaluate clouds in CAM5

“…As described in Tang and Zhang [], the 3DCVA follows the general idea of 1DCVA [ Zhang and Lin , ] that the atmospheric state variables (referred to as background data hereafter) u , v , q , and s are adjusted to minimize the cost function: while maintaining the column‐integrated conservation of mass, moisture, and energy simultaneously across all spatial grids in the analysis domain: …”