WELCOME FOLKS!!

Today we are going to find out what does a datum mean and why we require one? Also, what is WGS 84 and other datums?

I know most people onboard could not explain it beyond “it’s a datum on which all charts and GPS is made and we have to use both charts and GPS on the same datum otherwise there will be an error in position”. Though they all are right most of them fail to answer the magic word “WHY?”.

“The **World Geodetic System** (**WGS**) is a standard for use in cartography, geodesy, and navigation including GPS. It comprises a standard coordinate system for the Earth, a standard spheroidal reference surface (the *datum* or *reference ellipsoid*) for raw altitude data, and a gravitational equipotential surface (the *geoid*) that defines the *nominal sea level”*

This is a Wikipedia definition of term WGS , but as a sailor, it doesn’t help us much, does it? So forget about it right now but I promise if you read this article till the end you will get most of it.So let’s begin.

If earth would have been spherical It would be a piece of cake to plot our position on it. But as we have read in our great navigation books it is an oblate spheroid. Not quite accurate but roughly yes. So this is how an oblate spheroid look like flattened at poles and bulged at the equator.

Out of curiosity why earth happens to be an oblate spheroid not and a prolate spheroid (which is flattened at the equator and bulged at poles)? Stop here for some time and try to and guess the answer.

# WHY EARTH NEARLY RESEMBLES AN OBLATE SPHEROID?

Let’s see if you guessed it right or not? This happens because of the earth’s rotation and gravity. Let’s understand it by an example consider a point on earth surface on the equator and another point near the pole of the earth. Now in 24 hours of sidereal time, these points describe a full circle means both these points complete a circle. But the point on equator has to travel more distance in same time to complete the circle. It means the point on equator have greater linear velocity than a point near pole though their orbital velocities are same. So if we are on the earth (non- inertial rotating frame of reference) the point the point on equator and point near pole both must have to be applied with a centrifugal force of magnitude

The centrifugal force act vertically outwards from the center of the earth and depend on upon the radius of circular motion of the particle. It is clear that more the radius of motion more the centrifugal force is as it is directly proportional to radius. So the point on the equator will be pulled out more strongly than a point near pole (as the centrifugal force acts radially outwards). This effect causes bulging at the equator and flattening at poles. A real life example,assume a thin rubber ball as a size of a football rotating about an axis with very high velocity you will notice that it start flattening at poles and bulging at the equator. As the speed increases bulging also increases.

Coming back to our original question what is WGS 84? I am going to answer it in a moment but first, we need to know some basic things so that we can effectively understand WGS 84. Let’s start with earth’s shape.

Earth’s shape resembles an oblate spheroid but actually the shape of the earth is pretty irregular because of topography like mountains valleys etc. etc. Defining a position on an irregular shape is a difficult task and complex and difficult task. Let’s see what has been done, because the earth is pretty irregular two different model of the earth has been developed first “REFERENCE ELLIPSOID” and another is “GEOID”.

# REFERENCE ELLIPSOID

It is an idealized model of the earth which is an oblate spheroid also called ellipsoid or reference ellipsoid of a specific dimension(equatorial diameter and polar diameter) to match earth shape as closely as possible.

# GEODESY

Before we talk about geoids it will be useful to talk about “geodesy”. It is an art of measuring and representing earth including its gravitational field. Our brilliant scientists have these highly sophisticated satellites in space. And from a ground station, a beam of light is sent to the satellite which carries a reflector so this laser reflected back to earth and received by an another ground station. Time for this round trip of light is calculated and hence the distance between the ground station and satellite is calculated. With modern techniques, the accuracy of distance obtained is within few millimeters. This technique is called “LASER RANGING”.Using laser ranging we determine the present position of the satellite and we can calculate its expected position from the orbital data. We compare both and If there is the difference it should be because of the gravitational anomaly of that place which is proportional to the amount of deviation from the orbit. Hence gravitational field of every point on earth can be mapped using this technique. It is called “DYNAMIC SATTELITE GEODESY”.

# GEOID

Now let’s talk about geoid.Earth’s gravitational field is neither perfect nor uniform because under surface of the earth there is non- homogeneous magma distribution. And the density of ocean and earth crust is not the same everywhere.Also, there are mountains and valley’s on the surface of the earth which changes the gravitational force slightly causing a gravitational anomaly. Suppose if there are no gravitational anomalies(uniform and perfect gravitational field) then under the effect of gravity and rotation of the earth, the ocean will maintain a constant level everywhere (also assuming the density of ocean is same). We can call this level “assumed sea level” or anything else you want.

