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ENGINEERING HYDROLOGY

Hydrology is the science that treats of the waters of the earth, their occurrence, circulation and distribution, their

chemical and physical properties, and their reaction with their environment, including their relation to living things.

Engineering Hydrology includes segments of the fields pertinent to planning, design, and operation of engineering

projects for the control and use of water.

Branches of Hydrology

1. Scientific Hydrology: concerned with the discovery of basic principles and relationships.

2. Deterministic Hydrology: deals with the analysis of such physical characteristics such as slope, area, depth in a

case and effect sense.

3. Stochastic Hydrology: considers the statistical probability of occurrence of such events as peak floods.

4. Applied Hydrology: concerned with the use of hydrology in the design and management of civil works. Its

branches may study the hydrology of major storms, flood surface drainage, distribution of water supply and

irrigation.

Hydrologist is a person who studies hydrologic phenomena and gathers data pertaining to the occurrence and

distribution of water and other related factors.

Applications of Hydrology to Engineering

Water resources engineering projects, such as the following, needs hydrological investigations for the proper

assessment of the different factors affecting the project.

Irrigation

Water supply

Flood control

Reservoir

Water power

Navigation

Factors that needs hydrological investigations and assessment:

The capacity of storage structures such as reservoirs

The magnitude of flood flows to enable safe disposal of the excess flow

The minimum flow and quantity of flow available at various seasons

The interaction of the flood wave and hydraulic structures such as levees, reservoirs, barrages and bridges

These factors have to be considered to prevent failures of important projects such as:

Overtopping and failure of earthen dam due to inadequate spillway capacity

Failure of bridges and culverts due to excessive flow

Inability of the reservoir to fill up with water due to overestimation of stream flow

Relevant data required by a hydrologist:

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Weather records including temperature, humidity and wind velocity

Precipitation data

Stream flow records

Evaporation and transpiration data

Infiltration characteristics of the area

Groundwater characteristics

Physical and geological characteristics of the area under consideration

Hydrologic Cycle is a continuous process in which water is evaporated from the oceans, moves inland as moist air

masses, and produces precipitation if the correct condition exists. The circulation of water in the earth’s surface passes

three main routes:

1. Evaporation and transpiration

2. Precipitation

3. Run-off

The Hydrologic Cycle

Evaporation is the loss of moisture from the

bodies of water and the earth’s surface to the

atmosphere.

Transpiration is the loss of moisture from

plants to the atmosphere.

Evapotranspiration is the total loss of

moisture content from the bodies of water,

earth’s surface, plants, etc.

Run-off is the excess rainfall accumulated at

the earth’s surface.

Precipitation is the collective term used to

denote moisture in the liquid or solid form

which falls from the atmosphere to the

surface of the earth.

Factors needed for the formation of precipitation:

1. The atmosphere must have moisture.

2. There must be sufficient nuclei present to aid condensation.

3. Weather condition must be good for condensation of water vapor to take place.

4. The products of condensation must reach the earth.

Forms of Precipitation:

1. Rain: the principal form of precipitation in the Philippines. Rainfall is used to describe precipitation in the form

of water drops of sizes larger than 0.5 mm. The maximum size of a raindrop is 6 mm.

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2. Drizzle: a fine sprinkle of numerous water droplets of sizes less than 0.5 mm and intensity less than 1 mm/h. The

drops are so small that they appear to float in air.

3. Shower: precipitation characterized by sudden start marked by the occurrence of a few large drops followed by

a downpour lasting from ½ to 1 hour.

4. Glaze: is formed when rain or drizzle come in contact with cold ground at around 0°C.

5. Snow: consists of ice crystals which usually combine to form flakes.

6. Sleet: frozen raindrops of transparent grains which form when rain falls through the air at subfreezing

temperature.

7. Hail: showery precipitation in the form of irregular pellets or lumps of ice of size more than 8 mm. Hails occur in

violent thunderstorms in which vertical currents are very strong.

Measurement of Precipitation:

1. Amount of Precipitation: expressed as the depth of rain in inches or millimeters that fall on a level surface. This

may be measured as the depth of water deposited in an open, straight-sided container.

2. Duration of Rainfall: the beginning and cessation of precipitation determine the duration of each occurrence.

a. Continuous Rainfall – no rainless interval from the beginning to ending.

b. Intermittent Rainfall – characterized by varying intensity and there are more breaks of at least 15 but not

more than one hour.

3. Intensity of Rainfall: the amount of precipitation per unit time.

Rainfall Analysis:

Variables of rainfall considered are:

1. Space: the average rainfall over the area.

2. Intensity: how hard it rains.

3. Duration: how long it rains at any given intensity.

4. Frequency: how often it rains at any given intensity and duration.

Types of Precipitation:

1. Convectional Precipitation: this is in the form of local whirling thunderstorms and is typical of the tropics. The air

close to the warm earth gets heated and rises due to the low density, cools adiabatically to form a cauliflower

shape which finally bursts into a thunderstorm when accompanied by destructive winds. They are called

tornadoes.

2. Frontal Precipitation: this occurs when two or more masses clash with each other due to differences in

temperature and densities then condensates to form precipitation.

Front – the boundary between two masses

Cold Front – the cold air mass replaces a warmer air

Warm Front – the warm air replaces a colder air mass

Occluded Front – a cold front overtakes a warm front

Stationary Front – a front that is not moving

3. Orographic Precipitation: the mechanical lifting of moist air over mountain barriers causes precipitation to the

windward side.

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4. Cyclonic Precipitation: occurs due to the lifting in of moist air converging into a low pressure belt; due to

pressure difference created by unequal heating of the earth’s surface. Here the wind blows spirally inward

counterclockwise in the northern hemisphere and clockwise in the southern hemisphere.

Rain Gauge is a type of instrument used by meteorologists and hydrologists to gather and measure the amount of liquid

precipitation over a set period of time at a given location. It consists of a receiver in which an inner tube is located. The

falling rain is fed into the inner tube through the receiver and the total quantity measured by a measuring glass. The

height of the receiver and the diameter of the circular mouth are of standard dimensions.

Considerations in siting a rain gauge:

1. The ground must be level and in the open and the instrument must

present a horizontal catch surface.

2. The gauge must be set as near the round as possible to reduce wind

effects but it must be sufficiently high to prevent splashing, flooding,

etc.

3. The instrument must be surrounded by an open fenced area of at least

5.5mX5.5m. No object should be neared to the instrument than 30m

or twice the height of the obstruction.

Classification of Rain Gauges:

1. Non-recording Rain Gauge (Standard Rain Gauge)

The standard rain gauge consists of a funnel 8 inches in diameter discharging into a tube 2.53 inches in

diameter. The area of the inner tube is 0.1 times that of the funnel, and a stick graduated in inches and tenths

can be used to measure precipitation to the nearest 0.01 inch. Precipitation in excess of 2 inches overtops the

inner tube and collects in the overflow can or cylinder. The excess rainfall can be measures by placing it in the

inner tube and the depth is determined and added to the previously collected rain in the inner tube. For

uniformity, the rainfall is measured everyday at 8:30am and is recorded as the rainfall of the day. The rain gauge

should be properly maintained and must be free from the dust and dirt. This gauge can also be used in

measuring snowfall.

2. Recording Rain Gauge

Recording gauges produce a continuous plot of rainfall against time and provide valuable data of intensity and

duration of rainfall for hydrological analysis of storms. The following are the most commonly used recording rain

gauges:

a. Tipping Bucket Rain Gauge

This is a 30.5 cm size rain gauge adopted for use by the U.S. Weather Bureau. The catch from the funnel falls

onto one of a pair of small buckets. This bucket s are so balanced that when 0.25 mm of rainfall collects in

one bucket it tips and brings the other one in position. The water from the tipped bucket is collected in a

storage can. The tipping actuates an electrically driven pen to trace a record on a clockwork-driven chart.

