Geoscience Reference
In-Depth Information
by linear regression in a stepwise manner with an equation of the type
aB
b
C
c
D
d
=
...
Q
T
(13.91)
in which
b
are constants, whose values depend on the return period of the
quantile. Characteristics to be considered may include drainage area, main channel slope,
main channel length, mean annual precipitation, fraction of area with lakes and ponds,
mean annual runoff,
T
r
y 24 h rainfall, mean basin altitude, fraction of basin area covered
with forest, basin shape as ratio of main channel length and area, mean basin elevation,
and possibly others. The final selection of the characteristics to be included can be made
on the basis of their respective statistical significance and on the basis of the reduction
of the standard error caused by their inclusion.
The basic idea and early applications of the method to the quantiles of annual floods
were described by Benson (1962a, b) and Cruff and Rantz (1965). The method was also
explored for other streamflow characteristics, beside the annual maxima, by Thomas
and Benson (1970). The quantile regression procedure has subsequently been refined
by means of a generalized least squares (GLS) procedure (Tasker and Stedinger, 1986;
1989) to take account of the fact that the stations may have records of unequal lengths
and that concurrent observations at different stations may not be independent, but cross-
correlated. With these improvements the method has become the main tool of the US
Geological Survey to derive the frequency of flood flows for selected return periods
T
r
on a regional basis in different states. A nationwide summary of the information derived
as of 2002 was compiled by Ries and Crouse (2002). However, as more information is
becoming available and the streamflow records become longer, the regression equations
are periodically being revised. For some examples of recent updates by state the reader is
referred to the studies for Washington (Sumioka
et al
., 1998), Maine (Hodgkins, 1999),
Colorado, (Vaill, 2000), West Virginia (Wiley
et al
., 2000) and North Carolina (Pope
et al
., 2001).
In these more recent studies the frequency relationships for each of the individ-
ual gaged sites were commonly derived on the basis of the generalized log-gamma
distribution with a regionalized skew. In most cases the delineation of hydrologic
regions within the state and the identification of the important explanatory variables for
Equation (13.91) were next carried out in a stepwise manner by means of ordinary least
squares regression. The regions were usually delineated by inspection of the statewide
regression residuals. Once the explanatory variables were identified for each region, the
final predictive equations for the different quantiles in terms of the basin characteristics
were calculated by means of the GLS procedure, as outlined by Tasker and Stedinger
(1989). The explanatory variables that were found to affect the flow peak quantiles varied
greatly from one region to another, but the number of adopted variables was usually kept
as small as possible and restricted to two or three at most. In all regions the size of the
drainage was found to be the most important variable and key basin descriptor; for some
regions it was actually concluded to be the only significant one (Pope
et al
., 2001; Wiley
et al
., 2000). It has also been suggested on the basis of scaling arguments (Gupta
et al
.,
1994) that the sole dependency of
Q
T
on drainage area
A
, and on nothing else, can be
used as the criterion to define a hydrologically homogeneous region. In regions with
,
c
,
d
,...,
