Journal of Hydrology 414–415 (2012) 364–373

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Journal of Hydrology

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On the behaviour of dynamic contributing areas and flood frequency curvesin North American Prairie watersheds

Eghbal Ehsanzadeh a,c,⇑, Christopher Spence a, Garth van der Kamp a, Brian McConkey b

a National Hydrology Research Centre (NHRC), Environment Canada, 11 Innovation Boulevard, Saskatoon, SK, Canada S7N 3H5b Soil and Water Conservationist, Agriculture and Agri-Food Canada, Swift Current, SK, Canada S9H 3X2c Faculty of Agricultural Engineering, Ilam University, Pazhouhesh Blvd., P.O. Box 69315-516, Ilam, Iran

a r t i c l e i n f o

Article history:Received 19 March 2011Received in revised form 31 July 2011Accepted 3 November 2011Available online 12 November 2011This manuscript was handled by AndrasBardossy, Editor-in-Chief, with theassistance of Erwin Zehe, Associate Editor

Keywords:Contributing areaCanadian PrairiesReturn periodWetlandsFlood frequency curves

0022-1694/$ - see front matter � 2011 Elsevier B.V. Adoi:10.1016/j.jhydrol.2011.11.007

⇑ Corresponding author at: Faculty of AgriculturalPazhouhesh Blvd., P.O. Box 69315-516, Ilam, Iran.

E-mail addresses: eehsanzadeh@gmail.com,(E. Ehsanzadeh).

s u m m a r y

This statistical study examines the impact of storage upon the frequency and magnitude of runoff in thehummocky glacially transformed landscape of the Canadian Prairies. When runoff production is unaf-fected by depressions, the shape of the runoff frequency curve resembles the shape of the precipitationfrequency curve, adjusted for the effects of infiltration, evaporation, sublimation, and wind redistributionof snow. However, the shape and slope of the runoff frequency curve can be affected by storage thresh-olds associated with hillslope and wetland depressions, and reflect the number, size and spatial distribu-tion of depressions in the catchment. A comparison of runoff frequency curves from catchments with orwithout depressions provides a useful indicator of the amount of water retained by surface depressionswithout recourse to detailed topographic mapping of the basins. Results obtained from this study providevaluable insights into the complex function of closed and intermittently contributing drainage basins.

� 2011 Elsevier B.V. All rights reserved.

1. Introduction

Drainage area is regarded as the most observable and readilyobtainable characteristic of a basin. However, in regions such asthe semi-arid Canadian Prairies, where past glaciations have pro-duced a hummocky landscape, numerous depressions have thecapability to retain a great deal of water which may or may notbe released to contribute to runoff at the outlet of the watershed.It is not only the extent and distribution of these depressions butalso the antecedent storage held within them that control the areacontributing streamflow to the basin outlet. Stichling and Blackwell(1957) were the first to identify that in the Prairie landscape, tem-poral and spatial dynamic contributing areas can lead to substantialvariation in runoff. Since their initial attempt to stimulate researchinto contributing areas in this landscape, only a few studies relevantto this issue have aimed at defining the impact of various thresholdson Canadian Prairie runoff frequency and magnitude. The mecha-nisms by which surface water is retained or released downstreamare of particular importance for agriculture, industry, and ecosys-tems of the Prairie region. Furthermore, transport of sediment

ll rights reserved.

Engineering, Ilam University,

e.ehsanzadeh@mail.ilam.ac.ir

and nutrients to downstream lowlands or lakes due to occasionalcontributions from isolated depressions impact the soil and waterquality in this region. Understanding the relative behaviour ofhow watersheds retain water and its constituents is important forsound water resource management decision making.

Following an investigation of the hydrology of a Prairie slough,Woo and Rowsell (1993) suggested that surface water connectionsbetween wetlands are better described as a probability event withsome distribution over time and space rather than as absoluteevents being present or absent. Leibowitz and Vining (2003), work-ing in wetlands in North Dakota, USA, too hypothesised that surfacewater connections could be evaluated by their probability distribu-tions over time and space. Studies in other landscapes (i.e. Sivapa-lan, 2005; Lee et al., 2007; McGrath et al., 2007; Kusumastuti et al.,2007; Kusumastuti et al., 2008; Zehe and Sivapalan, 2009) also ad-dress the issue of storage and thresholds and their impact on runoffand flood frequency curves. Nevertheless, the majority of reportedinvestigations in the literature are based on small scale field studiesor model experiments.

For example, McGrath et al. (2007) analytically derived statisticsof the temporal dynamics of runoff generation mediated by rainfallintensity and soil moisture thresholds. The timing of triggering andthe magnitude of the events were related to one another throughsoil moisture storage. Kusumastuti et al. (2007) used a stochasticrainfall model to investigate the effects of catchment storage

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thresholds upon runoff behaviour, and their impact upon flood fre-quency. They showed that changes in runoff generation mecha-nisms associated with a given threshold are manifested in theflood frequency curve as a break in slope. Kusumastuti et al.(2008) conducted a study to illustrate the effects of spatial organi-sation of lake chains and associated storage thresholds upon differ-ent catchment response characteristics including flood frequency oflake overflows. They used a multiple bucket model of the lake chainsystem which incorporated three storage thresholds: a catchmentfield capacity threshold that governs catchment subsurface storm-flow, a total storage capacity threshold that governs catchment sur-face runoff, and a lake storage capacity threshold that determineslake overflow. The study suggested the crucial role of factors relat-ing to lake organisation, such as the average catchment area to lakearea (AC/AL) ratio and the distribution of AC/AL with distance in thedownstream direction.