The water in the storage can is measured at regular intervals to provide the total rainfall at the same time

checking the data plotted. The record from the tipping bucket gives data on the intensity of rainfall.

b. Weighing-Bucket Rain Gauge

In this rain gauge, the catch from the funnel empties into a bucket mounted in a weighing scale. The weight

of the bucket and its contents are recorded on a clockwork-driven chart. The clockwork mechanism has the

capacity to run for as long as one week. This instrument gives a plot of the accumulated rainfall against the

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elapsed time (mass curve of the rainfall). In some instruments of this type the recording unit is so

constructed that the pen reverses its direction at every preset value, say 7.5 cm (3 inches) so that a

continuous plot of the storm is obtained.

c. Natural Siphon Type Rain Gauge

This type of recording rain gauge is also known as float type rain gauge. Here the rainfall is collected by a

funnel-shaped collector then is led into a float chamber causing a float to rise. As the float rises, a pen

attached to the float through a lever system records the elevation of the float on a rotating drum driven by a

clockwork mechanism. A siphon arrangement empties the float chamber when the float has reached a

preset maximum level.

d. Telemetering Rain Gauge

This is one of the recording type rain gauges and contains electronic units to transmit the data on rainfall to

a base station both at regular intervals and on interrogation. The tipping bucket type is usually adopted for

this purpose. Telemetering gauges are of great use in gathering rainfall data from mountainous and

generally inaccessible places.

e. Radar Measurement of Rainfall

Meteorological radar is a powerful instrument for measuring the aerial extent, location and movement of

storms. The amounts of rainfall over large areas can be determined through the radar with a good degree of

accuracy.

Rain Gauge Network

Since the catching area of a rain gauge is very small compared to the aerial extent of a storm, it is necessary to have as

many rain gauge stations as possible in order to get a representative data of the storm. However, economic

considerations, topography, accessibility, etc. restricts the number of stations to be maintained. Hence, one aims at an

optimum density of gauges from which a reasonably accurate information about the storms can be obtained. WMO

(World Meteorological Organization) recommends the following densities:

1. In flat regions of temperate, Mediterranean and tropical zones:

Ideal : 1 station for 600-900 km2

Acceptable : 1 station for 900-3000 km2

2. In mountainous regions of temperate, Mediterranean and tropical zones:

Ideal : 1 station for 100-250 km2

Acceptable : 1 station for 250-1000 km2

3. In arid and polar zones:

1 station for 1500-10,000 km2 depending on the feasibility

Ten percent of rain gauge stations should be equipped with self-recording gauges to know the intensities of rainfall. The

following are recommended based on Indian standards:

1. In plains: 1 station per 520 sq. km.

2. In regions of average elevation of 1000 m: 1 station per 260-390 sq. km.

3. In predominantly hilly areas with heavy rainfall: 1 station per 130 sq. km.

Computation of Average Precipitation

Average Precipitation can be computed using any of the following methods:

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1. Average Method

This is the simplest method of getting the average precipitation. This is done by computing the arithmetic mean

or average of the recorded precipitation values at stations in or near the area. If precipitations are not uniform

and the gauge stations are not evenly distributed, the average may be incorrect.

Average Precipitation = (∑ P) / (Number of Stations)

Example:

Precipitations from 8 rain gauge stations are as follows:

Stations Precipitation

1 37 cm

2 49 cm

3 68 cm

4 52 cm

5 75 cm

6 86 cm

7 36 cm

8 78 cm

Total 481 cm

Average Precipitation = 481 / 8 = 60.125 cm.

2. Thiessen Method

Thiessen assumed that the rainfall reading measured at any gauge could be applied to a point halfway to the

next gauge. This method is applied by drawing lines joining gauge stations. Polygons are then drawn by

constructing perpendicular bisectors to lines joining the gage stations. The polygon formed by the bisectors

around a station encloses an area that is closer to the station than any other station. To compute the average

rainfall, the area represented by each station is expressed as a percentage of the total area.

Average Precipitation = (∑ AP) / (Total Area)

Example:

Precipitations from 8 rain gauge stations are as follows:

Stations Observed Precipitation (mm) Area (km2) P x A

1 17 18 306

2 37 311 11,507

3 49 282 13,818

4 68 311 21,148

5 39 52 2,028

6 76 238 18,088

7 127 212 26,924

8 114 197 22,450

Total 1,621 116,277

Average Precipitation = 116,277 / 1621 = 71.73 mm.

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3. Isohyetal Method

This is the preferred method for the analysis of individual storms because it gives the best approximation to the

rainfall pattern. To compute the average precipitation from an isohyetal map, the areas enclosed between

successive isohyets* are measured and multiplied by the average precipitation between the isohyets. The sum of

these products is divided by the total area to get the average precipitation.

Average Precipitation = (∑ AP) / (Total Area)

*Isohyets (iso means "identical", hyet comes from the Greek huetos, for "rain.") are lines on a map connecting

points of equal precipitation during a given time period or for a particular storm.

Example:

Precipitations from 7 rain gauge stations are as follows:

Isohyets Area bet. Isohyets (mi2) Average Precipitation (in) P x A

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3.5 19 3.45 65.55

4.0 106 3.75 397.50

4.5 102 4.25 433.50

5.0 60 4.75 285.00

5.5 150 5.25 787.50

6.0 84 5.75 483.00

6.5 47 6.20 291.40

Total 568 2,743.45

Average Precipitation = 2,743.45 / 568 = 4.83 in.

Preparation of Data

Before using the rainfall records of a station, it is necessary to check first the data for continuity and consistency. The

record may not be continuous due to a missing data due to damage of the rain gauge during the period or due to the

negligence of the person in-charge.

Estimation of Missing Data

The missing data can be estimated from observations at three stations as close as possible to the station in question. If

the annual precipitation at various stations are within about 10% of the normal annual precipitation at station X, then a

simple arithmetic average is used to estimate the missing data.

PX =

If the normal precipitation varies considerably, say by more than 10%, then the normal ratio method is used.

PX =

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where: N = annual mean

P = average precipitation

The National Weather Service has developed a procedure to calculate the rainfall at station X. First establish a set of

axes through X and determine the absolute coordinates of the nearest 3 surrounding stations A, B, and C. The estimated

precipitation of X is determined as the weighted average of the other three points. The weights are the reciprocal of the

squares of the direct distance from X to the surrounding stations.

PX =

where: W =

D = direct distance from station X

Test for Consistency of Record

Precipitation records may become inconsistent due to the following reasons:

1. Shifting of a rain gauge station to a new location.

2. The neighborhood of the station has undergone a marked change.

3. Change in the ecosystem due to calamities, such as forest fires, land slides; and

4. Occurrence of observational error from a certain date.

The checking for consistency is done by the double mass curve technique which is based on the principle that when each

recorded data comes from the same parent population, they are consistent. A group of 5 to 10 base stations is selected

in the neighborhood of the station in question. The data of the annual rainfall of station X and the base stations are

arranged in reverse chronological order. The accumulated annual precipitation of station X and the base stations are

calculated starting with the latest record. The accumulated rainfall of station X for each period is plotted against the

accumulated annual rainfall of the base stations. If the record is consistent, a straight line will be obtained. On the other

hand, a decided break in the slope of the resulting plot indicates a change in the precipitation regime of the station X.

The values of precipitation in station X beyond the period of change of regime are corrected by using the relation:

Correction Ratio =

=

PCX = PX (

)

where: PCX = corrected precipitation at any time period t1 at station X

PX = original recorded precipitation at any time period t1 at station X

Mc = corrected slope of the double-mass curve

Ma = original slope of the mass curve

In this way the older records are brought up to the new regime of the station.

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Presentation of Rainfall Data

1. Mass Curve of Rainfall

It is a plot of the accumulated precipitation against time, plotted in chronological order. Records of float type

and weighing bucket type are of this form. Mass curves of rainfall at a station during a storm are useful in the

extraction of information on the duration and magnitude of a storm. Intensities at various time intervals can also

be obtained from the slope of the storm.

2. Hyetograph

It is a plot of the intensity of rainfall against the time interval. The hyetograph is derived from the mass curve

and is usually representing the characteristics of a storm and is important in the development of design storms

to predict extreme floods. The area under the hyetograph represents the total precipitation received in that

period. The time interval used depends on the purpose; small durations are used in urban drainage problems

while intervals of about 6 hours are used for flood-flow computations.

Time

Cumulative Rainfall

Accumulated Annual Rainfall of Base Stations

Accumulated Rainfall of Station

a c

Time (h)

Rainfall Intensity (cm/h)

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3. Point Rainfall

Also known as station rainfall, this refers to the rainfall data of a station. The data can be listed as daily, weekly,

monthly, seasonal or annual values for various periods depending on the need. The data are represented

graphically by plots of magnitude versus chronological time in a form of a bar graph.

Frequency of Point Rainfall

The probability of occurrence of a particular extreme rainfall is important in many hydraulic engineering applications

especially those concerning with floods. This is obtained by the frequency analysis of a point rainfall data.

The purpose of the frequency analysis of an annual series is to obtain a relation between the magnitude of the event

and its probability of exceedence.

A simple empirical technique is used to arrange the given annual extreme series in descending order of magnitude and

to assign an order number m. Thus, for the first entry m = 1, for the second entry m = 2, and so on until the last entry for

which m = N (number of years of record). The probability P of an event equaled or exceeded is given by the Weibull

Formula:

P =

T =

=

where: T = the recurrence interval

After calculating P and T for all events in the series, the variation of the rainfall magnitude is plotted against the

corresponding T on a semi-log paper. By suitable extrapolation, the rainfall magnitude of specific duration for any

recurrence interval can be estimated.

Intensity-Duration-Frequency Relationship

The intensity of storms decreases with the increase in storm duration. A storm of any given duration will have a larger

intensity if its return period is large. In other words, for a given duration, storms of higher intensity are rarer than storms

of smaller intensity. The interdependency between the intensity, duration, and return period is commonly expressed in

a general form as

i =

where: k, x, a, and n are constants for a given catchment.

i is the intensity of storm in cm/h.

D is the duration of the storm in hours.

T is the return period in years.

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Water Losses

1. Interception Loss: due to surface vegetation, foliage, and buildings, water is returned to the atmosphere by the process of evaporation and transpiration without reaching the ground surface.

2. Evaporation: change of state from liquid to gas of water from water surfaces (reservoirs, lake, ponds, rivers, etc.) and from soil surface, appreciably when the groundwater table is near the soil surface.

3. Transpiration: from plants 4. Evapotranspiration 5. Infiltration: into the soil at the ground surface. 6. Watershed Leakage: groundwater movement from one basin to another or into the sea.

Evaporation

Evaporation is the transfer of water from the liquid to the vapor state.

Transpiration is the process by which plants remove water from the soil and release it into the air as vapor.

Evapotranspiration is the combined processes of losing water to the atmosphere from water surface, soil surface, and from plants.

Factors affecting the rate of Evapotranspiration

1. Vapor pressure at the water surface and air above. The rate of evaporation is proportional to the difference between the saturation vapor pressure at the water temperature, ew and the actual vapor pressure in the air, ea, thus, EL = c ( ew – ea )

where: EL = rate of evaporation (mm/day)

c = a constant ew and ea = vapor pressures in mm of mercury

Evaporation continues until ew = ea .If ew exceeds ea , condensation takes place.

2. Air and Water Temperatures

With all factors remaining the same, the rate of evaporation increases with an increase in the water temperature.

3. Wind Speed With aids in removing the evaporated water vapor from the zone of evaporation and consequently creates greater scope for evaporation. The rate of evaporation increases with the wind speed up to critical speed.

4. Atmospheric Pressure With all factors remaining the same, a decrease in barometric pressure increases evaporation.

5. Quality of Water When a solute is dissolved in water, the vapor pressure of the solution is lesser than that of pure water and hence causes reduction in the rate of evaporation.

6. Size of Water Bodies Deep water bodies have more heat storage than shallow ones. A deep lake may store radiation energy in summer and release it in winter causing less evaporation in summer and more evaporation in winter.

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Determination of Evaporation

Determination of Evaporation is very important in many hydrologic problems associated with planning and operation of reservoirs and irrigation systems. It is also important in areas where water is scarce. The exact measurement of evaporation is one of the most difficult tasks. It can only be estimated using the following methods:

1. Using evaporimeter data 2. Empirical evaporation equations 3. Analytical methods

Evaporimeters

Evaporimeters are water-containing pans which are exposed to the atmosphere and the loss of water by evaporation is measured in them at regular intervals. Factors affecting the rate of evaporation are also noted such as humidity, wind movement, air and water temperatures and precipitation.

Types of evaporimeters:

1. Class A Evaporation Pan This consists of 1210 mm width and a depth of 255 mm. It is used by the U.S. Weather Bureau and is known as Class A Land Pan. The depth of the water is maintained below 18 cm and 20 cm. The pan is normally made o unpainted galvanized iron sheet. Monel metal is used where corrosion is problem. The pan is supported by wooden platform of 15 cm height above the ground to allow free circulation of air below the pan. Evaporation measurements are made by measuring the depths of water with a hook gauge in a stilling well.

2. ISI Standard Pan This is known as modified Class A Pan. It consists of a pan 1220 mm in diameter with 255 mm of depth. Te pan is made of copper sheet of 0.90 mm thickness, tinned inside and painted white outside. A fixed point gauge indicates the level of water. A calibrated cylindrical measure is used to add or remove water, maintaining the water level in the pan to a fixed mark. The top of te pan is covered fully with a hexagonal wire netting on a galvanized iron to protect the water in the pan from birds and to make the temperature more uniform during the day and night. The evaporation of this pan is found to be less by 14% compared to the unscreened pan.

3. Colorado Sunken Pan This is a 920 mm square and 460 mm deep made up of unpainted galvanized iron sheet and buried into the ground within 100 mm of the top. The main advantage of this type is that radiation and aerodynamic characteristics are similar to a lake. However, it has the following disadvantages: a. Difficult to detect leaks b. Extra care is needed to keep the surrounding area free from all grass, dust, etc. c. Expensive to install

4. US Geological Survey Floating Pan

A square pan with 900 mm side and 450 mm depth supported by drum floats in the middle of a raft (4.25m x 4.87 m) is set afloat on a lake to simulate the characteristics of a large body of water. The water level is kept constant leaving a rim of 75 mm. Diagonal baffles provided in the pan reduce the surging in the pan due to wave action.

Evaporation pans are not exact models of large reservoirs and have the following drawbacks:

1. They differ in the heat-storing capacity and heat transfer from the sides and bottom. 2. The height of the rim in an evaporation pan affects the wind action over the surface. 3. The heat-transfer characteristics of the pan material are different from that of the reservoir.

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Due to the above drawbacks, the evaporation observed from the pan has to be corrected using pan coefficients.

Lake Evaporation = Cp x Pan Evaporation

Values of Pan Coefficients Cp

Type f Pan Average Value Range

Class A Land Pan 0.70 0.60-0.80

ISI Pan 0.80 0.65-1.10

Colorado Sunken Pan 0.78 0.75-0.86

USS Floating Pan 0.80 0.70-0.82

Evaporation Stations (Minimum network of evaporimeter stations)

1. Arid zones: 1 station for every 30,000 km2. 2. Humid temperature climates: 1 station for every 50,000 km2. 3. Cold regions: 1 station for every 100,000 km2.

