THE DECORRELATION SCALE: METHODOLOGY AND APPLICATION FOR PRECIPITATION FORECASTS

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1 THE DECORRELATION SCALE: METHODOLOGY AND APPLICATION FOR PRECIPITATION FORECASTS Madalina Surcel, Isztar Zawadzki and M. K. Yau Thanking Adam Clark (NSSL), Ming Xue (OU, CAPS) and Fanyou Kong (CAPS) for providing the data set

2 24-h forecast of hourly rainfall accumulations initialized at UTC on 24 April 28 mmh RADAR CN C N3 P1 P2 P3 N4 13km x 13km P4 N1 N2

3 24-h forecast of hourly rainfall accumulations initialized at UTC on 24 April 28 mmh RADAR CN C N3 P1 P2 P3 N4 13km x 13km P4 N1 N2

4 24-h forecast of hourly rainfall accumulations initialized at UTC on 24 April 28 mmh No radar DA RADAR CN C N3 P1 P2 P3 N4 13km x 13km P4 N1 N2

5 24-h forecast of hourly rainfall accumulations initialized at UTC on 24 April 28 mmh RADAR CN C N3 P1 P2 P3 N4 13km x 13km P4 N1 N2

6 24-h forecast of hourly rainfall accumulations initialized at UTC on 24 April 28 mmh RADAR CN C N3 P1 P2 P3 N4 3km x 3km P4 N1 N2

7 The scale-dependence of the predictability of precipitation patterns

8 The scale-dependence of the predictability of precipitation patterns The decorrelation scale - below which the forecasts are fully decorrelated - complete lack of predictability Power ratio X T = ( ) P N X i i=1 R = X i = X i DCT Power N i=1 P Xi P ( XT ) ( x, y) Usually for decorrelated fields R = 1 for

9 The scale-dependence of the predictability of precipitation patterns The decorrelation scale - below which the forecasts are fully decorrelated - complete lack of predictability Power ratio X T = ( ) P N X i i=1 R = X i = X i DCT Power N i=1 P Xi P ( XT ) ( x, y) Usually for decorrelated fields R = 1 for Compute and find for different fields. R ( )

10 The scale-dependence of the predictability of precipitation patterns The decorrelation scale - below which the forecasts are fully decorrelated - complete lack of predictability Power ratio X T = ( ) P N X i i=1 R = X i = X i DCT Power N i=1 P Xi P ( XT ) ( x, y) Usually for decorrelated fields R = 1 for ( ) = P X i + P Radar R P Xi +Radar Compute and find for different fields. R ( ) Measure of skill Model predictability of the atmospheric state

11 The scale-dependence of the predictability of precipitation patterns The decorrelation scale - below which the forecasts are fully decorrelated - complete lack of predictability Power ratio X T = ( ) P N X i i=1 R = X i = X i DCT Power N i=1 P Xi P ( XT ) ( x, y) Usually for decorrelated fields R = 1 for ( ) = P X i + P Radar R P Xi +Radar Compute and find for different fields. R ( ) Measure of skill Model predictability of the atmospheric state R = N i=1 P X P Xi Measure of spread Predictability of the model state

12 The scale-dependence of the predictability of precipitation patterns The decorrelation scale - below which the forecasts are fully decorrelated - complete lack of predictability Power ratio X T = ( ) P N X i i=1 R = X i = X i DCT Power N i=1 P Xi P ( XT ) ( x, y) Usually for decorrelated fields R = 1 for ( ) = P X i + P Radar R P Xi +Radar Compute and find for different fields. R ( ) Measure of skill Model predictability of the atmospheric state R R = N i=1 P X P Xi ( ) = P cn + P c P cn+c Measure of spread Predictability of the model state Model sensitivity - effect of radar DA

13 22 cases for the 28 NOAA HWT Spring Experiment Storm-scale ensemble forecasts - IC/LBC perturbations/mixed physics IC/LBC perturbations from NCEP SREF (dx=32-45 km) Convective allowing (dx=4km), mesoscale data assimilation (including radar) Averaged over all cases meso-α Predictability of the model state R = N i=1 P X P Xi NWP (ensemble) meso-β meso-γ

14 22 cases for the 28 NOAA HWT Spring Experiment Storm-scale ensemble forecasts - IC/LBC perturbations/mixed physics IC/LBC perturbations from NCEP SREF (dx=32-45 km) Convective allowing (dx=4km), mesoscale data assimilation (including radar) Averaged over all cases some predictability meso-α Predictability of the model state R = N i=1 P X P Xi NWP (ensemble) no predictability meso-β meso-γ No predictability of the model state at meso-γ and meso-β scales after 12 hours

15 22 cases for the 28 NOAA HWT Spring Experiment Storm-scale ensemble forecasts - IC/LBC perturbations/mixed physics IC/LBC perturbations from NCEP SREF (dx=32-45 km) Convective allowing (dx=4km), mesoscale data assimilation (including radar) Averaged over all cases some predictability NWP (ensemble) NWP Radar DA no predictability meso-α meso-β meso-γ Predictability of the model state R = N i=1 P X P Xi Model predictability of the atmospheric state R = P X i + P Radar P Xi +Radar Loss of predictability at meso-γ and meso-β after 2 hours Effect of radar DA?

