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Use of uncertainties in gravity model


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Good morning

I was looknig at the gravitational data provided in JGMRO_110C_SHA.TAB and I could not understand how to use the uncertainties provided.

I see that for example the third column of the first line provides a value of 1.9E-05 and the description of this number is "For a gravity field model the uncertainty in the gravitational constant GM in kilometers cubed per seconds squared for the planet"

I wanted to generate a "perturbed" gravity field based on this uncertainty. How would you recommend to do it? Shall I assume a uniform distribution and compute the

Real_GM = Nominal_GM + uniform(-1,1)*uncertainty

Or do you recomend using a gaussian distribution using the uncertainty as 1-sigma value?

In a similar way, the file also provides uncertainties for the coefficients Cmn and Smn.

How shall understand this  uncertainties if I want to create a perturbed (non-nominal) gravity field using all the coefficients and uncertainties provided in the file? Should I use a similar formulation of the one presented above?

Many thanks in advance

Kind regards,



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I took your question to Frank Lemoine on the MRO gravity team. His reply is below.

Susie Slavney

From Frank:

"The uncertainties that are provided with a gravity model are derived from the diagonal of the covariance matrix of the spherical harmonic solution. They are representation of the coefficient error, but do not account for the correlations between the coefficients in the least squares solution.

In order to obtain another realization of the gravity field solution that is perturbed according to the error information in the covariance, it is necessary to create clones, as discussed in this document (developed as part of the work on the GRAIL mission).


For Mars, the GSFC team has created clones of the GMM-3 gravity model which might be suitable for the user. This model is described in the paper by Antonio Genova et al. (Icarus, 2016).

The clones of GMM-3 are available at the following URL. http://pds-geosciences.wustl.edu/mro/mro-m-rss-5-sdp-v1/mrors_1xxx/extras/clones/

The GMM-3 model is available at the following URL. http://pds-geosciences.wustl.edu/mro/mro-m-rss-5-sdp-v1/mrors_1xxx/data/shadr/gmm3_120_sha.tab

The descriptive Label for the model is available at this URL. http://pds-geosciences.wustl.edu/mro/mro-m-rss-5-sdp-v1/mrors_1xxx/data/shadr/gmm3_120_sha.lbl

If the user wishes to create clones for the JPL gravity model, they can either ask Alex Konopliv at JPL, or download the error covariance (the SHBDR file),  and follow the procedure in the above pdf document to manufacture their own gravity field clones.

Frank Lemoine
NASA Goddard Space Flight Center

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