Chapter 1 - Main Hydrological Concepts

CHAPTER 1 MAIN HYDROLOGICAL CONCEPTS

Learning Objective This chapter is designed to assist the students to develop and enhance their ability and knowledge in main hydrological concepts such as hydrological cycle and water balance equation.

Learning Outcomes At the end of this chapter, students should be able to: 1. define hydrology. 2. apply fundamental knowledge of hydrology particularly use in civil and environmental engineering. 3. apply water balance equation as the base of a modeling of hydrology which covers processes of precipitation, evaporation, infiltration, runoff and groundwater.

Hydrology

1.1 Introduction to Hydrology And Its Utilizing Hydrology is a science that studies the availability and movement of water in the earth. Hydrology is also defined as a science related to the occurrence and distribution of natural water on the earth. As general, hydrology covers many type of water, including transformation among liquid, solid and gas in atmosphere, surface and subsurface land. The field of hydrology is of fundamental importance to civil and environmental engineers, hydrogeologists, and other earth scientists because of the environmental significance of water supply, major floods and droughts and their management, drainage and urban stormwater issues. Commonly, cases of hydrology are solved using various sciences such as mathematics, physics, statistic, meteorology, oceanography, geography, geology, geomorphology, hydraulics, and water resources engineering. In addition, many modern hydrology problems include considerations of water quality and contaminant transport. 1.2 Hydrology Cycle And Water Balance Equation Hydrologic cycle is a continues process in which water is evaporated from water surfaces and oceans, moves inland as moist air masses, and produce precipitation if the correct vertical lifting conditions exist. The precipitation that falls from clouds onto the land surface of the earth is dispersed to the hydrologic cycle via several pathways (Fig.1.1). Cloud

LS

P Cloud

Cloud

T P

P

F F

2

Wind

R

E

G P = Precipitation T = Transpiration F = Infiltration R = Run-off G = Groundwater flow E = Evaporation from lake, land surface and ocean LS = Land surface WT = Water table

WT

Lake

E

E LS

Figure 1.1: The Hydrologic Cycle

E Reservoir

R WT

G

Ocean

impermeable layer

Main Hydrological Concept

Hydrologic cycle is a very complex series of processes (Fig.1.1), but under certain well-defined conditions the response of a watershed to rainfall, infiltration, and evaporation can be calculated if simple assumptions can be made. A watershed is a contiguous area that drains to an outlet, such that precipitation that falls within the watershed runs off through that single outlet (the catchment is sometimes used synonymously for just the surface portion of the watershed).

Outlet a. Elongated shape

Outlet

b. Concentrated shape

Figure 1.2: Typical watershed areas

A portion of the precipitation (P), or rainfall, is retained in the soil near where it falls and returns to the atmosphere via evaporation (E), the conversion of water to water vapor from a water surface, and transpiration (T), the loss of water vapor through plant tissue and leaves. The combined loss, called evapotranspiration (ET), is a maximum value if the water supply in the soil is adequate at all times. Some water enters the soil system as infiltration (F), which is a function of soil moisture conditions and soil type, and may reenter channels later as interflow or may percolate to recharge the shallow groundwater. Groundwater (G) flows in porous media in the subsurface in either shallow or deeper aquifer systems that can be pumped for water supply to agricultural and municipal water systems. The remaining portion of precipitation becomes overland flow or direct runoff (R), which flows generally in a down-gradient direction to accumulate in local streams that then flow to rivers. Evaporation and infiltration are both complex

3

Hydrology

losses from input rainfall and are difficult to measure or compute from theoretical methods. Surface and groundwater flow from higher elevation toward lower elevations and may eventually discharge into the ocean, especially after large rainfall events (Fig.1-1). However, large quantities of surface water and portions of groundwater return to the atmosphere by evaporation or ET, thus completing the natural hydrologic cycle. Precipitation from the atmosphere is a major force that drives the hydrologic cycle, and understanding major weather parameters and systems is important for the prediction of precipitation events. In the learning of hydrology always there is a question how much water available in the earth. This question describes the main objective of hydrology, but human is not able to asses the volume of water in the earth exactly, however the availability of water can be estimated based on natural water circulation through hydrologic cycle. According to Water of the World (1964), the total volume of water in the world is about 1,358 million km 3 mainly in the form of sea water. The total volume of fresh water is only 2.8 % (most of fresh water are in the form of ice and glacier), thus the total volume of fresh water which can be used for human live is only 0.63% or 8.54 million km3 in the form of groundwater, lake, and rain. For any hydrologic system, a water budget can be developed to account for various flow pathways and storage components. The hydrologic continuity equation for any system is. IQ 

dS dt

(1-1)

where: I = inflow [L3/t] Q = outflow [L3/t] dS/dt = change in storage per time [L3/t] The same concept can be applied to small basins or large watersheds, with the added difficulty that all loss terms in the hydrologic budget may not be known. For a given time period, a conceptual mathematical model of the overall budget for Fig.1-1 would become, in units of depth (i. or mm) over the basin. P – R – G – E – T = S where: P = precipitation, R = surface runoff, G = groundwater flow, E = evaporation, 4

