The document explores the concept of total horizontal and vertical uncertainty in hydrographic surveying, emphasizing the critical importance of accurate coordinates for safe navigation and marine activities. It details the sources of uncertainty, methods for calculating both horizontal and vertical uncertainties, and provides standards for different survey orders to ensure data accuracy. The report underscores that precise measurements are essential for effective hydrographic surveying, particularly in environments where water levels and depths fluctuate.

1. (The concept of total Horizontal
and Vertical Uncertainty)
Student Name: Copyright
Class: 4th
Stage
Course Title: Hydrographic
Department: Geomatics (Surveying) Engineering
College of Engineering
Salahaddin University-Erbil
Academic Year 2019-2020

2. 1
Abstract
My aim in this report is showing The Importance and significance the subject
of hydrographic which is important science in our life especially for some
countries that's covered with the water or let's say the large amount of water
so we knew that survey engineer deals with the coordinates measurement,
errors ,accuracies , other sectors so hydrographic surveyor should observing
carefully because it deals with the water as we know water let's say level of
the water is not suitable changes from place to another due to the gravity of
the Earth and all above mentioned it should be considered for the the
movement of the ships the other water vehicles in the water .
Consequently the results I mean the results of coordinates as much as
possible must be accurate and precise, so in this report I showed and
mentioned the two types of uncertainty which are (horizontal uncertainty and
vertical uncertainty) and I mentioned the reasons and the sources that
affecting on the accuracy and uncertainty.
Of course we knew that if the data wrong and contain errors so the process
and the procedure will contain errors at the end the result will be inaccurate
and we get inaccurate coordinates that's not acceptable, therefore accurate
data means accurate procedure, accurate result at the end accurate
coordinates and useful coordinates.

3. 2
Table of Contents
Subject page
Abstract..........................................................................................................1
Table of Contents ..........................................................................................2
Chapter one - Introduction ............................................................................3
Chapter Two - Background & Review.........................................................5
Chapter Three - Method ................................................................................7
3.1. Horizontal Uncertainty .......................................................................7
3.2.Vertical Uncertainty.............................................................................8
Chapter four - theory...................................................................................13
Conclusion...................................................................................................17
Reference.....................................................................................................18

4. 3
Chapter One - Introduction
Positioning is the fundamental framework and starting point for every survey
operation. The position of any point (e.g. sounding, feature, etc.) can be
referenced using either geodetic coordinates defined by latitude (ϕ),
longitude (λ) and ellipsoid height (һ) or Cartesian coordinates (x, y, z).
Positions should be referenced to a geodetic reference frame, which can be
the realization of either a global (e.g. ITRS, WGS84) or a regional (e.g.
ETRS89, NAD83) reference system. As there are frequent updates to
geodetic reference systems, it is essential that the epoch is recorded for
surveys with low positioning uncertainty. Since positions are most often
referenced in a compound coordinate reference system such as geodetic,
geopotential, and height reference system, they can therefore be separated
into horizontal and vertical components during the survey process.
1.Horizontal Reference Frame If horizontal positions are referenced to a
local horizontal datum, the name and epoch of the datum should be specified
and the datum should be tied to a realisation of the ITRS (i.e. ITRFxx,) or
equivalent global geodetic reference frame (e.g. ITRS, WGS84, ETRS89,
NAD83 realisations). Transformations between reference frames/epochs
have to be taken into account, especially for surveys with low uncertainty.
2. Vertical Reference Frame If positions are referenced to a local vertical
datum, the name and epoch of the datum should be specified. Vertical
positions (e.g. depths, drying heights) should be referenced to a vertical
reference frame that is suitable for the data type and intended use. This
vertical reference frame may be based on tidal observations (e.g. LAT), on a
physical model (i.e. geoid) or on a geometric reference frame. height system
that is suitable for the data type and intended use such as Lowest
Astronomical Tide (LAT), a geoid model, or a reference ellipsoid.