Now with help of satellite geodesy, we can calculate the value of the gravitational field for every point on earth surface.And this non-uniform gravitational field, will change the shape of earth’s ocean i.e more water will accumulate where there is more gravitational attraction and less water will accumulate where there is lesser gravitational field creating small hills and valleys in oceans also these hills and valleys of water further deform because of rotation of the earth. Effect of wind and tides and other small influences is not considered while determining the shape of the geoid. On earth surface, there are also landmasses called continents to extend this concept to continents we assume we criss-cross continents with many hypothetical canals containing water of same density as the ocean and at the initial level of “assumed sea level” and keep gravitational field same as original (as if there are no canals). So the water in these canals also won’t be at same level everywhere because of gravitational anomalies. As mountain will attract more water than valley and rotation of the earth is also taken into account.So basically there will be an irregular shape of water but not as irregular as the earth itself because the height of the mountain may be 5000 ft but because of its gravity, water it will attract may rise up to only 100 ft. The shape of earth’s water will then take is called a geoid. Some say geoid is the true mathematical shape of the earth. A typical geoid looks like.

Another simple way of visualizing it would suppose our reference ellipsoid surface is made up of water now we put our gravitational anomalies and rotation of the earth and the shape of water will deform and somewhere it might get below our reference ellipsoid and somewhere it goes above reference ellipsoid. Roughly we can say that this is the shape of the geoid. Also where there is a positive gravitational anomaly(more mass) geoid surface will be above reference ellipsoid and vice versa. The height difference between reference ellipsoid and the geoid is called geodetic height or simply geoid height.

Huh! This is the best I can explain it. Remember it is a very difficult and complex process to determine a geoid. A picture of a geoid EGM 96 is shown below.

Also watching this video will clarify it further. I want to thank minute physics for making such a great video.

# DATUMS

To define a position of a point on a piece of paper we need a co- ordinate system. Just like that to define a position on earth surface we also need a coordinate system. So a datum is nothing but a coordinate system to define a position on earth surface. So to define a position on a piece of paper we just need two perpendicular lines (x-axis and y-axis). But that won’t work for the earth because the earth is a three-dimensional nearly spherical object so wee need a spherical coordinate system to determine the position on it.

This spherical coordinate system is essentially a reference ellipsoid of selected dimension and attached to a specific part of the earth for eg. People of South America will like to select a reference ellipsoid which is attached to their land mass i.e to represent their land mass most accurately but if this reference ellipsoid is used in India say results will be absurd heights might go in negative. Also, tectonic plates of South America will shift differently then tectonic plates of India which will further give more absurd results as time passes. So to overcome this problem India will select its own reference ellipsoid(select its own datum) which represent it more accurately. Like that local datums have come into force for eg. NAD 83 and ETRS 89.

And if a country prepares a chart of a place using its local datum and another country uses their own they will never agree on a position because both reference ellipsoids are different(means they are using different coordinate systems) and are differently aligned. There will always a shift in position derived if different datums are used to map a place. This is called datum shift

**THIS IS THE REASON WHY YOU REQUIRE TO HAVE THE SAME DATUM SELECTED ON GPS AS THAT OF CHARTS BECAUSE THERE WILL BE SHIFT IN POSITION CALLED DATUM SHIFT**

Huh! It was quite a discussion. But we are not finished yet.

# WORLD GEODETIC SYSTEM 84

So a solution to above problem is to use a common geodetic system, which means a coordinate system which can be used worldwide. Let’s see how it’s done. Unlike local datums, it is not attached to specific a specific land mass but in this case, its center is aligned with the center of mass of earth.Which is fair enough. But how the center of mass of the earth is determined. This is an interesting question. Think and we will talk about it later.

WGS 84 basically contains 3 things

- A reference ellipsoid
- A reference meridian
- A geoid model of earth

Dimensions of reference ellipsoid used in WGS 84 are

Equatorial radius= 6378137 m

Polar radius = 6356752.3142 m

Now we have defined our reference ellipsoid but to determine the position on earth we need reference lines from which position can be derived (prime meridian and equator basically).

