Reduction of uncertainties in the in the tropicszagarn/OLD/Var/PhDThesisPres_NZ.pdf · Dynamical...

Dynamical aspects of Dynamical aspects of

atmospheric data assimilation atmospheric data assimilation

in the tropics in the tropics

Nedjeljka ŽagarNedjeljka Žagar

Department of MeteorologyDepartment of Meteorology

Stockholm UniversityStockholm University

Dynamical aspects of atmospheric data assimilation in the tropics Dynamical aspects of atmospheric data assimilation in the tropics 19 May 200419 May 2004

Reduction of uncertainties

in the

atmospheric analysis fields

in the tropics

Purpose Purpose


Definition Definition

Observations (V,T,p,q)

A priori information

(model)

Analysis Weather forecast

Mass field

Climate simulations


Ingredients of the analysis Ingredients of the analysis

Observations:

Wind and mass information Wind and mass information

Smagorinsky (1969): ”... First of all, not all data are equal in their information-yielding capacity. Some are more equal than others…”


W I N D SW I N D S w a n t e d


À Observations:

Imbalance between the mass- and wind-field information in the present Global Observing System

¸ Balance properties:

Different in the tropics than in the mid-latitudes

� A priori information:

Physical laws governing the atmospheric flow

About the ingredients ... About the ingredients ...


ImprovementsImprovements

À New wind observing systems

H Improvements of data assimilation procedures

d Improvements of the models’s parameterizations and resolution

Subject of the thesis

work

Thesis assumes the model is excellent

Balance relationships in the tropics


Ð New wind observing systems

New wind data New wind data

Atmospheric Dynamic Mission

Peculiarity of ADM

line-of-sight (LOS) winds


Assimilation procedureAssimilation procedure

x

JbJo Joobs

obs

obs obs

xb

xa analysis

background

t1 t2

Jo

obs

time

JoJo

obs

Jo

Jo

obs

* ** ** * * * ** *

* * *

* ** ** * *

* ** ** * *

* ** ** * *

* ** ** * *

* ** ** * *

Jo distance to observations

Jb distance to the background J=Jo+Jb , minimal

3D-Var


Assimilation procedureAssimilation procedure

x

JbJo Joobs

obs

obs obs

xb

xa analysis

background

t1 t2

Jo

obs

time

JoJo

obs

Jo

Jo

obs

* ** ** * * * ** *

* * *

* ** ** * *

* ** ** * *

* ** ** * *

* ** ** * *

* ** ** * *

Jo distance to observations

Jb distance to the background J=Jo+Jb , minimal

4D-Var


Errors Errors

B I M P O R T A N TI M P O R T A N T

h Observations and a priori information are combined according to their error characteristics

( ) ( ) ( ) ( )b1b1 xxBxxyxRyxx −−+−−=+= −− TT

bo JJJ21

21)(

vector of observations background error covariance matrix

observation error covariance matrix

distance to background state (first guess)distance to observations

total distance

background state


Why is the B matrix important?Why is the B matrix important?

Observations are too few

Observed information needs to be spread to nearby points and levels in a dynamically consistent way

z

x

y


z

x

y

T

T

T

T

T

TT T

TT

T

TT

TT

T

TT

TT

TT

TT

T

T

T

@ To the same variable

Univariate analysisUnivariate analysis

Information spreadingInformation spreading


‘ Also to other variables

Multivariate analysisMultivariate analysis

z

x

y

T

T

T

T

TT T

TT

T

TT

TT

T

TT

TT

TT

TT

T

T

T

V,

, V

V,

V,

V,

V, V,V,

V,V,

V,, V

, V , V

, V, V

, V

, V

, V, V

, V

, V

, V, V

, V, V

TV




Ð Also to other variables in the tropics

Multivariate analysisMultivariate analysis

z

x

y

T

T

T

T

TT T

TT

T

TT

TT

T

TT

TT

TT

TT

T

T

T

V,

, V

V,

V,

V,

V, V,V,

V,V,

V,, V

, V , V

, V, V

, V

, V

, V, V

, V

, V

, V, V

, V, V

TV


Methodology Methodology

General philosophy: to simplify


Multivariate tropical analysis Multivariate tropical analysis

l Mid-latitudes: Rossby waves

� Tropics: Rossby, Kelvin, mixed Rossby-gravity and inertio-gravity waves



Mid-latitude approach

ø Mid-latitudes: Rossby waves

d Tropics: Rossby, Kelvin, mixed Rossby-gravity and inertio-gravity waves

singl

e zo

nal w

ind

obse

rvat

ion



Mid-latitude approach

h Mid-latitudes: Rossby waves

à Tropics: Rossby, Kelvin, mixed Rossby-gravity and inertio-gravity waves

singl

e zo

nal w

ind

obse

rvat

ion

A new modelling approach


Impact of ADM winds Impact of ADM winds

”Truth”: equatorial Rossby wave




Height data




Height dataHeight & ADM winds


Methodology Methodology

Question: How does the new methodology work in the ”real” (numerical weather prediction) framework?


How does it work? How does it work?

x In average about 60-70%

Unexplained variance ratio

h

u

v

100 hPa

500 hPa

900 hPa


On the way back On the way back


What have I achieved? What have I achieved?

p Developed an approach to multivariate analysis in the tropics based on equatorial waves coupled to convection

à Applied it for studing the impact of new wind observations

° Found that the same wave structures are present in an NWP system


What remains to be done? What remains to be done?

à Solving the methodology extention into the global NWP domain

h Representing the unexplained part of the variance field and remaining variables

” Taking into consideration discrepancy between theorethical assumptions and ”real” forecast error patterns

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