Empirical Evaporation Equations

1. E = 0.00241 (pvs – pv8) V8

where:

pvs = the vapor pressure at the water surface (inches of mercury) p8 = the vapor pressure 8 m above the water surface

2. Meyer’s Formula

EL = KM ( ew – ea ) ( 1 + u9 /16 ) where:

EL = lake evaporation in mm/day ew = saturated vapor pressure at the water surface temperature in mm of mercury ea = actual vapor pressure overlying air at about 9 m above the ground u9 = monthly mean wind velocity in km/h at about 9 m above the ground KM = coefficient accounting for various other factors with a value equal to 0.36 for large deep waters and 0.5 for small, shallow waters.

If given that wind velocity is at a level other than what is required in the formula, the wind velocity is assumed to follow the 1/7 power law as

u9 = u1 ( 9 )1/7 uh = u1 ( h )1/7

Values of ew are obtained from the following table: Saturation Vapor Pressure of Water

Saturation vapor pressure

Temperature ew (mm of Hg) A (mm/°C)

0 4.58 0.30

5.0 6.54 0.45

7.5 7.78 0.54

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10.0 9.21 0.60

12.5 10.87 0.71

15.0 12.79 0.80

17.5 15.00 0.95

20.0 17.54 1.05

22.5 20.44 1.24

25.0 23.76 1.40

27.5 27.54 1.61

30.0 31.82 1.85

32.5 36.68 2.07

35.0 42.81 2.35

37.5 48.36 2.62

40.0 55.32 2.95

45.0 71.20 3.66

3. Rohwer’s Formula

EL = 0.771 (1.465 – 0.000732 pa ) ( 0.44 + 0.0733u0 ) ( ew – ea )

where:

EL, ew and ea = are as defined in Meyer’s formula

pa = mean barometric reading in mm of mercury

u0 = mean wind velocity in km/h at ground level which can be taken to be the velocity at 0.6 m height above the ground

Sample Problem

A reservoir with a surface area of 275 hectares had the following average values of parameters during a week:

Water temperature = 25°C

Relative humidity = 30%

Wind velocity at 1.0 m above ground = 15 km/h

Estimate the average daily evaporation from the lake and the volume of water evaporated from the lake during the week.

Solution

From the table of saturation pressure, at 25°C, ew = 23.76 mm of Hg

ea = humidity x ew

ea = 0.30 x 23.76

ea = 7.128 mm of Hg

u9 = u1 (h)1/7

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u9 = 15 (9)1/7 = 20.53 km/h

KM = 0.36 for large reservoirs

Substituting this to Meyer’s formula,

EL = 0.36 (23.76 – 7.128) (1 + 20.53/16)

EL = 13.67 mm/day

Evaporated volume for one week = 13.67 mm/day x 1 m/1000mm (A)

= 0.01367 m/day x t days (A)

= 0.09569 m/week x 2750,000 m2

= 263,147.50 cu.m

Analytical Method of Estimating Evaporation

1. Water-Budget Method 2. Energy-Balance Method 3. Mass-Transfer Method

Water-Budget Method

P + Vis + V ig = Vos + V og + ∆S + TL + EL

where:

P = daily precipitation

Vis = daily surface inflow into the lake

V ig = daily groundwater inflow

Vos = daily surface outflow from the lake

V og = daily seepage outflow

∆S = increase in lake storage in a day

TL = daily transpiration loss

EL = daily lake evaporation

Energy-Balance Method

Hn = Ha + He + Hq + Hs + Hi

where:

Ha = sensible heat transfer from water surface to air

He = heat energy used up in evaporation

He = pLEL

p = density of water

L =latent heat of evaporation

EL = evaporation in mm

Hq = heat flux into the ground

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Hs = heat stored in water body

Hi = net heat conducted out of the system by water flow (advected energy)

Hi = Hc (1 – r) – Hb

Hb = back radiation (long wave) from the water body

Hc (1 – r) = incoming solar radiation into a surface of reflection coefficient (albedo), r

Ha is estimated using Bowen’s Ratio B

B = Ha / pLEL

= 6.1 x 10-4 x pa (Tw-Ta) / (ew – ea)

where:

pa = atmospheric pressure in mm of Hg

Tw = temperature of water surface in °C

Ta = temperature of air surface in °C

ew = saturated vapor pressure in mm of Hg

ea = actual vapor pressure of air in mm of Hg

Lake evaporation can be evaluated using the formula:

EL =

The volume of water lost due to evaporation in reservoirs can be calculated using the formula:

VE = A Epm Cv

where:

VE = volume of water lost in evaporation in a month (m3)

A = average area of reservoir during the month

Epm = pan evaporation loss in meters in a month

Epm = EL in mm/day x No. of days in the month x 10-3

Cv = relevant pan coefficient

Methods for Reduction of Evaporation Losses

1. Reduction of Surface Area The volume of water lost by evaporation is directly proportional to the surface area of the water body, thus reduction of surface area can reduce evaporation loss. Using deep reservoirs in place of wider ones can meet this method of reducing loss of water.

2. Mechanical Cover Permanent, temporary or floating roofs can be used to cover reservoirs, but this is only feasible for smaller water bodies.

3. Chemical Films This method consists of applying a thin chemical film on the water surface to reduce evaporation. This is feasible for reservoirs of considerable size.

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Certain chemicals such as cetyl alcohol (hexadecanol) and stearyl alcohol (octadecanol) form monomolecular layers on water surface. These layers act as evaporation inhibitors by preventing the water molecules to escape past them. The desirable features of the film include the following: a. The film is strong and flexible and does not break easily due to wave action. b. If punctured due to impact of raindrops or by birds, insects, etc., the film closes back after. c. It is pervious to oxygen and carbon dioxide; therefore the quality of water is not affected by its presence. d. It is colorless, odorless, and non-toxic.

Evapotranspiration

Transpiration is the process by which water leaves the body of a living plant and reaches the atmosphere as vapor. The water is taken up by the plant-root system and escape through the leaves.

Factors Affecting Transpiration:

1. Atmospheric vapor pressure 2. Temperature 3. Wind 4. Light intensity 5. Characteristics of plants

Consumptive Use – denotes loss by evapotranspiration.

Potential Evapotranspiration (PET) – the resulting evapotranspiration when sufficient moisture is always available to completely meet the needs of vegetation covering the area. This depends essentially on the climatic factors.

Actual Evapotranspiration (AET) – the real evapotranspiration occurring in a specific situation.

Field Capacity – the maximum quantity of water that the soil can retain against the force of gravity.

Permanent Wilting Point – the moisture content of a soil at which the moisture is no longer available in sufficient quantity to sustain the plants.

Available Water – the difference between the field capacity and the permanent wilting point.

If the water supply to the plant is adequate, soil moisture will be at the field capacity and AET will be equal to PET. If the water supply is less than PET, the soil dries out and the ratio AET/PET would be less than unity. When the soil moisture approaches the wiltng point, the AET will reduce to zero. The hydraulic budget can be written as:

P – Rs – Go – Eact = dS

where:

P = precipitation

Rs = runoff surface

Go = subsurface outflow

Eact = actual evapotranspiration (AET)

dS = change in the moisture storage

Measurement of Evapotranspiration

1. Lysimeter

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A special water tank containing a block of soil and set in a field of growing plants. The plants grown in the lysimeter are the same as in the surrounding field. Evapotranspiration is estimated in terms of the amount of water required to maintain constant moisture conditions within the tank measured wither volumetrically through an arrangement made in the lysimeter. Lysimeters should be designed to accurately reproduce the soil conditions, moisture content, type and size of the vegetable of the surrounding area. They should be buried so that the soil is the same level inside and outside the container.

2. Field Plot In a special plot all the elements of the water budget in a known interval of time are measured and the evapotranspiration is determined as: Evapotranspiration = (precipitation + irrigation input – runoff – increase in soil storage – groundwater loss) Measurements are usually confined to precipitation, irrigation input, surface runoff and soil moisture. Groundwater loss due to deep percolation is difficult to measure and can be minimized by keeping the moisture condition of the plot at the field capacity.

Evapotranspiration Equations

Penman’s Equation

This is based on sound reasoning and is obtained by a combination of the energy-balance and mass transfer approach.

