A two-dimensional variational analysis for surface temperature is developed for a limited domain (4° latitude × 4° longitude) in order to evaluate approaches to efficiently examine the sensitivity of similar variational analysis systems to the specification of observation and background errors. This work is intended to help facilitate improvements to the operational Real-Time Mesoscale Analysis (RTMA) developed by the National Centers for Environmental Prediction. The local surface analysis (LSA) uses the same projection and terrain (on a roughly 5-km × 5-km grid), background fields derived from 1-hr forecasts of the Rapid Update Cycle (RUC) downscaled to that grid, and observation assets used by the RTMA.
The observation error variance as a function of broad network categories and error variance and covariance of the downscaled 1-hr RUC background fields are estimated using a sample of over 7 million surface temperature observations in the continental United States collected during the period 8 May -- 7 June 2008. The ratio of observation to background error variance is found to be between 2 and 3, which is higher than that used operationally by the RTMA. This ratio is likely even higher in mountainous regions where the representativeness errors attributed to the observations are large. The background errors also tend to remain more strongly correlated over longer horizontal distances than those specified operationally for the RTMA.
Analysis sensitivity to both the ratio of the observation and background error variance and background error decorrelation length scale is examined for a single case (0900 UTC 22 October 2007) using the LSA centered over the Shenandoah Valley of Virginia. The RTMA surface temperature analysis for that case exhibited several unrealistic features in that region as a result of a pronounced surface-based temperature inversion. Sets of ten data denial experiments in which 10% of the observations are withheld randomly and uniquely from each analysis are used. The analysis error is estimated by the differences between the withheld observations and the corresponding analyses from which the observations are withheld while the analysis sensitivity to the withheld observations is computed from the differences between control analyses and the analyses from which the observations are withheld. For this case it is possible to improve analysis accuracy in multiple ways, i.e., by making the analysis less (more) detailed by broadening (shortening) the decorrelation length scales of the background error covariance in combination with increasing (decreasing) the observation to background error variance ratio. These results, not surprisingly, confirm the need to examine analysis sensitivity over many types of synoptic situations and the difficulty in specifying those parameters a priori.