MIDTERM LESSON

HYDROLOGIC LOSSES OVERVIEW WHY HYDROLOGIC LOSSES MATTER

These are the processes that reduce surface runoff Climate Change Adaptation
diverting water. Warming Trends Toc rise increase ET by 5 10 %, reducing Water
by storing can
: -

or

Types of Hydrologic Losses : availability

1 .

Evaporation (Et) -

Water lost to atmosphere via plants + soil ·

Engineered Response :
Updated IDF curves using future climate

.
2 Infiltration -
Water seeping into the ground .
projections .
.
3 Interception -

Rain trapped by leaves / buildings. Example : Future Rainfall Intensity Duration Frequency Projection using
.
4
Depression Storage -
Water held in puddles/depression .
Machine Learning

Evapotranspiration (ET) -

The Water Loss

ET =
Evaporation + Transpiration
Evaporation : Water >
-

Vapor from soil/surface water

Transpiration : Plants "Sweating" water through leaves.

Why Engineers Care About Evapotranspiration (ET)

Engineering Applications of ET Data

Irrigation Design & Water Conservation

WHY HYDROLOGIC LOSSES MATTER Problem : Over-irrigation Wastes Water

; under-irrigation reduces

Flood Prediction
-

and Urban Drainage crop yields .

Problem : Cities with > 80 % impervious surfaces (roads rooftops)

,
Solution : Use ET-based irrigation scheduling :

lose 50 % -90% of natural infiltration capacity. Video for Irrigation Scheduling :

Example : Houston Urban Flooding & Infiltration Loss

ETo =

ETcrop X Crop Coefficient (Kc)

Engineering Solution : Green infrastructure (permeable pavements,
rain gardens) to restore losses. Example : How much
irrigation is needed to sustain a corn field
with an estimated exapotranspiration of 5mm/day and a
crop
-
Water Supply & brought planning coefficient of 1 2 ? 6mm/ day of irrigation is needed·
.

ET's Role : In arid regions , > 60 % of rainfall may be lost Tech Tool :
Smart Irrigation Controllers

due to ET. Example :

With Flow

Example :
Smart Irrigation Systems
Reservoir & Water Supply Management
-
Infrastructure Design standards Impact : ET accounts for -60% of Water loss in reservoirs in

scs Curve Number : Mandated in . Stormwater

US .

regulations. arid regions.

Example : The SCS Runoff Method Engineering Response Floating : Solar Panels to reduce exaporation and

ET Forecasting to optimize Water releases,

Example Green Roofs :

Climate Change Adaptation Mass Transfer Approach Example
Data 10 temperature rise 5-10 % ET increase A lake has surface temperature of 250c The air above has vapor
>
: -

a a
.

Infrastructure Impact Longer Drought

: periods and need for pressure of 1 5kPa while the saturation Vapor
.

, pressure at 25% is

larger Water storage capacity. 3 17 kPa. The

.
empirical Coefficient Ce =
0 .

00039kg/m2 KPa, and the

Mind speed is 4m/ Estimate the.

evaporation rate.

MASS TRANSER APPROACH Given :

es = 3 17 KP .

Origin & Concept Developed based :

on Dalton's Law (1802), ea =
15
.
kPa

which states that evaporation is driven by the difference Ce =

0 .
0003949/mis KPa

between saturation vapor pressure at the water surface U =

4 M/s

and the actual vapor pressure of the air above it. b =

0 5 .

The idea is that evaporation increases with wind speed and Solution : Substituting values

vapor pressure gradient. E =

0 .

00039x (3 17 1 5) x (1 .
-
.
+ 0 .

5x4) =
0 .

00195kg/m2
Formula :

E =
Ce :

(es- ea) since

11-80400m
Where : E =
Evaporation (mm/day or
Cm/day) E =
0 00195 x
.
86400 =
168 5 mm/day
.

