Soil and Water Management. An Introductory Textbook

Textbook, 2020

162 Pages


Table of Content


Introduction to Surveying and Mapping
1.1 Introduction.
1.2 Importance of surveying
1.3 Types of surveys
1.4 Basic Error Theory
1.5 Classification of errors
1.6 Mapping in soil and water management
1.7 Methods of Distance Measurement
1.8 Direct Distance Measurement (DDM)
1.9 Obstacles in linear distance measurement
1.10 Slope distance measurement
1.11 Errors in taping
1.12 Optical distance measurement (ODM)
1.13 Electronic Distance Measurement (EDM)
1.14 Worked examples

Chapter 2
Determination of Land Area
2.1 Determination of Land Area
2.2 Methods of estimating area
2.3 Offsets
2.4 Trapezoidal rule
2.5 Simpsons rule
2.6 Other methods of area determination.
2.7 Worked example

Chapter 3
3.1 Introduction to levelling
3.2 Applications of levelling
3.3 Principles of levelling
3.4 Standard booking sheet
3.5 Plotting the Profile
3.6 Worked examples

Chapter 4
Contours and Contouring
4.1 Contours and Contouring
4.2 Applications of Contours
4.3 Characteristics of Contours
4.4 Methods of Locating Contours
4.5 Land features
4.6 Determination of land slope

5 Compass Surveying
5.1 Compass Surveying
5.2 Designation of bearings
5.3 Systems of Bearings
5.4 Conversion of bearings
5.5 Fore Bearing (FB) and Back Bearing (BB)
5.6 Local attraction.
5.7 Elimination of local attraction.
5.8 Traverse Survey
5.9 Procedure for traverse layout
5.10 Types of traverse
5.11 Traverse computation.
5.12 Review Questions-Section.



Chapter 6
Soil and Water Conservation.
6.10 The bottle test procedure for soil texture

Chapter 7
Hydrological Process

Chapter 8
Soil Erosion by Water
8.1 Soil Erosion Process
8.2 Factors affecting erosion by water
8.3 Visual Indicators of Soil Erosion.
8.4 Erosion Measurement
8.5 Forms of Erosion.
8.6 Erosion by Water
8.7 Water-induced Forms of soil erosion.
8.8 The Universal Soil Loss Equation (USLE)
8.9 Worked Examples
8.10 Review Questions

Chapter 9
Erosion by Wind
9.1 Wind erosion process
9.2 Factors affecting wind erosion.
9.2.1 Climate
9.2.2, land surface conditions
9.2.3 Soil properties
9.2.4 Land use/cover management
9.3 Forms of wind erosion.
9.4 Measurement of wind erosion.
9.5 Control of wind erosion.
9.6 Wind erosion equation (WEQ)
9.7 Wind erosion models
9.8 Worked examples
9.9 Review questions

Chapter 10
Methods of Controlling Soil Erosion.
10.1 Introduction to method of erosion control
10.2 Cultural/biological practices
10.3 Physical Measures
10.4 Terraces
Categories and types of bench terraces
10.5 Cross-sectional area of bench terrace
10.6 Field Terrace design and layout
10.8 Worked Examples
10.9 Review Questions



I express my sincere gratitude to the following people;

To my university mentors, namely Prof. Dr.-Ing. Benedict M. Mutua and Dr. (Eng). James M. Raude who has always made valuable assessment and suggestions for academic writing in Agricultural Engineering and related fields.

To my students I have taught over the years specifically in the fields of Agricultural Engineering, Agricultural Education and Extension, Water and Environmental Engineering, General Agriculture. Through class participation, the students training materials demand helped me formulate a vision for writing simplified books for learners and align it to University curriculum requirements.

‘Soil and Water management’ is part of my long-term personal interest that began numerous years ago when I was a small boy with acumen in writing and publishing. It has taken time to come up with a manuscript with worthwhile content. I hope the text book will be useful in learning and application scenarios.

