Cartography Basics *Map Projections *Datums *Coordinate Conversion *Modtran *Resampling

1. Cartography Basics *Map Projections *Datums *Coordinate Conversion *Modtran *Resampling

2. Map Projections * Spherical earth model Latitude, Longitude, Altitude * Meracator Projection *Universal Transverse Mercator (UTM)Projection zone, easting, northing, altitude * UTM Military Grid * Global Coordinate System (GCS)

3. DATUMS b Geodetic latitude a DATUM WGS 84 Semi-major axis = a = 6378137.000m Semi-minor axis = b= 6356752.314m Flattening =f 1/f = (a-b)/a = 1/298.257223563

4. DATUM TRANSFORM Lat/long/alt in datum 1 Same Lat/long/alt in different Datum Same earth point has different lat’/long’/alt’ in a different datum The same lat/long/alt numbers in two different datums refer to two different points on the earth. A Datum Transform converts the same point on the earth from lat/long/alt in one datum to lat’/long’/alt’ in second datum.

5. a=semi-major axis 1/f = reciprocal of flattening

6. Coordinate Conversion Projection 1 Datum 1 Projection 2 Datum 2 lat Zone, Easting long Easting = E(lat,long,alt,datum_parameters) Zone = Z (lat,long,alt,datum_parameters) Northing = N(lat,long,alt,datum_parameters) Alt = A(lat,long,alt,datum_parameters)

7. Modtran execution EXAMPLE

8. Resampling Projection 1 Datum 1 Projection 2 Datum 2 lat Zone, Easting long V(Easting,Zone, T(V(lat,long,alt,datum_parameters), Northing, Alt V(lat,long,alt,datum_parameters), datum_parameters) V(lat,long,alt,datum_parameters), V(lat,long,alt,datum_parameters))

9. Resampling Algorithm 1) Get point of interest P 2) Transform to coordinates P’ =T(P) in which data is available 3) Find surrounding data Values V(P’+1),V(P’-1) 4) Interpolate from surrounding values to the Value at the transformed point V(P’) = I(V(P’+1),V(P’-1),…) 5) Assign the interpolated value to the point of interest V(P) = V(P’)

10. Y+1 X’,Y’ Y X X+1 Interpolation *Nearest neighbor *Truncate *Bilinear Interpolation V(x’,y) =V(x,y) + {V(x+x,y) - V(x,y)}(x’-x)/((x+ x)-x) V(x’,y+1) =V(x,y+ y) + {V(x+ x,y+ y) - V(x,y+ y)}(x’-x)/(x) V(x’,y’) = V(x’,y) + {V(x’,y+ y) - V(x’,y’)} (y’-y)/(y)