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Assimilation of GPS Radio Occultation Data

Ying-Hwa KuoUCAR COSMIC Office

NCAR MMM Division

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Outline Characteristics of GPS radio occultation observation Factors affecting the results of GPS RO assimilation Practical considerations for the GPS RO assimilation:

– Choices of assimilation variables,

– Observation operators,

– Choices of Data assimilation systems (e.g., 3D-Var, 4D-Var, EnKF)

– Determination of observational errors

– Data quality control, … etc

Review of GPS RO assimilation and impact studies Comparison between WRF 3D-Var and WRF/DART Comparison of local and nonlocal observation operators

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The velocity of GPS relative to LEO must be estimated to ~0.2 mm/sec (velocity of GPS is ~3 km/sec and velocity of LEO is ~7 km/sec) to determine precise temperature profiles

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The velocity of GPS relative to LEO must be estimated to ~0.2 mm/sec (20 ppb) to determine precise temperature profiles

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Characteristics of GPS RO Data Limb sounding geometry complementary to ground and space

nadir viewing instruments High accuracy High vertical resolution All weather-minimally affected by aerosols, clouds or

precipitation Independent height and pressure Requires no first guess sounding Independent of radiosonde calibration No instrument drift No satellite-to-satellite bias

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Problems of using GPS RO data in weather models

GPS RO data (e.g., phase, amplitude, bending angles, refractivity) are non-traditional meteorological measurements (e.g., wind, temperature, moisture, pressure).

The long ray-path limb-sounding measurement characteristics are very different from the traditional meteorological measurements (e.g., radiosonde) or the nadir-viewing passive microwave/IR measurements. GPS RO observation is not a point observation like a radiosonde.

The GPS RO measurements are subject to various sources of errors (e.g., uncalibrated ionospheric effects, tracking errors, super-refraction, optimization of bending angle profiles, …etc). [see Kursinski et al. (1997), JGR, 102 (D19), 23429-23465]

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Assimilation of GPS RO data:

The purpose of data assimilation is to extract the maximum information content of the GPS RO data, and to use this information to improve analysis of model state variables (u,

v, T, q, P, …etc).

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GPS RO measurement and data processing procedures

Before we consider the assimilation of GPS RO data, we need to understand what are actually measured and the various data processing steps taken to reduce the data.

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GPS radio occultation measurements & processing

s1, s2, a1, a2

s1, s2

1, 2

N

T, e, P

Raw measurements of phase and amplitude of L1 and L2

Raw measurements of phase of L1 and L2

Bending angles of L1 and L2

Bending angle

Refractivity

Single pathGeom. Optics

Satellites orbits &Spherical Symmetry

Assumption

Ionospheric effect cancellation

High altitude Climatology & Abel inversion

Auxiliary meteorological data

Multi path, Wave Optics

See Kuo et al. (2000, TAO, 11 (1), 157-186) for details

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GPS/MET Variables

Raw measurements of L1 & L2 phase (s1, s2) and amplitude (a1, a2)

Raw measurements of L1 & L2 phase (s1, s2)

Bending angles of L1 & L2 (1, 2)

Bending angle (corrected for ionosphere) Refractivity N (through Abel inversion):

Retrieved T, e, and P

25 )10(73.36.77

T

e

T

PN +=

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Which variables should we use for the assimilation of GPS RO data?

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Choice of Assimilation Variable

Use the raw form of the data, to the extent possible (e.g., the more processing the less accurate the data due to additional assumptions or auxiliary data used in processing).

Ease to model the observables (and its adjoint) Minimize the need for auxiliary information (before the

assimilation of GPS RO data) Ease to characterize observational errors Computational cost

Should consider the following factors:

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Assimilation of L1 and L2 phase and amplitude

Most “raw” form of the data. No assumptions needed. Easy to characterize measurement

errors.

Observation operator need to model wave propagation inside weather models.

Require precise GPS and LEO orbits information.

Require ionospheric model to account for ionospheric delays (we don’t have very accurate ionospheric model)

Computationally very expensive.

Pros Cons

Not Practical

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Assimilation of L1 and L2 phase

Most “raw” form of the data. No spherical symmetry assumption. Easy to characterize measurement

errors.