Ce =
Empirical evaporation coefficient
es =
Saturation vapor pressure at Water Energy Budget Method

surface (Pa or mmHg) origin & Concept : Based on thermodynamics this method considers ,

ea =
Actual vapor pressure of the air energy fluxes at the water surface. It accounts for solar radiation,

(Pa or mmHg) heat storage ,

and latent heat loss during evaporation.
Refinement include wind function modifications leading Formula :
Rn -

6 -

H
E
,
=

to formulas like : N
E =
Celes -(a) (1 + bu)
Where : E =

Evaporation (mm/day)
where U is wind speed and b is a coefficient. Rn Net Radiation
=
(incoming -

outgoing energy)
= Ground heat flux
6
* Limitations H =
Sensible heat flux to air

Assumes evaporation only due to Vapor pressure Latest heat of vaporation (2 45 )

%
1 .
occurs X =
. at 20

.
2 Needs site-specific calibration for Ce. * Limitations

.
3 Not reliable over land surfaces with vegetation. 1 Difficult to measure heat fluxes (G and H)
.
2
Requires continuous meteorological monitoring
*
Applications : .
3 Not practical for small-scale studies.

Large Water bodies Lakes reservoirs and

↓ :
, ,
oceans * Applications
.
2 Climate Studies :
Estimating evaporation loss in 1 .
Climate modeling :
Used in global weather prediction.
Weather models .
.
2 Agriculture Helps :
calculate crop water demand.

3
.
Engineering projects :
Assessing evaporation in 3
. Water resources
planning :
Used in drought monitoring
.
hydropower dams.
 Energy Budget Example :
PAN EVAPORATION EXAMPLE

A water body receives a net radiation of 200 #/m?. The A Class A recorded 10 mm of evaporation in a day . The pan coefficient
# is
groundheat flux is 20 1m2 and the sensible heat flux 0 75.
.
.
Estimate the evaporation from a nearby lake.
,

is 30 /m Calculate
·
the evaporation rate in mm/day. Given :
Epan :
10 mm/day
Note : 1 * m2 =
86 .
4 m// m2 per day. kp =
0 75.

Given :
Solution :
Substituting the values

Rn =
200"Im2 E =
0 75 X 18
.

6 =
20 I/m2 E =
75 .
mm/day
H =
30 Mm2
x =
2 45 .

M/kg PENMAN METHOD

SOLUTION :
Substituting the values Origin & Concept Developed by
: Howard Perman (1948) ,
this method combines

(200 -

20
-

30)x06 4 . the Energy Budget and Mass Transfer approaches evaporation estimates
E
.

2 45.
It accounts for solar radiation wind speed and vapor pressure. , ,

E =
5290 8 . mm/day Formula :
$ (kn -

G) + y f (u)(es ea) -

E =

A + Y

PAN EVAPORATION METHOD Where : I :

slope of the vapor pressure curve

Origin & Concept : Uses Class A evaporation pan to measure y =

Psychometric constant

actual water loss overtime. Evaporation from the pan is empirically f(u) = Wind function

related to real-world Water bodies. * Limitations :

Formula :
E KpX
=

Epan 1 .
Data intensive /requires solar radiation wind and , ,
humidity
Where E Estimated Evaporation (mm/day) .
2 Difficult to apply in remote areas.
=
:

4p Pan Coefficient (typically

= 0 7 -0
. .
85) .
3 Over estimates
evaporation in arid regions.
Epan = Measured evaporation from the pan (a) * Applications
1 .
Water resource management : Used for reservoir design.
* Limitations .
2 Irrigation Helps :
in estimating crop water demand.

1 .
Not accurate for large water bodies due to differences in .
3 Hydrology models Used in flood :
prediction.
heat storage.
.
2 Affected by pan surrounding (e g. vegetation .
increases Penman Method Example
humidity) .
Problem : A water body has the
following conditions

.
3 Requires frequent maintenance (refilling cleaning , ,
etc) . ·
Net Radiation
,
Rn =
150 #/m2
* Applications ·
Ground heat flux 6
,
=
10 M/m2
1 .

Irrigation scheduling :
Farmers use pan readings to adjust · Air temperature ,
20%

watering .
·
Saturation Vapor pressure ,
2 34kPa
.

.
2 Reservoir management :
Helps predict storage loss. ·
Actual Vapor pressure ,
1 5 KPA
.

.
3 Drought monitoring : Used by meteorological agencies. ·
Wind speed 3 M/s
,

Psychometric constant ,
0 .

066kPa/0
 ·
slope of Vapor pressure curve , 0 .

144kPa/ % FACTOR'S CONTROLLING INFILTRATION

SOLUTION :
Substituting Values SOIL TYPE

0 .
144x(150 10) + -
0 066x
.

