Hydrologic Cycle
 The global scale endless circulation process linking water in
the atmosphere, on the continents, and in the oceans
 It is a complex web of continual flows, or fluxes, among the
major reservoirs or stocks of water.
 Flux: “amount that flows through a unit area per unit time” QL-2T-1
 Volumetric flux, the rate of volume flow across a unit area
(m3·m−2·s−1)
 Mass flux, the rate of mass flow across a unit area (kg·m−2·s−1)
 Energy flux, the rate of transfer of energy through a unit area
(J·m−2·s−1)
 Heat flux, the rate of heat flow across a unit area (J·m−2·s−1)
Hydrologic Cycle
 Solar energy drives the hydrologic cycle.
 Gravity and other forces play important roles.
 About 50% of the sun’s energy reaching the earth (In U.S ~400
cal/cm2/day) goes to vaporize vapor.
 Oceans lose more water by evaporation than they gain by
precipitation.
 Land surfaces receive more water as precipitation than they
lose by evaporation.
 The excess of water on land returns to the oceans as runoff,
balancing the deficit in the ocean-atmosphere exchange.
Hydrologic Cycle
 Precipitation (P): Falling products of condensation in the
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atmosphere as rain, snow, hail, sleet, dew, frost
Runoff (R): That part of the precipitation, snow melt, or
irrigation water that appears in uncontrolled surface streams,
rivers, drains or sewers
Infiltration (I): Flow of water from the land surface into the
subsurface
Percolation: The movement of water through openings in rock
or soil. Usually to contribute to groundwater replenishment.
Water Table: The top of the water surface in the saturated part
of an aquifer. It is the surface where water pressure is equal to
atmospheric pressure.
Hydrologic Cycle
 Groundwater: Water located beneath the ground surface in
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soil pore spaces and in the fractures of geologic formations
Evaporation (E): The process of liquid water becoming water
vapor, including vaporization from water surfaces, land
surfaces, and snow fields, but not from leaf surfaces
Transpiration (T): Process by which water that is absorbed by
plants, usually through roots, is evaporated into the atmosphere
from the plant surfaces, such as leaf surface
Evapotranspiration (ET): The sum of E & T
Interception: Precipitation that is intercepted by plant foliage
Basic Laws of Physics Commonly
Applied in Hydrology
 Conservation of Mass/Energy
 Newton’s Laws of Motion:
 Conservation of momentum
 Force equals mass times acceleration
 For every net force acting on a body, there is a
corresponding force of same magnitude in opposite
direction
 Laws of thermodynamics
 Fick’s Law of Diffusion
Water Budget
 Conservation of mass principle to hydrologic cycle
 The rate of change of mass stored within a compartment
(control volume) is equal to the difference between inflow
and outflow rates
i
S
q
 i(t) : Volumetric inflow rate (L3/T)
 q(t): Volumetric outflow rate (L3/T)
 S(t): Storage within the control volume (L3)
Water Budget
INFLOW
STORAGE
OUTFLOW
i
S
q
 Consider the time period Dt = t1 - t2
Total inflow volume I = ∫ i(t)dt
Total outflow volume Q = ∫ q(t)dt
Change in storage: DS
I  Q  DS
 Dividing both sides by Dt gives for very small Dt:
dS
iq 
dt
Global Water Budget
 Over a period of years the average amount of water stored
as ice surface water and groundwater does not change
significantly.
 Hence, we ignore the term dS/dt or DS in water budget
equations. Such systems are said to be at steady state.
P  R  ET  0
P  R  ET
P : average precipitation rate
R : average runoff either as surface or ground water
E T : average evapotranspiration (involves interception)
100=119,000 km3yr-1
Residence Time (Tr)
 Measure of how long on average a molecule of water
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spends in a subsystem before moving on to another
subsystem of the hydrologic cycle
Also called average transit time
Universal measure of the storage effect of a reservoir
Tr = S / Q (Steady state, i.e. i = q)
Also called turnover time because it is a measure of the
time it takes to completely replace the substance in the
reservoir
Example
 Let’s calculate the residence time of global atmospheric
moisture, i.e. how long on average a water molecule stays
in atmosphere:
Volume = 12,900 km3 (see table 1.1)
Outflow rate = (100+385)*119,000/100 km3/yr
Tr = V/Q = 12,900/(577,115) = 0.022 years (~8 days)
 Short Tr is why weather forecasts are very uncertain
beyond few days
Watershed Budget
 A watershed is a land area that drains water to a particular
stream, river, or lake.
