## Abstract

In this paper, we extend the 1985 work of Kuo and Anthes to develop a method to derive temperature and geopotential information from a network of wind profiler observations, which we define as a thermodynamic retrieval technique. We first reformulate the retrieval procedure on a terrain-following σ-coordinate, similar to that used in most limited-area models. We then examine the accuracy of the derived temperature and geopotential fields for six different synoptic situations using basic datasets generated by a high-resolution mesoscale model.

We found that in the middle and upper troposphere, the retrieved temperature is significantly more accurate than the direct temperature measurement from a combined satellite- and ground-based microwave radiometric system (using climatology as a basis for radiometric retrieval). At lower levels, however, the retrieved temperature is not as accurate, mainly due to the neglect of boundary layer momentum fluxes in the retrieval calculations. Because the boundary layer momentum fluxes are difficult to measure, this suggests a need for independent temperature measurements at these levels.

Formulating the retrieval procedure in either the p- or the σ-coordinate system gives similar results, with the retrieved temperature slightly more accurate in the σ-coordinate than in the p-coordinate formulation. The use of Neumann boundary conditions, with no independent temperature observations at the lateral boundaries, results in a 61% larger error than does the use of the Dirichlet boundary conditions when independent temperature observations, such as those from the rawinsonde systems, are available. A modified specification of the Dirichlet boundary condition is developed which utilizes an arbitrary number of temperature sounders in combination with the horizontal geopotential gradient estimated from the wind field. It is shown that better results are obtained when more temperature sounders are available at the boundaries. It is also shown that the utilization of the geopotential gradient, obtained from the wind field, reduces the number of independent sounders required at the boundaries.

The accuracy of the retrieved temperature is case-dependent. The retrieval procedure is shown to be more accurate in cases with weak dynamical forcing. When there is strong baroclinicity, vertical motion and divergence, the retrieved temperatures exhibit a larger error. This is caused, in part, by a lack of horizontal resolution of the hypothetical wind profiler network needed to resolve strong mesoscale circulations near the frontal zone, and partially by large errors produced in the calculation of divergence and vertical motion terms over these regions. To obtain a better assessment of the accuracy of the retrieved temperature, we define a parameter—the retrieval ratio—as the ratio of the rms temperature error of the retrieved temperature to that of a rawinsonde network which has the same horizontal resolution as the profiler network. We found that in a weak summertime case, the retrieval ratio is 1.0, indicating that the retrieved temperature is as accurate as that from a rawinsonde network. In cases with strong dynamical forcing, the retrieval ratio is about 1.4, indicating less accuracy in these situations. The mean for the six cases studied here is 1.25, showing that the retrieved temperature, on the average, contains 25% higher rms error than the simulated rawinsonde temperature. When the balance equation is used instead of the divergence equation in the retrieval calculation, the mean retrieval ratio for all six synoptic events is near 1.1.

The neglect of the local tendency of divergence, or terms related to divergence, produces considerable degradation of the retrieved temperature in an experiment with high-resolution perfect wind data. This implies that the local tendency term and the divergence terms are important for small mesoscale systems (those that can be resolved by a 40 km model). However, ignoring the divergence related terms in the divergence equation produces improved results in other experiments, when the profiler data are available at 360 km intervals with superimposed measurement errors. This is partially due to the fact that the divergence terms are less important for larger-scale systems, and partially because the calculation of these terms is very sensitive to measurement and analysis errors.