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Seasonal climate prediction using linear weighted multi model system W. T. Yun APCN/ Korea Meteorological Administration. Contents Introduction What is Multi Model Ensemble? Construction of Multi Model Ensemble System - Gauss-Jordan Elimination - PowerPoint PPT Presentation
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Multi Model Ensemble Prediction
Seasonal climate prediction using linear weighted
multi model system
W. T. Yun
APCN/
Korea Meteorological Administration
Multi Model Ensemble Prediction
Contents
Introduction
What is Multi Model Ensemble?
Construction of Multi Model Ensemble System
- Gauss-Jordan Elimination
- Singular Value Decomposition (SVD)
- Synthetic multi model ensemble
- Generating of Synthetic Dataset
Multi Model Ensemble Seasonal Forecast
Skill of Multi Model Forecast
Application
Multi Model Ensemble Prediction
Regional climate change and climate variability have various impacts on the socio-economic activities. The impacts increase as the socio-economic activities become complex and active.
One of important and challenging task in areas of meteorology is climate seasonal prediction.
The advance climate seasonal prediction of droughts, monsoon etc. is now scientifically feasible.
This can be enormously beneficial in national planning, e.g. in areas of water resources management, disaster management, and agricultural planning and food production.
Introduction
Multi Model Ensemble Prediction
What is multi model ensemble?
Multi Model Ensemble
An Ensemble comprising different models
weighted Multi Model Ensemble
Weighted Combination of Multi Models
Multi Model Ensemble Prediction
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Biased Ensemble Mean
Bias Corrected Ensemble Mean
weighted Combination of Multi Models
Multi-Model Ensemble Anomaly Forecast?
Multi Model Ensemble Prediction
ECMWF
GFDL
MPI
AMIP Model Forecasts (Dec. 1988) Superensemble Forecast
Obs
Sup
Sup-Obs
Why Multi-Model Ensemble Forecast?
Multi Model Ensemble Prediction
The climate system can be regarded as a dynamic nonlinear systemPrediction
Linear statistical methods
Nonlinear statistical methods, Artificial neural network methods
Construction of Multi-Model Ensemble
Multi Model Ensemble Prediction
jk
·····
···.
Input layerxk
Hidden layerhj
Output layeryi
x1
x2
x3
xk
Prediction
ij
Error
A feed-forward neural network with one hidden layer, where the jth neuron in this hidden layer is assigned the value hj.
A linear combination of the neurons in the layer just before the output layer.
The cost function is minimized by means of gradient descent.
Whole vector of weight are updated according to the back propagation learning rule.
The learning can be more efficient by including a momentum term, which refers to previous updating.
Local minimum in the network can be avoided by introducing noise to the gradient descent updating rule, which in the case considered here is following Manhattan updating rule.
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Neural Network Model with Back-Propagation
Multi Model Ensemble Prediction
RMSE of Global Precipitation for 12Months (Jan.-Dec. 1988) ANN Forecasts (using AMIP data)
1.1
1.15
1.2
1.25
1.3
1.35
1.4
1.45
1.5
1.55
1 2 3 4 5 6 7 8 9 10 11 12
R M
S
Bias Corrected
Climatology
ANN
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Skill Score of Non-Linear Multi-Model Ensemble Forecast
Multi Model Ensemble Prediction
Construction of weighted linear Multi-
Model Ensemble Prediction System
Multi Model Ensemble Prediction
Observed Analysis
Training Phase Forecast Phase
MME Forecast
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t=0
Multi-Model Ensemble Prediction System
Multi Model Ensemble Prediction
t=0
A
B
C
D
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t=t-1…
MME with Pointwise Regression
(1)
t=0
A
B
C
D
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t=t-1…(2) MME with Pattern
Regression
t=0
A
B
C
D
E
t=t-1…(3) MME with Spatio-
Temporal Regression
Weighted Multi-Model Ensemble Techniques
Multi Model Ensemble Prediction
Superensemble Based on
Gauss-Jordan Elimination
Multi Model Ensemble Prediction
Superensemble Forecast :
Where, Fi is the ith model forecast , is the mean of the ithforecast over the training period, is the observed mean over the training period, are regression coefficients obtained by a minimization procedure during the training period, and N is the number of forecast models involved.
