Data Assimilation

Andrew Collard

Overview

Introduction to Atmospheric Data Assimilation Control Variables Observations Background Error Covariance Summary

NEMS/GFS Modeling Summer School 2

Overview

Introduction to Atmospheric Data Assimilation Control Variables Observations Background Error Covariance Summary

NEMS/GFS Modeling Summer School 3

Introduction to Atmospheric Data Assimilation

The data assimilation step of the GFS system provides the initial conditions (“the analysis”) for a GFS forecast model run.

The analysis is obtained by optimally combining our best a priori knowledge of the atmosphere (through a short-range forecast) and a wide variety of observations of the atmospheric state.

This talk will focus on the operational hybrid EnKF/3DVar system.

NEMS/GFS Modeling Summer School 4

Data Assimilation as part of the GFS Suite (1)

NEMS/GFS Modeling Summer School 5

Data Assimilation as part of the GFS Suite (2)

NEMS/GFS Modeling Summer School 6

The Cost Function

c'o

'1T'o

''1Var

T''Var 2

121 JJ yHxRyHxxBxx

J : Penalty (Fit to background + Fit to observations + Constraints)x’ : Analysis increment (xa – xb) ; where xb is a backgroundBvar: Background error covarianceH : Observations (forward) operatorR : Observation error covariance (Instrument +

representativeness)yo’ : Observation innovationsJc : Constraints (physical quantities, balance/noise, etc.)

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Overview

Introduction to Atmospheric Data Assimilation Control Variables Observations Background Error Covariance Constraints and Balance Summary

NEMS/GFS Modeling Summer School 8

4 August 2013 DTC – Summer Tutorial

Analysis variables

The analysis variables areStreamfunction (Ψ)Unbalanced Velocity Potential (χunbalanced)Unbalanced Temperature (Tunbalanced)Unbalanced Surface Pressure (Psunbalanced)Ozone – Clouds – etc.Satellite bias correction coefficients

4 August 2013 DTC – Summer Tutorial

Analysis variables

χ = χunbalanced + A ΨT = Tunbalanced + B ΨPs = Psunbalanced + C ΨStreamfunction is a key variable defining

a large percentage T and Ps (especially away from equator). Contribution to χ is small except near the surface and tropopause.

4 August 2013 DTC – Summer Tutorial

Analysis variables

A, B and C matrices can involve 2 componentsA pre-specified statistical balance

relationship – part of the background error statistics file

Optionally a incremental normal model balance

Not working well for regional problem

Overview

Introduction to Atmospheric Data Assimilation Control Variables Observations Background Error Covariance Summary

NEMS/GFS Modeling Summer School 12

Observations

NEMS/GFS Modeling Summer School 13

c'o

'1T'o

''1Var

T''Var J

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21J yHxRyHxxBxx

The observation yo is compared with the model state x after the latter is transformed into observation space.

For many direct “conventional” observations such as temperature or wind speed this observation operator comprise a transform from the analysis variables and an interpolation to the observation’s time and position.

For other data sources, such as radiance observations, this operator is far more complex.

4 August 2013 DTC – Summer Tutorial

Input data – Conventional currently used

Radiosondes Pibal winds Synthetic tropical cyclone winds wind profilers conventional aircraft reports ASDAR aircraft reports MDCARS aircraft reports Dropsondes Doppler radial velocities Surface land observations Surface ship and buoy observation VAD (NEXRAD) winds

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Radiosondes

Radiosonde Data Coverage

NEMS/GFS Modeling Summer School 16

4 August 2013 DTC – Summer Tutorial

Satellite Derived Products currently used in Global Model

Atmospheric Motion VectorsMODIS IR and water vapor windsGMS, JMA, METEOSAT and GOES cloud

drift IR and visible windsGOES water vapor cloud top winds

Wind speeds from ocean surface stateSSM/I wind speedsQuikScat and ASCAT wind speed and

direction SSM/I and TRMM TMI precipitation estimates GPS Radio occultation refractivity and bending

angle profiles SBUV ozone profiles and OMI total ozone

Cloud Tracked Winds

Winds derived using full disk 15-minute Meteosat-8 10.8µm SEVIRI data for 12 UTC on 01 February 2007. These winds are derived from tracking cloud features using the 10.8µm channel. High level (100-400 hPa) winds are shown in violet; mid-level (400-700 hPa) are shown in cyan; and low levels (below 700 hPa) are shown in yellow.

