Seasonal climate prediction using linear weighted

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Seasonal climate prediction using linear weighted
multi model system W. T. Yun APCN/ Korea
Meteorological Administration
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• 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

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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.
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• What is multi model ensemble?
• Multi Model Ensemble
• An Ensemble comprising different models
• weighted Multi Model Ensemble
• Weighted Combination of Multi Models

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Biased Ensemble Mean
Bias Corrected Ensemble Mean
weighted Combination of Multi Models
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A feed-forward neural network with one hidden
layer, where the jth neuron in this hidden layer
is assigned the value hj.
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R M S
Bias Corrected Climatology ANN
Jan Feb Mar Apr May Jun Jul
Aug Sep Oct Nov Dec
RMSE of Global Precipitation for 12Months
(Jan.-Dec. 1988) ANN Forecasts (using AMIP data)
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Construction of weighted linear Multi- Model
Ensemble Prediction System
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Superensemble Based on Gauss-Jordan
Elimination
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Gauss-Jordan Elimination
AxB
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Superensemble Based on SVD
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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 x2 in the
least-square sense. x which minimizes r Cx -
b. SVD realizes a completely orthogonal
decomposition for any matrix. W.T.Yun, et al.,
2003, J. Climate
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Error Covariance Matrices (AMIP) (Precipitation
Gauss-Jordan and SVD)
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Relative explained variance r2 () of regression
models using Gauss-Jordan elimination and SVD
with zeroing the small singular values. All
values are averaged.
Relative unexpl. Variance 1 - r2
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SVD Mean RMSE
Conventional Superensemble
RMSE of MME based on SVD (Global, Precipitation)
Simple Ensemble
Conventional Superensemble
SVD
Training
Forecast
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The condition number of a matrix is defined as
the ratio of the largest (in magnitude) of the
wjs to the smallest of the wjs. A matrix is
singular if its condition number is infinite, and
it is ill-conditioned if its condition number is
too large.
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J.Climate, Yun et.al (2003)
Singular Values
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• Cancellation of bias among different models
• Not directly influenced by the models
  systematic errors
• Maximization of explained variance

• Removes singularity in matrix
• Best Linear Unbiased Estimator (BLUE)
• Zeroing the small singular values wj

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Synthetic Multi Model Ensemble
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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.
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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
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The residual error variance E(?2) is minimized.
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Schematic chart of the multi model synthetic MME
prediction. The synthetic data set is generated
from the actual data set.
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The weights are computed at each grid point by
minimizing the function
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.
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• 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 Kuos
  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
  computations
• KNR Kuo type convection with Lacis and Hansen
  radiation computation
• AOR Arakawa Schubert type convection with Chang
  radiation computations
• ANR Arakawa Schubert type convection with Lacis
  and Hansen radiation computation

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• 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
  dOcéanographie 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.

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Quality of Data Set Actual data set Synthetic
data set
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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)
ACC of Actual Data Set
RMS of Actual 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
RMS of Synthetic 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
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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)
ACC of Actual Data Set
87 88 89 90 91 92 93 94 95 96 97
98 99 00 01 Mean
RMS of Actual Data Set
87 88 89 90 91 92 93 94 95 96 97
98 99 00 01 Mean
RMS of Synthetic 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
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)
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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)
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The Synthetic Seasonal Forecasts
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FSU Unified Model Synthetic Ensemble/Superensemble
Prediction (Precipitation, 30?S-30?N, JJA 2001)
Obs.
EM
SEM
SSF
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DEMETER Multi Model Synthetic Ensemble/Superensemb
le Prediction (Precipitation, 5?N-40?N
150?W-50?W, JJA 2001)
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DEMETER Multi Model Synthetic Ensemble/Superensemb
le Prediction (Surface Temperature, 5?N-40?N
150?W-50?W, JJA 2001)
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DEMETER Multi Model Synthetic Ensemble/Superensemb
le Prediction (Wind Speed at 850hPa, India
10?SN-35?N 50?E-110?E, JJA 2001)
Obs.
EM
SSF
SEM
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The Skill Score of Synthetic Forecasts
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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 doesnt 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.
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The summer (JJA) and Winter (DJF)
precipitation anomaly correlation skill scores
for tropical domain (30?S-30?N). 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.
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Cross-validated RMS ACC for FSU Unified Model
Synthetic Superensemble (30?-30?N JJA, Average
over 1-3 months Precipitation Forecast, ANR, AOR,
KNR, KOR)
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
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)
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Cross-validated RMS ACC of the DEMETER Multi
Model Synthetic Superensemble (30S-30NJJA,
Average over 2-4 months Surface Temperature
Forecast)
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
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Cross-validated RMS ACC of the DEMETER Multi
Model Synthetic Superensemble (30S-30N JJA,
Average over 2-4 months Precipitation Forecast)
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
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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.
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GL-MAM
TR-MAM
NH-MAM
TR-SON
GL-SON
NH-SON
GL-JJA
TR-JJA
NH-JJA
GL-DJF
TR-DJF
NH-DJF
16 years (1987-2002) averaged (Fischer
Z-Transform) AC precipitation skill scores of all
seasons (MAM, JJA, SON, DJF) for global, tropical
(30?S-30?N), and north hemispheric (0?-60?N)
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.
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RMS-TR-JJA
RMS-TR-MAM
RMS-TR-DJF
RMS-TR-DJF
16 years (1987-2002) averaged RMS precipitation
skill scores of all seasons (MAM, JJA, SON, DJF)
for tropical (30?S-30?N) 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.
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Superensemble Precipitation Forecast for JFM
1988, 9 Year Training (AMIP MPI, CSI, ECMWF,
GFDL, NMC, UKMO, ECMWF Reanalysis)
FEBURARY
MARCH
JANUARY
OBS
SUP
DIF
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Superensemble Precipitation Forecast for AMJ
1988, 9 Year Training (AMIP MPI, CSI, ECMWF,
GFDL, NMC, UKMO, ECMWF Reanalysis)
MAY
JUNE
APRIL
OBS
SUP
DIF
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Superensemble Precipitation Forecast for JAS
1988, 9 Year Training (AMIP MPI, CSI, ECMWF,
GFDL, NMC, UKMO, ECMWF Reanalysis)
AUGUST
SEPTEMBER
JULY
OBS
SUP
DIF
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Superensemble Precipitation Forecast for OND
1988, 9 Year Training (AMIP MPI, CSI, ECMWF,
GFDL, NMC, UKMO, ECMWF Reanalysis)
NOVEMBER
DECEMBER
OCTOBER
OBS
SUP
DIF
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Application of Multi Model Ensemble Technique
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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
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Skill of Numerical Weather Prediction
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Real Time Hurricane Forecasts (Floyd of 1999)
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• Construction of MME Program

Input of Multi Model Dataset
Make Anomalies
Construct Covariance Matrix
Solve Covariance Matrix
Compute Weights
Reconstruction Forecast-Fields
MME Forecast
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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.