16 22 cases for the 28 NOAA HWT Spring Experiment Storm-scale ensemble forecasts - IC/LBC perturbations/mixed physics IC/LBC perturbations from NCEP SREF (dx=32-45 km) Convective allowing (dx=4km), mesoscale data assimilation (including radar) Averaged over all cases some predictability NWP No Radar DA NWP Radar DA NWP (ensemble) no predictability meso-α meso-β meso-γ Predictability of the model state R = N i=1 P X P Xi Model predictability of the atmospheric state R = P X i + P Radar P Xi +Radar

17 22 cases for the 28 NOAA HWT Spring Experiment Storm-scale ensemble forecasts - IC/LBC perturbations/mixed physics IC/LBC perturbations from NCEP SREF (dx=32-45 km) Convective allowing (dx=4km), mesoscale data assimilation (including radar) Averaged over all cases some predictability NWP No Radar DA NWP Radar DA NWP (ensemble) no predictability meso-α meso-β meso-γ Predictability of the model state R = N i=1 P X P Xi Model predictability of the atmospheric state R = P X i + P Radar P Xi +Radar Improvement only during the first 5 hours

18 22 cases for the 28 NOAA HWT Spring Experiment Storm-scale ensemble forecasts - IC/LBC perturbations/mixed physics IC/LBC perturbations from NCEP SREF (dx=32-45 km) Convective allowing (dx=4km), mesoscale data assimilation (including radar) Averaged over all cases some predictability NWP No Radar DA NWP Radar DA NWP (ensemble) no predictability Observations meso-α meso-β meso-γ Predictability of the model state R = N i=1 P X P Xi Model predictability of the atmospheric state R = P X i + P Radar P Xi +Radar Effect of observational uncertainty ( ) = P StageIV + P Radar R P StageIV +Radar

19 22 cases for the 28 NOAA HWT Spring Experiment Storm-scale ensemble forecasts - IC/LBC perturbations/mixed physics IC/LBC perturbations from NCEP SREF (dx=32-45 km) Convective allowing (dx=4km), mesoscale data assimilation (including radar) Averaged over all cases some predictability NWP No Radar DA NWP Radar DA NWP (ensemble) no predictability Observations meso-α meso-β meso-γ Range of scales with some predictability of the model state but no model predictability of the atmospheric state. The main errors in forecasting moist convection are not due to errors at convective scales, but to errors at larger scales and in the model formulation (biases)

20 The effect of radar data assimilation 7 (t)=24 (t)=161 t.3 (t)= CN-C CN-Radar C-Radar Model predictability of the atmospheric state R = P CN + P Radar R P CN+Radar ( ) = P C + P Radar P C +Radar Sensitivity to radar DA R = P CN + P C P CN+C Radar DA affects scales lower than 2km throughout the forecast lead time but no upscale growth - effect of LBCs In terms of gained predictability - mostly relevant during the first 5 hours -effect of assimilating reflectivity

21 The effect of radar data assimilation NRMSE CN/C C/Radar CN/Radar >4km >256km NRMSE = Time since UTC [h] NRMSE C/Radar x x y y ( X(x, y) Y (x, y) ) 2 ( X(x, y) + Y (x, y) ) 2 >4km NRMSE CN/Radar NRMSE C/Radar >256km.4 t=1h t=6h t=12h.2 t=18h t=24h. t=29h NRMSE CN/Radar (a) (b) (c) Effect radar DA at meso-α scales is maintained up to 18 hours for most case After 18 hours the CN and C forecasts become more similar at meso-α scales - effect of the diurnal cycle?

22 Very short-term prediction of precipitation (-6h) Performance of Lagrangian persistence (MAPLE) and NWP Corr. coeff CN (Radar DA) C (No radar DA) MAPLE Forecast time [h] Dashed lines: the differences in the correlation coefficient between CN and MAPLE and C and MAPLE are not statistically significant for a 99% CI. Cross-over time is between 2 and 4 hours.

23 Very short-term prediction of precipitation (-6h) Performance of Lagrangian persistence (MAPLE) and NWP Corr. coeff CN (Radar DA) C (No radar DA) MAPLE Forecast time [h] Dashed lines: the differences in the correlation coefficient between CN and MAPLE and C and MAPLE are not statistically significant for a 99% CI. Cross-over time is between 2 and 4 hours. How about for predictability loss?

