### Using The Cmapf Routines (C)

The Cmapf routines form a library of C-language 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 maparam structure with a Conformal Polar Projection;

• #include cmapf.h
• maparam stcprm;
• double reflon,tnglat;
• stlmbr(&stcprm, tnglat, reflon);

will fill the maparam 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.

1. Two-Point Specification:
• double x1, y1, lat1, lon1, x2, y2, lat2, lon2;
• stcm2p(&stcprm, x1, y1, lat1, lon1, x2, y2, lat2, lon2);

causes stcprm to be configured so that the grid point with grid coordinates x1,y1 will be located on the map at latitude lat1, longitude lon1, while x2,y2 is located on the map at lat2, lon2. 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.

2. One-Point Specification:
• double x1, y1, lat1, lon1, scalat, scalon, gsize, orient;
• stcm1p(&stcprm, x1, y1, lat1, lon1, 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 lat1, longitude lon1. The remaining configuration information is provided at the scaling point whose latitude and longitude are scalat, scalon. At that point, and incidentally every point 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 lat1,lon1, 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:
• maparam stcprm;
• double x, y, lat, lon;
• cll2xy(&stcprm, lat, lon, &x, &y);

will return grid coordinates x,y according to the grid configured as stcprm, for the point whose latitude and longitude are lat,lon. 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.

• cxy2ll(&stcprm, x, y, &lat, &lon);

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 willl 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:
• maparam stcprm;
• double x, y, lat, lon;
• double ue, vn, ug, vg;
• cc2gll(&stcprm, lat, lon, ue, vn, &ug, &vg);
and
• cg2cll(&stcprm, lat, lon, 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 lat,lon.

At the poles (lat = 90. or lat = -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 lon meridian. Thus, if lat,lon = 90.,-70., “North” will be asssigned to the direction of the 110E meridian.

• cc2gxy(&stcprm, x, y, ue, vn, &ug, &vg);
and
• 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 lat = 90.,lon = 180. for the North Pole, and lat = -90.,lon = 0. for the South Pole.

• cw2gll(&stcprm, lat, lon, ue, vn, &ug, &vg);
• cg2wll(&stcprm, lat, lon, ug, vg, &ue, &vn);
• cw2gxy(&stcprm, x, y, ue, vn, &ug, &vg);
and
• cg2wxy(&stcprm, x, y, ug, vg, &ue, &vn);

perform the same services as the above transforms, except that within 1° (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:
• maparam stcprm;
• double x, y, lat, lon, gsize;
• gsize = cgszll(&stcprm, lat, lon);
and
• gsize = cgszxy(&stcprm, x, y);

return the size, in kilometers, of a grid cell at the indicated point.

Curvature Vector:
• maparam stcprm;
• double x, y, lat, lon, gx, gy;
• ccrvxy(&stcprm, x, y, &gx, &gy);
• ccrvll (&stcprm, lat, lon, &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:
• maparam stcprm;
• double x, y, lat, lon, enx, eny, enz;
• cpolxy (&stcprm, x, y, &enx, &eny, &enz);
• cpolll (&stcprm, lat, lon, &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.