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Past operational methods: Perfect Prognosis (with multiple regression) Kalman filtering

The development of statistical interpretation and adaptation of NWP at FMI Juha Kilpinen, Ahti Sarvi and Mikael Jokimäki Finnish Meteorological Institute http://www.fmi.fi/. Past operational methods: Perfect Prognosis (with multiple regression) Kalman filtering Decision threes

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Past operational methods: Perfect Prognosis (with multiple regression) Kalman filtering

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  1. The development of statistical interpretation and adaptation of NWP at FMIJuha Kilpinen, Ahti Sarvi and Mikael JokimäkiFinnish Meteorological Institutehttp://www.fmi.fi/ • Past operational methods: • Perfect Prognosis (with multiple regression) • Kalman filtering • Decision threes • Present pre-operational methods: • Fuzzy systems for points • Perfect Prognosis for grid points

  2. The development of statistical interpretation and adaptation of NWP at FMI • Past operational methods: • Perfect Prognosis (with multiple regression) • for three stations, several parameters • Kalman filtering • temperature, min/max temperatute, off shore winds, PoP tests, for stations • Decision threes • several parameters, for grid data

  3. The development of statistical interpretation and adaptation of NWP at FMI • Present pre-operational methods: • Fuzzy systems for points • ECMWF temperature • Perfect Prognosis for grid data • temperature/ground temperature/Min-Max • HIRLAM and ECMWF data • to be used within the grid editing process

  4. HIRLAM model (CSC) Forecasting process at FMI Editing by forecasters (FMI) Post processing Climate database (FMI) Forecasters: Manual products Observations (Global & Local) Production Servers (FMI) Forecasts Customers: Public Web Business: Media Aviation Industry Security: General public Authorities Observations Boundaries Forecasts Real time Database (FMI) Post processing (e.g. statistical adaptation) ECMWF Graphics text forecasts etc. Monitoring SMS(FMI)

  5. The Grid Editor Smart Tools: ability to make Scripts to perform more Complicated and often Repeated editing actions in A more easy manner (suitable Also for adaptation purposes) IF (N>5) T=T+3

  6. MAE of temperature forecasts (3 stations, 9 seasons, 0.5-5 days) Centralized editing on commercial side

  7. HIRLAM DMO and Obs (25.4.2001) HIRLAM PPM and Obs (25.4.2001) Error ~ 10-15 degrees max error -20 degrees Error ~ 5-9 degrees max error 10 degrees

  8. Perfect Prognosis method for temperature forecasting • Juha Kilpinen • 2100 grid points, HIRLAM and ECMWF models • applies same models for both data sources (HIRLAM/ECMWF) • developmental data from TEMP’s of Jokioinen (02935) and Sodankylä (02836), 20 years of data • separate models for 00UTC, 03UTC, 06UTC, 09UTC, • 12UTC, 15UTC, 18UTC and 21 UTC (see Fig.) • over sea or lakes DMO is used • data stratification for four seasons, overlap of seasons 1 month (see Fig.) • TEMP data from surface up to 500 HPa used, also derived new predictors used • multiple linear regression (Systat 10) • forward selection of predictors, a new predictor should increase the reduction of variance of the model by at least 0.5%.

  9. Derived predictors for PPM • FF850 = SQRT(ABS(V850*U850)) • TYPE_PRHFF = (P_P0H-949)/15.6+(24-FF850)/3.93+(100-RH850)/28 • CL_MAX = MAX(RH500*RH500/100,RH700*RH700/100,RH850*RH850/100) • TYPE_PCLFF = (P_P0H-949)/15.6+(100-CL_MAX)/28.2+(24-FF850)/3.93 • P_P0H2 = P_P0H-1013 • Z8502 = Z850-1500 • Z7002 = Z700-3000 • Z5002 = Z500-5200 • COSINUS = COS(2*3.1417*JUL/360) • SINUS = SIN(2*3.1417*JUL/360)

  10. Estimation error of dependent PPM model UTC

  11. Estimation error of dependent PPM model UTC

  12. Connections of TEMP and SYNOP data in estimation 12 UTC TEMP SYNOP 09 12 15 18 21 00 03 06 UTC 00 UTC TEMP

  13. Data stratification and overlap of seasonal models Spring (3 months) Autumn (3 months) Winter (5 months) Summer (5 months) Winter (5 months) overlap 1 month

  14. Perfect Prognosis for temperature forecasts: A typical model • Data for the following results were selected according to: • (SEASON_SF= 2) AND (HH= 12) • 4 case(s) deleted due to missing data. • Dep Var: T2M_P0H N: 548 Multiple R: 0.98533425 Squared multiple R: 0.97088359 • Adjusted squared multiple R: 0.97050616 Standard error of estimate: 1.17789326 • Effect Coefficient Std Error Std Coef Tolerance t P(2 Tail) • CONSTANT -25.23580650 22.51961688 0.00000000 . -1.12061 0.26295 • Z500 0.00951429 0.00397318 0.21740651 0.0065415 2.39463 0.01698 • T700 -0.14111429 0.05617324 -0.12111370 0.0231975 -2.51213 0.01229 • RH700 -0.01421594 0.00192526 -0.06048159 0.8036540 -7.38390 0.00000 • T850 -0.49766238 0.03697928 -0.43038524 0.0527208 -1.34E01 0.00000 • COSINUS -1.75269612 0.19284168 -0.10759268 0.3847601 -9.08878 0.00000 • Z8502 0.25777160 0.00698847 3.60146923 0.0056557 36.88525 0.00000 • P_P0H2 -2.08679352 0.04590369 -3.40166499 0.0096300 -4.54E01 0.00000 • Analysis of Variance • Source Sum-of-Squares df Mean-Square F-ratio P • Regression 2.49825E+04 7 3.56892E+03 2.57232E+03 0.00000000 • Residual 7.49214E+02 540 1.38743253 • ------------------------------------------------------------------------------- • Durbin-Watson D Statistic 1.52355145 • First Order Autocorrelation 0.23719694

  15. Perfect Prognosis for temperature forecasts: A typical model • Data for the following results were selected according to: • (SEASON_WS= 2) AND (HH= 00) • 4 case(s) deleted due to missing data. • Dep Var: T2M_P0H N: 3335 Multiple R: 0.949 Squared multiple R: 0.901 • Adjusted squared multiple R: 0.901 Standard error of estimate: 1.404 • Effect Coefficient Std Error Std Coef Tolerance t P(2 Tail) • CONSTANT 22.426 0.529 0.000 . 42.386 0.000 • T850 0.063 0.023 0.065 0.054 2.753 0.006 • COSINUS -2.238 0.129 -0.147 0.418 -17.372 0.000 • Z8502 0.134 0.004 2.186 0.006 30.671 0.000 • P_P0H2 -1.050 0.036 -1.966 0.007 -29.113 0.000 • RH850 0.022 0.002 0.104 0.516 13.627 0.000 • SINUS -1.114 0.058 -0.155 0.460 -19.281 0.000 • TYPE_PNFFP0H -0.916 0.021 -0.365 0.433 -44.007 0.000 • Analysis of Variance • Source Sum-of-Squares df Mean-Square F-ratio P • Regression 59581.994 7 8511.713 4320.200 0.000 • Residual 6554.898 3327 1.970 • ------------------------------------------------------------------------------- • *** WARNING *** • Case 11951 has large leverage (Leverage = 0.012) • Durbin-Watson D Statistic 1.670 • First Order Autocorrelation 0.165

  16. Perfect Prognosis for temperature forecasts: • The models of Jokioinen (02935) used south of Jokioinen, the models of Sodankylä (02836) used north of Sodankylä and interpolation between these stations • PPM calculated after every HIRLAM run (4 times a day) and for ECMWF data once a day to a grid • Verification results available for stations (ME, MAE,...) • Verification results available for grid (based on MESAN analysis) • Timeseries of forecasts and observations for stations

  17. Location of Jokioinen and Sodankylä; ECWMF PPM and DMO

  18. Verification results of PPM: Mean Error ME (bias) Mean Absolute Error MAE HIRLAM 00 UTC analysis ECMWF 12 UTC corresponding to the same valid time 18h +48h +06h

