PROGRAMS AND PLANS--Recommendations for Regional Low-Flow Studies In Reply Refer To: July 7, 1989 WGS-Mail Stop 415 OFFICE OF SURFACE WATER TECHNICAL MEMORANDUM NO. 89.11 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 equations. 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 adequately. 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 follows: 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 characteristics. Charles W. Boning Chief, Office of Surface Water Attachment WRD Distribution: A, B, S, FO, PO