(1 + 0 5 3) (2 34 5)
.
x x .
-
1 .
-
Infiltration of Sand >
-
fast
E =

0 144 + 0 066
. .
-

Infiltration of Clay >

-

Slow

E =
96 7 .

mm/day LAND USE

Land used for vegetation and forestry there is infiltration

-

summary of Methods -
There is obstruction =
no infiltration

PRECIPITATION
-

High Intensity Precipitation creates high volume for

infiltration and an excess (runoff).

Key Notes :

The choice of method depends on data availability and MODELING INFILTRATION (HORTON'S INFILTRATION MODEL)
study area. Robert E Horton . (1875-1945) was a pioneering American hydrologist
-

Pan Evaporation is practical for farmers and water and civil engineer. He worked for the U S. .

Geological Survey and

managers .
later found his own
consulting firm. His work was driven by practical
-
penman Method is the most comprehensive for hydrology problems:

and irrigation studies. * Flood prediction for dam design .

-

Energy Budget and Mass Transfer are useful for scientific *Soil erosion control after the Dust Bow era.

climate models. * Urban drainage challenges during rapid industrialization.

Infiltration (Nature's Sponge The Dust Bowl was a period of severe drought and dust storms in

Water entering soil from the surface the 1930s that devastated the Great Plains region of the United States
↑

FACTOR'S CONTROLLING INFILTRATION

It was caused by a combination of factors including drought,
Sand Clay
and intensive farming practices that left the soil vulnerable
overgrazing

8
,
# E
to Wind erosion . The Dust Bow caused widespread ecological ,
economic , and

human suffering leading

,
to significant migration from affected areas.
Soil Type

Pavement
Forest Horton's breakthrough came from experimental field data (not just theory)
In the 1920s-1930s ,
he conducted :

Infiltration Infiltration
M
·
Rainfall simulators Spraying Water
:
on small plot of land to measure

infiltration rates.

- · soil column experiments

different soils overtime .
:
Tracking how water seeped through

Land Use Key Observations :

# High Intensity Precipitation creates high volume for Infiltration rates start high when soil is dry but decay

infiltration and an excess (runoff). exponentially as the soil saturates

, eventually reaching a

steady .
rate
 Horton modeled this behavior mathematically with :
Why this is not the
right answer ?
-k+
f (t) =

fe + (fo fc)e
-

F() =
19 04 Cm
.

Where :
-

The rate is not constant. It decays exponentially.

fo :
Initial Infiltration rate (dry soil)
tc- Final Constant rate (saturated soil)

k :
Decay coefficient

⑪Nomoderndol'ocomputersorelectronicsensoras sets
ignored soil layers Philip's Infiltration Model
Simplified assumptions : and

preferential flow (e g. .
cracks , Wormholes John Philip ,
an Australian mathematician ,
was frustrated by the

oversimplifications in hydrology .
He tackled the Richards Equation (a complex
Fun Fact :
Horton's original plots were hand-drawn on graph PDE for soil water flow) and derived an exact series solution-splitting
paper-today ,
we teach them as "Horton curves". infiltration into sorptivity (capillary suction) and gravity flow. His Work

Modeling Infiltration Example bridged theory and field observations

A 2 hour storm hits a

grassy clay-loam soil plot. Calculate the Formula :
F(t) =
s - + At

infiltration rate and cumulative infiltration using Horton's where : S= Sorpitivity (C)
parameters :
Initial infiltration rate =
12 cm/hr A =
Gravity-driven term= K, at long times

Final infiltration rate 3 /Ur

2t
=

+ (t) =
A
Decay coefficient =
0 4 hr
=a
.

1
Advantages
I

·
t(min) t Chr) +(t) Mathematically rigorous
k
f(t) +z + (fo fc)e
= -
O O > 12 00
.

Separates capillary vs .
gravity flow
15 0 25 . 11 14
.

Used in arid zone

hydrology
30 0 50 . 10 37 .

Limitations
45 0 75 .

Requires fitting S and A to data

60 1 00.
less intuitive for engineers
75 1 25
:
. 44
8 Limited for Layered Soils

90 1 50
.
7 94 .
Application
105 1 75
.
7 47 .

Drought Studies -
Predicts water uptake in dry soils

120 2 00 .
:7 04 . Theoretical Research -
Basis for advanced models

Jt(t) (fr
*
=
+
(fo-fr)e F(t) =
18 39
.
cm
Philip's Infiltration Model Example
A clay soil has sorpovity of 5cm/Tr and A 1cm/hr Find the
tofc(1-e
=
.