(1-2)

Main Hydrological Concept

T = transpiration, S = change in storage in a specified time period. Example 1.1 For a given month, a 121 ha lake has 0.43 m 3/s of inflow, 0.37 m3/s of outflow, and total storage increase of 1.97 ha-m. A USGS gage next to the lake recorded a total of 3.3 cm precipitation for the lake for the month. Assuming that infiltration loss is insignificant for the lake, determine the evaporation loss, in cm, over the lake for the month. Solution Solving the water balance for inflow I and outflow Q in a lake gives, for evaporation, E = I – O + P – S, 

m3   30day   24hr  3,600sec  0.43   1month    sec   1month  1day  1hour   I = 0.92 m = 92 cm 2   121ha  10,000m  1ha   

m3   0.37  1month   30day   24hr  3,600sec sec   1month  1day  1hour  Q = 0.79 m = 79 cm  10,000m2   121ha  1ha  

P = 3.3 cm ΔS 

1.97ha m 121ha

= 0.0163 m = 1.63 cm

E = 92 – 79 + 3.3 – 1.63 = 14.67 cm Example 1.2 A swimming pool (6m  6m  1.5m) has a small leak at the bottom. Measurements of rainfall, evaporation, and water level are taken daily for 10 days to determine what should be done for repair. Estimate the average daily leakage out of the

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Hydrology

swimming pool in cm3/day. Assume the pool is exactly 1.5 m deep at the end of day 1. Day 1 2 3 4 5 6 7 8 9 10

Evaporation (mm) 12.7 0 12.7 0 12.7 12.7 0 12.7 12.7 12.7

Rainfall (mm) 25.4 50.8 101.6 -

Measured Level (mm) 1,524

1,321

Solution The water balance equation becomes: Q = P – E – S Total change in storage, S = 1,321 – 1,524 = -203 mm Total precipitation, P = 25.4 + 50.8 + 101.6 = 177.8 mm Evaporation, E = (7)  (12.7) = 88.9 mm Thus, outflow = 177.8 – 88.9 – (-203) = 291.9 mm Outflow should be in cm3/day. The height change is distributed over the pool area.

Q=

6

 291.9mm 

1cm   100cm  100cm    6m    6m   3  10mm  1m   1m  = 1,050,840 cm /day 10days

Main Hydrological Concept

1.3

Hydrologic Data

Data on hydrologic variables are fundamental to analyses, forecasting, and modeling. Such data may be found in numerous publications of agencies, research institutes, universities, and other organizations. 1.3.1 General Climatology Data The most readily available sources of data on temperature, solar radiation, wind, and humidity are monthly climatological data published by the World Meteorogical Organization (WMO) summarizes wind, temperature, humidity, evaporation, precipitation, and solar radiation on a series of maps. For national climatologically data commonly is provided by department of agriculture of each country. 1.3.2 Weather Systems The atmosphere is the major hydrologic link between oceans and continents on the planet, facilitating the cycle of water movement on earth. The hydrologic cycle is shaped by the conditions of the atmosphere, with precipitation as the main input to the cycle. Water vapor content is both a major catalyst and a balancing factor of atmosphere processes that create the weather in the lower atmosphere. Atmosphere pressure is defined as the force per unit area exerted on a surface, and atmospheric pressure measures the weight of the air per unit area. Average air pressure at sea level is approximately 1 atmosphere or 1,013 millibars (mb). Humidity is a measure of the amount of water vapor in the atmosphere and can be expressed in several ways. Specific humidity is the mass of water vapor in a unit mass of moist air. The relative humidity is a ratio of the air’s actual water vapor content compared to the amount of water vapor at saturation for that temperature. Water vapor has the ability, unique among gases, to change from one state of matter to another (solid, liquid, or gas) at the temperatures and pressures that typically exist on earth. A change in phase requires that heat be released or absorbed. The process of converting solid ice to liquid water, called melting, and water to vapor, called evaporation, both require significant heat change. Atmospheric weather systems are fueled by solar input and characterized by air masses in motion, circulating winds, cloud generation, and changes in