Assume single ray propagation Observation operator needs accurate

ray tracing (shooting method required) between GPS and LEO

Require precise GPS and LEO orbits information.

Require ionospheric model to account for ionospheric delays (we don’t have very accurate ionospheric model)

Computationally very expensive.

Pros Cons

Not Practical

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Assimilation of L1 and L2 bending angles

Second “raw” form of the data. Does not require precise GPS and

LEO orbits information. Shooting method not required. Relative easy to characterize

measurement errors.

Observation operator needs to perform ray tracing with initial conditions.

Require ionospheric model to account for ionospheric delays (we don’t have very accurate ionospheric model)

Computationally expensive.

Pros Cons

Major difficulty: Hard to remove ionospheric effects

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Assimilation of neutral atmosphere bending angles

Third “raw” form of the data. Does not require precise GPS and

LEO orbits information. Does not require ionospheric model. Shooting method not required. Reasonably easy to characterize

measurement errors (still challenging for lower troposphere).

Observation operator need to perform ray tracing with initial conditions.

Uncalibrated ionospheric effects are a source of error (e.g., residual errors associated with ionospheric correction).

Still computationally expensive (hard to implement operationally current generation of computers)

Pros Cons

A possible choice

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Assimilation of neutral atmosphere refractivity

Observation operator easy to develop (local operator on model variables).

Does not require precise GPS and LEO orbits information.

Computationally inexpensive (operationally feasible).

Easy to characterize measurement errors.

Assuming Abel-inverted refractivity as the model local refractivity

4th raw form of the data. Requires initialization by

climatology (for upper boundary conditions). [Need to create an “optimized” bending angle profile based on observation and climatology, before the retrieval of refractivity.]

Uncalibrated ionospheric effects are a source of error.

Bias due to super refraction

Pros Cons

A possible, most popular choice

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Assimilation of retrieved T, q and P

Requires little or no work in the development of observation operator (as they are model state variables).

The retrieved T, q, and P can be assimilated by simple analysis or assimilation methods.

Computationally inexpensive.

Many data processing steps must be taken before T, q, and P are retrieved.

Auxiliary information is needed for retrieval, and it can introduce additional errors.

Hard to characterize observational errors (as it is mixed with the errors of the auxiliary information).

Bias errors due to superrefraction. Least accurate.

Pros Cons

Not a Good Choice

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Recent Development -- linearized non-local observation operators

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Linearized non-local operators A new class of linearized non-local (LNL) observation operators have been

developed recently that have the following features:– It makes use of simplified ray trajectories (can be straight line or curve line) that do

not depend on refractivity.– This linearizes the assimilation problem (wrt refractivity)

» Bending angle assimilation requires recalculation of ray trajectory at every iteration (since model refractivity is altered after assimilation)

» For the LNL operators, this is not necessary, since ray trajectory does not change for each occultation soundings during the iteration steps.

– Abel-inverted refractivity is no longer used as local refractivity. Rather, a new modeled observable is defined as a function of refractivity.

– The LNL operators are only slightly more expensive than local refractivity operator, but significantly (about 2 order of magnitudes) cheaper than bending angle assimilation.

– The LNL operators account for horizontal refractivity gradients and are much more accurate than local refractivity operator (only slightly less accurate than bending angle obs operator).

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The Abel-retrieved (AR) N is a non-local, non-linearfunction of the 2-D refractivity in occultation plane.

Modeling of RO AR N as the local N may resultin significant errors, especially, in the troposphere.

Accurate modeling of RO bending angle by ray-tracingis computationally expensive.

An alternative: to use simple linearized, non-localobservation operators:

(i) bending angle (Poli 2004); (ii) refractivity (Syndergaard et al. 2005);(iii) phase (Sokolovskiy et al. 2005)

Three possible LNL observation operators

LNL observation operators are NOT meant to represent the true GPS observables (s, , N). Rather they are “modeled observables”, which are functions of refractivity.

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References for LNL operators:Ahmad, B., and G. L. Tyler, 1998: The two-dimensional resolution kernel asociated with

refrieval of ionospheric and atmospheric refractivity profiles by Abelian inversion of radio occultation phase data. Radio Science, 33, 129-142.

Syndergaard, S., E. R. Kursinski, B. M. Herman, E. M. Lane, and D. E. Flittner, 2005: A refractive index mapping operator for variational assimilation of occultation data. Mon. Wea. Rev., 133, 2650-2668.

