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For a small area within the University, this exercise may be adequate but generally the sources of input data is too low to give accurate information needed but the heights are a fair reflection of the local variations in the topographic gradients or surfaces.

Odera et al. (2014) determined a local geoid model for application of GPS in heighting.GPS leveling data from dual frequency GPS and spirit leveling using a level instrumentwas used to provide height data for interpolation of local geoid models. Surfer software was used to generate/interpolate data for points not occupied. The geoid is used with the ellipsoidal height (h) to produce orthometric heights (H).

Accuracy of ±1cm in the study area using bi-quadratic polynomial interpolation method was achieved. This accuracy is sufficient for most engineering, planning and mapping projects of limited extent and relatively flat terrain or slope variation.

The spirit leveled differences was not corrected for gravity and the circuit closure was not stated. Type of leveling instrument was not stated as well as whether single or double run leveling was done. The study area size was not indicated.

Orthometric heights, obtained using this approach will be tremendously useful for engineering construction and topographical mapping for designs and preparation of bill of quantities as well as planning of physical developments and environmental studies.

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GNSS receiver was used to obtain ellipsoidal height (h) of points of observation within study area. Geodetic level was used for leveling over the same points to obtain orthometric heights (H) from reduced level over the same points.

Least squares adjustment was used to obtain satlevel geoidal coefficients. Surfer software was used to plot the undulations to show the geoidal surface from the 3D coordinates (East, North, and Undulations). Aleem (2013) developed “orthometric Height on fly” to compute the undulation which had been done with Microsoft Excel earlier. The same results were achieved after comparison. This acts as a check on the computations of undulations.

Geoid undulation computed from N = h – H and “satlevel” were put in tabular form and the differences are computed (as residuals). They are close. Coefficients obtained from least squares adjustment are used to develop a model of the undulation surface which can be used to compute orthometric height of points within the study area. Differential GPS (DGPS) method was adopted with spirit leveling to give h and H respectively. The GPS is a dual frequency model.

Orthometric corrections were not applied to elevation differences between control points before adjustments. Leveling routes were not stated for circuit closure. Stability of the observation stations was not mentioned either in the form of date stations was established orconstructed especially with the type of terrain within study area.

The process of removing outliers is adequate. But the optimum geoid for Nigeria is not yet officially given and may not have been integrated in the GNSS receivers used in the country, hence users are compelled to use whatever model the manufactures integrated as default. The need for local geoid model for transformation to orthometric height is important as a possible replacement for conventional leveling methods of height determination.

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Onwuzuligbo (2012) realized a local geoid model of NnmadiAzikwe University, Awka for processing orthometric heights within study area.

GPS/Leveling was done using DGPS Promark III and leveling (differential) was done with a leveling instrument. From N = h – H, interpolation was done to enable unoccupied points have the geoid undulation applied to ellipsoidal height(h) at that point to determine the orthometric height(H).

Ono (2011) was referred to highlighting the differences between global and local ellipsoids.

One of the assumptions made at starting point of geodetic datum is that there is no undulation at that point i.e. N =0 with the implication that deviation of the vertical is also zero and that normal to the ellipsoid and geoid coincides.Polynomial regression methods were reviewed and used to compute the differences and compared with observed .Surfer was used to plot the profile.Primary and secondary data sources were listed as well as the instruments used for data capture as well as processing methods with software used.

The results show the heights from GPS/leveling and spirit leveling which was used to compute the undulations (from N = h – H). Geoidal map was produced with surfer software where the height value is replaced with the undulation values (may be termed NAUGEOID).

This will enable use of GPS for orthometric height determination instead of spirit leveling for day to day application for engineering and survey works with the study area. The era of creating Temporary Bench Mark (TBM) in construction sites within NAU may be over with the development of this model i.e. no assumed height values anymore and the real surface is physically depicted and related to works being done.

As admitted by the researcher in the report, geodetic level and accessories with geodetic techniques were not employed. Since no gravity data was collected over the study area which

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is of small size, no orthometric corrections were also applied. The topography/slope and geology of the study area was not mentioned as well as the size/area.

