Hydrology
HDROLOGY
MODULE 2
Created by: Engr. Aline Benneth V. Jacobo
Hydrology
Phase 4
School of Engineering and Architecture
Department of Civil Engineering
Hydrology
Important Phases of Hydrologic
Cycle
Objective
After this chapter, the student should be able to
 Discuss and solve Evaporation from Free Surface
 Analyze and solve Transpiration and Evapotranspiration problems
 Explain Depression Storage
Content
This chapter focuses on:
• Evaporation, Transpiration, Interception and Depression Storage
• Evaporation from Free Surface:
o Water Balance Method,
o Energy Balance Method,
o Mass-Transfer Method,
o Penman Equation,
o Empirical Methods and Direct Measurement
• Transpiration and Evapotranspiration.
• Depression Storage
Related
Readings
 https://www.nationalgeographic.org/encyclopedia/hydrology/
References
J. E. Gribbin, P.E., (2014). Introduction to Hydraulics and Hydrology with
Applications for Stormwater Management. New York, USA: Delmar, Cengage
Learning
W. Brustsaert, (2005). Hydrology an Introduction. Cambridge CB2 8RU, UK:
Cambridge University Press, New York
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Hydrology
Phase 4
Important Phases of Hydrologic Cycle
Evaporation, Transpiration, Interception and Depression Storage
Evaporation from Free Water Surface
Water Balance Method
In the natural environment, water is almost constantly in motion and is able to change state
from liquid to a solid or a vapor under appropriate conditions. Conservation of mass requires that,
within a specific area over a specific period of time, water inflows are equal to water outflows, plus
or minus any change of storage within the area of interest. Put more simply, the water entering an
area has to leave the area or be stored within the area. The simplest form of water balance equation
is as follows:
𝑃 = 𝑄 + 𝐸 ± ∆𝑆
Where, P is precipitation, Q is runoff, E is evaporation and ∆S is the storage in the soil,
aquifers or reservoirs.
In water balance analysis, it is often useful to divide water flows into ‘green’ and ‘blue’ water.
‘Blue’ water is the surface and groundwater that is available for irrigation urban and industrial use
and environmental flows. ‘Green’ water is water that has been stored in the soil and that evaporates
into the atmosphere. The source of ‘green’ water is rainfall or ‘blue’ water has been used for irrigation.
A Water Balance Analysis Can Be Used to:
 Assess the current status and trends in water resource availability in an area over a
specific period of time.
 Strengthen water management decision-making, by assessing and improving the
validity of visions, scenarios and strategies.
Water balance estimates are often presented as being precise. In fact, there is
always uncertainly, arising from inadequate data capture networks, measurement errors and the
complex spatial and temporal heterogeneity that characterizes hydrological processes. Consequently,
uncertainty analysis is an important part of water balance estimation as is quality control of
information before used.
When the data sources are imprecise, it is often possible to omit components that
do not affect changes. For example, it is possible to omit storage from an annual water balance if
year-on-year storage changes (such as reservoirs) are negligible.
Some common problems that occur when water balance estimations are made include:
 Temporal and spatial boundaries are not defined.
 The quality of input data is poor.
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Phase 4
Important Phases of Hydrologic Cycle
 Double counting of water flows when water flows within an area added to water flow exiting
area.
 Inappropriate extrapolation of field level information to a larger scale. Many hydrological
relationships are scale dependent (e.g. runoff as a proportion of rainfall is almost always
higher at smaller spatial and temporal scales).
 Intuition (often based on popular myths) is used rather than good quality information.
 The storage term(s) of the water balance is omitted.
 Political or other pressures result in unreliable estimates that have been manipulated.
Materials and Resources
Techniques for carrying out water balance estimation range from very simple ‘back of the
envelope’ estimates to highly complex computer-based models. A sound knowledge of hydrological
processes of a prerequisite of water balance estimation. It is often advisable for a project or program
to employ the services of a specialist to produce water balance estimates or, at the very last, to provide
specialist advice as and when it is needed. Access to a quality-controlled information base is a good
starting point for water balance estimation.
