estimation of geomorphically significant flows in alpine streams of the rocky mountains, colorado...

REGULATED RIVERS: RESEARCH & MANAGEMENT

Regul. Ri6ers: Res. Mgmt. 15: 273–288 (1999)

ESTIMATION OF GEOMORPHICALLY SIGNIFICANT FLOWS INALPINE STREAMS OF THE ROCKY MOUNTAINS, COLORADO (USA)

NICOLA SURIANa AND E.D. ANDREWSb,*a Uni6ersity of Pado6a, Dipartimento di Geologia, Paleontologia e Geofisica, Via Rudena 3, 35123 Pado6a, Italy

b U.S. Geological Sur6ey, 3215 Marine Street, Boulder, CO 80303, USA

ABSTRACT

Streamflows recorded at 24 gauging stations in the Rocky Mountains of Colorado were analyzed to derive regionalregression equations for estimating the natural flow duration and flood frequency in reaches where the natural flowsare unknown or have been altered by diversion or regulation. The principal objective of this analysis is to determinewhether the relatively high, infrequent, but geomorphically and ecologically important flows in the Rocky Mountainscan be accurately estimated by regional flow duration equations. The region considered in this study is an area ofrelatively abundant runoff, and, consequently, intense water resources development. The specific streams analyzedhere, however, are unaltered and remain nearly pristine.

Regional flow duration equations are derived for two situations. When the mean annual discharge is known, flows]10% of the time can be estimated with an uncertainty of 99% for the 10% exceedance flow, to 911% for the 1.0%exceedance flow. When the mean annual discharge is unknown, the relatively high, infrequent flow can be estimatedusing the mean basin precipitation rate (in m3/s), and basin relief with an uncertainty of 923% for the 10%exceedance flow to 921% for the 1.0% exeedance flow. The uncertainty in estimated discharges using the equationsderived in this analysis is substantially smaller than has been previously reported, especially for the geomorphicallysignificant flows which are relatively large and infrequent. The improvement is due primarily to the quality ofstreamflow records analyzed and a well-defined hydrologic region.

KEY WORDS: regional streamflow analysis; flow duration; floods; regression equations; alpine streams; ungauged sites; RockyMountains; Colorado

INTRODUCTION

Hydrological and geomorphological studies, as well as effective management of water resources, fre-quently require streamflow information at locations where gauging station records do not exist. Thus,methods and procedures to estimate streamflow magnitude and duration at ungauged sites are essential.A regional analysis of streamflow attempts to extend existing records in space, and transfer streamflowcharacteristics recorded at gauging stations to ungauged sites (Riggs et al., 1980). The principal objectiveof this study was to determine whether the relatively high, infrequent, but geomorphically and ecologicallyimportant flows can be accurately estimated by regional flow duration equations in the Rocky Mountainsof Central Colorado. Regional regression equations will be derived to estimate streamflow duration andflood frequency in high mountain streams ]2300 m in the Rocky Mountains.

This study considers a region with relatively high runoff and abundant water resources. The regioncontributes more than 20% of the entire runoff of the Colorado River, although it represents B2.5% ofthe drainage area. Over the past century, the water resources of this region have been extensivelydeveloped through the construction of many reservoirs and transbasin diversions. Most streams with

* Correspondence to: U.S. Geological Survey, 3215 Marine Street, Boulder, CO 80303, USA. E-mail: [email protected]

Contract/grant sponsor: University of PadovaContract/grant sponsor: US Forest Service, Stream Technology Center, Ft. Collins, Colorado

This article is a US government work andis in the public domain in the United States.

Recei6ed 10 October 1997Re6ised 13 July 1998

Accepted 11 August 1998

N. SURIAN AND E.D. ANDREWS274

drainage areas \50 km2 have been significantly affected by flow depletion, artificial regulation, oraugmentation. The streamflow records analyzed here were collected primarily to facilitate additionalwater development. For a variety of reasons, water development has occurred in nearby basins, while thestreams studied have remained unaltered.

Bankfull discharge is the flow sufficient to overtop the banks of a natural channel and begin to spreadacross the floodplain. It is the discharge of incipient flooding. Although discharges within a relativelynarrow range above and below the bankfull stage typically occur B5% of the time, they are geomorphi-cally significant. Wolman and Miller (1960) investigated the relative importance of flow magnitude andfrequency on geomorphic effectiveness. They showed that most of the sediment transported by a streamover a period of years is carried by discharges that were equalled or exceeded by an average of severaldays per year. Andrews and Nankervis, (1995) analyzed bed-material transport past 17 gauging stationsin the Rocky Mountains of Central Colorado. On average, 80% of the mean annual bed-material load wastransported by discharges between 0.8 and 1.6 times the bankfull discharge, which occurred 15 days/year.In addition to their geomorphic importance, the highest several days of flow each year in these mountainstreams are also geochemically and biologically significant (Hornberger et al., 1994; Williams et al., 1996).These studies demonstrate the necessity of flow duration information, because knowledge of floodmagnitude and frequency alone are insufficient to understand the geomorphic processes that form andmaintain a stream channel over time. This analysis will develop equations for estimating the duration ofnatural, unimpaired flows, especially the relatively infrequent, but geomorphically significant, higher flowsin ungauged or briefly gauged stream reaches, as well as those reaches affected by regulation anddepletion.

