The Atmosphere-Vegetation-Soil System - Transport in the Atmosphere-Vegetation-Soil Continuum - page 5

see Question 1.1 ). As water can change phase within the volume, all phases have to
be accounted for in the total water balance of the control volume. The water balance
then reads:

PIRA ED +−+−−= ++

v

∆∆∆ WS S (1.2)

l g

where we distinguish the following transports across the boundaries of the control
volume: P is precipitation, I is irrigation (artiicial supply of water), R is runoff, D is
the drainage rate towards deeper soil layers, A v is advection of water vapour (which
can be positive or negative) and E is the water that leaves the system in gas phase
(water vapour; see Section 1.2.3 ). The different inputs and outputs do not necessarily
balance, so that water may be stored in the soil (∆ W , change in soil moisture content),
on the soil or on the vegetation in the liquid phase (∆ S l , e.g., intercepted rain or dew)
and in the air (∆ S g ) in the gas phase.
Water molecules can change phase. In Figure 1.4 this is indicated with the phase
change terms C l↔g (between liquid and vapour), C l↔s (between liquid and solid) and
C g↔s (between vapour and solid). These phase change terms, however, do not occur
in Eq. ( 1.2 ) because they do not change the number of molecules of water within the
control volume but only the phase in which they occur. On the other hand, as energy
is released or used when water changes phase, the phase change terms do affect the
energy balance, as we see later.

Question 1.1: Figure 1.4 shows the mass balances for water of a control volume
extending from the soil into the atmosphere, above the vegetation. Only liquid and gas-
eous water is dealt with.
a. Sketch the mass balance for solid water.
b. Enumerate all interactions between the mass balances for each of the phases (i.e.,
which phase changes can occur that exchange water in one phase for another?).

1.2.2 Energy Balance
Whereas in the water balance we have to distinguish between the three phases of
water, in the energy balance we distinguish between two forms of energy: sensible
heat and latent heat. Sensible heat is the energy contained in a substance that can
be extracted by cooling it. On the other hand, latent heat can be extracted only by a
phase change. It could be considered as similar to potential energy: a ball on a hill has
potential energy that could be extracted when it rolls down the hill. In a similar way,
water vapour contains latent heat that would be freed if it condenses to liquid water.
In the current context it is customary (but not necessary) to use liquid water as the
reference (i.e., ice contains negative latent heat because it would require input of heat
to bring it to liquid water).