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Phase 4
Important Phases of Hydrologic Cycle
Energy Balance Method
The potential evaporation by the Energy Balance method is given by:
𝐸𝑟 =
𝑅𝑛
𝑅𝑛
=
𝜌𝑤 𝑙𝑣
𝐿
Where L = 𝜌𝑤 𝑙𝑣 is the Latent Heat factor given in the table below:
Temp (°C)
0
5
10
15
20
25
30
35
40
Water Density (kg/m3)
1000
1000
1000
999
998
997
996
994
992
Latent Heat (J/kg)
2500000
2499988
2499976
2499965
2499953
2499941
2499929
2499917
2499906
L (W/m2) /(mm/day)
28.94
28.94
28.93
28.91
28.88
28.85
28.82
28.76
28.70
Example:
On 24 January 2013, in the Upper Brushy Creek watershed, the net radiation averaged over
the day from the National Land Data Assimilation System, is 52 W/m2. The average air temperature
through the day is 17°C. Compute the corresponding potential evaporation rate using the energy
balance method.
𝐸𝑟 =
𝑅𝑛
𝑅𝑛
=
𝜌𝑤 𝑙𝑣
𝐿
𝑊
( 2)
𝑚
𝐿 = 28.89 𝑚𝑚
𝑑𝑎𝑦
𝑅𝑛 = 52
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𝑊
𝑚2
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Important Phases of Hydrologic Cycle
𝑊
𝑚2
𝐸𝑟 =
𝑊
( 2)
𝑚
28.89 𝑚𝑚
𝑑𝑎𝑦
52
𝐸𝑟 = 1.80
𝑚𝑚
𝑑𝑎𝑦
Mass Transfer Method
Evaporation driven by
–Vapor pressure gradient
–Wind speed
𝐸 = 𝑓(𝑢)(𝑒𝑠 − 𝑒𝑎 )
𝐸 = (𝑎 + 𝑏𝑢)(𝑒𝑠 − 𝑒𝑎 )
Where:
eS = saturation vapor pressure at temperature T of the water surface
ea = vapor pressure at some fixed level above the water surface
u = wind speed at some level above surface
a,b = empirical constants
Some formulas use a zero value for the constant “a”in the formula due to the small local air
movements with velocities insufficient to remove excess vapor from a above a pan surface. Harbeck
and Meyers (1970) present the following equation.
𝐸 = (𝑏𝑢2 )(𝑒𝑠 − 𝑒2 )
Where:
E = Evaporation (cm/day)
eS = vapor pressure at water surface (mb)
e2 = vapor pressure 2 m above water surface (mb)
u2 = wind speed 2 m above water surface (m/s)
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Important Phases of Hydrologic Cycle
Penman Equation
The penman formula is a semi-empirical equation combining mass transfer (Ea) and energy
budget (H) methods. The formula was developed by Penman in 1948 and is still widely used for
calculating the potential evaporation using synoptic meteorological data.
According to Penman the potential evaporation Eo (in mm/day) can be calculated as:
∆
𝐻 + 𝐸𝑎
𝛾
𝐸𝑜 =
∆
+1
𝛾
∆
Where 𝛾 is an empirical parameter depending on temperature.
H is calculated as H = (1-r)Rin – Ro where Rin (incoming radiation) in given by:
𝑛
(1 − 𝑟)𝑅𝑖𝑛 = 0.95𝑅𝑎 (0.18 + 0.55 )
𝑁
Where:
Ra is the solar radiation,
Ro is the outgoing radiation,
r is the albedo (0.05 for water), and
n/N is the ratio between actual sunshine hours and possible sunshine hours.
