AOM 4346 - BASIC HYDROLOGIC CONCEPTS
As discussed last time -- hydrologic cycle describes the continuous circulation of water
from land and sea to the atmosphere and back again.
The concept is based on mass balance and is simply that water changes state and is
transported in a closed system which extends approximately 1 km down into the earth’s
crust and  15 km up into the atmosphere.
The hydrologic cycle is closed only globally, not on a watershed or continental scale.
Thus practicing hydrologists are typically faced with an open system.
Also, as we discussed last time, hydrologic phenomena (precipitation, ET, infiltration,
groundwater, overland, streamflow) are extremely complex and although quantifiable at
lab scale, may never be fully predictable at the watershed scale. Thus we represent them
in a simplified way by means of the systems concept.
Definition: A hydrologic system is defined as a structure (surface or subsurface) or
volume (atmospheric) in space, surrounded by a boundary, that accepts water and other
inputs (such as air or heat energy), operates (physical, chemical, biological) on them
internally and produces them as outputs. It represents flow paths though the system.
Thus we treat the hydrologic cycle as a system whose components are precipitation,
evapotranspiration, interception, runoff, infiltration, etc.. We give up the quest to know
the precise spatiotemporal water flow patterns within the system and settle instead for
knowing total water storage, and spatially averaged water fluxes in and out of the control
volume.
Example:
ET(t)
overland flow
surface runoff
groundwater
discharge
Q(t)
G(t)
The basic relations of physical hydrology for this system are derived from fundamental
laws of classical physics. Particularly:
1. Conservation of mass
(m = mass of water)
2. Conservation of energy
(internal energy, kinetic energy and potential energy
of the fluid)
Conservation of Mass
The most useful principal in hydrologic analysis and is required in almost all problems.
Stated mathematically
dS
 Q (t )  I (t )
dt
For our watershed problem:
ppt.
surface
outflow
gw
outflow
dS
 P (t )  Q (t )  G (t )  ET (t )
dt
These fluxes are spatially integrated over whole
control volume -- space is no longer considered an
independent variable. Do not consider within control
volume processes such as overland flow, gw discharge
to stream, within control volume streamflow.
open system so there
can be a change in
storage. If have a
closed system (i.e. cycle
over whole earth rather
than watershed) dS = 0
dt
If dS = 0  steady flow problem  inflows = outflows:
dt
P(t )  Q(t )  G (t )  ET
Energy Conservation Equation
Second fundamental physical law utilized in physical hydrology is the conservation of
energy. (energy is neither created or destroyed)
Total energy of a system = internal energy + kinetic energy + potential energy
extensive
property
or
E
Energy per
unit mass
intensive
property
=
Eu
+
1/2 mV2
+
mgz
=
eu
+
1/2 V2
+
gz
Internal Energy (eu)
Internal energy is the sum of sensible heat and latent heat.
Sensible heat is that part of the internal energy that is proportional to the substance’s
temperature
 temperature changes produce proportional changes in internal energy according to
deu = CpdT
specific heat of a substance at a constant pressure
(1.0 cal/g K for water)
(4.2 * 103 J/kg K for water)
(0.24 cal/ g K for dry air)
Latent heat - Amount of heat exchange required for inducing a phase change per gram of
substance without a change in temperature. Usually a function of temperature.
For example,
1. liquid water to vapor
Le = latent heat of evaporation
= 597.3 - 0.57 T cal/g
temp in C
This is heat absorbed (vaporized by water from surroundings) to break H bonds so
evaporation can take place.
 evaporation always accompanied by transfer of heat out of water body or
surroundings to vapor  latent heat transfer
2. vapor to liquid water
Lc = latent heat of condensation
= -597.3 + 0.57 T cal/g
C
This is heat released to surroundings when H bonds formed during condensation
3. ice to vapor
Ls = latent heat of sublimation
= 677 - 0.07 T cal/g
C
This is energy needed to:
a) disrupt molecular structure then
b) break H bonds
At typical atmospheric temp. and pressure on earth, energy required to sublimate
ice to vapor generally greater than that required to melt ice through evaporation.
Therefore, usually water goes through liquid phase first.
4. ice to liquid
Lm = latent heat of melting
= 79.7 cal/g
= 0.33 * 106 J/kg
Energy required to disrupt molecular structure.
5. liquid to ice
Lf = latent heat of fusion
= -79.7 cal/g = - 0.33 * 106 J/kg
Energy released as molecular structure is formed.
1952 J/kg K
Internal
energy
latent heat of
fusion
= 80 cal/g =
0.33*106 J/kg
latent heat of evaporation
539 cal/g at 100C
2.3*106 J/kg at 100C
specific heat
Cp = 1 cal/g C
=4183 J/kg K
water
vapor
ice
2106 J/kg K
liquid water
0
Temp C
100
Jumps in curve  latent heat transfer to water
Slope in curve  sensible heat transfer to water
In the SW use the latent heat of evaporation for air-conditioning houses  water and air
is run into evaporative cooler on roofs of houses -- as water evaporates absorbs heat from
air. Cooled air is returned to house.
Latent heat transfer is the dominant cause of internal energy change for water in most
hydrologic applications  temperatures usually only change a few degrees C so sensible
heat transfer is small.