For the size of the study area, the method used is adequate for applications in engineering and civil works and planning purposes. The topography would have assisted in the distribution of observation points.

Okiwelu et al. (2011) determined the Nigerian geoid undulation model using Spherical harmonic analysis to approximate the shape of the geoid (a surface of constant gravitational and centrifugal potential). The relationships for gravitational pull in Cartesian and polar coordinates were given as well as Laplace equation for a spheroidal earth. The geoid undulation as a function of the disturbing potential (T) was also stated. The relationship using GPS height (h) and orthometric height (H) through geoidal undulation (N) is well known.The gravity anomaly (∆g) is related to wavelength ( ) of the geoid undulation and degree (m) of the spherical harmonics. Geoid undulation for Nigeria was computed using a program (hsynth WGS84f) and minimum curvature program and surfer used for plotting.

EGM 2008 was very suitable with reference to WGS84 (this is the reference ellipsoid for GNSS/GPS) for geoid modeling because the extension to degree 2190 enables wavelengths from short (tens of kilometers) to long wavelengths (thousands of kilometers) to be obtained.

Nigerian geoidal undulation is vital to studying regional problems and to understand the relationship between geoid undulation and topographic features on the earth. The geoid undulation (N) peaks at Jos plateau and decreases towards the ocean.Nigeria has positive undulation i.e. N=h – H>o and has overall good correlation with topography. This highlights the need for terrain description in works concerning geoid modeling especially for deciding on interpolation techniques to be adopted.

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GPS/Leveling data would have impacted positively on the Nigerian geoid but for the large size of the country and the needed logistics and political will to embark on such projects.Since the author suggests that the geoid would be vital for regional problems, it is assumed that it may not be adequate for applications whose resolutions are not up to the geoid resolution i.e. day to day surveying, mapping and engineering activities.No validation was stated except the correlation with topography.

Reference to WGS84 ellipsoid is important since GPS uses this ellipsoid for referencing height. This is a national / regional issue and hence this approach may be better.The GPS/leveling data would have been integrated to assist the geodesists in defining a vertical datum for orthometric heights.

Nwilo et al. (2014) used interpolation method for geoid modeling over a small area of less than 10 square km. The local geoid model is to serve as alternative to conventional leveling operations and to determine orthometric height from GPS in the absence of an official geoid model for Nigeria and lack of quality gravity data over the country for gravmetric geoid development. A review of existing methods of geoid modeling was done and emphasis was placed on the interpolation technique. Model was formulated from the relationship between ellipsoidal height (h) and orthometric (H) i.e. N=h-H as a function of the coordinates of observed points i.e. = - = + (e,n) which can be written as

N= + +

Spirit leveling was used to to obtain the orthometric height while Promark 2 was used for ellipsoidal heighting determination in rapid static mode for 5 minutes.

Emelife (2012) used gravity data to develop a local geoid model for Awka and environs. The gravity observations were used to determine the geoid undulation (N) at several points to compute the gravity anomalies (δg) which was used with Stoke’s formula to provide geiod

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undulation (N). N computed from EGM84, EGM96, and EGM2008 was also used for comparisons with the observed terrestrial gravity. Gravity anomaly obtained from Nigerian Geological Survey Agency (NGSA) was used to plot map of study area as well as anomaly from terrestrial observations. Residuals were computed for each of the method.

It was recommended that to avoid generating parallel geospatial database infrastructure,geoid determination should be standardized.

Aina (2014) aimed at geoid model determination for transforming ellipsoidal height (h) using the space-based technique of GNSS within the Universitycampus as study area.GPS was used to determine h over points that have earlier been spirit leveled for orthometric height (H) determination. The difference between the two heights is called geoid undulation (N) which is given by N=h-H. Least squares technique was used to produce the most probable values of the coefficients of the curve fitting surface to derive a geoid model for the campus. Inverse Distance Weighting (IDW) and Kriging was the interpolation technique used. The studyrevealed the feasibility of adopting this method for orthometric heighting as an alternative to conventional leveling at the third order level of accuracy.