Sokolovskiy, S., Y.-H. Kuo, and W. Wang, 2005: Assessing the accuracy of linearized observation operator for assimilation of Abel-retrieved refractivity: Case simulation with a high-resolution weather model. Mon. Wea. Rev., 133, 2200-2012.

Sokolovskiy, S., Y.-H. Kuo, and W. Wang, 2004:Validation of the non-local linear observation operator with CHAMP radio occultation data and high-resolution regional analysis. Mon. Wea. Rev., 133, 3053-3059.

Poli, P., 2004: Assimilation of global positioning system radio occultation measurements into numerical weather forecast systems. Ph. D. Thesis, U. of Maryland, 127pp.

Poli, P., 2004: Effects of horizontal gradients on GPS radio occultation observation operators. II: A Fast atmospheric refractivity gradient operator (FARGO). Q.J. R. Met. Soc. 130, 2807-2825.

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Choice of observation operatorsC

ompl

exit

y

L1, L2 phase and amplitude

L1, L2 phase

L1, L2 bending angle

Neutral atmosphere bending angle

Linearized nonlocal observation operator

Local refractivity

Retrieved T, q, and P

Not practical

Not accurate enough

Possible choices

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Comparison between Ngps vs Nlocal

Ngps: refractivity calculated from ray-tracing and Abel transform based on NCEP global analysis.

Nlocal: refractivity calculated T, e, P of NCEP grid point data.

For most soundings, Ngps is very close to Nlocal, suggesting the validity of spherical symmetry assumption.

For some soundings, where gradients of N are large, Ngps can be significantly different from Nlocal.

62 soundings

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Case 1: Hurricane Isabel (2003)

Developed in the lower Atlantic ocean, tracked northwest and landed at North Carolina coast on Sept 18, 2003

The hurricane was category 4 or 5 for a period of 6 days.

The WRF simulation covered a period when the hurricane was category 2.

24-h forecast from 4-km WRF simulation, valid at 0000 UTC 17 September 2003.

A

B

A B

Equivalentpotential temperature

Radarreflectivity

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Errors in the troposphere: local refractivity >10%; non-local refractivity <2%;phase <1%

Original, 4 km WRF horizontal resolution

Error of observation operator

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Choice of Data Assimilation Systems

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Data Assimilation Systems

From F. Bouttier and P. Courtier

History of the main data assimilation algorithms used in meteorology and oceanography, roughly classified according to their complexity (and cost) of implementation, and their applicability to real-time problems. Currently, the most commonly used for operational applications are OI, 3D-Var and 4D-Var.

Based on ECMWF Training Materials

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Choices of Assimilation Systems

Ability to assimilate non-traditional variables (e.g., bending angles, refractivity, or other modeled observables):

– Simpler methods (Cressman objective analysis, nudging, OI) cannot assimilate in-direct variables.

– 3DVAR, 4DVAR, EnKF can assimilate any variables that can be expressed as functions of the basic model variables.

Ease for the implementation of observation operators:

– 3DVAR and 4DVAR require the development of adjoint of observation operator.

– EnKF only needs the forward observation operator. Computational cost:

– 3DVAR much cheaper than 4DVAR & EnKF

– 4DVAR & EKF compatible in cost Ability to assimilate data at the time and location when they are taken (4DVAR & EnKF). Ability to use model (or dynamics) constraints (4DVAR & EnKF). Ability to consider flow-dependent background errors (4DVAR & EnKF).

Factors that need to be considered:

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Variational assimilation of GPS RO data Assimilation of N or requires the use of variational data assimilation (or EKF)

systems, as N and are not model predictive variables. In Variational Analysis (e.g. 3D- or 4D-VAR, we minimize the cost function:

where xo = x(to) is the analysis vector, xb is the background vector, d is the observation vector, O is the observation error covariance matrix and B is the background error covariance matrix.

H is the forward model (observation operator) which transforms the model variables (e.g. T, u, v, q and P) to the observed variable (e.g. bending angle, refractivity, or other modeled observables).