5. 4
3. Uncertainties Position uncertainties must be expressed at the 95%
confidence level and should be recorded together with the survey data. The
capability of the survey system should be demonstrated by an a priori
positioning total propagated uncertainty (TPU) calculation. This statistical
calculation is predictive in nature and must be calculated for the survey
system as a whole, including all instrument, system integration and in-situ
environmental uncertainty. The a priori calculation should be updated during
the survey to reflect deviations from expected environmental conditions in
order to optimize the a priori TPU calculation. Whenever possible, an a priori
positioning TPU should be supplemented by an a posteriori positioning
uncertainty assessment based on measurement repeatability or comparison
that will validate the agreement between the a priori TPU and the a posteriori
uncertainty assessment. The positioning TPU may be separated into total
horizontal uncertainty (THU) and total vertical uncertainty (TVU)
components.

6. 5
Chapter Two - Background & Review
Hydrography is the branch of applied sciences which deals with the
measurement and description of the physical features of oceans, seas, coastal
areas, lakes and rivers, as well as with the prediction of their change over
time, for the primary purpose of safety of navigation and in support of all
other marine activities, including economic development, security and
defiance, scientific research, and environmental protection. (International
Hydrographic Organization).
The scientific description and analysis of the physical conditions,
boundaries, flow, and related characteristics of the earth's surface waters.
Figure 1 : Hydrographic survey

7. 6
Error Sources:
Although the following text focuses on errors in data acquired with swath
systems, it should be noted that it is in principle applicable to data acquired
with any depth measurement system.
With swath systems the distance between the sounding on the sea floor and
the positioning system antenna can be very large, especially in deep water.
Because of this, sounding position uncertainty is a function of the errors in
vessel heading, beam angle and the water depth.
Uncertainties associated with the development of the position of an
individual beam must include the following:
1) Positioning system errors, and range and beam errors.
2) The error associated with the ray path model (including the sound speed
profile), and the beam pointing angle.
3) The error in vessel heading.
4) System pointing errors resulting from transducer misalignment.
5) Sensor location, and vessel motion sensor errors i.e. roll and pitch.
6) Sensor position offset errors, and time synchronisation / latency.
Contributing factors to the vertical uncertainty include:
1) Vertical datum errors, and vertical positioning system errors.
2) Tidal measurement errors, including co-tidal errors where appropriate.
3) Instrument errors, and Sound speed errors.
4) Ellipsoidal / vertical datum separation model errors.
5) Vessel motion errors, i.e. roll, pitch and heave.
6) Vessel draught, and vessel settlement and squat, and sea floor slope.

8. 7
Chapter Three - Method
3.1 Horizontal Uncertainty
POSITIONING
Horizontal Uncertainty
The uncertainty of a position is the uncertainty at the position of the sounding
or feature within the geodetic reference frame. Positions should be
referenced to a geocentric reference frame based on the International
Terrestrial Reference System (ITRS) e.g. WGS84. If, exceptionally,
positions are referenced to the local horizontal datum, this datum should be
tied to a geocentric reference frame based on ITRF.
The uncertainty of a position is affected by many different parameters; the
contributions of all such parameters to the total horizontal uncertainty (THU)
should be accounted for.
A statistical method, combining all uncertainty sources, for determining
positioning uncertainty should be adopted. The position uncertainty at the
95% confidence level should be recorded together with the survey data.
The capability of the survey system should be demonstrated by the THU
calculation.
The position of soundings, dangers, other significant submerged features,
navaids (fixed and floating), features significant to navigation, the coastline
and topographical features should be determined such that the horizontal
uncertainty meets the requirements specified in Table1. This includes all
uncertainty sources not just those associated with positioning equipment.

