Advanced meteorological pre-processing for the real-time emergency response systems dealing

with the atmospheric dispersion in complex terrain

I. Kovalets (IPMMS NAS of Ukraine), S. Andronopolous (NCSR “Demokritos”, Greece),

J. Bartzis (Thessaloniki University, Greece)

The situation

Real-Time On-Line Decision Support System for Nuclear Emergency Management

In Europe (RODOS)

AtmosphericDispersion Model

(ADM)

MeteorologicalPre-processor

(MPP)

Other Modules

…

Measurement data frommeteorological stations

NWP prognosticMeteorological data

•ADMs: Key Role in DSSs – determine the current, and predict the future spatial distribution of radionuclides after an accidental release of radioactivity to the atmosphere•MPPs: Interface between the ADMs and the incoming meteorological data•Meteorological data: measurements from one or more stations in the vicinity of the NPP / prognostic data from Numerical Weather Prediction (NWP) models of National Weather Services

Example of RODOS calculations during nuclear emergency trainings on Zaporizzhe NPP 22.08.2002

a) Integral concentration of I-131 in air, calculated by RODOS with the use of NWP data

b) calculated by RODOS with the use of single meteorological observation in the point of release

c) Wind streamlines in domain of RODOS’s calculations, calculated by the NWP model MM5, operated in IPMMS NASU

a) b)

c)

Time of release:11-00 UTCTime of NWPAnalyses: 6-00

Measurements: past and current local conditions

NWP data: wide range in space and future time, where no measurements exist

Simultaneous

use by MPPConsistencyMethodology for reconciliation

The problem

Objective

The introduction of data assimilation (DA) techniques in the MPP of the RODOS, acting as diagnostic meteorological model to reconcile the NWP data with the local meteorological stations observations

Choosing method of solution

Strong need in real-time applicability

MPP acts as diagnostic wind model

Applicability to domains with complex geometry

Method of solution:Multivariate optimal interpolation

combined with various meteorological parameterizationsof atmospheric boundary layer (ABL)

and with variational divergence minimizing procedure

Only three dimensional data assimilation (3DDA): Statistical or variational ?

Statistical preferable Variational preferable

1. Calculating first guess fieldCalculated from the NWP data by 1/r2 interpolation:1) 3D fields of velocity, pressure, temperature, humidity2) 2D fields of precipitation, mixing layer height, sensible heat flux, cloud cover,

net radiation (if available from the NWP data)

2. Pre-processing of observations

1) calculation of the net radiation/cloud cover and sensible heat flux in the points of observations from measured values of surface temperature and cloud cover/netradiation (S. Hanna, J. Chang, 1993, van Ulden, Holstag, 1985)2) calculation of the friction velocity and Monin Obukhov length from the measured values of wind velocity and values of sensible heat flux (iterative procedure)3) vertical extrapolation of the measurements of the wind velocity to the vertical levels of MPP

up to the lower 200 m. of the atmosphere (Monin-Obukhov theory, van Ulden, Holstag, 1985)

Cycle of data assimilation

3. Data assimilation1) assimilation of the measured values of cloud cover/net radiation, surfece temperature,

precipitation2) assimilation of the measured (and vertically extrapolated) values of the wind velocities

4. Post-processing1) applying variational divergence minimizing procedure (Sasaki, 1952, Bartzis, et.al., 1998)2) calculation of all other variables needed for ADM using standard meteorological

parameterizations

General optimal interpolation algorithm (Daley, 1991)

Background field: ri

rk - Observations

KkIi 1,1

"a" - analyzed (improved forecast) field; "b" - background (unimproved forecast) field;"T" - true field, "o" - observations

I

j jbf

kjkbf

1)()( rr (1) forward interpolation operator

K

k

I

j jbf

kjkofikW

ibf

iaf 1 1)()()()( rrrr (2) – form of correction, Wik - unknown matrix

fboTiibia εεΩεWrr )()( (3),

)()()(iT

fia

fa

rrri

)()()(kT

fko

fo

rrri

)()()(iT

fib

fb

rrri

I

j jTf

kjkTf

kf 1)()( rrr

assumptions:( ) ( ) 0f f f

T T Tr ro b b b o i ib b ε ε ε ε ε ε ε ε0,fo b ε ε ε (4)

