observation targeting

Observation Targeting

Andy LawrencePredictability and Diagnostics Section, ECMWF

Acknowledgements:Martin Leutbecher, Carla Cardinali,

Alexis Doerenbecher, Roberto Buizza

ECMWF Predictability Training Course - April 2006

Contents

Introduction • What is Observation Targeting?

Targeting Methodology• Example using a simple model • Kalman Filter techniques• Singular Vector techniques• Summary of research issues

Operational targeting principles• Previous targeting campaigns• Operational structure and schedules• Results from ATReC 2003• Verification of forecast impacts• Future of observation targeting

ECMWF Predictability Training Course – April 2006

What is observation targeting?

Techniques that optimize a flexible component of the observing network on a day-to day basis with the aim to achieve specific forecast improvements.


Estimated ROUTINE observations = 10 6

Estimated TARGETED observations = 10 3

The concept of observation targeting

Forecast an event.


OBS

OBS

OBS

Improve forecast?

Use adjoint model transform algorithm to derive data-sensitive areas. Add extra observations

Verify with corresponding analysis.

The concept of observation targeting

Q: If we have the capability to add observations in data-sensitive areas to improve the forecast of a specific event, can these locations be determined using objective (model-based) methods?


A: This is an optimization problem with two constraints:

i. Probability of making an analysis error at a particular location

ii. The intrinsic ability of the flow at that location (i.e. sensitivity)

OBS

OBS

OBS

Where are observations needed to improve a 18-hour forecast?

Sensitive areas Verification region


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The Observation Targeting Question

How do identify optimal sites for additional observations?

Methodology


OR

How do we predict changes of forecast uncertainty due to assimilation of additional observations?

Information needed to answer this question:

1. Knowledge of the statistics of initial condition errors…and how they change due to an assimilation of additional observations.

– Gaussian error statistics– Kalman filter techniques

Methodology


For linear perturbation dynamics and Gaussian error statistics, optimal state estimation can be approximated by the Extended Kalman Filter… which can also be used to select optimal sites for additional observations.

2. Knowledge of the perturbation dynamics from the observation time to the forecast verification time

– NWP studies suggest that perturbation dynamics are approximated by a linear propagator defined by ensemble-based techniques or tangent-linear/ adjoint techniques.

Targeted observations in the framework of an Extended Kalman Filter(Illustration using the Lorenz-95 system - Leutbecher, 2003)

Extended Kalman Filter

• A chaotic system, where a time unit of 1 represents 5 days

dxi

dt = -xi-2 xi-1 + xi-1 xi+1 – xi + F

with i = 1,2,…40

x0 = x40 , x–1 = x39 , x41 = x1 and F = 8


A perturbation placed at i=10, propagates ‘eastward’ at a speed of 25 degrees/day.

For routine observations:Observations are constructed by adding noise (representing unbiased and uncorrelated normally distributed errors) to values taken from a ‘truth’ run..become available every 6 hours.

Over land (positions 21-40) we have observations at all locations 0 = 0.05clim

Over ocean (positions 1-20) we have observations at ‘cloud-free’ locations 0 = 0.15clim

Planet L95: routine observing network


2-day forecast errors for Europe

Planet L95: forecast errors


2-day fc errors for Europe (21-28)

assim. with KF using routine obs.

sample of 1000 daily forecasts

rms error= 0:23 = 0:06clim

try to reduce forecast errors using 1 tar-getedobs with o = 0:05clim over sea

A single observation over the ocean, with the error characteristics of a land observations is considered (i.e. at i=1,…20).

The aim of this is to provide a better forecast over ‘Europe’ on Planet L95.

