Revised 2007




Corrections Incorporated in 2007 Edition

This revised edition incorporates several minor changes. Several lines of text on pages 33-37 were duplicated or 

transposed in the 1994 edition; they are now placed correctly. Several data values in tables 8 and 9 have been replaced. 

In each case, the data value originally published was a typographical error or was superseded by reanalysis during the 

study; the corrected values that appear in this edition were used in the regression analysis.

An error in the computation of 7-day low flows for Middle Branch Westfield River at Goss Heights (station 

01180500) is explained and corrected on this page. Recognition and correction of this error allows me to infer that the 

regression equations presented in this report for the high-relief region of central New England are slightly better than the 

statistical indices reported in table 3 would indicate.

 From August 1965 through November 1967, flows of Middle Branch Westfield River at Goss Heights were 

occasionally affected by construction of a flood-control reservoir upstream. During these 28 months, there were several 

periods when daily flows of Middle Branch were abnormally low and steady, or abnormally high and steady, relative to 

the natural flow of Mill River at Northampton (station 01171500), an adjacent watershed of equal size and comparable 

terrain. The 7-day 2-year and 7-day 10-year low flows of Middle Branch presented in table 8 were based on a data set that 

included abnormal (regulated) 7-day low flows for the 1965, 1966, and 1967 climatic years.

To correct this error, I plotted a log-log graph of 7-day low flows for all years from 1941 through 1983 in Middle 

Branch versus 7-day low flows for the same years in Mill River. The data after construction of the flood-control reservoir 

on Middle Branch were consistent with those before construction, except for the three years mentioned above (1965-1967) 

and also 1978. I did not examine daily flows for 1978 for possible regulation. I estimated natural 7-day low flows of 

Middle Branch for 1966 and 1967 by entering that graph with the 7-day low flows of Mill River. In 1965, the 7-day low 

flow of Mill River occurred in July, before the start of obvious regulation of Middle Branch, and corresponded exactly to 

a 7-day period of low flow of Middle Branch, so I assumed that period represented the natural 7-day low flow of Middle 

Branch for 1965. Results of this exercise were: 

 

 CLIMATIC YEAR 7-DAY LOW FLOWS 7-DAY LOW FLOWS

 OBSERVED (REGULATED) ESTIMATED (NATURAL)

 1965 0.33 3.0

 1966 0.49 2.8

 1967 0.16 4.6

Finally, the 7-day low flows for Middle Branch for 1942-71, with these three estimated values substituted for the 

observed regulated values, were processed through USGS computer program PKWRCA to estimate 7Q2 and 7Q10 

according to a log-Pearson Type III distribution. (Program PKWRCA was written to estimate high-flow frequency, but 

works as well with low-flow frequency). Results were as follows:

 7Q2 7Q10

 Published in 1994 edition and used in regression analysis: 4.0 0.87 cubic feet per second

 Revised as described above 3.9 2.1 cubic feet per second

I replotted the data point for Middle Branch on several graphs of observed 7Q10 versus 7Q10 estimated from 

individual regression equations (such as figures 8-10 of this report). In every case, replotting moved the data point much 

closer to the equality line that represents perfect correlation. I conclude that each of these regression equations actually 

estimates 7Q10 slightly better than the coefficient of determination, standard error of estimate, or PRESS statistic in table 

3 would indicate. Of course, if the regressions were re-run with the corrected data from Middle Branch, slightly different 

equations with equal + and – residuals would result. Nevertheless, the correction of this computational error serves to 

reinforce or affirm the reliability of the equations and interpretations in this report.

Allan D. Randall May 2007

vi






















Effects of Environmental Characteristics 

on Low Flows

Surflcial Geology 

All types of equations tested were significantly 

improved when drainage area was replaced by two 

independent variablesarea of till and area of coarsegrained 

stratified drift. The percentage improvement was much 

greater for naturalvalue equations than for logarithmic 

equations, but all types of equations were consistent in 

indicating that, at 7Q10 low flow, groundwater discharge 

per square mile from coarse stratified drift is four to eight 

times that from till. This conclusion is based on (1) the 

ratios of regression coefficients for terms that include area 

of till and area of coarse stratified drift, respectively, in 

equations that do not have severe inflation of regression 

coefficients due to collinearity, and (2) the ratios of 

weighting factors for till and stratified drift within the 

complex expressions used in loganthmic equations. 

Accordingly, this geologic contrast is an essential 

component of general low4low estimating equations for 

this region, even though the percentages of basin area 

covered by coarse stratified drift are commonly small and 

are similar in many localities. 

In equation 5 (table 3), the stratified drift is divided 

into two broad categories-deposits that extend below stream 

surface profiles (including alluvium) and deposits perched 

above streams. The perched category includes many thick 

but largely unsaturated deposits on the valley sides (referred 

to as coarse perched’ in this report) and a few relatively thin 

stream-terrace and outwash deposits that cap finegrained 

sediments (referred to as coarse cap”). The deposits that 

extend below stream grade would include any productive 

Effects of Surticiai Geoiogy, Lakes and Swamps, Annual Water Availabiiity, and Related Variables on Low Flows 23

Table 3. Regression equations for estimation of low flows in the highrelief region of central New England--

Continued

B. StatIstical IndIces Pertaining to Each EquatIone

Standard error of estimate 

Equation 

number

Coefficient 

of determination (R2)

(units of 

7Q10 or 

7Q2)

(cubic feet 

per second) (percent)**

Median 

percent 

error of 

estimate†

Prediction 

sum of 

squares 

(PRESS) 

statistic

Maximum 

variance 

inflation 

factor

Maximum 

DFITS 

statistic††

1A 81.6 3.86 253 38 630 3.6 2.6

1B 75.1 3.36 676 63 533 3.6 3.3

2B 84.4 2.66 3226 51 277 2.4 2.8

3A 96.5 1.73 128 24 101 12.0 1.4

3B 95.3 1.49 353 22 91 12.0 2.9

4B 95.3 1.49 354 21 92 12.1 3.1

5B 95.7 1.46 311 38 98 26.4 3.2

6B 93.0 1.82 379 41 146 12.8 4.1

7B 93.9 (97.0)c. 0.47 (1.20)c (139)c (23)c (54)c 12.1 .94

8B 94.0 (97.2)c .48 (1.21)c (118)c (31)c (49)c 8.0 1.1

9A 93.6 (95.7)c .56 (1.92)c (108)c (23)c (136)c 6.2 1.5

9B 93.3 (95.7)c .49 (1.43)c (128)c (24)c (81)c 6.2 1.5

10A 87.5 (90.9)c .75 (2.68)c (121)c (28)c (240)c 3.4 .83

10B 85.8 (91.8)c .69 (1.91)c (263)c (26)c (113)c 3.4 .80

11A 87.2 (90.2)c .76 (2.77)c (115)c (32)c (236)c 4.2 .93

11B 85.1 (90.2)c .70 (2.09)c (1251)c (30)c (146)c 4.2 .90

12A 86.8 (82.3)d .23 (3.85)d (61)d (30)d (522)d 1.2 1.2

12B 77.1 (79.6)d .35 (3.41)d (167)d (37)d (448)d 1.2 .95

e

 The regression analysis included an incorrect estimate of 7Q10 for one station. Evaluation of this error (see page vi) suggests that the equations in this 

table estimate 7Q10 slightly better than the statistical indices presented here would indicate. 









the apparent effects of several basin characteristics or 

combinations thereof on low flows, as explained in the 

following section. Standard error expressed in cubic feet 

per second and coefficient of determination were the most 

useful indices of fit; standard error expressed in percent 

varied widely and seemed overly sensitive to a few small 

basins, as explained in a subsequent section on effects of 

scale transformations and individual basins. 

Effects of Environmental Characteristics 

on Low Flows

Surflcial Geology 

All equations indicate that low flow (ground-water 

discharge) per unit area from coarse stratified-drift is several 

times greater than that from till. Equation 13 suggests that 

low flow from areas of till is significant. In equation14, the 

regression coefficient for till area is much smaller than that for 

coarse stratified drift area. The same is true of equations 15 

through 19, althoug the coefficients for terms that incorporate 

coarse stratified drift must be divided by stream length, 

whose mean value is 11.1 mi, before they are compared with 

coefficients of similar terms that incorporate till. 

Dividing coarse stratified drift into perched deposits 

and deposits that extend below stream profiles did not 

improve regression equations significantly, perhaps because 

these two categories cannot be accurately distinguished in 

most low-relief basins without abundant data. In this study, 

stratified drift was assumed to extend below stream grade 

unless bedrock outcrops or boreholes provided evidence 

to the contrary. Combining fine-grained stratified deposits 

with till also had little effect; the final equations in table 5 

do so to include the entire basin area in one or the other of 

the two geologic terms. Dividing the total area of coarsegrained stratified drift by the length of the main stream 

channel gave some improvement in fit (compare eq. 15 

with eq. 14); this combination of variables was tested 

because large values tend to be associated with broad 

expanses of stratified drift, from which ground water might 

drain more slowly over long periods than from narrow 

riparian aquifers of equal area. 

Lakes, Swamps, and Related Indices of Evapotranspiration 

Areas of lakes and swamps bordered by stratified drift 

and those bordered by till were tested as independent variables 

in equation 13, as was total area of lakes and swamps. Each 

was negatively correlated with low flow, but regression 

Effects of Surticiai Geoiogy, Lakes and Swamps, Annual Water Availabiiity, and Related Variables on Low Flows 33

Table 5. Regression equations for estimation of low flows in the low-relief region of central New England--

Continued

B. StatIstical IndIces Pertaining to Each EquatIon

Standard error of estimate 

Equation 

number

Coefficient 

of determination (R2)

(units of 

7Q10 or 

7Q2)

(cubic feet 

per second) (percent)**

Median 

percent 

error of 

estimate†

Prediction 

sum of 

squares 

(PRESS) 

statistic

Maximum 

variance 

inflation 

factor

Maximum 

DFITS 

statistic†† 

for any basin

13A 83.2 3.79 519 37 610 1.3 3.4

13B 79.1 2.80 960 58 267 1.3 2.1

14B 88.3 2.20 759 59 235 29.9 4.2

15B 90.4 1.98 9,347 46 167 17.5 4.0

16B 92.4 1.73 8,977 61 110 11.7 2.6

17B 92.4 1.80 418 31 114 12.7 2.9

18B 94.8 (96.0)d 0.70 (1.24)d (358)d (28)d (58)d 1.3 1.9

19A 93.7 (94.5)d 1.04 (2.23)d (245)d (28)d (197)d 1.4 2.2

19B 92.3 (93.7)d .85 (1.57)d (586)d (54)d (88)d 1.4 2.0

20B 78.5 (75.0)e .44 (4.10)e (279)e (80)e (525)e 1.0 1.4



intermediate relief (sites 11, 37, and 44, fig. 1 and 

tables 7-9) were excluded. Regression coefficients and 

statistical indices of fit for equations 16B and 17B are 

nearly identical. Errors in estimating low flows from 

the three intermediate basins were within the range of 

error at the other 23 basins in all equations. Therefore, 

equations developed for the low-relief region can 

be applied to basins that are close to, or overlap, the 

boundary between regions (fig. 7).









b

a




11.70 7.90

5.90

.095 .33

dValue based on data set that included 7-day low flows affected by regulation in 1965, 1966, and 1967 climatic years. As explained on page vi, substitution of estimated natural (unregulated) 

7-day flows for these years changed the estimates of 7-day low flows at this station to 3.9 cubic feet per second at the 2-year recurrence interval, and 2.1 cubic feet per second at the 10-year recurrence interval.

d d
9.73

3.55

.81 .18 .01 .92 .57 .05