24 Very short-term prediction of precipitation (-6h) Predictability by Eulerian persistence, Lagrangian persistence and NWP NWP No Radar DA (obs) NWP Radar DA (obs) NWP Radar DA (intrinsic) (b) NWP No Radar DA Lagrangian persistence Lagrangian persistence Eulerian persistence some predictability Eulerian persistence NWP Radar DA NWP intrinsic no predictability Cross-over time between radar DA models and LP forecasts is 3 hours Promising for use of NWP for nowcasting LP better validating baseline than EP meso-α meso-β meso-γ

25 Case-to-case variability of predictability >.4.4 Slope [] < from Aitor Atencia following the methodology of Kalnay et al. (24) The predictability depends on the initial conditions - on the position in the attractor

26 Case-to-case variability of predictability Ensemble CN/N2 CN/C Radar DA NWP/Radar C/Radar LP/Radar

27 Can large-scale forcing explain the case-to-case variability? Classify cases according to the strength of the synoptic scale forcing (similarly to Duda et al., 212) into strongly and weakly forced cases Ensemble CN/N2 CN/C Radar DA NWP/Radar C/Radar LP/Radar

28 Can large-scale forcing explain the case-to-case variability? Classify cases according to the strength of the synoptic scale forcing (similarly to Duda et al., 212) into strongly and weakly forced cases Ensemble CN/N2 No it cannot! CN/C Radar DA NWP/Radar C/Radar LP/Radar

29 Can large-scale forcing explain the case-to-case variability? Classify cases according to the strength of the synoptic scale forcing (similarly to Duda et al., 212) into strongly and weakly forced cases Ensemble CN/N2 No it cannot! CN/C Why? Radar DA NWP/Radar C/Radar LP/Radar

30 Can large-scale forcing explain the case-to-case variability? Classify cases according to the strength of the synoptic scale forcing (similarly to Duda et al., 212) into strongly and weakly forced cases Ensemble Radar DA NWP/Radar CN/N No it cannot! Why? CN/C The predictability loss as function of time does not depend on the type of case. C/Radar LP/Radar

31 Can large-scale forcing explain the case-to-case variability? Classify cases according to the strength of the synoptic scale forcing (similarly to Duda et al., 212) into strongly and weakly forced cases Ensemble Radar DA NWP/Radar CN/N No it cannot! Why? CN/C The predictability loss as function of time does not depend on the type of case. Our case classification is inappropriate. C/Radar LP/Radar

32 Can large-scale forcing explain the case-to-case Ensemble variability? Classify cases according to the strength of the synoptic scale forcing (similarly to Duda et al., 212) into strongly and weakly forced cases CN/N WE DO Radar NOT DA NWP/Radar HAVE A SUFFICIENTLY C/Radar LARGE DATA LP/Radar SET FOR No it cannot! Why? CN/C The predictability loss as function of time does not depend on the type of case. Our case classification is inappropriate. A PROPER ANALYSIS

33 Extend the data set: Spring Experiment ensemble!"#$%&'%(&)#*+#,&)#-&./'&1#+*'#23!4#5&.1*6# precipitation forecasts from ! "#$%&!'(#)*&(+!'%&!,-./!!! 123!4(&+5%6!/787."#$"%$&'"()*"+,-!"$&.$)/"12345"67!89"!! )/"M))<&*".B"L5H=3"!! 2"%/#(#&'"')<.#/"BC.B"#$"-,R"O.*I&*"BC./"#/"+,-+"$&.$)/"1>#I%*&"-9"!! " JQQ"<&<?&*"#$"*%/P" Many thanks to Adam Clark (NSSL), Ming Xue (OU, CAPS) and Fanyou Kong (OU,CAPS) 29 WRF-ARW V ensemble members initialized at UTC for 3h 2 WRF-ARW V ensemble members initialized at UTC for 36h 211 WRF-ARW V ensemble members initialized at UTC for 36h same domain as WRF-ARW V ensemble members initialized at UTC for 36h same domain as WRF-ARW V ensemble members initialized at UTC for 48h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

