base flow recession rates, low flows, and hydrologic features of small watersheds in pennsylvania,...

ABSTRACT: This paper examines the relationships between mea-surable watershed hydrologic features, base flow recession rates,and the Q7,10 low flow statistic (the annual minimum seven-dayaverage streamflow occurring once every 10 years on average).Base flow recession constants were determined by analyzing hydro-graph recession data from 24 small (<130 km2), unregulated water-sheds across five major physiographic provinces of Pennsylvania,providing a highly variable dataset. Geomorphic, hydrogeologic,and land use parameters were determined for each watershed. Thebase flow recession constant was found to be most strongly correlat-ed to drainage density, geologic index, and ruggedness number(watershed slope); however, these three parameters are intercorre-lated. Multiple regression models were developed for predicting therecession rate, and it was found that only two parameters, drainagedensity and hydrologic soil group, were required to obtain good esti-mates of the recession constant. Equations were also developed torelate the recession rates to Q7,10 per unit area, and to theQ7,10/Q50 ratio. Using these equations, estimates of base flowrecession rates, Q7,10, and streamflow reduction under droughtconditions can be made for small, ungaged basins across a widerange of physiography.(KEY TERMS: surface water/ground water interactions; base flow;recession; low flow; geomorphology; physiography.)

Brandes, David, Justin G. Hoffmann, and James T. Mangarillo, 2005. Base FlowRecession Rates, Low Flows, and Hydrologic Features of Small Watersheds inPennsylvania, USA. Journal of the American Water Resources Association(JAWRA) 41(5):1177-1186.

INTRODUCTION

Recurring drought conditions in the eastern UnitedStates (U.S.) over the past few years have tested theability of small watersheds in the region to sustainbase flow. Maintaining dry season flows is critical towater quality, wildlife habitat, and recreation, and

such “instream uses” must be considered in allocatingwater withdrawals (Nuttle, 2002). Regional regressionmodels are a standard tool for prediction of low flowstatistics (e.g., Q7,10, the annual minimum seven-dayaverage streamflow occurring once every 10 years onaverage) and have been widely reported in the litera-ture (e.g., Flippo, 1982; Vogel and Kroll, 1992). How-ever, estimation methods for base flow recession ratesand associated time scales have not received the sameattention. These recession time scales are importantto water resources management because they give anindication of how rapidly drought conditions arereached.

One reason that regional low flow models are usu-ally targeted at predicting streamflow statisticsrather than the recession rate is the observed vari-ability in the recession limb of storm hydrographs.Despite this variability, previous research has shownthat after sufficient time has passed (i.e., during lowflow conditions), base flow recession data generally fita constant log linear slope which defines the classical“master recession curve” (Nathan and McMahon,1990). This common feature of recession data is due tothe dominance of ground water discharge as the pri-mary base flow mechanism during drought conditions.

This paper examines the relationship betweenthese late time recession slopes and measurablewatershed hydrologic and geomorphic features for 24small (<130 km2), unregulated watersheds across fivemajor physiographic regions of Pennsylvania. Thegoals are to identify the dominant parameters control-ling low flow response, and develop low dimensionalequations based on these parameters for estimating

1Paper No. 04058 of the Journal of the American Water Resources Association (JAWRA) (Copyright © 2005). Discussions are open untilApril 1, 2006.

2Respectively, Assistant Professor and Former Students, Department of Civil and Environmental Engineering, Acopian Engineering Cen-ter, Lafayette College, Easton, Pennsylvania 18042 (E-Mail/Brandes: [email protected]).

JOURNAL OF THE AMERICAN WATER RESOURCES ASSOCIATION 1177 JAWRA

JOURNAL OF THE AMERICAN WATER RESOURCES ASSOCIATIONOCTOBER AMERICAN WATER RESOURCES ASSOCIATION 2005

BASE FLOW RECESSION RATES, LOW FLOWS, AND HYDROLOGICFEATURES OF SMALL WATERSHEDS IN PENNSYLVANIA, USA1

David Brandes, Justin G. Hoffmann, and James T. Mangarillo2

both the recession rate constant and the Q7,10 valuesfor ungaged watersheds. The underlying hypothesis isthat ground water discharge to streams is an inher-ently low dimensional phenomenon (i.e., involving fewindependent variables and parameters) that shouldrequire a correspondingly low dimensional predictivemodel.

