The development of statistical interpretation and adaptation of NWP at FMI Juha Kilpinen, Ahti Sarvi

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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

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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

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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

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Forecasting process at FMI
Climatological
Visualisation and Editing by Forecaster (interpre
tations)
Customers
and editing of
database
Observations

satellites

weather radars
surface

observations

soundings
Numerical weather
forecast models (by
Old manual process
supercomputers)
Old Vax workstation
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Editing by forecasters (FMI) Post processing
Forecasting process at FMI
Climate database (FMI)
Forecasters Manual products
Observations (Global Local)
Production Servers (FMI)
Forecasts
Customers Public Web Business Media Aviation Ind
ustry 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)
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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 (Ngt5) TT3
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MAE of temperature forecasts (3 stations, 9
seasons, 0.5-5 days)
Centralized editing on commercial side
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HIRLAM DMO and Obs (25.4.2001)
HIRLAM PPM and Obs (25.4.2001)
Error 5-9 degrees max error 10 degrees
Error 10-15 degrees max error -20 degrees
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• 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 TEMPs 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.

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Derived predictors for PPM

• FF850 SQRT(ABS(V850U850))
• TYPE_PRHFF (P_P0H-949)/15.6(24-FF850)/3.93(100
  -RH850)/28
• CL_MAX MAX(RH500RH500/100,RH700RH700/100,RH850
  RH850/100)
• TYPE_PCLFF (P_P0H-949)/15.6(100-CL_MAX)/28.2(2
  4-FF850)/3.93
• P_P0H2 P_P0H-1013
• Z8502 Z850-1500
• Z7002 Z700-3000
• Z5002 Z500-5200
• COSINUS COS(23.1417JUL/360)
• SINUS SIN(23.1417JUL/360)

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Estimation error of dependent PPM model
UTC
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Estimation error of dependent PPM model
UTC
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Connections of TEMP and SYNOP data in estimation
12 UTC TEMP
SYNOP 09 12 15 18 21 00
03 06 UTC
00 UTC TEMP
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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 2.49825E04 7
3.56892E03 2.57232E03 0.00000000 Residual
7.49214E02 540 1.38743253  
-------------------------------------------------
------------------------------ Durbin-Watson D
Statistic 1.52355145 First Order
Autocorrelation 0.23719694
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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
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• 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

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Location of Jokioinen and Sodankylä ECWMF PPM
and DMO
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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
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ECMWF MAE Summer 2002
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Error of HIRLAM (and PPM) temperature forecasts
(summer 2002 30 stations)
Forecast length (hours)
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Error of ECMWF (and PPM) temperature forecasts
(summer 2002 30 stations)
Forecast length (hours)
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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
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Error of HIRLAM (and PPM) temperature forecasts
(autumn 2002 30 stations)
Forecast length (hours)
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Temperature error of HIRLAM (and PPM) at
Jokioinen (02935) summer 2002
Forecast length (hours)
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Temperature error of ECMWF (and PPM) at Jokioinen
(02935) summer 2002
Forecast length (hours)
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Temperature error of HIRLAM (and PPM) at
Sodankylä (02836) summer 2002
Forecast length (hours)
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Temperature error of ECMWF (and PPM) at Sodankylä
(02836) summer 2002
Forecast length (hours)
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Error of ECMWF (and PPM) temperature forecasts
(autumn 2002 30 stations)
Forecast length (hours)
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Error of HIRLAM (and PPM) temperature forecasts
(spring 2002 30 stations)
Forecast length (hours)
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Error of ECMWF (and PPM) temperature forecasts
(spring 2002 30 stations)
Forecast length (hours)
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Error of HIRLAM (and PPM) temperature forecasts
(winter 2002-2003 30 stations)
Forecast length (hours)
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Error of ECMWF (and PPM) temperature forecasts
(winter 2002-2003 30 stations)
Forecast length (hours)
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Residuals versus Estimates Sodankylä PPM model in
Winter (00 UTC)
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Error of ECMWF (and PPM) temperature forecasts
(summer 2002 30 stations)
Forecast length (hours)
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Error of ECMWF (and PPM) temperature forecasts
(winter 2002-2003 30 stations)
Forecast length (hours)
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Error of HIRLAM and ECMWF ( PPM) temperature
forecasts in Finland (one year, 30 stations)
Forecast length (hours)
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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.

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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

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

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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