 It is a land feature that can be identified by tracing a line
along the highest elevations between two areas on a map,
often a ridge.
 Large watersheds, like the Mississippi River basin contain
thousands of smaller watersheds.
 The term catchment is more common in Europe. In U.S. it
is sometimes used for small watersheds.
Reading Contours
 Valley contours
“point” upstream
 Ridge contours
“point” downhill
Valley
http://www.fws.gov/wetlands/Data/Mapper.html
City of Auburn GIS
Ridge
 Can you have a watershed inside a watershed (not its sub-
watershed?
Hydrologic Unit Code (HUC)
6 Digit HUCs
2 Digit HUCs
Watershed Budget
dS
 P  R  ET
dt
 R= Surface runoff and baseflow (from infiltrating water)
 Over a long period of time:
dS/dt = 0  P = R + ET (all average quantities)
 Often we are interested in what percent of precipitation is
lost through evaporation or what percent of precipitation
becomes streamflow.
 Runoff ratio: r = R / P
Example
 A = 11,834 km2, Qavg = 144.5 m3/s, P = 1080 mm/yr
Compute average ET and runoff ratio
 Qavg = 144.5 m3/s * (365*24*3600 sec) / (11,834x106 m2)
* 1000 mm
= 385 mm/yr
 r = 385/1080 = 36%
 i.e. 64% of the precipitation is lost to ET.
Annual Water Budget - Flatwoods
Rainfall (~ 140 cm)
Interception
(~ 30 cm)
Transpiration
(~ 70 cm)
Surface Runoff
(~ 3 cm)
Infiltration to Deep Aquifer
(~5 cm, though upto ~ 40 cm)
Subsurface Runoff
(~ 32 cm)
Annual Water Budget – Ag Land
Rainfall (~ 140 cm)
Interception
(~ 15 cm)
Transpiration
(~ 80 cm)
Surface Runoff
(~ 20 cm)
Infiltration to Deep Aquifer
(~5 cm, in areas much higher)
Subsurface
Runoff (~ 20 cm)
Annual Water Budget – Urban Land
Rainfall (~ 140 cm)
Interception
(~ 20 cm)
Transpiration
(~ 50 cm)
Surface Runoff
(~ 60 cm)
Infiltration to Deep Aquifer
(~ 2 cm)
Subsurface Runoff
(~ 5 cm)
Open System
 Surface water (1):
DSs= P+Qin-Qout+Qg-Es-Ts-I
 Ground water (2):
DSg= I+Gin-Gout-Qg-Eg-Tg
 Add (1) and (2):
D(Ss+Sg) = P- (Qout-Qin) (Es+Eg) - (Ts+Tg) - (Gout-Gin)
DS = P – Q – G – ET
• Generally more than one term is unknown
Example: Nile River Swamps
Region
A
(km2)
P
(md)
Inflow
(md)
Overbank
Spill (md)
Outflow
(md)
Loss
(md)
Machar
8,700
7.3
2.0
3.5
0.1
12.7
Jebel-Zeraf
8,300
7.5
27.0
-6.0
14.3
14.2
Ghazal
16,600
15.0
12.7
6.0
0.6
33.1
* md = milliard = 109 m3
 Over a year DS ~ 0, No information on groundwater, ~ 0
ET = P – Q (Q = Qout - Qin)
M: ET = 7.3 – (0.1 – 2.0 – 3.5) = 12.7 = 1.46 m
J: ET = 7.5 – (14.3 – 27.0 + 6.0) = 14.2 = 1.71 m
G: ET = 15.0 – (0.6 – 12.7 – 6.0) = 33.1 = 1.99 m
 Independent studies showed average ET=1.9 m.