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Tsann-wang Yu Environmental Modeling Center National Centers for Environmental Prediction

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### Variational data assimilation experiments at NCEP using ocean surface winds and sea surface temperatures data

### Ocean Forecasting – Present (1-2 days)

Tsann-wang Yu

Environmental Modeling Center

National Centers for Environmental Prediction

National Weather Service, NOAA

Washington, D. C., 20233

Outline

- Current status of NWP operations at NCEP
- Data assimilation and development strategies for ocean and atmospheric
- Use of QuikSCat winds and GOES and AVHRR data assimilation experiments
- Current developments in data assimilation at NCEP / JCSDA

Satellite data currently used in NCEP’s operational global and regional model data assimilation

- NOAA –14 TOVS radiance data (HIRS-2, MSU)
- NOAA-15, NOAA-16, NOAA-17 ATOVS radiance data (HIRS-3, AMSU-A, AMSU-B, SBUV etc. )
- SSMI ocean surface wind speed, QuikSCAT /SeaWind ocean surface wind vectors in GDAS
- SSMI / TRIM total precipitable water, and rain rate
- NEXRAD radar radial velocity in ETA model
- GOES radiance data in GDAS and EDAS

Data Assimilation

Observation pdf

Initial Condition:

Analysis Mean

Analysis pdf

For the Grid

t3

Forecast pdf

For the Grid

t1

t2

3D-Variational data assimilation at NCEP

Distance to forecast

Distance to observations

- x is a model state vector, with 106-8d.o.f. xaminimizes J
- yo is the set of observations, with 105-9 d.o.f.
- In 3D-Var B is assumed to be constant: it does not include “errors of the day”
- The methods that allow B to evolve are veryexpensive: 4D-Var and Kalman Filtering, and require the linear tangent and adjoint models.

Specifying background error covariances: general remarks

- There is not enough information (and never will be) to determine all the elements of (typically > O(1010)).
- must be approximated by a statistical model (e.g., prescribed covariance functions) with a limited number of tunable parameters.
- In 3D-Var/4D-Var, is implemented as an operator (a matrix-vector product).
- For the preconditioning transformation we require access to a square-root operator (and its adjoint ).
- Constructing an effective operator requires substantial development and tuning.
- It is preferable to have a flexible covariance model first before spending considerable effort tuning statistical parameters.

Specifying background error covariances: specific remarks for the ocean

- Ocean observations are relatively sparse so it is difficult to estimate background error statistics from innovations. Considerable spatial and temporal averaging is required (e.g., Martin et al. 2002).
- With few observations the role of is critical for exploiting available data-sets effectively (e.g., surface altimeter data).
- Added complexity due to the presence of continental boundaries (boundary conditions, scales, spectra, balance).
- Rich variety of scales: mesoscale (Gulf Stream, Kuroshio regions) ~O(10km) and synoptic scale (tropics) ~ O(100km).

Ocean surface winds and sea surface temperatures are two of the most important fields responsible for

- Physical coupling of ocean and atmosphere - air sea interaction.
- Directly driving ocean waves and current circulations – ocean general circulations.
- Affecting accuracy of numerical weather and climate forecasts.

Observing System Experiments (OSE) to test Quikscat winds

and infra-red sea surface temperatures data from

AVHRR and GOES

Data assimilation experiments to test QuikSCAT winds

and AVHRR and GOES infra-red radiance SST data

SCAT Winds, or SST＋ Conventional data Assimilation

Conventional data Assimilation

CNTL

TEST

Impact of SCAT winds or SST = (TEST –CNTL)

Effect of SCAT Winds（TEST – CNTL)

Radar backscattering

Specular scattering from a smooth surface - most energy is reflected away.

Defuse Scattering from a rough surface - energy is reflected in all directions.

Bragg Scattering and scatterometer wind retrieval geophysical model function

- Ocean surface waves with a wavelength that satisfies the Bragg resonance condition will contribute the most to radar cross section, 0
- 0 = function (S, , , P), where S is wind speed, , the incidence angle of radar beam to the ocean surface, is the relative angle of surface wind direction with respect to the radar beam, and P is polarization of radar beam.