The results of these studies highlight the importance of thresh-olds on the catchment response behaviour and provide insightsinto the complex interactions between rainfall variability andthreshold nonlinearities in the rainfall–runoff process, which areshown to have a significant impact on the resulting flood frequencycurves. The potential for use of long term historical runoff data tocharacterise the observed runoff response to a dynamic contribut-ing area, however, has not been fully addressed. Of key interest isto develop a statistical methodology that can account for complex-ity in contributing area using readily available streamflow data.Sophisticated models are of limited value to the practising hydrol-ogist because data requirements and boundary condition estab-lishment often cannot be met (Card, 1979). Sivapalan (2005)emphasises the use of patterns in the observations to characterisethe underlying process controls instead of using observations tocalibrate complex models that are based on small-scale theories.Physically based, distributed models have the disadvantage of de-tailed data requirements and conceptual lumped or semi-distrib-uted models suffer from the lack of physical basis (Lee et al.,2007). In recognition of the disadvantages of using either of thesemodelling approaches, it may be useful to explore how readilyavailable streamflow data can be used to characterise variabilityin contributing areas. This is in contrast to other recent theoreticalstudies of connectivity between depressions which are based onthe topography of the landscape but make little or no referenceto long term observations. Struthers and Sivapalan (2007) sug-gested that intra-catchment storage thresholds would be reflectedin a catchment runoff frequency curve. This may provide a usefulapproach to characterise the behaviour of dynamic contributingareas in the semi-arid Prairie pothole landscapes in North America.

The objective of the research summarised here was to deducecontributing area processes and variation in North American Prairiewatersheds through patterns observed in flood frequency curves.We propose that the traits of these curves can be used to deducethe relative importance of storage capacity and contributing areavariation for runoff frequency among different watersheds. We in-tend to demonstrate that variable contribution from surface depres-sions can be identified using historic runoff data. This could be alsodone by a simple plot of runoff against precipitation. However, var-iable antecedent moisture conditions which introduce strong com-plexity and nonlinearity to the watershed response make this adifficult task. We focus on the spring snowmelt runoff period be-cause this is the main source of runoff in the prairie region (Fanget al., 2010). The proposed statistical approach is not intended to ad-dress the year-to-year variability of runoff/precipitation ratioswhich are affected by many complex processes including anteced-ent moisture conditions, snow relocation, runoff over frozen soils,and the time sequence of the snowmelt. All the catchments chosenfor analysis are located in the undulating terrain, with many closeddepressions which is typical of the glaciated plains of North America.

2. Data and study area

2.1. Central Saskatchewan region

Spring runoff data from the St. Denis National Wildlife Area(SDNWA) located 45 km east of Saskatoon, Canada (Fig. 1) were se-lected for this study because the actual extent of the contributingwatersheds were mapped out by extensive field surveys duringthe snowmelt runoff of 2006. The SDNWA is typical of an undulat-ing Canadian Prairie landscape with an unorganised drainage net-work. The SDNWA contains over 100 depressions, some of whichhave been extensively researched (e.g. Woo and Rowsell, 1993;Hayashi et al., 1998a,b; Su et al., 2000; Hayashi and van der Kamp,2000; Conly and van der Kamp, 2001; Hayashi et al., 2003; van derKamp et al., 2003; Spence, 2007; van der Kamp and Hayashi, 2009).The topography of the SDNWA is typically marked by small depres-sions interspersed with hills of low relief ranging in elevation from550 to 570 masl. Soils are dominated by Dark Brown Chernozemsand Orthic Regosols, both developed from glacial till. Roughly100 m of clay rich glacial till of low permeability lies under thesoils. The SDNWA is under partial cultivation of wheat and alfalfa.Permanent grass occurs on several hillslopes and aspen is commonin larger depressions. The climate is predominantly semi-arid andis characterised with long cold winters followed by short warmsummers. The 30 year annual mean temperature is 1.7 �C and themean annual precipitation is 352 mm (Woo and Rowsell, 1993).

The focus of this study is on snowmelt driven events becausemost of the annual runoff is generated during the spring freshet.Within the SDNWA, water level data collected from 1969 to 2007for two ponds (Pond 90 and Pond 109) using the methods de-scribed in Conly and van der Kamp (2001) were selected for anal-ysis (Table 1). During the period of record these ponds did notspill to lower elevations so that runoff volume entering the pondscan be deduced from differences in pre- and post-snowmelt waterlevels. Snowmelt runoff from the catchment was defined as thedifference in the water volume of the pond in the previous fallimmediately before freeze-up and the water volume at the timeof the first water level measurement in spring, which is timedeach year to be done soon after the snowmelt runoff ends, asjudged by the disappearance of the last snowdrifts. This usuallyfalls in mid to late April but sometimes occurs in early May inyears of heavy snow accumulation and late spring thaw. This cal-culation of snowmelt runoff does not account for losses of waterfrom the ponds by evaporation and infiltration after the lastwater-level measurement in the fall and before the measurementin spring and thus will underestimate the total runoff to theponds. Due to the low permeability of the underlying clay-richdeposits (Van der Kamp and Hayashi, 1998), however, the infiltra-tion loss can be expected to be rather small. The error associatedwith this methodology is estimated to be less than 10–20% for thelarge semi-permanent ponds and may be as much as 40% forsmall ephemeral ponds, with maximum errors in years of littlesnowmelt runoff preceded by drying out of the ponds duringthe previous years. As a percentage, the possible error is smallestfor years of high runoff. The volume of water stored in each pondwas obtained from observed water depths and a depth-volumerelation developed by Hayashi and van der Kamp (2000). Runoffvolumes were converted to runoff depths by dividing by the grossdrainage area as defined with a Lidar derived DEM with a resolu-tion of 1 m and a vertical accuracy of 0.15 m. Areas contributingrunoff to Pond 90 and Pond 109 were mapped visually throughan on-foot field campaign during the spring melt of 2006 (Shaw,2010). These pond-based runoff data from the SDNWA are in-cluded in this paper because they represent a rare example ofPrairie watersheds for which the contributing areas have been di-rectly measured.