Raphael M. Wambua


This book is dedicated to students in Agricultural Education and extension, Horticulture, Farm management and Agronomy who use it to gain theoretical and practical skills of soil and water management and contribute to improved food security.

Instructors in higher education that find it useful in guiding and teaching at the institutions of higher learning; and This book is also dedicated to relevant professionals and field officers in soil and water management, especially the ones who use this book for reference in matters soil and water management -theory and field application.


Soil and Water Management is a text book intended for students and instructors in University or higher education for Certificate, Diploma and Degree students in a number of courses such as General Agriculture, Agricultural Education and Extension, Horticulture and other allied professions.

The content of the text book has been presented in a coherent format, arranged in an explicit style that adheres to University and higher education curriculum. The textbook is partitioned into section A and section B with Review questions at the end to explicitly help the trainees comprehend the topics. This makes the book suitable for easy reading. For the calculations, worked examples have been solved in a way of illustration and details are presented. Each chapter of the book has worked examples for the readers to expound on subject knowledge.

Raphael M. Wambua



Chapter 1

Introduction to Surveying and Mapping

Aims of the Chapter

The aim of this chapter is to offer knowledge and skills on:

- Introduction to surveying and its application in soil and water management
- Methods of measuring linear distance
- Distance Measurement on farm lands
- Field barriers and how to navigate through them during distance measurement
- Basic error theory in linear distance measurement
- Error correction in direct distance measurement

1.1 Introduction

Soil and water management refers to the application of the practices and operations that help in protection and conservation of soil and water for their enhanced performance and environmental needs. There are some practices and operations that require ‘surveying’ for the purpose of exploring and studying land where soil and water management is required. Thus the need to acquire some knowledge and skills of surveying as applied in soil and water management. The forces behind the soil erosion range from those caused by the main agents of soil erosion to those induced by climate change. To manage the soil and water for improved agricultural production all those forces causing any change should be considered.

Surveying refers to art and science of determining the relative positions of points on, above and below the surface of the earth by means of measurements in three elements of space namely distance, direction and elevation and presentation of this information in graphical or numerical form.

The dimensions of distance and elevation are measured in units of length while that of direction is measured in units of arc. Thus all surveying operations comprise the measurement of distance (horizontal and vertical) and angles. The resulting survey data may lead to computation of areas and volumes.

1.2 Importance of surveying

Survey is required during the planning, design, layout and construction of:

i) Soil conservation structures such as cut-off drains, water ways, terraces and gabions
ii) Water conservation structures including dams and water pans
iii) Irrigation systems
iv) Water supply and sewage systems layout
v) Drainage works
vi) Layout of pipeline for fluid transmission
vii) Tunnel design
viii) Farm Road, highways and railroads

Thus surveying is used for two specific purposes. These are to:

i) Make maps, charts and profiles: the maps are used to define land boundaries, size, shape and location of land and other objects
ii) Determination of positions: Layout and marking of the desired positions of objects and or features to be constructed is conducted

1.3 Types of surveys

Surveys can be classified based on three aspects; size of the earth surface covered, purpose of the survey, surveying techniques and survey equipment used during the operation.

a). Size of the earth surface covered

There are two major broad types of surveys as per the size of the earth area covered. These are described as:

i) Geodetic survey: A survey in which the earth’s spheroid shape is taken into account. It is applicable in large scale surveying such as provision of national controls.
ii) Plane survey: This is a survey in which the earth’s spheroid shape is ignored. In this case the earth’s surface is assumed to be a plane. It is applicable in small scale surveying.

b). Purpose or use of the survey

A survey may be conducted for a specific purpose or for two or multiple uses. The following types of surveys give the purpose of different surveys based on purpose.

i) Cadastral survey: This type of survey is meant to establish land boundaries on the ground and determine the area of land pieces. Thus it is used to establish land property lines and corners for specific ownership.
ii) Topographic survey: They are used to establish the position and shape of natural and man-made features over a given area. They are meant to produce a map of an area with certain geographical information systems.
iii) Engineering (construction) surveys: They are carried out for the purpose of executing engineering works such as roads, dams, railways, sewage works, tunnels etc.
iv) Hydro-graphic surveys: These are surveys done to study some characteristics of water bodies. These are used to determine size, shape and depth of lakes, rivers, harbours and oceans. The surveys sometimes establish flow characteristics of water in water bodies.

