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Can we Predict the Impact of Observations on 3 to 6 day Winter Weather Forecasts?

Can we Predict the Impact of Observations on 3 to 6 day Winter Weather Forecasts?

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## Can we Predict the Impact of Observations on 3 to 6 day Winter Weather Forecasts?

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**Can we Predict the Impact of Observations on 3 to 6 day**Winter Weather Forecasts? Masters Thesis Defense May 10, 2007 Kathryn J. Sellwood University of Miami, R.S.M.A.S., M.P.O. Dept.**Observations Upstream in Storm Tracks Used to Improve**Forecast in Downstream Locations Storm Tracks for 1994 winter season (left) 6 year average eddy kinetic energy (right) from James, 1994**Influence of Observations Propagates eastward**Poorly Observed Region Future Winter Storm Location**Upstream Observations improve the Downstream Forecast**More Accurate Forecast Early warning**IF**we can predict the impact of observations on specific 3-6 day winter weather forecasts THEN Observations can be used to improve accuracy and extend effective time range of forecasts**“Signal” from Observationsat t=0 (left) and t=80 hours**(right) combined 200 h-Pa u,v and T squared signal at 0 hours (left) and 80 hours (right)**Outline**• Background: Targeting ETKF Technique Results from Previous Targeting Field Programs • Research Methodology • Results • Conclusions • Future Work**Operational Targeting Timeline**Targeting Method Future Analysis Verification initialization time (targeting) time time ti ta tv Decision time 36-60 hours 1-7 days **Targeting in WSR**target regions identified for 2 day east coast forecast Observation time A Day 1 A B All WSR flight paths Operational flight path Day 2 -Verification time A B**Ensemble Transform Kalman Filter(ETKF)**• Quantifies impact of observations • Estimates the forecast error covariance matrix from an ensemble • Assimilates observational data using a Kalman filter • Computes resulting reduction in forecast error variance 5400m and 5820m 500 h-Pa height ensemble**Forecast error covariance matrix computed from**matrix of ensemble perturbations Z Pf = Zf ZfT Kalman Filter equation used to obtain new error covariance matrix if observations are assimilated Pq= Pr – Pr HqT (HqPrHqT+Rq)-1 HqPr Difference is the Signal Covariance Matrix Sq Sq=Pr–Pq Signal Variance = reduction in forecast error variance**ETKF Issues**• ETKF relies on linear theory • Depends on ensemble quality • Assumes Kalman filter data assimilation / operational scheme is 3D-Var • DA scheme introduces small scale noise that contaminates signal (Hodyss and Majumdar, 2007)**Results from previous Field Programs**• Targeting is effective in reducing short term forecast errors (Langland et al, 1999, Szunyogh et al., 1999, 2000, 2002) • ETKF effective for short range 1-3 day targeting (Majumdar et al., 2002-a, Szunyogh et al., 2000, 2002) • Flow regime related to effectiveness of ETKF • Data “signal” propagates in the form of upper tropospheric Rossby wave packets (Szunyogh et al., 2000, 2002) • Downstream development maintains wave packets and influences signal propagation (Szunyogh et al., 2002, Majumdar et al., 2002-b) • The presence of coherent wave packets beyond operational lead times is evidence of data influence in the medium range**Observations over Pacific improve 3 day forecast over U.S.**east coast and 6 day European forecast Improvement at 78 hours (u,v,T) 144 hour improvement (u,v,T)**Main Objectives**• Quantify ETKF’s ability to predict signal variance in the medium range • Determine scales at which ETKF is effective • Explore influence of flow regime • Determine whether ETKF can distinguish between promising targeting cases and those where observations would have minimal effect**2 Comparison Methods**• Method 1: measures the spatial correlation between the ETKF predicted signal variance and the squared GFS signal • Method 2: makes a quantitative evaluation of ETKFs’ skill in predicting signal variance**The Data Set**• Data is from the 2006 Winter Storm Reconnaissance Program • 19 individual cases • Forecast variables are 200 h-Pa winds and temperature • ETKF signal variance derived from a 50 member ECMWF ensemble • Signals calculated as the difference between 2 forecasts that are identical except 1 omits the WSR observations • Forecast produced using NCEPs Global Forecast System Model (GFS) • Both fields at 1 degree resolution**Methodology**• Spatial fields of ETKF “predicted” signal variance and GFS squared-signal (“verification”) are smoothed by averaging over lat-lon grid cells. • Field domain includes 180° W to 20° E from 20 to 80°N • Correlation coefficients between these smoothed spatial fields are calculated, at all lead times, for various grid spacings. • Correlation coefficients for actual case-specific predictions are then assessed relative to a “no-skill” baseline, constructed by randomizing the predictions of all 19 weather cases in the sample.**The Randomized Baseline**• Baseline random correlations are computed for all lead times from 0 to 144 hours • The ETKF predicted signal variance for each of the 19 cases is compared to the squared GFS signals from the 18 different cases • Results in a distribution of 342 random correlations • This baseline captures the (non) skill of case-independent spatial structure (like climatological storm tracks) • ETKF’s skill for the individual cases is compared against this baseline**Case Specific vs. Random Correlations**Same Case Similar Pattern Randomly Selected Case Less Correlated**Correlation skill of case-specific vs. randomized**predictions (2° grid) Blue = Random Red = ETKF**Average ETKF Correlations (solid) and Random Correlations**(dashed) as a Function of lead time and resolution**Significance test**• Are the ETKF correlation coefficientssignificantlygreater than the random distribution? • Use Kalmogorov-Smirnov test for the difference of two PDFs.**13/20 data points**= Maximum difference between distributions 4/ 16 data points**The Kolmogorov – Smirnov test**• Compares cumulative distribution function (CDF) • Produces 2 statistics based on “D” value • H statistic tests the null hypothesis that the 2 distributions are equal H = 0 cannot reject null hypothesis H = 1 can reject with 95% confidence • P statistic gives probability that the 2 distributions are indistinguishable • Test applied for all lead times and resolutions**5° grid**H = 1 for all lead times > 0**10° grid**H = 1 for all lead times > 0**15° grid**H = 1 for all lead times > 0**20° grid**H =1 for all lead times > 0**30° grid**H = 1 for all lead times > 0**ETKF significantly beats random for all grid spacing and**lead times > 0 • At 0 hour leads ETKF predictions are not significantly better than random climatology • ETKF case-specific predictions exhibit significantly better than random skill for the time ranges (3-6) days that we are interested in • Skill tends to improve (relative to random) at longer lead times • Higher correlations at lower resolution (larger grid)**ETKF has been shown to have skill in predicting the general**pattern of signal variance over a large domain but… • We want to apply ETKF to specific forecasts • Can the ETKF predict signal variance specifically in predetermined verification regions at 3-6 day lead times? • If so at what resolutions and for what size verification regions**Verification Regions**• Same methodology as full domain comparison • ETKF predicted signal variance compared to squared GFS signal over 20° x 20°, 40°x 40° and 60°x 60° verification regions • Verification regions selected using wave packet technique of Zimin et al., 2003 • Verification regions placed at the leading edge of wave packet maximum in ETKF predicted signal variance**Typical 120 hour V.R.s**60 X 60 40 x 40 20 x 20**ETKF vs Random20° Verification Region - 2° grid**RED = ETKFBLUE = RANDOM**K-S test20° Verification Region 2° grid**RED = ETKFBLUE = RANDOM