Using The Cmapf Routines (FORTRAN)
The Cmapf routines form a library of FORTRAN-language
subroutines and functions which process geographic and
dynamic data between grids and geographical coordinates
on a family of conformal map projections. Data characterizing
the map projections and the grids on them is embedded in
maparam structures. Note: in all cases, North latitudes
will be given as positive degrees, South latitudes negative
degrees, East longitudes positive degrees and West longitudes
negative degrees.
Initializing (configuring) the maparam structure:
- Stage I - Selecting a Map Projection.
- To initialize a map parameter (maparam) structure with
a Conformal Polar Projection;
- dimension stcprm(9)
- call stlmbr(stcprm, tnglat, reflon)
will
fill the structure "stcprm" with default data specifying
a Lambert Conformal Projection on a cone tangent to the
globe at latitude tnglat degrees. If a cut is needed
to lay the cone out flat on the plane, it will be made
opposite to (180° away from) longitude reflon. If
tnglat = 90 or -90, the map becomes a North or South
Polar Stereographic Projection (and the value of reflon
is immaterial). If tnglat = 0., the map becomes a Mercator
Projection.
For non-zero values of tnglat, between (but not including)
-90 and +90, the structure defines a Lambert Conformal
projection tangent to the Earth at "tnglat". If the
desired tangent latitude is not known, but the map
legend specifies two reference latitudes, the tangent
latitude may be found by
tnglat = eqvlat(reflat1,reflat2)
Caution:
this value is not the same as the mean latitude 0.5*(reflat1+reflat2).
Attempts to use the mean latitude will yield misleading
results.
- Stage II - Laying out a grid on a selected map projection.
- This stage configures the maparam structure with the
information to locate the points of the grid on the selected
map projection. Two alternative means are provided: Either
One-Point specification or Two-Point specification.
- Two-Point Specification:
- call stcm2p(stcprm, x1,y1,xlat1,xlon1, x2,y2,xlat2,xlon2)
causes
stcprm to be configured so that the grid point with
grid coordinates x1,y1 will be located on the map
at latitude xlat1, longitude xlon1, while x2,y2 is
located on the map at xlat2, xlon2. The two points
must be different.
This specification locates all other grid points,
assumed arranged on the projection with equal spacing
in the x- and y- directions.
The two points will often be opposite corners
of the intended grid, but many times a different
selection will be preferred. For example, in a
Mercator projection, it will often be better to
select two points of the same latitude or the same
longitude, to ensure exact N-S orientation of the
grid. Alternatively, several subgrids of an overall
grid may be guaranteed compatibility by using the
same two points of the overall grid, even if neither
of the points lie in the subgrid at all.
- One-Point Specification:
- call stcm1p(stcprm, x1,y1,xlat1,xlon1, scalat,scalon,
gsize,orient)
causes
stcprm to be configured so that the grid point with
grid coordinates x1,y1 will be located on the map
at latitude xlat1, longitude xlon1. The remaining
configuration information is provided at the scaling
point whose latitude and longitude are scalat, scalon.
At that point, and incidentally every on the latitude
circle scalat, the size of a grid cell is gsize in
both the x- and y- directions. Finally, at the scaling
point, the y-lines of the grid make an angle of "orient" degrees
clockwise (East) of the scalon meridian.
The x1,y1 coordinates can be thought of as "pinning" that
grid point to the map at xlat1,xlon1, the gsize
value can be thought of as "zooming" the grid in
and out until the desired size is attained, and
the "orient" specification can be thought of as
rotating the grid about the pinned point until
the grid has the wanted orientation.
Frequently, a grid will be published as having
an "lov" value of a longitude intended to be vertical;
for such grids, scalon = lov and orient = 0.
Using the configured maparams:
- Coordinate transforms:
-
- dimension stcprm(9)
- call cll2xy(stcprm, xlat,xlon, x,y)
will
return grid coordinates x,y according to the grid configured
as stcprm, for the point whose latitude and longitude
are xlat,xlon. Longitude values are adjusted to fit between
reflon-180. and reflon+180., so that nearby points on
the globe remain nearby points on the map, unless they
straddle the "cut" at longitude reflon+180., and find
themselves on opposite edges of an unrolled cylinder.