BACKGROUND

Base Flow Recession Models

An exponential decay function has been used forfitting base flow recession data since the early 20thCentury (Hall, 1968)

Q(t) = Qoe-kt

where Q(t) is the flow rate during the recession period(m3/s), Qo is the flow rate at the beginning of reces-sion (m3/s), and k is the recession rate constant (unitsof 1/day). It can readily be shown that the exponentialrecession model corresponds to a linear base flow stor-age model Q = kS, where S represents watershed stor-age (m3).

Recession analysis is a well known technique inhydrology, and a variety of methods and models havebeen used to extract useful hydrologic informationfrom base flow recession curves (Hall, 1968; Nathanand McMahon, 1990; Tallaksen, 1995). Many investi-gators have concluded that a single exponential func-tion (thus a single storage reservoir) is notappropriate to describe base flow recession over a fullrange of hydrologic conditions (Tallaksen, 1995).Research has shown that the recession rate followinga storm event generally decreases with time, often fol-lowing several distinct stages that are thought to cor-respond to different drainage processes and/or flowpaths within the watershed (Barnes, 1939; Kunkle,1962). Individual storm recession curves may varydue to a variety of factors, such as differences in evap-otranspiration, antecedent soil moisture and groundwater storage conditions, differences in rainfall inten-sity and spatial distribution of rainfall, and differingcombinations of drainage processes from multiplestorage reservoirs (Riggs, 1964). However, for suffi-ciently long recession periods (on the order of a weekor more), streamflow recession from small watershedsgenerally approaches log linear behavior indicative ofan exponential decay process. Although Whittenberg(1999) has argued that unconfined aquifers behave asnonlinear reservoirs, work by Zecharias and Brut-saert (1988b) in the Appalachian Plateau and Vogel

and Kroll (1992) in Massachusetts indicates that thelinear reservoir model with exponential recession is agood approximation for small basins during low flowperiods.

Recession equations of the exponential decay formcan also be derived directly from ground water flowtheory. Rorabaugh (1964) and Brutsaert and Nieber(1977) showed that the solution for unsteady drainagefrom a horizontal aquifer to a stream follows an expo-nential recession with a rate constant (k) of the form

where K is the aquifer hydraulic conductivity (m/s),D is a representative aquifer depth(D), St is theaquifer storativity (dimensionless), and L is the hori-zontal distance from stream to divide (m). For slopingaquifers, a similar expression can be derived thatshows k to be proportional to aquifer slope (Zechariasand Brutsaert, 1988b). Thus, theoretical models showthat base flow recession is low dimensional, anddepends on both aquifer hydraulic properties (K, St)and aquifer geometry (D, L, slope). Conditions favor-ing slow recession are shallow aquifers with low con-ductivity and high storativity (low hydraulicdiffusivity), as well as wide areal extent and lowslopes. The difficulty in the direct application of thesetheoretical models is the question of how theseaquifer properties relate to measurable parameters atthe watershed scale.

Empirical Base Flow Research in Pennsylvania

Significant work has been done in Pennsylvania onrelationships between drainage basin hydrologic prop-erties and base flow. Hely and Olmsted (1963) studiedbasins of the Delaware River drainage, including por-tions of the Piedmont, New England, Valley andRidge, and Appalachian Plateaus Provinces. Theyfound that the Q90/Qavg ratio (the discharge exceeded90 percent of the time divided by the average dis-charge) was strongly related to basin geology, as rep-resented by the well yields of the various geologicformations comprising the basin. The dominant con-trol of watershed geology on base flow and streamflowrecession in a variety of other geomorphic settingshas been well described in the literature (Farvolden,1963; Knisel, 1963; Tallaksen, 1995).

Kowall (1976) found that streams from the Ridgeand Valley Province exhibited flatter recessions (i.e.,lower recession rates) than those of the AppalachianPlateau Province. Of 11 geomorphic characteristics

JAWRA 1178 JOURNAL OF THE AMERICAN WATER RESOURCES ASSOCIATION

BRANDES, HOFFMANN, AND MANGARILLO

(1)

k constK D

S Lt= 2

(2)

investigated, hypsometric integral, stream length,and drainage density were the most strongly correlat-ed parameters with Q90.