34 Extend the data set: Spring Experiment ensemble!"#$%&'%(&)#*+#,&)#-&./'&1#+*'#23!4#5&.1*6# precipitation forecasts from ! "#$%&!'(#)*&(+!'%&!,-./!!! 123!4(&+5%6!/787."#$"%$&'"()*"+,-!"$&.$)/"12345"67!89"!! )/"M))<&*".B"L5H=3"!! 2"%/#(#&'"')<.#/"BC.B"#$"-,R"O.*I&*"BC./"#/"+,-+"$&.$)/"1>#I%*&"-9"!! " JQQ"<&<?&*"#$"*%/P" Many thanks to Adam Clark (NSSL), Ming Xue (OU, CAPS) and Fanyou Kong (OU,CAPS) 29 WRF-ARW V ensemble members initialized at UTC for 3h Effect of Radar DA 2 WRF-ARW V ensemble members initialized at UTC for 36h Spread for mixed physics and IC/BC perturbations ensemble Spread for mixed physics ensemble only 211 WRF-ARW V ensemble members initialized at UTC for 36h same domain as WRF-ARW V ensemble members initialized at UTC for 36h same domain as WRF-ARW V ensemble members initialized at UTC for 48h Sensitivity to microphysics only Sensitivity to PBL only "!"#$%&'()'*+,-$./."+/1'2+,/"'3+%'.4&'56(7'8&/9+':+$.&%'2+,/";'(566<=>?@)'A4&'9,/11' "&%'2+,/"':>66BC66@'"9'3+%'.4&'6666'DA*'EF!'&9&,G1&)'' Sensitivity to the type of IC perturbations " 2"#7'*8'.9#:'./(*6#! >*)<",,!9:&5;!,-./"BC*)%IC"<!=*6(!,-./" " GC&"+,-!"54HVJ55Y"ZNG"5T*#/I"=ST&*#<&/B@"."[)#/B"&(()*B".<)/I"JL22"5B)*<"4*&'#EB#)/" H&/B&*"154H9"./'"J.B#)/.O"5&6&*&"5B)*<"Y.?)*.B)*X"1J55Y9"./'"BC&"H&/B&*"()*"2/.OX$#$"./'" 4*&'#EB#)/")("5B)*<$"1H2459".B"F/#6&*$#BX")("L;O.C)<.@"A#OO")((#E#.OOX"+)#&)!%6!>!"#?!#6@!(6@! %6!<!=*6(@"A#BC"(#6&"'.X$"."A&&;"1Q)/'.X"BC*)%IC">*#'.X9"H245"+,-!"5T*#/I"4*)I*.<"?&I#/$"!" "

35 Reproduce results for Results for simulated reflectivity fields averaged over all cases meso-α meso-α meso-α meso-β meso-β meso-β meso-γ meso-γ meso-γ meso-α meso-α meso-β meso-γ meso-β meso-γ 2 3 4

36 Sensitivity to the type of perturbations Average results for all available cases Predictability of the model state R = N i=1 P X P Xi IC_BC PHYS MP WSM PBL meso-α meso-α meso-α meso-α meso-α meso-β meso-β meso-β meso-β meso-β meso-γ meso-γ meso-γ meso-γ meso-γ 8 s : CN + 8 members 29: CN + 8 members 2: CN + 9 members 211: CN + 17 members 212: CN + 9 members 213: CN + 13 members 2: CN + 5 members 211: CN + 21 members 212: CN + 7 members 213: CN + 11 members 211: CN + members 212: CN + 3 members 213: CN + 6 members 211: 5 members 211: CN + 8 members 212: CN + 4 members 213: CN + 4 members

37 Conclusions The decorrelation scale - a methodology to investigate the loss of predictability with scale and forecast lead time This methodology was used to investigate the predictability of precipitation by convective-allowing ensembles and lagrangian extrapolation nowcasting methods for many cases during Spring 28 Our results are consistent with previously proposed models of upscale error (Zhang et al., 27) growth despite the different type of perturbations The main errors in forecasting moist convection are not due to errors at convective scales, but to errors at larger scales and in the model formulation (biases) We have only applied this to precipitation and the results are relevant to forecasting applications using 2D QPFs Case-to-case variability needs to be further adressed

38 Conclusions The decorrelation scale - a methodology to investigate the loss of predictability with scale and forecast lead time This methodology was used to investigate the predictability of precipitation by convective-allowing ensembles and lagrangian extrapolation nowcasting methods for many cases during Spring 28 Our results are consistent with previously proposed models of upscale error (Zhang et al., 27) growth despite the different type of perturbations The main errors in forecasting moist convection are not due to errors at convective scales, but to errors at larger scales and in the model formulation (biases) We have only applied this to precipitation and the results are relevant to forecasting applications using 2D QPFs Case-to-case variability needs to be further adressed Good news: large and rich data set to investigate the importance of different types of ensemble methodologies and to allow more statistically rigorous studies

CAPS Storm-Scale Ensemble Forecasting (SSEF) System

CAPS Storm-Scale Ensemble Forecasting (SSEF) System Fanyou Kong, Ming Xue, Xuguang Wang, Keith Brewster Center for Analysis and Prediction of Storms University of Oklahoma (collaborated with NSSL, SPC,