Nov. 19, 2014 IPWG7 training course The IPWG7 Training Course Session 5: NWP applications and...
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Nov. 19, 2014 IPWG7 training course The IPWG7 Training Course Session 5: NWP applications and Assimilation Data Assimilation Kazumasa Aonashi Meteorological
Nov. 19, 2014 IPWG7 training course The IPWG7 Training Course
Session 5: NWP applications and Assimilation Data Assimilation
Kazumasa Aonashi Meteorological Research Institute/
[email protected]
Slide 2
Nov. 19, 2014 IPWG7 training courseOutlineIntroduction Why do
we need data assimilation technique in the first place? What is
Data Assimilation? Ensemble-Based Variational Assimilation Method
(EnVA) to Incorporate MWI TB into a Cloud- Resolving Model Summary
& Discussion
Slide 3
Nov. 19, 2014 IPWG7 training course Observed data Definition of
Data Assimilation NWP forecasts Assimilation Other Observations
Analysis data Analysis technique in which the observed information
is accumulated into the model state by taking advantage of
consistency constraints with the model equations
Slide 4
Satellite Observation (TRMM) InfraredImager SST, Winds Cloud
Particles Frozen Precip. Snow Aggregates Melting Layer Rain Drops
Radiation from Rain Scattering by Frozen Particles Radar Back
scattering from Precip. Scattering Radiation 00 Microwave
Radiometer Cloud Top Temp. 10m 3 mm-3cm GH 2cm GH GHz Nov. 19, 2014
IPWG7 training course
Slide 5
Current Retrievals vs. User needs Current Situation: Precip
retrievals from each sensors User Needs: The optimal retrieval
using all sensors Ret. Alg. Sat. Ret. Alg. Ret. Alg. Ret. Alg. Sat.
Precip. Sat. Retrieval Alg. Precip. Nov. 19, 2014 IPWG7 training
course
Slide 6
Future directions of retrieval algorithms Retrieved variables
(Precip, Temp, Qv, etc) In situ Obs. Satellite Radar Satellite MWR
We can use data assimilation techniques. Constraint (Governing
equations) Nov. 19, 2014 IPWG7 training course
Slide 7
Complementary Property of Upper-Air Sonde Data to Satellite
observation Weighting of AMSU-B B3 B4 B5 n GPS Occultation Nov. 19,
2014 IPWG7 training course
Slide 8
NWP can induce plausible precip from other variables (Ps, T,
U,V, etc) Nov. 19, 2014 IPWG7 training course Hourly precip
forecasts for FT=1-6hr
Slide 9
Data Assimilation Nov. 19, 2014 IPWG7 training course
Slide 10
Major NWP models at JMA MSM: Meso-Scale Model 5km (3600x2880km)
/ 50leves top 22km 15 hour forecasts 00,06,12,18UTC 33 hour
forecasts 03,09,15,21UTC Data Assimilation: 4DVAR GSM: Global
Spectral Model TL959 0.1875deg 20km / 60levels top 0.1hPa 84 hour
forecasts 216 hour forecasts 12UTC Data assimilation: 4DVAR Nov.
19, 2014 IPWG7 training course
Slide 11
Data used in the assimilation cycles (Jun 22, 2011) Nov. 19,
2014 IPWG7 training course Observation data: Non-uniform Different
from NWP variables
Slide 12
Nov. 19, 2014 IPWG7 training course Observed data Definition of
Data Assimilation NWP forecasts Assimilation Other Observations
Analysis data Analysis technique in which the observed information
is accumulated into the model state by taking advantage of
consistency constraints with the model equations
Slide 13
DA is important for NWP DA is important for NWP. T213L30
Revision of cumulus parameterization T213L40 Revision of cumulus
parameterization Revision of cloud MODIS AMVs Revision of radiation
TL319L40 4D-Var SSM/I and TMI VarBC QuikSCAT ATOVS BT 3D-Var CSR
Revision of VarBC Revision of RTM SSMIS, ASCAT TL959L60 Reduced
Grid TL959L60 Courtesy of Y. Sato (JMA) 500 hPa Geopotential Height
RMSE (NH) Nov. 19, 2014 IPWG7 training course
Slide 14
Nov. 19, 2014 IPWG7 training course Evolution of DA technique
DA started with interpolation of the observed data. Interpolation
is not appropriate in practice. Use of first guess of previous NWP
forecast (Optimal Interpolation) Statistical approach to produce
analysis data: Modeling the error of the observation, the NWP first
guess, and constraints. Find optimal values that minimize the
analysis error. Sophisticated assimilation techniques 4DVAR
Ensemble-based assimilation
Slide 15
Nov. 19, 2014 IPWG7 training course O/I for single point
Slide 16
O/I for multi-dimensional case Nov. 19, 2014 IPWG7 training
course
Slide 17
Example of O/I Nov. 19, 2014 IPWG7 training course 1 st Guess
(Prev. Fcst) Observation Filtering d=Y-H(X) Interpolation X = Wd