c).Surveying techniques

A number of techniques have can be used to conduct surveying exercise. Based on the survey operations, there are a number of different types of surveys listed below:

i) Traverse surveying
ii) Plane table surveying
iii) Chain surveying
iv) Triangulation surveying
v) Aerial surveying
vi) Tacheometric surveying

d). Surveying equipment/equipment

A number of surveying instruments/equipment can be used to carry out surveying operations. This instruments/equipment may fall into three main categories which define the survey types. These are

i) Linear and area measurement equipment: These include tapes, chains, levels and theodolite/transit, pins, substence bar, ranging rods, plumb bob, prism square, electronic measurement equipment (EDM), Odometers, plane table and alidade accessories
ii) Levelling instruments: these include line level, spirit level, levelling boards,, hand level, dumpy level, levelling staff, tripod stand, theodolite/transit, global positioning system (GPS), laser plane unit, altimeters
iii) Angle and direction measurement instruments: hand compass, prismatic compass, clinometers, theodolite/transit, GPS NB/ The surveyor will also need a field note book and a pencil for recording the field notes. Corrections on any wrong entry are done by drawing a line through the incorrect data and writing the correct entry above it.

1.4 Basic Error Theory


i) Error: It is the difference or deviation between a measurement and a true value. Most survey measurements have errors as the true value is always difficult to measure. An accurate measurement is the one with allowable error. This accurate value is normally taken to represent the true value. To correct a measurement, positive errors are normally subtracted while negative errors are added.
ii) Gross errors/blunder: These are none allowable errors considered to be too large to permit a measurement to represent a true or correct measurement. They are also called mistakes. These result from lack of skull, attention or knowledge.
iii) Accuracy: This refers to the degree with which a final measurement value differs from its correct value. For instance, consider two tapes A and B are having 0.1 cm and 0.001 cm difference respectively from the true length. The tape B is said to be more accurate.
iv) Precision: This is the refinement with which a physical measurement is made. It refers to the ability of an instrument and observer to reproduce a measurement for a number of times.

1.5 Classification of errors

Instrumental errors: These errors occur due to imperfection of the instrument used. It is due to faults in their manufacture or improper adjustment on one or more parts of the instrument.

Human/personal errors: these may be due to inaccuracy in sense of sight and touch. When the observer rounds off or estimates a fractional part, an error may be introduced. These type of errors are relative to the skill of the observer.

Environmental/natural errors: These are due to the natural phenomena such as changes in temperature, differential refraction of the atmosphere, wind drift and curvature of the earth.

Types of errors

There are three common types of errors that include

i) Systematic/cumulative errors: This type of error results from survey measurements in such a way that any increase in the measurement leads to an increase in the effect of the error. The error is either positive or negative and is said to be cumulative when more measurements are taken.
ii) Compensating/accidental errors: Are errors which are sometimes positive and sometimes negative and thus tend to correct or council each other when significant measurement is made.
iii) Gross/random errors: They arise from mistakes or carelessness and lack of experience. They are quite random and have large effect on the measured values.

1.6 Mapping in soil and water management

A map is a graphic depiction of all or portion of geographic features or their characteristics by use of symbols scaled onto a readable space in their spatial location and time. Maps perform the following functions

i) They act as storage medium for soil and water information and other features

ii) They provide a clear picture and form of land and water resources and other features
iii) The maps provide spatial patterns of soil, water and other features for easy interpretation
iv) They show spatial relationships across different features
v) Maps also give temporal patterns of features for change detection
vi) The maps are also use to study environmental complexity of land, water and other resources

Basic characteristics of all maps

The following basic characteristics apply to all maps. These are

i) Maps exhibit location of different features on space
ii) They depict specific attributes of interest
iii) The maps display reduction of reality on space and time
iv) The maps must have certain geometrical transformation / projection
v) Abstractions of the reality on the ground is represented for all maps
vi) Maps use symbols to represent features

For effective mapping of land features, information transformation is conducted. This involves

i) Selection of appropriate features
ii) Features and image classification
iii) Simplification where necessary
iv) Exaggeration where/when needed
v) Use of appropriate symbols to represent features

Scale of a map

Definition of scale: a scale of a map refers to the ratio of the distance on the map to the corresponding distance on the ground.

