CHAPTER FOUR

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CHAPTER FOUR

• HYDROLOGIC CYCLE AND SOME COMPONENTS
•  

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4.1 DEFINITION OF HYDROLOGY

• Hydrology is the science of the origin,
  distribution and properties of the waters of the
  earth.
• It deals with the study of water as it occurs on,
  over and under the earth surface.
• This includes precipitation, evaporation, runoff,
  groundwater etc.

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4.2 HYDROLOGIC CYCLE

• This is a graphical description of how water
  moves.
• The hydrologic cycle is a cyclic movement of
  water from the sea to the atmosphere and thence
  by precipitation to the earth where it collects
  in streams and runs back to the sea.
• The cycle can be visualized as beginning with the
  evaporation of water from oceans and land masses
  and by trees through transpiration.

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Hydrologic Cycle
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Hydrologic Cycle Contd.

• The vapour is carried by moving air masses which
  upon proper conditions is condensed to form
  clouds which in turn falls as precipitation to
  the earth.
• The greater part of the water which falls on the
  land is temporarily retained in the soil and
  returns to the atmosphere by evaporation and
  transpiration by plants.

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Hydrologic Cycle Contd.

• A portion of the water which enters the soil
  forms part of the groundwater and flows back to
  the stream.
• Another portion of it flows parallel to the soil
  surface and enters the stream. This portion of
  water does not hit the water table and is called
  lateral flow (see Fig. 1.1).
• There is also the overland flow which just moves
  on the surface of the soil into the stream.

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Hydrologic Cycle Concluded

• The overland flow (surface flow), the lateral
  flow and the groundwater under the influence of
  gravity move towards lower elevations from where
  they may eventually discharge into the ocean.
• A lot of this water is lost to the atmosphere by
  evaporation and transpiration before reaching the
  ocean.

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COMPONENTS OF THE HYDROLOGIC CYCLE

• The hydrologic characteristics of a given region
  are determined largely by its climate and its
  geological structure, the climate playing a
  dominant part.
• The climatic factors that affect the hydrological
  features of an area or region are
• Amount and Distribution of Precipitation,
• The occurrence of Snow and Ice (in Temperate
  Regions),
• The Effects of Wind, Temperature and Humidity on
  Evaporation.

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COMPONENTS OF THE HYDROLOGIC CYCLE CONTD.

• The design and operation of hydrologic projects
  involve meteorological considerations.
• Hydrologic problems in which meteorology plays an
  important role include the
• Determination of probable maximum precipitation
  for spillway design,
• Forecasts of precipitation for reservoir
  operation, and
• Determination of probable maximum winds over
  water surfaces for evaluating resulting waves in
  connection with the design of dams.  

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Temperature

• Temperature can be measured using the maximum and
  minimum thermometers.
•   Temperature Terminologies
• (a) Mean daily temperature This is the
  average of the maximum and minimum temperatures.
• (b) Mean monthly temperature The average of
  the mean monthly daily maximum and minimum
  temperatures. 

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Temperature Terminologies Continued

• (c) Mean annual temperature The average of
  the monthly means for the year.
• (d) Normal temperature The average daily
  mean temperature for a specified time usually 30
  years. Every 10 years, the data for the first 10
  years is dropped.

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Temperature Terminologies Concluded

• (e) Daily Range in Temperature The
  difference between the highest and lowest
  temperatures recorded on a particular day.
• (f) Lapse Rate or Vertical Temperature Gradient
  This is the drop of temperature with rise in
  elevation. For every 300 m rise, temperature
  drop is 3.6 or 2.1 C. 

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WIND

• The important parameters of wind are wind speed,
  wind run and wind direction.
• The wind speed is measured using an anemometer
  while its direction is measured with a wind vane.
  
• Wind speed is given in miles per hour, metres per
  second or knots(1 knot 1.151 miles/hr).

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Hand-Held Anemometer
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Wind contd.

• The conventional anemometer is the cup anemometer
  made up of 3 or 4 cups arranged in a circular
  form rotating around a vertical axis.
• The wind speed is the speed of rotation of the
  cups while the wind run, which is the distance a
  particular parcel of air is moving through in a
  given time, is given by the total revolutions
  around the axis of the cups.

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Wind Measurement Concluded

• The particular height of wind speed measurement
  should be specified. An empirical relationship
  exists between wind speed and height
• 
  
• U/Uo (Z/Zo)0.15
•  
• Uo is the wind speed at height Zo and U is that
  at higher level Z.