The term n/N can also be estimated using the cloudiness, e.g., a cloudiness of 60 %
gives an n/N of 40 % (= 100 - 60). Ro is calculated by:
𝑛
𝑅𝑜 = 𝜎𝑇𝑎 4 (0.56 − 0.09√𝑒𝑑 )(0.10 + 0.090 )
𝑁
where ed is the actual vapor pressure, and
σTa4 is the theoretical black body radiation
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Important Phases of Hydrologic Cycle
Ea is calculated by:
Ea = 0.35(0.5 + u2/100)(ea – ed)
where u2 is the wind speed in miles/day (1 mile = 1609 m) and
ea is the saturation vapor pressure
*Remember that the relative humidity RH = ed/ea.
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Empirical Methods and Direct Measurement
Most of the available empirical equations for estimating lake evaporation are a Dalton type
equation of the general form
(1) Meyer’s Formula
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Important Phases of Hydrologic Cycle
(2) Rohwer’s Formula - Accounts for the effect of pressure in addition to the wind speed effect
Transpiration and Evapotranspiration
Transpiration
Transpiration is the evaporation of water from plants. It occurs chiefly at the leaves while
their stomata are open for the passage of CO2 and O2 during photosynthesis.
Importance of Transpiration
Transpiration is not simply a hazard of plant life. It is the "engine" that pulls water up
from the roots to:
 supply photosynthesis (1%-2% of the total);
 bring minerals from the roots for biosynthesis within the leaf;
 cool the leaf.
Environmental factors that affect the rate of transpiration
1. Light
Plants transpire more rapidly in the light than in the dark. This is largely because light
stimulates the opening of the stomata (mechanism). Light also speeds up transpiration by
warming the leaf.
2. Temperature
Plants transpire more rapidly at higher temperatures because water evaporates more rapidly
as the temperature rises. At 30°C, a leaf may transpire three times as fast as it does at 20°C.
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Important Phases of Hydrologic Cycle
3. Humidity
The rate of diffusion of any substance increases as the difference in concentration of the
substances in the two regions increases. When the surrounding air is dry, diffusion of water
out of the leaf goes on more rapidly.
4. Wind
When there is no breeze, the air surrounding a leaf becomes increasingly humid thus reducing
the rate of transpiration. When a breeze is present, the humid air is carried away and replaced
by drier air.
5. Soil water
A plant cannot continue to transpire rapidly if its water loss is not made up by replacement
from the soil. When absorption of water by the roots fails to keep up with the rate of
transpiration, loss of turgor occurs, and the stomata close. This immediately reduces the rate
of transpiration (as well as of photosynthesis). If the loss of turgor extends to the rest of the
leaf and stem, the plant wilts.
. Evapotranspiration
Evapotranspiration (ET) is the combination of evaporation and transpiration. Evaporation
is water movement from wet soil and leaf surfaces. Transpiration is water movement through the
plant. This water movement helps move vital nutrients through the plant.
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Phase 4
Important Phases of Hydrologic Cycle
Depression Storage
Depression storage refers to small low points in undulating terrain that can store precipitation
that otherwise would become runoff. The precipitation stored in these depressions is then either
removed through infiltration into the ground or by evaporation. Depression storage exists on pervious
and impervious surfaces alike; however, depression storage is much greater on undisturbed, pervious
surfaces.
Standard design and construction practices remove these natural depressions in order to
promote drainage, which reduces depression storage.
References:
https://sswm.info/sswm-university-course/module-4-sustainable-water-supply/further-resources-watersources-software/water-balance-estimation
https://iahs.info/uploads/dms/16761.12-52-56-344-05-Ershadi_etal_JH2_v5CORR.pdf
https://www.caee.utexas.edu/prof/maidment/CE374KSpr13/Evaporation/EvaporationExample.pdf
http://www.uobabylon.edu.iq/eprints/publication_1_2387_723.pdf
https://www.biology-pages.info/T/Transpiration.html
https://www.pca.state.mn.us/sites/default/files/p-gen3-12e.pdf
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