Types of scales-there are three main scales used in mapping

i) Graphical scale-this uses a rule like scale on specific maps
ii) Fraction/ratio-this scale uses mathematical ratios for instance 1:20,000. This means one unit on the paper represent 20,000 units on the ground
iii) Fraction: usually written in words for instance one inch represent one kilometre

Large scale and small scale in mapping differ in magnitude of their denominator. Consider for example the scale 1: 20,000 and 1: 1000,000. The former is said to be large scale compared to the former since it has a small denominator.

Maps may be categorized into

i) Reference maps: are multipurpose that are used for multiple applications
ii) Thematic maps: they represent qualitative and quantitative attributes of specific features

Common symbols used in mapping

Different symbols are used to represent varying data categories. These symbols are categorized into

i) Norminal symbols: this is data representation of a place
ii) Ordinal: represents small, medium, large towns and cities
iii) Interval: they represent arbitrary data that is best presented within a range
iv) Ratio: a form of data on a map representing an absolute value

So how are the symbols inscribed on a map? The symbols are normally presented in form of:

i) Point symbols: such as spring, house, mine, tree location
ii) Line symbols: national border, trail, weather roads, tarmac/high way, river, contour
iii) Area symbols: land coverage for gravel, orchard, crop field, water body, irrigation scheme, settlement, town

Spatial data

The concept of spatial data which may also be represented in an ecoregion mapping involves presenting data attributes and their variation with respect to space (spatially). Some of the data represented on spatial domain and relevant to soil water management include and not limited to the following:

(i) Precipitation data
(ii) Soil moisture distribution
(iii) Temperature
(iv) Soil texture
(v) Vegetation
(vi) Agricultural land classification
(vii) Human influence on land change
(viii) Topography/slope of the area
(ix) Evapotranspiration
(x) Drainage characteristics of soil surface
(xi) Water distribution on land

1.7 Methods of Distance Measurement

For most construction work, true horizontal distances are considered. The best distance measurement equipment or method is the one that gives the most accurate value. There are three methods of measuring linear distances. These include:

i) Direct Distance Measurement (DDM)
ii) Optical Distance Measurement (ODM)
iii) Electronic Distance Measurement (EDM)

1.8 Direct Distance Measurement (DDM)

This involves measurement of linear distances using a measuring equipment, device or means that is in direct contact with the surface being measured. This may involve use of tapes and or chains. Some of the methods under this technique include pacing, chaining, use of pedometer, use of odometer and speedometer

Pacing: it is the process of counting the number of paces between two stations within a straight course. This is followed by establishing the individuals Pace Factor (PF) using the measured true horizontal distance determined by the use of a high precision taping method. Pace factor is the average length or distance of one pace. It is thus the ratio of the actual horizontal distance between two stations and the number of pace made.

Taping: it is the direct distance measurement of distance using a tape measure. Various types of tapes are used such as cloth or linen tape, steel tapes, invar tape, fibre glass tape and metallic tape

1.9 Obstacles in linear distance measurement

The common obstacles encountered in taping/ chaining include the following categories

a). obstacles which obstruct ranging but not taping/chaining
b). obstacles which obstruct taping/chaining but not ranging
c). obstacles which obstruct both ranging and taping/chaining

Obstacles which obstruct ranging but not taping/chaining; such a problem arises for instance when a rising ground or agricultural vegetation/forest area interrupts the tape/chain line. In this case the end stations are not inter-visible. When the end stations are not visible from intermediate points, the vegetation area comes across the tape or chain line. In this case, the obstacle may be crossed using a random line explained as illustrated in Figure 1.1 below:

Figure 1.1. Navigation over a barrier in ranging

(Source: Author’s own work)

Assuming uniform horizontal land topography, it can be shown by the rule of similar triangles that:

Abbildung in dieser Leseprobe nicht enthalten (1.1)

Obstacles Which Obstruct Chaining But Not Ranging: water bodies such as lakes, ponds and rivers are some of the examples of this type of obstacle. It may be possible to tape/chain around such obstacles by use of the method described in figure 1.2:

Abbildung in dieser Leseprobe nicht enthalten

Figure 1.2. Navigation over a barrier in taping

(Source: Author’s own work)

From the diagram the distance AB=BC (1.2)

Thus the distance AD is measured as BC assuming the land topography is horizontal or the same .

The obstacles that obstruct both ranging and taping/chaining include buildings and other engineering structures. Consider the following diagram (Figure 1.3):

Abbildung in dieser Leseprobe nicht enthalten

Figure 1.3. Navigation over a barrier in ranging and taping

(Source: Author’s own work)

The same principle applied earlier for the first obstacles can be applied on this one: students to practice by inputting labels and mathematically formulating the relevant formula.

1.10 Slope distance measurement

The slope of any land terrain may be stated in three ways. These are as shown in figures 1.4 and 1.5 and part c.

Abbildung in dieser Leseprobe nicht enthalten

Figure 1.4. Illustration of percent slope

(Source: Author’s own work)

a) Ratio: For instance 1:8

Abbildung in dieser Leseprobe nicht enthalten

Figure 1.5. Illustration of ratio and angle slope

(Source: Author’s own work)

b) Slope angle: for example α

The above methods are inter-convertible using trigonometric relationships (sin, cos,tan)

In case the tape used in any measurement is too short or too long compared to the nominal length, then the measured distances should be corrected as in the following examples

Taping or Chaining on a Sloping Ground

The horizontal distance may be measured directly or the slope distance may be measured and then converted into horizontal distance. The following methods are used to determine horizontal distances

i) Step taping/direct method: The total horizontal distance is measured in small horizontal steps or stretches and the total distance is obtained by summing up the individual step distances

Abbildung in dieser Leseprobe nicht enthalten

Figure 1.6. Principle of step-taping on sloping ground

(Source: Author’s own work)

ii) The total horizontal distance

Abbildung in dieser Leseprobe nicht enthalten

iii) Indirect methods a) Angle measurement: if L1, L2 up to Ln are the measured slope distances between AB and BC respectively, while θ is the slope angle, then it can be shown that the total horizontal distance is given by

Abbildung in dieser Leseprobe nicht enthalten

b). difference in level method: in this method the difference in height is found by a levelling instrument

If h is the difference between heights A and B, applying Pythagorean Theory

Abbildung in dieser Leseprobe nicht enthalten

1.11 Errors in taping

Errors made during taping and or chaining may result from different phenomena. However, these errors can be corrected via combined or net error correction

Combined error correction

Due to different errors resulting from linear distance measurement using a tape, corrections for several effects are normally combined. For instance, errors due to slope, tension, temperature and sag can be combined for a single net correction per tape or chain length. The following are respective corrections.

Slope correction

Abbildung in dieser Leseprobe nicht enthalten

Figure 1.7. Slope correction

(Source: Author’s own work)

If the slope distance L, is considered to represent the horizontal distance D, then it is said to be erroneous since L>D. However, L can be corrected to give the true horizontal distance D. Such a correction is called slope correction.

It can be shown that slope correction

Abbildung in dieser Leseprobe nicht enthalten

Slope correction presented by equation (1.5) may also be computed from the relation

Abbildung in dieser Leseprobe nicht enthalten

For a tape measure which is too long, the total error is added for each case and vice versa for the one which is too short compared with a standard tape measure.