PET =

where:

PET = daily potential evapotranspiration in mm/day

A = slope of the saturation vapor pressure versus temperature curve at the mean air temperature in mm of mercury per °C (from table of saturation vapor pressures)

= psychometric constant = 0.49 mm of mercury / °C

Ea = parameter including wind velocity and saturation deficit

Hn = net radiation in mm of evaporable water per day

The parameter Ea is estimated as:

Ea = 0.35 ( 1 + u2 / 160 ) (ew – ea )

where:

u2 = mean wind speed at 2 m above the ground in km/day.

ew = saturation pressure

Formula for computing Hn:

Hn = Ha ( 1 – r ) (a+ bn / N ) – σTa4 [ 0.56 – 0.092 ( ea )

½ x ( 0.10 + 0.90 n / N ) ]

where:

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a = a constant depending upon the latitude φ and is given by

a = 0.29 cos φ

b = a constant with an average value 0f 0.52

σ = Stefan-Boltzman constant = 2.01 x 10-9 mm/day

Ta = mean air temperature in degrees Kelvin ( °K = °C + 273 )

ea = actual mean vapor pressure in the air in mm of mercury.

n = actual duration of bright sunshine in hours

N = maximum possible hours of bright sunshine. It is a function of latitude as indicated in the following table:

Mean Monthly Values of Possible Sunshine Hours, N

North

Latitude Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

0° 12.1 12.1 12.1 12.1 12.1 12.1 12.1 12.1 12.1 12.1 12.1 12.1

10° 11.6 11.8 12.1 12.4 12.6 12.7 12.6 12.4 12.9 11.9 11.7 11.5

20° 11.1 11.5 12.0 12.6 13.1 13.3 13.2 12.8 12.3 11.7 11.2 10.9

30° 10.4 11.1 12.0 12.9 13.7 14.1 13.9 13.2 12.4 11.5 10.6 10.2

40° 9.6 10.7 11.9 13.2 14.4 15.0 14.7 13.8 12.5 11.2 10.0 9.4

50° 8.6 10.1 11.8 13.8 15.4 16.4 16.0 14.5 12.7 10.8 9.1 8.1

Ha = incident solar radiation outside the atmosphere on a horizontal surface, expressed in mm of evaporable water per day. It is a function of the latitude and period of the year as indicated in the table below:

Mean Solar Radiation, Ha

North

Latitude Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

0° 14.5 15.0 15.2 14.7 13.9 13.4 13.5 14.2 14.9 15.0 14.6 14.3

10° 12.8 3.9 14.8 15.2 15.0 14.8 14.8 15.0 14.9 14.1 13.1 12.4

20° 10.8 12.3 13.9 15.2 15.7 15.8 15.7 15.3 14.4 12.9 11.2 10.3

30° 8.5 10.5 12.7 14.8 16.0 16.5 16.2 15.3 13.5 11.3 9.1 7.9

40° 6.0 8.3 11.0 13.9 15.9 16.7 16.3 14.8 12.2 9.9 6.7 5.4

50° 3.6 5.9 9.1 12.7 15.4 16.7 16.1 13.9 10.5 7.1 4.3 3.0

r = reflection coefficient (albedo)

Values of r:

Surface Range of r values

Close ground crops 0.15 – 0.25

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Bare lands 0.05 – 0.45

Water surface 0.05

Snow 0.45 – 0.90

Problem:

Calculate the potential evapotranspiration from an area near Baguio City in the month of November by Penman’s formula. The following data are available:

Latitude = 28°04’ N

Elevation = 230 m

Mean monthly temperature = 19°C

Mean relative humidity = 75%

Mean observed sunshine hours = 9 h

Wind velocity at 2 m heights = 85 km/day

Nature of surface cover = close-ground crop

Initial Loss

Initial loss refers to the process of reducing the water volume for runoff. This consists of the interception process and the depression storage. This abstraction represents the quantity of storage that must be satisfied first before runoff begins.

Interception

Interception is the volume of water caught by the vegetation and the structures and the subsequently evaporated. The route of the intercepted precipitation may follow any of the following:

1. It may be retained by the vegetation as surface storage and returned to the atmosphere by evaporation; a process called interception loss.

2. It can drip off the plant leaves to join the ground surface or surface flow. This is known as a throughfall. 3. The rainwater may run along the leaves and branches and down the stem to reach the ground surface. This is

called stemflow.

Depression Storage

This is the volume of water that fills up all depressions when precipitation reaches the ground before overland flow occurs. This is lost through the process of filtration and evaporation.

Factors affecting depression storage:

1. The type of soil 2. The condition of the surface reflecting the amount and nature of depression 3. The slope of the catchment 4. The antecedent precipitation as a measure of soil moisture.

Infiltration

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This is the movement of water through the soil surface which plays an important role in the runoff process by affecting the timing, distribution, and magnitude of the surface runoff. It is also the primary step in the natural groundwater recharge.

Infiltration Capacity is the maximum rate at which the ground can absorb water.

Field Capacity is the volume of water that the soil can hold.

Infiltrometer is a device used to measure the rate of infiltration. It consists of a cylinder driven into the ground and a buffer cylinder driven into the ground concentric with the inner cylinder. The cylinders are filled with water up to the same level and the change in water levels is observed for a time duration. The purpose of the buffer cylinder is to ensure that the flow of water is truly vertical representing the infiltration.

Factors Affecting Infiltration:

1. Type of soil 2. Properties of soil 3. Structure of soil 4. Size of soil particle 5. Texture of soil 6. Condition of the surface

Horton’s Equation of Infiltration

f ( t ) = fc + ( fo – fc ) e –kt

where:

f= infiltration capacity at any time t

fc = equilibrium or constant infiltration capacity

fo = initial infiltration capacity

k = recession constant (/h)

t = time in hours

The volume of infiltration in inches over the watershed can be found by plotting the curve of infiltration versus time. The area below the curve is the volume of infiltration.

Infiltration Indices

Infiltration Index is the average infiltration rate used in the calculations involving floods.

Types of Indices:

1. φ– index The average rainfall above which the rainfall volume is equal to the runoff volume. The φ–index is derived from the rainfall hyetograph with the knowledge of the resulting runoff. If the rainfall intensity is less than φ–index, then the infiltration rate is equal to the rainfall intensity. The difference between rainfall and infiltration is runoff volume. The amount of rainfall in excess of the φ–index is called rainfall excess.

φ index = infiltration volume / (area x duration )

infiltration volume = volume of rainfall – runoff

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infiltration volume = volume of rainfall – C (volume of rainfall)

where: C is the coefficient of runoff

Factors affecting φ–index a. Soil type b. Vegetal cover c. Initial moisture condition d. Storm duration e. Intensity of rainfall

2. W-index

The average value of infiltration rate defined as:

W =

where: P = total storm precipitation (cm) R = total storm runoff (cm) Ia = initial losses (cm) te = duration of rainfall excess, the total time it which the rainfall intensity is

greater than W (in hours) W = average rate of infiltration (cm/h)

RUNOFF

Runoff means the draining or flooding off of precipitation from a catchment area through a surface channel.

Overland Flow is the excess precipitation moving over the land surfaces to reach smaller channels.

Surface Runoff is a flow travelling all the time over the surface as overland flow and through the channels as open channel flow and reaching the catchment area.

Interflow is a part of the precipitation that infiltrates and moves laterally through upper crusts of the soil and returns to the surface at some location away from the point of entry into the soil. This is sometimes called as through flow, storm seepage, subsurface flow, or quick return flow. Interflow is classified into:

1. Prompt interflow – an interflow with the least lag 2. Delayed flow

Groundwater Flow or Groundwater Runoff is a part of runoff that percolates deeper into the soil and reaching the groundwater storage.

Classification of Runoff

1. Direct Runoff The part of runoff that enters the stream immediately after the precipitation. It includes surface runoff, prompt interflow, and precipitation on the channel surface. This is sometimes called as direct storm runoff or storm runoff.