Flippo (1982) developed regional regression equa-tions for estimating annual low flow statistics ofPennsylvania streams, based on drainage area, pre-cipitation index (difference between annual precipita-tion and annual potential evapotranspiration), and ageologic index (GI). Building on the work of Hely andOlmsted (1963), Flippo developed the GI values forthe regression equations using well yield dataobtained from each bedrock unit (higher well yieldcorresponds to higher geologic index values). Theequations are best suited to watersheds with areas of50 to 500 mi2 (130 to 1,300 km2) (Flippo, 1982).

White and Sloto (1990) conducted frequency analy-sis on annual base flows per unit area (determined byhydrograph separation) for all Pennsylvania stream-flow gages, and summarized physical factors affectingbase flow volumes, including flow regulation, geology,climate, drainage area, and urbanization. Ehlke andReed (1999) recently determined Q7,10 values forgaged streams in Pennsylvania based on log-PearsonType III fitting and compared the results with theFlippo (1982) regression equations. Significant differ-ences were found in some regions of the state.

Zecharias and Brutsaert (1988a) used factor analy-sis to determine the geomorphic parameters mostclosely related to base flow for a dataset consisting of19 basins within the Allegheny Mountain region ofthe Appalachian Plateau. They found length of peren-nial streams, average basin slope, and drainage densi-ty to be most important to base flow in this particularregion. In their study, structural controls wereexplicitly removed by investigating basins within alimited geologic setting (Zecharias and Brutsaert,1988a). In a followup paper, they found that recessionconstants determined from hydrograph data correlat-ed well with basin slope, but not with basin conductiv-ity (K) (Zecharias and Brutsaert, 1988b).

Although much has been learned from these stud-ies regarding the dominant controls on base flow inthe region, practical methods for estimation of baseflow recession rates and time scales of small water-sheds are not currently available. Furthermore, therelationship between the recession rate and the wide-ly used Q7,10 statistic has not been investigated over arange of physiographic settings. This paper focuses onthese aspects of low flow analysis.

METHODS

Basin Selection

Streamflow data used in the study were chosenbased on four criteria. First, to provide a wide varietyof low flow responses, gages were selected from fivephysiographic provinces of Pennsylvania: Piedmont,Great Valley, Ridge and Valley, Appalachian Plateau,and Glaciated Appalachian Plateau. Second, to limitthe within basin heterogeneity of the watershedparameters (e.g., physiography and bedrock geology),watershed area was limited to 130 km2 (approximate-ly 50 mi2). Third, basins with significant knownanthropogenic influences, such as regulated reser-voirs, were eliminated from the study. Finally, ruralbasins were selected over urban or suburban locationsto limit the potential effects of discharges and leakagefrom water and sewer infrastructure and interbasintransfers. Using these criteria, 24 watersheds werechosen for analysis, as summarized in Table 1 andshown on Figure 1. Four of these were analyzed previ-ously by Zecharias and Brutsaert (1988b).

Recession Analysis

Fifteen hydrograph recessions were analyzed foreach flow gage to determine the recession constant.Winter season data (November through March) werenot used, to eliminate the possible effects of frozensoils and snowpack. Hydrographs identified for analy-sis were single peak hydrographs with recession peri-ods of at least one week. Flow data were log-transformed and linear regression was used to deter-mine the slope of the late time log-linear portion ofthe recession data, as in Moore (1992).

Watershed Descriptive Characteristics

For each watershed, six parameters relating to geo-morphology, three parameters relating to geology andsoils, and two parameters relating to land use weredetermined as described below. These parameters aresummarized in Table 2. The hypsometric integral aspreviously used by Kowall (1976) was not usedbecause values are not readily available for thisparameter. Furthermore, it is related to severalparameters that were included, such as GI andruggedness number.