Surface Analysis

integrating

ship & buoy observations

with

QuikSCAT winds

Wind speed (Knots)

6550 35302520

QuikSCAT winds – introduced into Ocean Prediction Center

operational workstations in the fall of 2001 – are now fully integrated into the warning & forecast decision process

QuikSCAT winds – a numerical model diagnostic

NCEP GFS 40m Winds - 6 hr FCST

1800 UTC 17 Feb 03

QuikSCAT Winds

1800 UTC 17 Feb 03

Wind Speed (Knots): 6550 35302520

Potential Rain

Contamination

- Subtropical System are most affected
- What is the warning category?
- Is it an open wave or is it closed?
- If closed, where is the center?

Wind speed (Knots)

6550 35302520

wind radii

Isabel (Cat 5) – In mature tropical cyclones,

strong convection and rain in inner core prevents

accurate wind speed retrievals. Even so, QuikSCAT

is used to help determine the radial extent of

tropical storm force winds

MSW = 140 kt. MSLP = 932 mb

Hurricane Force Extratropical Cyclone

48.5N 26.89W

Hurricane Force Winds

QuikSCAT pass from 06NOV 0630UTC

Summary of Results of GDAS experiment Using 100 km resolution QuikSCAT winds at NCEP

- NCEP Operational GDAS – T170, L42
- Assimilation Exp.- Oct. 2, 2001 to Nov. 10, 2001 (43 days)
- Found positive impact on heights and winds at all levels for both N.H. and S.H., especially over the ocean surface
- QuikSCAT winds became operational onJanuary 15, 2002

25

Fig.1 Five Regions of Deep Ocean Buoys used in the evaluation

North Sea

WestCoast

East Coast

Gulf of Mexico

TOGA

10-meter wind forecast errors (m/sec)

with respect to mid-latitude deep-ocean buoys

Courtesy of NCEP Environmental Modeling Center

Mean sea level pressure forecast errors (mb)

with respect to mid-latitude deep-ocean buoys

Courtesy of NCEP Environmental Modeling Center

Golbal data assimilation experiments at NCEP using high resolution QuikSCAT winds data ( Yu, 2003)

- Scientific objective: High resolution (50 km) QuikSCAT winds should improve mesoscale features of analyses
- Major findings: Most improvements are found in mesoscale winds forecasts over the tropics

Pre-implementation QuikSCAT winds (~50km) GDAS Run

---- OPNL Run (~100 km)

---- Pre-implementation Run (~50km)

Pre-implementation QuikSCAT winds (~50km) GDAS Run

---- OPNL (~100 km)

---- Pre-implementation Run (~50km)

Mean anomaly correlations at 850 mb for tropical winds

( ---o--- Opnl Run; ---+---- Pre-implementation Run)

U (waves 1-20)

U (waves 10-20)

V (waves 1-20)

V (waves 10-20)

Summary of GDAS experiment Using 50 km resolution QuikSCAT winds at NCEP

- NCEP Operational GDAS – T254, L64
- Assimilation Exp. – January 8, 2003 to March 8, 2003 (60 days)
- Found positive impact on heights and winds at all levels for both N.H. and S.H., especially for winds over the tropical oceans
- QuikSCAT winds (50 km) – were implemented at NCEP GDAS on March 11, 2003

35

Global data assimilation experiments using high resolution SST analyses at NCEP (Yu, 2004)

- Motivation: ECMWF has already used NCEP high resolution SST analysis in NWP operation; high resolution SST are already used in NCEP EDAS operation
- Purpose: To investigate the impact of high resolution SST on NCEP GDAS and NWP forecasts for possible implementation

Use of AVHRR and GOES satellite infra-red temperature data at NOAA Coastal Ocean Forecast System (O’Connor, Lozano, andYu, 2004)

- Scientific objective: High resolution (about 8km) infra-red sea surface temperatures data from AVHRR and GOES should improve mesoscale features of ocean analyses
- Major findings: use of GOES’ SST in ocean data assimilation is found to lead to large improvements for depicting Gulf Stream feature

