Geoscience Reference
In-Depth Information
The terms in the water balance equation can be
recognised as a series of fluxes and stores. A
flux
is
a rate of flow of some quantity (Goudie
et al
., 1994):
in the case of hydrology the quantity is water. The
water balance equation assesses the relative flux of
water to and from the surface with a storage term
also incorporated. A large part of hydrology is
involved in measuring or estimating the amount
of water involved in this flux transfer and storage of
water.
Precipitation in the water balance equation
represents the main input of water to a surface (e.g.
a catchment). As explained on p. 10, precipitation
is a flux of both rainfall and snowfall. Evaporation
as a flux includes that from open water bodies
(lakes, ponds, rivers), the soil surface and vegetation
(including both interception and transpiration from
plants). The storage term includes soil moisture,
deep groundwater, water in lakes, glaciers, seasonal
snow cover. The runoff flux is also explained on
p. 10. In essence it is the movement of liquid water
above and below the surface of the earth.
The water balance equation is probably the closest
that hydrology comes to having a fundamental
theory underlying it as a science, and hence almost
all hydrological study is based around it. Field
catchment studies are frequently trying to measure
the different components of the equation in order
to assess others. Nearly all hydrological
models
attempt to solve the equation for a given time
span - for example, by knowing the amount of
rainfall for a given area and estimating the amount
of evaporation and change in storage it is possible
to calculate the amount of runoff that might be
expected.
Despite its position as a fundamental hydro-
logical theory there is still considerable uncertainty
about the application of the water balance equation.
It is not an uncertainty about the equation itself but
rather about how it may be applied. The problem
is that all of the processes occur at a spatial and
temporal scale (i.e. they operate over a period of time
and within a certain area) that may not coincide
with the scale at which we make our measurement
or estimation. It is this issue of
scale
that makes
THE WATER BALANCE EQUATION
In the previous section it was stated that the
hydrological cycle is a conceptual model
representing our understanding of which processes
are operating within an overall earth-atmosphere
system. It is also possible to represent this in the
form of an equation, which is normally termed the
water balance equation
. The water balance
equation is a mathematical description of the
hydrological processes operating within a given
timeframe and incorporates principles of mass and
energy continuity. In this way the hydrological cycle
is defined as a closed system whereby there is no
mass or energy created or lost within it. The mass
of concern in this case is water.
There are numerous ways of representing the
water balance equation but equation 1.1 shows it in
its most fundamental form.
S
±
Q
= 0
P
±
E
±
(1.1)
where
P
is precipitation;
E
is evaporation;
S
is the
change in
storage
and
Q
is runoff. Runoff is
normally given the notation of
Q
to distinguish it
from rainfall which is often given the symbol
R
and
frequently forms the major component of precipita-
tion. The ± terminology in equation 1.1 represents
the fact that each term can be either positive or
negative depending on which way you view it - for
example, precipitation is a gain (positive) to the
earth but a loss (negative) to the atmosphere.
As most hydrology is concerned with water on or
about the earth's surface it is customary to consider
the terms as positive when they represent a gain to
the earth.
Two of the more common ways of expressing the
water balance are shown in equations 1.2 and 1.3
P
-
Q
-
E
-
S
= 0
(1.2)
Q
=
P
-
E
-
S
(1.3)
In equations 1.2 and 1.3 the change in storage term
can be either positive or negative, as water can be
released from storage (negative) or absorbed into
storage (positive).