- call cxy2ll(stcprm, x,y, xlat,xlon)
will
return latitude and longitude parameters according to
the grid configured as stcprm, for the point whose grid
coordinates are x,y. Longitude values will be returned
in the range from -180. to +180.
If the point x,y corresponds to the North or South
Pole, where longitude is undefined, the returned longitude
will be 180. for the North Pole, 0. for the South Pole,
for compatibility with the WMO standard for reporting
winds there. (In an earlier version of CMAPF, the value
of reflon was returned here.)
- Wind Vector transforms:
- dimension stcprm(9)
- call cc2gll(stcprm, xlat,xlon, ue,vn, ug,vg)
and
- call cg2cll(stcprm, xlat,xlon, ug,vg, ue,vn)
will
convert the East- and North- components ue,vn (Cartographic
components) of the wind to and from components ug,vg
of the wind in the x- and y- directions of the grid (Grid
components). The first transfers from cartographic components
to grid components, the second does the reverse. In both
cases, the wind is that observed at the specified cartographic
coordinates xlat,xlon.
At the poles (xlat = 90. or xlat = -90.), the direction
of "North", which determines the meaning of ue and
vn, is based on the nominal value of longitude. The
direction of North will agree with that perceived by
an observer stationed a short distance away on the
xlon meridian. Thus, if xlat,xlon = 90.,-70., "North" will
be assigned to the direction of the 110E meridian.
- call cc2gxy(stcprm, x,y, ue,vn, ug,vg)
and
- call cg2cxy(stcprm, x,y, ug,vg, ue,vn)
will
convert the East- and North- components ue,vn (Cartographic
components) of the wind to and from components ug,vg
of the wind in the x- and y- directions of the grid (Grid
components). The first transfers from cartographic components
to grid components, the second does the reverse. In both
cases, the wind is that observed at the specified grid
coordinates x,y.
If x,y refers to the North or to the South pole, the
orientation of "North" is defined according to World
Meteorological Organization (WMO) code 878. The direction
of "North" is that of the Greenwich meridian, which
is the equivalent of using xlat = 90.,xlon = 180. for
the North Pole, and xlat = -90.,xlon = 0. for the South
Pole.
- call cw2gll(stcprm, xlat,xlon, ue,vn, ug,vg)
- call cg2wll(stcprm, xlat,xlon, ug,vg, ue,vn)
- call cw2gxy(stcprm, x,y, ue,vn, ug,vg)
and
- call cg2wxy(stcprm, x,y, ug,vg, ue,vn)
perform
the same services as the above transforms, except that
within 1 degree (111km or 60nm) or either pole, ue and
vn are interpreted according to WMO code 878 above. In
an earlier version of CMAPF, this was the definition
of the c2g and g2c routines, above.
- Gridsize Evaluation:
- dimension stcprm(9)
- gsize = cgszll(stcprm, xlat,xlon)
and
- gsize = cgszxy(stcprm, x,y)
return
the size, in kilometers, of a grid cell at the indicated
point.
- Curvature Vector:
- dimension stcprm(9)
- call ccrvxy (stcprm, x,y, gx,gy)
- call ccrvll (stcprm, xlat,xlon, gx,gy)
return,
in gx and gy, the logarithmic gradient of the scale.
This vector represents the curvature on the Earth of
a straight line segment on the map. Units are in radians
per kilometer on the Earth's surface. See the paper for
details on usage in equations.
- North Polar Vector evaluations:
- dimension stcprm(9)
- call cpolxy (stcprm, x,y, enx,eny,enz)
- call cpolll (stcprm, xlat,xlon, enx,eny,enz)
return,
in enx, eny, and enz the components of the direction
of the Earth's axis. components enx and eny provide the
local direction of North in grid coordinates, while enz
is proportional to the local Coriolis parameter.
|
