Combining measurements and models in atmospheric physics

U Toronto Physics Colloquium, 10 Jan. 2008

Saroja PolavarapuData Assimilation and Satellite Meteorology Division

Meteorological Research DivisionEnvironment Canada

OUTLINE

1. What is data assimilation?

2. Recent advances in DA

3. A new application: data assimilation with a climate model

1. What is data assimilation?

Atmospheric Data Analysis

analysis

An analysis is a regular, physically consistent, representation of the state of the atmosphere

Instruments sample imperfectly and irregularly in space and time.

Why do people want analyses?

1.To obtain an initial state for launching weather forecasts

2.To make consistent estimates of the atmospheric state for diagnostic studies.

3.For an increasingly wide range of applications (e.g. atmospheric chemistry)

4.To challenge models with data and vice versa

http://www.wmo.ch/web/www/OSY/GOS.html

The Global Observing System

Data coverage examplesSome data used by CMC on Jan. 6, 2008 12 UT

Underdeterminacy

• Cannot do X=f(Z), must do Z=f(X)• Problem is underdetermined• Need more information!

Data Reports x items x levels

Sondes,pibal 720x5x27

AMSU-A,B 12000x12

SM, ships, buoys 6000x5

aircraft 20000x3x18

GOES 50000x1

Scatterometer 40000x2

Sat. winds 22000x2

TOTAL 1.6x106 =M

Model Lat x long x lev x variables

CMC global oper. 800x600x58x4

=1x108 =N

CMC meso-strato 800x600x80x4

=1.5x108

X = state vector Z = observation vector

60M

N

Optimal Interpolation

)( bba H xzKxx Analysis vector

Background or model forecast

Observation vector

Observation operator

Weight matrix

N×1 N×1 M×1N×M M×N N×1

1 RHBHBHK TT

NxN MxM

Can’t invert!

NxM

Bvxx ba

Analysis increments (xa – xb) must lie in the subspace spanned by the columns of B

Properties of B determine filtering properties of assimilation scheme!

The fundamental issues in atmospheric data assimilation

• Problem is under-determined: not enough observations to define the state

• Forecast error covariances cannot be determined from observations. They must be stat. modelled using only a few parameters.

• Forecast error covariances cannot be known exactly yet analysis increments are composed of linear combination of columns of this matrix

• Very large scale problem. State ~ O(108)• Nonlinear chaotic dynamics

model

assimil.scheme

Data assimilation cycle

forecast step

Analysis step

2. Recent advances in data assimilation at operational

weather forecasting centres

3D-Variational assimilation

)( bba H xzKxx

))(())(()()()( 1 xzRxzxxBxxx b1b HHJ TT

Instead of solving this:

Minimize this: 1 RHBHBHK TT

• Obs and models can be nonlinearly related. To assimilate radiances directly, H includes an instrument-specific radiative transfer model.• Matrix inverses can be avoided

OptimalInterpolation

Background trajectory

Analysis trajectory

))(())((2

1)()(

2

1)( 1

00

100 kk

Tkk

N

kb

Tb HHJ xzRxzxxBxxx

4D-Variational assimilation

500 hPa GZ (dam), avg. over Jan 1998

Differences between 4D-Var and 3D-Var RMS errors for day-1 forecasts

Dark areas: 4D-Varbeats 3D-Var

4D-Var beats 3D-Var over storm track areas

4D-Var is better at picking up unstable initial conditions

Klinker et al. (2000)

Popular assimilation techniques in weather forecasting centres

• 1980’s – Optimal interpolation

• 1990’s – 3D variational assimilation

• 2000’s – 4D variational assimilation

• Future – ?

Advances are being driven by improvements in computational power and increase in amount of observations.

Why are the lids of operational weather forecast models

moving up into the mesosphere (>80 km)?

10mb

100mb

1000mb

1mb

• By raising forecast model lid, satellite radiances are better analysed

• Satellite radiances sense deep layers of atmosphere so analyses are improved in troposphere as well as stratosphere

• Improved analyses give improved forecasts

• ECMWF, GMAO (NASA), UK Met Office have lids ~80 km

• CMC system with model lid at 65 km to be operational in 2008

Winter Polar vortex

• Westerly wind increasing with height

• Dominant feature of stratosphere in winter

• Occasional disruption of polar vortex by sudden warming events (in Arctic)

http://www.nasa.gov/images/content/113260main_arctic-vortex-447.jpg

Baldwin and Dunkerton (2001)

TimeTimedelaydelay

Long timescaleLong timescale

The stratosphere and troposphere are dynamically coupled. Low model lids compromise this coupling.