Fig. 1. The study area and the location of selected sites/watersheds within the region. The abbreviations used in the top left box are as follows: AB (Alberta), SK(Saskatchewan), and MB (Manitoba). The station names corresponding to the station IDs are as follows: Magnusson Creek (05MA021), Brightwater Creek (05HG002),Ironspring Creek (05MA012), Romance Creek (05MA016), Jumping Deer Creek (05JK004), and Rushlake Creek (05JC004). The solid square in Saskatchewan province indicatesthe location and the extent of the study area.

366 E. Ehsanzadeh et al. / Journal of Hydrology 414–415 (2012) 364–373

For comparison, spring runoff data from a number of Water Sur-vey of Canada Hydrometric Database (HYDAT, 2010) gauges werealso analysed (Fig. 1). Spring runoff was estimated as the sum of dai-ly discharges from January 1 to April 30 of each year. In central Sas-katchewan, Magnusson Creek (05MA021), Ironspring Creek(05MA012), Romance Creek (05MA016), Brightwater Creek(05HG002), and Jumping Deer Creek (05JK004) hydrometric stationswere selected. These watersheds have the longest record lengthsconcurrent with the SDNWA water level observations with fewestnumber of missing data during the record period. The longest andshortest record periods belong to Jumping Deer Creek (68 years)and Romance Creek (43 years), respectively. For consistency, onlythe observations concurrent to the SDNWA data (1969–2007) wereretained in this study. The ratio of effective drainage area (the per-centage of drainage basin which contributes to the outlet runoff un-der the watershed median precipitation) for the selected watershedsranges from 87% for Magnusson Creek to 9% for Jumping Deer Creek(Table 1). Spring runoff in the selected stations was obtained bydividing the summation of recorded discharge to the gross drainagearea of the corresponding watersheds. Data of total winter (Novem-ber–April) precipitation were obtained for Environment Canada’sSaskatoon A synoptic station �45 km west of SDNWA from onlinesources (http://www.climate.weatheroffice.gc.ca/climateData/can-ada_e.html). Winter precipitation at Saskatoon has been measuredwith weighing gauges with attached wind shields.

2.2. Swift Current region

The Swift Current study area lies in the high plains region of theGreat Plains of North America about 270 km south-west of

Saskatoon (Saskatchewan), Canada. Land use in south-westernSaskatchewan is predominantly treeless cropland interspersedwith smaller areas of perennial forages. Agriculture and Agri-FoodCanada has monitored runoff from three rectangular fields (5 haeach approximately) near Swift Current, Saskatchewan since1962. The topography of the gauged area is gently undulating withland slopes of 0–2%. A full description of these representative sitesand runoff measurement techniques is provided in McConkey et al.(1996). Runoff data for only one of these fields, Plot 3, were se-lected because the data for the adjacent plots are unreliable duringwet years when inflow from surrounding fields overtops the lowberms that surround the plots and create uncertainty in the sizeof the area contributing to runoff. Only Plot 3 data are not affectedby such inflows. The plot is sloped in a northwest direction withsome minor relief but with no significant surface storage. Runoffresponse of Plot 3 can be impacted by local soil conditions and in-ter-annual variability of cultivation/fallow patterns. Moreover,snow drifting from/to the plot may have some impacts upon runoffresponse. The observation period in Swift Current site (Plot 3)spans from 1962 to 2008 (46 years) but no measurement was per-formed in 1970. Runoff discharge measurements in this plot aredivided by the drainage area in order to obtain runoff depth in aunit drainage area, and are used as the best available example ofhillslope runoff in this region of Prairies.

In the Swift Current region, Rushlake Creek (WSC station05JC004) was selected for comparison based on the record period,quality of data, and proximity to Plot 3. Rushlake Creek discharge re-cords start from 1966 and extend to 2008 (43 years). The commonperiod of 1966–2008 in the Swift Current region was considered inthis study. The total November–April (NOV–APR) precipitation

Table 1A summary of hydro-physical characteristics of the ponds/watersheds used in the study.