Squaring (3), taking expected values and minimizing with respect to Wi gives: W

T

Ο ΩBΩ F ΩBii (5)TooOTff FTBBB

2B

B

Observation error covariance matrix (CV)

Forward interpolation error CV

Background field error CV

Vector of background field RMS errors

Procedure (1)-(5) is equivalent to minimizing functional:

1

1

T

a o a o

T

a b a b

J

Ωf f O F Ωf f

f f B f f

Assumed statistical structure of the background and measurement errors

Errors of the background field: isotropy, constant rms of each variable

Scalar field:2 2 2 2( ) ( ) exp( )0m r r r Rb ik b b ik b ik (6)

µ - correlation function,R0 – radius of influenceσB – root mean square error

Isotropic vector field,Batchelor, 1953:

Each isotropic homogeneous vector field can be represented as sum of the isotropic homogeneous potential and non-divergent non-correlating vector fields (Obukhov, 1954),

, 2

( ) ( ) ( ) ( )( , ) ( ) ( )

q i q j k i k j

vq vk i j tt qk tt ll

x r x r x r x rr r r r r

r

Let ψ – correspondent stream function, χ – correspondent potential with isotropic distributions:2( ) ( ) ( )ik ik ikm r r r 2( ) ( ) ( )ik ik ikm r r r

2 22

2

/

u

R

ν- ratio of divergent kinetic energy to the total horizontal kinetic energy, R - radius of influence in (r), then (Daley, 1991):

22 2 2 2

2

1( ) (1 )ll

d dr R R

r dr dr

22 2 2 2

2

1( ) (1 )tt

d dr R R

dr r dr

In current work =0

(7)

For all RMS errors of the background field B assumed: B= B(z), assumed also Bu=Bv (9)

(8)

Observation error covariance matrixTooO is assumed to be diagonal with RMS error: O= O(rk); assumed also: Ou=Ov (10)

exp /r R

Multivariate optimal interpolation algorithm for assimilation of wind velocities

Derived using standard OI algorithm (1)-(5) and assumptions (8)-(10)

u ( ) u ( ) uu O B uv O BA i B ir r W W u u v v

v ( ) v ( )r r W Wvu O B vv O Bi iBA u u v v(11)(1)

)( irBuvuvWB

uvuuWIBuu

)( irBuvuvWIB

vvuuWBuv

)( irBuvvvWB

uvvuWIBuu

)(2ir

BvvvvWO

BvvvuWB

uv

(12)(5)

Kkrrr

Klkrr

kOBkiBuuki

Buu

kOBlkBuukl

Buu

1,/),()(

,1,/),(22

22

Note, that in (12) included are only relative errors:

being the key parameter tuning between the observations and background field

2 2B O

2

0 20

( )( , ) exp( / ) 1 1 i j

uu i j

x xrr r r R

R r

2

0 20

( )( , ) exp( / ) 1 1 i j

vv i j

y yrr r r R

R r

0 20

( )( )( , ) exp( / ) i j i j

uv i j

x x y yrr r r R

R r

Determination of

Link can be established with the approach for weighting coefficient used in the MPP “CALMET” of CALPUFF system (Scire, et. al., 1999)

In CALMET: (1 )A O B O OW W f f f

From statistics for one-point measurements:

(12)

2

21

f foB O bfA

B O

HORI

HFINE

HCOARSE

Terrain height

ORICOARSECOARSEHHRMSRMS

FINECOARSEFINE

HHRMSRMS

SW

ZW

OW

20.1,2/

iz

finRMSMIN

ziW n

RMSori

RMSfin

RMSS

W

0

2 20 0/(1 )B O W W

Domain of calculations for ETEX experiment (300x300 km.)