Regional flood frequency relationships using physiographic and climatic characteristics as predictivevariables have been developed for most of the United States (Jennings et al., 1994). In contrast, relativelyfew studies have investigated the regionalization of flow duration information (Murdock and Gulliver,1993). Furthermore, the geographical extent of the hydrologic regions is limited, and studies typically haveemphasized relatively low flows. Kircher et al. (1985) developed regional flow duration equations forwestern Colorado. Their analysis concerned primarily the frequently occurring low-to-intermediatedischarges and covered relatively diverse watersheds. In addition, many of the streamflow records wereaffected to some degree by depletions, and therefore did not represent natural conditions. Standard errorsfor estimated discharges with durations from 10 to 90% of the time were large, varying from 45 to 59%.The purpose of this study was to refine and extend the current knowledge of flow duration characteristics.

STUDY AREA

The drainage basins selected for study are in the Rocky Mountains of Colorado, in a region approxi-mately 180 km long and 60 km wide (Figure 1). The region includes the Front Range, the Gore Rangeand the Elk Mountains. All the drainage basins are within the Upper Colorado Basin, except MichiganRiver and Middle Boulder Creek, which are in the Platte River Basin, and Halfmoon Creek, which is inthe Arkansas River Basin. The maximum elevations of the watersheds range from 3701 to 4399 m, andthe minimum elevations range from 2495 to 3167 m (Table I).

The region is underlain by a diverse bedrock geology (Tweto, 1979). For example, the north-easternslope of the Gore Range is composed of metamorphic and intrusive igneous rocks (gneiss, schist andgranite), whereas the south-western slope is mainly composed of sedimentary rocks (sandstone and shale).Most of the watersheds were glaciated, and glacial deposits are widespread in many basins down to about2400 m, the lower limit of glacial expansion during the Late Pleistocene. At present, hillslopes arerelatively stable compared to other mountain regions having similar relief, and erosion rates, typicallyB10 t/km2 per year, are small.

The spatial distribution of precipitation in Colorado is strongly influenced by relief and aspect (Doeskinet al., 1984). Precipitation increases significantly with elevation, typically doubling between 2500 and 3500m. Furthermore, the western side of a mountain range receives significantly more precipitation than the

Published in 1999 by John Wiley & Sons, Ltd. Regul. Ri6ers: Res. Mgmt. 15: 273–288 (1999)

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Table I. Hydrologic and drainage basin characteristics of selected streams

CS PNumberPeriod of AStation name HminU.S.G.S. Hmax DurationR QbkfE RunoffS CL Qmof years (mm) (m3/s)(km) (%)(m) (m3/s)(m)record of Qbkf(m)(km2) (m)station

(water years)number (%)

4.0 3167Michigan River nr. 3805 638 3440 0.496 3.7 0.109 1100 0.08 57 0.70 1.806614800 1974–1994 21Cameron Pass

93.8 2495 4083 1588 3170 0.319 21.9 0.0601908–1994 69006725500 1.51 72 9.50 1.787Middle BoulderCreek at NederlandHalfmoon Creek 48 61.1 2996 4399 1403 3600 0.517 14.3 0.066 700 0.81 58 7.08 0.407083000 1947–1994nr. Malta

14.2 3179 4131 952 3600 0.407 6.0 0.042 990 0.29 63Botail Creek nr.09034900 1966–1994 29Jones Pass

21.3 2771 3804 1033 3290 0.342 7.2 0.0931966–1994 86029 0.27 45 1.83 2.4Darling Creek nr.09035800Leal

29 70.7 2728 3888 1160 3320 0.384 19.8 0.037 850South Fork 0.90 46 8.36 0.309035900 1966–1994Williams Fork nr.Leal

47 149.4 2841 4349 1508 3480 0.379 15.91943–1946, 0.051 850 1.71 41 12.09 1.2Snake River nr.090475001952–1994Montezuma

Keystone Gulch nr. 37 23.6 2850 3782 932 3350 0.315 10.0 0.076 740 0.17 3009047700 1958–1994Dillon

