Line-of-Sight Wind Products

For each DWL line of sight perspective, a profile of forward model winds at each range gate is computed using the input horizontal wind components (converted to along track and cross track perspectives), platform geometry and the sampling scale uncertainties. 

V_for = ((U_ct+s_u* GN) * cos(ß) + (V_at+s_v* GN) * sin(ß)) * cos(Q) + W_vv+(s_w* GN) * sin(Q)

where

         V_for - the forward model line-of-sight wind velocity (m/s)

          U_ct - the cross track wind velocity at the shot location (m/s)

         s_{u - the sampling scale uncertainty in the cross track wind (m/s)}

         GN - gaussian distributed random number

        ß - heading angle (rad)

        V_at - the along track wind velocity at the shot location (m/s)

         s_{v - the sampling scale uncertainty in the along track wind (m/s)}

        Q - the elevation angle (rad)

         W_vv - the vertical velocity at the shot location (m/s)

     s_{w - the sampling scale uncertainty in the vertical velocity (m/s)}

The simulated DWL line-of-sight wind velocity is calculated by adding the line-of-sight uncertainty derived from the DWL's signal-to-noise model  to the forward model wind as follows:

where

         V_los - the line-of-sight wind velocity (m/s)

         s_los - the line-of-sight uncertainty (m/s).

DWL Shot Accumulation (grid volume averaging)

The Lidar Simulation Model estimates the performances of a pulsed DWL for a user-defined grid volume in order to define a lidar measurement of the line of sight wind.  The LSM supports two methods; single measurement LOS accumulation and multiple measurement volume accumulation.

Single shot mode: Along each DWL line of sight, each pulse within the user's defined vertical thickness resolution (with respect to the PBL) is accumulated to contribute to the DWL LOS wind estimate as depicted in the following figure:

 Accumulation Mode: The method the DLSM accumulates each pulse over an user-defined grid volume depends upon the user's scan mode: either conical or step/stare and fixed. 

For a conically scanned DWL, the grid volume is defined horizontally by the user's angle bin and number of scans for shot accumulation (shown in figure below) and the previously discussed vertical accumulation. Since this configuration is not likely and is only included in the DLSM for statistical purposes, the user is strongly cautioned when using this option. 

For step/stare and fixed beam DWL, the grid volume is defined horizontally by each dwell time of the stare and the previously discussed vertical accumulation. The percentage of shots to accumulate in a stare is preset to 100% in the DLSM Version 4.2.

A Vertical Example

Consider the following as an simple example of the disposition of 20 shots as they pass through the lowest 20 km of the earth’s atmosphere. Assume 10  DWL 'shots' per azimuth perspective (forward and aft) in two stares. The LSM computes the single shot DWL LOS winds from backscattering sources such as aerosols, molecules and clouds. Each backscattering source and perspective is considered to provide a unique measurement in each grid volume. A single representation of the wind in each grid volume for each source and perspective is computed by accumulating the single shot DWL LOS estimates. The LSM also computes the standard deviation of the accumulated single shot LOS winds. This standard deviation reflects not only system accuracy, but also representativeness as long as the single shots are distributed throughout the grid volume. The target data product  is a single LOS for each of the two perspectives within a volume defined by the dwell time of the stare and a vertical thickness above the PBL of 1 km. In this example the global atmospheric model (eg ECMWF) calls for 25% cloud coverage at 8 km, 50% coverage at 4 km and 40% coverage at 2 km.

At 8 km the clouds are taken to be cirrus, but the 25% coverage is not interpreted literally. Instead, we assume 100% cirrus coverage and use the value of 25% to scale the optical depth between 0 and 1.4 km. Thus all 20 shots would yield returns, 10 "forward" and 10 "aft", from cloud material at 8 km and pass, attenuated, through to lower levels. The two sets of 10 shots would be processed to produce one LOS wind speed for each perspective. The DWL LOS height assignments are SNR weighted and are usually near the top of the cirrus layer.

For the non-cirrus clouds at 4 km, the 50% coverage is taken literally. Hence, 5 forward/5 aft shots are intercepted by cloud and 5 forward/5 aft shots provide aerosol returns. In this case, the two LOS wind speeds (forward and aft) computed for the 1 km thickness layer are dominated by the cloud's presence. The DWL LOS height assignments are SNR weighted and are usually near the top of the cloud layer. Only the shots that missed the clouds continue on to lower levels.

At 2 km, the opaque cloud is non-contiguous with respect to the 4 km cloud layer. The DLSM uses the satellite view cloud overlap function to determine how much of the cloud is viewable. In this case consider fifty percent of the 40% impacts the DWL "shots". 1/1 shots are processed to provide two DWL LOS winds from a cloud dominate volume and as before the DWL LOS height assignments are SNR weighted and are usually near the top of the cloud layer. 4/4 shots  continue on to yield aerosol and surface returns. 

Additional Doppler shift effects that are computed for direct detection lidars by the DLSM 4.2  are the molecular Gaussian broadening, the Lorentzian aerosol broadening,  the Doppler shift due to Earth's motion and the Doppler shift due to Satellite's motion. The LOS wind models assume that the Earth and the satellite motion effects have been corrected for and therefore are not included in the wind calculations.

Horizontal Wind Products  (The LSM's Horizontal Wind Models are not included in the DLSM version 4.2) 

Last Updated: 02/07/2007