1. Daniel P. Tyndall and John D. Horel Department of Atmospheric Sciences, University of Utah Salt Lake City, Utah

2.  Note: This talk is an excerpt from a paper that has been recently submitted to WAF for review (with M. de Pondeca as a co-author)  Introduction  Research motivation  Goals  Development of a Local (2D-Var) Surface Analysis  Downscaled background  Observations  Specification of observation error variances and background error covariances  Data denial methodology  Hilbert curve withholding technique  Root-mean-square error and sensitivity  Case Study  Shenandoah Valley, morning surface inversion  Results  Summary

3.  High resolution mesoscale analyses becoming necessary in variety of fields  Research began in 2006 to help evaluate Real-Time Mesoscale Analysis (RTMA)  Estimate error (co)variances of background and observations  Identify overfitting problems in analyses  Developed a local surface analysis to help meet these goals  Goals of this presentation:  Describe the local surface analysis  Present estimates of the background error covariance and observation error variance  Present a data denial methodology to assess analysis accuracy and identify overfitting problems

4.  2D-Var surface temperature analysis  Background  5 km res. downscaled RUC 1-hr forecast  RTMA 5-km terrain developed from NDFD  Observations  Includes various mesonet and METAR observations  ±12 min time window; -30/+12 min time window for RAWS observations  Background and observation errors  Specified in terms of vertical and horizontal spatial distance using decorrelation length scales  Determined using month long sample of observations

5. 1. Horizontal bilinear interpolation 2. Vertical interpolation to height of RTMA terrain using RUC low level lapse rate  RTMA < RUC Elevation: RUC low level lapse rate multiplied by distance between two elevations and added to RUC 2-m temperature  RTMA > RUC Elevation: RUC 2-m temperature used  For complete downscaling description, see Benjamin et al. 2007  Problem: unphysical features in strong surface temperature inversions

6.  Statistical analysis performed on month-long sample of observations across CONUS  See paper for details; same method used by Myrick and Horel (2006)  Results of analysis show σ o 2 :σ b 2 should be doubled (2:1)

7. 00.10.2 0.30.4 0.50.60.70.80.91.0 R = 80 km, Z = 200 mR = 40 km, Z = 100 m

8.  Evaluation of analyses done by randomly withholding observations  Two error measures:  Root-mean-square error (RMSE) calculated at the observation gridpoints  Root-mean-square sensitivity computed across all gridpoints  Measures need observations that are randomly distributed across the grid to be effective

10.  4°x4° area centered over Shenandoah Valley, VA  Shenandoah Valley between Blue Ridge Mtns. And Appalachian Mtns.  Washington, D.C. located in eastern part of domain 01002003004005006007008009001000

11.  Analyzing analysis generated for 0900 UTC 22 October 2007  Strong surface inversion up to 1500 m in morning sounding 1200 UTC 22 October 2007 KIAD

12.  Downscaling leads southwest-northwest oriented bands  Observations provide detail along mountain slopes and in Shenandoah Valley 2345 6 78910 11 12131415 1617

13. METAR16/59/1,744 PUBLIC215/575/6,486 OTHER10/75/1,961 RAWS3/11/1,301

14. 2345 6 78910 11 12131415 1617 R = 40 km, Z = 100 m, σ o 2 /σ b 2 = 1 R = 80 km, Z = 200 m, σ o 2 /σ b 2 = 2

15. -5-4 -3 -201234 5 R = 40 km, Z = 100 m, σ o 2 /σ b 2 = 1 R = 80 km, Z = 200 m, σ o 2 /σ b 2 = 2

16.  Data denial methodology applied using 10 observation sets  RMSE and Sensitivity computed for each set of analysis characteristics  Right: Difference between control analysis and data withheld analysis  Blue (red) means control analysis was colder (warmer) than withheld 00.511.5 2 2.5-0.5-1.5-2-2.5

17. Measure of analysis quality in data rich areas Measure of analysis quality in data voids

18.  Local 2D-Var surface analysis developed for this research  Ratio of observation to background error variance and decorrelation length scales larger than previously assumed  Analysis of RMSE values using withheld observations and all observations provides a measure of analysis overfitting  For further information, see full article submitted to WAF for review

20.  Statistical analysis using month long sample to estimate error variances  See Myrick and Horel 2006  Background error covariance specified in terms of spatial distance:  Estimation shows a σ o 2 :σ b 2 of 2:1 and horiz. and vert. decorrelation length scales of 80 km and 200 m