Planet L95: targeted observation


Covariance evolution within the Kalman filter:

For Routine observations:

Analysis Step at time tj (Pra)-1 = (Pr

f)-1 + HrT Rr

-1 Hr

Forecast Step tj tj+ Prf = M Pr

a MT

Covariance prediction with the Kalman filter (routine + additional observations)


Optimal position i* (where i* gives the maximum reduction of forecast error variance) :

maxi=1..20 trace ( LEu (Prf - Pi

f ) LT

Eu )

For Routine + additional observations at position i (where i = 1,…20)

Analysis Step at time tj (Pia)-1 = (Pr

f )-1 + HrT Rr

-1 Hr + HiT Ri

-1 Hi

Forecast Step tj tj+ Pif = M Pi

a MT

Optimal position for an additional observation


Distribution of the optimal positionfor an additional obs in the Atlanticto improve the 2-day fc over Europe (KF full rank)

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Distribution of optimal position for an additional observation in L95 ‘Atlantic’(to improve the 2-day forecast over Europe)

Planet L95: Forecast impacts

How to measure the improvements in forecast skill:

• Compare with randomly placed observations

• Compare with impact obtained with observations that actually reduce the forecast error the most ( although never achievable as it requires information at verification time; position depends on realization of actual errors!)

• Compare with the impact of an observation added at a fixed site optimized for the forecast goal (a hard test).

– No such test with NWP system and real observations yet.

– How does last test look with L95?


Fixed location v. adaptive day-to-day location


Distribution of 2-day forecast errors: targeting versus addition at fixedsite

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targeting using full-rank Kalman filter for data assimilation and for forecast error variance prediction at

verification time

Method is good for a simple model, BUT

an extended Kalman filter is too expensive for a full NWP model

Targeting would require to run the Kalman filter several times

(i.e. each configuration of the additional observations considered in the

planning process is one among several feasible ones).

Approximations of the Kalman Filter

Solution:Calculate forecast error variance in small relevant subspace!

1. Perturbations of ensemble members about the mean: a proxy for data assimilation scheme (ETKF).

2. Based on singular vector schemes computed with an estimate of the inverse of the routine analysis error covariance metric as the initial time metric.


Reduction of forecast error variance using the ETKF (Majumdar, 2001)Signal = forecast error (routine +additional) – forecast error (routine)

Ensemble Transform Kalman Filter (ETKF)


Used in targeting for Winter Storms Reconnaissance Program (WSRP) (Bishop, Etherton and

Majumdar, 2001)

• Assumes linearity.‘linear combination of ensemble perturbations + ensemble mean = model trajectory’.

• Assumes optimal data assimilation.• No covariance localisation.

Singular vectors identify the directions (in phase space) that provide maximum growth over a finite period of time.


Singular Vector Schemes

• Dependent on model characteristics and optimization time

• Growth is measured by the inner product (or metric or norm):

If the correct norm is used, the resulting ensemble captures the largest amount of forecast error variance at optimization time (assuming that the forecast error evolves linearly).

• For targeting: Forecast error variance prediction from t0 to tv replaced by variance predictions in a singular vector subspace.

• Data assimilation can either use a full Kalman filter or Optimal Interpolation.

Singular Vector-based reduced-rank estimate:

• Initial time metric is the inverse of the routine analysis error covariance matrix (Pr

a)-1

• SV’s computed with this metric evolve into the leading eigenvectors of the routine error covariance matrix

trace (Leu Pf LTEu ) .

Singular vector targeting method 1


• Compute variance of forecast errors only in a subspace of leading singular vectors

trace (Ân LEu Pf LTEu Ân

T) instead of trace (LEu Pf LTEu )

Here, Ân denotes the projection on the subspace of the leading n (left) singular vectors of LEuM.

• Data assimilation uses full Kalman filter

Reduced-Rank approximation of covariance forecast step

Analysis error covariances in the subspace spanned by the leading n SV’s are represented by

Routine network Vn VnT where Vn

T ( Pra ) -1 Vn = I

Modified network Vn i iT Vn

T where (Vn i )T ( Pra ) -1 (Vn i) = I

The transformation matrix i is the inverse square root of the n x n matrix,Ci, that expresses the modified analysis error covariance metric in the basis of the singular vectors;

Ci = VnT ( Pr

a ) -1 Vn = In + VnT Hi

T R –1 Hi Vn .