In some instances the actual length of tape/chain may be determined by comparing it with a known standard base or against a reference tape. From standardization measurements, a connection is computed as follows:

Abbildung in dieser Leseprobe nicht enthalten

Sag correction

If a tape is suspended between two stations it tends to take up a catenary shape due to its weight and thus sags at the centre.

Abbildung in dieser Leseprobe nicht enthalten

Figure 1.8. Illustration of sag error

(Source: Author’s own work)

The effect of such a scenario is introduction of a sag error. Such an error can be corrected using the following formula:

Abbildung in dieser Leseprobe nicht enthalten

Temperature correction

The fluctuation in temperature cause either heating or cooling effect on the tape or chain. This is accompanied by changes in length due to expansion and contraction of the material making the tape. Temperature correction is determined form the function:

Abbildung in dieser Leseprobe nicht enthalten

Error due to tension

If the tension or pull applied on the tape less or more than that for which the tape is standardized, the tape is elongated or shortened. The correction for such a tension is computed from

Abbildung in dieser Leseprobe nicht enthalten

1.12 Optical distance measurement (ODM)

To measure horizontal distance by stadia method, a surveying instrument must be equipped with stadia hairs. Consider the stadia hair below:

Abbildung in dieser Leseprobe nicht enthalten

Figure 1.9. Principle of optical distance measurement

(Source: Author’s own work)

Abbildung in dieser Leseprobe nicht enthalten

From which

Abbildung in dieser Leseprobe nicht enthalten

But for any telescope the distance F (Principal focal length) and the distance i between the stadia hair are constant, the ratio Abbildung in dieser Leseprobe nicht enthaltenis also a constant represented by K. Thus

Abbildung in dieser Leseprobe nicht enthalten

Most manufacturers provide a constant K of 100. However, this can be verified practically by a site engineer. If this value holds, then

Abbildung in dieser Leseprobe nicht enthalten

Substense bar method

The distance is obtained by observing horizontal angles substended by targets fixed at a known distance apart on a horizontal substance bar. The distance between two targets is usually 2 m (Figure 1 below)

Abbildung in dieser Leseprobe nicht enthalten

Figure 1.10. Substence bar

(Source: Author’s own work)

The substance bar is set and aligned at right angles to the course by use of a sighting device. The horizontal angle subtended between the two targets is measured using a theodolite/transit as shown in figure 1.11.

Abbildung in dieser Leseprobe nicht enthalten

Figure 1.11. Principles of the substance bar method

(Source: Author’s own work)

It can be shown that the horizontal distance

Abbildung in dieser Leseprobe nicht enthalten

1.13 Electronic Distance Measurement (EDM)

Electronic distance measurement uses two principles; the pulse method and the phase difference method. These techniques are described below

Pulse method

In this approach a short pulse radiation is transmitted from an emitter to a reflector. The reflector then transmits the pulse/signal back to a receiver usually in the same position as the emitter along a parallel path. The layout of the transmission and reflection is presented in the following diagram (Figure 1.12):

Abbildung in dieser Leseprobe nicht enthalten

Figure 1.12.: principle of pulse distance meter

(Source: Author’s own work)

The measured distance is combined from the product of the velocity of the pulse and the half the time it takes to complete the journey as presented in the following equations.

Abbildung in dieser Leseprobe nicht enthalten

The maximum distance that can be measured is a function of the power of the light pulse. Currently, there are very powerful laser systems that can measure long distances when used with proper targets such as cube prisms.

Phase difference method

In this method a parameter which defines the extent by which the reflected signal is out of phase with the emitted pulse is used. The following diagrams (Figure 1.13 (a and b) show a signal in phase and a signal out of phase.

Abbildung in dieser Leseprobe nicht enthalten

Figure 1.13. Principle of phase difference method (a) signal in phase and b) signal out of phase)

(Source: Author’s own work)

For a signal which is out of phase by a magnitude of d, the following equation applies

Abbildung in dieser Leseprobe nicht enthalten

1.14 Worked examples

Example 1.1

A 30-m tape was used to measure the following slope distances.

i) 450 m on a 12% slope
ii) 322.8 m on a 1:9.8 slope and
iii) 295 m on a 6̊ 30′ slope

It was discovered that the tape used was 0.035 m too short. Compute total horizontal distance.

