PE EIE[R-Rg RESEARCH ON - HJ Andrews Experimental Forest

model being developed under the Coniferou s
Biome Program. The important underlying
feature throughout the entire study will b e
that all of the separately described hydrologi c
processes and phenomena are interlinked into
a total system . Thus, from the model, hope -
fully, it will be possible to evaluate the relative
importance of the various items, explore
critical areas where data and perhaps theor y
are lacking, and finally establish guidelines fo r
the improved management of forest water -
sheds .
INPU T
(lOVO
(A)
SYSTEM
(KNOWN )
SYSTEM SYNTHESI S
OUTPUT
^-TI €N NNowN 1
Hydrologic Systems Analysis 3
INPUT
(KNOWN)
SYSTE M
(UNKNOWN)
OUTPU
T (KNOWN )
The purpose of this research is to devise a
technique for statistical decomposition of a
hydrologic event such that system processe s
such as precipitation, subsurface flow, an d
evapotranspiration, which contribute to th e
observed streamflow can be separated and
described. This technique will therefore pro -
vide one more avenue for determination of
the subsurface flow process on forest soils .
The technique chosen for this research is a
form of systems analysis .
Systems, Definitions and Basic Principles
System may be defined as an aggregate of
physical parts that do not change with time ,
operating on an input to produce an output ,
both being functions of time . The simplified
representation of a watershed, given in figure
2, can be considered as a system whose input
is precipitation and runoff its output . Syste m
"synthesis" is a technique employed when th e
system is known in terms of a mathematical
equation; the objective is to determine th e
nature of the output for any class of inpu t
(fig. 7) . In system "analysis" a syste m
response function or kernel which best de -
scribes a given input-output pair is derived
(fig. 7) . The term "best" implies that the
derived kernels are not unique . Combination s
of both techniques can be used for the solution
of hydrologic problems . A system can
3 Authored by Z. G. Papazafiriou, Research
Associate, and R . H . Burgy, Professor, University o f
California, Davis .
(C)
(B)
SYSTEM ANALYSI S
MULTI-INPUT/OUTPUT SYSTEM
Figure 7 . Illustration of systems .
have one input and one output or many in -
puts and outputs (fig. 7). A system i s
"lumped parameter" if input and output ar e
functions of a single variable . Otherwise, th e
system is of the "distributed parameter" type .
If the system response at any time, due to a
given input, is uniquely determined, th e
system is said to be "deterministic." If the
system response is subject to uncertain influences,
the system is "stochastic o r
probabilistic . "
A quantity z is a "functional" for the function
x(t) in the interval (a,b), if it depend s
upon all values taken by x(t), when t varies i n
the interval (a,b) . An illustration of a functional
is given in figure 8 . The output of a
system is a functional of the input and, fo r
the same reason, runoff is a functional o f
precipitation. A system is "time invariant " if
it does not change with time. Such system s
can be represented by functionals . "Physically
realizable" is a system whose output at time t
depends only upon past values of the input .
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