Sensitivity of Surface Temperature Analyses to Background and

Sensitivity of Surface Temperature Analyses to Background and Observation Errors Daniel P. Tyndall and John D. Horel Department of Atmospheric Sciences, University of Utah Salt Lake City, Utah

Outline � 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 (2 D-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

Introduction 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 �

Local Surface Analysis (LSA) � 2 D-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

Background Downscaling for Temperature 1. 2. Horizontal bilinear interpolation 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 �

Observation and Background Error Variances � 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 σo 2: σb 2 should be doubled (2: 1) Network σb 2 (°C 2) σb 2 +σo 2 (°C 2) Avg. num. /hr ALL 1. 4 7. 5 6. 1 11, 464 METAR 2. 0 6. 2 4. 2 1, 744 PUBLIC 1. 4 6. 6 5. 3 6, 486 RAWS 2. 6 10. 0 1, 301 OTHER 1. 9 8. 1 6. 2 1, 961

Background Error Covariance: Example Correlation - Winchester, VA R = 40 km, Z = 100 m 0 0. 1 0. 2 0. 3 0. 4 0. 5 R = 80 km, Z = 200 m 0. 6 0. 7 0. 8 0. 9 1. 0

Data Denial Methodology � 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

Hilbert Curve Withholding Methodology

Shenandoah Valley Case Study ou nt ai KIAD Washington, D. C. Bl ue Ri dg e M ou nt Va ah an do en Sh ai ns lle y M ia n ch pa la Ap over Shenandoah Valley, VA � Shenandoah Valley between Blue Ridge Mtns. And Appalachian Mtns. � Washington, D. C. located in eastern part of domain ns � 4°x 4° area centered 0 100 200 300 400 500 600 700 800 900 1000

Case Study: Synoptic Situation � Analyzing analysis generated for 0900 UTC 22 October 2007 � Strong surface inversion up to 1500 m in morning sounding KIAD 1200 UTC 22 October 2007

Case Study: Background Field � Downscaling leads southwest-northwest oriented bands � Observations provide detail along mountain slopes and in Shenandoah Valley 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Case Study: Observations METAR PUBLIC 16/59/1, 744 OTHER 215/575/6, 486 RAWS 10/75/1, 961 3/11/1, 301

LSA Analyses R = 40 km, Z = 100 m, σo 2/σb 2 = 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 R = 80 km, Z = 2

LSA Analysis Increments R = 40 km, Z = 100 m, σo 2/σb 2 = 1 -5 -4 -3 -2 -1 0 1 2 3 R = 80 km, Z = 2 4 5

Data Denial Example � 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 -2. 5 -2 -1. 5 -1 -0. 5 0 0. 5 1 1. 5 2 2. 5

Results RMSE Using Withheld Observations (°C) Sensitivity (°C) # Experiment RMSE Using All Observations (°C) B Background 2. 15 - 1 R = 40 km, Z = 100 m, σo 2/σb 2 = 1 1. 62 1. 93 0. 26 2 R = 80 km, Z = 200 m, σo 2/σb 2 = 1 1. 80 1. 98 0. 29 3 R = 20 km, Z = 50 m, σo 2/σb 2 = 1 1. 41 1. 89 0. 20 4 R = 40 km, Z = 100 m, σo 2/σb 2 = 0. 5 1. 54 1. 94 0. 34 5 R = 40 km, Z = 100 m, σo 2/σb 2 = 2 1. 70 1. 93 0. 19 6 R = 80 km, Z = 200 m, σo 2/σb 2 = 2 1. 83 1. 89 0. 22 7 R = 20 km, Z = 50 m, σo 2/σb 2 = 0. 5 1. 67 1. 90 0. 26 Measure of analysis quality in data rich areas Measure of analysis quality in data voids

Summary � Local 2 D-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

Extra Slides

Specification of Observation Error Variance and Background Error Covariance � 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 σo 2: σb 2 of 2: 1 and horiz. and vert. decorrelation length scales of 80 km and 200 m