9. 8
3.2Vertical Uncertainty
DEPTHS
The navigation of vessels requires accurate knowledge of the water depth in
order to exploit safely the maximum cargo carrying capacity, and the
maximum available water for safe navigation. Where under-keel clearances
are an issue the depth uncertainties must be more tightly controlled and better
understood. In a similar way, the sizes of features that the survey will have
or, more importantly, may not have detected, should also be defined and
understood.
The measured depths and drying heights shall be referenced to a vertical
datum that is compatible with the products to be made or updated from the
survey e.g. chart datum. Ideally this sounding datum should also be a well-
defined vertical datum such as, LAT, MSL, a geocentric reference frame
based on ITRS or a geodetic reference level.
 Vertical Uncertainty
Vertical uncertainty is to be understood as the uncertainty of the reduced
depths. In determining the vertical uncertainty the sources of individual
uncertainties need to be quantified. All uncertainties should be combined
statistically to obtain a total vertical uncertainty (TVU).
The maximum allowable vertical uncertainty for reduced depths as set out in
Table 1 specifies the uncertainties to be achieved to meet each order of
survey. Uncertainty related to the 95% confidence level refers to the
estimation of error from the combined contribution of random errors and
residuals from the correction of systematic errors. The capability of the
survey system should be demonstrated by the TVU calculation.
Recognizing that there are both depth independent and depth dependent
errors that affect the uncertainty of the depths, the formula below is to be
used to compute, at the 95% confidence level, the maximum allowable TVU.
The parameters “a” and “b” for each order, as given in Table 1, together with
the depth “d” have to be introduced into the formula in order to calculate the
maximum allowable TVU for a specific depth:

10. 9
±√a2 + (b × d)2…………….equation (1)
Where:
a: represents that portion of the uncertainty that does not vary with depth
b: is a coefficient which represents that portion of the uncertainty that varies
with depth.
d: is the depth.
b x d : represents that portion of the uncertainty that varies with depth
The vertical uncertainty at the 95% confidence level should be recorded
together with the survey data.
Figure 2. Total Vertical Uncertainty (TVU) variation for Special Order, Order 1a and 1b
surveys.

11. 10
TABLE 1: Minimum Standards for Hydrographic Surveys
Order Special 1a 1b 2
Description of areas. Areas where under-keel
clearance is critical
Areas shallower than 100
metres where under-keel
clearance IS less critical
but features of concern to
surface shipping may
exist
Areas shallower than 100
metres where under-keel
clearance is not considered
to be an issue for the type
of surface shippmg
expected to transit the area.
Areas generally deeper
than 100 metres where a
general description of the
sea floor is considered
adequate
Maximum allowable
THU 95% Confidence
lever'
2 metres 5 metres + 5% of depth 5 metres + 5% of depth 20 metres + 10% of depth
Maximum allowable
TNT 95% Confidence
lever'
a=0.25metre
b= 0.0075
a=0.5metre
b= 0.013
a=0.5metre
b= 0.013
a=1.0metre
b= 0.023
Full Sea floor Search Required Not required Not required
Feature Detection Cubicfeatures > 1 metre Cubic features 2 metres,
in depths up to 40
metres; 10% of depth
beyond 40 metres
Not Applicable Not Applicable
Recommended maximum
Line Spacing
Not defined as full sea
floor search is required
Not defined as full sea
floor search is required
3 x average depth or 25
metres, whichever is
greater For bathymetric
lldar a spot spacing of 5 x
5 metres
4 x average depth
Positioning of fixed aids
to navigation and
topography significant
to navigation. (95%
Confidence level)
2 metres 2 metres 2 metres 5 metres
Positioning of the
Coastline and
topography less
significant to navigation
(95% Confidence level)
10 metres 20 metres 20 metres 20 metres
Mean position of floating
aids to navigation (95%
Confidence level)
10 metres 10 metres 10 metres 20 metres
Notes:
1: Recognising that there are both constant and depth dependent uncertainties
that affect the uncertainty of the depths, the formula below is to be used to
compute, at the 95% confidence level, the maximum allowable TVU. The
parameters “a” and “b” for each Order, as given in the Table, together with

