Geoscience Reference
In-Depth Information
12
STREAMFLOW RESPONSE AT THE
CATCHMENT SCALE
In this chapter different formulations are considered that are available to transform
the lumped water input by rainfall or melt events directly into streamflow output from
the catchment area. The basic philosophy of this type of approach is that the physical
processes are assumed to take place at the scale of the catchment, without consideration
for the detailed subscale processes or for the intricacies of the flow paths inside the
watershed. In a sense, this is analogous with the view espoused in continuum mechanics
or thermodynamics (albeit in their own respective scale ranges), where only the “macro”
or “everyday” properties of the fluids are taken into account, without consideration of
their properties at the molecular or nuclear scales. Because by far most applications of
the lumped approach in the past have been based on the assumptions of linearity and
stationarity, these will be treated first and in greatest detail.
12.1
STATIONARY LINEAR RESPONSE: THE UNIT HYDROGRAPH
12.1.1
Basic concept
Definition
The unit hydrograph, or unit graph, can be defined as the hydrograph of unit volume
of storm runoff produced by a unit volume of uniform (in space and in time) intensity
excess rainfall over a unit period
D
u
, with the basic assumptions of
linearity
and
time
invariance
. As defined here, the unit hydrograph is the response function of a linear
system, which is treated in more general terms in the Appendix, and can be denoted by
u
(
D
u
;
t
). Similarly, in what follows in this chapter,
y
x
(
t
) will denote,
respectively, the storm runoff per unit of catchment area and the intensity of excess
rainfall or other input per unit catchment area, which directly produces this storm runoff;
note that in some practical applications, the determination of
y
and
x
may require the
abstraction of baseflow and of the interception or deep infiltration of the precipitation.
According to the definition of Equation (A9), in the present context the assumption of
linearity or superposition means that the hydrograph, resulting from any input pattern of
rainfall or snowmelt, can be built up from separate unit hydrographs by superposition,
that is, after scaling them in magnitude and after sequencing them in time. In light of
the definition (A10), the assumption of invariance or stationarity means that the runoff
from a given catchment due to a given input pattern is the same, regardless of the
particular circumstances; thus there are no effects or feedbacks resulting from current
conditions (e.g. season) or antecedent input during the event. The unit volume and unit
period are arbitrary, but they can be taken, for example, as 1 cm over the entire area of the
=
y
(
t
) and
x
=