  19. ECMWF MAE Summer 2002

  20. Error of HIRLAM (and PPM) temperature forecasts (summer 2002 30 stations) Forecast length (hours)

  21. Error of ECMWF (and PPM) temperature forecasts (summer 2002 30 stations) Forecast length (hours)

  22. Jokioinen Summer 12 UTC TEMP PPM Models for 09 UTC and 12 UTC Dep Var: T2M_09UTC N: 3290 Multiple R: 0.962 Squared multiple R: 0.926 Adjusted squared multiple R: 0.926 Standard error of estimate: 1.354 Effect Coefficient Std Error Std Coef Tolerance t P(2 Tail) CONSTANT 25.947 0.238 0.000 . 109.076 0.000 V700 -0.007 0.004 -0.011 0.766 -2.042 0.041 T850 -0.411 0.017 -0.377 0.089 -23.784 0.000 COSINUS -1.556 0.092 -0.091 0.771 -16.947 0.000 CL_MAX -0.085 0.015 -0.031 0.803 -5.861 0.000 Z8502 0.246 0.003 3.617 0.010 77.126 0.000 P_P0H2 -1.995 0.027 -3.249 0.012 -73.829 0.000 Dep Var: T2M_12UTC N: 3289 Multiple R: 0.983 Squared multiple R: 0.967 Adjusted squared multiple R: 0.967 Standard error of estimate: 0.945 Effect Coefficient Std Error Std Coef Tolerance t P(2 Tail) CONSTANT 30.611 0.166 0.000 . 184.289 0.000 V700 -0.026 0.002 -0.039 0.767 -10.829 0.000 T850 -0.506 0.012 -0.445 0.089 -41.932 0.000 COSINUS -0.753 0.064 -0.042 0.771 -11.746 0.000 CL_MAX -0.317 0.010 -0.110 0.803 -31.163 0.000 Z8502 0.274 0.002 3.864 0.010 123.162 0.000 P_P0H2 -2.218 0.019 -3.459 0.012 -117.535 0.000

  23. Error of HIRLAM (and PPM) temperature forecasts (autumn 2002 30 stations) Forecast length (hours)

  24. Temperature error of HIRLAM (and PPM) at Jokioinen (02935) summer 2002 Forecast length (hours)

  25. Temperature error of ECMWF (and PPM) at Jokioinen (02935) summer 2002 Forecast length (hours)

  26. Temperature error of HIRLAM (and PPM) at Sodankylä (02836) summer 2002 Forecast length (hours)

  27. Temperature error of ECMWF (and PPM) at Sodankylä (02836) summer 2002 Forecast length (hours)

  28. Error of ECMWF (and PPM) temperature forecasts (autumn 2002 30 stations) Forecast length (hours)

  29. Error of HIRLAM (and PPM) temperature forecasts (spring 2002 30 stations) Forecast length (hours)

  30. Error of ECMWF (and PPM) temperature forecasts (spring 2002 30 stations) Forecast length (hours)

  31. Error of HIRLAM (and PPM) temperature forecasts (winter 2002-2003 30 stations) Forecast length (hours)

  32. Error of ECMWF (and PPM) temperature forecasts (winter 2002-2003 30 stations) Forecast length (hours)

  33. Residuals versus Estimates Sodankylä PPM model in Winter (00 UTC)

  34. Error of ECMWF (and PPM) temperature forecasts (summer 2002 30 stations) Forecast length (hours)

  35. Error of ECMWF (and PPM) temperature forecasts (winter 2002-2003 30 stations) Forecast length (hours)

  36. Error of HIRLAM and ECMWF (& PPM) temperature forecasts in Finland (one year, 30 stations) Forecast length (hours)

  37. A Fuzzy system for adaptation of ECMWF T2m forecastsAhti Sarvi • Fuzzy system has been applied to correct the temperature (T2m) forecasts of ECMWF. These forecasts as well as HIRLAM forecasts have errors (systematic) typically in stable conditions (inversions). The objective of fuzzy system approach has been to utilize the information included in forecasts and corresponding observations by constructing a set of 2m temperature estimators based on the verifications of the most recent 27 successive 10 day forecasts. • The set of estimates given by these estimators may involve missing values and outliers, but in fuzzy set approach these contradictions in the data do not cause problems provided that the amount of the information included in the set of estimates input to the system is sufficient.

  38. A Fuzzy system for adaptation of ECMWF T2m forecasts • In an iterative solution process of fuzzy system a membership function, the values of which are normalized between zero and one, assigns the grade of membership for each estimate and zero for messy data and thus excludes the messy data from the solution and prevents it from corrupting the final estimate given by the system. • The verification results for a short test period are presented

  39. Error of temperature forecasts (ECMWF/FUZZY_system 1-10 days mean) winter 2003 30 stations

  40. Concluding remarks • PPM system needs some tuning • After that it may be useful in editor environment • As a new SmartTool-script • As a method within the editor • Fuzzy system has to be studied further but the preliminary results look promising; • However, Fuzzy system needs a lot of work compared to other methods

  41. Reference Glahn, H.R.,1985: Statistical Weather Forecasting. Probability, Statistics and Decision Making in the Atmospheric Sciences, A.H. Murphy and R.W. Katz, Eds., Westview Press, 289-335. R

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