{'fraction_non_alphanumeric': 0.03004462862607587, 'fraction_numerical': 0.010519604717883328, 'mean_word_length': 4.557573073516386, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 1, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Comparison of different height systems

Geopotential, dynamic, orthometric and normal height systems and the corrections related to these systems are evaluated in this paper. Along two different routes, with a length of about 5 kilometers, precise leveling and gravity measurements are done. One of the routes is in an even field while the other is in a rough field. The magnitudes of orthometric, normal and dynamic corrections are calculated for each route. Orthometric, dynamic, and normal height differences are acquired by adding the corrections to the height differences obtained from geometric leveling. The magnitudes of the corrections between the two routes are compared. In addition, by subtracting orthometric, dynamic, and normal heights from geometric leveling, deviations of these heights from geometric leveling are counted.


Introduction
To determine heights of earth points, an origin surface with zero height must be described and the vertical distance of points from the surface must be determined. For heights, a variety of surfaces can be taken as reference. Of these, the most important surface is the geoid.
Reference surfaces and vertical distances of points from the surfaces have different physical and geometric meanings. Geodetic heights also have different physical and geometric meanings. Thus, several height systems have been introduced. Different height systems were examined in this study.

.1 Geopotential and dynamic heights
Geopotential height or geopotential number is a surface point's potential difference to the geoid po-tential. Put (1) can be obtained by the integral from Eq. (1). A C is known as the geopotential number and is path-independent; O W is the geoid potential; A W is a point's potential; dW is the potential difference in differential meaning; dn is the height difference in differential meaning; g is gravity.
The geopotential number is measured in kgal• m and C is equal in the same equipotential surface. Although it has no distance dimension, it is the natural criterion for heights.
Dynamic heights have been obtained from Eq. (2). The geopotential number is divided by the 0 γ constant where 0 γ is the normal gravity value at 45° latitude. The value is 45 o γ = 980.629 4 gal for international ellipsoids [1,2] .

Orthometric height
The distance of a surface point along the plumb line to the geoid, which is taken as the reference surface, is named the orthometric height. It can be obtained as follows: For the computation of actual average gravity g along the plumb line, actual gravity is required between the geoid and earth surface. However, gravity inside the earth can not be measured so a hypothesis regarding the mass distribution must be formed and g is computed on this basis. The orthometric height can not be determined without a hypothesis.
Orthometric heights are the natural "heights above sea level", that is, heights above the geoid. Therefore, they have an unequalled geometrical and physical significance [3] .

Normal height
The ellipsoid is the reference surface best resembling the geoid, which is the earth's basic shape. An ellipsoid's gravity field is called a normal gravity field. The Earth's actual gravity field is slightly different from the normal gravity field. The difference is called the disturbing potential.
We are going to assume that the actual gravity field is equal to the normal gravity field. In other words, we assume , , 0. W U g T γ = = = Hence, orthometric heights which correspond to this approximation are named normal heights and are shown by N H . They can be obtained as follows: where W is the actual gravity potential; U is the normal gravity potential; T is the disturbing potential; γ is the normal average gravity along a normal plumb line. A surface point P has W P actual and P U normal gravity potential and these potentials are not equal ( P P W U ≠ ). But on the plumb line that crosses point P, there is a Q point. In this Q point, the normal potential is equal to the actual potential ( P Q W U = ). The surface for which P Q W U = holds for every point is called a "Telluroid". The normal N H of a point P is equivalent to the height of the corresponding telluroid point Q above the ellipsoid (Fig.1).

Fig.1 Orthometric and Normal Heights
The physical and geometric meanings of normal heights are less obvious; they are dependent on the reference ellipsoid used [2] .

Computation of heights and corrections
Dynamic, orthometric and normal heights are obtained by using the geopotential number or by adding a correction magnitude to the result of leveling. In practice, these heights are generally obtained by making corrections to the result of leveling. In this study, these heights have also been computed by adding corrections.

Computation of geopotential heights
The geopotential height difference between two points is the geopotential height difference between points A and B; g is the measured actual gravity along the route; dn is the height difference in the meaning of the differential.

Dynamic height correction and dynamic height computation
In practice, height differences ( AB n Δ ) measured by leveling are converted into dynamic heights by adding a correction magnitude. This correction is called a dynamic correction ( AB DC ). It is calculated as follows: is obtained from Eq.(7) [1,4] .

Orthometric correction and orthometric height computation
Height differences ( AB n Δ ) measured by leveling are converted into orthometric heights by adding a correction magnitude. This correction is called an orthometric correction ( AB OC ). It is calculated as follows: where g is the actual gravity measured along the route; , A B g g are the actual average gravity. Actual average gravity values can be computed either by using this equation * 0.042 4 g g H = + (9) (The unit of g is gal; H * is km) or by using the reduction of Prey where g is the gravity measured on point A; 0 g is the gravity measured on point 0 A on the geoid corresponding to point A. Eq.(10) was put forward by Mader in 1954. Here, g is accepted to be linearly changing along the plumb line.
Consequently, the * AB H Δ orthometric height difference is given by In correction computations, 0 γ is taken as a constant gravity value (usually normal gravity 45 0 γ for the geographic latitude 0 45 ϕ = ) [1] .

