ADAS
Keith Brewster
Center for Analysis and Prediction of Storms
University of Oklahoma
Norman, OK
1. ANALYSIS GOALS
As part of the efforts of the Center for Analysis and Prediction of Storms (CAPS) to incorporate all available mesoscale data in a program that would be modular with the forecast model and allow for static analyses as well as assimilation, a program known as the ARPS Data Assimilation System (ADAS) has been developed. In developing ADAS the following goals were used:
1) Complete flexibility in specifying vertical coordinate heights.
2) Ability to use all forms of ARPS initial condition specifications as a background field.
3) Ability to handle single and multiple-level data.
4) Flexible, automated quality control
5) Fit data closely, without regard to geostrophic balance, yet be in proper balance to initialize the ARPS model.
6) Ability to handle gradients in data density without producing spurious gradients in the analysis fields.
2. TARGET DATA SETS
Single level
1) Surface observations (including Oklahoma mesonet)
2) ACARS
Multiple-level
1) NWS Rawinsonde data
2) Field experiment FCLASS and MCLASS rawinsonde data
3) Wind profiler data
4) WSR-88D VAD wind profiles
5) Satellite soundings
Special
1) Doppler radial winds
2) winds produced by single-Doppler retrieval techniques
3) Radar reflectivity
4) Dual-polarization radar parameters
5) Satellite radiances
3. ANALYSIS SPECIFICATIONS
While many operational centers employ a Statistical (or Optimal) Interpolation scheme (OI), Bratseth (1986) has shown that an iterative scheme will converge to OI. An iterative scheme offers computational savings in that large matrix solutions need not be found. Balancing and other adjustments can be made at the end of each iteration to control stability and other aspects of the evolving analysis. Iterations can be interspersed with model time-steps to form a dynamic initialization (nudging) process, or more detailed data can be introduced after a few iterations using broad-scale data. Like the OI scheme, the Bratseth interpolation methods allow accounting for the relative error between the background and the error in each observation source, and is relatively insensitive to large variations in data density. This type of scheme has been used successfully in research (e.g., Sashegyi et al., 1993) and operational (e.g., Lorenc', 1991) mesoscale modeling.
Five variables are analyzed on the ARPS sigma-z coordinate: u and v grid-relative wind components, pressure, potential temperature and RH*. RH* is a moisture variable analogous to dew-point depression:
where RH is the relative humidity and RHmax is the maximum relative humidity allowed (here set to 1.0, some might want to allow a greater value, for supersaturation). RH* is selected over specific humidity due to the non-linear change in saturation specific humidity with height -- small absolute changes in surface specific humidity can cause unrealistic relative changes aloft in the 3-D observation weighting. Other variables could be added with straight-forward modification to the code.
At this time the vertical velocity, w, is diagnosed from the horizontal winds and a constraint that the wind velocity normal to the bottom (terrain) and top boundaries be zero. Any inconsistency between these constraints and the analyzed velocity field is resolved by assuming error in the horizontal divergence is linear with height, and the w field is adjusted after that error is removed. After w has been found for each column, the horizontal wind fields are relaxed with the condition that the total mass divergence is zero everywhere. This is to help ensure a smooth start for the ARPS model.
Single and multiple-level data sources are supported and are carried in the code in separate arrays. Doppler radial winds are used in the wind analysis and radar reflectivities are used to establish minimum levels of relative humidity and cloud water. Routines for reading sounding, wind profiler and surface observations in LAPS format (as are archived for the 1994 and 1995 VORTEX field project) have been implemented. Other sounding and surface data sources can be added easily.
Nearly all analysis control parameters are specified through namelist input, in special namelists following the mandatory ARPS input namelists in the ARPS input file. Default
values are provided in the code and sample ARPS input file. A brief justification of the default values is provided below. Upper-air observation error is specified as a function of height, and is read-in from tables, one per input data source.
John Krause and Fred Carr have preliminarily concluded (Krause, 1996) that the best successive-corrections analysis is produced when the background field is first corrected for errors in the broad-scale features through the use of a long spatial correlation function (large scaling distance in the correlation model), then several passes are done using the target spatial correlation function. For this reason, a large-scale analysis is done first, followed by analysis iterations at the desired grid-scale resolution.
Through the namelist input, the scaling distance for the correlation function is set as a function of the iteration index. Furthermore, the scaling distance may be set to be different for each analysis variable, as one may wish to analyze humidity at a smaller scale than pressure, for example. A target scaling distance (variable named range, given in meters) is specified, and all other distances are specified as a fraction of that distance. For example, the first pass default is 3.0 times range, and the correlation distance for humidity is 0.9 of that. See the documentation in the default ARPS input file for further details on the mechanics of parameter specification.
4. BRATSETH SCHEME
The ADAS uses a successive correction scheme, known as the Bratseth method, which is described in this section. At grid points x and observation locations, j, the variable, s, is analyzed:
where
Correlations, r, are modeled as Gaussian in space:
In order to speed convergence the correlation distance factor, R, is
reduced from pass 1 to 4.