Statistical characteristics of wind field improvement

-1.35.918.76.74.269.55biasd, dec. deg.

424856313131rmsd, dec. deg.

-0.37-0.180.5-0.20.251.06biasu, m/s

2.01.942.212.532.533.19rmsu, m/s

IOSETEX2

OIETEX 2

ECMWF prognose

ETEX 2

IOSETEX 1.

OIETEX 1.

ECMWF analyses, ETEX1

Variable

-1.35.918.76.74.269.55biasd, dec. deg.

424856313131rmsd, dec. deg.

-0.37-0.180.5-0.20.251.06biasu, m/s

2.01.942.212.532.533.19rmsu, m/s

IOSETEX2

OIETEX 2

ECMWF prognose

ETEX 2

IOSETEX 1.

OIETEX 1.

ECMWF analyses, ETEX1

Variable

1.72, -9.22.63, -8.4MM5, dx = 4 km

2.23, -2.58, -RAMS, dx = 0.33 km

0.93, -3.63, -RAMS, dx = 1.32 km

With data assimilationrmsu (m/s), biasd (dec. degree)

Without data assimilationrmsu (m/s), biasd (dec. degree)

Model, scale of grid

1.72, -9.22.63, -8.4MM5, dx = 4 km

2.23, -2.58, -RAMS, dx = 0.33 km

0.93, -3.63, -RAMS, dx = 1.32 km

With data assimilationrmsu (m/s), biasd (dec. degree)

Without data assimilationrmsu (m/s), biasd (dec. degree)

Model, scale of grid

For comparison effect of 4DDA in some models (Seaman, 2000)

Vertical wind profilesa1) 24 October, 12 h

0

100

200

300

400

500

600

0 5 10 15 20

U, m/s

a2) 24 October, 12h

0

100

200

300

400

500

600

150 200 250 300

D, dec. degree

b1) 24 October 18h

0

100

200

300

400

500

600

0 5 10 15 20

U, m/s

b2) 24 October 18h

0

100

200

300

400

500

600

150 200 250 300

D, dec. degree

Vertical profiles of the wind velocity a1)-b1) and of the wind direction a2)-b2), calculated by the MPP with the use of observations (■), with the use of the ECMWF data only (▲), measured by the sodar (,line)Sodar measurements were notused in data assimilationa1), a2) – 12-00 UTC 24/10/1994.b1), b2) – 18-00 UTC24/10/1994.

a1)

a2)

b1)

b2)

Vertical wind profilesc1) 25 October, 00h

0

100

200

300

400

500

600

0 5 10 15 20

U, m/s

d1) 25 October, 06h

0

100

200

300

400

500

600

0 5 10 15 20

U, m/s

z, m

c2) 25 October, 00h

0

100

200

300

400

500

600

150 200 250 300

D, dec. degree

d2) 25 October, 06h

0

100

200

300

400

500

600

150 200 250 300

D, dec. degree

z, m

Vertical profiles of the wind velocity a1)-b1) and of the wind direction a2)-b2), calculated by the MPP with the use of observations (■), with the use of the ECMWF data only (▲), measured by the sodar (,line)Sodar measurements were notused in data assimilationa1), a2) – 00 UTC 25/10/1994.b1), b2) – 06-00 UTC25/10/1994.

Comparison of friction velocity and kinematic heat flux

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

23.5 24 24.5 25 25.5 26 26.5

time, days-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

23.5 24 24.5 25 25.5 26 26.5

time, days

U*, m/s

<w

'T '>

, mK

/s

a)T

ime

depe

nden

ce o

f th

e fr

ictio

n ve

loci

ty .

b)T

ime

depe

nden

ce o

f th

e ki

nem

atic

hea

t flu

xD

ots

- m

easu

red

valu

es (

soni

c an

emom

eter

at t

he M

onte

rfil)