All geomorphic parameters were determined fromU.S. Geological Survey (USGS) 7.5-minute (1:24000)topographic quadrangle maps (topo maps). The topomaps were obtained in digital form (PASDA, 2001)


BASE FLOW RECESSION RATES, LOW FLOWS, AND HYDROLOGIC FEATURES OF SMALL WATERSHEDS IN PENNSYLVANIA, USA

and were imported into AutoCAD 2000 (Autodesk,2001) for digitizing of the stream network (only peren-nial and intermittent streams shown in blue wereincluded). Total channel length (TCL), longest chan-nel length (LCL), drainage density (DD=TCL/A),basin relief (BR), ruggedness number (2*DD*BR), andbasin shape index (BSI=A/LCL2) were determinedbased on the digitized stream network. Relief andchannel slope were determined manually from thetopo maps, and contributing area (A) for each gage isgiven by the USGS (2001).

An area weighted GI was determined for eachbasin using the geologic map of Pennsylvania by Berget al. (1980) and the geologic formation indices (rang-ing from 0.3 to 6.0) developed for Pennsylvania byFlippo (1982). Data on hydrologic soil types for eachwatershed were taken from Natural Resources Con-servation Service county soil surveys. Hydrologic soilgroups identified as D, C, B, or A were assigned anindex from 1 to 4, respectively, and an area weightedindex (HSGI) was determined for each watershed(note that higher indices correspond to higherhydraulic conductivity, as for the GI). Soil depth datawere also obtained from the county soil surveys, andwere indexed (SDI) based on the range of valuesreported. Soil depth ranges of 0 to 50, 50 to 100, 100to 150, 150 to 200, and 200+ cm were assigned indexvalues of 1 to 5, respectively.



TABLE 1. U.S. Geological Survey StreamGages Used in the Study.

Area PhysiographicUSGS ID Gage Name (km2) Region

1428750 West Branch Lackawaxen 105.1 GAPRiver

1431673 Ariel Creek 40.4 GAP

1516500 Corey Creek 31.6 GAP

1552500 Muncy Creek 61.6 GAP

1545600 Young Womans Creek 119.6 AP

3011800 Kinzua Creek 120.1 AP

3026500 Sevenmile Run 20.3 AP

3037350 South Branch Plum Creek 86.2 AP

1549500 Blockhouse Creek 97.6 AP

1547700 Marsh Creek 114.2 AP

1542810 Waldy Run 13.6 AP

1449360 Pohopoco Creek 129.2 R&V

1555400 East Mahantango Creek 115.7 R&V

1557500 South Bald Eagle Creek 114.2 R&V

1613050 Tonoloway Creek 27.7 R&V

1452500 Monocacy Creek 115.2 GV

1573095 Bachman Run 18.9 GV

1569800 Letort Spring Run 55.9 GV

1457790 Cooks Creek 76.1 P

1473169 Valley Creek 53.9 P

1475850 Crum Creek 40.9 P

1479820 Red Clay Creek 73.3 P

1480500 West Branch Brandywine 118.6 PCreek

1480887 Valley Creek 37.5 P

Notes: GAP = Glaciated Appalachian Plateau; AP = Appalachian Plateau; R&V = Ridge and Valley; GV = Great Valley; and P = Piedmont.

Figure 1. Pennsylvania Physiography and USGS GagesUsed in the Study (base map from Pennsylvania Bureau

of Topographic and Geologic Survey, 2000).

TABLE 2. Summary of Watershed Hydrologic Parameters.

Parameter(units) Abbreviation Source

Basin Area (km2) A USGS

Drainage Density (/km) DD USGS 7-5 min topo quad

Basin Relief (km) BR USGS 7.5-min topo quad

Ruggedness Number RN Derived (2DD*BR)

Main Channel Slope CHS USGS 7.5-min topo quad

Longest Channel (km) LCL USGS 7.5-min topo quad

Basin Shape Index BSI Derived (A/LCL2)

Geologic Index GI Berg (1980, Flippo (1982)