3. A new application: Data assimilation with a climate

model

Middle Atmosphere Dynamics

• Brewer-Dobson circulation– wave driven, thermally indirect– affects temperature, transport of species

• Gravity waves also important– Helps drive meridional circulation– But normally seen as “noise” in assimilation process

Shaw and Shepherd (2008)

Ozone from OSIRIS for March 2004

http://www.ecmwf.int/newsevents/training/meteorological_presentations/MET_DA.htmlLars Isaksen (2007)

Approximate mass-wind balance in mid-troposphere extra-tropics

Williamson and Temperton (1981)

Balance in data assimilationTime evolution of surface pressure over 24 hours

• Because of obs errors, integrating a model from an analysis leads to motion on fast scales– Noisy forecasts, e.g.

precipitation– 6-h forecasts are used to

quality check obs

• Extra-tropical troposphere is largely balanced

• Historically, after the analysis step, a separate “initialization” step was done to remove fast motions

Initialized forecast

Raw forecast

T profiles over one night from lidar

http://pcl.physics.uwo.ca/science/temperature/R.J. Sica (U Western Ontario)

Gravity waves may be a nuisance in the troposphere, but they are prevalent in the mesosphere and are part of the signal!

conventionalobs + sat.

AMSU10-13

CMAM + 3DVar

CMAM = CanadianMiddle Atmosphere Model

obs

No obs

How does information propagate into the

mesosphere?

Sankey et al. (2007)

Global mean temperature profiles at SABER locationsfor various filtering options

SABERDF12DF6IAUCIAU6IAU4No obs

obs

Jan. 25, 2002Sponge layer

There are more resolved waves in the upper mesospherewith less filtering

More waves --> more damping--> more heating

Sankey et al. (2007)

• Changing the assimilation scheme in the stratosphere and troposphere has huge impacts on the mesosphere!

• Waves (real or spurious) in the lower atmosphere propagate up to the mesosphere

• Small errors lower down can look big in the mesosphere

Information from below propagates to the

mesosphere. Is the mesosphere improved?

70ºN zonal mean temperatures during 2006 SSW

Gloria Manney, JPL

Stratopause is above 0.01 hPa!

ECMWFtoo lowtoo cold

GEOS-5too lowtoo warm

• Low lids of operations models deterrent to study of stratopause region

• Research models with higher lids show improvement relative to operational systems, in this region– CMAM-DAS with no mesospheric DA– NOGAPS-ALPHA with MLS, SABER data

• Compared to independent data, CMAM-DAS looks reasonable

Climate models are extensively validated statistically against observations.

Data assimilation with a climate model allows one to compare to measurements on a specific day.

Stratospheric Sudden Warming (SSW)

• Dramatic event: T increases near pole of 40-60 K in 1 week at 10 hPa

• Every couple of years in NH (+2002 SH)• Major SSW (1+2), Minor SSW (1 only)

1. Poleward increase of zonal-mean temperature between 60° and pole at 10 hPa

2. Zonal mean zonal wind reverses

• Waves propagate up from troposphere, interacts with mean flow (Matsuno 1971).

http://www.gsfc.nasa.gov/topstory/20020926ozonehole.html

Total column ozone from Earth Probe Total Ozone Mapping Spectrometer (EPTOMS)

August 15 – September 26, 2002

C

C

W

Mesospheric Coolingsschematic diagram NH winter 2005/06

(Labitzke 1972)

Courtesy of Kirstin Krüger

10 hPa (30km) 0.1 hPa (65 km)

South Pole temperature in 2002 during stratospheric warming

hits

misses

Ren et al. (2008)

1995-2005 Met Office analyses

<“hits”> - <“misses”>

obs

No obs

“hits” are warmer in the stratosphere

Zonal mean temperature difference (K)

“hits” are colder in the mesosphere

Ren et al. (2008)

GWDhitsmisses

GWD

Resolvedwaves

Waves 1-5

All waves

Averages over Sept. 25 – Oct. 1, 2002

Ren et al. (2008)

2002 Stratospheric Warming study

• Assimilation with a climate model allowed us to understand what caused the mesospheric cooling above the stratospheric warming in our simulations

• Planetary waves responsible for mesospheric cooling below 60 km

• Mesospheric cooling is mainly due to parameterized GWs above 75 km

• Observations inserted in stratosphere and troposphere indirectly impact the mesosphere through a GWD scheme!

Summary

• The atmospheric data assimilation problem is characterized by huge, nonlinear systems and insufficient observations.

• Because the math is well known, the key to progress is using atm physics to make the right approximations

• Information from below propagates to the mesosphere (through both resolved and parameterized waves) during 6-h forecasts

Other areas of current research in data assimilation

• Chemical weather forecasting

• Ensemble Kalman filtering

• Inferring winds from tracer measurements

• Improving climate models by determining uncertain parameters

• Evolving 4D-Var covariances from one cycle to the next

• Improving tropical analyses

The End