28 22.2 2883 3988 1105 3440 0.484 9.5 0.0861967–1994 1000Boulder Creek at 0.48 65 1.1209052400upper station nr.Dillon

28 36.8 2755 4029 1274 3320 0.495 13.7 0.0921967–1994 1000 0.72 5909052800 Slate Creek atupper station nr.Dillon

09052400 35 38.9 2667 4029 1362 3440 0.554 10.5 0.094 1200 0.89 57Black Creek below 1943–1949,Black Lake nr. 1997–1994Dillon

31.1 2623 4099 1476 3290 0.368 12.6 0.075 1000 0.56 56 1.4109055300 281697–1994Cataract Creek nr.Kremmling

09058500 38 33.7 2787 4099 1312 3320 0.499 15.0 0.0491948–1954, 1000 0.69 62 2.43 9.9Piney River belowPiney Lake nr. 1964–1994Minturn

1965–1994 30 9.4 2882 3860 978 3140 0.227 6.6 0.099 870 0.12 46 0.58 6.7East Meadow09058800Creek nr. Minturn

22.7 2791 3701 910 3320 0.280 6.8 0.0361965–1994 88030 0.24 36 0.84 8.3Wearyman Creek09063200nr. Red Cliff

61.6 2718 3701 983 3290 0.303 10.6 0.057 860 0.62 36 2.69 6.6Turkey Creek nr.09063400 1964–1994 31Red CliffGore Creek at 1948–1956, 2621 4017 1396 3380 0.440 11.1 0.07240 1000 0.83 6837.309065500

1964–1994upper station nr.Minturn

40 32.6 2789 3853 1064 3290 0.309 9.3Black Gore Creek 0.051 840 0.47 53 3.29 3.21948–1956,090660001964–1994nr. Minturn

11.8 2629 3950 1321 3380 0.565 7.4 0.1341964–1994 96031 0.28 76 1.04 8.9Bighorn Creek nr.09066100Minturn

13.8 2598 3990 1392 3350 0.533 8.1 0.122 1000Pitkin Creek nr. 0.32 71 2.44 1.309066150 1967–1994 28Minturn

15.6 2537 3975 1438 3320 0.518 7.2 0.1491965–1994 99030 0.34 67 3.27 0.9Booth Creek nr.09066200Minturn

31Red Sandstone 19.0 2808 3767 959 3260 0.259 8.7 0.081 870 0.25 47 3.22 0.409066400 1964–1994Creek nr. Minturn

83.4 2774 4348 1574 3510 0.453 14.0 0.0551970–1994 950Castle Creek abv. 1.22 47 4.45 6.52509074800Aspen

25Maroon Creek 91.7 2658 4315 1657 3510 0.562 15.5 0.062 1000 1.90 6309075700 1970–1994abv. Aspen


eastern side. Accordingly, mean annual precipitation varies substantially among the watersheds used inthe investigation, from 690 mm in Middle Boulder Creek drainage basin to 1200 mm in Black Creekdrainage basin. The average value of mean annual precipitation for the 24 drainage basins studied is 930mm.

The main source for winter precipitation is the Pacific Ocean, whereas the primary source of moisturefor spring and summer thunderstorms is the Gulf of Mexico. In winter, almost all precipitation falls assnow. At the highest elevations (\4000 m) the mean monthly temperature is below 0°C for 8–9 monthsof the year; whereas at lower elevations (about 2500 m) the mean monthly temperature is below 0°C for4–5 months of the year. Because mean monthly temperatures are below freezing for many months eachyear, precipitation falling as snow accumulates throughout the winter. Accordingly, runoff is relativelylow for most of the year, except during the period from May to July, when snowmelt occurs. Figure 2compares the mean monthly runoff for four of the 24 selected streams. This region is hydrologicallyhomogeneous and a similar distribution of runoff occurs at all streams. Four streams (Middle BoulderCreek, Slate Creek, Bighorn Creek and Maroon Creek) were chosen to describe the variability that existsamong the selected drainage basins due to differences in drainage area, geology and location. These fourexamples (Figure 2) have a similar distribution of runoff throughout the year; June is the month withhighest runoff, while the lowest runoff occurs in February.