Hydro Soil Group Index HSGI NRCS/SCS county soilmapping

Soil Depth Index SDI NRCS/SCS county soilmapping

Population Index PI 2000 U.S. Census

Forest Cover Index FCI USGS 7.5-min topo quad

As a surrogate for anthropogenic influences relatedto land development, a population density index (PI)was developed from the 2000 U.S. Census Bureaudatabase (U.S. Census Bureau, 2003) at the townshiplevel. For townships that overlapped the watershedboundaries, half of the township population wasassigned to the watershed. Densities of 0 to 10, 10 to100,100 to 1,000, 1,000 to 10,000, and more than10,000 persons/km2 were assigned indices of 5, 4, 3, 2,and 1, respectively. Finally, a forest cover index (FCI)was estimated based on green shaded areas shown onthe USGS topographic maps. Watershed forest coverpercentage ranges of less than 25 percent, 25 to 50percent, 50 to 75 percent, 75 to 90 percent, and morethan 90 percent were assigned index values of 1 to 5,respectively.

Statistical Analyses

The correlation matrix was used to determine the degree of correlation between the watershedparameters and the recession constants. To developpredictive relationships, backward stepwise multipleregression was used. The data were log-transformed(base 10) prior to analysis, as quantitative relation-ships between these parameters are typicallydescribed by power law functions of the form

where P1, P2, P3, and P4 are the watershed parame-ters and a, b, c, d, and e are values to be determinedby regression (Haan, 1977).

Intercorrelation among various watershed parame-ters is typical in these type of studies, and can lead toproblems such as irrational regression coefficients(Haan, 1977). Starting with the entire list of parame-ters used in developing the correlation matrix, param-eters that were highly correlated to several othersand not strongly correlated to the recession constantwere eliminated from consideration in the regressionmodel. The remaining variables were then fit with thelog-transformed regression equation. One parameterat a time was eliminated in a backward stepwiseregression starting with the parameter having thelowest t-statistic. Additional parameters were theneliminated until all remaining parameters were sig-nificant at p < 0.05 and the predictive power of theequation (as determined by the adjusted R2) began todecline.

RESULTS AND DISCUSSION

Recession Constants

A summary of the watershed descriptive parametervalues and recession constants is shown in Table 3.The dataset contains a wide range in values of thehydrologic parameters such as geologic index,drainage density, basin relief, and forest cover. Thebase flow recession constants vary from 0.027 to0.229/day with a mean of 0.110/day. Table 4 shows themean recession constants and time scales for eachphysiographic region. A clear trend with physiogra-phy is evident, in that base flow of AppalachianPlateau streams tends to recede rapidly (90 percentflow reduction within approximately two weeks), andthat of the Piedmont and Great Valley region streamsgenerally recede more slowly (90 percent flow reduc-tion in nearly eight weeks for the Great Valley). Thevalues for the Appalachian Plateau streams areslightly lower than those of Zecharias and Brutsaert(1988b), who included early time recession data intheir rate constant estimates. Ridge and Valleystreamflow generally recedes at intermediate rates,consistent with the findings of Kowall (1976).

Correlation Matrix

The correlation matrix based on the data of Table 3is shown in Table 5. Correlations above 0.5 are consid-ered significant, based on the t-test (McCuen, 1985).The recession constant (k) is positively correlatedwith drainage density, ruggedness number, and popu-lation index, and negatively correlated with geologicindex and hydrologic soil group. The recession con-stant is independent of both of the watershed sizeparameters (area and longest channel length). Thepositive correlations with drainage density andruggedness (basin slope) are consistent with the theo-retical models discussed previously, and the results ofZecharias and Brutsaert (1988a). Drainage densitycan be considered the reciprocal of the average dis-tance between streams within a basin (2L) (Zechariasand Brutsaert, 1988a). Therefore, Equation (2) indi-cates that k should increase with drainage density. Analternative conceptualization is that a high drainagedensity means that aquifers are able to drain readilyto the stream channel network, thus giving a large k.

The negative correlations between k and geologicindex, and k and hydrologic soil group appear incon-sistent with the theoretical models (Equation 2), in



k a P P P Pb c d e= 1 2 3 4 ..... (3)

that higher aquifer conductivity (K) and soil infiltra-tion rates theoretically correspond to higher recessionrates. However, Table 5 shows that high geologicindices generally correspond to low drainage densityand ruggedness values, which are associated with lowk values. This suggests that the negative correlationbetween k and geologic index may be an artifact ofintercorrelation.