4 August 2013 DTC – Summer Tutorial

Satellite Radiances currently used in Global Model

Infrared Sounders:  GOES-15 Sounder: Channels 1-15, Ocean Only

Aqua AIRS: 148 ChannelsMetOp-A IASI: 165 Channels

MetOp-A HIRS: Channels 2-15Microwave Sounders:

AMSU-A on:NOAA-15 Channels 1-10, 12-13,

15NOAA-18 Channels 1-8, 10-13, 15NOAA-19 Channels 1-7, 9-13, 15METOP-A Channels 1-6, 8-13, 15AQUA Channels 6, 8-13

NPP ATMS: Channels 1-14,16-22MHS on:

NOAA-18 Channels 1-5NOAA-19 Channels 1-5METOP-A Channels 1-5

Meterological SatelliteConstellation(from WMO)

Currently operationallyAssimilate radiances atNCEP

Typical Satellite Data Coverage

NEMS/GFS Modeling Summer School 21

An Infrared (IASI) Spectrum

O3

CO2

CO2

H2O

Wavelength (μm)

Brig

htne

ss T

empe

ratu

re (K

)

Q-branch

Longwave window

Shortwave window (with solar contribution)

Observation Operators for Infrared Radiances

HIRS-4

HIRS-5

HIRS-6

HIRS-7

HIRS-8

Selected AIRS Channels: 82(blue)-914(yellow)

1000 hPa

100 hPa

Satellite Radiance Observation Operator

The observation operator for radiance assimilation needs to accurately model the observed radiance

The calculations are complex comprise a significant fraction of the total data assimilation run time

For certain situations the first-guess fields and/or the radiance calculation is not accurate enough (e.g., clouds)

Quality control in these situations is very important. Even after quality control biases remain in the

observed-calculated differences and sophisticated bias control algorithms are used to remove these.

NEMS/GFS Modeling Summer School 24

Overview

Introduction to Atmospheric Data Assimilation Control Variables Observations Background Error Covariance Summary

NEMS/GFS Modeling Summer School 25

Variational Data Assimilation

c'o

'1T'o

''1Var

T''Var 2

121 JJ yHxRyHxxBxx

J : Penalty (Fit to background + Fit to observations + Constraints)x’ : Analysis increment (xa – xb) ; where xb is a backgroundBvar: Background error covarianceH : Observations (forward) operatorR : Observation error covariance (Instrument +

representativeness)yo’ : Observation innovationsJc : Constraints (physical quantities, balance/noise, etc.)

B is typically static and estimated a-priori/offline

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Kalman Filter in Var Setting

KFKF BKHIA

ab xx M

yHxKxx bba

1TKF

TKF

HHBRHBK

QMAMB TKFKF

Forecast Step

Analysis

• Analysis step in variational framework (cost function)

Extended Kalman Filter

''o

1T''o

'1KF

T''KF 2

121 HxyRHxyxBxx J

• BKF: Time evolving background error covariance• AKF: Inverse [Hessian of JKF(x’)]

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Motivation from KF

TbbKF 1

1 XXBB e K

ab XX

• Problem: dimensions of AKF and BKF are huge, making this practically impossible for large systems (GFS for example).

• Solution: sample and update using an ensemble instead of evolving AKF/BKF explicitly

TaaKF 1

1 XXAA e K

Ensemble

Perturbations

ba XX Forecast Step:

Analysis Step:

What does Be gain us?

Temperature observation near warm front

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Bf Be

Single Temperature Observation

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3DVAR

bf-1=0.0 bf-1=0.5

Summary

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• The analysis is produced through an optimal combination of information from the model forecast and the observations

• Observations come from a large number of sources, each with different strengths and weaknesses

• Accurate simulation of observed values is very important, particularly for radiance observations.

• Quality control and bias correction are crucial.• The use of background information from an EnKF

system greatly improves our ability to spread the information supplied by the observations is a realistic manner.