Figure 1. Map showing the location of streamflow gauging stations selected for analysis


ESTIMATION OF GEOMORPHICALLY SIGNIFICANT FLOWS 277

Figure 2. Graph showing mean monthly discharge of four examples from the selected streams: Middle Boulder Creek, Slate Creek,Bighorn Creek and Maroon Creek

METHODS

The purpose of this study was to develop methods for estimating the duration of natural streamflows atungauged sites, as well as at gauged sites where the natural regime of streamflow has been altered bydepletion and/or artificial regulation. All watersheds in the Rocky Mountains of Central Colorado with20 or more years of gauged streamflows were carefully examined to determine whether streamflows werenatural and unaltered in quantity and temporal distribution. Only those gauging stations where stream-flows were unaffected by depletion or artificial regulation were used for the analysis. Most of the streamsused for this study receive runoff from natural lakes, and are affected to some degree by naturalregulation. The 24 streamflow records selected for this study are listed in Table I, including the gaugingstation name, number and period of record. Summary information describing the drainage basin,physiography, and hydrology is also shown in Table I.

In general, the utility and precision of a regression model will be improved by considering as manygauging stations as possible with long, concurrent periods of record (Helsel and Hirsch, 1992). In practice,however, a trade-off exists between including as many sites as possible, and insuring that the periods ofrecords are concurrent (Fennessey and Vogel, 1990). The average period of record of the 24 selected



gauging stations is 34 years; the shortest is 21 years (Michigan River) and the longest is 87 years (MiddleBoulder Creek) (Table I). Six of the 24 selected stations (Boulder Creek, Slate Creek, Black Creek,Cataract Creek, Castle Creek, and Maroon Creek) were discontinued in September 1994.

The streamflow records analyzed in this study are unique. We have been unable to identify ageographical area of comparable extent with as many long, continuous streamflow records for drainagebasins in nearly pristine hydrologic condition. Twenty-two percent of the combined drainage areas of the24 basins studied is designated as Wilderness Area administered by the U.S. Forest Service. Withrelatively few exceptions, the drainage basins do not have paved roads, buildings, or permanenthabitation. Only one basin, the Snake River near Montezuma, has a permanent settlement. In the past,mining and/or logging have occurred in parts of many of the drainage basins, but neither activity isongoing to any appreciable degree in any basin. The primary human activity in all basins is recreational,especially hiking, camping and skiing.

The selected gauging station records were retrieved from the WATSTORE database, maintained by theU.S. Geological Survey (U.S.G.S.). Observed daily mean discharges for the entire period of record arearranged by magnitude from largest to smallest. The duration of a given discharge is computed from therank ordered sequence. The length of gauging station records varies from 21 to 87 years, and the durationtables are computed from 7665–31755 daily observations. Records of annual peak discharge are analyzedfollowing the guidelines of the U.S. Water Resources Council (1981). These guidelines recommend fittingthe logarithms of the annual peak discharges to a Pearson Type III distribution using the methods ofmoments for parameter estimation.

Previous studies have evaluated a number of physical attributes to predict streamflows at ungaugedsites. Jennings et al. (1994) summarized published regional regression equations for estimating floods andfound 17 different watershed and climatic characteristics used in these studies. The three most frequentlyused attributes were drainage area, main-channel slope and mean annual precipitation. In developingregional flow duration models, however, only a few physiographic and climatic variables have generallybeen tested. Dingman (1978) used drainage area and mean basin elevation, Mimikou and Kaemaki (1985)used drainage area, mean annual precipitation, basin relief fall and length of the main river channel, andFennessey and Vogel (1990) used drainage area and basin relief.

The following eight physiographic and climatic characteristics were compiled and considered for thisstudy (Table I). Two characteristics (basin relief and mean annual precipitation) were specificallydetermined for this study, whereas the other characteristics were available from an existing data base(Richter et al., 1984). Basin characteristics were defined as follows.

1. Drainage area (A), in km2, is the area upstream of the gauging station site.2. Basin relief (BR), in m, is the difference in elevation between the highest and the lowest points in the

drainage basin determined from the 1:24000 U.S.G.S. topographic maps.3. Mean basin elevation (E), in m, was measured on 1:24000 U.S.G.S. topographic maps by overlaying

a grid such that at least 25 intersections were within the basin boundary, and then determining theaverage elevation at the several intersections.

4. Mean basin slope (S), is a dimensionless variable calculated by determining 25 or more slopesmeasured at points on an equally spaced grid overlain on 1:24000 U.S.G.S. topographic maps.

5. Channel length (CL), in km, was calculated from topographic maps as the distance along the primarychannel from the gauging station to the basin divide.

6. Channel slope (CS), is a dimensionless variable, calculated by measuring the slope between two points,10 and 85% of the distance along the main channel from the gauging station to the basin divide.

7. Mean annual precipitation (P), in mm, was determined using an isohyetal area-weighted method fromthe map of Colorado average precipitation, 1951–1980 (Doeskin et al., 1984).

8. Mean annual discharge (Qm), in m3/s, was determined from the gauging station streamflow records.

A ninth basin characteristic, the mean basin precipitation rate in m3/s computed as the product of themean annual precipitation times the basin area divided by the number of seconds in a year, was computedfrom the characteristics listed above.



