5
$\begingroup$

I've implemented the Earth harmonics calculation in JGM-3 model, using the coefficients from here

2    0   -0.10826360229840e-02     0.0
2    1   -0.24140000522221e-09     0.15430999737844e-08
2    2    0.15745360427672e-05    -0.90386807301869e-06
3    0    0.25324353457544e-05     0.0

Now, I want to switch to EGM2008, the coefficients are taken from here (Tide-free).

2    0   -0.484165143790815e-03    0.000000000000000e+00
2    1   -0.206615509074176e-09    0.138441389137979e-08
2    2    0.243938357328313e-05   -0.140027370385934e-05
3    0    0.957161207093473e-06    0.000000000000000e+00

There is a major difference. Probably, I should make some operations on the coefficients? For example, multiply $C_{20}$ by $\sqrt{5}$?

Multiplied all coefficients of EGM2008 by $\sqrt{2*degree+1}$, got

2   0   -1.082626173852220E-03  0.0000000000000E+00
2   1   -4.6200632349558E-10    3.0956435701202E-09
2   2   5.4546274930574E-06 -3.1311071889349E-06
3   0   2.5324105185677E-06 0.0000000000000E+00

Especially for $C_{21}$ and $C_{22}$ the difference is still major.

Extra

To calculate the Earth gravity potential in JGM-3, the equation was used: $U_{har}=\frac{\mu}{r}[1+\sum_{i=2}^d\sum_{j=0}^o (\frac{R_{eq}}{r})^iP_{ij}(\sin\phi)(S_{ij}\sin{j\lambda}+C_{ij}\cos{j\lambda})]$,

As you see, the argument of Lejendre polynom $P_{ij}$ is $sin\phi$.

However, here for EGM2008 it's said to use $cos\phi$. Is it specific for EGM2008 model?

$\endgroup$
5
  • 1
    $\begingroup$ sqrt(5) is for C20, but you also need to normalize/unnormalize the other coefficients: sqrt(degree * 2 + 1). $\endgroup$
    – Cristiano
    Commented Aug 3, 2018 at 10:41
  • 1
    $\begingroup$ Both C and S. It depends only on the degree. No link, sorry. $\endgroup$
    – Cristiano
    Commented Aug 3, 2018 at 10:58
  • $\begingroup$ @Cristiano I multiplied all coefficients by $\sqrt{degree*2+1}$, but the results are still strange. Probably, there is something specific with EGM2008 $\endgroup$
    – Leeloo
    Commented Aug 3, 2018 at 16:33
  • $\begingroup$ Then probably it's an overflow problem; what does "the results are still strange." mean? $\endgroup$
    – Cristiano
    Commented Aug 3, 2018 at 16:46
  • $\begingroup$ @Cristiano I don't undertand why for $C_{22}$ in JGM-3 the value is 0.15e-5, but in EGM-2008 it's 0.54E-05. So major difference? May be it depends on order also? Added the coefficients to the question. $\endgroup$
    – Leeloo
    Commented Aug 3, 2018 at 17:24

1 Answer 1

6
$\begingroup$

Spherical harmonics coefficients for gravity models can span several orders of magnitude. To avoid underflow problems and loss of accuracy, they are commonly normalized with a factor that depends on both $n$ and $m$. It looks like the coefficients reported by JGM-3 are the unnormalized $C_{n,m}, S_{n,m}$, while the ones in EGM2008 are the normalized $\overline{C}_{n,m}, \overline{S}_{n,m}$.

From Montenbruck and Gill (2000): Screenshot from Montenbruck and Gill describing normalized / unnormalized coefficients

$\endgroup$
3

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.