SSI analysis system documentation

For recent changes please refer to NWS technical procedure bulletins

Jan 18, 2005 - Turn off NOAA-16 AMSU-A channels 10-13.

May 25, 2004 - Turn off NOAA-16 HIRS/3 observations.

Nov 20, 2003 - Package of minor analysis changes (see description)

Oct 28, 2003 - NOAA-17 AMSU-A radiances turned off.

Mar 11, 2003 - NOAA 17 1B radiances assimilated, NOAA-16 AMSU-A radiances restored, QuikSCAT winds superobbed at 0.5 degrees.

Oct 29, 2002 - Background error recomputed, AMSU-A channels 12 and 13 from NOAA-15 and NOAA-16 and HIRS from NOAA-16 used, METAR surface pressure observations used, divergence tendency constraint turned off, increase resolution to T254L64.

Apr 10, 2002 - 19Z AMSU-A channel 11 for NOAA-15 failed.

May 15, 2001 - 12Z Inclusion of cloud liquid water in forecast model. Tightening of quality control for Microwave satellite data. Add NOAA-16 SBUV

Mar 27, 2001 - 06Z Remove NOAA-14 SBUV (data bad)

Feb. 12, 2001 - 12Z NOAA-16 AMSU-A and AMSU-B included. NOAA-15 AMSU-B radiances and GOES-10 radiances included. Precip. Assimilation for SSM/I, update of bias correction scheme and the inclusion HIRS channel 12 over land

May 15, 2001 - 12Z Inclusion of cloud liquid water in forecast model. Tightening of quality control for Microwave satellite data.

June 11, 2000 - 00Z NOAA-15 HIRS is turned off due to continuing instability of instrument and observational biases.

Apr. 13, 2000 - Loss of NOAA-11 HIRS. Apparent instrument failure.

Mar. 29, 2000 - VAD winds reintroduced into analysis with improved quality control.

Jan. 24, 2000 - T 170L42 higher resolution version implemented.

Jan 17, 2000 - Officially operational on IBM-SP computer.

Mar. 16, 1999 - Mar. 23 GOES high density winds lost due to NESDIS Y2K conversion error.

Mar. 8, 1999 - Inclusion of NOAA-15 HIRS and AMSU-A data.

Mar. 1, 1999 - Mar.21 No NOAA-11 1b HIRS data. Script at NCEP unable to handle missing MSU from NOAA-11. Script modified.

Feb. 26, 1999 - No NOAA-11 1b microwave data. Apparent instrument failure.

Dec. 14, 1998 - No NOAA-12 1b microwave data. NESDIS stopped producing this data.

Documentation

The initial version of the SSI analysis system is presented in Parrish and Derber (1992) and Derber et al. (1991). The direct use of radiances are described in Derber and Wu(1998) and McNally et al. (1999). More up-to-date information can be found in recent technical procedures bulletins.

Numerical/Computational Properties

Horizontal Representation

The analysis variables are defined spectrally. For comparison to the observations, the variables are transformed to Gaussian grid and then linearly interpolated to observation locations.

Horizontal Resolution

Same as forecast model with a spectral triangular truncation of 254 (T254). The quadratic T254 Gaussian grid has 768 gridpoints in the zonal direction and 384 gridpoints in the meridional direction. Due to computation limitations the analysis uses a linear representation of the T254 Gaussian grid. This 512x256 grid contains two additional rows over that the true linear grid in order to describe the north and south pole points. This resolution is essentially equivalent to 0.7x0.7 degree latitude/longitude. The resolution of the quadratic T254 Gaussian grid is approximately 0.5x0.5 degree.

Vertical Representation and domain

The analysis is performed directly in the model's vertical coordinate system. This sigma (pressure over surface pressure) coordinate system extends over 64 levels from the surface to about 0.27hPa. The vertical sigma levels and the approximate pressures are listed below.

