Modelling Catchment and Fluvial Processes and their Interactions - Environmental Modelling: Finding Simplicity in Complexity - page 188

may be as short as a single year, or may develop over
many decades, depending on the process rates.
Over timescales of centuries to millennia, the topo-
graphic feedbacks start to dominate. Wainwright (2006)
demonstrated using a modelling study how these feed-
backs can start to lock in the fluvial system to a particular
response, occupying a relatively small phase space that
is not simply dependent on climatic variability. Thus,
the history of a catchment, initial conditions and the
contingency of events strongly control the response of
catchments at this timescale (and typically at corre-
spondingly large spatial scales). Subsequent analyses have
used palaeoenvironmental data to demonstrate that these
results are representative (Briant et al ., forthcoming). A
more recent study by Perron and Faggerazzi (2012) fur-
ther emphasizes the importance of initial conditions and
path dependency at these scales of analysis (see also
Chapter 19).

One approach for simplifying the spatial complexity is
to use a statistical approach that takes account of appro-
priate structures in the landscape. However, as noted
above, hydrological response is strongly dominated by
the connectivity of runoff-producing elements. Simple
statistical approaches to distributing parameters do not
take sufficient account of spatial autocorrelation to be able
to represent such connectivity. M uller et al . (2007) used
stochastic simulation of spatial patterns of K sat and surface
roughness based on semi-variogram analysis of field mea-
surements from the Jornada LTER site in New Mexico.
When using autocorrelation based simply on the semi-
variogram, the connectivity was poorly reproduced and
hydrographs typically poorly estimated. Conditioning the
spatial pattern based on separate distribution functions
for vegetated and non-vegetated surfaces, using a vegeta-
tion map derived from aerial photography improved the
representativity. The best results were typically obtained
when the patterns were further conditioned by includ-
ing mapped rill networks, emphasizing the connectivity
of parameters along established flowlines, and thus the
significance of the structural-functional feedbacks noted
above (Figure 11.9). Similar techniques were successfully
used by Turnbull et al . (2010) to parameterize initial soil
moisture for simulations at a series of field sites with
different vegetation types at the Sevilleta LTER site in
New Mexico. These studies show the importance of using
an appropriate conceptual (statistical) model to parame-
terize models with relatively sparse information. Further
discussion of this issue can be found in Chapter 8.

11.3 The simplicity

11.3.1 Simplifyingspatial complexity

Thus far we have concentrated on understanding the
implications of spatial complexity for modelling needs at
the catchment scale. We know that lumped models do
not represent this variability and that distributed models
do insofar as they can but do not insofar as the required
data are often not available. Semi-distributed (or semi-
lumped!) approaches are a compromise between the two
end points but say nothing of the interaction between
neighbouring patches, which can be important in hydro-
logical studies. Different aspects of the spatial variability
of catchments have different magnitudes of impact on the
hydrological system and different spatio-temporal scales
of interaction with it. Soil and vegetation properties are
likely to be more important for small catchments and
short periods but their influence will become smaller
as the size of the catchment or length of the period
increase, at which point geomorphological and geomor-
phometric processes become more important. A nested
hierarchy of catchment response units might be identi-
fied with climate, geomorphology, vegetation and soils
having progressively greater variability and progressively
smaller scales of influence (see Mulligan, 1996). The
increasing use of remote sensing for hydrological mod-
elling can significantly improve the spatial realism of
distributed models (see Mulligan, 2009), but only if scale
implications are explicitly considered (see Chapter 5).

11.3.2 Simplifyingtemporal complexity
In addition to spatial complexity, catchment models must
also handle the temporal complexity of hydrological pro-
cesses and their interaction with each other. Catchments
integrate rapid rate processes such as the partitioning of
rainfall into runoff and infiltration or the routing of water
through channels, with slower rate processes such as the
trickle of groundwater recharge and the continuous draw
of evapotranspiration. Hydrological models are sensitive
to the time step of simulation, large errors can ensue by
aggregating evapotranspiration calculations (from hourly
through day/night to daily) and by representing instanta-
neous rainfall intensities that can reach over 100 mm h − 1
as hourly averages, which are unlikely ever to do so (see
Wainwright et al ., 1999 for an extended analysis). The
temporal and spatial complexity of a catchment model
must match the spatio-temporal complexity of the pro-
cesses, although the availability of data is usually the