Page 193 - Biosystems Engineering

172 Cha pte r F i v e

Although most present-day models are deterministic models, as
many of the input variables, model parameters, and modeled pro-
cesses are stochastic in nature, stochasticity is introduced through
model uncertainty analysis.
Because watershed-scale models have mostly nonlinear compo-
nents, based on the mathematical properties of the operator function,
they can best be regarded as nonlinear models. Linear models, such as
the unit hydrograph theory, are based on two simple principles: the
principle of proportionality and the principle of superposition. The
former can be stated as follows: if f(x) is a solution of a system, then
c⋅f(x) is also a solution of the same system, with c being a constant. The
latter principle implies that if f (x) and f (x) are both solutions of the
1 2
same system, then f (x) + f (x) is also a solution of the same system.
1 2
Based on the length of simulation, models can be characterized as
event or continuous. An event model represents runoff event occur-
ring over a period of time ranging from hours to several days, whereas
a continuous simulation model can operate over an extended period
of time, simulating flows and conditions during both runoff periods
and nonrunoff periods. Continuous models keep a continuous
account of watershed characteristics. Watershed models can also be
characterized as lumped or distributed parameter models. A distrib-
uted parameter model directly uses the areal variations in watershed
characteristics (e.g., soils, land use, slope, and rainfall); a lumped
parameter model cannot do this. Most watershed-scale models, how-
ever, are lumped to some extent. Based on the criteria listed above,
currently used popular watershed-scale hydrologic and NPS models
can be characterized as nonlinear, process based, deterministic, dis-
tributed parameters, and events or continuous simulations. In this
chapter, we limit our discussion to these types of models.

5.2.4 Important Components of Watershed Models
Although descriptions of processes vary in different watershed-scale
models, most models allow various physical, chemical, and biologi-
cal processes to be simulated in a watershed. Furthermore, because
water balance is the driving force behind accurate prediction of move-
ment of sediment, nutrients, and pesticides, accurate simulation of
various components of hydrologic cycle is important for watershed
models. The following water balance equation, especially in continu-
ous simulation models, is often used (Neitsch et al. 2005):

t
SW = SW + ∑ ( R − Q − E − w − Q )
t 0 day surf a seep gw
i=1
where SW = the final soil water content (mm H O)
t 2
SW = the initial soil water content on day i (mm H O)
0 2
t = the time (days)