7

Hydrology

temperature and pressure. Lifting mechanisms are required for moist air masses to cool and approach saturation conditions. As a result of the interaction of rising air masses with atmospheric moisture, the presence of small atmospheric nuclei, and droplet growth, precipitation in the form of rain, snow, or hail can result. The exact mechanisms that lead to precipitation are sometimes quite complex and difficult to predict for specific areas. Horizontal variations in atmosphere pressure cause air to move from higher pressure toward lower pressure, resulting in the generation of wind. Vertical displacement causes air to move as well, but at a far slower rate than horizontal winds. The vertical movement and lifting of air results in the formation of clouds. Clouds are familiar to all of us, and represent collections of small droplets of water or tiny crystals of ice. Atmospheric moisture is a necessary source for precipitation and is generally provided from evaporation and transpiration. Common measures of atmospheric moisture, or humidity, include vapor pressure, specific humidity, mixing ratio, relative humidity, and dew point temperature. Under moist conditions, water vapor can be assumed to obey the ideal gas law, which allows derivation of simple relations between pressure, density, and temperature. The partial pressure is the pressure that would be exerted on the surface of a container by a particular gas in a mixture. The partial pressure exerted by water vapor is called vapor pressure and can be derived from Dalton’s law and the ideal gas law as e

ρ wRT 0.622

(1-3)

where: e = vapor pressure (mb) w = vapor density or absolute humidity (g/cm 3) R = dry air gas constant = 2.87 x 103 mb cm3/g 0K T = absolute temperature (0K) Relative humidity (RH) is approximately the ratio of water vapor pressure to that which would prevail under saturated conditions at the same temperature. It can also be stated as RH = 100 e/e s. Specific humidity is the mass of water vapor contained in a unit mass of moist air (g/g) and is equal to w/m, where m is the density of moist air. Using Dalton’s law and assuming that the atmosphere is composed on only air and water vapor, then,

8

Main Hydrological Concept

ρm 

 P  e  0.622e RT

P 1 0.378e/P RT

(1-4)

Equation (1-4) shows that moist air is actually lighter than dry air for the same pressure and temperature. Thus, q

ρw 0.622e  ρm P  0.378e

(1-5)

Where: q = specific humidity (g/g) e = vapor pressure (mb) P = total atmospheric pressure (mb) m = density of mixture of dry air and moist air (g/cm 3) Finally, the dew temperature Td is the value at which an air mass just becomes saturated (e – es), when cooled at constant pressure and moisture content. An approximate relationship for saturation vapor pressure over water e s as a function of temperature T is 4278.6   es  2.7489 108 exp    T  242.79

(1-6)

In order for vapor to condense to water to begin the formation of precipitation, a quantity heat known as latent heat must be removed from the moist air. The latent heat of condensation Lc is equal to the latent heat of evaporation L e, the amount of heat required to convert water to vapor at the same temperature. With T measured in 0C, Le = – Lc = 597.3 – 0.57 (T – 00C)

(1-7)

where Lc is in cal/g. The latent heat of melting and freezing are also related: Lm = – Lf = 79.7

(1-8)

where Lm is also in cal/g. Thus it takes about 7.5 times the energy to evaporate a gram of water compared to melting a gram of ice. Meteorologists use the moisture relationship and the latent-heat concepts to obtain pressure-temperature relationships for cooling of rising moist air in the atmosphere. The rate of temperature change with elevation in the atmosphere is

9

Hydrology

called the adiabatic lapse rate. The dry adiabatic lapse rate (DALR) is 9.8 0C per km and assumes no phase changes of water. Precipitation is the primary input to the hydrologic cycle, whether in the form of rainfall, snow, or hail, and is generally derived from atmospheric moisture. In order for precipitation to occur at the earth’s surface, 1. a moisture source must be available, 2. moist air must undergo lifting and resultant cooling, 3. a phase change must occur with resulting condensation onto small nuclei in the air, 4. droplets must large enough to overcome drag and evaporation to reach the ground. Temperature of environment (0C)

Altitude (m)

00

70C/1000m 2000

160

Dry adiabatic rate

1000

100C/1000m 0

0 32

10 50

20 68

0

10

230

200

300

300

0

30 C 860F

3000

00

Temperature of lifted unsaturated air (0C) (dry rate)

(a) The unsaturated parcel of air at each elevation is colder than its surroundings. The atmosphere is stable with respect to unsaturated, rising air

Altitude (m)

Environmental Lapse rate

3000

Temperature of environment (0C)

Moist adiabatic rate 60C/1000m

2000

1000

Environmental Lapse rate

70C/1000m 0

0 32

10 50

20 68

120

160

180

230

240

300

300

0

30 C 860F

Temperature of lifted saturated air (0C) (moist rate)

(b) The lifted, saturated air parcel is warmer at each elevation than its surroundings. The atmosphere is unstable with respect to saturated, rising air

Figure 1.3: Vertical temperature and stability

10

00

Main Hydrological Concept

Type of precipitation is determined from factors that lift moist air to atmosphere which consist of frontal, orographic, and convective precipitations. Frontal precipitation (Fig.1.4) resulted from warm air which is blown by wind to atmosphere and cooled through adiabatic process to generate cloud. The rate of cooling is 50C/100m up to the moist air to reach the dew temperature. If the cooling process is continued, then the cloud will be melted and precipitation occurs. Orographic precipitation (Fig.1.5) occurs do to the warm air moves to the mountain area and cooling process is exist. Convective precipitation (Fig.1.6) occurs do to elements of air which have difference temperature and density crashing to one another and the evaporation process occurs.

