Fortran codes for numerical integral of terrain Helmert condensation effects on various field elements
https://www.zcyphygeodesy.com/en/h-nd-129.html
Using the rigorous numerical integral algorithm, from the ground digital elevation model and ground ellipsoidal height grid, compute the terrain Helmert condensation effects on the height anomaly (m), gravity (anomaly/disturbance, mGal), vertical deflection (ʺ, to south, to west) or (disturbing) gravity gradient (E, radial) on or outside the geoid.
Since the normal gravity field keeps unchanged, the terrain Helmert condensation effect on the gravity disturbance and gravity anomaly is always equal to the terrain Helmert condensation effect on gravity.
Compared with local terrain effects, terrain Helmert condensation has more ultrashort wave components. Affected by the continental topography, there is terrain Helmert condensation in the nearshore sea area, and the terrain Helmert condensation in the deep ocean area is equal to zero.
TerrainHelmertintgrl.f90
The record format of the input calculation point file: ID (point no / point name), longitude (decimal degrees), latitude (decimal degrees), ellipsoidal height (m)......
The record format of the output file reslt.txt: Behind the record of the calculation point file, appends 5 columns of terrain Helmert condensation effects on the height anomaly (m), gravity (anomaly/disturbance, mGal), vertical deflection (ʺ, to south, to west) or (disturbing) gravity gradient (E, radial) on or outside the geoid.
LTerAllBLH(BLH,dtm,sfh,nlat,nlon,hd,dr,GRS,ter)
Input parameters:BLH(3)－longitude (decimal degrees), latitude (decimal degrees), ellipsoidal height (m) of the calculation point.
Input parameters:dtm(nlat,nlon) - the ground digital elevation model (normal /orthometric height) grid, which is employed to indicate terrain relief.
Input parameters: sfh(nlat,nlon) - the ground ellipsoidal height grid, which represents the terrian surface position employed to calculate the integral distance.
Input parameters: dr, hd(6) - the integral radius (m) and grid specification parameters (minimum and maximum longitude, minimum and maximum latitude, longitude and latitude intervals of a cell grid).
Input parameters: GRS(6) - gm, ae, j2, omega, 1/f, default value
Return parameters: ter(5) - local terrain effects (in unit of SI) on the height anomaly, gravity (anomaly/disturbance), vertical deflection (to south, to west) or (disturbing) gravity gradient (radial).
(2) Algorithm module for numerical integral of local terrain compensation effects on various field elements
TercmpnBLH(BLH,mu,sfh,nlat,nlon,hd,dr,GRS,ter)
Input parameters: mu(nlat,nlon) - the terrain compensation density grid.
Input parameters: sfh(nlat,nlon) - the ground ellipsoidal height grid, which represents the terrian surface position employed to calculate the integral distance.
Return parameters: ter(5) - local terrain compensation effects (in unit of SI) on the height anomaly, gravity (anomaly/disturbance), vertical deflection (to south, to west) or (disturbing) gravity gradient (radial).
normdjn(GRS,djn); GNormalfd(BLH,NFD,GRS)
Return parameters: NFD(5) - the normal geopotential (m2/s2), normal gravity (mGal), normal gravity gradient (E), normal gravity line direction (', expressed by its north declination relative to the center of the Earth center of mass) or normal gravity gradient direction (', expressed by its north declination relative to the Earth center of mass).
LegPn_dt2(pn,dp1,dp2,n,t) ! t=cos ψ
BLH_RLAT(GRS, BLH, RLAT); BLH_XYZ(GRS, BLH, XYZ)
RLAT_BLH(GRS, RLAT, BLH)
CGrdPntD(lon,lat,dt,row,col,hd); CGrdPntD2(lon,lat,dt,row,col,hd)
CShepard(lon,lat,dt,row,col,hd); Gauss2D(lon,lat,dt,row,col,hd)
PickRecord(str0, kln, rec, nn)
Fortran90, 132 Columns fixed format. Fortran compiler for any operating system. No external link library required.
[Algorithmic formula] PAGravf4.5 User Reference https://www.zcyphygeodesy.com/en/
1.4.1 Format convention for geodetic data file
7.7 Local terrain compensation and terrain Helmert condensation
7.5.2 Integral formula of local terrain effect outside the Earth
7.1(4) Low-dgree Legendre function and its first and second derivative algorithms
The zip compression package includes the test project in visual studio 2017 - intel fortran integrated environment, DOS executable test file and all input and output data.