The objective of this study was to develop regional flow duration equations which could be applied toestimate the discharge with a given duration, particularly the relatively infrequent, geomorphicallysignificant discharges, at an ungauged stream, a gauged stream with a relatively short period of record,or a gauged stream where flow is affected by regulation. Regional flow duration equations were derivedby fitting information from a network of 24 streamflow records using a stepwise multiple regressionanalysis.

Even in a hydrologically homogeneous region such as that considered in this study, precipitation doesnot explain all of the variations in streamflow, because of geologic, geomorphologic, and climaticdifferences among the basins. By using other physiographic characteristics as predictive variables in theregression equations, streamflows can be estimated more precisely, even if the underlying physicalprocesses (i.e. evapotranspiration, infiltration, etc.), influencing runoff are not directly represented. Theapproach used to derive the best multiple regression equation was a stepwise procedure involving asequence of partial F or t-tests to evaluate the significance of each independent variable.

Multiple linear regression is a useful approach when the objective is to predict a certain hydrologicvariable as accurately as possible. However, when using several predictive variables and a stepwiseprocedure, there is a risk of building models which are physically difficult to interpret (Wallis, 1965). Thelikelihood of such an outcome can be reduced by using a small number of predictive variables which havea clear physical relationship with the predicted hydrologic process. Our objective was to obtain a modelthat estimates streamflows as accurately as possible, but also has a plausible physical interpretation.

An ordinary-least-squares regression procedure was used for this study. Alternative regression proce-dures exist, however, e.g. weighted-least-squares (Tasker, 1980) and generalized-least-squares (Stedingerand Tasker, 1985). The weighted-least-squares procedure takes into account the unequal record lengths atgauging stations, whereas the generalized-least-squares procedure takes into account both unequal recordlengths and cross-correlations among concurrent flows. Because the streamflow records selected for thisstudy are relatively long and concurrent, the ordinary-least-squares procedure was considered to besuitable for this study (Stedinger and Tasker, 1985; Vogel and Kroll, 1990).

RESULTS AND DISCUSSION

Flow duration

The observed duration of streamflows at a given gauge can be normalized by dividing the variousdischarges by the mean annual discharge. The duration of normalized streamflows recorded at the 24gauging stations selected for this study is compared in Figure 3. The conventional method for plottingflow duration information using log-probability and logarithmic scales distorts the relative area underthe curves. In fact, the area under each curve is identical—a stream with relatively large low-flows hasrelatively small high-flows, the converse also being true. The flow duration curves shown in Figure 3cross over one another at flows that were equalled or exceeded between 5 and 20% of the time. Forstreamflows that were equalled or exceeded B30% of the time, the streams show remarkably similarnormalized flow durations. For example, the discharge that was equalled or exceeded 2.0% of the time(approximately the bankfull discharge) is six times the mean annual discharge, with a mean difference of912%. For streamflows that were equalled or exceeded \30% of the time, distinct differences amongthe watersheds are apparent, and they become increasingly significant at progressively lower flows. Theclose agreement among the flow duration relationships at relatively high flow suggests that the genera-tion of snowmelt runoff is similar throughout the study area. In contrast, watershed characteristics suchas geology, soil thickness, and vegetation cover differ significantly, resulting in large differences in thefrequent, low flows.

The streamflows with a given observed duration from 0.1 to 40% of the time are shown in Figure 4 asa function of the mean annual discharge. Least-squares linear regressions have been fit to the log-trans-formed values for selected durations. The regression coefficients and standard errors are listed in TableII. As shown above, mean annual discharge is a very good predictor of discharges that were equalled or



exceeded B30% of the time. For the eight relationships shown in Figure 4, the coefficients ofdetermination, R2, range from 0.95 to 0.99. For discharges with a duration of B30% of the time, thestandard errors range from 9 to 17%. The durations of bankfull discharges listed in Table I vary from 0.3to 9.9% of the time. The average duration of bankfull discharge is 3.8% of the time for the 16 gaugingstations, which receive relatively small contributions of runoff from lakes and ponds.

With this analysis, we have shown that given the mean annual discharge, the duration of the bankfulldischarge at a specific location can be estimated with a standard error of about 910%. The uncertaintyin the estimated infrequent, high streamflows is substantially less than has been reported in previousstudies. The regression relationships listed in Table II and described above are useful in situations wherethe mean annual discharge is known, but the duration of naturally occurring high discharges is poorly, or

Figure 3. Graph showing duration of streamflows of the selected streams; discharges are expressed as the ratio to the mean annualdischarge



Figure 4. Graph showing comparison of streamflows having a duration from 0.1 to 40% with mean annual discharge

wholly, unknown. Such conditions are quite common and occur at gauging stations where streamflowsare regulated by reservoir storage. The regression relationships can be used to estimate the magnitude ofstreamflows with various durations that would have occurred without regulation.