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Precipitation

•  Precipitation includes mainly
• Rainfall,
• Dew,
• Fog drip,
• Hail and
• Drizzle, also called mist.
•  

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MEASUREMENT OF PRECIPITATION

• Rain gauges are used, There are two rain
  gauge types.
• (a) Non-recording gauges for taking daily values
• (b) Recording gauges. 
• If the volume of water entering the rain gauge is
  known, divide it by the area of the catching
  device to get the depth of rain. 
• ie. depth per unit area Volume(mm3)/
  Area(mm2)

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Non-Recording Gauges

• Non-Recording gauges measure only the total
  amount of rainfall and not the intensity of the
  rainfall from time to time.
• A typical non-recording gauge is the Rain
  Gauge.   

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Rain Gauge
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Rain Gauge

• All measurements are made with the USWB(United
  States Weather Bureau) rain gauge in order to
  effect standardization.
• The rain gauge is approximately 20 cm in diameter
  and has 4 components 
• (a) Collector or receiver - 20 cm diameter
  (b) Cylindrical measuring tube
• (c) Overflow can
• (d) Measuring stick.

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Rain Gauge Concluded

• Water enters the receiver and goes into the
  measuring tube through the funnel.
• To measure precipitation, the funnel is removed
  and the precipitation measured with a measuring
  stick.
• The overflow can is 10 times the size of the
  measuring tube so as to collect excess water when
  the need arises.

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Recording Gauges

• Recording gauges measure both the amount of
  rainfall and the intensity.
• Two main types exist tipping bucket and the
  weighing gauge types.
• (a) Tipping Bucket Gauge There are two conical
  compartments fixed at a point.
• When rain that enters the equipment from the
  receiver reaches 0.25 mm, it tips and empties its
  contents to the reservoir below.
• This tipping is recorded by a needle on a paper
  wrapped round a rotating cylinder.

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Tipping Bucket Gauge
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b) Weighing Type Recording Gauge

• This is similar to the non-recording type gauge
  but the overflow can rests on a scale.
• The weight of rainfall is measured on the scale
  and transmitted to a Lab's rotating shaft
  through an electric wire.
• There is a calibration to get the amount of
  precipitation.
• Alternatively, a bucket can be set on a platform
  of a spring or lever balance.
• The increasing weight of the bucket and its
  contents is recorded on a chart.
• The record then shows the accumulation of
  precipitation.

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Weighing-Type Gauge
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Missing Precipitation Data

• The missing data can result from
• Technical fault e.g. power failure(for the
  gauge) or
• From the inability of the observer to record it.
  

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Estimating Missing Rainfall Data

• Missing Rainfall Data Can be estimated Using
• a) Arithmetic Average Method If normal
  annual precipitation at each of the three
  index(nearest) stations around the missing data
  gauge is within 10 of that of the missing data,
  use the arithmetic average of the stations to
  estimate the current rainfall amount.

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Missing Rainfall Data Contd.

• Example The annual and current rainfall values
  for stations A, B, and C are known.
• The annual rainfall for station X is also known
  but the current data is missing.
• The current missing value for station X is
•  
• Total current rainfall values for stations
• A, B, C / 3

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b) Normal Ratio Method

• If the annual rainfall values are not within 10,
  weighted average or the Normal Ratio method is
  used
•  
• Px 1/3( Nx/Na Pa Nx/Nb Pb Nx/Nc Pc)
•  Where Px is the current rainfall value for
  station X
• Pa, Pb, and Pc are the current rainfall values
  for stations A, B, and C.
• Na, Nb, Nc, and Nd are the annual values for
  stations A, B, C, and X

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AVERAGE PRECIPITATION OVER AN AREA

•  
• The depth of precipitation over a specified area,
  either on a storm, seasonal or annual basis is
  required in many types of hydrologic problems.
  There are three major methods
•  Arithmetic Mean
• Thiessen Polygon Method
• Isohyetal Method    

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Arithmetic Mean

• This is the simplest method.
• Arithmetic mean (3.6 4.8 8.8 12.4 8.6
  12.7)/ 6 8.5 cm.
• The method yields good estimates in flat
  country, if the gauges are uniformly distributed
  and the individual gauge catches do not vary
  widely from the mean.