2. Baseflow The delayed flow that reaches the stream essentially as groundwater flow including delayed interflow.

Runoff Hydrograph

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It is an expression for surface water discharge over time. It is an expression of the watershed characteristics that invariably govern the relationship between rainfall and the resulting runoff. It represents the integrated effects of rainfall and watershed characteristics, such as area, shape, drainage patterns, land use, land and channel properties.

Watershed Characteristics Affecting Runoff Hydrograph

1. Area (A) – the total volume of runoff and peak discharge are proportional to the area of the watershed. 2. Overland Slope (So) – this is the average vertical elevation change per horizontal distance. In the general case,

the time it takes water to get to a point of discharge is the sum of overland flow and channel or pipe flow. As watershed size increases, overland slope decreases in significance. The greater the overland flow time, (less slope), the less is the peak discharge.

3. Channel Slope (Sc) – the average vertical elevation change per horizontal distance along a watercourse bed. The steeper the channel slope, the greater the velocity and the peak discharge.

4. Channel Area (Aα) – the cross-sectional area has an effect on storage and thus attenuation of the hydrograph can be expected as storage increases. Attenuation is a term used to express a hydrograph shape with longer base time and less peak discharge.

5. Soil type and vegetation cover – this affects the amount of rainfall excess and thus the peak of a hydrograph. The greater the initial abstraction and infiltration, the less the rainfall excess.

6. Basin Length (L) – the travel length associated with the longest time it takes for a particle of water to flow overland. The basin length and slope determines the watershed time of concentration.

7. Stream pattern and watershed shapes – a fan-shaped area with streams radiating from the same point suggests contributing incremental areas increasing with time such that a late but high peak in the hydrograph is suggested, whereas an elongated area traversed by one major stream with some relatively uniformly spaced tributaries suggest a less pronounced rise and fall of the hydrograph.

8. Channel Roughness – the lower the roughness the higher the velocity and possibly the peak discharge.

Time of Concentration

It is defined as the longest travel time it takes a particle of water to reach a discharge point in a watershed. There are three common ways that water is transported:

1. Overland flow 2. Pipe flow 3. Channel flow, including gutter flow

Each method has a separate formula for estimating time of concentration.

Time Concentration Formula for Overland Flow:

1. Izzard’s Formula

tc =

( for for i x L < 500)

where: tc = time of concentration (min) L = overland flow (ft) i = rainfall intensity (in/hr) K = (0.007 i + Cr) / s 2/3

and s = slope (ft/ft) Cr = retardance coefficient, given as: Very smooth asphalt 0.007 Tar and sand pavement 0.0075

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Crushed-slate roof 0.0082 Concrete 0.012 Tar and gravel pavement 0.017 Closely clipped sod 0.046 Dense grass 0.060

2. Kerby’s Equation tc = c ( Lns -0.5) 0.467 for L < 365 m (1000ft)

where: tc = time of concentration (min) L = length of flow (ft) (generally less than 1000 ft) s = slope (ft/ft) c = 0.83 (when using feet) or 1.44 (when using meters) n = retardance roughness coefficient, given as: smooth pavement 0.02 poor grass, bare sod 0.30 average grass 0.40 dense grass 0.80

Calculation of Runoff by Rational Method

Q = c i A

where:

c = runoff coefficient, variable with land use

i = intensity of rainfall of chosen frequency for a duration equal to the time of concentration tc (in/hr)

tc = time for rainfall at the most remote portion of the basin to enter or travel to the outlet (min, hr)

A = area of watershed (acres, sq. m)

If c is not given:

c = t / ( 8 + t ) for impervious surface

c = 0.3 t / ( 20 + t ) for pervious surfaces

Intensity Formula (Talbot’s Formula)

i =

inches / hr

i =

mm / hr

Basic assumptions for using the rational formula

1. The rainfall intensity must be constant for a time interval at least equal to the time of concentration. 2. The runoff is a maximum when the rainfall intensity lasts as long as the time of concentration. 3. The runoff coefficient is constant during the storm volume. 4. The watershed area does not change during the storm.

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Streamflow Measurement

Streamflow – represents the runoff phase of the hydrologic cycle. It is the most important basic data for hydrologic studies.

Stream – a flow channel into which the surface runoff from specified basin drains.

Hydrometry – the science and practice of water measurement.

Classification of Streamflow Measurement Techniques:

1. Direct determination of stream discharge a. Area-velocity methods b. Dilution techniques c. Electromagnetic method d. Ultrasonic method

2. Indirect determination of streamflow a. Hydraulic structures, such as weirs, flumes, and gated structures b. Slope-area method

Continuous measurement of discharge in a stream is very difficult to obtain. Direct measurement is a very time consuming and expensive procedure. To make the measurement easier, the following method is used. First, the discharge in a given stream is related to the elevation of the water surface (stage) through a series of careful measurements. The next step consists of observing the stage of the stream routinely and estimating the discharge using the previously determined stage-discharge relationship.

Measurement of Stage

Stage of a River – the water surface elevation measured above a datum. This datum can be the mean sea level or any arbitrary datum connected independently to the mean sea level.

1. Manual Gages a. Staff Gage – a scale set so that a portion of it is always in the water. By this the stage or the elevation of the

water surface can be determined. The gage may consist of a vertical scale attached to a bridge, pier, piling wharf or other structures that extends into the low stage channel of the stream.

b. Sectional Staff Gage – used when there is no suitable structure present in a station. It is usually mounted on a specially constructed supports in such a way that it is always accessible.

c. The Wire-Weight Gage – has a drum with a circumference such that each rotation unwinds one foot of wire.

2. Recording Gages a. Continuous Chart Recorder – the motion of the float waves a pen across a long strip chart. When the pen

reaches the edge of the chart it reverses direction and records in the other direction of the chart. b. Punched Tape – punches the stage at fixed intervals usually 15 min on paper tape. The tape is read by

electronic equipment. c. Float Type Water Stage Recorders – are usually installed in shelter house and stilling well which serves to

protect the float and counterweight cables from floating debris and suppress fluctuations from the surface waves in the stream.

d. Bubble Gages – record the pressure required to maintain a small flow of gas from an orifice submerged in the stream.

e. Crest-Stage Gage – consists of a standpipe with holes to admit water. A ground cork and a graduated staff are placed inside the gage. The cork floats on the surface of the water and as the water rises up then lowers down, the cork will stick to the graduated staff marking the highest level reached by the water.

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Stage Data – is often presented in the form of a plot of stage against chronological time known as stage hydrograph. It is used in the determination of stream discharge and also in the design of flood warning and flood protection works. River stage forms an important hydrologic parameter chosen for regular observation and recording.

Stream Gauging – is the most satisfactory determination of runoff from a catchment by measuring the discharge of the stream draining it.

Methods of Stream Gauging

1. Venturi Flumes or Standing Wave Flumes – used for small channels. 2. Weir Method

Types of Weirs: A. Sharp-crested and Free-flowing

a. Rectangular Suppressed Weir Q = 1.84 LH3/2 Francis Formula

b. Rectangular Contracted Weir Q = 1.84 ( L – 0.20H ) H3/2

c. Triangular or V-notched

Q = CH5/2 where:

C = C’ 8/15 (2g) ½ tan θ/2 C’ = 0.6

H = head over the vertex

d. Trapezoidal Weir Q = 1.86 LH3/2 when tan θ/2 = ¼

B. Sharp-crested and Submerged Weir Q = Q’ ( 1 – Sn ) 0.385

where: Q’ = discharge using free slowing weir n = 1.5 for rectangular weir and 2.5 for triangular weir S = H’ / H H = height of water in the upstream side above the crest H’ = height of the water in the downstream side above the crest.