€

J(xo) =1

2(x(to) − xb )T B−1(x(to) − xb )

+1

2(H(x(tr

r

∑ )) − d(tr))T Or

−1(H(x(tr)) − d(tr))

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COSMIC (Constellation Observing System for Meteorology, Ionosphere and Climate) 6 Satellites was launched:

01:40 UTC 15 April 2006 Three instruments:

GPS receiver, TIP, Tri-band beacon Weather + Space Weather data Global observations of:

Pressure, Temperature, HumidityRefractivityIonospheric Electron DensityIonospheric Scintillation

Demonstrate quasi-operational GPS limb sounding with global coverage in near-real time

Climate Monitoring A Joint Taiwan-U.S. Mission FORMOSAT-3 in Taiwan

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1.7 Million Profiles in Real Time 4/21/06 – 5/6/2009

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Sean Healy, ECMWF

ECMWF SH T Forecast Improvements from COSMICAssimilation of bending angles above 4 km

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ECMWF Operational implementation of GPSRO on Dec 12, 2006

Neutral in the troposphere, but some improvement in the stratospheric temperaturescores. Obvious improvement in time series for operational ECMWF model.

Dec 12, 2006 Operational implementation represented a quite conservative use of data. No measurements assimilated below 4 km, no rising occultations.

Nov 6, 2007 Operational assimilation of rising and setting occultations down to surface

↑

Sean Healy, ECMWF

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100 hPa Temperature vs. radiosondes

NH

tropics

SH

Sean Healy, ECMWF

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NCEP Impact study with COSMIC

• 500 hPa geopotential heights anomaly correlation (the higher the better) as a function of forecast day for two different experiments: – PRYnc (assimilation of operational obs ), – PRYc (PRYnc + COSMIC)

• Assimilated ~1,000 COSMIC profiles per day• Assimilated operationally at NCEP 1 May 2007• Assimilating refractivities from rising and setting

occultations at all levels (including low level), provided they pass QC

• Results with COSMIC “very encouraging”

Lidia Cucurull, JCSDA

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Temp, 250 hPa, SH Wind speed, 100 hPa, SH

UKMO Bias and RMS as function of forecast range

mean mean

RMS RMS

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Prediction of Typhoon Shanshan (2006)

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Typhoon Shanshan (Sept 10-17, 2006)

Central SLP pressureCentral SLP pressure

Operational forecasts using variational assimilation failed to predict the curving of the typhoon.

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RO soundings are randomly distributed over the domain, provide large-scale information.

COSMIC RO soundings (September 13, 2006)

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WRF/DART ensemble assimilation at 45km resolution for 8-14 September 2006.

32 ensemble members.

Control/NoGPS run:

Assimilate operational datasets including radiosonde, cloud winds, land and ocean surface observations, SATEM thickness, and QuikScat surface winds.

• GPS run:

Assimilate the above observations + RO refractivity.

Assimilation Experiments

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Impact of RO Refractivity on Ensemble Forecasts

• 16 members

• with a finer nested grid of 15km

• initialized at 00UTC 13 Sept 2006

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Probability forecast of accumulated rainfall

(24hours, 12Z 14-15 Sep., > 60mm/day, %)

NOGPS GPS OBS

Rainfall forecast is enhanced in Northern Taiwan with COSMIC data. This is closer to the observed rainfall.

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Intensity is increased with RO data. Ensembles give significance.

Observed Observed Ensemble Ensemble

meanmean

NoGPS GPS

ObservedObserved

Ensemble Ensemble MeanMean

Ensemble Forecasts of Central Sea Level Pressure

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Comparison of WRF 3DVAR and WRF/DART forecast of Shanshan (2006)

Assimilation for 24 hours starting 00Z 13 September 2006 using both 3DVAR and WRF/DART ensemble system

Assimilation of CWB conventional data with/without RO data

DARTNBNG: NO GPS run using DART DARTNB: With GPS run suing DART CYCLNBNG: NO GPS run using 3dvar CYCLNB: With GPS run using 3dvar

Followed by a 3-day forecast on 14 September 00Z.