3.6
.4.8
.8.8
.12.7
.12.4
.8.6
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Thiessen Method

• The method allows for non-uniform distribution of
  gauges by providing a weighting factor for each
  gauge.
• The stations are plotted on a map and connecting
  lines are drawn.
• Perpendicular bisectors of these lines form
  polygons around each station.
• The sides of each polygon are the boundaries of
  the effective area assumed for the station.

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Isohyetal Method

• The most accurate method of averaging
  precipitation over an area is the isohyetal
  method.
• Station locations and amounts are plotted on a
  suitable map and contours of equal precipitation
  (isohyets) are then drawn.
• Multiply the areas enclosed by the isohyetal
  lines by the average of their two rainfall
  values.
• Do the same to all the areas, and then sum the
  whole product and divide by the total area.

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FREQUENCY ANALYSIS OF RAINFALL DATA

•           Definitions
• a) Historical or Actual Rainfall Data The
  historical rainfall data is the actual recorded
  rainfall during a specified period.
•  
• b)  Average or Normal Rainfall This is the
  arithmetic mean derived from a record of several
  years of historical rainfall data.

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Definitions Contd.

• a) Dependable Rainfall Dependable rainfall is
  defined as the rainfall which can be expected a
  set number of years out of a total number of
  years.
• For instance, the dependable rainfall may be the
  rainfall which can be expected in 9 years out of
  10 years (90).
• The percentage (90) gives the probability, that
  the rainfall will be obtained or exceeded i.e.
  the probability that the actual rainfall will be
  equal to or higher than the dependable rainfall.
  
• One year out of 10, the rainfall amount will be
  smaller.

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Dependable Rainfall Selection.

• The determination of the probability level is
  related to the risk, one wants to accept.
• In the case of expensive structures such as
  bridges or dams and intakes in rivers one may
  want to restrict the risk, that the rainfall
  (causing the flood damage) will exceed a certain
  value, to once in 50 or once in 100 years.
• The corresponding probabilities of exceedance
  here are 2 and 1 respectively.

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Dependable Values For Agriculture

• For agriculture, the risks involved are the
  reduction in or the loss of the yield once in so
  many years.
• The selected dependable level of rainfall is the
  depth of rainfall that can be expected 3 out of 4
  years or 4 out of 5 years.
• The probabilities of exceedance are respectively
  75 and 80. This minimum rainfall is used as
  a design norm for the dimensioning of the
  irrigation system as well as for water
  management.

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  Frequency Analysis

• Frequency analysis based on depth ranking and
  assuming a log normal distribution is worked out.
  
• The log normal distribution has been found by
  Ekwue et al. (1997) to be very good for analyzing
  monthly rainfall data in the Caribbean Region.
• The procedure is as follows
• - Rank the (n) data (Pi) in a descending order,
  the highest value first and the lowest value
  last.

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Procedure of Frequency Analysis Contd.

• Attach a serial rank number, r to each value (Pi)
  with r 1 for the highest value (Pi) and r n
  for the lowest value (Pn)
• -Calculate the frequency of exceedance F (PgtPi)
  as
• Method Frequency of exceedance
• California r / n
• Hazen (r 0.5)/n
• Weibull r / (n1)
• Gringorten (r 0.44) / (n 0.12)
• The frequency of exeedance corresponds with the
  plotting position on the probability scale of the
  probability paper. Plot data on normal
  Probability Paper.

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Example

• 1.      Depth Ranking
• For demonstration, use will be made of the
  monthly rainfall data for the month of January
  for Marper Farm, Manzanilla, Trinidad (Table 2.1)

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2.      Plotting

• After ranking the data and calculating the
  frequency of exceedance (Table 4.2), the
  calculated frequencies of exceedance are plotted
  on normal probability paper (Figure 4.6).

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Plotting Continued

• The plotted data fall in a reasonable alignment
  so, it can be assumed that the data can be
  approximated by the assumed log normal
  distribution.
• In some instances the normal distribution will
  suffice in which case the actual rainfall values
  are used in the plot instead of the transformed
  log values.

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Plotting Concluded

• After fitting a straight line through the points,
  the magnitude of rainfall corresponding to
  various probabilities is derived from the
  probability plot (Figure 4.6).
• In this example, the probability of January
  rainfall exceeding 66 mm is 80. The 20
  dependable rainfall is 210 mm.