C. Broad-crested Weir a. Square Upstream Corner

Q = CLH3/2

b. Rounded Upstream Corner

Q = 1.7 LH3/2

where: C = 1.82 for b/H < 2

c. Ogee-shaped Crest Q = CLH3/2 for 1.94 ≤ C ≤ 2.21

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3. Slope-Area Method

Q = AV

a. Chezy’s Formula

V = C √

b. Manning’s Formula

V =

R2/3 S1/2

where: R = hydraulic radius R = A / P S = slope of energy gradient A = sectional area P = wetted perimeter

C =

n = coefficient of roughness m = coefficient of roughness for Bazin’s Formula

4. Contracted-Area Method Q = Cd At [ 2g (dh + ha ) ] ½ where: Cd = coefficient of discharge

At = area of the most contracted section dh = difference in water surface between upstream and downstream sides ha = head due to the velocity of approach

5. Sluiceways, Spillways and Power Conduits

The discharge is equal to the sum of the flow through the outlets in the structure

6. Salt-concentration or Dilution Method The discharge is determined by introducing the chemical at a known constant rate into the flowing water and determining the quantity of chemical in the stream through mixing of the chemical with water. Tracers Used for Dilution Process a. Chemicals (common salt and sodium dichromate) b. Florescent dyes (Rhodamine-Wt and Sulfu-Rhodamine B Extra) c. Radioactive Materials (Bromine-B2, Sodium 24 and Iodine 312)

Properties of the Tracer a. It should not be absorbed by the sediment, channel boundary and faces and also should not be lost by

evaporation b. It should be non-toxic c. It should be capable of being detected in a distinctive manner in small concentrations. d. It should not be expensive.

Q = q ( C1 – C2 ) / ( C2 – C1 )

where:

q = quantity of solution injected (cc/sec)

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C1 = concentration of tracer injected into the stream

C2 = concentration of tracer in the sample downstream

This method is usually used in turbulent waters.

7. Area-Velocity Method

Q = A V

The area is determined by sounding and plotting the profile. The velocity is determined by various methods which includes the following: a. By surface Floats b. By Velocity Rods (Pitot Tube) c. By Current Meter

Current Meter Method

Types of Current Meter

1. Vertical-axis meter – consists of a series of conical cups mounted around a vertical axis. The cups rotate in a horizontal plane and a cam attached to the vertical axial spindle records generated signals proportional to the revolutions of the cup assembly.

2. Horizontal-axis meter – consists of a propeller mounted at the end of a horizontal shaft. These types of current meter can register velocities in the range of 0.15 to 4.0 m/s. The velocity of water at a particular point using a current meter can be calculated by using the straight-line formula:

V = a + b N where:

b = constant of proportionality a = the starting velocity or velocity required to overcome mechanical friction N = number of revolutions per second

Steps in Measuring the Stream Velocity

1. Divide the stream into a number of vertical sections. 2. Measure total depth of water by sounding or a meter stick for shallow rivers or streams. 3. Raise meter to eight-tenths depth to determine the number of rotations for a certain time elapsed. 4. Raise meter to two-tenths depth and repeat step 3.

In shallow water near the shore or banks, a single reading is made at sixth-tenth depth.

Steps in Computing Total Discharge

1. Compute average velocity in each vertical by averaging velocities at two-tenths and eight-tenths depths. 2. Multiply the average velocity in a vertical by the area of a vertical section extending halfway to adjacent

verticals. 3. Add the increments of discharge in the several verticals.

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Ultrasonic Method – another method of area-velocity measurement of discharge.

Average velocity is measured by ultrasonic signals.

Advantages of Ultrasonic System

1. It is rapid and gives high accuracy. 2. It is suitable for automatic recording of data. 3. It can handle rapid changes in the magnitude and directions of flow, as in tidal rivers. 4. The cost of installment is independent of the size of the river.

The accuracy of this method is limited by the following factors:

1. Unstable cross-section 2. Fluctuating weed growth 3. High loads of suspended solids 4. Air entrainment 5. Salinity and temperature changes

Streamflow Variations

1. Variations in the total runoff from year to year 2. Seasonal variations in runoff 3. Variations of daily rates of runoff throughout the year

HYDROGRAPHS

Hydrographs is a plot of discharge versus time. It consists of the following elements:

1. The rising limb AB, joining point A, the starting point of the rising curve, and point B, the point of inflection.

Discharge (cm) B

A

P

C

D

tpk

TB

Lag time tL

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2. The crest segment BC between the two points of inflection with a peak P in between. 3. The falling limb or depletion curve CD, starting from the second point of inflection C.

Other points considered:

1. tpk = the time to peak from the starting point A. 2. Lag time tL = the time interval from the center of mass of rainfall to the center of mass of hydrograph. 3. Qp = peak discharge 4. TB = the time base of the hydrograph

Types of Hydrographs:

1. Annual hydrograph showing the variation of daily or weekly or 10 daily mean flows over a year. 2. Monthly hydrograph showing the variation of daily mean flows over a month. 3. Seasonal hydrograph depicting the variation of the discharge in a particular season. 4. Flood hydrograph due to a storm over a catchment.

Applications of Hydrographs:

1. Annual hydrograph and seasonal hydrograph are used in: a. Calculating the surface water potential of stream b. Reservoir studies c. Drought studies

2. Flood hydrographs are essential in analyzing stream characteristics associated with floods. 3. A study of the annual hydrographs of streams enables us to classify streams into three classes:

a. Perennial Stream – always carries some flow. There is considerable amount of groundwater flow throughout the year. Even during dry season the water able is above the stream bed.

b. Intermittent Stream – has limited contribution from the groundwater. During the wet season the water table is above the stream bed and there is a contribution of the base flow to the stream flow. However, during dry season the water tale drops lower than the stream bed causing the stream to dry up.

c. Ephemeral Stream – one which does not have any base flow contribution. The annual hydrograph of such river shows a series of short duration spikes marking flash flows during storms. The river dries up after the storm.

Factors Affecting the Flow Characteristics of a Stream:

1. The rainfall characteristics, such as magnitude, intensity, distribution in time and space and its variability 2. Catchment characteristics such as soil, vegetation, slope, geology, shape and drainage density 3. Climatic factors which influence evapotranspiration

Factors affecting Flood Hydrographs

1. Physiographic Factors A. Basin Characteristics

a. Shape b. Size c. Slope d. Nature of the valley e. Elevation f. Drainage density

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B. Infiltration Characteristics a. Land use and cover b. Soil type and geological conditions c. Lakes, swamps and other storage

C. Channel Characteristics a. Cross-section b. Roughness c. Storage capacity

2. Climatic Factors

A. Storm Characteristics a. Precipitation b. Intensity of storm c. Duration of storm d. Magnitude e. Movement of storm

B. Initial Loss C. Evapotranspiration

BASE-FLOW SEPARATION

Base-flow is the flow of water in streams that is relatively constant for longer period. There are several methods used in separating base-flow from the direct runoff discussed as follows:

Method I:

A line is simply drawn tangent to both limbs at their lower portion. This method is very simple and can be used only for preliminary estimates.

Method II:

In this method, the separation of the baseflow is achieved by joining with a straight line the beginning of surface runoff to a point ion the recession limb representing the end of the direct runoff. The end of direct runoff on the hydrograph is not easy to determine, thus an empirical equation for the time interval N (days) from the peak to that point is used.

N = 0.83 A 0.2

where: A = drainage area in km2

N = number of days

Method III:

In this method, the baseflow curve existing prior to the commencement of runoff is extended until it intersects the ordinate drawn at the peak (pt. P). This point is joined to the point where direct runoff ends using a straight line. This curve demarcates the baseflow and surface runoff.

Method IV:

In this method, the baseflow recession curve after the depletion of floodwater is extended backwards until it intersects the ordinate at the point of inflection after the peak. This point is then joined to the starting point of runoff using a straight line.

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DIRECT RUNOFF HYDROGRAPH – the surface runoff hydrograph obtained after the baseflow separation.