, sol

id b

lack

line

-

calc

ulat

ed d

ata

with

the

use

of D

A p

roce

dure

s, d

ashe

d lin

e -

calc

ulat

ed w

ith th

e us

e of

the

EC

MW

F d

ata

only

Mea

sure

men

ts o

f so

nic

anem

omet

er w

ere

not u

sed

in D

A p

roce

dure

0 100000

x , m

0

100000

y, m

0 100000

x , m

0

100000

y, m

0 100000

x , m

0

100000

y, m

0 100000

x , m

0

100000

y, m

a) b)

d) c)

Ground level wind fields

a) Backgroundfrom ECMWFb) IOSc) IOd) Measured

2D fields of net radiation and cloud cover

50000 100000 150000 200000 250000 300000 350000

x , m

N et rad ia tion, w ith D A , 25 O ctober 00h.

50000

100000

150000

200000

250000

300000

350000

y, m

-75

-70

-65

-60

-55

-50

-45

-40

-35

-30

50000 100000 150000 200000 250000 300000 350000

x , m

N et rad ia tion, w ithout D A , 25 O ctober 00h.

50000

100000

150000

200000

250000

300000

350000

y, m

-80

-75

-70

-65

-60

-55

-50

-45

-40

-35

-30

50000 100000 150000 200000 250000 300000 350000

x , m

C loud cover (oktas), w ith D A , 25 O ctober 00h.

50000

100000

150000

200000

250000

300000

350000

y, m

50000 100000 150000 200000 250000 300000 350000

x , m

C loud cover (oktas),w ithout D A , 25 O ctober 00h.

50000

100000

150000

200000

250000

300000

350000

y, m

0

1

2

3

4

5

6

7

8

0

1

2

3

4

5

6

7

8

Further developments

1. D

A d

eve

lop

ed n

eed

mo

re e

nha

nce

d c

apa

bili

ty to

dea

l with

flow

s in

com

ple

x g

eom

etri

esN

ow w

e re

ly o

n: 1

) qu

ality

of

the

NW

P m

odel

; 2)

rela

tions

for

B

2 / O

2 ; 3

)div

erge

nce

min

imiz

ing

proc

edur

e

Wha

t fur

ther

can

be

done

?

1)A

dvan

ced

met

eoro

logi

cal

para

met

eriz

atio

ns f

or p

re-p

roce

ssin

g of

obs

erva

tions

in

com

plex

geo

met

ries

: i.e

., fo

r ca

lcul

atio

n of

fl

ux p

aram

eter

s (s

ensi

ble

heat

flu

x an

d ot

her,

Bar

low

, B

elch

er,

et.

al.,

2000

), f

or e

stim

atin

g m

ixin

g he

ight

and

ver

tical

ex

trap

olat

ion

of

win

d/te

mpe

ratu

re

mea

sure

men

ts

in

com

plex

ge

omet

ries

(e

.g.,

Zili

tinke

vich

, 200

4)

2)R

evis

ing

corr

elat

ion

func

tions

(6)

, (8)

to a

ccou

nt f

or a

niso

trop

y in

trod

uced

by

com

plex

geo

met

ries

2.1)

sim

ples

t app

roac

h (u

sed

in D

A o

f th

e so

me

mes

osca

le m

odel

s, e

.g. M

M5,

S

eam

an, 1

998)

is to

use

for

m: µ

(ri ,

rj )

=µ

1(|r

j-ri |

)µ2(z

)µ3(

z b)2.

2) e

nsem

ble

met

hod

(Zup

ansk

i, an

d ot

her)

2.3)

may

be

som

ethi

ng w

ill b

e kn

own

from

nat

ure

?