The positive correlation of recession rate with pop-ulation index (the inverse of population density) isalso not expected, as development is thought toreduce recharge and base flow. However, becausealmost all of the more highly populated watershedsinvestigated are located in the Piedmont and GreatValley regions where recession rates are low, thisapparent relationship should not be interpreted ascausal.

Expected strong cross correlations also occurbetween the two size parameters: area and longestchannel length; the three slope parameters: basin



TABLE 3. Summary of Watershed Hydrologic Properties.

USGS k A DD BR LCLID (/day) (km2) (/km) (km) RN CHS (km) BSI GI HSGI SDI PI FCI

1428750 0.124(0.052) 105.1 0.900 0.427 0.769 0.0125 19.4 0.279 0.9 2.0 2.7 4 3

1431673 0.182(0.101) 40.4 0.922 0.126 0.232 0.0060 13.4 0.225 1.2 2.0 2.8 4 2

1516500 0.182(0.068) 31.6 0.923 0.341 0.629 0.0199 10.1 0.310 0.4 2.0 2.8 4 1

1545600 0.087(0.035) 119.6 0.915 0.437 0.800 0.0160 22.5 0.236 0.7 2.1 2.1 5 4

1552500 0.106(0.044) 61.6 1.048 0.420 0.880 0.0226 16.7 0.221 0.7 2.0 3.4 5 4

3011800 0.104(0.053) 120.1 1.028 0.204 0.419 0.0071 27.6 0.158 0.6 2.5 3.1 4 5

3026500 0.139(0.069) 20.3 1.289 0.159 0.410 0.0139 10.2 0.195 0.6 2.5 3.1 5 5

3037350 0.229(0.094) 86.2 1.625 0.159 0.517 0.0043 21.4 0.188 0.5 2.1 2.4 4 2

1549500 0.111(0.074) 97.6 1.091 0.398 0.868 0.0135 26.4 0.140 0.8 2.0 3.3 4 5

1547700 0.167(0.102) 114.2 1.193 0.488 1.164 0.0157 27.2 0.154 0.7 1.8 1.5 4 4

1542810 0.129(0.121) 13.6 1.300 0.341 0.887 0.0337 7.6 0.235 0.6 2.5 3.2 4 5

1449360 0.053(0.024) 129.2 0.814 0.406 0.661 0.0158 20.1 0.320 0.9 2.5 3.5 3 3

1555400 0.117(0.067) 115.7 1.146 0.373 0.855 0.0070 29.9 0.129 0.8 2.3 3.8 4 2

1557500 0.082(0.050) 114.2 1.044 0.490 1.023 0.0124 18.4 0.337 0.7 2.3 3.1 4 5

1613050 0.201(0.103) 27.7 1.396 0.453 1.265 0.0312 8.6 0.375 0.8 1.8 2.2 4 3

1452500 0.068(0.041) 115.2 0.704 0.209 0.294 0.0057 25.9 0.172 3.2 2.6 3.8 3 1

1573095 0.030(0.008) 18.9 0.584 0.172 0.201 0.0063 7.9 0.303 4.8 2.3 4.0 3 1

1569800 0.027(0.008) 55.9 0.282 0.079 0.045 0.0029 14.7 0.259 5.0 2.5 3.0 3 1

1457790 0.118(0.090) 76.1 1.012 0.261 0.528 0.0119 16.2 0.290 2.1 2.4 3.0 3 2

1473169 0.047(0.031) 53.9 0.938 0.186 0.349 0.0070 14.4 0.260 5.4 2.6 2.6 3 1

1475850 0.064(0.044) 40.9 1.233 0.117 0.289 0.0072 13.4 0.228 1.5 3.0 2.3 3 2

1479820 0.078(0.063) 73.3 1.270 0.110 0.279 0.0055 15.8 0.294 1.5 3.0 2.0 3 1

1480500 0.062(0.042) 118.6 0.800 0.218 0.349 0.0055 26.3 0.171 0.9 3.0 2.4 3 2

1480887 0.122(0.078) 37.5 1.022 0.145 0.296 0.0078 11.3 0.294 3.3 2.6 2.6 3 1

Note: For the recession constant (k), both mean and standard deviation (in parentheses) are shown.