For obtaining the weights, the covariance matrix is built with the seasonal cycle-removed anomaly ( )
,
where, t and i, j denote time and ith - ,jth – forecast model, respectively. After calculation of the covariance matrix C, we can construct the weighting component for each grid point of each model.
T.N. Krishnamurti et al., 1999, Science
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Construction of Superensemble
Multi Model Ensemble Prediction
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Multi Model Ensemble Prediction
Superensemble Based on SVD
Multi Model Ensemble Prediction
Where, Fi is the ith model forecast, is the mean of the ith forecast over the training period, is the observed mean over the training period, ai are regression coefficients obtained by a minimization procedure during the training period, and N is the number of forecast models involved. For obtaining the weights, the covariance matrix is built with the seasonal cycle-removed anomaly (F’).
Where, t and i, j denote time and ith- ,jth– forecast model, respectively. After construction of the covariance matrix C, weights are computed for each grid point of each model.
Best Linear Unbiased Estimation (BLUE)
This will be the solution-vector of smallest length |x|2 in the least-square sense. x which minimizes r ≡||C·x - b||. SVD realizes a completely orthogonal decomposition for any matrix.
W.T.Yun, et al., 2003, J. Climate
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MME System based on SVD
Multi Model Ensemble Prediction
This will be the solution-vector of smallest length in the least-square sense.
x which minimizes
In the case of an underdetermined system, m<n, fewer equations than unknowns, SVD produces a solution whose values are smallest in the least-square sense.
In the case of an overdetermined system, m>n, more equations than unknowns, SVD produces a solution that is the best approximation in the least-square
sense.
The SVD technique removes the singularity problem.
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SVD realizes a completely orthogonal decomposition for any matrix A
Multi Model Ensemble Prediction
Error Covariance Matrices (AMIP) (Precipitation: Gauss-Jordan and SVD)
Total Variance
UnexplainedVariance (%)
ExplainedVariance
Multi Model Ensemble Prediction
%)100or (
varianceecorrelativ22
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rBrB
r
variancetotal
varianceexplained2 r Relative unexpl. Variance = 1 - r2
Variables
Total
Variance
r2 (%)Gauss-Jordan
SVDw(1) w(1-2) w(1-3) w(1-4) w(1-5) w(1-6)
Precipitation 1.2496 85.0723 92.2724 90.4899 89.1822 87.8679 86.5430 85.2433
T850 2.3328 90.3815 97.4425 95.8743 94.4600 93.2157 91.9906 90.5030
u200 19.3385 87.1593 93.6309 92.3347 91.1363 89.8606 88.6386 87.3436
u850 4.2623 90.1600 96.2329 95.0812 93.7804 92.7039 91.5405 90.3010
v200 10.7958 92.5053 98.0942 96.9052 95.9238 94.8459 93.7451 92.6036
v850 2.3297 92.7304 98.6048 97.2439 96.1230 95.0179 93.9193 92.8188
Relative explained variance r2 (%) of regression models using Gauss-Jordan elimination and SVD with zeroing the small singular values. All values are averaged.
Explained Variance of Regression Models
Multi Model Ensemble Prediction
Training ForecastConventional Superensemble SVD
SVD Mean RMSE
Conventional Superensemble
Simple Ensemble
RMSE of MME based on SVD
(Global, Precipitation)
Multi Model Ensemble Prediction
The condition number of a matrix is defined as the ratio of the largest (in magnitude) of the wj’s to the smallest of the wj’s. A matrix is singular if its condition number is infinite, and it is ill-conditioned if its condition number is too large.
The solution vector x obtained by zeroing the small wj’s and then using the equation (1) is better than SVD solution where the small wj’s are left nonzero. It may seem paradoxical that this can be so, since zeroing a singular value corresponds to throwing away one linear combination of the set of equations that we are trying to solve. The resolution of the paradox is that we are throwing away precisely a combination of equations that is corrupted by roundoff error. If we let the small wj’s nonzero, it usually makes the residual larger. We don’t know exactly what threshold to zero the small wj’s is acceptable.
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Zeroing the Small Singular Values
Multi Model Ensemble Prediction
w(1) w(1-2) w(1-3) w(1-4) w(1-5) w(1-6)0
2
4
6
8
10
12
14
16
0
50
100
150
200
250
300
w1, 2, 3, 4, 5, 6
Singular Values n
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Singular Values & Variance in the estimate of xj
(Precipitation, for one grid point)
Multi Model Ensemble Prediction
1.27
1.28
1.29
1.3
1.31
1.32
1.33
1.34
1.6
1.61
1.62
1.63
1.64
1.65
1.66
1.67
3.62
3.64
3.66
3.68
3.7
3.72
3.74
3.76
3.78
4.7
4.75
4.8
4.85
4.9
4.95
5
5.05
5.1
5.15
5.2
w (1), (1-2), (1-3), (1-4), (1-5), (1-6) G Clim w (1), (1-2), (1-3), (1-4), (1-5), (1-6) G Clim
w (1), (1-2), (1-3), (1-4), (1-5), (1-6) G Clim w (1), (1-2), (1-3), (1-4), (1-5), (1-6) G Clim
Global mean precipitation RMSE Global mean T850 RMSE
Global mean v200 RMSEGlobal mean u200 RMSE
Global Mean RMSE
(with Zeroing the Small Singular Values)
Multi Model Ensemble Prediction
Cancellation of bias among different models
Not directly influenced by the model’s systematic errors
Maximization of explained variance
Removes singularity in matrix
Best Linear Unbiased Estimator (BLUE)
Zeroing the small singular values wj
High Prediction Skill of Multi-Model Ensemble
Multi Model Ensemble Prediction
Synthetic Multi Model Ensemble
Multi Model Ensemble Prediction
The MME prediction skill during the forecast phase could be degraded if the training
was executed with either a poorer analysis or poorer forecasts.
This means that the prediction skills are improved when higher quality training data sets
are deployed for the evaluation of the multi model bias statistics.
Synthetic Multi Model Ensemble
Multi Model Ensemble Prediction
E(2) – Minimization
Actual Data SetSynthetic Ensemble Prediction
Synthetic Data Set
Superensemble Prediction
Schematic chart for the synthetic superensemble prediction system. The synthetic data are generated from the FSU coupled multi-model outputs by minimizing the residual error variance E(2).
W.T. Yun, 2004, Tellus accepted
Synthetic Multi Model Ensemble
Multi Model Ensemble Prediction
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2 - Minimization
Multi Model Ensemble Prediction
Actual Data Set (N) Synthetic Data Set (N) Prediction
E(2) -Minimization
Schematic chart of the multi model synthetic MME prediction. The synthetic data set is generated from the actual data set.
N - Actual Data Set
N - Synthetic Data Set
Estimating Consistent PatternWhat is matching spatial
pattern in forecast data, Fi(x,T), which evolves according to PC time series O(t) of observation
data, O(x,t)?
Observed Analysis
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Generating Synthetic Data Set
Multi Model Ensemble Prediction
N - Synthetic Data Set
Observed Analysis
Training Phase Forecast Phase
SyntheticMME Forecast
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The weights are computed at each grid point by minimizing the function:
train
ttt OSG
0
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The synthetic data set generated is separated into training and forecast phases. During training phase, optimal weights are computed which are used for producing synthetic MME forecast.
Synthetic MME Prediction
Multi Model Ensemble Prediction
Atmospheric Global Spectral Model (T63L14)+Hamburg Ocean Model HOPE
Starting from 31 December 1986 (to Dec. 2002), every 15 days three months forecasts were made with the four different versions of the coupled model. The multimodels are constructed using two cumulus parameterization schemes (modified Kuo’s scheme following Krishnamurti and Bedi, 1988; and Arakawa-Schubert type scheme following Grell, 1993) and two radiation parameterization schemes (an emissivity-abosrbtivity based radiative transfer algorithm following Chang 1979 and a band model for radiative transfer following Lacis and Hansen 1974) in the atmospheric model only. KOR – Kuo type convection with Chang radiation computationsKNR – Kuo type convection with Lacis and Hansen radiation computation AOR – Arakawa Schubert type convection with Chang radiation computationsANR – Arakawa Schubert type convection with Lacis and Hansen radiation computation
FSU Unified Model Data Set
Multi Model Ensemble Prediction
DEMETER (Development of a European Multi-Model Ensemble System for Seasonal to Inter-Annual Prediction) system comprises 7 global coupled ocean-atmosphere models.