Regional flow duration equations can also be used to improve estimates of relatively infrequentdischarges at gauging stations with fewer than 10 years of records. With relatively short streamflowrecords (510 years), the uncertainty in the mean annual discharge is much less than the uncertainty inthe infrequent discharges, (i.e. flows that are equalled or exceeded less than 5% of the time). As the periodof record increases from approximately 10 to 20 years, uncertainty in the estimation of small durationflows improves more rapidly than does the uncertainty in the mean annual discharge. Accordingly, abetter estimate of the magnitude of flows with small durations can be obtained from short gauging

Table II. Regression coefficients and statistics for regional flow duration equations (Q40

to Q0.1) using mean annual discharge as the predictor.

ln Qp=b+a1 ln Qm

b a1 R2 S s (%)Qp

1.186Q40 0.95 0.225 23−0.833170.1710.971.182−0.333Q30

0.141 140.980.360 1.154Q20

Q10 0.986 0.99 0.090 91.1321.534 0.935Q5 0.98 110.1061.736Q3 110.1050.980.920

0.98 0.111 11Q1 2.008 0.8920.95 0.164 16Q0.1 2.354 0.849



Table III. Regression coefficients and statistics for regional flow duration equations(Q99 to Q50) using mean basin precipitation

ln Qp=b+a1 ln(PA/t)

Qp b a1 R2 S s (%)

Q99 −3.269 1.177 0.85 0.406 43Q97 −3.081 1.175 0.88 0.356 37Q95 −3.033 1.203 0.88 0.364 37Q90 −2.912 1.170 0.88 0.363 37Q80 −2.690 1.173 0.89 0.336 35Q70 −2.487 1.159 0.90 0.315 33Q60 −2.284 1.167 0.90 0.328 34Q50 −1.989 1.196 0.92 0.293 30

records by using the observed mean annual discharge and the regional flow duration equations shown inTable II than one would be likely to obtain solely from the record of observed flows. For example,considering all possible consecutive 5-year records at Middle Boulder Creek at the Nederland gauge(1908–1994), the standard error in estimating the 1.0% exceedance discharge was 98.0% using theregional flow duration relationship. Estimating the 1.0% exceedance discharge based solely on relativelyshort periods of recorded streamflows, however, would have yielded a significantly larger standard errorof 913%. Over the 80 possible consecutive 5-year periods, observed flows equalled or exceeded 1.0% ofthe time (Q1.0) varied from 8.46 to 14.2 m3/s. In contrast, calculation of Q1.0 using the regional flowduration relationship gave estimated magnitudes from 9.1 to 12.70 m3/s. When the entire period of recordis considered, however, the regional flow duration relationship slightly overestimated the magnitude ofQ1.0, giving a value of 10.9 m3/s compared to the observed value of 10.5 m3/s.

Precise estimates of the mean annual discharge are frequently unavailable. In such circumstances,regional flow duration equations using mean annual discharge as a predictor cannot be applied.Accordingly, an alternative set of regional flow duration equations were developed which use precipitationand drainage basin characteristics as predictors. As described above, the significance of the several basincharacteristics was evaluated using a stepwise multiple regression approach. An independent variable was

Table IV. Regression coefficients and statistics for regional flow duration equations(Q40 to Q0.1) using mean basin precipitation and basin relief as predictors in

Qp=b+a1 ln(PA/t)+a2 ln BR

a2 R2 SQp b a1 s (%)

0.92 0.293 301.187Q40 −1.5740.987 0.989 0.95 0.243 24−8.606

0.90 0.327Q30 −1.074 1.157 340.2530.941.236 250.907−9.862

0.85 0.380Q20 −0.367 1.096 390.93 0.269 27−11.574 0.778 1.5770.86 0.313Q10 0.511 0.937 32

231.242 0.2320.930.686−8.3170.87 0.291 30Q5 0.945 0.8950.91 0.238 24−6.205 0.692 1.0060.88 0.277Q3 1.157 0.885 290.920.939 0.229 230.695−5.515