Analysis Obs error Covariance Fcst error Covariance
Slide 18
Nov. 19, 2014 Statistical Approach Modeling of the errors
Observation error o =Y-H(Xt) where observation (Y) and the model
counterpart H(X) First guess & analysis error f =Xf Xt, a
=Xa-Xt where Xf,Xa are First guess & analysis of the model
state IPWG7 training course
Slide 19
Nov. 19, 2014 IPWG7 training course Statistical Approach Bayes
rule (conditional PDF) Conditional PDF of X given obs. Y: If errors
are Gaussian: The maximum likelyhood state is the one minimizes the
cost function J: (3DVAR)
Slide 20
Nov. 19, 2014 IPWG7 training course Simple Example We have a
temperature observation T o with STD o, given first guess T f with
STD f. The maximum likelyhood state is the one minimizes the cost
function J: TfTf ToTo TaTa
Slide 21
Basic Idea of 4DVAR Generalization of 3DVAR for observations
distributed in time: Use model equations as constraints: Nov. 19,
2014 IPWG7 training course
Slide 22
Basic Idea of Ensemble-based assimilation Obs. Analysis
ensemble mean T=t0T=t1T=t2 Analysis w/ errorsFCST ensemble mean
Estimating first-guess error with Ensemble forecasts Nov. 19, 2014
IPWG7 training course
Slide 23
Nov. 19, 2014 IPWG7 training course Ensemble-Based Variational
Assimilation Method (EnVA) EnVA Incorporation of MWI TB into a
Cloud-Resolving Model
Slide 24
2014/1/15 GPM PI WS GOAL: Ensemble-based Variational
Assimilation System to incorporate MWR TBs into CRMs SST, Winds
Cloud Particles Frozen Precip. Snow Aggregates Melting Layer Rain
Drops Scattering Radiation 00 MWR TBs MWR TBs are functions of
various atmospheric and surface variables 3 mm-3cm Water Vapor
JMANHM Saito et al,2001) Resolution: 5 km Grids: 400 x 400 x 38
Ensemble-based Variational Assim System
Slide 25
Cloud-Resolving Model used JMANHM Saito et al,2001) Resolution:
5 km Grids: 400 x 400 x 38 Time interval: 15 s Explicitly forecasts
6 species of water substances Nov. 19, 2014 IPWG7 training
course
Slide 26
Ensemble-based Assimilation System Obs. T=t0T=t1 T=t2 Ensemble
forecasts Mean of Ensemble forecasts Calculation of analysis of
Ensemble mean 26 Calculation of analysis of error cov. and Ensemble
member.
Slide 27
EnVA: min. cost function in the Ensemble forecast error
subspace Minimize the cost function with non-linear Obs. term.
Assume the analysis error belongs to the Ensemble forecast error
subspace Lorenc, 2003): Forecast error covariance is determined by
localization Cost function in the Ensemble forecast error subspace
Nov. 19, 2014 IPWG7 training course
Slide 28
Why Ensemble-based method?: 200km 10km Heavy Rain AreaRain-free
Area To estimate the flow-dependency of the error covariance
Ensemble forecast error corr. of PT (04/6/9/22 UTC) Nov. 19, 2014
IPWG7 training course
Slide 29
Why Variational Method ? Why Variational Method ? MWI TBs are
non-linear function of various CRM variables. TB becomes saturated
as optical thickness increases: TB depression mainly due to frozen
precipitation becomes dominant after saturation. To address the
non- linearity of TBs Nov. 19, 2014 IPWG7 training course
Slide 30
Detection of the optimum analysis Detection of the optimum by
minimizing where is diagonalized with U eigenvectors of S
Approximate the gradient of the observation with the finite
differences about the forecast error: To solve non-linear min.
problem, we performed iterations. Following Zupanski (2005), we
calculated the analysis of each Ensemble members, from the Ensemble
analysis error covariance. Nov. 19, 2014 IPWG7 training course
Slide 31
Case 2004/6/9/22 UTC) TY CONSON TMI TB19 RAM (mm/hr) Assimilate
TMI TBs Assimilate TMI TBs (10v, 19v, 21v) at 22UTC (10v, 19v, 21v
) at 22UTC Nov. 19, 2014 IPWG7 training course
Slide 32
Ensemble Forecasts & RTM code Ensemble forecasts 100
members started with perturbed initial data at 04/6/9/15 UTC (FG)
Geostrophically-balanced perturbation (Mitchell et al. 2002) plus
Humidity RTM: Guosheng Liu (2004) One-dimensional model
(Plane-parallel) Mie Scattering (Sphere) 4 stream approximation
Ensemble mean (FG) Rain mix. ratio TB19v cal. from FG Nov. 19, 2014
IPWG7 training course
Slide 33
TB19v from TMI and CRM outputs FG First guess DE After DEC ND:
NoDE+ EnVA CN DE+ EnVA TMI Nov. 19, 2014 IPWG7 training course
Slide 34
RAM and Rain mix. ratio analysis (z=930m) FGDE RAM NDCN Nov.
