Dear Abdel,

from what I know dV_ELL_RET2012 is not a model of topography but it is a model of the gravitational field due to topography. So if you are interested in the gravitational field you can use a spherical harmonic synthesis SW (e.g. hmanipulator from A. Gatti http://sourceforge.net/projects/hmanipulator/files/).

If you want to compute the digital elevation model used to create dV_ELL_RET2012 it should be Earth2012.topo_bathy.SHCto2160.zip in http://geodesy.curtin.edu.au/research/models/Earth2012/.

I think that you can use hmanipulator also to synthesize the topography, however I have never tried to synthesize it. I will try and come back to your question in a couple of days.

Regards,

Daniele

Dear Dr. Daniele Sampietro

Thank you very much

I'm waiting for you

Thank

Abdel Rahim

You can use the DTM2006 spherical harmonic coefficients (up to d/o 2160), I can provide a MatLab script for you. I guess you would like to compute the residual terrain modelling (RTM) quanties (residual height anomalies, gravity anomalies, etc.) , is it?

All the best,

Vagner

Dear Dr. Vagner

yes , I  would like to compute the residual terrain modelling quantities (residual height anomalies, gravity anomalies,) 

I am waiting for sending program (a MatLab script) to do that

Thank you very much

Abdel Rahim

Re; the original post "I want DTM (Digital Terrain Models) from SHM (Spherical Harmonic Models)".

So does the FAA UAV Committe, or the will, when they realize that terabytes of Google Earth DTM data compresses to megabytes of SHM data, which can be stored in each GPS-equipped drone to keep it firstly, out of the navigable airspace, and secondarily, from crashing into the Earth.

Doug

DTM2006.0 is part of:

Pavlis, N.K., S.A. Holmes, S.C. Kenyon, and J.K. Factor, An Earth Gravitational Model to Degree

2160: EGM2008, presented at the 2008 General Assembly of the European Geosciences Union,

Vienna, Austria, April 13-18, 2008.

nga.mil

http://earth-info.nga.mil/GandG/wgs84/gravitymod/egm2008/README_FIRST.pdf

I have snipped the first two columns (n and m) of the DTM2006.0 dataset for import into MathCAD becase 8 million Floats would not fit in 2.8 GB RAM but 4 million would--the coefficients only. Then I made a square matrix, upper diagonal m>n the Sine coefficients, lower diagonal n>n the Cosine coefficients, using the same RAM, letting MathCAD manage the memory, but I am stalled at expanding the geodesic associated Legendre polynomial in powers of cosine theta to degree 2190. MathCAD can't nor can I. So I am stuck. I found:

https://github.com/USNavalResearchLaboratory/TrackerComponentLibrary/blob/master/README.md

which contains useable C++ code.

Doug

Dear Dr. Douglas

Thanks for helping me and many thanks for this good information

Abdel Rahim

AFAIK, and with my limited read into the area--I could be completely wrong, nobody has taken the initiative to recompile using a symbolic algebra the huge problem of spherical harmomic expansion of the "associated Legendre polynomial coeffient of cosine theta", but, since the model (DTM2006.0) *is* of finite degree, this expanion *is possible*. Let me say more. Cosine theta is expandable as a Taylor series in powers of theta, and the ALP, the Associated Legendre Polynomial, is already in such powers, powers of cosine theta. So I will try it, not to order 2190 (Yikes!) but order...5?

In Mathcad writing

Elevation ==

Sum, for n = 1 to 2190,

for m = 1 to n, of

Coefficient C.m Cosine Lamda + Coefficient S.m Sine Lamda

is so easy, since the proper notation is available, but in Mathcad, we can *write*

d^n / d cos^n (theta) inline but it won't expand, even with Live Symbolics *on*.

So what is needed is to write it out of line, with Live Symbolics on, Evaluate Symbolically, and Paste the result. However, even at order 5, the result may be what Mathcad calls Huge. Too big. So we shall see.

Hello every one,

sorry where could I get this DTM 2006.0 SHs model. anyone to send me a link please?

And is there any way of converting Global DEMs models (e.g. SRTM) into spherical harmonics coefficients?

Kindly Regards

Dear Mchila

You can download spherical harmonic coefficients for Earth's Elevation (DTM2006.0) from this link:

https://earth-info.nga.mil/GandG/wgs84/gravitymod/egm2008/Coeff_Height_and_Depth_to2190_DTM2006.0.gz

Greetings,