1. HYDROLOGIC CYCLE AND SOME COMPONENTS
CHAPTER FOUR
HYDROLOGIC CYCLE AND SOME COMPONENTS

2. 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.

3. 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.

4. Hydrologic Cycle

6. 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.

7. 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.

8. 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.

9. 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.

10. 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.  

11. 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. 

12. 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.

13. 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. 

14. 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 = miles/hr).

15. Hand-Held Anemometer

16. 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.

17. 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.

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

19. 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)

20. 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.   

21. Rain Gauge

22. 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 cm diameter (b) Cylindrical measuring tube
(c) Overflow can
(d) Measuring stick.

23. 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.

24. 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.

25. Tipping Bucket Gauge

26. 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.

27. Weighing-Type Gauge

28. 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.

29. 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.

30. 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

31. 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

32. 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    

33. Arithmetic Mean This is the simplest method.
Arithmetic mean = ( )/ 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

34. 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.

35. 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.

36. 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.

37. 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.

38. 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.

39. 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.

40.   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.

41. 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 (P>Pi) as:
Method Frequency of exceedance
California r / n
Hazen (r – 0.5)/n
Weibull r / (n+1)
Gringorten (r – 0.44) / (n )
The frequency of exeedance corresponds with the plotting position on the probability scale of the probability paper. Plot data on normal Probability Paper.

42. 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)

45. 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).

47. 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.

48. 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.

49. 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.

50. 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. 

51. 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.

52. 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.

53. 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 > 10 years, annual series is equal to the partial duration series.

54. (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.

55. 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, , , , , 73.15, , , , , 91.44, , , and (14 years of record).
Rearranging this in descending order of magnitude, we have: (2), (2), 128,02, , (2), (2), , 91.44, 85.34, and

56. 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.

57. For the Iowa intensity values above the ranks are:

58. 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.

59. 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.

62. Steps Contd.
Plot graphs of Intensity Vs Duration for different return periods as shown in Figure 4.8

64. 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.

65. 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)

66. 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.