data assimilation, short-term forecast, and forecasting error at convective scales kao-shen chung...

Data assimilation, short-term forecast, and forecasting error at convective scales

Kao-Shen Chung鍾高陞

Department of Atmospheric and Oceanic Sciences McGill University

April 19 2010

Outline

1. Introduction

2. McGill radar assimilation system * impact of the background term 3. Initialization and the short term forecast * case study on 12 July 2004

4. Sensitivity test of the short term forecasts

5. Summary / conclusion

6. Future work

1.What is Data Assimilation ?1.What is Data Assimilation ?

Assimilation of meteorological or oceanographical observationscan be described as the process through which all the availableinformation is used in order to estimate as accurately as possiblethe state of atmospheric or oceanic flow.

Talagrand (1997):

The physical laws: Govern the evolution of the flowe.g. Equation of Motion, Thermodynamic Equation, Mass and Water Continuity ……etc

Satellite

Radiosonde

Radar

Observations

Information coming from previous model forecast

Data Assimilation NWP

Purpose of Data AssimilationPurpose of Data Assimilation

Best estimate of the initial conditions

At large scale

Main observing system : radiosonde network

only W (vertical velocity) is unknown for initialization of a forecast model

Main objective: optimal interpolation

Doppler Radar provides: - high spatial resolution ( 1km ) - high temporal resolution ( ~ 5 min )

Capable of sampling the structure of individualConvective cells in a convective system.

Main observing system at convective scales

Data assimilation at convective scale:Data assimilation at convective scale:

Challenge :

• High temporal and space variability

• No simple balances can be used

• Observing system: measurements (e.g. radar network)

are not direct model variables ( U,V,W,P,T)

Radial component

Real wind Radar observations

(Doppler wind, reflectivity)

To Initialize Numerical Weather Prediction

(U,V,P,T…)

History of the McGill radar Assimilation system

Laroche and Zawadzki (1994): retrieved 3D wind within precipitation area

McGill Radar observations network McGill Radar observations network

2rV

1rV

Protat and Zawadzki (1999, 2000)

Horizontal Wind Vector Vertical Velocity (w)

Pressure perturbation Temperature perturbation

Initialize the numerical modelMontmerle et. al (2001)

Current McGill radar observations Current McGill radar observations

McGill S-Band Radar:

1. Reflectivity2. Doppler Velocity

2rV

1rV

Challenge and main objective of the research

• Observations: single Doppler radar (radial velocity, reflectivity )

• Information other than radar: a prior forecast of a high-resolution model

• The predictability / uncertainty of the short term forecast at convective scale

Cost Function (J)

bJ Background

oJ Observations

mJA Cloud model: weak constraint

Best estimate the state of the atmosphere

2. McGill Radar Data Assimilation System2. McGill Radar Data Assimilation System

Based on Caya (2001): Variational algorithm

•Consider model is not perfect •No Adjoint model, reduce the computational time

Present state of the Model Governing Equations

du

dt fv R(T T )

x

mxq

ddt

wg

RT u

x

v

y

w

z

1

(T T )

d T

dtco

q

dw

dt g

T

T g(M Qc )

R(T T )

z

mzq

dv

dt fu R(T T )

y

myq

Momentum equations

(u,v,w)

Mass continuity equation

Thermodynamic equation

Kessler microphysics

(rain and cloud)

Single observation test

Horizontal Wind Temperature

Impact of including model term in the cost function

Impact of the background term

Background field, xb

Fill the non-precipitation area in the domain

)b-1Tb x-(xB)x-(x xbJ

nnnn

n

n

T

eeeeee

eeee

eeeeee

......

...........

...........

.......

......

B

21

222

12111

Background error matrix, B: determine the filtering and propagation of the observed information

Role of the background term:

nnn

n

aa

aa

aaa

.........

...............

...............

.........

......

1

2221

11211

Diagonal Part:Variance

2

22

21

00...0

...........

.0.......

....00

0......0

n

Assume:Uncorrelated

Too simplifiedneed smoothness constraint in the algorithm

smob JJJJJ

xyz

yxyx

yy

xx

22

222

222

2

2

)(2)()(

Smoothness Term

Former assimilation system

Without penalty term:Horizontal Wind

With penalty term:

Vertical Velocity mob JJJJ

smob JJJJJ

In the current assimilation system

• B is modeled by a recursive filter [followed Purser et al. (2003)]

* Assume the error correlation of the control variables is isotropic and homogeneous

* Applied the filters to control variables

• A prior high-resolution model forecast is used as the background field

* MC2 (Mesoscale Compressible Community)

Non-hydrostatic Horizontal resolution: 1km Stretched vertical levels Explicit scheme in microphysics process

smob JJJJJ

Former assimilation system Modified assimilation system(Recursive filters)

mob JJJJ

No penalty term (smoothness constraint)

Comparison of the two assimilation systems

McGill assimilation system

3. Initialization and the short term forecast

Deep convective andlong lasting storm system

Case Study (12th July, 2004 ):

Radar site

1810 UTC 1840 UTC 1910 UTC

1940 UTC 2010 UTCWe start from the earlystage of the storm !!

Impact of using a previous numerical weather prediction

CAPE value Convective potential

0 Stable0-1000 Marginally Unstable1000-2500 Moderately Unstable2500-3500 Very Unstable3500 + Extremely Unstable

Impact of assimilating radar observationsBefore assimilation After Assimilation

UU UU

VV VV

Results of short term forecast at 30 minVertical velocity

Radar observation Model simulation

1840 UTC

Results of short term forecast at 60 min

Radar observation Model simulation

1 hour forecast

1910 UTC

Radar observation

Radar observation

Model simulation (60 min)

Model simulation (90 min)

1940 UTC

2010 UTC

Forecast results with a cycling strategy

Verification:Verification:

r

zVw

r

yv

r

xuV tr )( • Radial component :

Observed radial velocity

1910Z H = 2.5km

Simulated radial velocity

1910Z H = 2.5km

RMSE of Doppler wind

The errors are larger in the upper levels

Observation Reflectivity Simulated Reflectivity

At what kind of scales do we have more predictability?

