Environmental Engineering Reference
In-Depth Information
of distributed model included the seminal papers
of Freeze (1972) and Stephenson and Freeze (1974)
using finite difference solutions to the partial
differential equations for one-dimensional (1D)
surface and two-dimensional (2D) (vertical slice)
subsurface flows at the hillslope scale. Beven
(1977; see also 2001b) also later introduced vari-
able width, vertical slice, finite element solutions
to 2D subsurface flow for hillslopes linked to 1D
surface flow routing.
The first fully distributed catchment model
based on the Freeze and Harlan blueprint to
achieve more widespread use was the Systeme
Hydrologique Europ ยด en (SHE) model (Beven
et al. 1980; Abbott et al.1986; Bathurst 1986). The
original SHE model was implemented, primarily
for computational reasons as 2D saturated zone
and surface runoff components, solved on a square
grid, linked by 1D unsaturated zone components.
More recently two different versions of SHE
(MIKE SHE at Danish Hydraulic Institute and
SHETRAN at Newcastle University) have been
implemented with fully 3D variably saturated
subsurface components, which avoids the internal
coupling problems between the unsaturated and
saturated zone components. The rapid increase in
available computer power has also allowed much
finer spatial discretizations to be used (although
this also, as in any numerical approximation to
time-dependent partial differential equations, re-
quires the use of shorter time steps). There have
been published applications of SHE that use grids
up to 4 km in large catchments (Jain et al.1992),
which, while allowing the inputs and character-
istics of the model to vary spatially, clearly limits
the extent to which the sub-grid-scale variability
in hydrological responses can be resolved (and also
compromises the calculation of any fluxes based
on gradients in the continuum representation).
More recently the Integrated Hydrological
Model (InHM) has been used to predict the R5
catchment in Chickasha, Oklahoma, and the
Coos Bay experimental hillslope in Oregon,
with variable sized finite elements of the order of
10m (VanderKwaak and Loague 2001; Loague
et al. 2005; Ebel et al. 2008). InHM uses a finite
element solution of the continuum equations,
The Evolution of Distributed Models in
Hydrology and Hydraulics
Early distributed models
The first distributed models in hydrology and
hydraulics belong to the pre-digital computer age.
The idea that different areas in a catchment might
produce different amounts of storm runoff, which
would then need to be routed to a point of interest,
goes back at least to Imbeaux (1892), who calcu-
lated snowmelt runoff on the Durance river in
France based on different contributing areas at
different time delays from the catchment outlet.
This time-area histogram approach was later used
by Ross (1921), Zoch (1934) and Clark (1945) in the
USA, and Richards (1944) in the UK. Robert
Horton (1938) also made use of a predictive model
that allowed for different infiltration characteris-
tics ondifferent parts of a catchment (Horton1938;
Beven 2004). Within these subcatchment areas,
however, predictions of runoff were lumped, so
that these early attempts at distributed predic-
tions might be called semi-distributed (while
noting that many modern distributed models are
also of this type).
The freeze and Harlan blueprint
More explicitly distributed predictions of hydro-
logical processes at hillslope and catchment
scales, and distributed hydraulic models, had to
await the more widespread availability of digital
computers. In particular the 'blueprint for a phys-
ically based digitally simulated hydrologic
response model' of Freeze and Harlan (1969) set
the scene for most of the distributed hydrological
models that have been developed since. Freeze and
Harlan (1969) laid out the continuum partial
differential equations required: two- and three-
dimensional Darcy-Richards equations in the
subsurface, and one- and two-dimensional equa-
tions of the depth-averaged St-Venant equations
for the surface, how they might be internally
coupled, and how they might be coupled to
additional snowmelt and evapotranspiration
components. Early implementations of this type