Region/site Variable

Grossa

drainage basinarea (ha)

Effectivea

drainage area(ha)

Effectiveb

drainage arearatio

Surfacec

depressionarea ratio

Averaged annualprecipitation(mm)

Averaged winter/spring precipitation(mm)

Averaged

snowmeltrunoff (mm)

Recordperiod

Recordlength

St. Denis Wildlife AreaPond 90 1085 – – 0.24 345 92 1.4 1969–

200840

Pond 109 8.4 – – 0.21 345 92 5 1969–2008

40

Central SaskatchewanMagnusson

Creek(05MA021)

12,100 8600 0.87 – 345 92 28 1969–2008

40

IronspringCreek(05MA012)

57,174 31,695 0.55 – 345 92 15 1969–2008

40

RomanceCreek(05MA016)

53,717 20,626 0.38 – 345 92 11 1969–2008

40

BrightwaterCreek(05HG002)

90,000 28,800 0.22 – 345 92 5 1969–2008

40

Jumping DeerCreek(05JK004)

171,500 15,491 0.09 – 345 92 1 1969–2008

40

Swift CurrentPlot 3 4.9 4.9 1.00 0 368 96 23 1966–

200843

RushlakeCreek(05JC004)

32,500 24,900 0.81 – 368 96 14 1966–2008

43

a The presented gross and effective drainage areas are based on Prairie Farm Rehabilitation Administration (PFRA, 2010) report.b The effective drainage area ratio is defined as the ratio of the effective drainage area to the gross drainage area of the watershed.c The surface depression area ratio is defined as the percentage of the catchment area occupied by surface depressions.d The mean values for precipitation and runoff data are based on 1969–2007 and 1966–2007 observation periods for central Saskatchewan and Swift Current regions,

respectively.

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records for the Swift Current region were obtained from the Environ-ment Canada’s Swift Current CDA synoptic station about 1 km southof the Agriculture and Agri-Food Canada plots which uses the samemethodologies as the Saskatoon A station described above.

The data used in the study were tested for independent andidentically distributed (iid) conditions (independence, stationarity,and homogeneity). The nonparametric Mann–Kendall (MK) statis-tical test (Mann, 1945; Kendall, 1975) was used to assess the sta-tionarity of the sample data. The Wald and Wolfowitz (1943)independence test was used to verify the independence of theobservations and the Wilcoxon (1945) rank sum test was used toevaluate the homogeneity of the time series.

3. Methodology

The return period, or recurrence interval, is of great importancefor statistical analysis of time series. The mean of intervals be-tween two discharges each equal to or greater than a given oneis the return period (Gumbel, 1958). The probability of a value lar-ger than runoff, x, or probability of exceedance of that runoff, P(x),is defined as:PðxÞ ¼ 1� FðxÞ ð1Þwhere F(x) is the probability of nonexceedance (i.e., the probabilityof a value equal or smaller than x). The theoretical return period,T(x), is the inverse of the probability that the event will be exceededin any 1 year:TðxÞ ¼ 1=PðxÞ ¼ 1=ð1� FðxÞÞ ð2Þ

Plotting positions were used as estimates of F(x). The rank valueof the mth (ascending) ordered variate was used to determine an arti-ficial plotting position, F(m), for that variate. This is the controversial

part of the method as there is no single definitive formula or equa-tion for plotting positions. The choice of an optimum plotting posi-tion depends on the purpose for which the results are to be usedand may also depend on the underlying distribution (Harter,1984). More than ten plotting position formulae have been sug-gested in the literature (Guo, 1990). Most of suggested models arein the form of (Blom, 1958; Cunnane, 1978; Harter, 1984):

FðmÞ ¼ m� a=ðnþ 1� 2aÞ ð3Þ

where m is the rank of the variate, a is a constant usually rangingfrom 0 to 1, and n is the sample size. Hydrologists concerned withthe return period (theoretical recurrence interval) of floods or otherhydrologic events have usually favoured the Weibull (1939) plot-ting position (Harter, 1984). For the Weibull’s plotting positionthe constant a in Eq. (3) is set to zero. The employment of Weibullplotting position has received some support (e.g. Gumbel, 1943,1958) as well as some criticism (e.g. Kimball, 1946; Cunnane,1978) in the literature. Determination of the unbiased value of ain Eq. (3) has been the subject of a number of studies in the litera-ture. For example, for the natural events represented by a two-parameter gamma distribution the value of a is set to 2/5 (Blom,1958; Harter, 1984) and for those represented by normal and twoparameter log normal (LN2) distributions an a of 3/8 has been sug-gested (Blom, 1958; Cunnane, 1978; Harter, 1984). If the underlyingmechanism of the variable under study is represented using generalextreme value then a equal to 0.44 provides the best estimate of theprobability of nonexceedance (Cunnane, 1978; Guo, 1990).

In this study we tested the most commonly used probability dis-tribution functions in hydrology (Ehsanzadeh et al., 2010) includingextreme value Type 1 (EV1) also known as Gumbel, extreme valueType 2 (EV2) also known as Frechet, Halphen Type A (HA), Halphen

368 E. Ehsanzadeh et al. / Journal of Hydrology 414–415 (2012) 364–373

Type B (HB), Halphen inverse Type B (HIB), two parameter log nor-mal (LN2), gamma (G), inverse gamma (IG), and log Pearson Type 3(LP3) to define the most appropriate underlying distribution of pre-cipitation data. A range of available parameter estimation methodswas used to find the best distribution/parameter estimation combi-nation for each of precipitation sample data. The Akaike Informa-tion Criterion (AIC) (Akaike, 1977) and the Bayesian InformationCriterion (BIC) (Schwarz, 1978) were used to identify the modelthat fits the observational data with the lowest uncertainty.