F(t) =
fct +
cumulative infiltration after 30 mins.

F(t) St + At F(t) =
4 04cm

+ (1 4(2)
= .

F(t) b(2) = -
20 .

F(t) =
50 5 .
+ 1/0 5)
.
 G
Green-Ampts Infiltration Model
Two Australian Scientists Wilhelm Green and
,
George Ampt,

where studying why some soils absorbed water faster than

others. Watching water seep into dry farmland they ,

noticed

a clear boundary between wet and dry soil-like a

"front" advancing downward This .

inspired their sharp wetting

front assumption simplifying Darcy's
,
Law into a workable

for engineers.
equation

Green & Ampt wanted predict fast water soaks into

k(0)t
to how

dry soil -

a critical problem for agriculture and flood control.

h
= + z a = -

they started with Darcy's Law (1854) for flow through n = 4 + z

(hsurt-hurt)
q = -

fE -
ks
porous media . hwf = 4 +
( 2)
-

Esurf-Zwf
Formula hourt (0 (4 + ( 2)
kth
:
= 0 -

9 = -
-

f = -

k,
87 Esurf = 0 o -

( 2)
-

(flow per minute im

k)1 E)
Where 9 :
=
Water flux unit are
+
,
= -

k =
Saturated hydraulic conductivity (c)
dh/dz =
Hydraulic gradient (change in head n with depth z) F =
r(ts fi)
- =
Lud

(1-4m
Md
=
Es -ti

To make Darcy's Law tractable they assumed :

, E
=
1 Sharp Wetting Front : A distinct boundary separates Md

saturated soil (above) from dry soil (below).

Op
.
2 Uniform soil :

Homogeneous properties (no cracks or layers)

.
3 Constant suction The :
wetting front has a fixed soil suction
head (4)

Infiltrating Water
0 %0 8
: : 10 10
saturated
If F is small and this term Und F is large and this term
Soil
becomes larger. und becomes smaller
Wetting Front
Green and Ampt's Infiltration Model
#

C
Early Infiltration into dry clay soil .

Given kg 0 5
Im
(1 4m)
: =
.

f =
k, -

↑ = 30 CM

1025
Md 0 25

5)1
30 .
= .

f() =
0 .
-

f(t) =
0 .
49 im
 Why This Matters Storm Data :

1 Flood Prediction Short storms may overwhelm soils initial p 10 Im over 5 hours
=
.
:

capacity (high F(t)). A 4 cm

=

Irrigation Sandy soils (high Ks) drain too fast for crops When
P-Q
2
. :
10 -
p :
; p =

FIt) is large . 5

3
. Contaminant Transport : Slow gravity-driven flow (f(t) = ks) affects 6 =
1 2 .

ar
pollutant spread .
Phi-Index Infiltration Example

PH1-INDEX METHOD Time Step -

Calculation

In the early-to-mid 20th century there

,
was a need for a simple
, Step 1 . Divide the storm into discrete time steps.

empirical took to estimated runoff during flood events ,

especially for Step .
2 For each step , compare rainfall intensity to phi,
military and agricultural planning. They needed an estimation method Step 3 .
Sum run-off across all steps to match observed Q
.

designed for rapid calculations in data-scarce regions ,

without the Rule

use of computers. it i -$ All rainfall infiltrates

The U S. Army
.
Corps of Engineers (USACE) and soil conservation it i < &
,
Runoff =
i =
&

(SC)
- -
NRCs) developed the Phi-Index

j
Service ,
now Method.

The Phi-Index is derived from water balance

approach
assuming : E

1 .
Infiltration is constant during a storm.

.
2 Runoff occurs only when rainfall intensity (i) exceed 4

Water Balance :
Storm Data :

p =
Q + Infiltration + Abstraction (Initial Losses) P :
10cm over 5 hour,

Note : For 4-index abstraction is ,

lumped into infiltration Q = 4cm

where :
Hourly rainfall :

p :
Precipitation [1 0 .

,
2 . 0
,
3 .
0
,
2 5 1
.

,
.
5] cm
Q = Run off Runoff occurs when i > 1 2 .

cm/hr
(1) (2 . 0 -

4) +
(1)(3 . 0 -

4) +
(1)(2 .
5 -
4) +
(1)(1 5
.
-

4) =
3 9am
.