19, 2014 IPWG7 training course
Slide 35
RH(contours) and W(shades) along N-S FGDE CNND M Nov. 19, 2014
IPWG7 training course
Slide 36
Hourly Precip. forecasts (FT=0-1 h) 22-23Z 9th RAM DE CN ND FG
Nov. 19, 2014 IPWG7 training course
Slide 37
Hourly Precip. Forecasts (FT=3-4 h) 01-02Z 10th RAM DE CN ND FG
Nov. 19, 2014 IPWG7 training course
Slide 38
Summary Why do we need data assimilation technique in the first
place? What is Data Assimilation? Ensemble-Based Variational
Assimilation Method (EnVA) to Incorporate MWI TB into a Cloud-
Resolving Model Nov. 19, 2014 IPWG7 training course
Slide 39
Nov. 19, 2014 IPWG7 training course Any questions?
Slide 40
Nov. 19, 2014 IPWG7 training course EnVA to incorporate MWR TBs
into a CRM Problems in EnVA for CRM Displacement error correction
Application results
Slide 41
Problem in EnVA (1): Displacement error Large scale
displacement errors of rainy areas between the MWI observation and
Ensemble forecasts Presupposition of Ensemble assimilation is not
satisfied in observed rain areas without forecasted rain. AMSRE
TB18v (2003/1/27/04z) Mean of Ensemble Forecast (2003/1/26/21 UTC
FT=7h Nov. 19, 2014 IPWG7 training course
Slide 42
Presupposition of Ensemble-based assimilation Obs. Analysis
ensemble mean T=t0T=t1T=t2 Analysis w/ errorsFCST ensemble mean
Ensemble forecasts have enough spread to include (Obs. Ens. Mean)
Nov. 19, 2014 IPWG7 training course
Slide 43
Ensemble-based assimilation for observed rain areas without
forecasted rain Ensemble-based assimilation for observed rain areas
without forecasted rain Obs. Analysis ensemble mean T=t0T=t1T=t2
Analysis w/ errors FCST ensemble mean Assimilation can give
erroneous analysis when the presupposition is not satisfied.
Signals from rain can be misinterpreted as those from other
variables Displacement error correction is needed! Nov. 19, 2014
IPWG7 training course
Slide 44
Displacement error correction (DEC)+EnVA Methodology
Application results for Typhoon CONSON (T0404) Application results
for Typhoon CONSON (T0404)Case Assimilation Results Impact on
precipitation forecasts Nov. 19, 2014 IPWG7 training course
Slide 45
Displaced Ensemble variational assimilation method In addition
to, we introduced to assimilation. The optimal analysis value
maximizes Assimilation results in the following 2 steps: 1) DEC
scheme to derive from 2)EnVA scheme using the DEC Ensembles to
derive from Nov. 19, 2014 IPWG7 training course
Slide 46
Problem in EnVA (1): Displacement error Large scale
displacement errors of rainy areas between the MWI observation and
Ensemble forecasts Presupposition of Ensemble assimilation is not
satisfied in observed rain areas without forecasted rain. AMSRE
TB18v (2003/1/27/04z) Mean of Ensemble Forecast (2003/1/26/21 UTC
FT=7h Nov. 19, 2014 IPWG7 training course
DEC scheme: min. cost function for d Bayes Theorem can be
expressed as the cond. Prob. of Y given We assume Gaussian dist. of
where is the empirically determined scale of the displacement
error. We derived the large-scale pattern of by minimizing (Hoffman
and Grassotti,1996) Nov. 19, 2014 IPWG7 training course
Slide 49
Detection of the large-scale pattern of optimum displacement We
derived the large-scale pattern of from, following Hoffman and
Grassotti (1996) We transformed into the control variable in wave
space, using the double Fourier expansion. We used the quasi-Newton
scheme (Press et al. 1996) to minimize the cost function in wave
space. we transformed the optimum into the large-scale pattern of
by the double Fourier inversion. Nov. 19, 2014 IPWG7 training
course