TABLE 4. Base Flow Recession Rates and Time Scalesfor 50 Percent and 90 Percent Flow Reduction.

Mean k t0.5 t0.1Physiographic Region (1/day) (days) (days)

Glaciated Appalachian Plateau 0.148 04.7 15.6

Appalachian Plateau 0.138 05.0 16.7

Ridge and Valley 0.113 06.1 20.4

Piedmont 0.082 08.5 28.1

Great Valley 0.042 16.5 54.8

relief, ruggedness number, and channel slope; and thetwo land use indices: population and forest cover.

Multiple Regression

The high degree of intercorrelation among many ofthe watershed parameters indicates that a smallnumber of the parameters should be able to accountfor much of the variability in the recession rate con-stant, thus suggesting a low dimensional estimationmodel. Power law equations in the form of Equation(3), based on four, three, and two parameters, aregiven below.

k = 0.419 DD1.24 GI-0.226 HSGI-1.95 RN-0.319

adj R2 = 0.79

k = 0.504 DD1.38 HSGI-2.11 RN-0.216

adj R2 = 0.77

k = 0.406 DD1.09 HSGI-1.68

adj R2 = 0.70

In all three equations, DD is in /km and k in /day.Table 6 summarizes goodness-of-fit statistics forEquations (4) through (6) based on the original(untransformed) data. The fitted equations are slight-ly biased due to the log-transformation of the data(McCuen et al., 1990); however, the relative bias islow.

Figure 2 shows a comparison between the estimat-ed k values using these regression equations with theactual k values for all 24 watersheds. It is apparentthat as few as two parameters, drainage density andhydrologic soil group, can be used to estimate k forthese watersheds with reasonable accuracy, despitethe wide range in physiography represented. Theemergence of drainage density as the most importantparameter in determining k is not surprising, giventhat it is related to both permeability of the aquifermaterial (inversely), and the geometry of the aquiferswithin the watershed (Horton, 1932), both of whichare important controls on ground water flow from thewatershed. The inclusion of ruggedness number andgeologic index results in moderate improvements tofit and should improve prediction.



TABLE 5. Correlation Matrix of Watershed Parameters and Recession Constants.

k A DD BR RN CHS LCL BSI GI HSGI SDI PI FCI

k 1.000

A -0.066 1.000

DD 0.745 -0.061 1.000

BR 0.358 0.289 0.323 1.000

RN 0.616 0.187 0.709 0.896 1.000

CHS 0.455 -0.264 0.444 0.770 0.782 1.000

LCH 0.003 0.945 0.001 0.241 0.180 -0.300 1.000

BSI -0.160 -0.375 -0.144 -0.016 -0.080 0.242 -0.657 1.000

GI -0.698 -0.139 -0.608 -0.562 -0.703 -0.550 -0.198 0.241 1.000

HSGI -0.562 -0.010 -0.166 -0.594 -0.520 -0.491 -0.008 0.000 0.412 1.000

SDI -0.349 -0.187 -0.379 -0.038 -0.206 -0.025 -0.173 0.060 0.219 0.134 1.000

PI 0.601 -0.040 0.416 0.502 0.569 0.543 0.055 -0.247 -0.739 -0.635 -0.091 1.000

FCI 0.391 0.151 0.441 0.598 0.652 0.595 0.219 -0.272 -0.705 -0.358 -0.029 0.705 1.000

NOTE: Data were log-transformed (base 10) prior to analysis.

(4)

(5)

(6)

TABLE 6. Summary of Goodness-of-Fit Statisticsfor Fitted Equations (4) Through (6).