Using these representations (of the aecm), the forecast error variance in the verification region becomes:

trace (Ân LEu ( Pfj+ ) LT

Eu ÂnT ) = n

j=12j routine network

trace (T diag (21… 2

n ) ) modified network

where j denotes the singular value of the j-th SV vj


Singular vector targeting method 2


Approximate full Kalman filter by replacing the routine forecast error covariance matrix Pf

r by a static background error covariance matrix B (Optimal Interpolation scheme)• In the variance prediction (for targeting) and • In the assimilation algorithm

Analysis error covariance matrix given by

A-1 = B-1 + HTR-1H

In L95 system, static background error covariance matrix B = (xf - xt ) (xf - xt)T

is a sample covariance matrix computed from (forecast – truth) differences from

a 1000 day sample → combine with reduced-rank technique

Method 1: Method 2:

Full KF- SV subspace Optimal Interpolation – SV subspace

L95 comparisons : SV reduced-rank schemes


Approximation of the background error covariances

Replace the routine background error covariance matrix P fr by a static backgrounderror covariance matrix B (OI)

in the variance prediction (targeting) and

in the assimilation algorithm.

magic B: The static background error covariance matrix is a sample covariancematrix computed from forecast truth differences.Several iterations of updating B=h(x f xt)(x f xt)Ti over a 1000 day sample.

KF versus OI performance, global rms errors

range (d) 0 1 2 3 4 5KF 0.11 0.17 0.25 0.38 0.57 0.80OI 0.33 0.49 0.74 1.04 1.38 1.74clim =3:6; o;land = 0:18; o;ocean= 0:54

L95 comparisons : SV full rank v reduced-rank schemes


Distribution of 2-day forecast errors: KF-full rank versus KF-rank 1

tg obs (KF-rank 1)

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targeting using full-rank Kalman filter for data assimilation and a rank-1 approximation for the forecast

error variance prediction at verification time

Distribution of 2-day fc errors over Europe (OI-rank 1)

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Distribution of 2-day forecast errors over Europe

Full KF v. Method 1 ( Reduced-rank Kalman filter)

Full KF v. Method 2 ( Reduced-rank OI)

• Targeted observations should be directed to ‘sensitive’ regions of the atmosphere.


SV dependency on initial time metric

p1

p0 S S

• For predictability studies, an appropriate metric is based on energy.–Total Energy provides a dynamical basis (has no knowledge of error statistics):

||x||e2 = xTEx = ½ u2 + v2 + (cp/Tr) T2 dp dS + ½ Rd Tr pr ( ln psfc )2 dS

• Correct metric is dependent on the purpose for making the targeted observations (study precursor developments or to improve forecast initial conditions).

Hessian Singular Vectors


• The Hessian of the cost-function provides the estimate of the inverse of the analysis error covariance matrix:

J(x) = Jb (x) + Jo (x)

J = B-1 + HTR-1H = A-1

• Initial error estimates are consistent with the covariance estimates of the variational data assimilation scheme (incorporates error statistics).

ECMWF SV VT:Tuesday 23 December 2003 12UTC Model Level 46 temperature

0.02

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TESV ‘Full’ Hessian SV ‘Partial’ Hessian SV J = Jb + Jo J = Jb


Total energy SV v Hessian SV

Hessian reduced-rank estimate


• Similar to Kalman Filter/ OI- reduced rank estimate but is based on a subspace of Hessian Singular vectors vi computed with the metric Jroutine (using only observations from the routine network in Jo) (Leutbecher, 2003)

• Estimate of forecast error variance reduction due to additional observations

trace ([I – C-1] diag (21…. 2

n))

where j denotes the singular value of the routine Hessian SV vj

• Efficient computation of the Hessian metric for modified observation network (routine + additional) in the subspace:

Cij = vTi Jmod vj = vT

i (Jroutine + HTa R-1

a Ha) vj

= ij + (Ha vi)T R-1a Ha vj

Comparison of flight track ranking


Winter Storms Reconnaissance Program 2003Additional observations on 4th Feb 00UT for forecast verification time: 6thFeb 00UT

Hessian Reduced-rank estimate ETKF

(Doerenbecher et al., 2003)

Summary & Research Issues


Aim of observation targeting:

Prediction of forecast error variance due to modifications of observing

network.

Factors that affect skill of forecast error variance predictions in operational NWP:

• Covariance estimates – Skill of forecast error variance predictions depends on quality of background

error covariance estimate…incorporate flow-dependant wavelet approach.

– Account for correlations between observation error in current schemes (Important for satellite data with observation error correlations in space and between channels optimal thinning - Liu & Rabier, 2003)

– Predict spatial resolution of routine observations. Harder to do with day-to-day variability of targeted observations, particularly for satellite data affected by cloud.



• Error dynamics– TL/AD model simplified due to resolution and physical process

parameterisation. Advances in formulation (moist processes, sensitivity of observation targeting guidance to spatial resolution) should improve variance predictions.

– Validity of tangent linear assumption:

Gilmour et al. 2001: probably not useful beyond 24h; but measure of nonlinearity dominated by small scales

Reynolds & Rosmond 2003: SV’s usefully up to 72h (diagnostic in SV-space and scale dependant diagnostic)

• Reduced Rank SV’s (Subspace): How many SV’s are needed to reliably predict forecast error variance reductions?

– L95: 1 SV is sufficient: the leading SV explains a large fraction of the total forecast error variance in the verification region (Rank 1KF full KF)

– NWP: For rank (LEuM) number of grid-points in verification region times number of variables.



• Observation types– Forecast error variance reductions can be determined for different observation

types in sensitive areas. – Will the abundance of satellite data eliminate the need for in-situ

measurements? – Satellite sampling is limited through cloud layers → in-situ measurements

useful if dynamically-sensitive areas are beneath clouds.

• Targeting methodology– Perhaps combination of SV and ensemble-based approach? (expensive, as

requires a dedicated ensemble).– Does validity of linear transformation in ETKF technique extend further than

the validity of the TL-approximation?

• Contribution of model error?– To initial condition error at t0

– To growth of error from t0 to tv

Previous targeting campaigns

Targeted observation techniques and methods were tested during numerous operational campaigns:

FASTEX (Fronts and Atlantic Storm-Track Experiment 1997)Improving forecasting of atmospheric cyclone depressions forming in the North-Atlantic and reaching the west-coast of Europe.

NORPEX (North Pacific Experiment 1998)North Pacific winter-season storms that affect the United States, Canada, and Mexico.

WSRP (Winter Storms Reconnaissance Program 1999-2006)North-Eastern Pacific storms affecting the west-coast of the United States. Use of targeted observations has a positive effect on forecast skill (Majumdar et al. 2001)

ATReC (Atlantic THORPEX Regional Campaign 2003)North-Atlantic storms affecting east-coast United States and Europe.


1. Case selection: Decision made at tc on whether or not to commit additional observing resources at t0. Decide for which forecast verification time tv and which region R adaptive observations should be taken.

NWP Centres

ECMWF UK MO NCEP NRLMF

Operations Centre

Operational Structure for Observation Targeting

1 2 3 4 5

tc td t0 tv time


2. Sensitive area prediction: Compute which configuration for adaptive observations (to be taken at t0) is likely to best constrain error of forecast for (tv,R).


