The development of statistical interpretation and adaptation of NWP at FMI Juha Kilpinen, Ahti Sarvi and Mikael Jokimäki Finnish Meteorological Institute 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

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

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

and editing of Real time database: observations numerical forecasts final forecasts interpretations Climatological database Post processing: creates customer products from the data edited by forecasters; texts, graphics, etc. Customers: Observations: satellites weather radars surface observations soundings Numerical weather forecast models (by supercomputers) Forecasting process at FMI Visualisation and Editing by Forecaster (interpretations) Old Vax workstation Old manual process

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

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

MAE of temperature forecasts (3 stations, 9 seasons, days) Centralized editing on commercial side

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

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%.

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 = Z Z7002 = Z Z5002 = Z COSINUS = COS(2*3.1417*JUL/360) SINUS = SIN(2*3.1417*JUL/360)

Estimation error of dependent PPM model UTC

Estimation error of dependent PPM model UTC

UTC TEMP 00 UTC TEMP SYNOP UTC Connections of TEMP and SYNOP data in estimation

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

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: Squared multiple R: Adjusted squared multiple R: Standard error of estimate: Effect Coefficient Std Error Std Coef Tolerance t P(2 Tail) CONSTANT Z T RH T E COSINUS Z P_P0H E Analysis of Variance Source Sum-of-Squares df Mean-Square F-ratio P Regression E E E Residual E Durbin-Watson D Statistic First Order Autocorrelation

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: Squared multiple R: Adjusted squared multiple R: Standard error of estimate: Effect Coefficient Std Error Std Coef Tolerance t P(2 Tail) CONSTANT T COSINUS Z P_P0H RH SINUS TYPE_PNFFP0H Analysis of Variance Source Sum-of-Squares df Mean-Square F-ratio P Regression Residual *** WARNING *** Case has large leverage (Leverage = 0.012) Durbin-Watson D Statistic First Order Autocorrelation 0.165

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

Location of Jokioinen and Sodankylä; ECWMF PPM and DMO

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 +06h +48h 18h

ECMWF MAE Summer 2002

Error of HIRLAM (and PPM) temperature forecasts (summer stations) Forecast length (hours)

Error of ECMWF (and PPM) temperature forecasts (summer stations) Forecast length (hours)

Dep Var: T2M_09UTC N: 3290 Multiple R: Squared multiple R: Adjusted squared multiple R: Standard error of estimate: Effect Coefficient Std Error Std Coef Tolerance t P(2 Tail) CONSTANT V T COSINUS CL_MAX Z P_P0H Dep Var: T2M_12UTC N: 3289 Multiple R: Squared multiple R: Adjusted squared multiple R: Standard error of estimate: Effect Coefficient Std Error Std Coef Tolerance t P(2 Tail) CONSTANT V T COSINUS CL_MAX Z P_P0H Jokioinen Summer 12 UTC TEMP PPM Models for 09 UTC and 12 UTC

Error of HIRLAM (and PPM) temperature forecasts (autumn stations) Forecast length (hours)

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

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

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

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

Error of ECMWF (and PPM) temperature forecasts (autumn stations) Forecast length (hours)

Error of HIRLAM (and PPM) temperature forecasts (spring stations) Forecast length (hours)

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

Error of HIRLAM (and PPM) temperature forecasts (winter stations) Forecast length (hours)

Error of ECMWF (and PPM) temperature forecasts (winter stations) Forecast length (hours)

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

Error of ECMWF (and PPM) temperature forecasts (summer stations) Forecast length (hours)

Error of ECMWF (and PPM) temperature forecasts (winter stations) Forecast length (hours)

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

A Fuzzy system for adaptation of ECMWF T2m forecasts Ahti Sarvi Fuzzy system has been applied to correct the temperature (T 2m ) 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.

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

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

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

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, R