The Application of Observation Adjoint

Sensitivity to Satellite Assimilation Problems

Nancy L. BakerNaval Research Laboratory

Monterey, CA

Outline

• Introduction and motivation• Data assimilation adjoint theory – what is

observation sensitivity?• Examples of observation sensitivity with

NAVDAS adjoint– 00 UTC 7 February 1999 for TOVS– 00 UTC 10 February 2002 for ATOVS/AMSU-A

• Summary and conclusions

Introduction to Observation Adjoint Sensitivity

• A significant component of the medium-range forecast error is due to errors in the initial conditions – particularly true for relatively poorly sampled regions

• Classical adjoint sensitivity computes the sensitivity of a cost function J (e.g., 72-h forecast error) to the initial conditions for that forecast.– highlights regions that are very sensitive to small errors in

the initial conditions (e.g., temperatures and winds).

• The complete NWP adjoint sensitivity to J must include the adjoint of the data assimilation system.– sensitivity of J to the observations and background

Motivation

• Research was originally motivated by preparations for FASTEX in late 1996 – targeting methods were not able to take into account how the

data assimilation system would use the additional observations – the presence of other observations in the area – as such, could not provides guidance on where to place the

adaptive observations in the sensitive region

• Observation sensitivity has applicability far beyond targeting applications– help us to understand how observations are used by the

assimilation system– help us identify potential sources of forecast errors due to

errors in the initial conditions

Observations(y)

Data AssimilationSystem

Forecast Model

Forecast(xf)

Gradient ofCost Function J

(J/ xf)

Background(xb)

Analysis(xa)

Adjoint of the Data AssimilationSystem

Adjoint of theForecast Model Tangent Propagator

ObservationSensitivity

(J/ y)

BackgroundSensitivity(J/ xb)

Sensitivity to the

Analysis(J/ xa)

What is observation sensitivity?

forward problem

adjoint problem

• NAVDAS adjoint computes the sensitivity of the forecast aspect J (such as forecast error) to the observations and background.

• The sensitivity of J to the observations is given by

J/xa - sensitivity of J to the initial conditions.

1( ) ,T Tb b

a a

J J J

K HPH R HP

y x x

( )a b b x x K y Hx

NAVDAS* ADJOINT*NRL Atmospheric Variational Data Assimilation System

Compare to linear analysis equation

Sensitivity of the 72-h energy-weighted NOGAPS forecast error to the initial wind and height fields at 00 UTC 07Feb 1999. Verification area over west coast of U.S.

Magnitude of the sensitivity of the 72-h NOGAPS energy-weighted forecast error to the MSU-2 brightness temperatures. The “t” indicates time-window discontinuities.

t

Sensitivity to MSU-2 Brightness Temperatures

• Maximum MSU-2 sensitivity occurs when– the observations are relatively isolated, or – the observation density abrupt changes, – coincident with large amplitude and spatial scale

sensitivity to the initial fields.

• Large observation sensitivities near 45oN, 175oE – occur in the middle of a large-scale sensitivity to the

initial 700-hPa temperature field, – and are associated with a time-window data

discontinuity

Sensitivity to TOVS Brightness Temperatures

• Other abrupt changes in TOVS brightness temperature density may be associated with larger observation errors. – TOVS brightness temperatures over land and ice are more

difficult to assimilate properly and are eliminated in the present NAVDAS configuration

– This creates an abrupt change in the observation density along the coastlines and ice-edge boundaries where the observations are less accurate (mixed field-of-view).

– Abrupt changes in the data density also occur for the less accurate observations along the edges of the satellite scan.

Implications

• Sensitivity to the relatively inaccurate observations along the data discontinuity is larger than the sensitivity to the more accurate (data dense) observations. – assuming identical observation errors are assigned

• This implies that the less accurate observations have greater potential to change the forecast aspect, and to influence the analysis.

• Increasing the assumed observation error variance will decrease both the observation sensitivity and the influence of the observation on the analysis.

Estimate of the potential forecast impact due to the observations

• Define the change in J as the projection of the analysis error (a) onto the analysis sensitivity gradient

•

• The reduction in the expected variance of the change in J due to the observations is

2( )

T

Tb

o

J JJ

HPH Ry y

Ta

a

JJ

x

Sensitivity of NOGAPS 72-h forecast error to the initial T,u,v,p fields

10 UTC 09 February 2002

2

oJ for different observation

types

Discussion

• Are very large values of observation sensitivity desirable?– implies that the analysis depends upon a few observations

in highly sensitive regions– even small errors in the observation may contribute to the

forecast error– the corresponding background sensitivity is large– as observations are added, the analysis becomes less

dependent upon individual observations and the background, and the observation and background sensitivities decrease

– intermediate values of observation sensitivity are desirable

Conclusions and Future Work

• The observation sensitivity gives an estimate of the potential for an observation to make changes to the analysis with the amplitude and structure suggested by the analysis sensitivity.

• Actual impact cannot be determined until the observations have been taken and the forecast computed.

• Develop observation sensitivity techniques to diagnose sources of forecast error

• Investigate alternate impact functions

( )

T

b

JS

y Hxy

(Doerenbecher and Bergot, 2001)

Supplemental Slides

Summary

• The observation sensitivity is largest when – the analysis sensitivity is large in amplitude– the spatial scales of the analysis sensitivity and background error

covariances are similar (i.e., large targets)– the observation is assumed to be more accurate than the

background– the observations are relatively isolated or associated with an abrupt

change in the observation density (e.g, along coastlines or edges of satellite swaths)

• The observation sensitivity is weak when– the analysis sensitivity is weak amplitude or small-scale– the length scales of the analysis sensitivity is shorter than the

background error covariance length scales – the observation is assumed to be less accurate than the

background– the observation density is high

Understanding Observation Sensitivity

• For relatively isolated observations, K and KT

are large in amplitude and spatial scale.– When KT projects strongly onto the analysis

sensitivity, both and the potential change to J will be large

– the observation has more independent information– the observation will be given more weight in the

analysis– potential changes to the analysis due to the

observation are large in amplitude and spatial scale

TaJ J y K x

J y

( )a b b x x K y Hx

Understanding Observation Sensitivity

• For high density observations, KT is small in amplitude and spatial scale.– The projection of KT onto the analysis sensitivity

will be weaker, and both and the potential change to J are small.

• Similarly, if the observations are more accurate than the background, the observations will be given more weight and the potential changes to J are larger.

TaJ J y K x

J y

( )a b b x x K y Hx

Observation Sensitivity for a Hypothetical Flight Path

Understanding Observation Sensitivity