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Vijay K. Gupta Research Group
Rainfall, evaporation, transpiration, and runoff generation from hillslopes,
and water transport on channel networks in river basins are highly
variable in space and time. Despite this space-time complexity, observations
show that the statistics of many coupled hydrologic phenomena in river
basins exhibit power laws. Contemporary theoretical advances show that
power laws describe self-similarity, or scale invariance, with respect
to geometrical, statistical and dynamic properties of complex nonlinear
systems. Four hydrologic examples are given to illustrate presence
of power laws in data.
Figure 1. Observed power law in a plot
of peak discharge Q(A) versus drainage area A for a rainfall-runoff
event in the Goodwin Creek basin, Mississippi (Ogden and Dawdy,
J. Hydro. Eng., March/April, 2003). |
Figure 2. Observed power laws and the fluctuations surrounding them
in the hydraulic geometry variables (channel width, W; channel depth,
D; mean stream velocity, V; channel slope, S) on the Ashley River basin,
New Zealand (McKercher et. al., Water Resour. Res., 34, 1998). |
Figure 3. Observed power laws in the 2-year and 100-year flood quantiles
versus drainage area on the Walnut Gulch basin, Arizona (Goodrich et.
al, Water Resour. Res., 33, 1997). |
Figure 4. Observed power laws in a plot of drainage density versus
Thornthwaite index, TI, representing arid (left) to humid (right) climates
(Abrahams, Water Resour. Res., 20, 1984). |
What are the physical processes that give rise to observed power laws
in these diverse hydrologic phenomena? A physical understanding of
mean power-law relationships, and the fluctuations surrounding them,
is necessary to address this question and to solve the long-standing
problem of predicting flows in ungauged basin across multiple space
and time scales. Our research is focused on answering this fundamental
issue. |
Group Members
Vijay K. Gupta
Peter Furey
Keith Nordstrom
Ricardo Mantilla
Megan McConnell |