Level	sigma	approximate pressure (hPa)
64	0.00027	0.27
63	0.00099	0.99
62	0.00179	1.79
61	0.00269	2.69
60	0.00372	3.72
59	0.00490	4.90
58	0.00625	6.25
57	0.00780	7.80
56	0.00956	9.56
55	0.01157	11.57
54	0.01387	13.87
53	0.01649	16.49
52	0.01948	19.48
51	0.02288	22.88
50	0.02675	26.75
49	0.03115	31.15
48	0.03615	36.15
47	0.04182	41.82
46	0.04823	48.23
45	0.05549	55.49
44	0.06367	63.67
43	0.07289	72.89
42	0.08324	83.24
41	0.09483	94.83
40	0.10778	107.78
39	0.12218	122.18
38	0.13815	138.15
37	0.15579	155.79
36	0.17517	175.17
35	0.19635	196.35
34	0.21939	219.39
33	0.24429	244.29
32	0.27102	271.02
31	0.29953	299.53
30	0.32970	329.70
29	0.36138	361.38
28	0.39437	394.37
27	0.42843	428.43
26	0.46329	463.29
25	0.49863	498.63
24	0.53415	534.15
23	0.56950	569.50
22	0.60438	604.38
21	0.63846	638.46
20	0.67148	671.48
19	0.70319	703.19
18	0.73339	733.39
17	0.76194	761.94
16	0.78872	788.72
15	0.81366	813.66
14	0.83674	836.74
13	0.85797	857.97
12	0.87739	877.39
11	0.89506	895.06
10	0.91106	911.06
9	0.92552	925.52
8	0.93849	938.49
7	0.95012	950.12
6	0.96049	960.49
5	0.96973	969.73
4	0.97793	977.93
3	0.98522	985.22
2	0.99165	991.65
1	0.99734	997.34

Computational performance

The current version is a MPP version running on an IBM-SP. It has run on Cray - Y/MP, C90, and EL at various resolutions.

Analysis Components and basic properties

Basic Problem

The problem being solved is to minimize the equation:

J = J_b + J_o+ J_c

where J_b is the weighted fit of the analysis to the six hour forecast (background or first guess), J_o is the weighted fit of the analysis to the observations and J_c is the weighted fit of the divergence tendency to the guess divergence tendency. Also included in J_c is a constraint to limit the number of negative and supersaturated moisture points. The weights are given by the statistics described below.

Analysis variables

The analysis variables can be uniquely transformed into the model variables of vorticity, divergence, temperature, ln(surface pressure) and specific humidity. The analysis variables are normalized vorticity, unbalanced divergence, unbalanced temperature, ozone, surface skin temperature, specific humidity and coefficients for the bias correction of the satellite radiance data. Each of these variables are deviations from the background decomposed in the vertical based on the vertical error covariance and are normalized with the standard deviation of the error. The balanced part of the divergence and the temperature are implied using a linear balance equation from the vorticity.

Observation types

Currently, the regional and global analysis systems use the following data:

Observation type	Regional (NAM)	Global (GFS)	Comments
Radiosonde	u,v,T,q,Ps	u,v,T,q,Ps
Pibal winds	u,v	u,v
Synthetic tropical cyclone winds	used	not used*	*used when storm not in background
wind profilers	u,v	u,v
conventional aircraft reports	u,v,T	u,v,T
ASDAR aircraft reports	u,v,T	u,v,T
MDCARS aircraft reports	u,v,T	u,v,T
Dropsondes	u,v,T,Ps	u,v,T,Ps
MODIS IR and water vapor winds	not used	u,v
GMS, METEOSAT, GOES cloud drift IR and visible winds	u,v	u,v	Hi density GOES cloud drift winds used. GOES hi density visible winds are not yet operational.
GOES water vapor cloud top winds	u,v	u,v	high density winds used
GOES cloud top data	p,T	not used
Surface land observations	u,v,T,Ps,q	Ps
Surface ship and buoy observations	u,v,T,Ps,q	u,v,T,Ps,q
SSM/I wind speeds	u,v	Speed	Regional system assigns direction from guess. Global uses speed directly.
QuikScat wind speed and direction	not used	used
SSM/I precipitable water	used	not used	Undesirable tropical results when used in global system.
SSM/I precipitation estimates	not used	used	Precipitation included through variational scheme and model physics.
TRMM TMI precipitation estimates	not used	used	Precipitation included through variational scheme and model physics.
GOES precipitable water	not used	not used	Same information contained in radiances
NOAA-17 HIRS 1b radiances	used	used	Data thinned to reduce density.
AQUA AIRS 1b radiances	used	used	Data thinned to reduce density.
NOAA-15, NOAA-16, NOAA-18 and AQUA AMSU-A 1b radiances	used	used	Radiances thinned to reduce density
NOAA-15, -16, and -17 AMSU-B 1b radiances	used	used	Radiances thinned to reduce density.
GOES-12 5x5 cloud cleared radiances	used	used	Most channels not used over land because of quality control and surface emissivity problems.
NOAA-16 and -17 SBUV ozone profiles	not used	used
Doppler radial velocities	used	not used	Level 2.5 product used in regional
VAD (NEXRAD) winds	used	used	Reintroduced with improved quality control Mar. 29, 2000

In addition, the analysis systems process line-of-sight winds directly, as provided by Doppler radar or wind lidar, without the requirement to first retrieve the full wind from the measurements. However, these winds are not available operationally. The data from NWS 88-D network should be operationally available in the future. Degraded resolution and accuracy Doppler radar observations are available, but are not being used operationally.