0.867 0.89 0.251Q1 251.448210.2110.930.8280.700−4.436

0.840 0.90 0.236Q0.1 241.8230.694 0.726 0.93 0.204 20−3.335



Figure 5. Graph showing comparison of observed and computed flow durations using regional relationships at four gaugingstations: Middle Boulder Creek, Slate Creek, Bighorn Creek and Maroon Creek

included in the regression equation only when the absolute value of the t-ratio was \2.0. The best fitequations for the frequently exceeded streamflows, Q99 to Q50, are summarized in Table III. Only meanbasin precipitation rate is a statistically significant predictor of the frequently exceeded streamflows, Q99

to Q50. None of the other basin characteristics provided much predictive value. This result is notunexpected, since the basin characteristics considered are not indicative of the shallow groundwatersystem which largely controls the magnitude of the relatively frequent, low streamflows. Bedrock lithologyand the extent of alluvial and colluvial material would most likely be better predictors of low magnitudes.The shortcomings involved with using basin morphology to estimate streamflows have been previouslyrecognized (Riggs et al., 1980; Dingman, 1984). The mean standard error of estimate varies from 943%for discharges equalled or exceeded 99% of the time, to 930% for discharges equalled or exceeded 50%of the time.

Regional flow duration equations for the less frequently exceeded streamflows, Q40 to Q0.1, aresummarized in Table IV. Mean basin precipitation rate explains most of the variation in magnitude of the



Table V. Regression coefficients and statistics for the regional flood frequency equa-tions (Q1.25 to Q10)

ln Qt=b+a1 ln(PA/t)+a2 ln BR

Qt b a1 a2 R2 S s (%)

Q1.25 1.295 0.888 – 0.79 0.398 42−6.455 0.672 1.092 0.84 0.357 37

Q2 1.627 0.849 – 0.81 0.358 37−5.233 0.658 0.967 0.85 0.324 33

Q5 1.946 0.800 – 0.81 0.330 34−4.088 0.632 0.850 0.85 0.302 31

Q10 2.107 0.770 – 0.81 0.321 33−3.511 0.613 0.792 0.85 0.297 31

shorter duration streamflows. Basin relief is also a significant predictor, and provides a moderatelyimproved estimate of the less-frequent streamflows. The standard error of the regional flow durationequations vary from 27% for Q40 to 20% for Q0.1. The standard errors are roughly twice as large as thestandard errors for the flow duration equations derived by using mean annual discharge as the predictor,as can be seen in Table II. A fairly consistent trend towards decreasing standard error with decreasingflow duration is shown in Tables III and IV. Accordingly, the magnitude of relatively infrequent, highflows can be predicted more accurately than can be expected for frequent low flows. This result isconsistent with observations elsewhere in the continental United States (Thomas and Benson, 1970).

Observed and computed flow durations for four streams are compared in Figure 5. In general, thecomputed flow durations are in good agreement with the observed durations. The shape of durationcurves can be used to compare hydrologic and geologic characteristics of different drainage basins(Dingman, 1984). The slope of the relationship is related to streamflow variability, a steeper slopeindicating higher variability. The upper parts of the four curves in Figure 5 are not very steep, as is typicalof streams with high flows coming from snowmelt. The lower part of the curves are generally related togeologic characteristics of the basins, especially their capacity to retain shallow groundwater. Forexample, the lower portion of the Maroon Creek curve is flatter than that of Bighorn Creek. Thisdifference suggests that the Maroon Creek basin has a higher storage capacity. In fact, Maroon Creek hasa wider valley bottom, and more extensive alluvial deposits than Bighorn Creek.

Basin relief is an important characteristic of fluvial systems which influences the movement of waterand sediment (Schumm, 1977). Given the relation between basin relief and average slope of the basin(Strahler, 1950) as well between basin relief and the slope of the main channel (Leopold et al., 1964), someinfluence of basin relief on streamflow characteristics should be expected. In fact, basin relief and meanannual discharge are positively correlated, R2=0.75. Thus, one might expect that basins with higher reliefwould have greater discharge. This result arises, however, because drainage area has not been considered.When the basin relief ratio (the ratio of basin relief to basin length) is considered, the largest dischargesare associated with lower relief ratios.

Table VI. Regression coefficients and statistics for the regional flood frequency equa-tions (Q25 to Q100)

ln Qt=b+a1 ln(PA/t)

b s (%)Qt SR2a1

0.317Q25 332.276 0.735 0.800.711 0.79 0.318 33Q50 2.3830.688 0.77 0.320 33Q100 2.478



Figure 6. Graph showing relative magnitude (peak discharge/mean annual flood) and temporal distribution of floods: MiddleBoulder Creek (�), Slate Creek (�), Bighorn Creek (�), and Maroon Creek ( )

Flood frequency

For completeness, regional flood frequency equations were determined for the 24 gauging stationsstudied. As with flow duration analysis, a stepwise procedure was used to derive multiple regressionequations to estimate flood frequency at ungauged sites. The stepwise analysis resulted in two sets ofregression equations; floods with recurrence intervals from 1.25 to 10 years were predicted using meanbasin precipitation and basin relief (Table V), whereas for floods with recurrence intervals from 25 to 100years only mean basin precipitation rate was significant (Table VI). Considering all the equations, R2

varied from 0.77 to 0.85, and the standard errors varied from 31 to 37%. It is noteworthy that in thesimple linear regression, the coefficient of the predictive variable varies consistently with flood frequency.The coefficient (a1) is always B1 and varies inversely with flood recurrence interval, e.g. a1=0.888 forQ1.25 and a1=0.688 for Q100. Thus, flood magnitude at given recurrence intervals is relatively smaller forlarger basins, especially for infrequent floods.