Assume Infiltration = X + (1) (2 0 .

-
1 .
25) (1)(3 + . 0 -
1 .
25) + (1) (2 5 1 5) .
- . +
(1) (1 5
.
-
1 .

25) =
4 . 0 cm

where t =
storm duration

p =
Q + & Xt Phi-Index Method

P =

Q Advantages
# =

t simple , no soil data required

Useful for quick estimates
 Disadvantages Interception Streamflow Mechanisms

Oversimplifies infiltration Water that flows down branches and trunks to the base of the plant.
soil moisture variability
Ignores Channeling :

less accurate for long storms

Interception
-
The capture and retention of rainfall by Vegetation (canopy litter)
,

before it reaches the ground.

Impact on Hydrology :

* Reduces net rainfall available for infiltration / runoff.

* Delays peak flow in storms (temporal redistribution)

* Significant in forested Watersheds (up to 20-30% of annual rainfall .

Interception Initial Wetting Phase

When rainfall begins the first droplets are retained on leaf surfaces,
,

filling small depressions and advering to

wavy cuticles.

The maximum water volume a canopy can hold (typically 0 5-5mm).

depending on
vegetation type
Storage Capacity (s)
Lower storage (l-3mm) due to smoother leaves.

Str
Higher storage (3-5mm) due to needle structures

Roots
Interception Throughfall (Mechanisms Factors Throughtall)
Affecting

Precipitation that drips through gaps in the canopy or

along stems.

Direct Throughfall : Rain bypasses leaves (e g

.
.
in sparse canopies)
Drip Throughfall : Water droplets coalesce on leaves until gravity
overcomes surface tension .
 NODELING INFILTRATION ACTIVITY Green-Ampt Model
Horton's Infiltration Equation .
3 An agricultural field has been recently plowed and is being
soil plot. Calculate the irrigated. The soil homogenous and be modeled using the
1 .
A 2 hour storm hits a
grassyclay-loam is can
(n)
infiltration rate and cumulative infiltration using Horton's Green-Ampt infiltration model.

parameters :
Initial infiltration rate = 10 Cm/hr known soil and initial conditions :

Final infiltration rate = 2 (m/Ur Suction head

· at
Wetting front Y =
12 cm
,

Decay coefficient =
0 6
.
nut ·

porosity As =
0 45.

solution :
f(t) :
fc + (fo-fale * ·
Initial volume moisture content ti
,
=
0 20
.

0 6x2
(10 2)2 Hydraulic conductivity K 0 4 cm/hr
+

f (2)
.

= 2 + = · = .

Answer : f =
4 41.

Cm/nr a .

Having cumulative infiltration # is

loand ,
find infiltration

time (t) When the infiltrated depth reaches 10 cm.

.
2 A farmer wants to estimate how much irrigation b Determine the infiltration rate at that
.
moment.

will be absorbed by the soil in hours. The Solution : a .)

fi)(n(1 y(f +i))

Water 15
.

F =

4(ts - + +
kt
soil has : -

)1 + 25)
·
Initial infiltration rate to =
6 umIhr
·
Final rate fo =
2 cmihr
10 =

12(0 25) .
In
0 .
+ 0 .
47
/

3(n(1
Decay constant K 0 4hr
b)
· = .

&
10 =
+ + 0 . 4t
a Estimate infiltration rate at 15 hours

b
. Calculate cumulative infiltration over 1 5 hours,
.

10 =

3 (n(4 333) .
+ 0 .
4t /Using caltech)
Solution : Answer :
+ =
14 02 hours
.

a .
Infiltration rate at t = 1 .
55 . b. Infiltration rate (f)
k

k() 4(ts- t)
f(t) +z + (fo fc)e
= -

0 4x 1 5
f = -

f (1 5) (6 2)e
. .

. =
2 + -

Answer + umIhr
4)1 12 x0 25)
: =
4 20.

+ = 0 .
-

b
. Total Infiltration

F(1 5) .
=
2 x 15.
+ (1-e-0 6)
.

f =
0 28
.
Cm/nr
Answer :
F =
7 51. cm
 CABAUATAN SANDARA
,
MARIE M.

BSCE-3C / HYDROLOGY

CHANNELING STREAMFLOW (Mechanism of Interception)

FUNNELING STREAMFLOW (Mechanism of Interception)