Cloud with temperature of 50C

100 m

Warm surface

Figure 1.4 Front precipitation

Cloud

Dry 11

Moist Figure 1.5 Orographic precipitation

Hydrology

Cloud

Warm air

Cold air

Figure 1.6: Convective precipitation

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Main Hydrological Concept

Problems Q1.

What kind water is good for human consumption, how do we get it?

Q2.

Can we consume river water?

Q3.

Do you know the source of river water? Give short explanation.

Q4.

Do you know well water? Where do we get it?

Q5.

Who are the users of knowledge of hydrology?

Q6

Why do we need to control and manage water?

Q7.

An area has problem of water every year. During rainy season the volume of water is adequate to fulfill the requirements; even sometime it is too much and causes flooding. But, during dry season it is insufficient, even sometime drought is occurred. Therefore, please give an idea how to solve this problem.

Q8

A canal is 80 km long and has an average surface width of 15 m. If the evaporation measured in a class A pan is 0.5 cm/day, what is the volume of water evaporated in a month of 30 days. Answer: 180,000 m3

Q9.

A reservoir has the following inflows and outflows (in cubic meters) for the first three months of the year. If the storage at the beginning of January is 65 m3, determine the storage at the end of March. Month Inflow Outflow Answer: 63.5 m3

January 3.5 6.4

February 5.7 7.1

March 8.3 5.5

Q10. The drainage area of the Sembrong River at Parit Raja, Batu Pahat, is 11,839 km2. If the mean annual runoff is determined to be 144.4 m 3/s and the average annual rainfall is 1.08 m, estimate the evaporation losses for the area. Answer: 0.7 m

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Hydrology

Q11. At a particular time the storage in a river reach is 55.3 acre-ft. At that instant, the inflow into the reach is 375 cfs and the outflow is 563 cfs. After two hours, the inflow and outflow are 600 cfs and 675 cfs, respectively. Determine: a) The change of storage during 2 hours and 2) The storage volume after 2 hours. Answer: a) –21.73 acre-ft and b) 33.57 acre-ft.

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Main Hydrological Concept

World Water Balance Statistic Total volume of water in the world is constant = 1.36 x 10 18 m3     

Ocean Icebergs and glaciers Groundwater Lakes and rivers Atmosphere

-

97.2 % 2.15 % 0.64 % 0.0085 % 0.0015 %

Malaysia Water Balance Statistic Total volume of water Malaysia is = 990 billion m 3   

360 billion m3 evaporates back to the atmosphere in the vapour form 566 billion m3 in the form of surface runoff 64 billion m3 in the form ground water

Water Measurement Units Water can be measured using different types of units depending on their purposes and usages. i)

measurement in the form of depth Unit : mm, cm, m, inch, feet Average daily rainfall is 300 mm Maximum depth of River X is 10.5m Daily requirement of water for plant is 0.5 cm

ii)

measurement in the form of volume Unit : cm3, m3, liter, ft3, hectare-meter (ha-m), acre-ft The volume of water for that swimming pool is 60 m 3 500 litre of water is required to water that small garden daily 15

Hydrology

iii)

The reservoir can hold a total volume of 150 hactare-metre of water measurement in the form of discharge Unit : Liter per second/min/hour (lps, lpm, lph), m3/sec/min/hr, ft3/s/m/hr.

Scopes of Hydrological Study 1. Water Resources Development: To determine the availability of water resources in any catchment areas in term of volume and the when it is available. Important in planning and designing of water supply projects for industries, agricultures, domestics, recreations, transportations, fishing, etc. 2.

Predicting and Designing of Flood Control: To assist in predicting the probability of flood occurrence to any one area in term of time, frequency and magnitude. These information are used to avoid or reduce the damages caused by the flood, as well as to plan and design the drainage related structures such as bridges, drainage systems, culverts, reservoirs, detention and retention ponds, etc.

3. Planning an Alternative Water Resources Development (Groundwater) : To determine the availability of water in the ground as an alternative and additional resources especially during a long dry seasons and its effect to the earth surface. 3. Planning Preservation and Rehabilitation of Ecosystem : Most of the natural ecosystem depends on the ecosystem regime of the catchment areas. As an example, the water populations such fishes and aquatic plants depends wholly on the hydrological regime of the river valley.

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