1 2 3 4 5

tc td t0 tv time


NWP Centres


Operations Centre

3. Select and request additional observations at td.


1 2 3 4 5

tc td t0 tv time


NWP Centres


Operations Centre

Observation control centre

4. Observing platforms deployed at t0 and observations taken.


1 2 3 4 5

tc td t0 tv time


NWP Centres


AMDAR Radiosonde Res. AircraftASAP

Observation control centreData

Monitoring

Operations Centre

NWP Centres



1 2 3 4 5

tc td t0 tv time


AMDAR Radiosonde Res. AircraftASAP

Observation control centreData

Monitoring

Operations CentreOperations Centre

5. Forecast verification time at tv

NWP Centres


Atlantic THORPEX Regional Campaign 2003


First field campaign in which multiple observing systems were used.

Dropsondes from research aircraft, ASAP ships, AMDAR, land radiosonde sites.

Observation targeting guidance to predict the sensitive areas based on

• UKMO: ETKF based on ECWMF ensemble• Meteo-France: total energy SV’s run on a (possibly perturbed) trajectory• NRL: SV’s and sensitivity to observations• NCEP: ETKF based on combined ECWMF and NCEP ensembles.

• ECWMF: 2 flavours of total energy SV’s and Hessian SV’s

Config. initial norm TLM res. TLM physicsTE-d42 Total Energy T42 dry

TE-m95 Total Energy TL95 moistH-d42 Hessian T42 dry

Dry TESV (ECMWF) Moist TESV (ECMWF)

Hessian SV (ECMWF) ETKF (Met Office using ECMWF ensemble)

ATReC_029_1: Obs. time: 20031208, 18UT ; Ver. time 20031211, 00 (54h opt)


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Valid time: 20031208, 18 UTUKMO-SAP based on ETKF signal and ECMWF MSL

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ECMWF calculated overlap ratios for a = 4 x 106 km2 (Leutbecher et al. 2004)

SAP1 SAP2 Number of cases with overlap >0.50 SV TE-d42 SV TE-m95 42/43 98%SV TE-d42 SV H-d42 35/42 83%SV TE-d42 ETKF 31/67 46%SV H-d42 ETKF 32/67 48%

Sensitivity area prediction


How do we determine where to send the observations?

In ATReC 2003, level of agreement between the sensitive area predictions can be quantified in terms of geographical overlap.

Sensitive area 1: Sj of area a

Sensitive area 2: Sk of area a

Geographical overlap

Ojk = area ( Sj Sk ) /a

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TESV vs Hessian SV vs ETKF


DESIGNATED TARGET AREA

ETKF sensitivity across Atlantic, main area 40-55N,20-30W; secondary max 45N60W (this is also secondary area for Hessian SVs). Main HSV and dry TESV centre is South tip of Greenland (and down to 50N), and back into Canada at 60N. Moist TESVs have significant area 35N65W (Odette)

Case 43: Obs. time 8th Dec 18UT, Verif. time 11th Dec 00UT


Radiosonde, Satellite rapid-scan winds, AMDAR flights

Case 47: Obs time 11th Dec 18UT, Verif. Time 13th Dec 12UT


Radiosondes, ASAP, Satellite, AMDAR

Case 36: Obs time 4th Dec 18UT, Verif. Time 6th Dec 12UT


Radiosonde, ASAP, AMDAR

Case 37: Obs. Time 5th Dec 18UT, Verif. Time 7th Dec 12UT


Radiosonde, ASAP, Satellite, AMDAR and Dropsondes

East Coast USA storm 5-7th December 2003


A major winter storm impacted parts of the Mid-Atlantic and Northeast United States during the 5th-7th. Snowfall accumulations of one to two feet were common across areas of Pennsylvania northward into New England. Boston, MA received 16.2 inches while Providence RI had the greatest single snowstorm on record with 17 inches, beating the previous record of 12 inches set December 5-6, 1981. (from http://www.met.rdg.ac.uk/~brugge/world2003.html)

NASA-GSFC, data from NOAA GOES

http://www.met.rdg.ac.uk/~brugge/world2003.html

Control (routine observations)

ATReC (routine + additional observations)

Summary of ATReC forecast Impacts


ATReC (routine + additional observations in target area)

Case 37: Obs. Time 5th Dec 18UT, Verif. Time 7th Dec 12UT


ControlATReC (routine + additional observations)ATReC (routine + additional observations in target area)

• Statistical verification of forecast impacts:– Large sample needed to estimate forecast skill differences in verification regions.– Data denial experiments may provide larger sample size.

