PROGRAMS AND PLANS--Recommendations for Regional Low-Flow Studies

In Reply Refer To:                               July 7, 1989
WGS-Mail Stop 415


Subject:  PROGRAMS AND PLANS--Recommendations for Regional
                              Low-Flow Studies

Office of Surface Water (OSW) Technical Memorandum No. 87.08
announced the availability of the generalized least squares
regression program for the regionalization of flood characteris-
tics and network analysis.  This program has now been revised for
use in the regionalization of low-flow characteristics.  The pur-
pose of this memorandum is to make recommendations concerning
regionalization of low-flow characteristics and to describe the
programs for undertaking this analysis.

Multiple-regression procedures based on watershed characteristics
have been used for years for regionalizing flood characteristics.
In the last few years, there has been increased effort in the
regionalization of N-day T-year low-flow characteristics, such as
the 7-day 10-year low flow.  The regionalization of these low-flow
characteristics can be very challenging due to difficulty in quan-
tifying pertinent geologic and watershed characteristics and due
to the high incidence of zero values of N-day T-year low flows.

Traditionally the logarithmic transformation has been used to
linearize the relation between flow characteristics and water-
shed/geologic characteristics.  However, zero values of flow can-
not be easily included in a regional analysis if the logarithmic
transformation is used.  The following approaches commonly have
been employed:  (1) use only the non-zero flow sites in the
regional analysis and identify a drainage area below which all
N-day T-year low flows are zero; (2) do not transform the flow
char-acteristics to logarithms; or (3) add a constant to the
dependent variable prior to making the logarithmic transformation.
Each of these approaches has flaws.  First, omitting zero flow
sites results in regional equations that tend to overestimate the
N-day T-year low flows, and it is often difficult to use drainage
area alone to identify regions of zero N-day T-year low flows.
Secondly, not transforming the flow characteristics (dependent
variable) to logarithms often results in unequal variances of the
residuals in the regression analysis making it difficult to evalu-
ate the accuracy of any regression estimate.  Finally, adding a
constant to the dependent variable is usually a subjective trial
and error process that causes difficulty in interpreting the
predictive error of the equation and in comparing different

Another problem in the regionalization of low-flow characteristics
is how to properly incorporate partial-record sites.  Low-flow
characteristics at partial-record sites, estimated from base-flow
measurements, are generally less reliable than those at daily-flow
stations and are highly correlated with many of the daily-flow
stations.  Therefore, these sites should be weighted appropriately
when included in a regional analysis.  The generalized least
squares regression technique permits these partial-record sites to
be weighted on the basis of their variance and correlation with
nearby stations.

OSW Technical Memorandum No. 86.02 identified at least three
acceptable methods for estimating low-flow characteristics at par-
tial-record sites:  graphical, MOVE.1, and the moment approach
proposed by Stedinger and Thomas in U.S. Geological Survey Open-
File Report 85-95 (distributed with OSW Technical Memorandum
No. 85.09).  It is recommended that low-flow estimates from these
methods be included in the regional generalized least squares
regression analysis.

As announced in OSW Technical Memorandum No. 89.04, the low-flow
frequency program that fits the logarithms of the annual N-day low
flows to a Pearson Type III distribution (program A193 in
WATSTORE) is now available in ANNIE.  The user is still cautioned
that the base method for low-flow frequency analysis is the graph-
ical method.  Therefore, the Pearson Type III frequency curve
should be revised graphically if it does not fit the data

The generalized least squares regression program has been revised
to accommodate the above situations.  This regression program is
now available in ANNIE for regionalizing low flows including the
use of low-flow estimates at partial-record sites.  Therefore, the
recommended major steps in a regional low-flow analysis are as

1.  Define station low-frequency curves for all stations with 10
or more years record using program A193 (including any graphical
adjustments) in ANNIE.  This program will store the logarithmic
mean and standard deviation and the skew of the non-zero annual
values and the T-year low flows in the Watershed Data Management
(WDM) file for subsequent use.  A Kendall's tau program is avail-
able for checking for trends in the annual data series to make
sure the data are suitable for frequency analysis.

2.  Estimate the T-year low flows at the partial-record site
using the graphical, MOVE.1, or moments approach.  The graphical
and MOVE.1 estimates of T-year low flows are made outside of ANNIE
and are entered manually into the WDM file.  The moments estimates
can be made within ANNIE if the base-flow measurements and concur-
rent daily flows are in ADAPS or are entered into an appropriate
flat file.  The moments approach is recommended, if there are 10
or more base-flow measurements, because the variance of the T-year
low flows can be computed and multiple index stations also can be
used in estimating the low-flow characteristics.  The variance of
the T-year low flows are needed in the generalized least squares
regional analysis.  The moments and MOVE.1 approach assume a lin-
ear relation between the concurrent flows or the logarithms of
these flows.  If a linear relation does not exist, then graphical
techniques should be used.

3.  Utilize the generalized least squares program to relate the
T-year low flows at daily-flow and partial-record stations to
watershed and geologic characteristics.  If there are several
stations in a region with zero N-day T-year low flows, the
following analysis may be needed.

Because it is not possible to derive logarithms of zero N-day
T-year low flows, a reasonable approach is to relate the mean,
standard deviation,  and skew of the logarithms of the non-zero
annual events to watershed and geologic characteristics.  The fre-
quency curve based on the above moments can then be adjusted using
the conditional probability adjustment as employed for annual N-day
low flows at gaging stations.  The probability of the annual N-day
low flow being zero can be estimated using logistic regres-sion based
on watershed/geologic characteristics.  The logistic regression must
be performed outside of ANNIE.  The attached paper by Gary Tasker
illustrates the logistic regression approach for a network of low-
flow sites in Florida.  More details on this technique will be
described in another memorandum.

The new procedures described above facilitate the estimation of
low-flow characteristics at partial-record stations and the
regional analysis of low-flow characteristics.  Documentation on
using these new techniques in ANNIE will be provided in the near
future.  The generalized least squares program and the program for
estimating low-flow characteristics at partial-record sites are
available from Kate Flynn in the Office of Surface Water (KMFLYNN,
FTS 959-5313).  The techniques described in this memorandum should
be of interest to those involved in the estimation of low-flow

                                       Charles W. Boning
                                       Chief, Office of Surface Water


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