New Procedures for Hydrologic Regression and Network Analysis Using Generalized Least Squares

In Reply Refer To:                                  April 22, 1987
WGS-Mail Stop 415


Subject:  PROGRAMS AND PLANS--New Procedures for Hydrologic
                              Regression and Network Analysis
                              Using Generalized Least Squares

New procedures for hydrologic regression and network analysis
using generalized least squares regression are described in the
attached report.  These procedures will be of interest to
personnel involved in regionalizing streamflow characteristics and
evaluating the stream-gaging network.  These new procedures are an
extension and improvement of procedures known as Network Analysis
for Regional Information (NARI) that are documented in U.S.
Geological Survey Water-Supply Paper 2178.

The generalized least squares program provides many advantages
over ordinary least squares regression.  The regression
coefficients are estimated by taking into consideration the time-
sampling error in the dependent variable and the cross correlation
between sites.  A weighting matrix is computed so that each
watershed in the data set is weighted proportional to the accuracy
(variance) and cross correlation of the dependent variable.  The
prediction error for ungaged sites is partitioned into model error
and sampling error (including both time- and spatial-sampling
errors).  The model error is that portion of the total error
(prediction error) that cannot be reduced by additional data
collection.  On the other hand, the sampling error can be reduced
by operating the existing stations longer, or by installing new
stations, or some combination of both.  This approach to error
analysis makes generalized least squares regression a useful tool
for network design and analysis.  Using generalized least squares,
it is possible to determine the existing or proposed stations that
are most important in reducing the sampling error.  This provides
the data manager with a tool to determine the specific stations
(including proposed stations) that are providing the most
information in a regional sense.

Additional input data are needed in the generalized least squares
over that required in ordinary least squares regression.  The
preparation of this input data is time consuming if done manually.
Therefore, ANNIE, an interactive data processor, is being used to
prepare these input files.  ANNIE and the associated Watershed
Data Management (WDM) File is used for Office of Surface Water
application programs and provides a mechanism for not only
preparing the input data but also to store and manipulate data,
make transformations, prepare tables and plots, and guide the user
through the analysis.

ANNIE/WDM has been developed for several years, and new features
are continually added to the system.  The development of this
system is being coordinated by Alan Lumb, Office of Surface Water,
and its purpose is to facilitate hydrologic analyses and
particularly the use of hydrologic and hydraulic models.  The
ANNIE/WDM system is also very helpful in managing data for a
statistical analysis such as generalized least squares regression.
Only a brief overview of ANNIE/WDM is provided in the attached
document.  More detailed documentation of ANNIE/WDM is available
from the Office of Surface Water.

The attached report contains an example of using ANNIE and
generalized least squares to develop regression equations for
estimating flood discharges and to analyze the regional hydrology
network in southeastern Illinois.  The regional hydrology network
is composed of those stations useful in estimating streamflow
characteristics at ungaged sites.

A magnetic tape of the ANNIE/GLS programs including the necessary
run files, message files, Command Procedure Language (CPL)
routines, and test data can be obtained by sending a blank tape to
Kate Flynn in the Office of Surface Water (FTS 959-5313 or
KMFLYNN@RVARES).  Please put your name and address on this tape so
that it is easy to identify who sent the tape.  The test data and
example output are the same as given in the attached report.

Technical questions on the generalized least squares regression
program should be directed to Gary Tasker, Northeastern Region
Research (FTS 959-5892), or Will Thomas, Office of Surface Water
(FTS 959-5318).  Additional copies of the attached documentation
are also available from the Office of Surface Water.

                                   Verne R. Schneider
                                   Chief, Office of Surface Water


WRD Distribution: FO-LS, SL