Followed Turner et al. (2004)

Wavelet Transform Analysis:

Similar to the Fourier transform, but the wavelet transform are moreeffective in representing localized, intermittent fields.

Wavelet analysis

The simulation has more predictability at the longer scale( > 30 km) beyond 20 minutes.

4. Sensitivity test of the short term forecasts

What is the Forecasting (background) errors?

Due to the uncertainty in the initial conditions

(assumption: model is perfect)

Truth

The best estimate of atmosphereForecasting errors

Short-range forecast

Definition of the forecasting error

• We want to know how sensitive of the short-term forecasts relative to the uncertainty of the initial conditions

• What is the structure of the forecasting/background errors at convective scale?

• In data assimilation: The “optimal” analysis fields can be obtained only if the statistics of the background and observations errors can be accurately described.

• Hamill et al. 2001 and Anderson 2001: the underestimate of the forecasting error covariances Due to the small size of ensemble members Any other factor could cause the underestimate of the forecasting error?Ensemble forecasts :

characterize the forecasting errors

Motivation

McGill radar Data assimilation

)(

)2(

)1(

Ny

y

y

io

i

io

i

io

i

)(

)2(

)1(

Nx

x

x

ia

ia

ia

)(

)2(

)1(

Nx

x

x

if

if

if

1h forecast

Model simulation

Calculate the Statistics of

forecasting errors.

Ensemble scheme

Background at 1500, 1600 and 1700 UTC

Perturb observations(error of observation)

About the observation errors

Uncorrelated observations errors

By given the standard deviation of the observational variablese.g. Reflectivity: 2~5dB ; Radial velocity: 1m/s

However…..

Berenguer and Zawadzki (2008)

Errors have correlation in space / time !

Correlated observation errors

Reflectivity: error correlation length: 10km (Hori), vertical correlation = 0.85 (250m) standard deviation: 2.5 dB

Radial velocity: error correlation length: 5km (Hori), vertical correlation = 0.75 (250m) standard dev: 1m/s

Prescribed observation errors

Characterize the forecasting error

Variance(Ensemble spread)

Correlation Prescribed errors correlation length

Convective Storm: 12 Jul 2004 1800UTC to 1900 UTC

McGill Radar

1 hour forecast

The impact of the observation errors(Ensemble mean)

Correlated noiseUncorrelated noise

Unperturbed reference

The impact of the observation errors(Ensemble spread)

Correlated noise

Correlated noise

Uncorrelated noise

Uncorrelated noise

Forecasting error of ACF - T

lag [km]

The impact of the observation errors:(Forecasting error of ACF in space )

Forecasting error of ACF - U

Uncorrelated noise Correlated noise

Forecasting error of ACF - U

Uncorrelated noiseCorrelated noise

Forecasting error of ACF - T

lag [km]

The impact of the observation and background errors(Ensemble spread)

Uncorrelated noise Correlated noise

Perturbed both observation and background

Forecasting error of ACF :

Entire domain v.s. precipitation area

Forecasting error of ACF - U Forecasting error of ACF - U

The error structure could be different within and outside of precipitation area

Cross correlations errors:

Strong connection between dynamics and microphysics processes

Vertical velocity and cloud water

30 min simulation 40 min simulation

Verification of the ensemble forecasts

Error growth of the forecasting error:

• It takes about 10-15 min to double the error growth

• The limit of predictability depends on the rate of error growth by one assimilation window, the one hour forecast may reach the limit of the predictability at this scale

5. Summary / Conclusion

• The McGill radar assimilation system successfully triggered the convective storms at the right time and place based on single Doppler radar observations.

• The cycling process helps to capture the evolution of the storm in intensity and location. However, after 1.5- hour forecast the result indicates an error in the position of the convective cells. • The verification of the radial wind in time reveals that the errors are larger in the high levels. In addition, the simulation has more predictability at the longer scale( > 30 km) beyond 20 minutes.

• The verification of the radial wind in time reveals that the errors are larger in the high levels. This may explain the position errors of the simulation.

•Show how sensitive forecasting errors are to the representation of the initial perturbation (from observation error correlation).

•The correlation of the errors greatly increases the spread of the ensemble as well as its correlation in space.

•The result of error ACF indicates the need to discriminate background error covariances within and outside the precipitating areas

•Cross-correlation errors reveal the strong coupling between dynamics and microphysics.

6. Future work

Semi-Operational mode: Meso-Analysis System (MAS)

Convective system

Stratiform system

• Investigate the impact of flow-dependent background errors in the short term forecast. (cycling process)

• Study and apply the observation error covariance into the system.

• Investigate the model error at the very short term forecast. ( model is not perfect )

mob JJJJ

oJ

mJ

background + observation + model

• Extend the radar observation to the radar network.