Constrained Variational Analysis of Sounding Data Based on Column-Integrated Budgets of Mass, Heat, Moisture, and Momentum: Approach and Application to ARM Measurements

For the purpose of deriving grid-scale vertical velocity and advective tendencies from sounding measurements, an objective scheme is developed to process atmospheric soundings of winds, temperature, and water vapor mixing ratio over a network of a small number of stations. Given the inevitable uncertainties in the original data, state variables of the atmosphere are adjusted by the smallest possible amount in this scheme to conserve column-integrated mass, moisture, static energy, and momentum. The scheme has the capability of incorporating a variety of supplemental measurements to constrain large-scale vertical velocity and advective tendencies derived from state variables. The method has been implemented to process the Atmospheric Radiation Measurement Program’s (ARM) soundings of winds, temperature, and water vapor mixing ratio at the boundary facilities around the Cloud and Radiation Testbed site in northern Oklahoma in April 1994. It is found that state variables are adjusted by an amount comparable to their measurement uncertainties to satisfy the conservation requirements of mass, water vapor, heat, and momentum. Without these adjustments, spurious residual sources and sinks in the column budget of each quantity have the same magnitudes as other leading components. Sensitivities of the diagnosed vertical velocity and apparent heat, moisture, and momentum sources to the number of conservation constraints are presented. It is shown that constraints of column budget of moisture and dry static energy can make large differences to these diagnostics, especially when some original sounding data are missing and have to be interpolated. Analysis of the moisture budget shows that large-scale convergence often corresponds to precipitation, but there are occasions when precipitation corresponds to a large reduction of column precipitable water and columnmoisture divergence. Analysis of momentum budget shows large magnitudes of subgrid-scale momentum sources and sinks (about 4 m s21 h21) in the convective events.