## IERS REFERENCE

WGS 84 uses IERS reference(also called IRM) meridian as its prime meridian. Not meridian passing through royal observatory Greenwich London(as defined by the UK) they are approximately 102 m apart and this shift might increase as time passes. Why? For two reason first the position of royal observatory will shift as tectonic place shift and another is plane of IERS reference meridian passes through center of mass of earth and the plane of reference meridian defined by the UK(Greenwich meridian) passes through their local vertical e.i using gravity their local vertical direction was calculated and it was assumed center of mass of earth must be In direction of local gravity.

Now the question is how IRM is maintained because we can’t fix it to any landmark because the land mass will shift constantly as tectonic plates shift.But we can not allow shifting of our prime meridian. This is done using averaging of data obtained from hundreds of ground stations. For example, Say a reference meridian is chosen now co-ordinates of all the ground stations are calculated. Now shift of these ground stations because of tectonic plate movement is calculated for a period of time and correction is applied to their co-ordinates. From these corrected coordinates position of the reference meridian is calculated backward. Each station will give a slightly different value of reference meridian because of correction applied for tectonic plate movement is not hundred percent accurate so an average of these positions is taken to obtain the position of reference meridian.

## WHY GEOID MODEL IS REQUIRED?

In any datum(WGS 84, NAD 83, ETRS 89) there are two kind of datums embedded first is horizontal datum and another is vertical datum. Understand it like this horizontal datum tell’s us reference point’s from where we can locate our position on the globe but it gives no information about the height of a particular object. For this a vertical datum is used don’t get confused in words vertical datum is nothing but just specifying a reference from where all heights are measured. For local datums, it can be anything as desired by the local government, for example, Mean Sea Level, MHHW level etc. But for a universal datum like WGS 84, it can’t work on MSL of any country. Say if WGS 84 use mean Sea level of a certain place in the US. Then readings of height all over the world will be absurd. To overcome this difficulty WGS 84 uses a geoid model of the earth as a reference for calculating heights. To be more precise it uses EGM 96 (Earth Gravitational Modal 96) as its geoid model for vertical datums. Another way of saying it is that EGM 96 defines the sea level for WGS 84. And GPS uses WGS 84 coordinate system(datum) to define position. So EGM 96 defines sea level for height calculations by GPS. And this is logical too because if instead of the geodetic model if reference ellipsoid would have been chosen to define sea level, again heights shown by GPS might go in negative, also if you are sitting on a beach it might show that you are actually 100 m above sea level. Because reference ellipsoid is passing 100 meters below you. To solve this problems geoid is used to define sea level/ reference level above which heights are measured.As it represents earth more accurately then reference ellipsoid.

Please note that horizontal datum of the nautical chart may be WGS 84 but for height, determination charts use local vertical datums mostly( local MSL, or MHHW or Lowest astronomical tide of an area). Say if the chart is showing a depth of 30 meters it means land is below water surface by 30 m at times of lowest astronomical tide(not at 30 m below geoid). So charts cleverly use WGS 84 as their horizontal datum so GPS position can be plotted directly on the chart. And local datum for depths and heights because that is more relevant to a mariner. Mostly lowest astronomical tide for depths and mean high water spring for heights is used as a reference, but it is not necessary and depends on upon the decision of the local government.

# OVERVIEW

Here we just quickly revise what we have learned today. Datum is nothing but a coordinate system designed for deriving position(lat, long, height) of an object on earth. Any datum basically has two components first is horizontal datum which determines latitude and longitude with help of a reference ellipsoid and a reference meridian. And vertical datum provides us a reference from which heights are measured. Our most common WGS 84 uses a reference ellipsoid of specified dimensions and IRES reference meridian as a prime meridian for horizontal datum and EGM 96(a geodetic model fo earth)

as a reference to determine the height of an object. Different datums use different reference ellipsoid, reference meridians, and vertical datums so while we compare positions of two different datums there will always be a shift in a position called datum shift.

Now again read the initial definition of WGS 84 as written above I bet you will understand most of it by now.If you think this article was worth reading please like it, share it and comment on it. Also give me your valuable suggestions. “AS LONG AS YOU KEEP ME INSPIRING, I WILL KEEP ON WRITING”

Fun Facts:

While writing this article I was stuck at geoid because It was too difficult to be understood by me, first I searched the internet but I still had doubts, so in my desperation I searched geophysicist and geologist on facebook and sent a custom prepared message to all of them asking them to help me clear my doubts. To my surprise, some of them did reply and offered their help. Thanx to them. But I am still not sure about it and need to dig deeper.