Normal correction and normal height computation
Height differences ( AB n Δ ) measured by leveling are converted into normal heights by adding a correction magnitude. This correction is called a normal correction (

AB NC
γ is obtained as follows: ; ω is the angular velocity of the earth's rotation; a is the semi major axis of the ellipsoid, and b is the semi minor axis of the ellipsoid [3] .

Lang measures
To compute geopotential, dynamic, orthometric and normal heights, various measurements were done along two different routes. These routes' lengths are nearly equal but one is relatively even while the other is rough land.

Study area
Application was done along two different routes. The first route is relatively even, approximately 5.25 km in length and has a 7.87 m height difference. This route lies between RS points. These RS points have been established by mapping authorities in Trabzon, Turkey (Fig.2).
The second route is relatively rougher, approximately 4.78 km in length, and has a 385 m height difference. The route's initial and final points have been established by another project at the Karadeniz Technical University in Trabzon , Turkey (Fig.3).

Precision Leveling
Precision leveling was done according to a double run measure plan. In the measurements, the double run's difference does not exceed 6 K mm (K is the length of the route in km units). Leveling was done with a DL-101C electronic digital leveler. To improve both accuracy and precision, invar rods were operated with two ground plates. In addition, backward and foresight distances were taken to be equal while maximum sighting distances were 30 m for 30x magnification [5] .
The heights of the initial and final points are as follows: H

Gravity measurements
For these measurements, a Worden Master Gravimeter was used. First, the instrument's constant was checked in the port of Trabzon. The values read inland were multiplied by the instrument constant to arrive at values measured in mgal [6] Along the first route, gravity measurements were done in every other point established digital level with simultaneous leveling. The gravity values of the omitted points were determined by interpolating the gravity values at the points which were measured.
Since the second route is rougher, gravity measurements were done more frequently, approximately with 70~100 intervals.
The gravity values of the omitted points were also determined by interpolating the gravity values at the points which were measured.

GPS measurements
For determining the latitudes of the routes' initial and final points, we have used a SPORTRAK Map (MAGELLAN) handheld GPS device. By using the latitude values in Eq.(14), we obtained the normal gravity values ( γ ) of the routes' initial and final points.

Results and evaluation
Height differences obtained by leveling along routes are shown in Table 1. Actual average gravity g , normal gravity i γ and normal average gravity γ have been alternately obtained by Eqs.(9), (14) and (13) and these values are shown in Table 2. Table 3 was prepared using Table 2 and by measurements done inland. In this table, dynamic, orthometric and normal corrections are shown. Here, dynamic corrections have been computed from Eq.(6), orthometric corrections have been computed from Eq.(8) and normal corrections have been computed from Eq.(12). Thus, we could compute geopotential, dynamic, orthometric and normal height differences for each route as double runs. Table 5 has been prepared from  Table 4 by subtracting going and turning measurements from each other. These differences are very small, smaller than a mm unit. This is because the going and turning routes are partly the same. Geopotential height differences were computed using Eq.(5). Computed corrections were added to the measured height differences like the markings in Eqs.(7), (11) and (15). Then, Table 4 was prepared. Average heights were obtained by taking the average of going and turning height differences using Table 4. These average heights are shown in Table 6. By making use of the data in Table 6 and Table 1, all of the height differences were subtracted from average geometric height differences. Then, Table 7 was prepared. In this table, we can see the minimum deviation of height from geometric leveling.
According to Table 7, the dynamic correction is one hundred fold bigger than the orthometric correction and the normal correction is twofold bigger than the orthometric height in the even field (first route). Along the rough route (second route), the dynamic correction is twenty fold bigger than the orthometric correction and the normal correction is twofold bigger than the orthometric height.
For each route, the smallest correction is the orthometric correction. The normal correction is closer to the orthometric correction but the dynamic correction is much bigger than the other two.

Conclusions
1) In the even field, the orthometric correction is smaller than a mm level but in the rough field, it is at mm level. The normal correction is smaller than the mm level in the even field, but in the rough field it is at cm level. The dynamic correction is at mm level in the even field but in the rough field it is at dm level.
Therefore, we can conclude that in even fields all of the corrections are too small but in the rough fields these values increase.
2) The difference of dynamic, orthometric and normal heights from geometric leveling are as follows, respectively: along the first route, which is nearly 5 km in length and has a 7 m height difference, they are -3 mm, -0.03 mm and 0.04 mm. Along the second route, which is nearly 5 km in length and has a 387 m height difference, they are -15 cm, 8 mm and 1.7 cm.
Here, the corrections can be arranged in order from small to large as the orthometric, normal and dynamic correction.
3) The smallest correction is the orthometric correction. The height type which deviates the least from geometric leveling is the orthometric height. 4) Orthometric heights have been found to be the best kind of height in geodesy. This is because their correction magnitudes are small, and they take the geoid as the reference surface as well as their geometric meaning.