Expanded Rationale for the IPO/NOAA Bracketing OSSEs

G. D. Emmitt

10/20/99

The bracketing OSSEs are meant to explore the bounds of the potential impacts of a space-based wind sounder on today's operational forecast models for several "technology neutral" observation coverage and measurement error characterizations. By "technology neutral" we mean that the instrument details are ignored but the general sense of how a lidar measurement is made is retained. Thus, the following aspects of making wind measurements with space-based Doppler wind lidars are captured:

• Observations from a sun synchronous polar orbit
• Cloud obscuration and fractional coverage
• Variance of the wind on scales ranging from the illuminated cylindrical volume
• (~ 1km x 10 km) to the targeted resolution volume (TRV) of 200 km x 200 km x 1 km.
• Winds derived from sensing the molecular returns from the cloud free atmosphere
• Winds derived from aerosols of any concentration
• Winds derived from aerosols of high backscatter returns such as those from the PBL and clouds

Distributed vs. cluster sampling of the wind field within the TRV.

There are several reasons for conducting a series of bracketing OSSEs prior to performing future OSSEs for very specific instrument concepts. First, we want to know the "ultimate" sensitivity of our OSSE to the atmospheric parameter in questionin this case, winds. In other words, the question is how much of an impact would be reported if perfect wind observations from the Nature Run were available to the operational model. If the answer were "hardly detectable" then there would be no reason to continue with the rest of the planned OSSEs. The second reason for the bracketing OSSEs is to provide some measure of the relative return on investment for several general DWL data products. In this case, some general form of "cost/benefit" analyses can be achieved. A third reason is to develop the tools to evaluate the more specific concepts that will be proposed to meet some stated requirements. A fourth reason is to develop the understanding and experience of assimilating DWL data products long before the instrument is launched. In this case, such a long lead-time increases the likelihood that the instrument design may also benefit from the OSSE results.

The bracketing OSSEs listed in TABLE 1 are designed to establish the range of impacts that could be expected from a range of DWL data product coverages and accuracies as they compare with a "reference impact". The "reference impact" is that associated with the use of perfect wind observations from the Nature Run. The perfect observations are constrained to the temporal and spatial coverage of a space-based observing system. Otherwise, no cloud or subgrid scale wind variance effects are simulated. The data product simulated for the "reference" OSSE (R) is a wind profile from a Nature Run grid point closest to the center of a 200 km x 200 km data grid. This "reference" OSSE does not map to any real DWL. This data set can be used with several assigned RMSEs to test for basic accuracy sensitivities of the OSSE system.

The next four OSSEs in Table 1 have been defined to explore selected or limited data product coverages that may, in a very general sense, be mapped to DWLs of differing coverage potentials (referred to as the Coverage Series). The "Accuracy Series" of experiments uses the same coverage scenarios as the Coverage Series but varies the instrument measurement accuracy (e.g. _m = 2 m/s or 7 m/s). Cloud and wind variance effects are invoked in all of the OSSEs except for the "reference" OSSE (R).

The Experiment 1 data product is meant to represent that achieved with a very sensitive DWL that is only prevented from making an observation by optically thick clouds. In some parlance this data product would be referred to as the Holy Grail (200 km x 200 km version). The coverage and accuracy (_o << 1.0 mps) imply DWL systems which are well beyond the current state of the art. In the "Accuracy Series" of OSSEs, the cases where _m 1.0 mps would map to all coherent systems and the increasing values of the measurement error would map to less and less capable direct detection systems. (See discussion below regarding the accuracy experiments.) Note that the coverage series data assumes perfect pointing knowledge while the RMSE added for the accuracy series should account for all random measurement errors.

Experiment 2 is designed to evaluate the relative impact of wind data that is obtained only from clouds or the planetary boundary layer. The resulting data product might be similar to that from a very modest sized coherent lidar. i.e. very accurate measurements from single shots. As various amounts of measurement error are added to the base data product, the data product begins to map to a direct detection aerosol lidar.

Experiment 3 represents a data product that would be obtained with an instrument that would provide useful data only when there was a cloud free scene. Since a totally cloud free scene is a very rare event for a 200km x 200km target area, we have used 50% cloud cover as the cutoff for useful data. This product may map to the data product of a system that relies solely on molecular returns.

Experiment 4 represents a bounding extreme in horizontal coverage. Whereas the swaths of data in OSSE Experiments R,1,2 and 3 were all ~ 2000 km wide, the data in this case is obtained from a non-scanning instrument. The resulting data pattern is a single LOS profile provided every 200 km along the satellite ground track. The data product coverage in the vertical is consistent with the same rules for Experiment 1, except that the shots within a 200 km x 200 km area are assumed to be clustered within a very small area of a few tens km dimension.

(Note that an Experiment 5 OSSE has been added which represents a distinctly unique combination of Experiments 2 and 3. While not considered a "bracketing OSSE" this experiment should give some insight relative to the impact of data from high accuracy and resolution in the PBL combined with lower accuracy and resolution in the mid- and upper-troposphere.)