No effort was made to define the underlying probability densityfunction of runoff data used in this study. This decision was madefor two main reasons. First, the runoff samples used in the studymay not represent the real population from which they come. Thisis due to the fact that the contributing areas may have not reachedtheir maximum extents during the observation period for some ofthe watersheds. Secondly, and again owing to the dynamic natureof contributing areas, the underlying mechanism of runoff eventsfor different return periods may be described the best by a mixtureof distributions (rather than a single distribution) and identifyingthese is beyond the scope of this study. Cunnane (1978) states thatif a single simple distribution free plotting position is required thenan a equal to 2/5 (Eq. (3)) would be the best compromise. This sug-gestion has been found acceptable to many hydrologists (King,1981; Harter, 1984; Guo, 1990). As such, we define the plotting po-sition of runoff samples using the following equation:

FðmÞ ¼ ðm� 2=5Þ=ðnþ 1=5Þ ð4Þ

To link the contributing area to the catchment frequency curvesa simple quantile-return period curve (referred to as a frequencycurve) of precipitation events was constructed making use of theunbiased plotting positions identified through frequency analysis.The runoff frequency curves were constructed on the basis of run-off data for watersheds with small to large depression storageemploying the distribution free plotting position. The return period(Eq. (2)) was plotted on a logarithmic scale as the abscissa againstobserved runoff (x) traced on an arithmetic scale as the ordinate.Depending on the density function of the observations, the curvex = F (logT(x)) can have a concave or convex shape. In addition,the runoff production behaviour of different landscapes in re-sponse to precipitation inputs was explored using precipitation–runoff quantile–quantile (Q–Q) plots.

4. Results

4.1. Exploratory data analysis

Pond 109 generally experienced higher runoff than Pond 90(Table 1, Fig. 2a), because for Pond 109 the fraction of the gross

Fig. 2. Time series of precipitation and runoff in the selected sites: (a) snowmelt runoSaskatoon airport and snowmelt runoff in WSC gauging stations in central Saskatchewa

drainage area that is depression-free and contributes hillslope run-off directly to the pond even in dry years, about 10% (Hayashi et al.,1998a,b), is much larger than for Pond 90 (about 1%). Runoff inMagnusson (Jumping Deer) Creek was the highest (lowest) com-pared to other hydrometric stations (Fig. 2b) reflecting the large(small) ratio of effective to gross drainage area (Table 1). The aver-age November–April precipitation for 1969–2007 in the Saskatoonregion was 92 mm. Comparable precipitation at Swift Current was96 mm. Rushlake Creek and Plot 3 tended to produce similar runoffwith average spring runoff from Rushlake Creek and Plot 3 of 14 and22 mm, respectively (Fig. 2c, Table 1). All the data used in the studypassed the homogeneity and the stationarity tests. The indepen-dence assumption was not satisfied by the runoff data from Iron-spring and Jumping Deer Creeks and also Pond 90 in the SDNWAindicating that the observations in these catchments are seriallycorrelated. It is therefore assumed for the purpose of this paper thatthere have been no major changes in the catchments due to drain-age, land-use changes, or long-term climate change.

Based on both AIC and BIC, a G distribution fitted using a max-imum likelihood (ML) parameter estimation method was found tobe the most appropriate probability density function to describethe underlying mechanism of precipitation data from SaskatoonA. Therefore, the value of a in the plotting position formula [Eq.(3)] was set to 2/5. A two parameter log normal (LN2) distribution(fitted using the ML parameter estimation method) was identifiedas the best model to represent the Swift Current CDA precipitationdata based on both AIC and BIC. Thus, a constant (a) of 3/8 [Eq. (3)]was chosen for the plotting position of precipitation in the SwiftCurrent CDA.

4.2. Runoff response

The statistical approach introduced in this study examines ba-sin runoff response from the perspective of the long term overallregime and do not indicate runoff ratios for a given magnitude ofwinter precipitation on a deterministic year by year basis. It ratherdescribes statistical behaviour over the period of record. On a sta-tistical basis, as reflected in Q–Q and return period plots, the snow-melt runoff response to winter precipitation of Pond 109catchment is muted until precipitation inputs exceed 75 mm(Fig. 3a) upon which runoff increases disproportional to precipita-tion. There is no or little runoff response from the Pond 90 catch-ment at precipitation amounts under 100 mm. These patternsimply the presence of storage thresholds in each catchment. Con-vergence at the upper end of the graph implies that the runoff gen-eration efficiency of the Pond 90 catchment begins to emulate thatof Pond 109 in wetter conditions.

At Saskatoon A, the minimum observed cumulative Novem-ber–April precipitation was 40 mm and the median precipitation

ff obtained from pond water levels in the SDNWA; (b) NOV–APR precipitation inn; and (c) NOV–APR precipitation and snowmelt runoff in the Swift Current region.

Fig. 3. The SDNWA site: (a) precipitation–runoff Q–Q plots and (b) quantile-return period curves for runoff and a gamma distribution plot representing the long-termprecipitation data in Saskatoon A station.

E. Ehsanzadeh et al. / Journal of Hydrology 414–415 (2012) 364–373 369

(corresponding to a 2-year return period) was 90 mm (Fig. 3b).The frequency curve of precipitation for return periods exceeding2 years is represented by a relatively straight line. The slope ofthe lower end of runoff frequency curves from SDNWA was muchgentler than the precipitation curve and reflects the patterns inFig. 3a. The frequency curve of Pond 90 has a flat slope for returnperiods up to 10 years which indicates minimal runoff responseto precipitation of less than 120 mm (corresponding to a �6-yearreturn period). There are two major breaks in slope of the fre-quency curve: one at the 12-year return period, and a secondand much sharper change at the �25-year return period(Fig. 3b). The frequency curve of Pond 109 is represented by astraight line showing almost no break in slope for the observa-tional period (Fig. 3b). The slope of the runoff frequency curveof this pond is steeper compared to Pond 90 for return periodsup to 25 years. This implies that the catchment of Pond 109 ismore efficient at producing runoff than the catchment of Pond90 for precipitation events smaller than a �150 mm thresholdor less frequent than those with a 25-year return period. The run-off production efficiency of Pond 90 is intensified, however, as theprecipitation exceeds this threshold and it approaches that ofPond 109 for precipitation events exceeding 170 mm (Fig. 3b).