Here
and the primary radius is different for each variable, allowing for the
shorter correlation distance in moisture, for example.
The ratio of observation error variance to background error variance is given by s2.
5. TREATMENT OF DOPPLER RADIAL WINDS
The radial velocities are converted to increments to the u and v wind components by subtracting the observed radial wind, vr, from the dot product of the analysis wind and the observing angle (radar azimuth). The imputed correction is assigned a direction parallel to the azimuth, i.e.
The covariance between two Doppler radial winds requires special treatment in that the
correlation between two radial wind observations is affected by the azimuth angle separation between the data. As described by Cole (1994),
So, for example, if radial velocities at a given point are available from two radars observing perpendicular to each other, the covariance model correctly indicates the observations are not correlated.
Similarly for mixed data types, the covariance is reduced from that of two complete wind observations:
and
Where ui' and vi' are increments from a radial wind observation and uj' and vj' are from a complete wind observation (e.g., an anemometer or a rawinsonde).
6. RADAR PREPROCESSING
The radar data are read from tape or a live data stream in radar coordinates (azimuth, range, elevation angle). The data are converted to Cartesian coordinates by averaging all data that fall in each grid volume. The averaged variables are reflectivity factor, radial velocity, Nyquist velocity and observation time. The grid volumes are specified using the same parameters and routines as the grid volumes in the ARPS model. A minimum percentage data coverage of each grid box is required to create a valid average for that volume, and grid volumes which contain a high variance among the data are rejected. The remapped radar data are then written to file, organized as columns of data; only those columns that contain volumes with valid averages are written. Each column is identified by its latitude, longitude and originating radar, so that the data may be used on a different grid than the grid on which they were originally collected.
In the ADAS, the radar data are compared to the background field and tested for folding. Since the Nyquist velocity can change during a volume scan, care is taken during the averaging process to insure that all data contributing to the average lie within the same Nyquist interval. That way the average Nyquist value can be used to do the unfolding in the analysis quality control procedure. Data are rejected if, after unfolding, they differ from the background data by a user-specified threshold.
7. CONVERSION OF RADAR REFLECTIVITY TO MOISTURE VARIABLES
If one assumes there exists a threshold of radar reflectivity factor above which hydrometeors are present, one can then assume that, at a minimum the relative humidity is high in the vicinity. In the ADAS, RH* increments are created where the remapped reflectivity factor is above a user-specified threshold (15 dBZ is used) and the background relative humidity is less that 95%. The increment is set so that the analysis will be driven toward a relative humidity of 95%. In other words, the observations will not create saturation, but they won't ever decrease the humidity.
For higher values of reflectivity, one can assume that a minimum level of cloud water is present. Since cloud water is distributed in the atmosphere with very small scales, the cloud water derived from the reflectivity is not analyzed in the same manner as other scalars. Instead a separate procedure is used. For each column in the analysis grid, the nearest remapped radar observation is located. Where a high reflectivity is observed the cloud water is specified by:
where qca is the analyzed cloud water, qcb is the background cloud water and qcmin is the minimum cloud water assumed where the reflectivity is higher than a threshold. Currently a value of 15 dBZ is used as the threshold (threshold under investigation), and the minimum cloud water is specified as 10-3 kg/kg.
It is worth noting that the rainwater is not specified where reflectivity is observed due to the the fact that the model's initial reaction to the introduction of hydrometeors would be to increase downdrafts, while in many cases the desired increment to the vertical velocity field is positive.
8. REFERENCES
Bratseth, A.M., 1986: Statistical interpolation by means of successive corrections. Tellus, 38A, 439-447.
Brewster, K., F. Carr, N. Lin, J. Straka, and J. Krause, 1994: A local analysis system for initializing real-time convective-scale models. Preprints, Tenth Conf. on Num. Wea. Prediction, Portland, OR, Amer. Meteor. Soc., 596-598.
Krause, J.M., 1996: Application of the Bratseth technique to mesoscale analysis. Master's Thesis, Univ. of Oklahoma. In preparation.
Lorenc, A.C., R.S. Bell and B. MacPherson, 1991: The Meteorological Office nalysis correction data assimilation scheme. Quart. J. Roy. Meteor. Soc., 117, 59-89.
Sashegyi, K.D., D.E. Harms, R.V. Madala, S. Raman, 1993: Application of the Bratseth scheme for the analysis of GALE data using a mesoscale model. Mon. Wea. Rev., 121, 2331-2350.
Xue, M., K. Droegemeier, V. Wong, A. Shapiro and K. Brewster, 1995: ARPS Version 4.0 User's Guide. Center for Analysis and Prediction of Storms, University of Oklahoma, 100 E. Boyd, Suite 1110, Norman, OK 73019.