There is an issue of how individual lidar shots are combined to yield a single wind observation that will be assimilated into NWS models. Those DWL concepts that provide cross-track coverage by scanning the lidar beam usually employ either a constant rate conical scan at a fixed nadir angle (~30 45 degrees) or a step-stare conical scan, dwelling at prescribed azimuth angles long enough to get sufficient signal to make a useful wind measurement. The following can be taken as generally true for envisioned DWLs: Direct detection systems require averaging multiple shots to obtain measurements with useful accuracy the more photons collected, the lower the RMSE. Coherent detection systems have a basic accuracy of ~1.0 m/s but may use shot accumulation to improve sensitivity in regions of lowest backscatter. Thus, scanning and averaging imply including data taken over some extended areas to obtain a single wind estimate for the models to use. The simulated data is used as if it pertained only to the lat/long/height accompanying the wind speed. A data product based upon areal averaging is treated with caution by the assimilation routines. Therefore, we have generated simulated DWL data sets that include both the products resulting from large spatial averaging and an observation that would result from a system that could concentrate all of its shots (that would have been into the 200 km x 200 km column) into a very small area (~ 10 km x 10 km). The OSSEs can then be run that should reveal the merits of the two extreme sampling strategies.

The following discussion addresses how various levels of RMSE can be added to the base simulated data products provided for "Coverage Series" OSSEs.

The simulated DWL data sets are based upon a continuous conical scan and a prf of which produces ~ 30 shots (15 forward and 15 aft) into a 200km x 200km area at the top of the atmosphere. As the shots are propagated down through the Nature Run atmosphere, the number of shots reaching a given level can be reduced by clouds in levels above. Thus N (number of LOS samples) is not constant throughout a column.

In order to bracket the impacts due to instrument accuracy, errors of measurement and representativeness need to be added to the simulated data used in the coverage OSSEs. That additional error needs to be added in a RMSS manner and be a function of the number of samples taken. There are two basic forms of the observation error (or weighting function used in the assimilation cost function) that apply. Both forms derive from the following general expression for _o (observation error):

_m = single shot measurement RMSE (illumination volume is ~ 100-1000 meters long and 10 meters diameter)

_s = standard deviation of the wind field variability over the TRV

N_m = number of shots used to produce a single LOS wind observation where each shot has a RMSE of _m .

N_s = "effective" number of shots that reduce the potential sampling RMSE of _s .

(Note: N_m and N_s are obtained by dividing the N in the simulated data records by the numbers provided in Table 2.

In the Coverage Series of OSSEs the first term in this expression is assumed to be very close to zero. Since we don't know _s a priori, we might use the assigned _o values for rawinsondes (_r) as substitutes for _s (see Table 2).

Thus the weighting function that should be applied is

N_s = N/X for distributed shot case where X is found in Table 2; N_s = 1 for clusters

In the Accuracy Series of OSSEs, a Gaussian random error is added to represent various instrument accuracies. It is taken that the accuracy applied is that which the instrument would claim at the top of the atmosphere after accumulating or averaging all the returns from a homogeneous, non-turbulent flow in a 200 km x 200 km x 1 km volume. As an example, for a direct detection DWL system that is designed for a 3 m/s RMSE for a cloud free LOS measurement using 25 shots, this would be interpreted to mean that

For the Accuracy Series of OSSEs the assimilation weighting function should be:

N_s = N/X for distributed shot case where X is found in Table 2; N_s = 1 for clusters

Table 1

Experiment Name

(Coverage Series)

	Reference	1	2	3	4	5
Description of data product without regard to specific DWL technology	Perfect u,v observations from an orbiting instrument at single points within the TRV. No cloud or sub-grid wind variability effects accounted for.	Ultimate DWL that provides full tropospheric soundings, clouds permitting.	An instrument that provides only wind observations from clouds and the PBL	An instrument that provides mid and upper tropospheric winds only down to the levels of significant cloud coverage.	A non-scanning instrument that provides full tropospheric soundings, clouds permitting, along a single line that parallels the ground track	An instrument that provides all the data of experiment 2 plus some low resolution, lower accuracy data within the mid and upper cloud-free troposphere
Vertical domain (km)	0-20	0-20	0-20	3-20	0-20	0-20
Target Volume (km x km x km) (z> 2km) (z<2km)	200 x 200 x 1 200 x 200 x.25	200 x 200 x 1 200 x 200 x.25	200 x 200 x.25	200 x 200 x 1	200 x 200 x 1 200 x 200 x.2	500 x 500 x 2 200 x 200 x.25
Swath width (km)	2000	2000	2000	2000	<200	2000
C: clustered shots D: distributed shots	C	C&D	C&D	C&D	C&D	C&D

Table 1. DWL data height assignments and Observational errors 
         Height (km)    X        Standard deviation 
         .125           2         1.4
         .375           1         1.6
         .625           1         1.8
         .875           1         1.9
         1.125          2         2.0
         1.375          1         2.2
         1.625          1         2.3
         1.875          1         2.4
         2.5	        5         2.4
         3.5            5         2.6
         4.5            5         2.8
         5.5            5         3.0
         6.5       	5         3.2
         7.5       	5         3.4
         8.5       	5         3.4
         9.5       	5         3.4
         10.5           5         3.2
         11.5           5         3.1
         12.5           5         3.0
         13.5           5         2.7
         14.5           5         2.6
         15.5      	5         2.5
         16.5           5         2.5
         17.5           5         2.5
         18.5           5         2.5
         19.5           5         2.7