UNIT HYDROGRAPH

Unit Hydrograph – the hydrograph of direct runoff resulting from one unit depth (1 cm) of rainfall excess occurring uniformly over the basin and at uniform rate for a specified duration D in hours. The duration, being a very important characteristic, is used as a prefix to a specific unit hydrograph (6-h unit hydrograph, 12-h unit hydrograph, etc.) The definition of the unit hydrograph implies the following:

1. The unit hydrograph represents the lumped response of the catchment to a unit rainfall excess of D-hr duration to produce a direct runoff hydrograph. It relates only the direct runoff to the rainfall excess. Hence the volume of water contained in the unit hydrograph must be equal to the rainfall excess. Volume = 1 cm over the catchment.

2. The rainfall is considered to have an average intensity of excess rainfall 1cm/D-hr for the duration of the storm. 3. The distribution of the storm is considered to be uniform all over the catchment.

Derivation of Unit Hydrograph

The unit hydrograph is best derived from the hydrograph of a storm of reasonably uniform intensity, duration of desired length and relatively large runoff volume. The steps are as follows:

1. Plot the hydrograph of the storm. 2. Separate the baseflow from direct runoff. 3. Divide the ordinates of the direct runoff hydrograph by the observed runoff depth. 4. Plot the adjusted ordinates. This will form the unit hydrograph.

Uses of the unit hydrograph

1. Used in the development of flood hydrographs for extreme rainfall magnitudes for use in the design of hydraulic structures.

2. Used in the extension of flood-flow records based on rainfall records. 3. Used in the development of flood forecasting and warning systems based on rainfall.

Limitations of Unit Hydrograph

1. Precipitation must be from rainfall only. 2. The catchment should not have unusually large storages in terms of tanks, ponds, large flood banks storages,

etc. which affect the linear relationship between storage and discharge. 3. Non-uniform precipitation does not result to a good unit hydrograph.

Example:

The runoff data at a steam gauging station for a flood are given below. The drainage area is 40 km2. The duration of rainfall is 3 hours. Derive the 3-hour unit hydrograph for the basin and plot the unit hydrograph.

Date Time (hr) Discharge (m3/sec) Date Time (hr) Discharge (m3/sec)

1-5-1970 2 50 2-5-1970 2 110

5 47 5 90

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8 75 8 80

11 120 11 70

14 225 14 60

17 290 17 55

20 270 20 51

23 145 23 50

GROUNDWATER FLOW

Groundwater is a vital source of water supply, especially in areas where dry summers or extended droughts can cause streamflow to stop.

Zones of Subsurface Water

1. Saturated Zone – also known as groundwater zone. This is that portion where all pores of the soil are filled with water. The water table forms its upper limit and marks a free surface having an atmospheric pressure.

2. Zone of Aeration – in this zone, the soil pores are only partially filled with water. The extent of this zone is from the surface of the ground to the water table. This zone is subdivided into three subzones namely: a. Soil Water Zone – this lies close to the ground surface in the major root hand of the vegetation from which

the water is lost to the atmosphere by evapotranspiration. b. Capillary Fringe – in this zone, the water is held by capillary action. This extends from the water table

upwards to the limit of the capillary rise. c. Intermediate Zone – this lies between the soil water zone and the capillary fringe.

Categories of Saturated Formations

1. Aquifer- a saturated formation of earth material which do not only store water but yield it in sufficient quantity. A good aquifer is formed by unconsolidated deposits of sand and gravel. It transmits water relatively easily due to its high permeability.

2. Aquitard – a formation through which only seepage is possible thus the yield is insignificant compared to aquifer. It is partly permeable.

3. Aquiclude – a geological formation which is essentially impermeable to the flow of water. It may be considered as closed to water movement even though it may contain large amounts of water due to its high porosity; example is clay.

4. Aquifuge – a geological formation which is neither porous nor permeable. It cannot transmit water since there are no interconnected openings. Massive compact rock without fracture is an aquifuge.

Classification of Aquifer

1. Unconfined Aquifer – also known as water table aquifer is one with free surface. 2. Confined Aquifer – also known as artesian aquifer is confined between two impervious layers.

Water Table – divides the two major subsurface zones. It is the locus of points in the unconfined material where hydrostatic pressure equals atmospheric pressure.

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Properties of an Aquifer

1. Porosity – the amount of pore space per unit volume of the aquifer material. 2. Specific Yield – the actual volume of water that can be extracted by the force of gravity from a unit volume of

aquifer material. 3. Specific Retention – the fraction of water held back in the aquifer.

Classification of Soil Moisture

1. Gravity Water – water transmitted through larger pore spaces. 2. Capillary Water – water present in smaller pores. Capillary potential is the work required to move a unit mass of

water from the reference plane to any point in the soil column. It is the potential energy per unit mass of water. 3. Hygroscopic Water – water adhering in a thin film to soil grains. It is held by molecular attraction and is not

normally removed from the soil under usual climatic conditions.

States of Water in Soil

1. Field Capacity – the moisture content of soil after gravity drainage is complete. 2. Moisture Equivalent – the water retained in a soil sample. 3. Wilting Point – represents the soil moisture level when plants cannot extract water from soil. It is the moisture

held at a tension equivalent to the osmotic pressure in the plant roots. 4. Available Moisture – the difference between the field capacity and the wilting point.

Sources of Groundwater

1. Meteoric Water – derived from precipitation 2. Connate Water – present in the rock at its formation and is frequently saline 3. Juvenile Water – formed chemically within the earth and brought to the surface in intrusive rocks. Connate and

juvenile waters are common sources of undesirable minerals in water. 4. Influent Streams – streams contributing to groundwater

Discharge of Groundwater

Groundwater in excess of the local capacity of an aquifer is discharges by evapotranspiration and surface discharge. Direct discharge by transpiration to the atmosphere is done whenever the capillary fringe reaches the root systems of the vegetation. Some plants have root systems that reach more than 30 feet to reach the underground water.

If the water table or an artesian aquifer intersects the ground surface, water is discharged as surface flow. If the flow is spread over a large area, diffuse seepage may occur. In this case, the water does little more than wet the ground from which it evaporates. A large discharge from the aquifer concentrated in small area is called spring.

Types of Spring

1. Water hole or dimple spring 2. Perched Spring 3. Anticlinal Spring 4. Spring from solution of channel

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Potential of a Groundwater Reservoir

The potential of a groundwater reservoir is limited to the permissible rate of withdrawal from a groundwater basin.

Safe Yield – the rate at which water can be withdrawn for human use without depleting the supply to such an extent that withdrawal at this rate is no longer economically feasible.

Mining – the permanent withdrawal of groundwater from storage.

The safe yield of groundwater basin is governed by many factors. One of the most important is the quantity of water available. Transmissibility of an aquifer may also limit the safe yield. Economic considerations must also be considered. The deeper the location of the underground water, the more expensive will be the extraction.

Artificial Recharge

The yield of an aquifer may be increased artificially by introducing water into it. The methods employed are controlled by the geologic situation of an area and by economic considerations. The possible methods include the following:

1. Storing flood waters in reservoirs constructed over permeable areas. 2. Storing flood waters in reservoirs for later release into the stream channel at rates approximating the

percolation capacity of the channel. 3. Diverting streamflow to spreading areas located in a highly permeable stratum. 4. Excavating recharge basins to reach permeable formations. 5. Pumping water through recharge wells into the aquifer. 6. Over-irrigating in areas of high permeability. 7. Construction of wells adjacent to a stream to induce percolation from streamflow.

RESERVOIRS

Water supply, irrigation or hydro-electric project getting water directly from streams may not be able to satisfy the consumers especially during low flows. The stream may also dry out during extended drought; therefore it is necessary to store water for future use. This can be done by the use of reservoirs. Reservoirs can be used to store excess flow during storms at the same time can help in controlling floods.

Reservoir Capacity – the volume of water that can be accommodated or stored in the reservoir to be used during dry periods.

Zone of Storage in a Reservoir