12. 11
the depth “d” have to be introduced into the formula in order to calculate the
maximum allowable TVU for a specific depth:
±√a2 + (b × d)2 ………….. Eq (1)
Where:
a: represents that portion of the uncertainty that does not vary with depth
b :is a coefficient which represents that portion of the uncertainty that varies
with depth
d :is the depth
b x d: represents that portion of the uncertainty that varies with depth
2: For safety of navigation purposes, the use of an accurately specified
mechanical sweep to guarantee a minimum safe clearance depth throughout
an area may be considered sufficient for Special Order and Order 1a surveys.
3: A cubic feature means a regular cube each side of which has the same
length. It should be noted that the IHO Special Order and Order 1a feature
detection requirements of 1 meter and 2 meter cubes respectively, are
minimum requirements. In certain circumstances it may be deemed
necessary by the hydrographic offices / organizations to detect smaller
features to minimize the risk of undetected hazards to surface navigation. For
Order 1a the relaxing of feature detection criteria at 40 meters reflects the
maximum expected draught of vessels.
4: The line spacing can be expanded if procedures for ensuring an adequate
sounding density are used. "Maximum Line Spacing" is to be interpreted as
the: - Spacing of sounding lines for single beam echo sounders, or the -
Distance between the useable outer limits of swaths for swath systems.
5: These only apply where such measurements are required for the survey.
Example one :
Define the order of the following depths and calculate the horizontal &
vertical uncertainty for table 2.

13. 12
Sounding 43.25m 74.3m 81.97m
Description Under - keel
clearance critical
Features detection
is not applicable
Features of concern
to surface shipping
may exist.
Distance Class THU TVU
43.25m Special ±2𝑚 a=0.25, b=0.0075
𝑇𝑉𝑈 = √(√𝑎2 + (𝑏 ∗ 𝑑)2
= ±0.4095𝑚
74.3m 1b THU= 5𝑚 + 5 ×
(74.3) =
±8.715𝑚
a=0.5,b=0.013
𝑇𝑉𝑈 = √(√𝑎2 + (𝑏 ∗ 𝑑)2
= ±1.0876𝑚
81.97m 1a THU= 5𝑚 + 5 ×
(81.97) =
±9.0985𝑚
a=0.5,b=0.013
𝑇𝑉𝑈 = √(√𝑎2 + (𝑏 ∗ 𝑑)2
= ±1.1770𝑚
Table 2
Table 3: answer for example one

14. 13
Chapter four - theory
1 Horizontal Position Uncertainty the NOS specification for hydrographic
positioning is that the Total Horizontal Uncertainty (THU) in position of
soundings, at the 95 percent confidence level, will not exceed 5 m + 5 % of
the depth. This accuracy requirement is independent of survey scale. For
hydrographic surveys using single-beam echosounders, the uncertainty of
the vessel position can be considered the THU of the sounding obtained by
that vessel, taking into account transducer offsets. However, for multibeam
surveys, due to the oblique sounding pattern, the position of a sounding may
be at some distance from the vessel position. The uncertainty requirement
for the vessel position will depend upon how accurately the sounding is
positioned relative to the vessel. That, in turn, will depend upon the
characteristics of the multibeam system, depth of water, the accuracy with
which heave, roll, pitch, heading, and latency are accounted for and applied,
and the reliability with which the speed of sound profile is known.
”Uncertainty Budget Analysis for Depths”, for a more detailed discussion of
those specifications related to horizontal positioning uncertainty.
Positions reported in survey records and deliverables shall be recorded in
meters, with a precision of at least decimeters. This precision shall be
maintained throughout the processing pipeline and digital data.
2 Vertical Position Uncertainty This section applies to depths or heights
obtained through 3D-positioned surveying. Total allowable vertical
uncertainty for reduced soundings is detailed”Uncertainty Standards”. There
is no intrinsic maximum allowable uncertainty prescribed for vertical
positioning accuracy.
The hydrographer must account for all of the uncertainties which contribute
to the vertical position, and ensure that their combined effect does not cause
the total vertical uncertainty for soundings to exceed the allowable limits.