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Zonal wind Analysis along the typhoon centers (125.8E) on 00Z 14 September

3DVARWRF/DART

Zonal wind is stronger in WRF/DART analysisZonal wind is stronger in WRF/DART analysis

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Vorticity Analysis along typhoon centers (125.8E) on 00Z 14 September

WRF/DART

3DVAR

Vortex is stronger in WRF/DART analysisVortex is stronger in WRF/DART analysis

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Analysis at 00Z 14 Sept 2006

GPS -

NO GPS

EnKF -

3D-Var

WRF/DART WRF-3D-Var

With GPS Without GPS

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Typhoon intensity (central pressure)

3DVAR

WRF/DART

OBS

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Typhoon track error

3DVAR

WRF/DART

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Forecast of Integrated Cloud Water at 00Z 16 Sept. 2006

3DVAR

WRF/DART IR image

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Atmospheric River case: Nov 6-8, 2006

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Observed Daily Precipitation

24-h precipitation

Ending at

1200 UTC 7 November 2006

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Experiment Setup

CTRL: operational observation data;

LOC: CTRL+GPS with Local operator

NON: CTRL+GPS with Non-local operator

Three runs:

System: NCEP Gridpoint Statistical Interpolation (GSI) + WRF ARW Case: AR took place in the early of Nov.2006 Setup:

Cycling Assimilation: 36km38L; Ptop: 50hPa 24h Forecast: triple nested domain, 36x12x4km

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GPS Soundings for one week (Nov. 3-9, 2006)

The distribution of GPS RO soundings with the time in each 3h cycling assimilation window.

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Cycling: PWV at 0600 UTC 07 Nov. 2006

SSM/I observation Non-Local analysis Local minus Non-Local

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The 3-h WRF forecasts fit to GPS refractivity with time. The value is cost function for CTRL (blue), LOC (red) and NON-LOC (green) runs, respectively.

Cycling: 3h Forecast Verification

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The statistics of difference for the assimilation domain from 0000 UTC 03 to 1800 UTC 09 November 2006. Bias (left panel) and Standard Deviation (middle panel) errors of 3-h WRF forecasts verified against GPS RO refractivity for CTRL (dashed curve), LOC (thin curve) and NON-LOC (thick curve). The right panel shows the total number of verifying GPS soundings at each level during one-week cycling period.

Cycling: 3h Forecast Verification …

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GPS Impact on 24h WRF forecast

24h forecast starting from 1200 UTC 6,

3 domains nested. Assimilation on

domain D1.

D3 only covers Washington and Oregon

states.

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Bias and Standard Deviation of 24h forecast fit to GPS Refractivity on domain D1

Forecast: Verification with GPS Refractivity

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Forecast: Verification with SSM/I

Valid at 0200 UTC 7 November 2006 on domain D1

obs

nonlocallocal

No GPS

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6/15 6/16 6/17 6/18 7/02 7/03 7/04 7/05 AVG

FCST 3 h 4 h 5 h 6 h 14 h 15 h 16 h 17 h

CNTL -0.152 -0.231 -0.137 -0.283 -0.303 -0.237 -0.311 -0.179 -0.229

LOCAL -0.148 -0.243 -0.154 -0.297 -0.274 -0.211 -0.306 -0.176 -0.226

N-LOCAL -0.163 -0.228 -0.138 -0.276 -0.255 -0.192 -0.291 -0.171 -0.214

6/15 6/16 6/17 6/18 7/02 7/03 7/04 7/05 AVG

FCST 3 h 4 h 5 h 6 h 14 h 15 h 16 h 17 h

CNTL 0.39 0.339 0.331 0.349 0.456 0.443 0.405 0.334 0.381

LOCAL 0.41 0.338 0.339 0.347 0.454 0.432 0.401 0.355 0.385

N-LOCAL 0.40 0.330 0.327 0.332 0.432 0.421 0.378 0.341 0.371

Mean errors as a function of time

Standard deviations as a function of time

Forecast: Verification with SSM/I …

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QPF and evaluation data

SITES• 50 sites in WA, OR, & CA (117” precip.

total) •22 sites in “wet” region (107” precip.

total) •28 sites in “dry” region (10” precip.

total) WA

OR

CA

DATA• 1200 UTC 6 Nov. to 1200 UTC 7 Nov. 2006

• Model quantitative precipitation forecast (QPF) –Forecasts made from 12 Z to 12 Z–Resolution of 4 km

• Quantitative precipitation estimates (QPE)–From NWRFC –Gauge-based –12 Z to 12 Z–Resolution of 4 km