The Q–Q plot of Magnusson Creek is characterised by a gentleand almost constant slope for winter precipitation less than120 mm and by a steeper slope when winter precipitation exceeds

Fig. 4. The WSC gauged watersheds: (a) precipitation–runoff Q–Q plots and (b) quantile-term precipitation data in Saskatoon A station.

this threshold (Fig. 4a). This implies that the runoff production effi-ciency of this watershed increases nonlinearly around this specificprecipitation threshold. The Q–Q plots of all other Creeks exhibitnonlinear responses, particularly around 120 mm of winter precip-itation. Runoff does not increase substantially between 120 and140 mm of winter precipitation, and then increases linearly withprecipitation exceeding 140 mm.

Similar to the SDNWA ponds, all runoff frequency curves esti-mated from the records from the WSC gauges start from zero indi-cating that the basins used in this study represent drainage areaswith ephemeral runoff with little or no base flow (Fig. 4b). The run-off frequency curve of Magnusson Creek has the smallest distanceto the precipitation frequency curve. One should note that this wa-tershed has the highest effective to gross drainage area ratioamong the WSC gauged catchments (Table 1). There is a signifi-cantly large transition of the runoff frequency curve at the 4-yearand 15-year return periods during which runoff increases nonlin-early with precipitation amount of �30 mm and 140 mm, respec-tively. Similar increases at similar return periods occur in otherwatersheds, but the Ironspring watershed experiences a relativeincrease in runoff more frequently, corresponding to roughly a 9-year return period.

The runoff frequency curves of Romance Creek and IronspringCreek with 537 and 571 km2 gross drainage areas, respectively,overlap for the return periods up to 4 years (third quartile)

return period curves for runoff and a gamma distribution plot representing the long-

370 E. Ehsanzadeh et al. / Journal of Hydrology 414–415 (2012) 364–373

suggesting similar runoff response behaviour (Fig. 4b). However,the runoff frequency curve of Ironspring Creek deviates from thatof Romance Creek for larger return periods and reaches somewherehalfway between Magnusson Creek and Romance Creek at theupper end. The effective to gross drainage area ratios for IronspringCreek and Romance Creek are 0.55 and 0.38 (Table 1), respectively.The runoff frequency curve of Brightwater Creek with an effectivedrainage area ratio of 0.22 has a gentler slope compared to the pre-viously discussed watersheds (Fig. 4b). The runoff frequency curveof this watershed is relatively smooth and straight for return peri-ods under 15 years. The runoff frequency curve experiences a con-siderable upward break for larger return periods (up to 25 years)where it reaches a slope comparable to those of other watersheds(Romance Creek, Ironspring Creek, and Magnusson Creek). Theleast efficient runoff response (among selected watersheds) to pre-cipitation belongs to Jumping Deer Creek (Fig. 4). The runoff fre-quency of this catchment is represented by a straight line with agentle and consistent slope for the entire observation period. Thiswatershed has the smallest effective to gross drainage area ratio(0.09) and the largest gross drainage area (Table 1) among testedwatersheds.

The Q–Q plots of Plot 3 and Rushlake Creek both show that wa-tershed response to precipitation input starts when precipitationexceeds a �70 mm threshold (Fig. 5a). The catchment responsein both cases is equally intensified but there seems to be a breakin Q–Q plots of both catchments at about 90 mm precipitation.The rate of increasing runoff is larger for Plot 3 and smaller forRushlake Creek for larger precipitation. This relates to the differ-ence between the effective drainage area ratios of the two water-sheds (Table 1).

The November–April cumulative precipitation frequency curvefor the Swift Current region follows a straight line for return peri-ods over 2 years (Fig. 5b). The frequency curve of Plot 3 has a con-siderably milder slope than that of precipitation for return periodsup to 2 years (corresponding to median). For return periods largerthan 2 years, the runoff frequency curve is characterised with anoverall increasing slope with some fluctuations. The frequencycurve of runoff from Rushlake Creek (Fig. 5b) overlaps that of Plot3 for the return periods up to 2 years. Then it follows a straight linewith a slope considerably milder than that of precipitation andrunoff from Plot 3 for the return periods over 2 years and up to�30 years. For the return periods over 30 years the runoff fre-quency curve of this watershed experiences an upward break here-by minimising the difference between its slope and that of theprecipitation curve.

Fig. 5. The Swift Current catchments: (a) precipitation–runoff Q–Q plots and (b) quantilterm precipitation data in Swift Current CDA station. The vertical distance between precheld/lost through infiltration and evaporation; the vertical distance between plot 3 and Rthe Rushlake Creek watershed.