15. 14
Definition
definition given below should be used in relation to these standards.
Accuracy: The extent to which a measured or enumerated value agrees with
the assumed or accepted value (see: uncertainty, error).
Confidence level: The probability that the true value of a measurement will
lie within the specified uncertainty from the measured value. It must be noted
that confidence levels (e.g. 95%) depend on the assumed statistical
distribution of the data and are calculated differently for 1 Dimensional (1D)
and 2 Dimensional (2D) quantities. In the context of this standard, which
assumes Normal distribution of error, the 95% confidence level for 1D
quantities (e.g. depth) is defined as 1.96 x standard deviation and the 95%
confidence level for 2D quantities (e.g. position) is defined as 2.45 x standard
deviation.
Correction: A quantity which is applied to an observation or function
thereof, to diminish or minimise the effects of errors and obtain an improved
value of the observation or function. It is also applied to reduce an
observation to some arbitrary standard. The correction corresponding to a
given computed error is of the same magnitude but of opposite sign.
Error: The difference between an observed or computed value of a quantity
and the true value of that quantity. (NB The true value can never be known,
therefore the true error can never be known. It is legitimate to talk about error
sources, but the values obtained from what has become known as an error
budget, and from an analysis of residuals, are uncertainty estimates, not
errors. See uncertainty.)
Feature: in the context of this standard, any object, whether manmade or
not, projecting above the sea floor, which may be a danger for surface
navigation.
Feature detection: The ability of a system to detect features of a defined
size. These Standards specify the size of features which, for safety of
navigation, should be detected during the survey.

16. 15
Full sea floor search: A systematic method of exploring the sea floor
undertaken to detect most of the features specified in Table 1; utilising
adequate detection systems, procedures and trained personnel. In practice, it
is impossible to achieve 100% ensonification / 100% bathymetric coverage
(the use of such terms should be discouraged).
Reduced depths: Observed depths including all corrections related to the
survey and post processing and reduction to the used vertical datum.
Sea floor search: A systematic method of exploring the sea floor in order to
detect features such as wrecks, rocks and other obstructions on the sea floor.
Sounding datum: The vertical datum to which the soundings on a
hydrographic survey are reduced. Also called „datum‟ for sounding
reduction.
Total horizontal uncertainty (THU): The component of total propagated
uncertainty (TPU) calculated in the horizontal plane. Although THU is
quoted as a single figure, THU is a 2 Dimensional quantity. The assumption
has been made that the uncertainty is isotropic (i.e. there is negligible
correlation between errors in latitude and longitude). This makes a Normal
distribution circularly symmetric allowing a single number to describe the
radial distribution of errors about the true value.
Total propagated uncertainty (TPU): the result of uncertainty
propagation, when all contributing measurement uncertainties, both random
and systematic, have been included in the propagation. Uncertainty
propagation combines the effects of measurement uncertainties from several
sources upon the uncertainties of derived or calculated parameters.
Total vertical uncertainty (TVU): The component of total propagated
uncertainty (TPU) calculated in the vertical dimension. TVU is a 1
Dimensional quantity.
Uncertainty: The interval (about a given value) that will contain the true
value of the measurement at a specific confidence level. The confidence level
of the interval and the assumed statistical distribution of errors must also be
quoted. In the context of this standard the terms uncertainty and confidence
interval are equivalent.

17. 16
Uncertainty Surface: A model, typically grid based, which describes the
depth uncertainty of the product of a survey over a contiguous area of the
skin of the earth. The uncertainty surface should retain sufficient metadata
to describe unambiguously the nature of the uncertainty being described.
Figure 3 : vertical and horizontal uncertainty

18. 17
Conclusion
Finally it had been shown the importance hydrographic surveying with it is
methods within all application and advantages of these methods for us and
we knew that the most important thing in hydrographic surveying is
coordinate and the most important thing in coordinate is accuracy and
uncertainty that must be accurate data for the purpose of getting accurate and
corrected coordinates and also we learnt the IHO standards that should be or
used in hydrographic survey measurement and observation.

19. 18
Reference
[1] - International Hydrographic Organization (IHO)
http://www.iho.int
[2] - https://confluence.qps.nl/qinsy/9.1/en/how-to-total-propagated-
uncertainty-tpu-182619364.html
[3] - Ellipsoidally Referenced Surveying for Hydrography
https://www.fig.net/resources/publications/figpub/pub62/Figpub62.pdf
[4] - https://meridian.allenpress.com/jcr/article/doi/10.2112/SI76-
002/27968/Depth-Calibration-and-Validation-of-the