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RAINFALL-INTENSITY-DURATION-FREQUENCY ANALYSIS

• The purpose of the analysis is to predict
  rainfall for design projects. There is the need
  to know how often rainfall is expected to occur.

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Definitions

• a) Rainfall Intensity The amount of
  precipitation accumulated over a unit time.
•  
• b) Duration A continuous period of rainfall.
•  
• c) Frequency/Return Period/Recurrence Interval
  This gives the average number of years within
  which a given event will be expected to occur at
  least once. 

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Frequency Analysis

• (a) Need Definitions This can be used for
  different purposes e.g.
• i) the design of urban storm village system ii)
  
• Design of highway culverts
• iii) Design of airport drainage.

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Frequency Analysis Contd.

• Frequency analysis of rainfall is based on
  historical data. Two methods of selecting
  extreme rainfall data(design rainfall data) are
• i) Annual Series This involves selecting
  the maximum value for each calendar year of
  record.
• ii) Partial Duration Series This involves
  first establishing a base value and selecting all
  values equal to or greater than the base value.

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Annual and Partial Duration Series

• Annual Series The highest rainfall event for
  each year is chosen so that the number of values
  is same as the number of years considered.
• Partial Duration Series, a base value is set so
  that each year has at least one event.
• For times of years or record gt 10 years, annual
  series is equal to the partial duration series.

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(b) Steps in the Analysis

• a) Choose the station to be studied.
• b) Assemble as much data as are available for the
  station (total series).
• c) Decide which series will be used in the
  analysis and compile the series) arranging the
  data in a descending order of magnitude.

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Example

• See data sheet in tutorial sheet (Table 4.4).
  E.g. for 5 min duration, annual highest rainfall
  intensities of Iowa(Annual series) from 1953 to
  1966 are 85.34, 103.63, 152.40, 106.68, 121.91,
  73.15, 124.97, 152.40, 128.02, 121.92, 91.44,
  137.16, 106.68, and 137.16 (14 years of record).
  
• Rearranging this in descending order of
  magnitude, we have 152.40(2), 137.16(2), 128,02,
  124.07, 121.92(2), 106.68(2), 103.63, 91.44,
  85.34, and 73.15.

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Definition of Rank

• Rank is the number of any event(intensity) when
  arranged in the decreasing order of magnitude.
• It is equal to 1 for the first event and n for
  the last one.
• Rank can also be defined as the number of events
  greater than or equal to the required value.

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For the Iowa intensity values above the ranks are

•  Intensity 152.40 137.16 128.02
• Rank 2 4 5
• Intensity 124.97 121.92 106.68
• Rank 6 8 10
• Intensity103.63 91.44 85.34 73.15
• Rank 11 12 13 14

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Steps in Frequency Analysis Contd.

• d) Apart from the 5 min duration rainfall,
  values for other durations can be ranked. Plot
  Intensity Vs Rank for all rainfall durations as
  shown in Figure 4.7.
• (e)   To relate these to return period, an
  empirical plotting equation (Gumbel's plotting
  equation) is used.
• T (n 1)/ m
• n is the number. of years of record (in this
  case, 14)
• m is the rank or order number and T is the return
  period.

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Steps in Frequency Analysis Contd.

• For T 2 years, for example, given that n 14,
  m (n 1)/T (14 1)/2 7.5
• Plot m 7.5 in Figure 4.7 and read values of
  intensities for each duration ie. for same T.
  Similarly plot m 3 and m 1.5 for return
  periods of 5 years and 10 years and read up
  values of rainfall intensity for various
  durations. These values are shown in Table 4.5.

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Steps Contd.

• Plot graphs of Intensity Vs Duration for
  different return periods as shown in Figure 4.8

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Extrapolation of Results

• In order to extrapolate rainfall intensity
  values of given durations for longer return
  periods (longer than the period of record), plot
  log intensity Versus log return period.

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Example

• Extrapolate the intensity values of 30 min
  duration with 50 year return period.
• Solution.
• Table 2.6 30 minute duration rainfall
• Intensities
• Return Period (years) 30 minute duration
  intensity (mm/hr)
• 2 51
• 5 69
• 10 88

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Solution Concluded

• Plot Log Rainfall Intensity Vs Return period as
  shown in Figure 4.9.
• Extend the line and extrapolate the value of
  intensity with 50 year return period as 160
  mm/hr.

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