Temporal distribution and relative magnitude (peak discharge/mean annual flood) of floods for fourstreams (Middle Boulder Creek, Slate Creek, Bighorn Creek and Maroon Creek) are shown in Figure 6.Floods occur from May to the beginning of August, and June is the month with the highest concentrationof floods. Floods are primarily the result of snowmelt, rather than rainfall runoff. Consequently, the rangeof flood discharges is extremely small. Most annual peak discharges are less twice the mean annual peakdischarge. Floods having an estimated recurrence interval of 100 years are typically less than 2.5 times themean annual flood magnitude (Pitlick, 1994).



CONCLUSIONS

The Rocky Mountains of Central Colorado contribute more than 20% of the entire runoff of theColorado River, although it represents less than 2.5% of the drainage area. Over the past century, thewater resources of the region have been extensively developed by the construction of many reservoirsand transbasin diversions. Rivers and streams throughout the region have been significantly affectedby flow depletion, artificial regulation, or augmentation. In this study, regional regression equationswere developed to estimate the natural flow duration and flood frequency throughout the RockyMountains of Colorado at ungauged reaches, or where the natural flow regime has been altered bydiversion or regulations. Regression equations were derived from 24 relatively long-term gaugingstation records ranging from 21 to 87 years. Contributing drainage area varies from 4 to 149 km2,basin relief varies from 638 to 1660 m. and mean annual precipitation varies from 690 to 1230 mm.Eight climatic and geomorphic basin characteristics were evaluated for significance as predictors usinga stepwise multiple regression approach. Mean annual discharge is the best predictor, with no otherbasin characteristic significantly improving the estimate of flow magnitudes having durations from 0.1to 30% of the time. Uncertainty in the estimated flows varies from 917% for the 30% flow ex-ceedance to only 99% for the 0.1% flow exceedance. The uncertainty in estimated discharges usingthe equations derived in this analysis are substantially smaller than has been previously reported,especially for the geomorphically significant flows that are relatively large and infrequent. To obtainsimilar levels of uncertainty from a gauging station would typically require more than 10 years ofrecords. The improvement is due primarily to the quality of streamflow records analyzed and awell-defined hydrologic region.

Where the mean annual discharge is poorly known, flows that are equalled or exceeded B30% ofthe time can be estimated from regression equations using mean basin precipitation rate and basinrelief as predictors. Uncertainty in the estimated flows varies from 924% for the 40% flow ex-ceedance to 920% for the 0.1% flow exceedance.

Only mean basin precipitation rate is a statistically significant predictor of the frequently equalled orexceeded streamflows, Q99 to Q50. Standard errors of the estimated flows vary from 943% for the99% exceedance flow to 930% for the 50% flow exceedance. Thus, the uncertainty in estimatingrelatively frequent flows is substantially greater than would be expected for the relatively infrequentflows. This analysis shows that the geomorphically significant flows, which transport most of thesediment load over a period of years and maintain the bankfull channel, can be estimated quiteaccurately throughout the Rocky Mountains of Colorado using regional equations.

ACKNOWLEDGEMENTS

This research was conducted while the first author was a visiting scholar at the Boulder Laboratory ofthe US Geological Survey with a post-doctoral fellowship provided by the University of Padova.Additional financial support was contributed by the US Forest Service, Stream Technology Center, Ft.Collins, Colorado. The authors are grateful for this generous support. John Potyondy and two anony-mous reviewers made many helpful suggestions which were greatly appreciated.

APPENDIX A. NOTATION

A drainage areaCL channel lengthCS channel slopeE mean basin elevationHmin minimum elevation of the drainage basinHmax maximum elevation of the drainage basin



P mean annual precipitationQbkf bankfull dischargeQm mean annual dischargeQma mean annual floodQp average daily streamflow with exceedance probability pQt flood-peak discharge having t-year recurrence intervalBR basin reliefR2 coefficient of determinationS mean basin slopes standard error of the regressiont time

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estimation of geomorphically significant flows in alpine streams of the rocky mountains, colorado...

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