Verification Region

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All 50 sites (wet area and dry area)  24 h COSMIC QPF (in) NWRFC (in)  CTRL LOCAL NONLOCAL ObservedAvg Precipitation 1.72 1.72 1.86 2.33Avg Bias 0.74 0.74 0.80  

      24 h COSMIC QPF (in)  NWRFC (in)

  Site ID CTRL LOCAL NONLOCAL ObservedAstoria, OR AST 2.07 2.44 4.87 3.03Frances, WA FRAW1 4.40 4.60 2.69 3.00Cinebar, WA CINW1 3.69 4.20 4.84 4.80Cougar, WA CUGW1 5.42 6.59 8.52 6.97Packwood, WA OHAW1 4.52 4.88 6.02 5.70Aberdeen, WA ABEW1 4.31 4.17 3.77 5.34Enumclaw, WA ENUW1 3.18 2.90 3.16 7.16Glacier, WA GLAW1 3.42 3.78 3.36 4.60Leavenworth, WA LWNW1 3.23 3.03 3.16 4.30Marblemount, WA MARW1 5.97 6.26 5.40 3.90Seattle, WA SEA 1.74 1.40 1.70 3.06Skykomish, WA SKYW1 3.76 3.97 4.20 8.60Stampede Pass, WA SMP 2.85 3.05 3.78 7.47Quillayute, WA UIL 2.28 1.92 3.37 2.35Verlot, WA VERW1 7.54 7.61 8.51 3.40Bonneville Dam, OR BONO3 2.96 2.46 2.24 5.24Detroit Dam, OR DETO3 2.24 2.36 1.75 2.33Lees Camp, OR LEEO3 3.10 3.09 3.69 13.60Portland, OR PDX 1.07 0.79 0.94 2.57Three Lynx, OR TLYO3 1.84 1.86 1.26 3.70Salem, OR SLE 1.15 0.79 0.52 2.16Summit, OR SMIO3 2.03 1.34 1.15 3.50  Avg ppt 3.31 3.34 3.59 4.85

  Avg Bias 0.68 0.69 0.74  

      24 h COSMIC QPF (in)  NWRFC (in)

  Site ID CTRL LOCAL NONLOCAL ObservedBrookings, OR 4BK 0.33 0.33 1.08 0.48Burns Airport, OR BNO 0.43 0.35 0.22 0.00Cougar Dam, OR CGRO3 1.24 1.13 1.42 0.85Colville, WA CQV 0.17 0.12 0.26 0.44Crater Lake, OR CRLO3 1.58 1.54 1.82 0.20The Dalles, OR DLS 0.07 0.02 0.00 0.52Eugene, OR EUG 1.06 0.68 0.68 1.25Spokane, WA GEG 0.64 0.49 0.76 0.22Agness, OR ILHO3 0.96 0.60 0.78 0.10Klamath Falls, OR LMT 0.14 0.08 0.02 0.00Meacham, OR MEH 0.55 0.68 0.26 0.98Rogue Valley, OR MFR 0.09 0.15 0.30 0.00Mazama, WA MZAW1 1.44 1.99 1.16 1.55Enterprise, OR NTPO3 0.20 0.22 0.30 0.00Oak Knoll, CA OKNC1 0.02 0.13 0.24 0.01Omak Airport, WA OMK 0.49 0.31 0.50 0.19North Bend, OR OTH 1.09 0.97 0.83 0.30Owyhee, NV OWYN2 0.06 0.00 0.02 0.01Rome, OR P88 0.01 0.00 0.01 0.00Pendleton, OR PDT 0.06 0.06 0.01 0.03Prairie City, OR PRCO3 0.83 0.89 1.37 0.00Riddle, OR RDLO3 0.01 0.05 0.13 0.10Redmond Roberts, OR RDM 0.00 0.00 0.00 0.10Glide, OR SRSO3 0.29 0.33 0.49 0.10Goldendale, WA SSPW1 1.16 1.21 1.17 1.40Sexton Summit, OR SXT 0.05 0.11 0.03 0.00Williams, OR WLMO3 0.08 0.08 0.09 0.10Yakima, WA YKM 0.00 0.00 0.03 0.94

  Avg 0.47 0.45 0.50 0.35  Avg Bias 1.32 1.27 1.42  

Site Forecast and Observed Data

“Wet” region sites “Dry” region sites