CERFACS (European Centre for Research and Advanced Training in Scientific Computation, France), ECMWF (European Centre for Medium-Range Weather Forecasts, International Organization), INGV (Istituto Nazionale de Geofisica e Vulcanologia, Italy), LODYC (Laboratoire d’Océanographie Dynamique et de Climatologie, France), Météo-France (Centre National de Recherches Météorologiques, Météo-France, France), Met Office (The Met Office, UK), MPI (Max-Planck Institut für Meteorologie, Germany)
The DEMETER hindcasts have been started from 1st February, 1st May, 1st August, and 1st November initial conditions. Each hindcast has been integrated for 6 months and comprises an ensemble of 9 members.
The multi-model synthetic ensemble/superensemble is formed by merging the 15 yr (1987-2001) ensemble hindcasts of the seven models, thus comprising 7x9 ensemble members.
DEMETER Model Data Set
Multi Model Ensemble Prediction
Quality of Data Set
Actual data setSynthetic data set
Multi Model Ensemble Prediction
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
ACC & RMS of the DEMETER Multi Model & Synthetic Data Set (Average over 2-4 months Global Precipitation Forecast, JJA)(ECMWF, UKMO, Meteo France, MPI, LODYC, INGV, CERFACS)
0
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RMS of Actual Data Set
RMS of Synthetic Data Set
ACC of Actual Data Set
-0.4
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ACC of Synthetic Data Set
87 88 89 90 91 92 93 94 95 96 97 98 99 00 01 Mean
87 88 89 90 91 92 93 94 95 96 97 98 99 00 01 Mean
87 88 89 90 91 92 93 94 95 96 97 98 99 00 01 Mean
87 88 89 90 91 92 93 94 95 96 97 98 99 00 01 Mean
Multi Model Ensemble Prediction
ACC & RMS for FSU Unified Model Data Set & Synthetic Data Set (Average over 1-3 months Global Surface Temperature Forecast, JJA; ANR, AOR, KNR, KOR)
-0.6
-0.4
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0123456789
101112
0123456789
101112
RMS of Actual Data Set
RMS of Synthetic Data Set
ACC of Actual Data Set
ACC of Synthetic Data Set
87 88 89 90 91 92 93 94 95 96 97 98 99 00 01 Mean
87 88 89 90 91 92 93 94 95 96 97 98 99 00 01 Mean
87 88 89 90 91 92 93 94 95 96 97 98 99 00 01 Mean
A : Arakawa Schubert cumulus parameterization K : FSU- modified Kuo cumulus parameterization algorithm. NR : Band model radiation code (New radiation scheme) OR : Emissivity absorbtivity radiation code (old radiation scheme)
87 88 89 90 91 92 93 94 95 96 97 98 99 00 01 Mean
Multi Model Ensemble Prediction
The Global Distribution of Weights for the DEMETER Multi Model & Synthetic Data Set (Average over 2-4 months Global JJA 2001 v-Wind at 850hPa Forecast)
(ECMWF, UKMO, Meteo France, MPI, LODYC, INGV, CERFACS)
Weights of Actual Data Set Weights of Synthetic Data Set
ECMWF
INGV
CERFACS
LODYC
Meteo France MPI
UKMO ECMWF
INGV
CERFACS
LODYC
Meteo France MPI
UKMO
Multi Model Ensemble Prediction
The Synthetic Seasonal Forecasts
Multi Model Ensemble Prediction
FSU Unified Model Synthetic Ensemble/Superensemble Prediction (Precipitation, 30S-30N, JJA 2001)
Obs.
EM
SEM
SSF
Multi Model Ensemble Prediction
DEMETER Multi Model Synthetic Ensemble/Superensemble Prediction (Precipitation, 5N-40N 150W-50W, JJA 2001)
Obs.
SSF
EM
SEM
Multi Model Ensemble Prediction
DEMETER Multi Model Synthetic Ensemble/Superensemble Prediction (Surface Temperature, 5N-40N 150W-50W, JJA 2001)
Obs.
