Water Balance in Catchments
19.4 The Quotient PIEr: Key Variable
for Determining Water Balance
277
The above-mentioned relationships between the annual values of the hydrological variables can be understood when the quotient PIEr is considered.
When P is much greater than Er, as is the case at Hubbard Brook, the evaporative demand can be totally satisfied and the remaining water becomes
streamflow. In consequence, there is a positive relationship between P and Q,
and annual EA can be considered constant (Likens et al. 1977). In contrast,
when P is lower than Er, as in Prades, the water supply in the wetter years is
still not enough to satisfy the transpiration and evaporation possible in this
climate. Thus, at Prades, the water surplus of rainy years is evaporated (EA increases) rather than lost by streamflow; streamflow is more dependent on the
rainfall distribution in time than on the annual volume. For instance, the
Avic catchment had its maximum annual Q (95 mm) in the hydrological year
1982-1983 but not the highest precipitation (only 576 mm) because a major
part of the streamflow (75 mm) occurred during 2 wet months (185 mm rain
in October and 151 mm in November). In the Avic catchment, linear correlation between annual Q and the rainfall of the 3 months with the highest precipitation is much higher (r2 = 0.71) than between annual Q and annual P
(r2 = 0.42; Table 19.2). At Montseny, P is only slightly greater than Er: these
catchments present an intermediate behaviour between those of Prades and
those of more humid regions.
In dry climates like that of Prades, annual EA can be very different in different years, and neither annual EA nor annual transpiration can be considered as conservative hydrological variables, as Roberts (1983) considered
them for temperate climates. The higher transpiration rate that can be
maintained in humid years allows a higher CO 2 fixation rate in dry sites. At
Prades this effect was clearly shown by the much higher rate of stem growth
of holm oak trees in the rainy summer of 1992 than in the average of the 3
preceding years, which had normal dry summers (Mayor et al. 1994). Thus,
the study of the hydrologic cycle in dry areas is important not only by itself,
but also because of its influence on many other ecological and biogeochemical processes occurring in the catchment. The present book contains plenty
of examples showing that water availability is the single most important factor in the ecology and nutrient cycling in Mediterranean forests.
The above relationship between the components of the water balance under different climates can be described more formally. It is a usual practice in
hydrology to take into account Er in order to estimate EA' The classical expressions of Turc (1954) and Budyko (1974) both include Er in their formulation. Pifiol et al. (1991) developed a new expression, based on a previous
work of Hsuen-Chun (1988), to predict EA as a function of Er and P. This expression includes an additional parameter (k) that can be considered as a
lumped parameter of the non-climatic catchment characteristics relevant for
the water balance. The expression was:
19.4 The Quotient PIEr: Key Variable
for Determining Water Balance
277
The above-mentioned relationships between the annual values of the hydrological variables can be understood when the quotient PIEr is considered.
When P is much greater than Er, as is the case at Hubbard Brook, the evaporative demand can be totally satisfied and the remaining water becomes
streamflow. In consequence, there is a positive relationship between P and Q,
and annual EA can be considered constant (Likens et al. 1977). In contrast,
when P is lower than Er, as in Prades, the water supply in the wetter years is
still not enough to satisfy the transpiration and evaporation possible in this
climate. Thus, at Prades, the water surplus of rainy years is evaporated (EA increases) rather than lost by streamflow; streamflow is more dependent on the
rainfall distribution in time than on the annual volume. For instance, the
Avic catchment had its maximum annual Q (95 mm) in the hydrological year
1982-1983 but not the highest precipitation (only 576 mm) because a major
part of the streamflow (75 mm) occurred during 2 wet months (185 mm rain
in October and 151 mm in November). In the Avic catchment, linear correlation between annual Q and the rainfall of the 3 months with the highest precipitation is much higher (r2 = 0.71) than between annual Q and annual P
(r2 = 0.42; Table 19.2). At Montseny, P is only slightly greater than Er: these
catchments present an intermediate behaviour between those of Prades and
those of more humid regions.
In dry climates like that of Prades, annual EA can be very different in different years, and neither annual EA nor annual transpiration can be considered as conservative hydrological variables, as Roberts (1983) considered
them for temperate climates. The higher transpiration rate that can be
maintained in humid years allows a higher CO 2 fixation rate in dry sites. At
Prades this effect was clearly shown by the much higher rate of stem growth
of holm oak trees in the rainy summer of 1992 than in the average of the 3
preceding years, which had normal dry summers (Mayor et al. 1994). Thus,
the study of the hydrologic cycle in dry areas is important not only by itself,
but also because of its influence on many other ecological and biogeochemical processes occurring in the catchment. The present book contains plenty
of examples showing that water availability is the single most important factor in the ecology and nutrient cycling in Mediterranean forests.
The above relationship between the components of the water balance under different climates can be described more formally. It is a usual practice in
hydrology to take into account Er in order to estimate EA' The classical expressions of Turc (1954) and Budyko (1974) both include Er in their formulation. Pifiol et al. (1991) developed a new expression, based on a previous
work of Hsuen-Chun (1988), to predict EA as a function of Er and P. This expression includes an additional parameter (k) that can be considered as a
lumped parameter of the non-climatic catchment characteristics relevant for
the water balance. The expression was: