A Logistic Regression Equation for Estimating the Probability of a Stream Flowing Perennially in Massachusetts

By GARDNER C. BENT and STACEY A. ARCHFIELD

Abstract (CMR) 10.58(2)(a) were not considered when des- ignating the perennial or intermittent status of a A logistic regression equation was stream site. The database used to develop the developed for estimating the probability of a equation included a total of 305 stream sites (84 stream flowing perennially at a specific site in intermittent- and 89 perennial-stream sites in the Massachusetts. The equation provides city and State, and 50 intermittent- and 82 perennial-stream town conservation commissions and the sites in the South Coastal Basin). Stream sites Massachusetts Department of Environmental included in the database had drainage areas that Protection with an additional method for assessing ranged from 0.14 to 8.94 square miles in the State whether streams are perennial or intermittent and from 0.02 to 7.00 square miles in the South at a specific site in Massachusetts. This informa- Coastal Basin. tion is needed to assist these environmental agen- cies, who administer the Commonwealth of Results of the logistic regression analysis Massachusetts Rivers Protection Act of 1996, indicate that the probability of a stream flowing which establishes a 200-foot-wide protected river- perennially at a specific site in Massachusetts can front area extending along the length of each side be estimated as a function of (1) drainage area of the stream from the mean annual high-water (cube root), (2) drainage density, (3) areal percent- line along each side of perennial streams, with age of stratified-drift deposits (square root), exceptions in some urban areas. The equation was (4) mean basin slope, and (5) location in the South developed by relating the verified perennial or Coastal Basin or the remainder of the State. intermittent status of a stream site to selected basin Although the equation developed provides an characteristics of naturally flowing streams (no objective means for estimating the probability of a regulation by dams, surface-water withdrawals, stream flowing perennially at a specific site, the ground-water withdrawals, diversion, waste-water reliability of the equation is constrained by the discharge, and so forth) in Massachusetts. Stream data used to develop the equation. The equation sites used in the analysis were identified as peren- may not be reliable for (1) drainage areas less nial or intermittent on the basis of review of than 0.14 square mile in the State or less than measured streamflow at sites throughout 0.02 square mile in the South Coastal Basin, Massachusetts and on visual observation at sites (2) streams with losing reaches, or (3) streams in the South Coastal Basin, southeastern draining the southern part of the South Coastal Massachusetts. Measured or observed zero flow(s) Basin and the eastern part of the Buzzards Bay during months of extended drought as defined by Basin and the entire area of Cape Cod and the the 310 Code of Massachusetts Regulations Islands Basins.

Abstract 1

INTRODUCTION on either of these two maps can be considered perennial if (1) evidence can be established of the presence The Commonwealth of Massachusetts Rivers of aquatic invertebrates that require perennial flows, or Protection Act (Chapter 258 of the Acts of 1996; The (2) evidence of a stream order of two or greater, or Commonwealth of Massachusetts, 1996) specifies that (3) there is a USGS streamflow-gaging station riverfront areas be protected on all rivers that flow on a upstream from the stream site, or (4) the drainage area year round basis. The Massachusetts Department of upstream from the stream site is greater than 3 mi2, Environmental Protection (MADEP) adopted regula- except in the Buzzards Bay Basin, Cape Cod Basin, tions to enforce the law, which defines rivers that flow Islands Basin, South Coastal Basin, and Taunton River on a year round basis as perennial streams. The river- Basin, or (5) other credible evidence is available. To the front area is defined in 310 Code of Massachusetts contrary, a stream site shown as perennial on USGS or Regulations (CMR) 10.58(2)(a) (hereafter referred to MADEP maps can be considered intermittent if (1) the as the Regulations) as the 200-ft wide area extending river at the site is observed not flowing, provided the along the length of each side of the stream from the observation is not during an extended drought, or mean annual high-water line on each side of perennial streams, with exceptions in some urban areas (2) no stream channel or banks are present, or (3) soils (Massachusetts Department of Environmental information shows that the ground-water elevation is Protection, 2000, p. 393-402). The Regulations define not at or near the streambed, or (4) other credible evi- the mean annual high-water line as the line that is dence is available. A problem, however, is that USGS apparent from visible markings or changes in the char- topographic maps are not made to the level of detail acter of soils or vegetation due to prolonged presence and accuracy presumed by the Regulations; therefore, of water and that also distinguishes predominantly they may not accurately represent whether a stream site aquatic from predominately terrestrial land. Streams is perennial or intermittent. The USGS, therefore, in that do not flow on a year round basis, intermittent cooperation with the Massachusetts Executive Office streams, have no jurisdictional riverfront area along of Environmental Affairs (MAEOEA) and the MADEP, the stream. City or town conservation commissions began a study in 1999 to develop a statistical method to are charged with administering the Regulations by more accurately determine whether a stream at a spe- determining the perennial or intermittent status of a cific site is perennial or intermittent in Massachusetts. stream site and by regulating work in the riverfront areas. The MADEP addresses appeals of decisions made about the perennial or intermittent status of Purpose and Scope stream sites by city or town conservation commissions. The logistic regression equation provides these agen- cies with an additional method for assessing the status This report describes the development and appli- of stream sites. cation of a logistic regression equation for estimating the probability of a stream flowing perennially at a spe- A river is defined in the Regulations as any cific site in Massachusetts. The equation is based on natural flowing body of water that discharges into an historical streamflow data in Massachusetts from water ocean, lake, pond, or another river, and which flows 1 throughout the year (Massachusetts Department of years 1960 through 1998 and on field data collected as Environmental Protection, 2000, p. 394). Perennial a pilot project in the South Coastal Basin during the streams are rivers, but intermittent streams are not summer of 1999. Basin characteristics used in the anal- rivers. The Regulations specify that perennial streams ysis were obtained from digital data layers. Limitations be represented as such on the most current U.S. of the logistic regression are discussed and areas for Geological Survey (USGS) topographic map or on a further study are presented. more recent map developed by the MADEP (if available), unless a competent source can provide adequate 1A water year is the 12-month period beginning October 1 evidence to the contrary. A stream site shown as inter- and ending September 30. It is designated by the calendar year in which it ends. mittent on USGS or MADEP maps or a site not shown

2A Logistic Regression Equation for Estimating the Probability of a Stream Flowing Perennially in Massachusetts

Acknowledgments and 1997; Ries and Friesz, 2000). Till, an unsorted, unstratified mixture of clay, silt, sand, gravel, cobbles, The authors thank the MADEP’s Perennial/ and boulders, was deposited by glaciers directly on Intermittent Advisory Committee; the MADEP, Bureau bedrock throughout much of the State. Till primarily is of Resource Protection, Wetlands and Waterways found in the upland areas. Stratified drift is a common Program; MAEOEA, Massachusetts Watershed Initia- term for sorted, layered glaciofluvial and glaciolacus- tive; and George Zoto of the MAEOEA for providing trine deposits. Glaciofluvial deposits are material of all input on the State’s and South Coastal Basin’s perspec- grain sizes (clay, silt, sand, gravel, and cobbles) depos- tive related to perennial/intermittent issues. The authors ited by glacial meltwater streams in outwash plains and also thank Gregory F. Koltun, USGS, for providing valleys. Glaciolacustrine deposits generally consist of statistical assistance for the study. clay, silt, and fine sand deposited in temporary lakes that were present after the retreat of the glacial ice DESCRIPTION OF sheet. Stratified-drift deposits are more wide spread in STUDY AREA eastern Massachusetts than in western Massachusetts (Ries, 1994a, p. 6). In eastern Massachusetts, stratified- The geography, climate, and surficial geology of drift deposits overlie till deposits, particularly in the a basin upstream of a selected stream site are factors southeast. In other areas of the State, stratified-drift that can affect whether the stream at that location will deposits are more likely to be in river valleys. be perennial or intermittent. In Massachusetts and the South Coastal Basin these factors, and particularly the The extent and types of surficial deposits are extent and type of surficial deposits, affect streamflow important factors that help explain flow characteristics characteristics. of Massachusetts streams (Ries, 1994a; 1994b; and 1997; Ries and Friesz, 2000). Till and fine-grained Characteristics of stratified-drift deposits generally have a lower infiltra- Massachusetts tion capacity than medium- to coarse-grained stratified- drift deposits. The lower infiltration capacity of these Massachusetts encompasses 8,093 mi2 in the materials results in greater direct runoff of precipita- northeastern United States (fig. 1). Altitudes range tion; therefore, less precipitation is available to infil- from 1 to 2 ft above sea level in coastal areas to more trate the soil and recharge the aquifer than from than 3,900 ft above sea level in the northwest. The cli- medium- to coarse-grained stratified-drift deposits. mate in Massachusetts is humid. Average annual pre- During dry periods, the primary source of streamflow is cipitation ranges from about 40 to 45 in. in eastern ground-water discharge from the aquifer to the stream. Massachusetts and from about 40 to 50 in. in western Thus, basins underlain predominantly by till and fine- Massachusetts where higher altitudes may cause oro- grained stratified-drift deposits generally have a lower graphic effects. Average annual temperature is about streamflow per unit area during dry periods than basins 50˚F in eastern Massachusetts and about 45˚F in underlain predominantly by medium- to coarse-grained western Massachusetts. stratified-drift deposits. Surficial deposits that overlie bedrock in most of Massachusetts were deposited mainly during the last glacial period, but can include areas of recent Characteristics of South floodplain alluvium deposits. In this report, these surficial deposits are classified as either till (which includes Coastal Basin till or bedrock, sandy till over sand, and end moraine deposits) or stratified-drift deposits (which includes The South Coastal Basin is one of 27 river basins 2 sand and gravel, large sand, fine-grained, and flood- in the State, and encompasses 240 mi in southeastern plain alluvium deposits). This classification maintains Massachusetts (fig. 2). The basin includes all or part of consistency with characterizations of surficial deposits 18 towns. Altitudes range from 1 to 2 ft above sea level reported in four reports that discuss low-flow to about 400 ft above sea level. The basin mainly has characteristics in Massachusetts (Ries, 1994a; 1994b; low relief and is characterized by low-gradient streams.

Description of Study Area 3

o 73 30' o 72 30' 72o00'

VERMONT NEW HAMPSHIRE 331960 333100 332900 170240 1 166400 331400 166105 7 163298 331380 3 165250 o 42 30' 169800 170902 174050 172100 197080 174000 197090 197130 179900 8 173100 6 173150 172900 173260 2 197140 197700 173400 NEW YORK 4 197300 Western Region 173230 197600 180650 174900 175700 197180 173300 180000 171800 175660 197960 180800 197240 173450 175670 176450 175790 197210 180900 197200 175910 175730 198062 175760 198137 176100 175890 198040 5 124390 198060 198110 176200 198070 123100 198100 176300 1 198120 198160 123161 10 177360 124800 198020 123200 198260 187400 9 184200 184282 124100 124750 CONNECTICUT 42o00'

184200 BASIN BOUNDARY PERENNIAL STREAM SITE AND U.S. GEOLOGICAL SURVEY SUBBASIN BOUNDARY IDENTIFIER* 176450 HYDROLOGIC REGIONS INTERMITTENT STREAM SITE BOUNDARY AND (USGS) IDENTIFIER* STATE BOUNDARY * All (USGS) identifiers are preceded by 01, which is not shown. See table 2.

Figure 1. Location of discontinued and continuous streamflow-gaging stations and partial-record stations designated as perennial or intermittent stream sites used in development of the logistic regression equation for estimating the probability of a stream flowing perennially in Massachusetts.

4A Logistic Regression Equation for Estimating the Probability of a Stream Flowing Perennially in Massachusetts

71o00' 18 100810

100800 073860 100802 71o30' 100665 100700 100650 100808 100817 13 ATLANTIC OCEAN NEW HAMPSHIRE 100655 100400 100640 095960 100350 16 100300 095940 096504 096505 100050 100633 100100 095928 100623 100200 100618 101850 095989 100607 100616 100608 100628 17 15 100617 102053 100593 1024592 1024596 102482 18 11 100572 102470 096906 097200 102490 096910 104400 19a 094760 096850 104405 096855 103015 Massachusetts 14a 095380 14b BOSTON Bay 109950 103440 096600 103415 19c19c19c 104910 105525 103360 105614 105630 Eastern Region 105830 105575 105670 111142 20 19b 105600 103214 104880 111160 105400 105573 12 104960 105568 105820 105150 130253 104980 105100 112190 106430 o 107010 21a 70 00' 111225 106460 107000 9 105861 108600 108350 70o30' RHODE ISLAND 27 25 109381 21b 109200 108140 108180 109185

109225 109090 1059106 Southeast 24 22 26 105930 Coastal 105937

105935 Region 106000

41o30' Nantucket Sound 0 50 MILES 23

0 50 KILOMETERS 23

Description of Study Area 5

6A Logistic Regression Equation for Estimating the Probability of a Stream Flowing Perennially in Massachusetts

70o49'19" 70o43'19"

71˚00' ATLANTIC OCEAN 73˚00' 72˚00'

42˚30' MASSACHUSETTS

70˚00'

42˚00' STUDY AREA

0 50 MILES 0 50 KILOMETERS

42o 09' 34" 21a

012 MILES

0 1 2 KILOMETERS

42o 03' 34"

EXPLANATION

TOWN/CITY BOUNDARY

MAJOR BASIN BOUNDARY— 21 South Coastal

SUBBASIN BOUNDARY— 21a North and South River 21b South Coastal Shore

PERENNIAL STREAM SITE AND IDENTIFIER

INTERMITTENT STREAM SITE 21b AND IDENTIFIER

Figure 2. Location of field visited stream sites in the South Coastal Basin, southeastern Massachusetts, designated as perennial or intermittent stream sites used in development of the logistic regression equation for estimating the probability of a stream flowing perennially in Massachusetts. ecito fSuyAe 7 Description of Study Area

Surficial geology is mainly stratified-drift during abnormally dry periods and observations of flow deposits, as 65 percent of the 240-mi2 basin is under- at stream sites during abnormally wet periods were not lain by these deposits and the remaining area (35 per- included in the study database, to avoid observations cent) is underlain by till and bedrock. However, that are unrepresentative of normal climatic conditions. surficial geology in the basin is distinctly different If zero flows were measured in the eastern or 2 from the northern 105 mi (North and South River western region of the State during a month that Subbasins), where about 33 percent of the area is occurred within an extended drought, as defined in the underlain by stratified-drift deposits, and from the Regulations, those flows were not included in the data- 2 southern 135 mi (South Coastal Shore Subbasin), base. The months that met the definition of an extended where about 90 percent of the area is underlain by drought for both the eastern and western regions are stratified-drift deposits (Ries, 1994b). listed in table 1. The Regulations define an extended drought DATABASE as a period of below normal precipitation for that DEVELOPMENT month and the three previous months, with at least 3 of the months having 75 percent or less of the normal pre- To develop an equation for estimating the proba- cipitation and 2 months having 50 percent or less of bility of a Massachusetts stream flowing perennially at normal precipitation (Massachusetts Department of a specific site, a database was developed that contains Environmental Protection, 2000, p. 395). This defini- basin characteristic information on both perennial- and tion was used to analyze precipitation records from intermittent-stream sites in the State. Development of January 1960 through August 1999 (the period of mea- this database involved screening data to avoid entries sured streamflow used for development of the data- for stream sites affected by regulation, drought condi- base) at 19 index-precipitation stations in the State tions, or other factors that may alter the perennial or (fig. 3), which included 10 index-precipitation stations intermittent status of streams. The stream sites were from the eastern region and 9 index-precipitation selected from the USGS database of measured stream- stations from the western region. Although the NWS flow in the State from water years 1960 through 1998 (National Weather Service) precipitation station in and from sites visited in the South Coastal Basin in the Ashburnham is about 1 mi within the eastern region summer of 1999. boundary (fig. 3), it was used for the western region, because there were no other index stations in the eastern part of the western region. The Massachusetts Factors That Affect the Department of Environmental Management (MADEM) Perennial/Intermittent maintains the database of precipitation measured at Status of Streams these index-precipitation stations. To determine when the eastern or western For this study, determination of the perennial or regions met the Regulation’s extended drought defini- intermittent status of a stream site in Massachusetts tion, the following steps were used (1) the average was completed only for naturally flowing streams (no long-term monthly precipitation for June 1960 through regulation). Regulated streams are those affected by August 1999 was determined for each of the 19 index dams, surface-water withdrawals, ground-water with- stations, (2) the average long-term monthly precipita- drawals (pumping wells), diversions, wastewater dis- tion for the eastern region was determined by calculat- charges, and so forth. The perennial or intermittent ing the average long-term monthly precipitation status of a stream at a specific site cannot be estimated (determined in step 1) of the 10 index stations and was accurately if the flows above or near the site are regu- determined for the western region by calculating the lated, because regulations vary from site to site, and the average long-term monthly precipitation (determined majority of regulations are not quantified or easily in step 1) of the 9 index stations, (3) the average quantifiable. Observations of no flow at stream sites monthly precipitation for each individual month and

8A Logistic Regression Equation for Estimating the Probability of a Stream Flowing Perennially in Massachusetts

Table 1. Months that the eastern or western regions of year for the eastern region was determined by calculat- Massachusetts met the 310 Code of Massachusetts ing the average monthly precipitation for the 10 index Regulations (CMR) 10.58(2)(a) definition of extended stations and was determined for the western region by drought from January 1960 through August 1999 calculating the average monthly precipitation for the 9 [Monthly precipitation average based on Massachusetts Department of index stations, and (4) the regional average monthly Environmental Management precipitation data. The eastern region is precipitation for each individual month and year (deter- based on precipitation stations at Brockton, Buffumville Lake, Concord, mined in step 3) was then tested against the regional Falmouth, Lawrence, Lowell, Middleborough, New Bedford, Northbridge, and Waltham. The western region is based on precipitation stations at average long-term monthly precipitation (determined in Amherst, Ashburnham, Chesterfield, Dalton, Greenfield, Otis, Plainfield, step 2) to determine if each month in each region from Stockbridge, and Worthington. Precipitaiton station locations shown in January 1960 through August 1999 met the extended figure 3] drought definition. This definition eliminated 3.8 per- Month Year cent of the months in the eastern region and 2.7 percent Eastern region of the months in the western region during January 1960 through August 1999 (table 1). June...... 1964 August ...... 1964 Because the Regulations have no operational def- May...... 1965 inition of an abnormally wet month, only those peren- June...... 1965 nial-stream sites measured at least three times were July ...... 1965 included in the database. By measuring a perennial- August ...... 1965 stream site at least three times, it would be likely that at January...... 1966 least one measurement was made during relatively June...... 1966 normal climatic conditions. September...... 1968 October ...... 1968

February...... 1980 Site Selection March...... 1980 March...... 1981 Selecting stream sites for inclusion in the data- November ...... 1984 base of perennial- and intermittent-stream sites in April...... 1985 Massachusetts involved (1) reviewing available September...... 1988 USGS measured streamflow data from sites in the August ...... 1993 State (table 4, at back of report), and (2) visiting sites in September...... 1997 the South Coastal Basin (table 5, at back of report). A Western region list of perennial-stream sites in the State was available from Ries (1997), in which equations were developed to November ...... 1964 estimate the August median streamflow at ungaged sites December...... 1964 in Massachusetts. Locations of intermittent-stream sites January...... 1965 were determined through review of streamflow-mea- May...... 1965 surement data collected from sites in the State. Stream June...... 1965 sites in the South Coastal Basin (fig. 2) were evaluated February...... 1968 visually in the field during the summer of 1999, to April...... 1978 determine their perennial or intermittent status. As part May...... 1978 of the stream-site-selection process, stream sites were February...... 1980 accessed with the World Wide Web application March...... 1980 STREAMSTATS, http://ma.water.usgs.gov/stream- March...... 1981 stats/ (Ries and others, 2000), to determine if there were December...... 1988 public community surface-water or ground-water January...... 1989 withdrawals upstream of or nearby the sites.

Database Development 9

0A Logistic Regression Equation for Estimating the Probability of a Stream Flowing Perennially in Massachusetts 10

73o00'

NWS LawrenceLawrence NWS NWS LowellLowell 203 AshbAshburnhamurnham 205 Greenfield 70o00' Plainfield 104 42o30' Dalton 704 ConcordConcord 209 NWS Chesterfield AmhearAmherstst 709 Waltham 208 WWoorrthington 109 Western Region Eastern Region StockbridgeStockbridge COE Buffumville Lake 515 115 NorthbridgeNorthbridge Otis 803 BrocktonBrockton

809 EXPLANATION MidMiddleboroughdleborough

HYDROLOGIC REGION BOUNDARY CITY AND TOWN BOUNDARY 817 NeNeww BedfBedfordord 115 PRECIPITATION STATION AND IDENTIFIER—Alphanumeric code is Otis Massachusetts Department of Environmental Management, Division of 904 Resource Conservation, Office of Water Resources station number Falmouth or cooperating agency: Army Corps of Engineers (COE), and National Weather Service (NWS). NWS Ashburnham precipitation 41o30' station used in western region analysis.

0 50 MILES

0 50 KILOMETERS

Figure 3. Location of precipitation stations analyzed to determine if the eastern region or western region of Massachusetts met the 310 Code of Massachusetts Regulations (CMR) 10.58(2)(a) definition of extended drought.

Approximately 1,300 stream sites (partial- omitted from the database because of one or more of record, discontinued streamflow-gaging, or continuous the following conditions: (1) regulation of streamflows streamflow-gaging stations) in the USGS National by dams, ground-water or surface-water withdrawals Water Information System (NWIS) database were upstream or nearby, diversions, wastewater discharges, evaluated for measured zero flow(s) for water years and so forth, (2) the stream site previously was identi- 1960 through 1998 to determine intermittent sites in fied as an intermittent (zero flow) site, and (3) the Massachusetts. Of these 1,300 stream sites, zero drainage area of the stream site was greater than flow(s) had been measured at 174 sites. Of these 9.00 mi2 (the intermittent-stream sites had a maximum 174 stream sites, 90 sites were omitted from the data- drainage area of 8.04 mi2) and would not aid in base because of one or more of the following condi- development of the logistic regression equation. The tions: (1) regulation of streamflow by dams, ground- remaining 89 perennial-stream sites included in the water or surface-water withdrawals upstream or nearby, 2 diversions, wastewater discharges, and so forth, database had a maximum drainage area of 8.94 mi (2) zero flow(s) measured only during an extended (station 01106460), a minimum drainage area of 2 drought period, (3) the stream site was outside of 0.78 mi (station 01197210), a mean drainage area of 2 2 Massachusetts, (4) questionable streamflow measure- 5.16 mi , and a median drainage area of 5.27 mi ments, (5) the stream site was in the Buzzards Bay, (table 4). North Coastal, or Taunton River Basins (where no digi- In the South Coastal Basin, 397 stream sites tized stream-network-data layers were available for were visited from June through August 1999. These these three basins in STREAMSTATS as of March 1, stream sites were at road crossings where access per- 2001), and (7) the site was in the Cape Cod Basin, mitted a visual inspection to determine if there were Islands Basin, southern part of the South Coastal Basin, flow in the stream. These stream sites were evaluated or eastern part of the Buzzards Bay Basin (labeled as Southeast Coastal Region in fig. 1) where the areas during periods of little to no precipitation that occurred contributing ground water and surface water to a spe- at least 3 to 5 days following a precipitation event total- cific stream site may be appreciably different. Only ing 0.10 in. or greater. Observations recorded during 84 zero-flow sites from the USGS NWIS database the visual inspection at each stream site included of approximately 1,300 stream sites met these criteria whether the streambed was dry, had disconnected pools and were used as part of the intermittent-stream sites of water in the streambed, had water but no velocity in Massachusetts. These stream sites had a maximum (no flowing water), or had flowing water. The stream drainage area of 8.04 mi2 (station 01175790), a mini- sites were inspected on both the upstream and down- mum drainage area of 0.14 mi2 (stations 01100572, stream sides of each road crossing and documented 01100618, and 01100623), a mean drainage area of with digital photographs of the upstream and down- 2 2 2.63 mi , and a median drainage area of 2.02 mi stream stream-channel conditions at each site. Those (table 4). stream sites with a dry streambed or disconnected An initial list of perennial-stream sites in pools of water were classified as intermittent on the Massachusetts was created from the 205 sites used by basis of on the definition that perennial streams are Ries (1997). Of the 205 stream sites, 116 sites were rivers that flow throughout the year.

Database Development 11

Of the 397 stream sites visited in the South water discharges, and so forth, (2) no visible streambed Coastal Basin, 261 sites were omitted because of one observed in the ﬁeld, although the site was shown as a or more of the following conditions: (1) regulation of stream on a USGS topographic map, (3) water but no streamﬂows by dams, ground-water or surface-water velocity observed at the stream site (a velocity was not withdrawals upstream or nearby, diversions, waste- verified with a flow meter; therefore, the perennial or

A. B. 10.0 10.0 9.5 9.5 (50) (45) (44) 9.0 9.0 8.5 8.5 (25) 8.0 8.0 7.5 7.5 (59) (82) (45) 7.0 7.0 6.5 6.5 6.0 6.0 (59) 5.5 5.5 (82) 5.0 5.0 4.5 4.5 4.0 4.0 (25) 3.5 3.5 (44)

DRAINAGE AREA, IN SQUARE MILES 3.0 3.0 2.5 2.5 (50)

2.0 DRAINAGE DENSITY, IN MILES PER SQUARE MILE 2.0 1.5 1.5 1.0 1.0

0.5 0.5 0 0

PERENNIAL-ER PERENNIAL-WR PERENNIAL-ER PERENNIAL-SCB PERENNIAL-WR PERENNIAL-SCB INTERMITTENT-ER INTERMITTENT-WR INTERMITTENT-ER INTERMITTENT-SCB INTERMITTENT-WR INTERMITTENT-SCB

STREAM TYPE AND LOCATION STREAM TYPE AND LOCATION

EXPLANATION

(59) Number of observations Outlier data value more than 3 times the interquartile range outside the quartile Outlier data value less than or equal to 3 and more than 1.5 times the interquartile range outside the quartile Data value less than or equal to 1.5 times the interquartile range outside the quartile 75th percentile Median

25th percentile

Figure 4. Distribution of (A) drainage area, (B) drainage density, (C) areal percentage of stratified-drift deposits, and (D) mean basin slope for intermittent- and perennial-stream sites in the eastern region (ER), western region (WR), and South Coastal Basin (SCB) of Massachusetts used in development of the logistic regression equation for estimating the probability of a stream flowing perennially in Massachusetts.

12 A Logistic Regression Equation for Estimating the Probability of a Stream Flowing Perennially in Massachusetts

intermittent status could not be determined), (4) the (6) the shape of the drainage-basin boundary drawn stream site was just outside the South Coastal Basin, by STREAMSTATS did not match that determined (5) no digitized stream-network data were available from USGS topographic maps [because small drainage for the stream site in STREAMSTATS (because the areas in low slope areas, such as the South Coastal stream is not shown on a USGS topographic map), Basin (ﬁg. 4D), determined from STREAMSTATS

C. D. (59) (50) (82) 100 26 (45) (44) 95 24 90

85 (25) 22 80 20 75 (25)

70 (44) 18 65 16 60

55 14 50 12 45

40 10 35 (59) 30 8

25 MEAN BASIN SLOPE, IN PERCENT 6 20 (45) (82) (50) 15 4 AREA OF STRATIFIED-DRIFT DEPOSITS, IN PERCENT 10 2 5 0 0

PERENNIAL-ER PERENNIAL-WR PERENNIAL-ER PERENNIAL-SCB PERENNIAL-WR PERENNIAL-SCB INTERMITTENT-ER INTERMITTENT-WR INTERMITTENT-ER INTERMITTENT-SCB INTERMITTENT-WR INTERMITTENT-SCB

STREAM TYPE AND LOCATION STREAM TYPE AND LOCATION

EXPLANATION

(44) Number of observations Outlier data value more than 3 times the interquartile range outside the quartile Outlier data value less than or equal to 3 and more than 1.5 times the interquartile range outside the quartile Data value less than or equal to 1.5 times th interquartile range outside the quartile 75th percentile Median

25th percentile

Database Development 13

sometimes may not compare well to drainage areas setts. These characteristics, therefore, also may be for stream sites determined from topographic maps important in predicting the probability of a stream (P.A. Steeves, U.S. Geological Survey, oral commun., flowing perennially at a specific site in Massachusetts. 2000)], and (7) the drainage area was greater than These four basin characteristics 9.00 mi2. These criteria resulted in 50 intermittent- and currently (November 1, 2001) are determined by 82 perennial-stream sites in the South Coastal Basin STREAMSTATS. Drainage areas were determined being included in the database. The intermittent-stream from 1:25,000 scale digital elevation models (DEMs). sites had a maximum drainage area of 1.92 mi2 (station Length of streams were determined with centerline NL-19), a minimum drainage area of 0.02 mi2 (station data of streams from a 1:25,000 scale hydrography NL–42), a mean drainage area of 0.34 mi2, and a digital data layer. The areas of stratified-drift deposits median drainage area of 0.21 mi2 (table 5). The peren- were determined from a 1:250,000 scale surficial nial-stream sites had a maximum drainage area of geology digital data layer. Mean basin slopes were 7.00 mi2 (station HR–30), a minimum drainage area of determined from 1:250,000 scale DEMs. 0.06 mi2 (station HR–03), a mean drainage area of 1.00 mi2, and a median drainage area of 0.45 mi2 Drainage density (length of streams divided (table 5). The final database used in the analysis con- by drainage area) and the percentage of the drainage tained 305 stream sites, of which 134 sites were identi- area of each basin underlain by stratified drift (area of fied as intermittent, and 171 sites were identified as stratified-drift deposits divided by drainage area) also perennial. were determined for each stream site for use in developing a logistic regression equation. Drainage density represents the magnitude per area of a network of SELECTION AND streams within a basin for drainage of runoff. The areal MEASUREMENT OF BASIN percentage of stratified-drift deposits within a basin CHARACTERISTICS indicates whether a large or small proportion of the basin contains stratified-drift deposits. Basin characteristics for most stream sites were determined with STREAMSTATS (Ries and others, 2000), unless the characteristics for a site had been LOGISTIC REGRESSION determined for the Statewide August median stream- EQUATION flow study by Ries (1997). STREAMSTATS was not used to verify basin characteristics determined in Logistic regression is a statistical technique that Ries (1997), because digital data layers were the can be applied in water resources. In this technique, the same and STREAMSTATS is an automated procedure probability of a result being in one of two response of the technique used in the earlier study. The basin- groups (binary response) is modeled as a function of characteristics values determined for possible use in the magnitudes of one or more explanatory variables developing a logistic regression equation are drainage (Helsel and Hirsch, 1992, p. 393–402). For instance, area, length of streams, area of stratified drift, and the probability whether or not a stream site is intermit- mean basin slope. Ries and Friesz (2000) found these tent or perennial may be modeled as a function of the characteristics to be the most significant explanatory magnitudes of one or more basin characteristics. For variables for using regression equations to estimate this study, the response variable is “1” when the stream low-flow characteristics at ungaged sites in Massachu- is perennial and “0” when the stream is intermittent.

14 A Logistic Regression Equation for Estimating the Probability of a Stream Flowing Perennially in Massachusetts

Other studies have used logistic regression to Two additional explanatory variables were tested determine the intermittent or perennial status of that indicate whether the stream site was located in the streams or to investigate other water-resource issues. In western or eastern region of the State (fig. 1) and a study by Kliever (1996), logistic regression was used whether the site was located in the South Coastal Basin to determine the probability that streamflow would be (fig. 2) or in the remainder of the State. The South zero for a particular low-flow statistic at a partial- Coastal Basin stream sites were those visited in the record station given the same low-flow statistic at summer of 1999. Four stream sites in the South Coastal nearby index stations in northern Rhode Island. Other Basin, selected from review of the 205 perennial- applications of logistic regression analyses in water stream sites in Massachusetts used by Ries (1997) resources have been completed by Eckhardt and others (table 4), were not included with those sites visited in (1989), Eckhardt and Stackelberg (1995), Koltun and the summer of 1999. Massachusetts was split into Sherwood (1998), and Squillace and others (1999). western and eastern regions on the basis of observed differences in relations between the perennial or intermittent status of streams and their areal percentage of Development stratified-drift deposits and mean basin slope (figs. 4C and D). Logistic regression methods were used for esti- Median drainage area and drainage density for mating the probability of a stream being perennial at a perennial-stream sites in the eastern region were specific site as a function of basin characteristics for slightly greater than in the western region (figs. 4A and the 84 intermittent- and 89 perennial-stream sites in the B). The median areal percentage of stratified-drift State and for the 50 intermittent- and 82 perennial- deposits for perennial-stream sites in the eastern region stream sites in the South Coastal Basin. Basin charac- was about eight and a half times greater than in the teristics tested in the regression methods were drainage western region (fig. 4C). The median mean basin slope area, drainage density, areal percentage of stratified- for perennial-stream sites in the eastern region was drift deposits, and mean basin slope (tables 4 and 5). about three and a half times lower than in the western Drainage density and areal percentage of stratified-drift region (fig. 4D). For drainage areas from 0.01 to 2 deposits represent a more relative measure of how 0.99 mi , the observed frequency of perennial-stream these basin characteristics may affect the probability of sites was greater in the western region than in the east- a stream flowing perennially. These characteristics, ern region (figs. 5A and B). Additionally, Ries (1997) therefore, were chosen over more absolute measures found in a Statewide August median streamflow study such as length of streams and area of stratified-drift that the western region of the State had a higher August deposits. Also, drainage density and areal percentage of median streamflow per unit area than the eastern stratified-drift deposits provide a more equal compari- region. As a result of these tests, the regions were son of basins over a wide range of drainage-area sizes, divided along the eastern border of the Connecticut as is the case in this study. Additionally, the four basin River Basin or the eastern border of the Millers and characteristics were transformed (square, cube, square Chicopee River Basins, which are a part of the root, and cube root), and then tested as possible explan- Connecticut River Basin (fig. 1). Ries (1997) divided atory variables. Transforming data is a common proce- the State along these same borders. dure that makes the data more symmetric, linear, and The South Coastal Basin, which is part of the constant in variance (homoscedasticity) (Helsel and eastern region, was assigned its own location identifier Hirsch, 1992, p. 12–14). because the data for this area of the State indicates a

Logistic Regression Equation 15

A. EASTERN REGION n = 7 B. WESTERN REGION n = 9 100 100

95 95

90 n = 8 90 n = 7 85 85 n = 5 80 80 n = 8 75 75 n = 7 70 n = 6 70 65 65

60 n = 9 60 55 n = 8 55 n = 6 50 n = 15 50 45 n = 14 45 n = 12 n = 5 n = 10 40 40

35 35

30 30

DRAINAGE-AREA RANGE, IN PERCENT 25 n = 21 25

20 20

15 15

OBSERVED FREQUENCY OF PERENNIAL-STREAM SITES BY 10 10

5 n = 16 5 0 0

0.01-0.99 1.00-1.99 2.00-2.99 3.00-3.99 4.00-4.99 5.00-5.99 6.00-6.99 7.00-7.99 8.00-8.99 0.01-0.99 1.00-1.99 2.00-2.99 3.00-3.99 4.00-4.99 5.00-5.99 6.00-6.99 7.00-7.99 8.00-8.99 DRAINAGE AREA, IN SQUARE MILES DRAINAGE AREA, IN SQUARE MILES

C. SOUTH COASTAL BASIN n = 11 100

80 n = 27 n = 12 75

60 n = 26 n = 29 55

45 n = 27 40

DRAINAGE-AREA RANGE, IN PERCENT 20

OBSERVED FREQUENCY OF PERENNIAL-STREAM SITES BY 5

0.01-0.12 0.13-0.24 0.25-0.49 0.50-0.99 1.00-1.99 2.00-7.00 DRAINAGE AREA, IN SQUARE MILES

Figure 5. Observed frequency of perennial-stream sites by drainage-area range in the (A) eastern region, (B) western region, and (C) South Coastal Basin of Massachusetts (n, number of observations).

16 A Logistic Regression Equation for Estimating the Probability of a Stream Flowing Perennially in Massachusetts

different relation between the perennial or intermittent variable i. More detailed information on logistic status of stream sites and their drainage area, areal per- regression can be found in Collett (1991) and Hosmer centage of stratified-drift deposits, and mean basin and Lemeshow (1989). slope that is different than the relation in the eastern and western regions of the State (figs. 4A, C, and D). All potential explanatory variables (basin charac- For example, drainage area and mean basin slope were teristics; square, cube, square root, and cube root trans- lower for stream sites in the South Coastal Basin than formations of the basin characteristics; and location in the eastern and western regions, and areal percentage identifiers) were evaluated by using the procedures of of stratified-drift deposits was greater in the South forward selection, backward elimination, stepwise Coastal Basin than in the eastern and western regions selection, and best subset selection to help determine (figs. 4A, C, and D). In the South Coastal Basin, the the best possible logistic regression equations (SAS observed frequency of perennial-stream sites for drain- Institute, Inc., 1995, p. 51–65). A statistical signifi- 2 age areas from 0.01 to 0.12 mi is similar to the cance level of 0.05 for p-values of explanatory vari- observed frequency of perennial-stream sites in the ables was used for entry or retention in the equations. eastern region for drainage areas from 1.00 to 1.99 mi2 These equations developed during the variable-evalua- and in the western region for drainage areas from 0.01 tion process were used for estimating the probabilities to 0.99, 1.00 to 1.99, and 2.00 to 2.99 mi2 (figs. 5A–C). This greater observed frequency of a perennial-stream that each of the stream sites was perennial. site for small drainage areas in the South Coastal The results of the equations were summarized in Basin, as compared to the remainder of the State, likely classification tables (SAS Institute, Inc., 1995, p. 45– results because of the greater areal percentage of stratified-drift deposit (fig. 4C). If the South Coastal Basin 50). These tables provide information about the predic- drainage area classes (fig. 5C) 0.01 to 0.12, 0.13 to tive accuracy of an equation by summarizing the fre- 0.24, 0.25 to 0.49, and 0.50 to 0.99 mi2 were combined, quency with which observations are correctly and the observed frequency of perennial-stream sites would incorrectly classified as events or nonevents for differ- be 55 percent (62 perennial-stream sites of the 113 sites ent probability cutpoints. Because the same data are in those classes). This observed frequency of perennial- used to develop the equation and to test its predictive stream sites in the South Coastal Basin (55 percent) is accuracy, a method that approximates the unbiased not reached in the eastern region until the drainage area jackknifing procedure was used to create the classifica- 2 is from 2.00 to 2.99 mi (fig. 5A), and is not reached in tion tables (SAS Institute Inc., 1995, p. 45). Jack- the western region until the drainage area is from 3.00 knifing minimizes bias caused when an independent set to 3.99 mi2 (fig. 5B). of observations is not available to test the predictive After stream sites were evaluated with basin accuracy of the equation. characteristics for any regionalization, logistic regression analyses were done with the SAS statistical soft- Goodness-of-fit of the potential logistic ware package (SAS Institute, Inc., 1989; 1995). The regression equations were evaluated with the Hosmer general form of a logistic regression equation is and Lemeshow (1989) goodness-of-fit test, which compares the observed to the predicted distribution of exp()b +++b x … b x P = ------0 1 1 1 1 , outcomes (SAS Institute, Inc., 1995, p. 67–72). Regres- 1 + exp()b0 +++b1x1 … b1x1 sion diagnostics of the equations also were evaluated to determine how each observation affects the fit of the where P is the probability of the condition being true, exp is the exponential function and is written as exp(x) logistic regression equation (SAS Institute, Inc., 1995, or e(x) (where “e” is the base of the natural logarithm p. 73–79). Finally, receiver-operating-characteristic and is approximately equal to 2.7183), b0 is the (ROC) curves were evaluated to assess the predictive intercept, b1...i is the coefficient for explanatory accuracy of the logistic regression equation (SAS variable i, and x1...i is the value of explanatory Institute Inc., 1995, p. 87–92).

Logistic Regression Equation 17 The best logistic regression equation determined from data in this study is:

13⁄ 12⁄ exp(– 5.6325 ++++3.2619()x – 0.2566()x 0.1248()x 0.1929()x 3.3236()x ) P = ------1 2 ------3 4 5 - , 13⁄ 12⁄ 1 + exp(– 5.6325 ++++3.2619()x1 – 0.2566()x2 0.1248()x3 0.1929()x4 3.3236()x5 )

where P is the probability of a stream flowing perennially at a specific site, exp is approximately 2.7183, x1 is the 2 2 cube root of the drainage area of the basin (mi ), x2 is the drainage density in the basin (mi/mi ), x3 is the square root of the areal percentage of stratified-drift deposits in the basin (percentage), x4 is the mean basin slope of the basin (percentage), and x5 is an integer variable for the location of the stream site in the South Coastal Basin identifier (1 = in the South Coastal Basin, and 0 = in the remainder of State). Results of the analysis of the maximum estimates of this equation are presented in table 2 (SAS Institute Inc., 1995, p. 20–22). The p-values of each explanatory variable (parameters) are less than 0.05, the value used as the statistical significance level for entry or retention in the equation. Summary statistics of the logistic regression analyses for this equation with ﬁve explanatory variables (parameters) and other selected equations, which were determined to be the best equations of the equations tested with one to four variables, are presented in appendix A.

Application

An example application of the equation is provided for station NL—29 (table 5 and fig. 2) in the South Coastal Basin. Flow was observed at this stream site on August 20, 1999, and the site is represented as perennial on the USGS topographic map (Cohasset, Mass.). The values of the explanatory variables for input to the logistic 2 2 regression equation were the cube root of a drainage area of 0.79 mi (x1), a drainage density of 2.26 mi/mi (x2), the square root of areal percentage of stratified-drift deposits of 45.61 percent (x3), and a mean basin slope of 1.47 percent (x4). The location-integer variable determined from a map was 1 (x5), because the stream site is located in the South Coastal Basin. The equation for this stream site, therefore, is:

exp – 5.6325 ++++3.2619 0.79 13⁄ – 0.2566 2.26 0.1248 45.61 12⁄ 0.1929 1.47 3.3236 1 P = ------( () ()------() () ()) - . 13⁄ 12⁄ 1 + exp(– 5.6325 ++++3.2619() 0.79 – 0.2566() 2.26 0.1248() 45.61 0.1929() 1.47 3.3236() 1 )

Table 2. Analysis of maximum likelihood estimates for the logistic regression equation for estimating the probability of a stream flowing perennially in Massachusetts

[SAS Institute, Inc., 1995; 1/3, cube root; 1/2, square root; <, actual value less than value shown] Degrees of Standard Explanatory variable Estimate Chi-square p-value freedom error

Intercept...... 1 -5.6325 0.9406 35.8614 <0.0001 Drainage area1/3...... 1 3.2619 .4829 45.6267 <.0001 Location (SCB or remainder of State)...... 1 3.3236 .5381 38.1495 <.0001 Mean basin slope ...... 1 .1929 .0636 9.1909 .0024 Areal percentage of stratiﬁed-drift deposits1/2 ...... 1 .1248 .0496 6.3344 .0118 Drainage density...... 1 -.2566 .1134 5.1242 .0236

18 A Logistic Regression Equation for Estimating the Probability of a Stream Flowing Perennially in Massachusetts The resulting probability, P, that this stream site is result in about 70 percent of the events (perennial perennial, as determined with the logistic regression streams) and nonevents (intermittent streams) in the equation, is 0.76 (or 76 percent). Probabilities database being correctly classsified (table 3). Probabil- calculated with the logistic regression equation are ity cutpoints other than 0.50 could be used, but the given for the 173 stream sites in Massachusetts (table larger the cutpoint used, the greater the likelihood that 4) and for the 132 sites in the South Coastal Basin a stream site will be classified as intermittent (table 3, (table 5). False Negative column; events or perennial streams are The logistic regression equation developed incorrectly classified as nonevents or intermittent during this study could be used for estimating the prob- streams) and the smaller the cutpoint used, the greater ability of a stream flowing perennnial at a specific site the likelihood that a stream site will be classified as at a probability cutpoint of 0.50, where a stream site perennial (table 3, False Positive column; nonevents or would have an equal likelihood of being classified as intermittent streams are incorrectly classified as events perennial. The 0.50 cutpoint for this equation would or perennial streams).

Table 3. Classification table for the logistic regression equation for estimating the probability of a stream flowing perennially in Massachusetts

[Correct columns provide the frequency with which observations are correctly classified. Incorrect columns provide the frequency with which observations are incorrectly classified. Event is a perennial observation. Nonevent is an intermittent observation. Percent columns—Correct is the probability that the equation correctly classifies the sample data for each probability cutpoint. Sensitivity is the ratio of correctly classified events over the total number of events. For instance, at a cutpoint of 0.50 the sensitivity is 79.5 percent, because 136 of the 171 events are correctly classified. Specificity is the ratio of correctly classified nonevents over the total number of nonevents. For instance, at a cutpoint of 0.50 the specificity is 56.7 percent, because 76 of 134 nonevents are correctly classified. False positive is the ratio of the number of nonevents incorrectly classified as events over the sum of all observations classified as events. For instance, at a cutpoint of 0.50 the 58 nonevents incorrectly classified as events over the sum of 194 events. False negative is the ratio of the number of events incorrectly classified as nonevents over the sum of all observations classified as nonevents. For instance, at a cutpoint of 0.50 the 35 events incorrectly classified as nonevents over the sum of 111 nonevents. SAS Institute, Inc., 1995, p. 45–50] Correct Incorrect Percent Probability False False level Event Nonevent Event Nonevent Correct Sensitivity Specificity positive negative

0.00 171 0 134 0 56.1 100.0 0.0 43.9 0.0 .05 171 8 126 0 58.7 100.0 6.0 42.4 .0 .10 171 15 119 0 61.0 100.0 11.2 41.0 .0 .15 168 29 105 3 64.6 98.2 21.6 38.5 9.4 .20 167 36 98 4 66.6 97.7 26.9 37.0 10.0 .25 164 41 93 7 67.2 95.9 30.6 36.2 14.6 .30 162 45 89 9 67.9 94.7 33.6 35.5 16.7 .35 159 58 76 12 71.1 93.0 43.3 32.3 17.1 .40 151 65 69 20 70.8 88.3 48.5 31.4 23.5 .45 141 73 61 30 70.2 82.5 54.5 30.2 29.1 .50 136 76 58 35 69.5 79.5 56.7 29.9 31.5 .55 127 86 48 44 69.8 74.3 64.2 27.4 33.8 .60 112 97 37 59 68.5 65.5 72.4 24.8 37.8 .65 100 100 34 71 65.6 58.5 74.6 25.4 41.5 .70 86 108 26 85 63.6 50.3 80.6 23.2 44.0 .75 68 121 13 103 62.0 39.8 90.3 16.0 46.0 .80 57 128 6 114 60.7 33.3 95.5 9.5 47.1 .85 33 130 4 138 53.4 19.3 97.0 10.8 51.5 .90 23 133 1 148 51.1 13.5 99.3 4.2 52.7 .95 11 133 1 160 47.2 6.4 99.3 8.3 54.6 1.00 0 134 0 171 43.9 .0 100.0 .0 56.1

Logistic Regression Equation 19 LIMITATIONS OF THE LOGISTIC ground-water contributing area is less than the surface- REGRESSION EQUATION AND water-drainage area, the equation may overestimate the AREAS FOR FURTHER STUDY probability that a stream is perennial. The accuracy of the logistic regression equation The logistic regression equation developed is is a function of the quality of the data used in its devel- applicable for stream sites with drainage areas between opment. This data includes the measured perennial or 0.02 and 7.00 mi2 in the South Coastal Basin and intermittent status of a stream site, the occurrence of between 0.14 and 8.94 mi2 in the remainder of unknown regulation above a site, and the measured Massachusetts, because these were the smallest and basin characteristics. The measured perennial or inter- largest drainage areas used in equation development for mittent status of stream sites in Massachusetts is based their respective areas. The equation may not be reliable on information in the USGS NWIS database. Stream- for drainage areas less than 0.14 mi2 in the State and flow measured as less than 0.005 ft3/s is rounded down less than 0.02 mi2 in the South Coastal Basin. For to zero, so it is possible that several streamflow mea- drainage areas greater than 8.94 mi2 in the State and surements reported as zero may have had flows less greater than 7.00 mi2 in the South Coastal Basin the than 0.005 ft3/s in the stream. This measurement would equation could be used. It may not be necessary, how- cause stream sites to be classified as intermittent when ever, because all stream sites greater than 8.04 mi2 in they actually are perennial. Additionally, of the stream the State and 1.92 mi2 in the South Coastal Basin were sites selected from the NWIS database, 61 of 62 perennial. The equation may not be reliable for losing intermittent-stream sites and 89 of 89 perennial-stream reaches of streams, such as for streams that flow off an sites were represented as perennial streams on USGS area underlain by till or bedrock onto an area underlain topographic maps; therefore, the Statewide database by stratified-drift deposits (these areas are likely more (sample) used in development of the equation may not prevalent where hillsides meet river valleys in central be random, because stream sites often selected for and western Massachusetts). At this juncture of the dif- streamflow measurements are represented as perennial ferent underlying surficial deposit types, the stream can streams on USGS topographic maps. Also, the drainage lose streamflow through its streambed. Generally, a area of stream sites selected for streamflow measure- losing stream reach occurs where the water table does ments generally is greater than about 1.0 mi2, which not intersect the streambed in the channel (water table may result in the sample not being random. is below the streambed) during low-flow periods. In The observed perennial or intermittent status of these reaches, the equation would tend to overestimate stream sites in the South Coastal Basin database may the probability of a stream flowing perennially at a site. also be biased, because the sites were measured during The logistic regression equation may not be the summer of 1999. The summer of 1999 did not meet reliable in areas of Massachusetts where ground-water the definition of an extended drought; but monthly pre- and surface-water drainage areas for a stream site dif- cipitation near the South Coastal Basin was less than fer. This condition may be present in southeastern 50 percent of average in April, less than 25 percent of Massachusetts, particularly for streams draining the average in June, about 75 percent of average in July southern part of the South Coastal Basin, the eastern (excluding one station), and about 50 percent of aver- part of the Buzzards Bay Basin, and the entire area age in August (excluding one station) (fig. 6). Addi- of the Cape Cod and Islands Basins (labeled as the tionally, Socolow and others (2000) reported Southeast Coastal Region in fig. 1). In these areas, streamflows and ground-water levels well below ground water can flow from one basin into another; normal throughout most of Massachusetts during the therefore, in basins that have a larger ground-water summer of 1999. Consequently, stream sites classified contributing area than the surface-water drainage area as intermittent would have been omitted from the data- the equation may underestimate the probability that a base had this period been classified as an extended stream is perennial. Conversely, in areas where the drought. This climatic condition during the summer of

20 A Logistic Regression Equation for Estimating the Probability of a Stream Flowing Perennially in Massachusetts 300 areal percentage of sand and gravel deposits may be an 803 BROCKTON, MASSACHUSETTS important explanatory variable for estimating the 280 904 FALMOUTH, MASSACHUSETTS 809 MIDDLEBOROUGH, MASSACHUSETTS probability that a stream site is perennial. 817 NEW BEDFORD, MASSACHUSETTS 260 The accuracy of the logistic regression equation 240 also may be improved with the testing of additional

220 basin characteristics as explanatory variables. These explanatory variables could include areal percentage 200 of wetlands (forested and non-forested), areal percent- 180 age of water bodies, areal percentage of forested land,

160 areal percentage of urban land, or mean, minimum, and maximum basin elevation. Soils data from county 140 soil surveys completed by the Natural Resources 120 Conservation Service (formerly the Soil Conservation

100 Service) eventually will be available for all counties of Massachusetts as a digital data layer referred to as 80 PRECIPITATION FOR 1960-99 AVERAGE SSURGO (U.S. Department of Agriculture, Natural

TOTAL MONTHLY PRECIPITATION IN 1999, AS A 60 Resources Conservation Service, Soil Survey Division, 2000). This data layer would allow testing of soil char-

PERCENTAGE OF THE AVERAGE LONG-TERM MONTHLY 40 acteristics (such as the four different hydrologic soil 20 groups A, B, C, and D, which relate to the infiltration 0 JAN. FEB. MAR. APR. MAY JUNE JULY AUG. SEPT. rate of particular soil types) as potential explanatory 1999 variables. Physically measured characteristics of the stream at the stream sites also may be reflective of its perennial or intermittent status, such as the width of the Figure 6. Total monthly precipitation from January through stream channel at the mean annual high-water line September 1999, as a percentage of the average long-term monthly precipitation for 1960–99 at the Brockton, Falmouth, (bankfull), the stream channel area at bankfull, and Middleborough, and New Bedford precipitation stations near general streambed material. the South Coastal Basin, southeastern Massachusetts. The logistic regression equation for this study or future studies could be incorporated into the 1999 could bias the logistic regression equation toward STREAMSTATS, so that the probability of a stream a lower probability of a stream site being considered flowing perennially at a specific site could be calcu- perennial in the South Coastal Basin. lated interactively by users on the World Wide Web. Basin characteristics of the stream sites used in The equation also could be used to develop maps the logistic equation development are limited by the depicting intermittent and perennial streams in accuracy of the digital data layers used. In the future, Massachusetts, if a particular threshold of acceptable digital data layers (such as hydrography, surficial geol- probability for classifying a stream as perennial at a ogy, soils, DEMs, and land use) will be at lower scales, site were determined. such as 1:5,000 or 1:25,000. This would improve the accuracy of the measured basin characteristics used as explanatory variables to predict the probability of a SUMMARY AND stream flowing perennially. For this study, the area of CONCLUSIONS stratified-drift deposits and consequently the areal per- City and town conservation commissions and centage of stratified-drift deposits included areas with the Massachusetts Department of Environmental sand and gravel, large sand, fine-grained, and flood- Protection (MADEP) are charged with protecting plain alluvium deposits. Future studies would allow the riverfront areas of all rivers that flow on a year more specificity in testing the areal percentage of surfi- round basis within Massachusetts, as specified in the cial deposits as explanatory variables. For example, the Commonwealth of Massachusetts Rivers Protection

Summary and Conclusions 21 Act of 1996. The 310 Code of Massachusetts Basin, southern part of the South Coastal Basin, or Regulations (CMR) 10.58(2)(a) defines the riverfront eastern part of the Buzzards Bay Basin (where ground- areas as the 200-ft wide area extending along the length water and surface-water-source areas differ). The data- of each side of the stream from the mean annual high- base used to develop the logistic regression equation water line on each side of perennial streams, with included 305 stream sites (84 intermittent and 89 exceptions in some urban areas. Initial designation of a perennial sites in the State, and 50 intermittent and 82 stream being perennial or intermittent at a site is deter- perennial sites in the South Coastal Basin). Stream mined by the representation on the most current USGS sites used in the database had drainage areas that topographic map, which may or may not accurately ranged from 0.14 to 8.94 mi2 in the State and from 0.02 represent a perennial or intermittent status, or on a to 7.00 mi2 in the South Coastal Basin. more recent map developed by the MADEP (if available). The Regulations, however, do allow the reversal The basin characteristics determined for the 305 of the perennial or intermittent status at a stream site if stream sites were drainage area, drainage density, areal a competent source can provide specific evidence to the percentage of stratified-drift deposits, and mean basin contrary. slope. These basin characteristics, transformations (square, cube, square root, and cube root) of the basin To assist city and town conservation commis- characteristics, a variable that identified whether the sions and the MADEP in determining whether a stream is perennial or intermittent at a site, a logistic regres- stream site was in the western or eastern region of the sion equation was developed by the U.S. Geological State, and a variable that identified whether the site was Survey, in cooperation with the Massachusetts in the South Coastal Basin or in the remainder of the Executive Office of Environmental Affairs (MAEOEA) State, then were tested as explanatory variables in the and the MADEP, for estimating the probability of a logistic regression analyses. Results of the logistic stream flowing perennially at a specific site as a func- regression analyses indicate that the probability of tion of upstream basin characteristics. Approximately a stream flowing perennially at a specific site in 1,300 stream sites in Massachusetts in the USGS Massachusetts can be estimated as a function of National Water Information System (NWIS) database (1) drainage area (cube root), (2) drainage density, and 397 stream sites visually inspected in the South (3) areal percentage of stratified-drift deposits (square Coastal Basin were reviewed for possible inclusion in root), (4) mean basin slope, and (5) location of the the database used for equation development. Stream stream site in the South Coastal Basin or the remainder sites had to meet four main requirements to be included of the State. in the database. The main requirements for stream sites The logistic regression equation developed pro- to be included in the database were that (1) the stream site had to be a natural flowing stream (no regulation vides an objective means for estimating the probability by dams, surface-water withdrawals, ground-water of a stream being flowing perennially at a specific site; withdrawals, diversion, wastewater discharge, and so however, the reliability of the equation is constrained forth), (2) measured or observed zero flow(s) could not by the data used to develop the equation. The equation occur during a month of an extended drought, as may not be reliable for (1) drainage areas less than 2 2 defined by the Regulations, (3) the perennial-stream 0.14 mi in the State and less than 0.02 mi in the sites had to have at least three streamflow measure- South Coastal Basin, (2) streams with losing reaches, ments to insure that it was likely that at least one mea- or (3) streams draining the southern part of the South surement was made during normal climatic conditions Coastal Basin and the eastern part of the Buzzards Bay (only for sites in the NWIS database), and (4) the Basin and the entire area of the Cape Cod and Islands stream site could not be in the Cape Cod Basin, Islands Basins.

22 A Logistic Regression Equation for Estimating the Probability of a Stream Flowing Perennially in Massachusetts REFERENCES CITED _____1997, August median streamflows in Massachusetts: U.S. Geological Survey Water- Collett, D., 1991, Modelling binary data: New York, Resources Investigations Report 97-4190, 27 p. Chapman and Hall, 369 p. Ries, K.G., and Friesz, P.J., 2000, Methods for Eckhardt, D.A.V., Flipse, W.J., and Oaksford, E.T., estimating low-flow statistics for Massachusetts 1989, Relation between land use and ground-water streams: U.S. Geological Survey Water-Resources quality in the upper glacial aquifer in Nassau and Investigations Report 00-4135, 81 p. Suffolk Counties, Long Island, New York: U.S. Geological Survey Water-Resources Investigations Ries, K.G., Steeves, P.A., Freeman, Aleda, and Singh, Report 86-4142, 35 p. Raj, 2000, Obtaining streamflow statistics for Eckhardt, D.A.V., and Stackelberg, P.E., 1995, Relation Massachusetts streams on the World Wide Web: of ground-water quality to land use on Long U.S. Geological Survey Fact Sheet 104-00, 4 p. Island, New York: Ground Water, v. 33, no. 6, SAS Institute, Inc., 1989, SAS/STAT User’s guide, p. 1019–1033. version 6, fourth edition, volume 2: Cary, N.C., Helsel, D.R., and Hirsch, R.M., 1992, Statistical 846 p. methods in water resources: New York, Elsevier Science Publishing Company, Inc., Studies in _____1995, Logistic regression examples using the Environmental Science 49, 522 p. SAS system, version 6 (1st ed.): Cary, N.C., 163 p. Hosmer, D.W., and Lemeshow, Stanley, 1989, Applied Socolow, R.S., Zanca, J.L., Murino, Domenic, Jr., and logistic regression: New York, John Wiley and Ramsbey, L.R., 2000, Water resources data Sons, 307 p. Massachusetts and Rhode Island, water year 1999: Kliever, J.D., 1996, Low-flow characteristics of U.S. Geological Survey Water Data Report selected streams in northern Rhode Island: U.S. MA-RI-99-1, 401 p. Available online at Geological Survey Water-Resources Investigations http://ma.water.usgs.gov/current_cond/adr/adr99/ Report 95-4299, 11 p. default.htm. Koltun, G.F., and Sherwood, J.M., 1998, Factors Squillace, P.J., Moran, M.J., Lapham, W.W., Price, related to the joint probability of flooding on C.V., Clawges, R.M., and Zogorski, J.S., 1999, paired streams: U.S. Geological Survey Water- Volatile organic compounds in untreated ambient Resources Investigations Report 98-4238, 32 p. groundwater of the United States, 1985–1995: Massachusetts Department of Environmental Environmental Science and Technology, v. 33, Protection, 2000, Wetlands protection act no. 23, p. 4176–4187. regulations, 310 CMR 10.00, accessed November 5, 2001, at URL http://www.state.ma.us/dep/brp/ The Commonwealth of Massachusetts, 1996, An act ww/files/310cmr10.pdf. providing protection for the rivers of the Commonwealth, accessed November 5, 2001, at Ries, K.G., 1994a, Estimation of low-flow duration discharges in Massachusetts: U.S. Geological URL http://www.state.ma.us/dep/brp/ww/ Survey Water-Supply Paper 2418, 50 p. files/riveract.htm. _____1994b, Development and application of U.S. Department of Agriculture, Natural Resources generalized-least-squares regression models to Conservation Service, Soil Survey Division, estimate low-flow duration discharges in 2000, National SSURGO database—data, Massachusetts: U.S. Geological Survey Water- accessed December 23, 2000, at URL Resources Investigations Report 94-4155, 33 p. http://www.ftw.nrcs.usda.gov/ssur_data.html.

References Cited 23

Tables 4 and 5

4 wing 18 37 83 62 77 30 47 83 74 82 17 44 66 24 46 82 61 73 76 53 (%) o ﬂ of stream Probability stream site perennially at perennially ; miles per square mile; ; miles per square 2 P P P P P P P P P P P P P P P P P P P P P USGS stream site of status of topographic ontinuous streamflow-gaging ontinuous ontinuous streamflow-gaging streamflow-gaging ontinuous map designation ssion equation for estimating the for estimating ssion equation ssion equation for estimating the for estimating ssion equation I I I I I I I I I I I I I I P P P P P P P status of recorded stream site Measured or 1.93 2.14 6.37 3.63 1.36 3.81 2.45 2.28 0.84 1.96 4.93 3.91 1.97 3.66 1.99 5.96 3.99 3.47 2.37 3.71 3.61 (%) Mean basin slope ed- ﬁ 2.23 2.90 2.25 (%) drift 79.17 16.86 23.72 71.56 21.86 67.54 98.36 25.42 11.21 22.98 11.18 63.24 12.57 28.72 29.51 48.44 26.59 57.21 Area of deposits strati ) 2 1.70 2.67 1.67 2.36 1.94 1.72 1.86 2.30 4.61 2.99 2.25 2.08 2.86 1.86 1.79 2.19 1.71 2.75 2.22 2.80 1.77 density (mi/mi Drainage Drainage ) 2 .69 area 1.92 1.72 7.03 6.73 4.33 7.41 6.84 1.83 4.23 5.89 1.36 3.91 1.61 2.72 4.26 6.79 4.61 5.87 6.62 2.76 (mi Drainage Drainage

Nashua River Basin Nashua River ″ North Coastal Basin Concord River Basin Concord River EASTERN REGION

′ Merrimack River Basin Merrimack River ° 71 33 55 71 15 16 71 46 06 71 37 59 71 15 38 71 46 48 71 32 54 70 51 59 71 16 02 71 16 10 71 46 39 71 34 52 71 30 02 71 34 39 70 56 55 71 45 31 71 50 12 71 35 09 71 13 08 71 34 00 71 41 18 Longitude

″

Given in degrees, minutes, seconds. I, Intermittent; P, Perennial; USGS, U.S. Geological Survey; mi/mi Geological Survey; Perennial; USGS, U.S. P, seconds. I, Intermittent; minutes, in degrees, Given ′

° 42 40 03 42 42 08 42 42 07 42 16 16 42 38 58 42 23 49 42 41 23 42 51 00 42 39 48 42 41 08 42 40 24 42 27 10 42 26 44 42 27 04 42 33 34 42 40 42 42 23 00 42 24 59 42 40 47 42 23 57 42 38 53 Latitude Latitude and longitude: Latitude and

Station name Location shown in ﬁgure 1. Location shown

aushacum Brook near West Boylston West aushacum Brook near Townsend West Brook near alker rout Brook near Dracut rull Brook near Lowell rout Brook near Holden Ashby Brook near rapfall Bartlett Brook near Dracut Heath Hen Meadow Brook at Stow Heath Hen Meadow T Richardson Brook near Lowell T Andover Fish Brook near Unkety Brook near Pepperell Unkety Westborough at Assabet River Mill Brook near Hudson Danforth Brook at Hudson Boulder Brook near East Bolton Boulder Brook at East Bolton T T Townsend West Brook at Locke W Townsend Bixby Brook near Brook at East Pepperell Reedy Meadow Small Pox Brook at Salisbury Crane Brook at Danvers W Description, basin characteristics, and perennial- or intermittent-status determination for stream sites at discontinued and c stream sites at discontinued determination for or intermittent-status and perennial- basin characteristics, Description, Description, basin characteristics, and perennial- or intermittent-status determination for stream sites at discontinued and c and discontinued sites at for stream determination or intermittent-status and perennial- characteristics, basin Description, No. USGS , square mile; %, percent] , square mile; station 01100350 01097200 01100050 01100100 01100200 01100300 01096505 01096600 01096850 01096855 01096906 01096910 01095380 01095928 01095940 01095960 01095989 01096504 01073860 01102053 01094760 2 USGS Station No.: USGS Station stations and partial-record stations by region and major river basin in Massachusetts used in development of the logistic regre in development of Massachusetts used major river basin in by region and partial-record stations stations and perennially in Massachusetts of a stream flowing probability Table 4. stations and partial-record stations by region and major river basin in Massachusetts used in development of the logistic regre in development of Massachusetts used major river basin in by region and partial-record stations stations and perennially in Massachusetts of a stream flowing probability Table 4. Table [ mi

Table 4 27 1 8 2 3 8 7 4 4 5 wing 12 19 71 14 20 65 12 53 53 77 14 36 22 (%) o ﬂ of stream Probability stream site perennially at perennially I I I I P P P P P P P P P P P P P P P P P P USGS stream site of status of topographic ontinuous streamflow-gaging streamflow-gaging ontinuous map designation ssion equation for estimating the for estimating ssion equation I I I I I I I I I I I I I I I I I I I P P P status of recorded stream site Measured or Measured .70 .14 3.15 2.34 2.78 3.18 2.11 2.69 3.37 2.85 4.27 2.09 2.17 1.94 1.37 2.57 1.75 1.12 4.13 4.28 2.61 2.00 (%) Mean basin slope ed- ﬁ .00 .00 .00 .00 9.15 7.14 (%) drift 31.58 31.05 44.74 11.27 13.79 13.73 11.67 32.50 53.06 17.72 28.95 77.03 12.50 30.60 18.69 Area of 100.00 deposits strati ) 2 .96 2.57 1.28 1.82 1.50 5.14 1.30 1.80 1.86 1.75 2.14 2.87 1.40 2.89 1.90 2.50 1.99 3.11 2.34 2.41 1.62 3.10 Continued density (mi/mi Continued Drainage Drainage ) 2 .76 .38 .14 .29 .51 .14 .77 .14 .80 .38 .27 area 1.40 5.54 1.42 1.41 6.68 4.09 4.35 6.66 2.48 1.34 1.46 (mi Drainage Drainage

Ispwich River Basin Ispwich River ″

′ Shawsheen River Basin Shawsheen River ° 71 08 27 71 10 19 71 01 59 71 09 58 71 08 45 71 07 41 70 58 04 71 14 47 70 58 45 71 19 05 71 01 10 71 07 35 71 13 27 71 08 59 71 12 44 71 08 17 71 10 23 70 57 12 71 00 05 70 56 45 71 13 15 71 08 02 Longitude EASTERN REGION— Merrimack River Basin— Merrimack River Continued

″

′ ° 42 37 32 42 46 35 42 48 41 42 37 31 42 38 25 42 47 00 42 48 25 42 31 29 42 47 53 42 28 06 42 50 55 42 39 30 42 42 15 42 44 38 42 37 14 42 45 06 42 40 01 42 39 17 42 50 03 42 47 33 42 37 56 42 40 49 Latitude Station name wksbury est Newbury Te Andover W est Meadow Brook near Haverhill Brook est Meadow Merrimac Pye Brook near Topsﬁeld Pye Brook near Shawsheen River Tributary #3 at Ballardvale Tributary River Shawsheen Andover #5 near Tributary River Shawsheen Andover #6 near Tributary River Shawsheen Andover at Tributary Rogers Brook Andover Brook near Hussey North #8 near Tributary River Shawsheen Elm Brook Tributary near Concord Tributary Elm Brook Brook near Billerica McKee near Street Brook at Kendall Meadow Tewksbury Brook near Meadow Cobbler Brook near Merrimac Cobbler Brook at East Main Street at Newbury West Brook at Sawmill Newbury West near Indian River near Tributary Reservoir Artichoke Upper Bartlett Brook near Methuen near Methuen Brook Bare Meadow at North Street near Methuen Brook Hawkes near Methuen Brook Hawkes W near Haverhill River East Meadow Description, basin characteristics, and perennial- or intermittent-status determination for stream sites at discontinued and c and discontinued sites at for stream determination or intermittent-status and perennial- characteristics, basin Description, No. USGS station 01101850 01100616 01100617 01100618 01100623 01100628 01100633 01100572 01100593 01100607 01100608 01100800 01100802 01100808 01100810 01100817 01100400 01100640 01100650 01100655 01100665 01100700 stations and partial-record stations by region and major river basin in Massachusetts used in development of the logistic regre in development of Massachusetts used major river basin in by region and partial-record stations stations and — perennially in Massachusetts of a stream flowing probability Table 4. Table

28 A Logistic Regression Equation for Estimating the Probability of a Stream Flowing Perennially in Massachusetts 4 9 wing 15 67 77 18 10 29 36 56 58 27 11 21 72 31 43 59 73 32 60 12 57 20 84 12 68 (%) o ﬂ of stream Probability stream site perennially at perennially I P P P P P P P P P P P P P P P P P P P P P P P P P P USGS stream site of status of topographic ontinuous streamflow-gaging streamflow-gaging ontinuous map designation ssion equation for estimating the for estimating ssion equation I I I I I I I I I I I I I I I P P P P P P P P P P P P status of recorded stream site Measured or Measured .92 1.66 2.13 1.52 1.57 2.34 4.38 3.90 2.41 1.27 1.58 2.46 2.63 1.96 2.29 3.21 1.90 3.03 3.01 3.21 1.65 1.30 1.38 2.27 2.56 1.82 1.63 (%) Mean basin slope ed- ﬁ .58 .00 2.88 5.09 (%) drift 20.45 26.41 65.56 42.13 54.96 15.38 33.56 60.10 27.03 15.08 11.15 52.31 57.65 31.41 42.24 28.27 47.33 19.65 25.46 45.44 39.08 94.93 74.13 Area of deposits strati ) 2 .85 .26 .91 2.93 1.04 1.73 1.83 3.02 2.50 1.80 1.80 2.93 2.59 2.66 2.55 1.66 1.97 1.72 2.48 1.96 1.76 1.52 1.85 2.52 1.79 1.74 2.22 density (mi/mi Continued Drainage Drainage ) 2 .39 .19 .33 area 1.53 1.72 5.76 6.17 2.04 2.08 4.47 3.91 2.24 1.04 1.28 7.23 3.05 1.30 3.40 2.14 5.35 2.37 4.31 1.00 8.64 1.30 4.52 4.91 (mi Drainage Drainage

Charles River Basin Charles River ″ Boston Harbor Basin

′ ° 71 14 54 71 00 42 71 07 50 71 07 44 71 16 12 71 10 48 71 15 01 71 06 44 70 56 43 71 17 18 71 28 46 71 11 01 71 11 24 71 25 26 71 10 34 71 21 25 71 11 47 71 18 48 71 08 59 71 13 29 71 01 37 71 01 13 71 12 31 71 16 51 71 06 45 70 55 08 70 53 06 Longitude EASTERN REGION— Continued

″

′ ° 42 09 55 42 11 02 42 29 48 42 29 36 42 26 11 42 08 52 42 12 04 42 28 45 42 11 25 42 17 45 42 10 48 42 28 48 42 12 54 42 08 27 42 28 16 42 15 34 42 09 36 42 12 38 42 25 20 42 11 04 42 09 19 42 09 59 42 10 26 42 10 29 42 26 17 42 12 52 42 12 53 Latitude Station name ymouth We Center raphole Brook near Norwood umbling Brook at Holbrook Mill Brook near Medﬁeld Indian Brook near Sherborn Wellesley Fuller Brook at Hobbs Brook near Lincoln Hobbs Brook at Mill Street near Lincoln Whitmans Pond Outlet Tributary #2 at East Tributary Whitmans Pond Outlet near Hingham River Meadow Crooked Brook near Holliston Beaver Medway West Brook near Chicken Pequid Brook near Canton Brook at Islington Purgatory at Holbrook Cochato River T Cranberry Brook at Braintree Highlands Weymouth near South River Old Swamp Neponset River Tributary near Walpole near Tributary Neponset River Westwood Bubbling Brook North Street near Brook near Norwood Germany Brook at Norwood Hawes T #2 near Sharon Tributary Neponset River Sweetwater Brook at Stoneham Sweetwater Woburn Little Brook near Woburn Glen Brook near Shaker Arlington Mill Brook at Aberjona River Tributary #1 near Woburn #1 near Tributary Aberjona River Woburn #3 near Tributary Aberjona River Description, basin characteristics, and perennial- or intermittent-status determination for stream sites at discontinued and c and discontinued sites at for stream determination or intermittent-status and perennial- characteristics, basin Description, No. USGS station 01103360 01103415 01103440 01104400 01104405 01105614 01105630 01103214 01103253 01105400 01105525 01105568 01105573 01105575 01105600 01104880 01104910 01104960 01104980 01105100 01105150 01102470 01102482 01102490 01103015 011024592 011024596 stations and partial-record stations by region and major river basin in Massachusetts used in development of the logistic regre in development of Massachusetts used major river basin in by region and partial-record stations stations and — perennially in Massachusetts of a stream flowing probability Table 4. Table

Table 4 29 wing 14 84 71 55 84 77 40 16 69 52 38 59 80 76 48 69 17 86 72 78 40 81 (%) o ﬂ of stream Probability stream site perennially at perennially P P P P P P P P P P P P P P P P P P P P P P USGS stream site of status of topographic ontinuous streamflow-gaging streamflow-gaging ontinuous map designation ssion equation for estimating the for estimating ssion equation I I I I P P P P P P P P P P P P P P P P P P status of recorded stream site Measured or Measured .61 .95 .32 .96 .28 .96 .61 1.52 1.50 1.26 1.82 0.81 1.51 1.14 1.81 1.10 1.94 1.06 1.09 1.62 1.11 1.24 (%) Mean basin slope ed- ﬁ 4.65 9.32 2.25 (%) drift 38.07 45.90 64.20 36.91 41.92 54.55 24.29 35.78 18.68 49.33 27.84 89.03 94.15 85.12 65.01 40.48 39.53 63.57 44.87 Area of deposits strati ) 2 1.85 1.78 1.48 2.14 1.93 3.15 2.18 1.53 2.21 1.92 2.04 1.47 1.54 2.50 1.67 7.02 1.95 2.97 1.70 1.61 1.34 2.15 density (mi/mi Continued Drainage Drainage ) 2 area 1.72 8.59 5.86 4.33 8.94 8.35 2.64 1.61 7.99 3.17 4.22 4.71 7.48 7.47 4.74 2.82 8.20 3.83 5.88 7.21 2.58 8.09 (mi Drainage Drainage enmile River Basin enmile River aunton River Basin aunton River

Buzzards Bay Basin South Coastal Basin ″ T T

′ ° 70 46 49 71 01 05 71 13 47 71 15 18 70 58 17 71 07 35 71 00 47 70 43 44 71 07 47 70 47 20 71 05 23 71 03 59 71 02 54 71 05 43 70 47 18 71 17 08 70 59 19 71 14 27 71 00 45 71 15 03 70 52 04 70 58 39 Longitude EASTERN REGION— Continued

″

′ ° Narragansett Bay and Mt. Hope Bay Shore Basin Narragansett Bay and Mt. Hope Bay Shore 42 11 30 41 40 55 41 51 36 41 52 46 42 02 43 42 01 07 41 34 20 42 11 35 41 33 30 42 09 36 41 46 36 42 03 41 41 52 57 42 03 57 41 59 47 41 55 37 41 54 20 41 59 11 42 05 26 41 46 32 41 44 35 41 40 43 Latitude Station name Bedford Rochester est Branch Palmer River near Rehoboth River est Branch Palmer rout Brook at Brockton askamanset River at Turner Pond near New Pond near New Turner at askamanset River Rocky Run near Rehoboth Rocky Attleboro Brook at Speedway Cotley River at East Taunton at East River Cotley Brook near Easton Center Mulberry Meadow Mansﬁeld West Hodges Brook at Assonet Brook near Rattlesnake near Rehoboth River East Branch Palmer W T Brook near East Bridgewater Beaver Dorchester Brook near Brockton Queset Brook at North Easton Brook near North Middleboro Poquoy P Destruction Brook near South Dartmouth near North Dartmouth Shingle Island River Adamsville, R.I. Adamsville Brook at Satuit River at Scituate Satuit River at Norwell Second Herring Brook Scituate Center First Herring Brook near Brook near Kingston Jones River Massttapoisett River Tributary #1 near Tributary Massttapoisett River Description, basin characteristics, and perennial- or intermittent-status determination for stream sites at discontinued and c and discontinued sites at for stream determination or intermittent-status and perennial- characteristics, basin Description, No. USGS station 01109225 01109381 01108180 01108350 01108600 01109090 01109185 01109200 01106430 01106460 01107000 01107010 01108140 01105930 01105935 01105937 01106000 01105670 01105820 01105830 01105861 011059106 stations and partial-record stations by region and major river basin in Massachusetts used in development of the logistic regre in development of Massachusetts used major river basin in by region and partial-record stations stations and — perennially in Massachusetts of a stream flowing probability Table 4. Table

30 A Logistic Regression Equation for Estimating the Probability of a Stream Flowing Perennially in Massachusetts 6 wing 73 84 12 84 68 32 28 84 73 38 81 52 34 69 94 63 82 (%) o ﬂ of stream Probability stream site perennially at perennially P P P P P P P P P P P P P P P P P P USGS stream site of status of topographic ontinuous streamflow-gaging streamflow-gaging ontinuous map designation ssion equation for estimating the for estimating ssion equation I I I I I I I P P P P P P P P P P P status of recorded stream site Measured or Measured 3.82 3.09 4.34 6.21 3.98 4.83 4.77 8.26 5.96 4.96 3.15 4.63 3.38 4.90 7.01 7.39 (%) 11.40 11.38 Mean basin slope ed- ﬁ .12 .00 .00 2.05 4.98 4.10 4.13 1.17 (%) drift 35.87 20.48 22.93 14.35 28.61 23.33 35.81 15.40 22.89 23.66 Area of deposits strati ) 2 3.32 1.51 1.59 1.64 5.83 2.06 3.04 2.33 3.55 2.52 2.66 2.37 2.95 2.63 2.66 1.08 2.04 2.02 density (mi/mi Continued Drainage Drainage ) 2 .52 area 8.58 7.22 7.08 2.79 1.55 5.67 1.35 6.57 2.40 2.23 7.26 4.39 6.17 2.10 7.03 4.02 5.24 (mi Drainage Drainage

French River Basin River French Millers River Basin Millers River ″

Deerﬁeld River Basin Deerﬁeld River WESTERN REGION ′ Blackstone River Basin Blackstone River Quinebaug River Basin Quinebaug River ° 71 54 47 72 05 28 72 14 51 72 34 18 71 51 16 71 39 23 72 13 08 72 11 36 71 56 19 71 49 51 71 44 23 71 37 21 72 09 45 71 31 11 71 35 46 72 24 00 72 44 47 72 21 41 Longitude EASTERN REGION— Continued

″

′ ° 42 09 16 42 35 49 42 32 17 42 39 33 42 04 01 42 11 25 42 07 10 42 06 52 42 01 42 42 0 324 42 17 29 42 02 40 42 03 41 42 05 35 42 11 13 42 36 08 42 29 16 42 35 39 Latitude Station name yup Brook at Erving Depot est Brook near Shrewsbury ales Brook at Brimﬁeld rout Brook near Baldwinville ufts Branch near Dudley Whetstone Brook at Depot Road at Wendell Wendell Whetstone Brook at Depot Road at Ke Poland Brook near Conway Mill Brook near Bernardston Browns Brook near Webster Brook near Browns Webster Brook near Sucker T Athol Brook near South Riceville Mountain Brook near Brimﬁeld W Brook at Holland Stevens T at Richardson Road Corners Little River W Miscoe Brook near Grafton Center Brook at Upton Emerson Brook near Uxbridge Milford Muddy Brook at South Description, basin characteristics, and perennial- or intermittent-status determination for stream sites at discontinued and c and discontinued sites at for stream determination or intermittent-status and perennial- characteristics, basin Description, No. USGS station 01166105 01166400 01169800 01170240 01124750 01124800 01163298 01165250 01123100 01123161 01123200 01124100 01124390 01109950 01111142 01111160 01111225 01112190 stations and partial-record stations by region and major river basin in Massachusetts used in development of the logistic regre in development of Massachusetts used major river basin in by region and partial-record stations stations and — perennially in Massachusetts of a stream flowing probability Table 4. Table

Table 4 31 7 wing 73 33 57 34 89 43 34 70 47 20 11 81 60 78 80 14 30 47 68 17 53 49 65 85 (%) o ﬂ of stream Probability stream site perennially at perennially P P P P P P P P P P P P P P P P P P P P P P P P P USGS stream site of status of topographic ontinuous streamflow-gaging streamflow-gaging ontinuous map designation ssion equation for estimating the for estimating ssion equation I I I I I I I I I I I I I I I P P P P P P P P P P status of recorded stream site Measured or Measured 4.60 6.98 5.46 5.10 5.12 5.96 2.79 2.97 2.63 3.55 5.20 3.92 5.64 4.42 4.27 2.98 2.86 4.09 1.66 6.53 3.42 6.93 3.63 4.67 3.20 (%) Mean basin slope ed- ﬁ .00 .06 .33 .69 .10 .20 .46 .00 .23 .14 .41 .16 1.07 4.05 2.06 1.36 (%) drift 14.31 12.77 56.93 64.78 36.69 18.87 15.15 80.84 66.04 Area of deposits strati ) 2 .87 1.25 1.53 1.93 3.37 1.87 2.07 2.59 3.23 2.34 1.65 1.60 1.31 2.16 1.64 2.51 2.06 2.86 2.55 2.35 3.40 3.45 1.57 2.93 1.80 density (mi/mi Continued Drainage Drainage ) 2 .77 .54 area 5.03 1.83 8.69 5.54 2.46 2.89 5.27 4.06 2.80 5.56 1.77 3.55 6.60 5.48 2.60 1.65 4.62 3.39 8.04 1.30 4.20 6.13 6.92 (mi Drainage Drainage

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Chicopee River Basin Chicopee River ′ Connecticut River Basin Connecticut River ° 72 13 27 71 55 28 72 00 19 72 08 44 72 07 39 72 22 12 72 41 00 72 28 25 72 03 04 72 41 16 72 05 56 72 10 12 72 06 17 72 15 53 72 02 41 72 38 03 72 06 09 72 02 44 72 08 51 72 20 05 72 08 05 72 12 24 72 13 16 72 00 04 72 28 50 Longitude WESTERN REGION— Continued

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′ ° 42 28 49 42 28 47 42 15 54 42 20 33 42 22 16 42 20 08 42 02 31 42 12 09 42 02 44 42 18 09 42 24 29 42 13 31 42 23 52 42 14 56 42 24 16 42 28 30 42 10 51 42 19 27 42 23 52 42 28 42 42 14 01 42 12 56 42 22 06 42 17 30 42 05 06 Latitude Station name Spencer East Longmeadow inimusset Brook at Wheelwright inimusset Brook at atchaug Brook near East Longmeadow Brook near Princeton Wachusett est rout Brook near Brookfield T Brookfield West Brook at Coys Warren Naultaug Brook near Warren Brook at Cheney Cadwell Creek near Belchertown 31 near at State Highway River Sevenmile near Spencer River Sevenmile Maynard Brook near Oakham Great Brook near East Brookfield Moose Brook near Barre W Muddy Brook near Hardwick Ware Flat Brook near Salem Hop Brook near New Brook near Petersham East Branch Fever W Potash Brook near Barre Brook near Barre Galloway Smith Brook near South Barre Pine Hill Brook at Barre Plains Bloody Brook near South Deerfield Bloody Brook near South Bassett Brook near Northampton at Porter Road near South Branch Mill River Agawam West Still Brook near W Description, basin characteristics, and perennial- or intermittent-status determination for stream sites at discontinued and c and discontinued sites at for stream determination or intermittent-status and perennial- characteristics, basin Description, No. USGS station 01175760 01175790 01175890 01175910 01174900 01175660 01175670 01175700 01175730 01173260 01173300 01173400 01173450 01174000 01174050 01172100 01172900 01173100 01173150 01173230 01170902 01171800 01177360 01184200 01184282 stations and partial-record stations by region and major river basin in Massachusetts used in development of the logistic regre in development of Massachusetts used major river basin in by region and partial-record stations stations and — perennially in Massachusetts of a stream flowing probability Table 4. Table

32 A Logistic Regression Equation for Estimating the Probability of a Stream Flowing Perennially in Massachusetts wing 91 72 96 40 33 94 69 31 80 69 77 27 61 45 56 74 85 53 14 30 (%) o fl of stream Probability stream site perennially at perennially P P P P P P P P P P P P P P P P P P P P USGS stream site of status of topographic ontinuous streamflow-gaging streamflow-gaging ontinuous map designation ssion equation for estimating the for estimating ssion equation I I I I I I P P P P P P P P P P P P P P status of recorded stream site Measured or Measured 8.54 4.36 4.76 5.34 3.76 4.74 7.07 9.72 6.46 7.88 9.29 8.59 5.76 (%) 12.36 11.04 10.61 11.08 10.82 10.52 10.86 Mean basin slope ed- fi .00 .62 .00 .00 .00 .00 .46 .50 .00 .00 .43 1.07 4.07 9.50 2.94 8.37 7.37 (%) drift 21.46 10.24 27.27 Area of deposits strati ) 2 .86 1.33 3.33 1.17 2.37 1.66 2.49 1.05 1.54 2.17 2.08 1.24 1.90 1.46 1.57 1.50 1.26 2.81 1.28 1.75 density (mi/mi Continued Continued Drainage Drainage ) 2 .81 .46 .78 area 6.57 7.71 7.62 2.95 7.37 1.26 6.46 2.34 2.77 6.35 3.96 1.74 4.16 4.07 2.18 5.95 3.64 (mi Drainage Drainage estfield River Basin estfield River

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armington River Basin armington River W ′ Housatonic River Basin Housatonic River F ° 72 15 31 72 15 41 73 12 53 73 02 48 72 55 49 73 20 40 72 59 19 73 24 58 72 24 18 73 05 09 72 16 08 73 13 35 72 52 15 73 17 11 73 09 55 73 17 56 73 15 26 72 54 12 73 21 02 73 11 53 Longitude Chicopee River Basin— Chicopee River WESTERN REGION— Continued

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′ ° 42 07 43 42 10 13 42 17 59 42 15 49 42 02 03 42 25 23 42 25 21 42 19 48 42 14 07 42 19 56 42 09 41 42 25 07 42 17 27 42 15 22 42 12 49 42 20 59 42 22 51 42 14 22 42 25 38 42 13 21 Latitude Station name yringham Shaker Village Shaker T Huntington est Brook near South Lee alker Brook near Becket Center Brook near Becket alker okun Brook near Lenox alley Brook near West Hartland, Conn. West Brook near alley rout Brook at West Worthington West rout Brook at oskett Mill Stream near Fentonville oskett Baldwin Brook near State Line Greenwater Brook at East Lee Greenwater Tyringham Hop Brook near Road, near Monterey Tributary, Unnamed W Marsh Brook at Lenox V North Branch Mount Lebanon Brook at Village Mount Lebanon Brook near Shaker Brook at Pittsfield Sykes Y Sykes Brook at Knightville Sykes Mill Brook at Becket Shaker W near Avenue Roaring Brook at Fisk Blodgett Mill Brook at West Brimfield West Blodgett Mill Brook at Brimfield West Kings Brook at F Roaring Brook near Belchertown T Description, basin characteristics, and perennial- or intermittent-status determination for stream sites at discontinued and c and discontinued sites at for stream determination or intermittent-status and perennial- characteristics, basin Description, No. USGS station 01197600 01197180 01197200 01197210 01197240 01197300 01187400 01197080 01197090 01197130 01197140 01180000 01180650 01180800 01180900 01176100 01176200 01176300 01176450 01179900 stations and partial-record stations by region and major river basin in Massachusetts used in development of the logistic regre in development of Massachusetts used major river basin in by region and partial-record stations stations and — perennially in Massachusetts of a stream flowing probability Table 4. Table

Table 4 33 wing 15 97 60 91 74 91 66 92 87 93 91 90 91 53 26 88 72 99 (%) o ﬂ of stream Probability stream site perennially at perennially P P P P P P P P P P P P P P P P P P USGS stream site of status of topographic ontinuous streamflow-gaging streamflow-gaging ontinuous map designation ssion equation for estimating the for estimating ssion equation I I I I P P P P P P P P P P P P P P status of recorded stream site Measured or Measured 5.46 7.89 6.22 8.87 8.19 5.28 6.20 4.27 (%) 19.38 13.04 13.77 10.15 13.86 13.90 18.95 10.47 15.45 24.58 Mean basin slope ed- ﬁ .00 .28 .28 .00 .00 .00 8.38 1.21 1.03 3.19 8.19 2.75 2.73 9.70 3.28 (%) drift 28.11 11.29 26.87 Area of deposits strati ) 2 .80 1.93 1.72 1.37 1.74 1.25 1.12 2.17 2.23 1.31 1.10 1.82 1.25 1.75 1.33 1.35 1.23 1.49 density (mi/mi Continued Drainage Drainage ) 2 area 5.25 1.05 1.59 3.70 2.87 8.29 1.95 8.46 7.36 3.35 2.91 7.03 7.68 1.91 1.71 8.87 6.70 3.49 (mi Drainage Drainage

Hudson River Basin Hudson River ″

′ ° 73 13 50 73 12 15 73 19 49 73 23 38 73 19 38 73 18 59 73 25 46 73 14 40 73 05 48 73 25 49 73 26 51 73 09 06 73 06 48 73 28 09 73 26 40 73 14 00 73 12 39 73 21 35 Longitude WESTERN REGION— Housatonic River Basin--Continued Housatonic River Continued

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′ ° 42 41 16 42 11 26 42 07 35 42 06 41 42 06 25 42 06 32 42 16 42 42 05 26 42 42 59 42 02 58 42 09 17 42 33 40 42 35 20 42 09 37 42 09 55 42 02 46 42 40 38 42 23 17 Latitude Station name illiamstown Canaan Valley, Conn. Canaan Valley, W Richmond near South Egremont Egremont illard Brook near Sheffield South Brook at Cheshire Adams Dry Brook near Hudson Brook at Middle Road at Clarksburg Hopper Brook, Hopper Road, near South Williamstown Hemlock Brook near Unnamed Tributary, Hupi Road, at Monterey Tributary, Unnamed at Southfield Umpachene River Road, near Campbell Falls Whiting River, Unnamed Tributary, Rt.23, near South Tributary, Unnamed W Brook near Sheffield Ironworks Soda Creek at Fink Road near Sheffield Soda Creek at County Road near Sheffield Cone Brook at Sleepy Hollow Road near Hollow Cone Brook at Sleepy Alford Scribner Brook near Conn. Taconic, Brook near Sages Ravine Road Washington Karner Brook near Mount Fenton Brook near South Egremont Description, basin characteristics, and perennial- or intermittent-status determination for stream sites at discontinued and c and discontinued sites at for stream determination or intermittent-status and perennial- characteristics, basin Description, No. USGS station 01331380 01331400 01331960 01332900 01333100 01198137 01198160 01198260 01198062 01198070 01198100 01198110 01198120 01197700 01197960 01198020 01198040 01198060 stations and partial-record stations by region and major river basin in Massachusetts used in development of the logistic regre in development of Massachusetts used major river basin in by region and partial-record stations stations and — perennially in Massachusetts of a stream flowing probability Table 4. Table

34 A Logistic Regression Equation for Estimating the Probability of a Stream Flowing Perennially in Massachusetts 53 34 75 73 81 43 70 78 60 81 62 55 56 72 45 57 66 wing (%) site; o ﬂ at stream of stream Probability perennially perennially I I I I I P P P P P P P P P P P P graphic status of nation of map desig- stream site USGS topo- I I I I I I I P P P P P P P P P P in the South Coastal Basin, in the South in the South Coastal Basin, Basin, South Coastal in the site status lowing perennially in Massachusetts lowing perennially of stream lowing perennially in Massachusetts in Massachusetts lowing perennially Observed , square mile; %, percent] , square mile; 2 Date 7-15-99 8-05-99 8-05-99 8-05-99 8-05-99 8-05-99 8-06-99 8-06-99 8-05-99 8-05-99 8-05-99 7-15-99 8-05-99 8-06-99 8-05-99 8-05-99 8-05-99 stream site was status of observed .71 .80 .80 .49 .97 .39 .88 .54 .43 .55 .96 .82 .96 .47 0.68 1.61 2.33 (%) Mean basin slope ed- ﬁ .00 0.00 , miles per square mile; mi , miles per square (%) drift 2 94.07 84.48 35.32 99.52 94.42 81.48 40.58 55.35 Area of 100.00 100.00 100.00 100.00 100.00 100.00 100.00 deposits strati ) 2 .76 .37 .59 .47 .98 1.65 5.22 1.07 1.41 3.39 1.69 1.25 2.01 1.13 1.13 1.27 2.05 density (mi/mi Drainage Drainage ) 2 .12 .30 .31 .62 .09 .24 .83 .77 .18 .14 .08 .22 .22 .09 .27 area 0.41 0.09 (mi Duxbury Cohasset Drainage

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′ ° 70 47 33 70 45 56 70 44 15 704 4 08 70 45 09 70 41 10 70 45 45 70 45 19 70 44 11 70 45 11 70 44 59 70 44 32 70 41 50 70 44 22 70 45 10 70 45 16 70 48 44 Longitude

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′ ° 42 13 36 42 01 30 42 02 26 42 02 27 42 01 34 42 01 18 42 03 45 42 04 22 42 01 29 42 01 19 42 01 39 42 01 29 42 01 20 42 02 24 42 01 45 42 05 03 42 13 46 Latitude Given in degrees, minutes, seconds. CT, Cohasset; DY, Duxbury; HR, Hanover; HN, Hanson; I, Intermittent; KN, Kingston; MD, Intermittent; KN, Kingston; HN, Hanson; I, HR, Hanover; Duxbury; Cohasset; DY, seconds. CT, minutes, in degrees, Given Latitude and longitude: Latitude and Stream-site name and location Stream-site name and inter Street eene Street State Route 3A Clearwater Drive Clearwater K W Old Railroad Grade Chandler Street Locations shown in figure 2. Locations shown eene Brook, Union Street eene Brook, Congress Street Unnamed Tributary to The Gulf, Main Street to Tributary Unnamed to Lily Pond, Tributary Unnamed Unnamed Tributary to Pine Brook, Pine Street Tributary Unnamed Road Tom Halls Brook, Hitty Drive Halls Brook, Clearwater Halls Brook, to Tributary Unnamed to Pudding Brook, Tributary Unnamed Unnamed Tributary to South River, Bianca Road South River, to Tributary Unnamed Bolas Road to South River, Tributary Unnamed Halls Brook, Autumn Avenue K K Unnamed Tributary to Bassett Brook, to Tributary Unnamed Bay Road to Kingston Bay, Tributary Unnamed to Kingston Bay, Tributary Unnamed South River, to Tributary Unnamed Bassett Brook, State Route 53 Description, basin characteristics, and perennial- or intermittent-status determination for field-visited stream sites by town field-visited stream determination for or intermittent-status and perennial- basin characteristics, Description, Description, basin characteristics, and perennial- or intermittent-status determination for field-visited stream sites by town sites stream for field-visited determination or intermittent-status and perennial- characteristics, basin Description, -27 -29 -30 -31 -37 -14 -15 -21 -25 -26 -05 -11 -12 -13 -04 No. Station Station No.: Station No.: DY DY DY DY DY DY DY DY DY DY DY DY DY DY CT-04 CT-10 DY southeastern Massachusetts used in development of the logistic regression equation for estimating the probability of a stream f estimating the probability equation for of the logistic regression used in development Massachusetts southeastern Table 5. southeastern Massachusetts used in development of the logistic regression equation for estimating the probability of a stream f estimating the probability equation for of the logistic regression used in development Massachusetts southeastern Table 5. Table [ Marshfield; NL, Norwell; P, Perennial; PE, Pembroke; RD, Rockland; SE, Scituate; USGS, U.S. Geological Survey; mi/mi U.S. Geological Survey; SE, Scituate; USGS, RD, Rockland; Pembroke; Perennial; PE, NL, Norwell; P, Marshfield;

Table 5 35 64 55 50 31 76 83 49 54 47 42 60 73 58 wing (%) site; o ﬂ at stream of stream Probability perennially perennially I I I P P P P P P P P P P graphic status of nation of map desig- stream site USGS topo- I I I P P P P P P P P P P in the South Coastal Basin, Basin, South Coastal in the site status of stream lowing perennially in Massachusetts in Massachusetts lowing perennially Observed Date 8-05-88 8-12-99 9-03-99 8-13-99 8-13-99 8-13-99 8-13-99 9-03-99 8-13-99 8-13-99 8-13-99 8-13-99 8-13-99 stream site was status of observed .96 .90 .57 .69 .49 .71 .37 .13 .02 1.28 1.91 1.15 1.14 (%) Mean basin slope ed- ﬁ (%) drift Area of 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 deposits strati ) 2 .64 .43 2.21 1.53 3.15 2.42 3.03 4.58 2.98 2.95 1.56 3.98 4.22 density (mi/mi Drainage Drainage Continued ) 2 .54 .27 .11 .56 .07 .21 .13 .11 .21 .17 .27 area 0.22 0.06 (mi Hanover Drainage Duxbury—

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′ ° 70 41 46 70 49 20 70 40 37 70 49 33 70 50 28 70 50 53 70 50 20 70 49 47 70 49 47 70 49 59 70 50 39 70 50 39 70 40 40 Longitude

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′ ° 42 01 00 42 06 52 42 01 43 42 06 08 42 05 49 42 05 52 42 06 18 42 06 14 42 06 27 42 06 33 42 06 32 42 06 38 42 01 39 Latitude Stream-site name and location Stream-site name and ater Street ater Street artridge Road Laurie Lane Drive Pine Tree Reed Drive Broadway Street Broadway Karen Road Street Broadway W W Street Broadway P Surplus Street Unnamed Tributary to Indian Head River, Tributary Unnamed to Indian Head River, Tributary Unnamed to Indian Head River, Tributary Unnamed Unnamed Tributary to Indian Head River, to Indian Head River, Tributary Unnamed to Indian Head River, Tributary Unnamed Indian Head River, to Tributary Unnamed Iron Mine Brook, Rockland Street to Indian Head River, Tributary Unnamed to Indian Head River, Tributary Unnamed Indian Head River, to Tributary Unnamed Unnamed Tributary to Kingston Bay, Bay Road to Kingston Bay, Tributary Unnamed to Blueﬁsh River, Tributary Unnamed to Blueﬁsh River, Tributary Unnamed Description, basin characteristics, and perennial- or intermittent-status determination for field-visited stream sites by town sites stream for field-visited determination or intermittent-status and perennial- characteristics, basin Description, -41 -53 -54 No. Continued Station HR-13 HR-15 HR-16 HR-10 HR-11 HR-12 HR-03 HR-07 HR-08 HR-09 DY DY DY southeastern Massachusetts used in development of the logistic regression equation for estimating the probability of a stream f estimating the probability equation for of the logistic regression used in development Massachusetts southeastern — Table 5. Table

36 A Logistic Regression Equation for Estimating the Probability of a Stream Flowing Perennially in Massachusetts 99 83 36 97 69 97 66 43 45 58 54 48 83 88 88 wing (%) site; o ﬂ at stream of stream Probability perennially perennially I I I P P P P P P P P P P P P graphic status of nation of map desig- stream site USGS topo- I I I I P P P P P P P P P P P in the South Coastal Basin, Basin, South Coastal in the site status of stream lowing perennially in Massachusetts in Massachusetts lowing perennially Observed Date 8-12-99 8-13-99 8-12-99 8-12-99 8-12-99 8-12-99 8-10-99 8-10-99 8-13-99 8-12-99 8-10-99 8-10-99 8-12-99 8-12-99 8-10-99 stream site was status of observed .71 .54 .55 .26 .54 .46 .46 .49 1.02 0.10 1.28 1.28 1.17 1.24 1.22 (%) Mean basin slope ed- ﬁ (%) drift 62.09 76.81 77.14 99.88 52.47 99.17 59.85 30.49 27.94 73.87 27.12 62.37 Area of 100.00 100.00 100.00 deposits strati ) 2 .75 .87 3.05 1.30 2.47 3.26 2.49 2.02 4.34 1.59 1.88 1.82 3.28 1.21 1.00 density (mi/mi Drainage Drainage ) Continued 2 .64 .37 .23 .04 .71 .31 .24 .17 .46 area 7.00 4.09 0.07 4.15 1.03 1.09 (mi Drainage Hanover—

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′ ° 70 52 37 70 52 09 70 52 59 70 51 10 70 52 47 70 50 51 70 53 15 70 53 23 70 51 14 70 51 28 70 51 38 70 51 52 70 51 53 70 52 10 70 51 50 Longitude

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′ ° 42 07 03 42 06 00 42 07 11 42 06 46 42 07 05 42 07 06 42 06 47 42 07 11 42 07 54 42 07 42 42 07 44 42 08 17 42 08 24 42 09 02 42 09 02 Latitude Stream-site name and location Stream-site name and alnut Street Main Street W Cedar Street Main Street Main Street Hanover Street Hanover Union Street Main Street Summer Street orrey Brook, Winter Street Winter Brook, orrey Unnamed Tributary to Shinglemill Brook, Tributary Unnamed Pond, to Hackett Tributary Unnamed Unnamed Tributary to Drinkwater River, River, Drinkwater to Tributary Unnamed River, to Drinkwater Tributary Unnamed River, to Drinkwater Tributary Unnamed Cushing Brook, Pleasant Street French Stream, to Tributary Unnamed River, to Drinkwater Tributary Unnamed River, Drinkwater to Tributary Unnamed Mollys Brook, Grove Street Mollys Brook, Grove T Mollys Brook, Main Street Street Brook, Hanover Drinkwater Street Cushing Brook, Hanover to French Stream, Tributary Unnamed Description, basin characteristics, and perennial- or intermittent-status determination for field-visited stream sites by town sites stream for field-visited determination or intermittent-status and perennial- characteristics, basin Description, No. Continued Station HR-48 HR-49 HR-41 HR-44 HR-45 HR-33 HR-34 HR-39 HR-40 HR-22 HR-25 HR-28 HR-30 HR-31 HR-32 southeastern Massachusetts used in development of the logistic regression equation for estimating the probability of a stream f estimating the probability equation for of the logistic regression used in development Massachusetts southeastern — Table 5. Table

Table 5 37 70 70 83 71 75 11 72 71 36 50 30 33 42 67 67 67 95 wing (%) site; o ﬂ at stream of stream Probability perennially perennially I I I I P P P P P P P P P P P P P graphic status of nation of map desig- stream site USGS topo- I I I I I I I I P P P P P P P P P in the South Coastal Basin, Basin, South Coastal in the site status of stream lowing perennially in Massachusetts in Massachusetts lowing perennially Observed Date 8-10-99 8-10-99 8-10-99 8-10-99 8-10-99 8-10-99 7-19-99 7-19-99 8-10-99 8-10-99 8-10-99 7-19-99 7-19-99 8-10-99 8-10-99 8-10-99 7-19-99 stream site was status of observed .60 .59 .71 .69 .46 .83 .23 .63 .73 .70 .91 .61 .74 .58 2.69 1.82 1.96 (%) Mean basin slope ed- ﬁ 0.00 (%) drift 59.76 67.70 49.43 44.43 72.52 57.00 79.24 73.79 78.99 45.72 66.28 52.70 Area of 100.00 100.00 100.00 100.00 deposits strati ) 2 .85 .36 1.59 2.52 2.09 2.07 2.40 9.34 2.03 2.14 3.14 2.08 4.71 8.33 3.89 0.98 3.97 density (mi/mi Drainage Drainage ) Continued 2 .45 .54 .60 .67 .23 .89 .36 .39 .15 .36 .06 .02 .21 area 1.14 0.11 0.10 3.99 (mi Hanson Drainage Hanover—

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′ ° 70 52 54 70 52 15 70 52 36 70 52 29 70 52 32 70 50 44 70 52 54 70 52 16 70 52 16 70 53 45 70 52 14 70 51 21 70 51 12 70 51 54 70 50 45 70 51 45 70 52 29 Longitude

″

′ ° 42 08 40 42 08 46 42 08 31 42 08 30 42 08 55 42 04 32 42 07 54 42 08 55 42 08 50 42 08 17 42 08 54 42 05 13 42 05 10 42 05 01 42 04 39 42 08 40 42 07 40 Latitude Stream-site name and location Stream-site name and inter Street ebster Street est Street Street Brook Street Puritan Street Old Pine Drive W W Road Cedarwood Cedarwood Road Cedarwood Road Brookwood Dillingham Street W Cedar Street Unnamed Tributary to Oldham Pond, State Tributary Unnamed to Oldham Pond, Tributary Unnamed Unnamed Tributary to Indian Head Brook, Tributary Unnamed to Indian Head Brook, Tributary Unnamed to Indian Head Brook, Tributary Unnamed Shinglemill Brook, Hacketts Pond Drive Shinglemill Brook, Hacketts Shinglemill Brook, Country Road Mann Brook, to Tributary Unnamed to Shinglemill Brook, Tributary Unnamed Shinglemill Brook, Webster Street Webster Shinglemill Brook, to Shinglemill Brook, Tributary Unnamed to Shinglemill Brook, Tributary Unnamed Street Webster Shinglemill Brook, Unnamed Tributary to Drinkwater River, River, to Drinkwater Tributary Unnamed River, to Drinkwater Tributary Unnamed River, to Drinkwater Tributary Unnamed Road Brook, Cedarwood Longwater Description, basin characteristics, and perennial- or intermittent-status determination for field-visited stream sites by town sites stream for field-visited determination or intermittent-status and perennial- characteristics, basin Description, No. Continued Station HN-07 HN-08 HN-03 HN-04 HN-05 HR-62 HR-63 HR-65 HR-68 HR-56 HR-59 HR-60 HR-61 HR-50 HR-53 HR-54 HR-55 southeastern Massachusetts used in development of the logistic regression equation for estimating the probability of a stream f estimating the probability equation for of the logistic regression used in development Massachusetts southeastern — Table 5. Table

38 A Logistic Regression Equation for Estimating the Probability of a Stream Flowing Perennially in Massachusetts 54 74 72 39 56 71 31 65 97 97 95 81 26 56 56 12 81 54 wing (%) site; o fl at stream of stream Probability perennially perennially I I I I I I P P P P P P P P P P P P graphic status of nation of map desig- stream site USGS topo- I I I I I I I I I P P P P P P P P P in the South Coastal Basin, Basin, South Coastal in the site status of stream lowing perennially in Massachusetts in Massachusetts lowing perennially Observed Date 7-19-99 8-31-99 9-03-99 8-23-99 8-23-99 8-31-99 8-31-99 8-31-99 9-03-99 8-23-99 9-03-99 8-23-99 8-23-99 8-31-99 8-30-99 7-19-99 7-19-99 8-31-99 stream site was status of observed .71 .15 .87 .93 .59 .24 .61 3.36 3.77 4.34 1.21 2.76 3.93 2.83 4.35 1.72 0.09 1.21 (%) Mean basin slope ed- fi .00 .00 4.08 2.55 0.00 (%) drift 57.12 86.85 86.56 80.05 96.95 97.70 86.41 23.56 Area of 100.00 100.00 100.00 100.00 100.00 deposits strati ) 2 .87 .41 .97 .50 2.36 2.11 4.78 3.70 3.60 1.97 1.29 7.30 1.83 1.26 7.93 1.46 5.50 3.26 density (mi/mi Drainage Drainage ) Continued 2 .68 .10 .03 .22 .86 .88 .24 .06 .09 .02 .23 area 0.22 4.47 4.18 1.85 0.68 1.45 0.09 (mi Kingston Marshfield Drainage Hanson—