SSF
EM
SEM
Multi Model Ensemble Prediction
DEMETER Multi Model Synthetic Ensemble/Superensemble Prediction (Wind Speed at 850hPa, India 10SN-35N 50E-110E, JJA 2001)
Obs.
SSF
EM
SEM
Multi Model Ensemble Prediction
The Skill Score of Synthetic Forecasts
Multi Model Ensemble Prediction
The Skill Metrics of Forecasts in a Deterministic Sense
The AC is a measure of how well the phase of the forecast anomalies corresponds to the observed anomalies. The overbar denotes mean, and the summation can be either in space or in time, depending on whether spatial or temporal anomaly correlation is computed and G is the number of either grid points or time points.
The RMSE is a measure of the average magnitude of the forecast error.
Despite the fact AC is a good measure of phase error and doesn’t take bias into account, it is possible for a forecast with large errors to still have a good correlation coefficients. So, it is necessary to evaluate the average magnitude of the forecast errors.
22 )()(
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GRMS
Skill Score Metrics
Multi Model Ensemble Prediction
-0.1
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0.8Member ModelEM
SEM SF SSF
JJA-TR
1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002
1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002
DJF-TRMember ModelEM
SEM SF SSF
The summer (JJA) and Winter (DJF) precipitation anomaly correlation skill scores for tropical domain (30S-30N). The bars in diagram indicate skill scores of the 4 FSU member models, bias corrected ensemble mean (EM), synthetic ensemble mean (SEM), superensemble (SF), and synthetic superensemble (SSF) from left to right.
Cross Validated ACC for FSU unified Model & synthetic MME
Multi Model Ensemble Prediction
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Cross-validated RMS & ACC for FSU Unified Model & Synthetic Superensemble (30-30N JJA, Average over 1-3 months Precipitation Forecast, ANR, AOR, KNR, KOR)
A : Arakawa Schubert cumulus parameterization K : FSU- modified Kuo cumulus parameterization algorithm. NR : Band model radiation code (New radiation scheme) OR : Emissivity absorbtivity radiation code (old radiation scheme)
ANR, AOR, KNR, KOR FSU EM SEM SSF
1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 Mean
1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 Mean
Multi Model Ensemble Prediction
Cross-validated RMS & ACC of the DEMETER Multi Model & Synthetic Superensemble (30°S-30°NJJA, Average over 2-4 months Surface Temperature Forecast)
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1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 Mean
1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 Mean
ECMWF, UKMO, Meteo France, MPI, LODYC, INGV, CERFACS DEMETER EM SEM SSF
Multi Model Ensemble Prediction
Cross-validated RMS & ACC of the DEMETER Multi Model & Synthetic Superensemble (30°S-30°N JJA, Average over 2-4 months Precipitation Forecast)
0
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-0.1
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1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 Mean
1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 Mean
ECMWF, UKMO, Meteo France, MPI, LODYC, INGV, CERFACS DEMETER EM SEM SSF
Multi Model Ensemble Prediction
MAM JJA SON DJF
PODy
EM 0.55 0.55 0.55 0.56
SEM 0.58 0.58 0.58 0.58
SF 0.55 0.55 0.55 0.55
SSF 0.58 0.58 0.58 0.60
PODn
EM 0.60 0.61 0.60 0.61
SEM 0.61 0.60 0.61 0.61
SF 0.60 0.60 0.60 0.61
SSF 0.61 0.59 0.60 0.61
ETS
EM 0.11 0.11 0.10 0.11
SEM 0.13 0.13 0.13 0.12
SF 0.10 0.11 0.10 0.10
SSF 0.13 0.12 0.13 0.13
TSS
EM 0.16 0.16 0.15 0.16
SEM 0.19 0.18 0.19 0.19
SF 0.14 0.15 0.15 0.16
SSF 0.19 0.17 0.19 0.20
Overall average statistics of seasonal precipitation categorical forecast. Statistics are given for March-April-May (MAM), June-July-August (JJA), September-October-November (SON), and December-January-February (DJF). EM, SEM, SF, and SSF indicate unbiased ensemble mean, synthetic ensemble mean, superensemble based on SVD, and synthetic superensemble forecast, respectively.