Coastal Ocean Forecast System (COFS)

Princeton Ocean Model

Domain: East Coast

Vertical Coordinate: Sigma (19 levels)

Horizontal Resolution: 10 km near coast to 20 km in deep ocean

Lateral Boundary Condition: Monthly mean values for temperatures, salinity, and transport at the open ocean boundaries and monthly mean values for river run-off at the coastal boundaries

Predictionof SST, Gulfstream, Hurricane-Ocean Coupling, Tides and Water Levels, Boundary Conditions for Bays and Estuaries, Search & Rescue Operations, Toxic Spill Containment, Ecosystem Management,..

Features:Primitive Equations, Forced by ETA Model Fluxes; Assimilation of SST, XBT, altimetry.

SST

Surface Currents

Recent developments of the satellite assimilation at NCEP /JCSDA

- AQUA / AIRS (Advanced Infra-red Sounder) radiance assimilation –2378 channels
- AQUA / AMSUR–E wind speed data and NRL’s Windsat polar-metric radiometer derived ocean surface vector winds
- GPS occultation data for global 3DVar
- NOAA –15, NOAA –16, NOAA-17, AMSU radiance, GOES, AVHRR infra-red SST and altimeter data are being tested in ocean data assimilation

- SWindSat was successfully launched on January 6th 2003 with the objectives to:
- Ddemonstrate the capability of Polarimetric Microwave Radiometry to measure the Ocean Surface Wind Vector from Space, and show the potential to measure other EDR’s: SST, Water Vapor, Cloud liquid water, rain rate, sea ice and snow cover.

Concluding Remarks

- Remote sensing data are important for oceanic atmospheric research and applications, and numbers of observations will continue to increase in the future.
- Data assimilation is the most scientifc approach to effectively use the remote sensing data.
- Current and near future research efforts are centered on the specification of background error covariances in the 3D-VAR and 4D-VAR variational analysis for NWP operations.
- Ensemble forecast and Kalman Filter approaches are the most active areas of research and development in the data assimilation.

Modelling background error covariances

- We write the matrix-vector product as
- We solve a generalized diffusion equation (GDE) to perform the smoothing action of the square-root of the correlation operator ( ).
- We multiply by the standard deviations of background ( ) error ( ).

Univariate correlation modelling using a diffusion equation

(Derber & Rosati 1989 - JPO; Egbert et al. 1994 - JGR; Weaver & Courtier 2001 - QJRMS)

- A simple 1D example:
- Consider with constant .

on with as

- Integrate from and with as IC:

- This integral solution defines, after normalization, a correlation operator :
- The kernel of is a Gaussian correlation function

where is the length scale.

- Basic idea : To compute the action of on a discrete grid we can iterate a diffusion operator.

This is much cheaper than solving an integral equation directly.

Constructing a family of correlation functions on the sphere using a GDE

- (Weaver & Courtier 2001, QJRMS; Weaver & Ricci 2004 – ECMWF Sem. Procs.)

shapespectrum

L = 500 km

Gaussian

Gaussian

GDE-generated correlation functions

Example: T-T correlations at the equator

Multivariate covariance structures

Example: covariance relative to a T point at (0o,156oW,168m)

General formulation of the assimilation problem

- Let denote the vector of model state variables.
- Let denote the vector of analysis control variables where
- Find that minimizes where

background term

observation term

Choice of analysis control variables

- We try to choose so that has a simplified structure.
- If is linear(ized) then we can interpret it as a constraint on the error covariances for

(Derber and Bouttier 1999, Tellus):

- dim( ) can be less than dim( ) so that may have a nullspace.

Incremental formulation

- Let be an increment to the state
- Let be an increment to the control where
- Find that minimizes where

background term

quadratic obs. term

where

Choice of linear propagator

- involves integrating the nonlinear forward model from initial time to the observation times.
- involves integrating a linear forward model:

In 3D-Var (FGAT)persistence

In 4D-Varapprox. TL model

where

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