3) M

inim

izin

g ab

ovem

entio

ned

cost

fun

ctio

nal w

ith c

onst

rain

ts: v

aria

tiona

l app

roac

h (P

enen

ko a

nd o

ther

)

Variational approach for 3DDA

Min

imiz

e fu

nctio

nal:

(1)

with

con

stra

ints

(2)1 2( ( ), ( ),..., ( ))nJ dF f f f

r r r

1,..., 0, 1,i nf f i l

For

inst

ance

, “di

verg

ence

min

imiz

ing”

: 1

u v w

x y z

min

imiz

ing

Lag

rang

ian:

B=

0;

;

22 2 22 0 0 01 2 12 2 2

2

u v w

x y zx y z

G

ener

ally

, ver

y fe

w c

ases

, whe

n L

agra

ngia

n si

mpl

ifie

s si

tuat

ion,

one

mor

e is

:

222 2 2 2

( , , , ) 1 0 1 0 2 ( , , )L u v w u u v v w w dVV

u v wx y z

x y z

2 222 2 2( , , ) 1 0 1 0 2 0J u v w u u v v w w dV

V

adju

stm

ent o

f th

e w

ind

velo

citie

s pe

rtur

batio

ns in

the

oute

r re

gion

of

the

cano

py f

low

:

1u pU

x x

1w p

Ux z

0u w

x z

whe

n z>

>l

22( , , ) 0 0J u v w u u w w dV

V

01u w

x z

02

u w

z x

0 02 21 1

1 1; ;

2 2u u v v

x y

2 20 01 1

2 22

u w

x z x z

2 2

0 02 22 2

2u w

x z z z

2

0

2

0

1

2

,1 2( , , )

,

,

L u wV

u u

w w

u wx z

x x

u wx z dV

z x

Variational approach for 3DDA

1 1T T

a o a o a b a bJ Ωf f O F Ωf f f f B f f

Gen

eral

cas

e fo

r 3D

DA

: min

imiz

e fu

nctio

nal (

the

sam

e as

in O

I):

(3)

with

con

stra

ints

:

0, 1,ai i n f (4)

Pro

blem

(3)

-(4)

usu

ally

can

be

solv

ed n

umer

ical

ly u

sing

sta

ndar

d ap

proa

ches

(e

.g.,

pena

lty +

des

cent

alg

orith

ms

or o

ther

mor

e ad

vanc

ed).

T

he m

ain

com

plex

ity o

f th

e pr

oble

m is

cau

sed

by th

e ch

oice

of

the

con

stra

ints

(4)

Conclusions

1.M

etho

dolo

gies

for

the

ass

imila

tion

of t

he o

bser

vatio

ns o

f w

ind

velo

citie

s an

d ot

her

in th

e M

PP

of

the

ER

S s

yste

m R

OD

OS

wer

e de

velo

ped

2.T

he m

ultiv

aria

te o

ptim

al i

nter

pola

tion

sche

me

com

bine

d w

ith t

he r

elat

ions

for

th

e w

eigh

ting

coef

fici

ent

used

in

M

PP

C

AL

ME

T

was

fo

r th

e fi

rst

time

impl

emen

ted

as a

3D

DA

sch

eme

in th

e M

PP

of

the

real

-tim

e E

RS

sys

tem

3.C

ompa

riso

ns

of

the

mod

el

resu

lts

with

th

e m

eteo

rolo

gica

l m

easu

rem

ents

pe

rfor

med

in

the

ET

EX

exp

erim

ents

sho

wed

goo

d ag

reem

ent

of c

alcu

late

d va

lues

with

mea

sure

men

ts a

nd i

mpr

ovem

ent

of t

he f

irst

gue

ss f

ield

pro

duce

d us

ing

the

NW

P r

esul

ts w

ith th

e us

e of

the

3DD

A p

roce

dure

s4.

Fur

ther

dev

elop

men

t of

the

dat

a as

sim

ilatio

n pr

oced

ures

for

the

MP

Ps

of t

he

ER

S

shou

ld

be

perf

orm

ed

for

prod

ucin

g m

ore

phys

ical

ly

cons

iste

nt

met

eoro

logi

cal f

ield

s w

hen

appl

ied

in c

ompl

ex g

eom

etri

es

Acknowledgements

The

pre

sent

wor

k ha

s be

en f

ully

sup

port

ed b

y th

e E

urop

ean

Com

mis

sion

thr

ough

the

EU

RA

TO

M g

rant

in

conn

ectio

n to

the

E

urop

ean

Pro

ject

"R

OD

OS

Mig

ratio

n".