Observational error statistics

The observational error statistics vary with each observation type and can vary with each observation location. The specified observational error statistics contain both instrument error and representativeness error.

Background error statistics

The background error statistics are used to weight the background (first guess) field. They are defined spectrally and are currently nearly homogeneous around a latitude band. The structure of these fields is very similar to that used at the ECMWF (Derber and Bouttier, 1999). The statistics are calculated by scaling the statistics from a sequence of differences between 24 and 48 hour forecasts valid at the same time.

Balance constraint

A nonlinear balance constraint is currently being used in the analysis system. The nonlinear balance constraint is a divergence tendency equation linearized around the guess in the analysis system. Vertical advection, surface friction and diabatic heating are not yet incorporated. The analysis system penalizes for differences from the guess divergence tendency. The penalty is defined in spectral space and the weights are defined as for the background error statistics.

Analysis Procedure

The analysis procedure is performed as series of iterative problems. There is an external iteration which partially accounts for nonlinearities in the objective function. In this external iteration, some parts of the transformation of the analysis variables into the pseudo-observations (see below) are linearized around the current solution. In the first external iteration, the current solution is the 6 hour forecast. In later iterations, the current solution is the result from the previous external iteration. Currently, the number of external iterations is limited to 2 by computation considerations.

Inside each external iteration, a series of operations are performed to create the analysis. First, The difference between the current solution and the observations is found by interpolating the 3, 6 (or the current solution after the first external iteration) and 9 hour forecasts of the model variables to the observation time. The model variables are then transformed to the pseudo-observation variables. For example, for a temperature observation no transformation is necessary. For a satellite measured radiances the profile of temperature, moisture and ozone along with various surface quantities are transformed into pseudo-radiances. The pseudo-observations are then compared to the observations and an observational increment is created.

The current solution is then iteratively updated by use of a nonlinear conjugate gradient algorithm which attempts to find the solution which minimizes J. To perform the conjugate gradient algorithm, it is necessary to have the gradient of J with respect to the analysis variables. The gradient is evaluated using the adjoint of the transformation of the analysis variables into the observation variables and the adjoint of the divergence tendency constraint.

Current results

Current results and further information can be found at global data assimilation group notes, manuscripts, and presentations.

Ongoing development

The analysis system is undergoing many enhancements as new data systems are included or new techniques developed. Many changes to the analysis system are currently under development. A few of the major development projects are listed below.

Grid point version - The background error covariance is currently defined in spectral coefficients. A version of the analysis which defines the background error covariance in grid space using recursive filters is being developed. The major advantage of defining the covariance is that it will be much easier to define spatially varying covariance structures.

Inclusion of GOES imager data - The GOES imager produces hemispheric data which can be used as if it were sounder data. Perhaps most useful is channel 3 which measures upper level moisture.

Improved radiative transfer - Geostationary and Polar orbiting sounders and imagers measure the outgoing radiation in certain frequency bands. The simulation of these measurements in an accurate and computationally efficient manner is an area of intense ongoing research.

Inclusion of GPS occultation measurements - The delay time between a low earth orbiting satellite as it sets over the horizon and a GPS satellite provides information on the density of the atmosphere between the satellites. The data has the potential to provide high vertical resolution, low horizontal resolution information. The complete use of this data may require the use of a ray tracing algorithm between the satellites. Development work is underway for incorporating this type of data in the analysis. For this type of data, the computational expense of the algorithm plays an important role. A draft office note on this subject is now available (Matsumura, 1999)

References

Derber, J. C., D.F. Parrish and S. J. Lord, 1991: The new global operational analysis system at the National Meteorological Center. Wea. and Forecasting, 6, 538-547.

Derber, J. C. and W.-S. Wu, 1998: The use of TOVS cloud-cleared radiances in the NCEP SSI analysis system. Mon. Wea. Rev., 126, 2287 - 2299.

Derber, J. C. and F. Bouttier, 1999: A reformulation of the background error covariance in the ECMWF global data assimilation system. Tellus, 51A, 195-221.

Matsumura, T.,J.C. Derber, J.G. Yoe, F. Vandenberghe, X. Zou 1999: The inclusion of GPS limb sounding data into NCEP's global data assimilation system. NOAA/NWS/NCEP Office Note 426, Available from Environmental Modeling Center, W/NP2, Rm 207, WWBG, NOAA, 5200 Auth Rd, Camp Springs MD 20746-4304.

McNally, A.P., J.C. Derber, W.-S. Wu and B.B. Katz, 2000: The use of TOVS level-1B radiances in the NCEP SSI analysis system. Q.J.R.M.S., 126, 689-724.

Parrish, D. F. and J. C. Derber, 1992: The National Meteorological Center's spectral statistical interpolation analysis system. Mon. Wea. Rev., 120, 1747 - 1763.