Details of Terrain Processing

The terrain processing software originated with the Regional Atmospheric Modeling 
System (RAMS).  FSL used this software in WRFSI because it has the desired 
projections, global localization flexibility, was well tested and was the most 
efficient for meeting the initial 1999 release.  The method allows usage of the 
full resolution (30 arc second, ~1km) raw USGS topography data reformatted into 
10 by 10 degree tiles.   The robust software allowed FSL to also process the raw 
land use data, soil texture categories, (both also 30 arc second and in 10x10 
tiles), and other categorical data. The technique is nicely described by 
documentation that comes with the RAMS software (Walko and Tremback 2004).  The 
terrain processing relies on the settings of namelist variables: silavwt_parm_wrf 
and toptwvl_parm_wrf (hereafter silavwt and toptwvl).  

SILAVWT: this namelist variable controls the type of processing of topographic 
data from input files that are specified by the path to raw terrain data 
"TOPO_30S" to final values defined on a WRF grid.  This is a 3-step process,
 which involves topography information being defined successively on 4 different 
grids, called the "O", "P",  "Q", and "R" grids.  First, a horizontal 
interpolation is carried out in order to transfer data from the "observed" or 
"O" grid of the input file, to a projection (Lambert, Mercator, or polar 
stereographic) grid of comparable resolution, which is the P-grid.  The P-grid 
uses the same projection as the WRF grid (the R-grid) where the data will reside 
in its final state, but is usually of much higher resolution.  

Second, data are averaged from this P-grid to a lower-resolution Q-grid, (also a 
grid in projection coordinates) and have a horizontal grid spacing that is an 
integer multiple of that on the P-grid.  This step automatically filters out 
small-scale variations, which are not desired on the model grid.  In this second 
averaging step, a choice of averaging algorithms exists and SILAVWT_PARM_WRF is 
the flag that selects the choice to be used.  If SILAVWT_PARM_WRF is set to 1, a 
conventional mean is used where terrain heights for all P grid cells in a single 
Q grid cell are summed and divided by that number of P values, to obtain the 
value for that Q cell.  

For SILAVWT_PARM_WRF equal to 1, both the conventional mean and a silhouette 
average are computed, and the value assigned to the Q grid   cell is a weighted 
average of these, with the weights controlled by SILAVWT_PARM_WRF.  That is, an 
envelope orography results when SILAVWT_PARM_WRF equals 2 or 3. The silhouette 
average finds the mean height of the silhouette, as viewed from the east or west, 
of the set of P grid terrain heights contained within a single Q grid cell, and 
a separate silhouette height as viewed from the north or south and averages the 
two silhouette heights together.  This becomes the computed silhouette height 
for that coarse-grid cell.  While the conventional average preserves total 
terrain volume above sea level, the silhouette average adds mass by filling in 
valleys.  It is used to maintain the effective mean barrier height that air must 
rise to when crossing a topographic barrier such as a ridge.  The conventional 
average lowers this barrier height, particularly when the barrier height is 
poorly resolved.  

When SILAVWT_PARM_WRF equals 2, an envelope topography scheme is used to obtain 
Q Grid values from P grid values, and this scheme is an alternative method of 
attempting to preserve barrier heights.  When SILAVWT_PARM_WRF equals 3, a 
reflected envelope topography scheme is used which aims to preserve both barrier 
heights and valley depths.  Naturally, this method leads to the steepest 
topography in WRF, while still filtering the shortest wavelengths.  In the third 
and final step, topography is interpolated from the Q grid to the R grid, where 
the R grid is usually of moderately higher resolution than the Q grid.

TOPTWVL: this is a grid dependent namelist variable specifying the wavelength, 
in grid-cell size units, of the smallest horizontal modes of terrain height data 
which are to be present on a given model grid.  It is applicable only for 
namelist variable SILAVWT_PARM_WRF set to 1.  Referring to the description of 
namelist variable SILAVWT_PARM_WRF above,  the value of TOPTWVL_PARM_WRF controls 
the ratio of resolution between the Q and R grids.  The shortest mode that any 
grid can resolve is that with a wavelength of twice the grid cell size.  In 
general, the Q grid will contain all wavelengths of topographic data from its 
own 2 delta-X scale and larger.  Hence, if the WRF "R" grid, to which data are 
interpolated from the Q grid, has, for example, half the cell size of the model 
grid, the smallest mode that it will receive from the Q grid will be 4 delta-X 
on the R grid.   This smallest mode, in delta-X units of the R grid, is the 
number specified for TOPTWVL_PARM_WRF.  In other words,  while the R grid 
spacing is set by the user, the Q grid spacing will be TOPTWVL_PARM_WRF/2 times 
the R grid spacing.  This is how smoothing of the topographic data is achieved 
in WRFSI while allowing the variety of enhancing schemes described for 
SILAVWT_PARM_WRF.  Because the numerical model does not properly handle the 
smallest modes resolvable on a grid, it is generally important not to force 
these modes into the meteorogological fields through overly fine terrain height 
modes.
