2011 - Cooperative Institute for Research in Environmental Sciences ...

Vijay Gupta
Understanding Multi-Scale Infiltration in River
Basins as a Statistical-Dynamical Problem
Last year, my colleagues
and I uncovered
that “random selfsimilarity”
in the spatial
branching pattern of river
networks provides a key
physical basis to understand
the underlying
spatial pattern of floods.
Self-similarity means that
each part of a network
is a tiny version of the
whole. The observed pattern
in floods appears as
a power law, or a scaling
relation, that is being tested
in several river basins
of the world.
The presence of power
laws in floods is being
used to develop a predictive model based in multi-scale
solutions of mass and momentum conservation equations
in random self-similar channel networks. It requires a pre-
Goodwin Creek
Experimental Watershed
(GCEW) in Mississippi.
dictive understanding of infiltration and runoff generation
as a multi-scale problem. We are developing and testing
a theory of multi-scale infiltration in the Goodwin Creek
Experimental Watershed (GCEW) in Mississippi. GCEW
is an experimental watershed of Agriculture Research
Service (ARS). It has excellent space-time observations of
rainfall and stream flows for about 30 years, which are
needed to understand multi-scale infiltration.
Our goal is to develop a rainfall-runoff model that
can be used to assign infiltration thresholds to hillslopes,
which are the smallest geomorphic units in a river basin.
To reach this goal, we represent threshold values for a
rainfall-runoff event at three different spatial scales: 1) the
drainage area of a ``parent’’ basin; 2) the drainage area of
unnested sub-basins within the parent basin; and 3) the
drainage area of hillslopes within the unnested sub-basins.
For GCEW, the drainage area at the outlet of the largest
stream gauged basin gives 21 km 2 . The drainage areas of
unnested gauged sub-basins within GCEW range from
0.17 to 3.58 km 2 such that mean area is approximately
1.6 km 2 . Likewise, the mean drainage area of hillslopes
within GCEW is approximately 0.038 km 2 . Observations
needed to determine infiltration thresholds are generally
available for the entire basin and at several sub-basins that
are typical of medium-size basins worldwide. However,
they have not been made at the hillslope scale, which is
practically impossible because the number of hillslopes is
typically very large; GCEW has approximately 800 hillslopes.
Our model is being developed under the postulate
that certain threshold properties observed in sub-basins
are preserved at the hillslope scale. It requires a statisticaldynamical
formulation that is being developed and tested.
CIRES Annual Report 2011 37