Solution 1.1

Abbildung in dieser Leseprobe nicht enthalten

For 1: 9.8 slope

Abbildung in dieser Leseprobe nicht enthalten

Example 1.2

A tape of nominal length 20.00 m when compared with a standard measures 20.05 m. if this tape is used to measure a line AB and the recorded measurement is 131.35 m, what is the correct length of AB

Solution 1.2

Abbildung in dieser Leseprobe nicht enthalten

In case an area is computed and requires corrections, the following correction may be applied:

Abbildung in dieser Leseprobe nicht enthalten

Example 1.3

Abbildung in dieser Leseprobe nicht enthalten

Example 1.4

Two points P1 and P2 were marked by use of pegs. A 30-m steel tape standardized at a tension of 52 N and 250C was suspended between the two pegs. A tension of 135 N was then applied. The mean tape readings at the pegs were found to be 0.50 m and 28.10 m. The difference in elevations between the two pegs was 0.089 m. Determine the total corrected horizontal distance between points P1 and P2 given further that:

i. Cross sectional area of the tapeAbbildung in dieser Leseprobe nicht enthalten
ii. Mass of the tape=0.028 kg/m
iii. Mean ambient temperature during observation=290C
iv. Modulus of elasticity E =Abbildung in dieser Leseprobe nicht enthalten

Solution 1.4

Abbildung in dieser Leseprobe nicht enthalten

Chapter 2

Determination of Land Area

Aims of the Chapter

The aim of this chapter is to offer knowledge and skills on:

- Need for land area determination
- Methods of determining area on agricultural land
- Illustrate how land can be partitioned for ease of area determination
- Error correction in direct distance measurement

2.1 Determination of Land Area

Determination of land area especially agricultural fields is very important. Area measurement is in numerous applications particularly where

i). Planning, design and management of land and water resources is required
ii).Buildings are to be constructed
iii). Surface runoff is to be computed from a catchment
iv). Land or cadastral property is to be purchased or sold
v). Estimation of output or productivity of agricultural land for instance total crop yield
vi). Excavation such as road construction site, terrace and Cut Off Drain are to be put up so as to establish the volume and the corresponding cost of excavation.

2.2 Methods of estimating area

There are two main methods of obtaining information for area measurement. These include

A). Dividing the area into geometrical figures and then applying geometrical computations

i) divide the area into triangles and then apply the formulae for calculating areas for triangles such the ones discussed below
ii) measure the area by use of squared transparent paper
iii). Measure the ordinates: after measuring the ordinates/offsets the apply mathematical formulae such as trapezoidal rule or Simpson’s rule

B) Using a planimeter on a map or plan, determine the area

Some of the methods especially the ones falling in category A above are described below:

Triangulation method: this method is based triangulation approach in taping or chaining. The sides of various triangles make up a given area measured directly in the field and no angular measurements are taken. Three sides of a triangle are measured using a tape measure or chain and then plotted to scale on a piece of paper. Then depending on the given sides or angle, the following formulae may be applied

Abbildung in dieser Leseprobe nicht enthalten

Traversing method: the area to be measured consist of a framework that comprise a series of connected lines. The length and direction of the limes are measured.

2.3 Offsets

An offset is a perpendicular distance taken from any point on a base line to another point, object or feature. Offsets are normally measured to locate stations, boundaries, buildings, fences, roads among others. Any offset involve two measurements; distance along the baseline and length of the offset. After establishing the offsets in the field, the following methods may be used in area determination:

2.4 Trapezoidal rule

Consider the diagram (Figure 2.1) below

Abbildung in dieser Leseprobe nicht enthalten

Figure 2.1.: principle of trapezoidal rule

(Source: Author’s own work)


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Soil and Water Management. An Introductory Textbook
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Dr Raphael Muli Wambua (Author), 2020, Soil and Water Management. An Introductory Textbook, Munich, GRIN Verlag,


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