Statistics of seasonal precipitation categorical forecasts
Multi Model Ensemble Prediction
0
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0.5
GL-DJF TR-DJF NH-DJFGL-JJA TR-JJA NH-JJA
GL-SON TR-SON NH-SONGL-MAM TR-MAM NH-MAM
Member ModelEM
SEM SF SSF
16 years (1987-2002) averaged (Fischer Z-Transform) AC precipitation skill scores of all seasons (MAM, JJA, SON, DJF) for global, tropical (30S-30N), and north hemispheric (0-60N) domains. The bars in the diagram indicate the 4 member models, unbiased ensemble mean (EM), synthetic ensemble mean (SEM), superensemble based on SVD (SF), synthetic superensemble (SSF) of FSU model.
Averaged ACC for All Season (FSU unified Model & synthetic MME)
Multi Model Ensemble Prediction
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
RMS-TR-JJA
Member ModelEMCLIM
SEM SF SSF
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
RMS-TR-DJF
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
RMS-TR-MAM
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
RMS-TR-DJF
16 years (1987-2002) averaged RMS precipitation skill scores of all seasons (MAM, JJA, SON, DJF) for tropical (30 S-30N) domains. The bars in the diagram indicate the 4 member models, unbiased ensemble mean (EM), climatology (CLIM), synthetic ensemble mean (SEM), superensemble based on SVD (SF), synthetic superensemble (SSF) of FSU model.
Averaged ACC for Tropic (FSU unified Model & synthetic MME)
Multi Model Ensemble Prediction
Superensemble Precipitation Forecast for JFM 1988, 9 Year Training(AMIP: MPI, CSI, ECMWF, GFDL, NMC, UKMO, ECMWF Reanalysis)
OBS
SUP
DIF
JANUARY FEBURARY MARCH
Multi Model Ensemble Prediction
Superensemble Precipitation Forecast for AMJ 1988, 9 Year Training(AMIP: MPI, CSI, ECMWF, GFDL, NMC, UKMO, ECMWF Reanalysis)
OBS
SUP
DIF
APRIL MAY JUNE
Multi Model Ensemble Prediction
Superensemble Precipitation Forecast for JAS 1988, 9 Year Training(AMIP: MPI, CSI, ECMWF, GFDL, NMC, UKMO, ECMWF Reanalysis)
OBS
SUP
DIF
JULY AUGUST SEPTEMBER
Multi Model Ensemble Prediction
Superensemble Precipitation Forecast for OND 1988, 9 Year Training(AMIP: MPI, CSI, ECMWF, GFDL, NMC, UKMO, ECMWF Reanalysis)
OBS
SUP
DIF
OCTOBER NOVEMBER DECEMBERAMIP Model Forecast for December 1988
ECMWF
GFDL
MPI
Multi Model Ensemble Prediction
Application of Multi Model Ensemble Technique
Multi Model Ensemble Prediction
Cor: 0.72
Cor: 0.41
Forecasting Floods from the Superensemble
One of the areas of strength of the superensemble is in its ability to predict
heavy rains better than any existing models.
Mozambique Floods, Feb. 2000
Multi Model Ensemble Prediction
Skill of Numerical Weather Prediction
Multi Model Ensemble Prediction
Real Time Hurricane Forecasts (Floyd of 1999)
Multi Model Ensemble Prediction
Input of Multi Model Dataset
Make AnomaliesConstructCovariance
MatrixSolve
CovarianceMatrixCompute
WeightsReconstruction Forecast-FieldsMME
Forecast
Construction of MME Program
Multi Model Ensemble Prediction
Summary
• The synthetic multi model algorithm for climate predictions shows better skill scores than the individual member models, and more importantly, better than the unbiased ensemble of member models.
• The synthetic algorithm can be applied to weather and climate forecasting (Short-, Medium-, Long-Range forecasts, and Hurricane prediction).
• The synthetic algorithm can be incorporated into a state-of-the-art dynamic model. Given a number of physical parameterizations of a given process in a dynamical model, the statistical multi model approach can be applied towards the calculation of an optimal unified parameterization scheme.