Equation Equation EquationStatistic (4) (5) (6)

Standard Error (Se) 0.0221 0.0242 0.0278

Error Ratio (Se/Sy) 0.41 0.45 0.52

R2 0.83 0.80 0.73

Adj R2 0.79 0.77 0.70

Bias (mean error) -0.0017 -0.0028 -0.0037

Rel Bias (percent) -1.5 -2.6 -3.4

Relationship Between Base Flow Recession Constantsand Q7,10

Because the Q7,10 streamflow value is probably themost widely used and tabulated statistic of low flow, itis desirable to be able to relate the watershed reces-sion constants to the Q7,10 values. Estimation equa-tions for Q7,10 sometimes include the recessionconstant as a model parameter (Vogel and Kroll, 1992;Kroll et al., 2004), which improves model accuracy butlimits its application in ungaged basins unless therecession constant can be independently determined.Therefore, the quantitative relationship betweenthese two parameters has practical significance. Q7,10values have previously been published for a subset ofthe study watersheds (Ehlke and Reed, 1999).

The Q7,10 value invariably depends on watershedarea, whereas the recession rate was shown above tobe independent of area. Kowall (1976) found that therecession constant was well correlated with the Q90value when the Q90 is defined on a per unit area basis[e.g., cubic meters per second (cms) per km2], thusimplying that low flow is proportional to drainagearea. Vogel and Kroll (1992) also found close to directproportionality of Q7,10 with watershed area in devel-oping the relationship between low flow statistics,drainage area, and recession constant of small water-sheds in Massachusetts.

Based on these considerations, two equations weredeveloped relating Q7,10 to the recession constants ofthe watersheds studied. The first is a power law fit ofQ7,10 per unit area versus recession constant. The sec-ond is a power law fit using a dimensionless low flowratio (LFR), defined as Q7,10/Q50, where Q50 is themedian streamflow value. This ratio describes thefractional reduction in streamflow from average todry conditions, and thus is a useful descriptor ofdrought sensitivity. Intuitively, both measures shouldbe inversely correlated with recession rate (i.e., highrecession rates give low Q7,10 per unit area and lowLFRs).

Figures 3 and 4 show the data and fitted equations,and Table 7 gives a summary of goodness-of-fit statis-tics for both equations, based on the original(untransformed) data. The fitted equations are as fol-lows.

Q7,10 = 0.0000567k-3.041 R2 = 0.89

LFR = 0.000175k-2.545 R2 = 0.84

where the Q7,10 is in cms per 100 km2. These equa-tions can be used with Equations (4) through (6) toestimate Q7,10 and fractional reduction in streamflowunder drought conditions. Caution should be observedin applying the equations for k < 0.05 /day, as Q7,10and LFR become highly sensitive to k in this region.



Figure 2. Comparison of Measured and Modeled Base FlowRecession Constants Using the Two-Parameter (DD andHSGI), Three-Parameter (DD, HSGI, and RN), and Four-

Parameter (DD, GI, HSGI, and RN) Regression Equations.

(7)

(8)

Figure 3. Power-Law Fit of Q7,10 Per Unit Area(cms/100 km2) Against the Recession Constant.

Q7,10 data from Ehlke and Reed (1999).

CONCLUSIONS

Recession rates of 24 gaged streams located acrossfive physiographic provinces of Pennsylvania werefound to vary with physiography. AppalachianPlateau streams generally have high recession ratesand low Q7,10/Q50 ratios, and thus are more sensitiveto drought conditions than those in the Great Valleyand Piedmont regions. These broad spatial variationsin recession rate are due to differences in watershedgeomorphology, geology, and soils; In particular,drainage density, landscape slope (ruggedness num-ber), bedrock geology, and soil infiltration rate (hydro-logic soil group) have the most influence on recessionrate.

The high degree of cross correlation among thewatershed parameters as well as the results of multi-ple regression demonstrate that only two parameters,drainage density and hydrologic soil group, are neces-sary to estimate base flow recession constants forthese watersheds. The equations developed here areexpected to provide first-order estimates of recessionrates, drought sensitivity, and Q7,10 values for smallwatersheds in areas of similar geomorphology, geolo-gy, and climate. However, they have not yet been test-ed and thus require further investigation as to theirpractical limits. For example, highly urbanized basinswere explicitly avoided and thus may not recede aspredicted by these relationships.

ACKNOWLEDGMENTS

The authors are grateful to Dru Germanoski for his suggestionsin the early phases of this research and his review comments. Twoanonymous reviewers provided additional comments that improvedthe final paper.

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Error Ratio (Se/Sy) 0.37 0.4

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Rel Bias (percent) -0.8 -4.4

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