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′ ° 70 52 42 70 45 48 70 44 02 70 46 07 70 45 25 70 44 40 70 47 09 70 47 16 70 42 32 70 44 32 70 39 08 70 44 35 70 52 35 70 44 50 70 45 49 70 41 57 70 45 23 70 52 55 Longitude

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′ ° 42 05 14 42 00 36 41 59 17 42 08 07 42 08 26 42 00 32 42 00 12 42 00 47 41 58 46 42 07 06 42 04 18 42 09 07 42 04 58 41 58 52 42 00 38 42 06 23 42 07 41 42 04 55 Latitude Stream-site name and location Stream-site name and Pembroke Street Pembroke Sylvia Place Road Whitman Street Whitman Street South River Road South River Drive Stonewood Unnamed Tributary to Jones River, to Jones River, Tributary Unnamed Reed Street Jones River, to Tributary Unnamed Smelt Brook, Main Street Unnamed Tributary to Jones River, Brook Street Jones River, to Tributary Unnamed to Soules Pond, Tributary Unnamed Street Winthrop Bassett Brook, Street Lake Jones River, Street Grove Jones River, Unnamed Tributary to Factory Pond, to Factory Tributary Unnamed Pond, King Street to Factory Tributary Unnamed Pond, to Factory Tributary Unnamed Cut River, Canal Street Cut River, Furnace Brook, School Street to South River, Tributary Unnamed Brook, Oak Street to Cove Tributary Unnamed Brook, Union Street to Cove Tributary Unnamed to Oakham Pond, Tributary Unnamed Hannah Eames Brook, State Route 3A Description, basin characteristics, and perennial- or intermittent-status determination for field-visited stream sites by town sites stream for field-visited determination or intermittent-status and perennial- characteristics, basin Description, No. Continued Station MD-47 MD-20 MD-26 MD-34 MD-35 MD-36 KN-21 KN-22 KN-31 MD-01 KN-07 KN-11 KN-15 KN-17 KN-18 HN-14 HN-15 HN-16 southeastern Massachusetts used in development of the logistic regression equation for estimating the probability of a stream f estimating the probability equation for of the logistic regression used in development Massachusetts southeastern — Table 5. Table

Table 5 39 51 54 84 36 65 76 62 35 55 15 89 63 65 57 61 57 74 88 wing (%) site; o ﬂ at stream of stream Probability perennially perennially I I I I I I I P P P P P P P P P P P graphic status of nation of map desig- stream site USGS topo- I I I I I I P P P P P P P P P P P P in the South Coastal Basin, Basin, South Coastal in the site status of stream lowing perennially in Massachusetts in Massachusetts lowing perennially Observed Date 8-13-99 8-13-99 8-13-99 8-20-99 8-23-99 8-20-99 8-20-99 8-20-99 8-23-99 8-23-99 8-20-99 8-13-99 8-23-99 8-20-99 8-13-99 8-20-99 8-20-99 8-20-99 stream site was status of observed .32 .25 1.57 1.55 2.26 1.41 1.47 3.40 3.26 2.30 3.57 3.36 3.07 1.88 1.45 1.52 1.57 1.28 (%) Mean basin slope ed- ﬁ 6.04 5.89 6.36 1.57 5.35 6.17 (%) drift 75.31 26.84 86.13 63.16 18.37 45.61 14.99 19.37 81.09 12.91 10.41 Area of 100.00 deposits strati ) 2 .50 .71 3.98 2.60 2.48 3.00 1.78 2.56 2.37 1.08 2.41 2.31 6.66 1.76 1.84 4.40 2.69 1.56 density (mi/mi Drainage Drainage ) 2 .22 .10 .09 .79 .54 .24 .89 .26 .27 .33 .02 .27 .36 .13 area 1.46 0.49 2.16 1.92 (mi Norwell Drainage

″

′ ° 70 48 58 70 49 12 70 49 00 70 46 15 70 48 23 70 46 01 70 48 26 70 48 11 704 8 43 70 47 35 70 47 43 70 48 13 70 48 14 70 46 27 70 49 08 70 48 17 70 48 30 70 50 21 Longitude

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′ ° 42 08 58 42 08 43 42 09 26 42 10 18 42 07 01 42 09 53 42 09 17 42 07 44 42 09 05 42 09 53 42 09 57 42 10 24 42 10 21 42 09 54 42 10 24 42 07 34 42 07 32 42 09 51 Latitude Stream-site name and location Stream-site name and any Street any ff rout Brook Lane arker Street arker orest Street Leonard Lane Ti Central Street T P Norwell Avenue Prospect Street F Pine Street Circuit Street Mill Lane Central Street ildcat Brook, Main Street Lane Wildcat ildcat Brook, ildcat Brook, Pleasant Street ildcat Brook, Pleasant Unnamed Tributary to Third Herring Brook, Third Herring to Tributary Unnamed Brook, Third Herring to Tributary Unnamed Unnamed Tributary to Stony Brook, to Stony Tributary Unnamed Brook, Main Street Stony W W Creek, Wildcat to Tributary Unnamed Unnamed Tributary to Second Herring Brook, Tributary Unnamed Second Herring Brook, to Tributary Unnamed Brook, Cross Street Stony Unnamed Tributary to Wildcat Brook, Wildcat to Tributary Unnamed to Second Herring Brook, Tributary Unnamed Second Herring Brook, to Tributary Unnamed Copeland Tannery Brook, Meadow Brook Road Brook, Meadow Tannery Copeland to Burnt Plain Swamp, Tributary Unnamed W Brook, Wildcat to Tributary Unnamed Third Herring Brook, to Tributary Unnamed Description, basin characteristics, and perennial- or intermittent-status determination for field-visited stream sites by town sites stream for field-visited determination or intermittent-status and perennial- characteristics, basin Description, No. Continued Station NL-46 NL-47 NL-25 NL-29 NL-33 NL-41 NL-42 NL-20 NL-21 NL-24 NL-16 NL-18 NL-19 NL-03 NL-07 NL-12 NL-13 NL-14 southeastern Massachusetts used in development of the logistic regression equation for estimating the probability of a stream f estimating the probability equation for of the logistic regression used in development Massachusetts southeastern — Table 5. Table

40 A Logistic Regression Equation for Estimating the Probability of a Stream Flowing Perennially in Massachusetts 66 94 97 77 41 43 98 43 87 65 88 12 42 41 40 48 65 40 75 wing (%) site; o ﬂ at stream of stream Probability perennially perennially I I I I I P P P P P P P P P P P P P P graphic status of nation of map desig- stream site USGS topo- I I I I I I P P P P P P P P P P P P P in the South Coastal Basin, Basin, South Coastal in the site status of stream lowing perennially in Massachusetts in Massachusetts lowing perennially Observed Date 8-04-99 7-29-99 8-04-99 7-29-99 8-03-99 7-29-99 7-29-99 7-29-99 7-29-99 8-03-99 7-29-99 8-04-99 8-31-99 7-29-99 8-04-99 8-04-99 7-29-99 8-04-99 8-04-99 stream site was status of observed .56 .52 .52 .07 .99 .72 .20 .48 .66 .47 .09 .98 2.08 0.94 1.02 1.50 9.95 1.44 0.54 (%) Mean basin slope ed- ﬁ .00 .36 4.96 2.68 (%) drift 47.65 95.16 48.79 34.26 96.64 56.87 88.67 61.42 33.53 56.45 68.11 33.20 Area of 100.00 100.00 100.00 deposits strati ) 2 .93 2.43 1.98 2.42 1.77 2.80 4.15 5.31 4.84 1.25 3.43 2.26 1.42 3.34 2.14 4.65 3.79 1.37 2.33 density (mi/mi Drainage Drainage ) 2 .19 .91 .39 .19 .50 .12 .17 .18 .40 .07 .57 .08 area 2.95 5.07 6.14 0.22 1.12 1.39 0.52 (mi embroke Rockland P Drainage

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′ ° 70 55 25 70 49 26 70 54 33 70 47 57 70 56 03 70 48 04 70 46 39 70 46 43 70 47 15 70 54 26 70 45 25 70 49 29 70 53 33 70 53 59 70 54 17 70 54 44 70 55 32 70 55 22 70 46 44 Longitude

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′ ° 42 07 17 42 04 29 42 06 33 42 04 38 42 08 11 42 04 30 42 04 09 42 03 58 42 05 57 42 08 05 42 05 10 42 04 53 42 06 43 42 05 24 42 06 35 42 06 43 42 07 52 42 07 42 42 04 16 Latitude Stream-site name and location Stream-site name and ashington Street W Road Lowell Reed Street Spring Street North Avenue Summer Street Beech Street Summer Street Unnamed Tributary to Swamp Brook, to Swamp Tributary Unnamed Pudding Brook, Spring Street Street Water Robinson Creek, Brook, Congress Street McFarland McFarland Brook, Washington Street Washington Brook, McFarland Brook, to McFarland Tributary Unnamed Brook, Elm Street to Swamp Tributary Unnamed Street Herring Brook, Barker Street Little Pudding Brook, Barker Unnamed Tributary to Studleys Pond, to Studleys Tributary Unnamed Street Webster Cushing Brook, Unnamed Tributary to French Stream, Tributary Unnamed Street Water French Stream, West French Stream, Spruce Street Pond, to Studleys Tributary Unnamed Unnamed Tributary to French Stream, to Tributary Unnamed to French Stream, Tributary Unnamed to French Stream, Tributary Unnamed French Stream, Summer Street Description, basin characteristics, and perennial- or intermittent-status determination for field-visited stream sites by town sites stream for field-visited determination or intermittent-status and perennial- characteristics, basin Description, No. Continued Station RD-11 RD-19 RD-06 RD-07 RD-09 RD-10 RD-01 RD-02 RD-03 RD-04 PE-17 PE-19 PE-20 PE-23 PE-08 PE-09 PE-10 PE-12 PE-13 southeastern Massachusetts used in development of the logistic regression equation for estimating the probability of a stream f estimating the probability equation for of the logistic regression used in development Massachusetts southeastern — Table 5. Table

Table 5 41 84 84 92 68 71 79 34 33 55 33 73 65 57 79 63 wing (%) site; o ﬂ at stream of stream Probability perennially perennially I I I I P P P P P P P P P P P graphic status of nation of map desig- stream site USGS topo- I I I I I I I P P P P P P P P in the South Coastal Basin, Basin, South Coastal in the site status of stream lowing perennially in Massachusetts in Massachusetts lowing perennially Observed Date 7-16-99 7-16-99 8-04-99 8-03-99 7-16-99 7-16-99 7-16-99 7-16-99 7-16-99 8-03-99 8-04-99 7-16-99 8-04-99 7-16-99 7-16-99 stream site was status of observed .60 .61 .49 .88 .60 .30 .27 .04 .60 0.41 1.03 2.17 1.21 1.16 2.13 (%) Mean basin slope ed- ﬁ .00 .09 4.46 4.56 8.22 1.27 (%) drift 41.28 85.34 12.85 12.66 73.13 23.40 10.65 26.56 25.23 Area of deposits strati ) 2 .81 .17 1.44 1.43 3.48 2.42 1.92 1.72 2.25 3.37 1.33 1.56 3.35 2.02 2.92 density (mi/mi Drainage Drainage Continued ) 2 .55 .71 .86 .32 .19 .34 .25 .33 .33 area 1.79 1.75 0.57 2.55 0.80 1.26 (mi Scituate Drainage

Rockland— ″

′ ° 70 46 38 70 46 47 70 54 18 70 56 02 70 44 20 70 44 04 70 53 44 70 55 21 70 46 16 70 46 05 70 45 53 70 46 12 70 47 25 70 46 17 70 54 11 Longitude

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′ ° 42 11 31 42 11 31 42 07 54 42 07 43 42 11 55 42 11 36 42 05 52 42 07 30 42 12 59 42 12 39 42 12 25 42 11 48 42 12 33 42 11 56 42 08 48 Latitude Stream-site name and location Stream-site name and Captain Pierce Road Branch Way Road First Parish Booth Hill Road State Route 3A Hollett Street Hingham Street Millbrook Street Plain Street First Herring Brook, Maple Street to Bound Brook, Tributary Unnamed to First Herring Brook, Tributary Unnamed Street First Herring Brook, Grove Unnamed Tributary to Musquashcut Brook, to Tributary Unnamed to Musquashcut Brook, Tributary Unnamed to First Herring Brook, Tributary Unnamed Satuit Brook, Beaver Dam Road Satuit Brook, Beaver Road Tilden Satuit Brook, to Musquashcut Brook, Tributary Unnamed Cushing Brook, Liberty Street Cushing Brook, Liberty Avenue French Stream, North to Mann Brook, Tributary Unnamed to French Stream, Tributary Unnamed Pond, to Studleys Tributary Unnamed Description, basin characteristics, and perennial- or intermittent-status determination for field-visited stream sites by town sites stream for field-visited determination or intermittent-status and perennial- characteristics, basin Description, No. Continued Station SE-14 SE-16 SE-19 SE-21 SE-06 SE-07 SE-12 SE-01 SE-02 SE-04 RD-20 RD-21 RD-23 RD-28 RD-40 southeastern Massachusetts used in development of the logistic regression equation for estimating the probability of a stream f estimating the probability equation for of the logistic regression used in development Massachusetts southeastern — Table 5. Table

42 A Logistic Regression Equation for Estimating the Probability of a Stream Flowing Perennially in Massachusetts Appendix A

.1473 .4121 .5778 .5141 0.7686 t p-value ﬁ 8 8 8 8 8 of freedom Degrees Akaike Information Information Akaike

goodness-of- robability of a stream of a stream robability 4.8962 7.2108 8.2218 6.6225 Hosmer and Lemeshow Hosmer and Lemeshow AIC: Chi- 12.0893 square <.0001 <.0001 <.0001 <.0001 <0.0001 p-value 1 4 3 2 5 of Score freedom Degrees , square root; <, actual value is less than value shown] value is less than <, actual value , square root; 1/2 Chi- nc., 1995; Squillace and others, 1999. and others, 1999. nc., 1995; Squillace 21.7610 72.0429 68.7859 62.9280 77.7929 square Analyses , cube root; 1/3 <.0001 <.0001 <.0001 <.0001 p-value <0.0001 1 4 3 2 5 of freedom Degrees Likelihood ratio Chi- 86.1994 80.8074 72.4206 22.9409 91.7166 square -2 Log 332.121 337.513 345.900 395.379 326.604 likelihood C .786 .774 .759 .641 0.790 AIC 345.513 351.900 399.379 338.604 342.121 1/2 1/2 ariables v Equation No. 1/3 1/3 1/3 1/3 and explanatory Summary statistics for selected logistic regression analyses tested for use in development of an equation for estimating the p the for estimating an equation of in development for use tested analyses regression logistic for selected statistics Summary rank correlation coefficient of predicted probabilities and observed responses. SCB, South Coastal Basin; responses. SCB, South probabilities and observed of predicted coefficient rank correlation C: Location (SCB or remainder of State) Mean basin slope Intercept Drainage area Location (SCB or remainder of State) Intercept Drainage area Location (SCB or remainder of State) Mean basin slope Areal percentage of stratified-drift deposits Intercept Drainage area Intercept Drainage area of State) Location (SCB or remainder Mean basin slope deposits Areal percentage of stratified-drift Drainage density Intercept Drainage area #4 #5 #3 #1 #2 flowing perennially in Massachusetts flowing perennially Criterion. Appendix A. Appendix I 1995; SAS Institute Eckhardt and Stackelberg, and Hirsch, 1992, p. 393–402; Collett, 1991; Helsel 1989; Lemeshow, [Hosmer and

Appendix A 45