Hydrology

Chia-Ming Fan

Department of Harbor and River Engineering National Taiwan Ocean University

2010/03/11

Contents

• Ch 1 Introduction• Ch 2 Precipitation• Ch 3 Abstractions from Precipitation• Ch 4 Streamflow Measurement• Ch 5 Runoff• Ch 6 Hydrographs• Ch 7 Floods• Ch 8 Flood Routing• Ch 9 Groundwater• Ch 10 Erosion and Reservoir Sedimentation

Chapter 2 Precipitation• 2.1 Introduction• 2.2 Forms of precipitation• 2.3 Weather systems for precipitation• 2.4 characteristics of precipitation in India• 2.5 Measurement of precipitation• 2.6 Raingauge network• 2.7 Preparation of data• 2.8 Presentation of rainfall data• 2.9 Mean precipitation over an area• 2.10 Depth-area-duration relationships• 2.11 Frequency of point rainfall• 2.12 Maximum intensity-duration-frequency relationship• 2.13 Probable maximum precipitation (PMP)• 2.14 Rainfall data in India

2.1 Introduction

• The term precipitation denotes all forms of water that reach the earth from the atmosphere. (rainfall, snowfall, hail, frost, dew,…)

• Variation floods and droughts

• For precipitation to form 1. the atmosphere must have moisture 2. there must be sufficient nuclei present to aid condensation 3. weather conditions must be good for condensation of water

vapour 4. the products of condensation must reach the earth

2.2 Forms of precipitation

• Rain• Snow• Drizzl

e • Glaze• Sleet• Hail

2.3 Weather systems for precipitation

• Front: a front is the interface between two distinct air masses.

• Cyclone( 氣旋 ): a cyclone is a large low pressure region with circular wind motion

1. Tropical cyclone (hurricane, typhoon) 2. Extratropical cyclone• Anticyclone( 反氣旋 ): high pressure• Convective precipitation( 對流雨 ): usually, the area

l extent of such rains is small, being limited to a diameter of about 10 km.

• Orographic precipitation( 地形雨 ):

2.3 Weather systems for precipitation

2.5 Measurement of precipitation

• Raingauge: 1. nonrecording 2. recording

• For sitting a raingauge the following considerations are important:

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 ground 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 5.5m * 5.5m

2.6 Raingauge network

• An optimum density of gauges (Storm--Catchments)

• Optimum number of stations:

2

vCN

Optimum number of stations

Coefficient of variation of the rainfall values at the existing m stations

Allowable degree of error in the estimate of the mean rainfall

2.6 Raingauge network

• If there are m stations in the catchment each recording rainfall values P1,P2,…Pm in a known time, the coefficient of variation Cv is calculated as:

21

1 1

m

i

m

P P

m

1100 mvC P

1

1 m

iP Pm

Coefficient of variation

Standard deviation

Mean precipitation

Ex 2.1

2.7 Preparation of data

• The normal rainfall is the average value of rainfall at a particular date, month ot year over a specified 30-year period.

• Estimation of missing data within 10%

Pj: annual precipitations Nj: normal annual precipitations

1 2 3

1...x mP P P P P

m

31 2

1 2 3

...x mx

m

N P PP PP

m N N N N

Normal ratio method

Ex 2.2

2.7 Preparation of data (Test for consistency of record)

Ex 2.3

2.8 Presentation of rainfall data• Mass Curve of Rainfall ( 降雨累積曲線 )

2.8 Presentation of rainfall data

• Hyetograph （降雨組體圖）

2.8 Presentation of rainfall data

• Point rainfall (station rainfall)• Moving average• Ex 2.4

TABLE 2.2

2.9 Mean precipitation over an area

• Arithmetical-mean method 算數平均法• Thiessen-polygon method 徐昇多邊形法• Isohyetal method 等雨量線法

Arithmetical-mean method

In practice, this method is used very rarely.

1 2 3

1

.... .... 1 Ni n

ii

P P P P PP P

N N

2.9 Mean precipitation over an area

• Thiessen-polygon method

2.9 Mean precipitation over an area

• Thiessen-polygon method

1 1 2 2 3 3 4 4 5 5 6 6

1 2 3 4 5 6

PA P A P A P A P A P AP

A A A A A A

2.9 Mean precipitation over an area• Isohyetal method

2.9 Mean precipitation over an area

• Isohyetal method

2 3 11 21 2 1.......

2 2 2n n

n

P P P PP Pa a a

PA

Ex 2.5

Ex 2.6

2.10 Depth-area-duration relationships

• Depth-area relation

0 expnP P KA

Average depth in cm over an area A km2

Highest amount of rainfall in cm at the storm center

K and n are constants in a given region

2.10 Depth-area-duration relationships

• Maximum Depth-Area-Duration (DAD) Curves

2.11 Frequency of point rainfall

• The probability of occurrence of an event of a random variable (rainfall) whose magnitude is equal to or in excess of a specified magnitude X is denoted by P.

• The recurrence interval (also known as return period) is defined as

T=1/P

• This represents the average interval between the occurrence of a rainfall of magnitude equal to or greater than X.

2.11 Frequency of point rainfall• If the probability of an event occurring is P, the

probability of the event not occurring in a given year is q=(1-P).

• The binomial distribution can be used to find the probability of occurrence of the event r times in n successive years. Thus

,

!

! !n r n r r n r

r n r

nP C P q P q

n r r

2 22,

!

2 !2!n

n

nP P q

n

0, 1nn

nP q P

1 1 1 1nnP q P

Ex 2.7

2.11 Frequency of point rainfall

• Plotting Position (empirical formula) The probability analysis may be made

either by empirical or by analytical methods.

Ex 2.8

2.12 Maximum intensity-duration-frequency relationship

Ex 2.9

2.13 Probable maximum precipitation (PMP)

• The probable maximum precipitation (PMP) is defined as the greatest or extreme rainfall for a given duration that is physically possible over a station or basin.

(1) Meteorological methods(2) The statistical study of rainfall

data

Problems

• 2.1/2.2/2.6/2.7/2.12/2.14/2.16/2.19