• Sensitive area prediction method:– Sample similar observational coverage for both SV and ETKF sensitive regions

…not possible during ATReC.

• ATReC can be used as to plan future adaptive observation campaigns :– Use observation targeting for medium range. – Improve efficiency so as to shorten warning time for observation providers.– Identify cost-effective observation platforms (i.e. dropsondes).– Cancel cases that show sharp reduction in uncertainty as observation time

approaches.

Some ATReC 2003 conclusions


Jy

J is measures the forecast error: its gradient with respect to the observation vector y.

This gives the forecast error sensitivity with respect to the observations used in the initial condition for model forecast

J ax

ax

ythe sensitivity respect the initial condition xa

Analysis sensitivity with respect the observation

Forecast sensitivity


From Cardinali & Buizza, 2003

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Forecast and Analysis Sensitivity


• Forecast sensitivity to observations has been computed for the campaigns showing a forecast impact (ATreC-Control)/Control ≥ ± 10%

• In general, results show that in 13 cases out of 38: 9 positive and 4 negative– Targeted observations decrease the forecast error in verification area for

60% of cases (ALTHOUGH high skill in control forecasts). – Differences in forecast impact come also from the continuous assimilation

cycling that provides different model trajectories

• From the campaigns of 5th Dec at 18 UTC - Targeted observations improved the forecast of a cyclone moving along the east coast of North America for which severe weather impact was forecast.

Forecast impact of observations


Adding targeted observations in the Pacific is expected to have a rather small impact (5% on z500/z1000 forecast errors over North America)

Adding targeted observations in the Atlantic is expected to have an even smaller impact (3% on z500/z1000 forecast errors over Europe)

Value of observations taking in oceans is regionally dependant and depends on the underlying observation system.

Up to the optimization time, the value of observations taken in SV-target areas is higher than the value of observations taken in similar size random areas.

Future of Observation Targeting

• Studies of the value of targeted observations:

Buizza et al. (2005) performed experiments on 100+ cases to:(a) Assess impact of observations taken in Pacific and verified over North America

(b) Assess impact of observations taken in Atlantic and verified over Europe

(c) Compare impact of observations taken in SV-target areas to observations taken in random areas.

(d) Estimate the average impact of targeted observations.



• Data denial studies (Kelly, Buizza, Thepaut, Cardinali)– Relatively inexpensive and incorporate a large number of cases (~ 6 months).– Assess value and impacts of specific types of observation platforms.

• Hurricane targeting (Majumdar et al. 2005, 2006)– Improve short-range forecasts of cyclone tracks – Provides useful comparison on ETKF and SV targeting techniques.

• Satellite Targeting – Targeting provides utilisation of ‘dynamical thinning’ techniques.– Improved channel selection can reduce problems in cloudy conditions



• Targeted observation campaigns:– Winter Storms Reconnaissance Program (ongoing) (NCEP/ NRL)– European THORPEX Regional Campaign 2007 : a `virtual’ targeting experiment.– African Monsoon Multidisciplinary-Analyses (AMMA) Observing System test

2005-2010– Pacific-Asian Regional Campaign (PARC) 2008.

• Improve adaptive parts of the observing network– New platforms (e.g driftsondes) are being developed – Rocketsondes– Aerosondes


observation targeting

Documents

hour forecast

obsobsobsimprove forecast

observation time

specific forecast improvements

methodologythe observation

analysis error

optimal sites

adjoint model