5. Discussion

Both runoff frequency curves at SDNWA begin at zero becausewinter precipitation in some years was not sufficient to producespring runoff. This also indicates that there was no significant baseflow from groundwater seepage, which is in agreement with whatis known about hydrogeology in this portion of the Canadian Prai-ries (van der Kamp and Hayashi, 2009). The curves, however, devi-ate from each other as return period and precipitation increase(Fig. 3). The catchments at SDNWA are known to have comparablesoils and land cover and their proximity suggests they presumablywill experience similar antecedent soil moisture and evapotranspi-ration demands. The differences between the runoff frequencycurves can be attributed to differences in depressional storage. Sur-face depressions intercept the runoff and recent studies haveshown that they can prevent it from reaching the bottom of thecatchment either by surface (Spence, 2007) or subsurface (Hayashiet al., 2003) pathways. This increases the threshold for the initia-tion of runoff production and forces the runoff frequency curvedown (Fig. 3).

There are sometimes disproportionate and abrupt changes in therunoff frequency curve of Pond 90 that are not associated with com-parable changes in either the precipitation or Pond 109 runoff fre-quency curves (Fig. 3). These changes represent a relatively largeincrease in runoff with a minor increase in precipitation and returnperiod that is unlikely to be associated with disproportionate de-creases in infiltration or evapotranspiration. A sustained changein slope over several return periods that are different than in theprecipitation curve or in runoff curves from nearby catchmentsmay indicate a decrease in the amount of water directed to storage.Depressions do not have infinite storage capacities and once filledwill permit water to move further downslope. The disproportionatechanges in the Pond 90 runoff frequency curve and runoff genera-tion (Fig. 3) are concurrent with observed increases in contributingarea. Field observations at SDNWA indicated that areas contribut-ing runoff to Pond 90 were very limited in 2003 after several dryyears; close to zero (Fig. 6). In 2007, on the other hand, a much lar-ger portion of the drainage basin contributed to runoff after severalwet years. The locations of the 2003 and 2007 events on the fre-quency curves imply that the significant changes in slope of runofffrequency curve of this pond may be attributed to the periodic pro-found increases in contributing area. The result is a concave shapeto the runoff frequency curve of the catchment.

The antecedent condition related to multi-year wet or dry spellsintroduces a temporal aspect to water surface connectivity which

e-return period curves of runoff and an LN2 distribution plot representing the long-ipitation and Plot 3 frequency curves represents the amount of precipitation being

ushlake Creek runoff frequency curves represents the effect of surface depressions in

Fig. 6. The boundary of the gross drainage areas of Ponds 90 and 109. The reddashed line indicates the upper boundary below which the catchment contributedrunoff to the pond in 2007. The blue dotted line in the most downstream part ofPond 90 represents the portion of the gross drainage area which contributed runoffto the pond in 2003. The green and black lines represent the boundaries of Ponds109 and 90 gross drainage areas, respectively. The dark areas within the catchmentsrepresent surface depressions.

Fig. 7. The year to year precipitation–runoff relationship in the semi-arid Prairielandscapes in presence of memory associated with antecedent moisture condition.

E. Ehsanzadeh et al. / Journal of Hydrology 414–415 (2012) 364–373 371

can have a substantial impact on runoff in a pothole dominatedlandscape. The impact of antecedent moisture is to increase the to-tal runoff associated with a given return period relative to a driercondition with the same precipitation input (Struthers and Sivapa-lan, 2007). In addition, the magnitude of threshold mediated runoffwill increase after an episode of wet years such that the break ofslope in the runoff frequency curve will occur at lower return peri-ods. Fig. 7 illustrates a year to year precipitation–runoff relation-ship in Pond 90 (SDNWA) and Plot 3 (Swift Current). It can beseen that the relationship is not linear and the maximum runoff re-sponse (efficiency) may not be necessarily associated with themaximum precipitation in the semi-arid Prairie landscapes whichis attributed, in part, to the antecedent moisture condition. It canbe concluded, therefore, that the antecedent condition of the land-scape plays an important role in defining contributing area withina gross drainage area and should be considered when interpretingthese types of curves. This approach examines basin runoff re-sponse from the perspective of the long term overall regime. Thecurves do not necessarily indicate runoff ratios for a given returnperiod but are expected to denote overall behaviour.

The steady slope of the runoff frequency curve from some pondsand watersheds (e.g. Pond 109 in the SDNWA and MagnussonCreek in central Saskatchewan) suggests that there is a relativelycontinuous increase in runoff generation efficiency in the wa-tershed. Shaw (2010) suggests such patterns are indicative of alow threshold at which all gross drainage area is filled and all high-er hillslope runoff, above this threshold value contributes flow tothe outlet (Figs. 3a and 4a). However, a continuously increasingdistance between a runoff and precipitation frequency curve (e.g.Jumping Deer Creek) indicates that a proportion of the depression-al storage within the gross drainage area has never reached capac-ity and as such many parts of the gross drainage area remaineddisconnected from the outlet during the period of record (Figs.3b and 4b).

The shape of the runoff frequency curve indicates the degree towhich storage thresholds mediate catchment runoff response. Acurve with a consistent slope implies few storage thresholdbreaches. Conversely, a curve with a variable slope is indicativeof a period of record during which several different thresholds have

been exceeded. The relative size of these thresholds can be gleanedby the difference between the precipitation and runoff curves. Forinstance, the difference at the upper end of the frequency curves ofMagnusson Creek and Ironspring Creek indicates the storagecapacity in the former is �15 mm lower than the latter (Fig. 4b).It can be similarly concluded that the catchments of RomanceCreek, Brightwater Creek, and Jumping Deer Creek can hold about40, 60, and 90 mm, respectively, more water than the catchment ofMagnuson Creek.

