You may need to check input data (gravity, terrain, GGMs) and validation data (GNSS/levelling). It is also advisable to transform gravity data coordinates from the local reference system to the global reference system (GRS80 which is very similar to WGS84). This would take care of the errors associated with multiple transformation of global-based data sets (GGMs, satellite terrain models, GNSS etc.) to the local reference system (given the errors in the transformation parameters). You may find the attached paper useful.

Best wishes.

Thanks so much Odera for your wonderful and prompt response/input. The gravity data were locally obtained in the study area using a gravimeter. They are not local gravity data obtained from transformation of global data set. Is it ideal to find the mean of the differences between the known orthometric heights and model orthometric heights and apply it as a correction at every new point during the application of the determined model?

Dear, Okiemute

The reason for the large differences (bias) is mainly from the following:-

1. The defects in the local vertical datum, where the assumption of zero-level, which is different from the global zero vertical datum due to the sea-surface topography.

2. The difference in semi-major axis of the ellipsoid used to derive ellipsoidal heights from the GPS-derived Cartesian coordinates and that of the "ideal" mean-Earth ellipsoid with respect to which our geoid undulations were computed.

The most popular and usually best fitting method to remove the bias and tilt is considered to be the classic 4-parameter model, which was used for determining gravimetric geoid models in several countries such as Egypt (Shaker et al., 1997; Ghanem, 2001); Canada (Sideris & She, 1995); Sweden (Nahavandchi & Sjöberg, 2001); Australia (Fotopoulos et al., 2002); Great Britain (Iliffe et al., 2003) and Argentina (Pinon, 2016).

Regards

Abdelrahim

Dear Okiemute,

I agree with Dr. Ruby. Just want to add, go for 7-parameter model to account for bias and tilts in the geometric and gravimetric values. It presents better results as compared to 4-paramter model.

Regards,

Ropesh Goyal

Hi Sylvester,

I think the answers so far have been wonderful and helpful.

However, I would take a second look at the input data as suggested by Dr. Petroba Odera.

Here are a few suggestions:

1. Ensure uniformity in terms of tide systems and reference ellipsoid. Depending on the study area, the effect of tide system may be small. Still, it’s proper to be consistent

2. Find a way of validating your GPS/leveling data. Depending on what research has been conducted in your study area, a high-resolution GGM could be used to, as it were, validate the GPS/leveling data (and perhaps your gravimetric data). You could either add RTM effects to the GGM and find the difference between height anomalies computed from the GGM and GPS/leveling data. But in the case where your study area is relatively flat, a direct comparison should suffice.

3. Of course, there’s also the points raised by Ropesh and Ruby. All the same, I would pay more attention to the accuracies of the (terrestrial) data sets.

4. I have a paper under production on validating height data. I think it could help you with the accuracy of your GPS/leveling data. If you’re interested, I could send you the preprint.

Here are a number of helpful references

1. Towards the Selection of an Optimal Global Geopotential Model for the Computation of the Long-Wavelength Contribution: A Case Study of Ghana

This should serve as a guide to validating your data set

2. https://www.researchgate.net/publication/226954086_The_Permanent_Tide_In_Height_Systems

4. https://www.researchgate.net/publication/224970095_Assessment_of_the_LVD_offsets_for_the_normal-orthometric_heights_and_different_permanent_tide_systems_-_A_case_study_of_New_Zealand

5. https://www.researchgate.net/publication/257338644_Estimation_of_the_zero-height_geopotential_level_W_o_LVDin_a_local_vertical_datum_from_inversion_of_co-located_GPS_leveling_and_geoid_heights_A_case_study_in_the_Hellenic_islands

Dear Ropesh Goyal and Caleb Yakubu, thanks so much for your responses and contributions to my question. If all that you have just contributed and suggested have been taken care of and there are still large differences in heights, what would be the way forward.

Hi Sylvester,

Your best bet then would be to replace the data with more accurate ones, or find other techniques like the one suggested by Ropesh and Ruby.

Your question states that you're "sensing..." Have you conducted any experiments regarding the likely accuracy of your geoid model? How are you "sensing" that you'll have large differences?

I think you should take it one step at a time. Compute the geoid (if you haven't). Validate it. And if your error is indeed large, you could read around to get ideas on how to reduce it.

For now, try comparing the geoid from a GGM with the geometric approximation from GPS/levelling data. This may give you an idea of the error to expect.

And when you've finally computed your geoid and verified that the difference is large, you could look for ways of reducing it.

Cheers!

Caleb

Dear Okiemute,

I fully agree with Dr. Yakubu.

In addition, it will be helpful if you can plot the differences between i.) geoid and GGM and ii.) geoid and GNSS/levelling. See if there are any patterns in the differences.

And if not, then you have to change your dataset.

Though you must have taken care of that, but kindly see if the horizontal datums are all same. Like in India, we previously used to have the Everest datum..so it may be possible that GPS/levelling data may not be actually GPS/levelling, and some transformations are needed.

Regards,

Ropesh Goyal

The adopted methods and the way forward have been discussed with Dr. Patroba Achola Odera.

Mainly reasons for this would be:

1. Old, so inaccurate levelling points(orthometric heights)-solution -you must remeasure the network what is a difficult work!!!!

2.The used global geopotential model does not fit well to your region -solution- try onother one or fit it to your data before the calculation of gravimetric geoid.

3. Gravity measurements do not account to all parameters(buildings, water table, cavities etc ) in your local area.-solution - try to estimate corrections for every parameter that can affect your measurements and recalculate it.

differences up to 0.5 meters and maybe more could be fitted with a 4-parameter GPS/Levelling fitting method in order to calculate the best fitted geoid to your region.