Fig. 5 provides another illustrative example of precipitation–runoff relationship in the depression dominated Canadian Prairies.Plot 3 has no significant depression storage, and has typical slopeand soil features of southwest Saskatchewan landscape (McConkeyet al., 1996) and Rushlake Creek is characterised with a significantsurface depression capacity typical for Prairie landscapes (Table 1).The Q–Q plots of Plot 3 and Rushlake Creek overlap and indicateminimal runoff production for the precipitation inputs up to90 mm (Fig. 5a). Although runoff response of both catchmentsexperience a break when precipitation exceeds 70 mm, the Q–Qplot of Rushlake Creek deviates from that of Plot 3 due to a secondbreak corresponding to a 90 mm precipitation threshold. The fre-quency curves of both catchments overlap and show considerablymilder slope than that of precipitation for return periods up to2 years (Fig. 5b). While comparable slopes of precipitation and Plot3 runoff curves at the upper end reflects the full drainage area con-tribution, the persistently increasing distance between precipita-tion curve and that of Rushlake Creek is indicative of increasingsurface water detention in the noncontributing part of the grossdrainage basin.

It is evident that the shape of the runoff frequency curve is re-flected in how each catchment responds to increasing winter pre-cipitation inputs. The differences in these responses can beconceptualised by a set of curves that express how losses to theatmosphere and surface and subsurface storage impact Prairiecatchment runoff frequency and magnitude (Fig. 8). The generalshape of the precipitation quantile-return period curve is convex.The curves presented here constructed with empirical data supportthe theoretical curves proposed by Shaw (2010) that imply the spa-tial and size distribution of surface depressions should influencethe shape of the frequency curves. The shape of the runoff quan-tile-return period curve from a catchment with few depressionsis a relatively straight line with a slope at the upper end compara-ble to that of precipitation. Runoff from Prairie pothole landscapesthat have more surface storage capacity may be represented by

Fig. 8. A conceptual model representing the shape of precipitation and runofffrequency curves under different capacity and spatial distribution of surfacedepressions in a pothole dominated landscape. Curve (a) represents the shape ofrunoff frequency curve originated from a hillslope dominated landscape with nodepressional storage. The curves (b)–(d) represent runoff frequency curves origi-nated from a pothole dominated landscape with increasing effects of surfacedepressions on the runoff frequency curve.

Fig. 9. The relationship between runoff ratio and effective to gross drainage arearatio for the Central Saskatchewan WSC gauged watersheds used in the study.

372 E. Ehsanzadeh et al. / Journal of Hydrology 414–415 (2012) 364–373

curves of increasing concavity depending on the capacity and spa-tial distribution of surface depressions. Larger storage demands bydepressions will create an increasingly concave curve. Suddenchanges in slopes or consistently larger slopes relative to the pre-cipitation curve for comparable return periods indicate the exis-tence of different thresholds associated with a change ofcatchment runoff generation mechanism, or increase in contribut-ing area.

Fig. 8 provides a qualitative framework with which to judge rel-ative storage capacity of different watersheds. Precipitation–runoffrelationships provide information on the precipitation thresholdsrequired to produce disproportionate increases in runoff in eachwatershed. The frequency curves provide information on how of-ten these thresholds tend to occur. Together, these two character-istics of a watershed provide some information on the level of riskassociated with perhaps rare and unexpected large streamflows.

The effective drainage area commonly used by Agriculture andAgri-Food Canada (PFRA, 2010) and Water Survey of CanadaHydrometric Database (HYDAT, 2010) is defined as the portion ofthe gross drainage area that contributes runoff to the outlet duringa flood with a return period of 2 years (Godwin and Martin, 1975;Pomeroy et al., 2005). These areas were measured by excluding up-stream drainage areas from depressions that were deemed largeenough to retain the 1:2 year flood by two independent investiga-tors manually inspecting 1:50,000 and 1:250,000 National Topo-graphic System maps (PFRA, 1983). Contributing areas to runoffare dynamic, as illustrated by the 2003 and 2007 observations atSDNWA. An index of contributing area based upon runoff responseand frequency would be advantageous for water management.Fig. 9 illustrates the relationship between the ratio of effective togross drainage area and the 1:2 year runoff ratio for the five WaterSurvey gauges presented in Fig. 4. The patterns reveal a regionalrelationship among the WSC gauged catchments that suggeststhe median year runoff ratio of snowmelt runoff to winter precip-itation is roughly 0.25 for a drainage basin that has a 100% contrib-uting area. Basins with smaller contributing to gross drainage arearatios have proportionately smaller runoff. This implies that onaverage even if all the gross drainage area were contributing, threequarters of winter precipitation would not leave the basin asstreamflow. Similar regional curves could be plotted for larger re-turn periods.

6. Conclusions

This study introduced a straightforward method for deducingrelative depression storage capacity and contributing area dynam-ics and differences using readily available runoff and precipitationdata without recourse to detailed topographic mapping. This isparticularly valuable in Prairie and other landscapes with discon-tinuous stream networks and intermittent streamflow. The meth-odology can be used to discern the quantity of the water storageand retention capacity of surface depressions in a hummocky land-scape. This study suggests improvements could be made to howoperational effective drainage areas are estimated. The approachdescribed here shows promise for further research as well as prac-tical applications for water management and infrastructure designin the Prairie region, including relating contributing area andstreamflow to wetland drainage, land-use changes, sedimenttransport, and nutrient loading.

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