journal of hydrology - usask.ca · 2.1. prairie hydrography and hydrology the canadian prairies are...

Journal of Hydrology 521 (2015) 395–409

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Journal of Hydrology

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The transformation of frequency distributions of winter precipitationto spring streamflow probabilities in cold regions; case studiesfrom the Canadian Prairies

http://dx.doi.org/10.1016/j.jhydrol.2014.12.0140022-1694/� 2014 Elsevier B.V. All rights reserved.

⇑ Corresponding author.E-mail address: [email protected] (K. Shook).

Kevin Shook a,⇑, John Pomeroy a, Garth van der Kamp ba Centre for Hydrology, University of Saskatchewan, Saskatoon, SK, Canadab Environment Canada, Saskatoon, SK, Canada

a r t i c l e i n f o s u m m a r y

Article history:Received 29 July 2014Received in revised form 6 December 2014Accepted 10 December 2014Available online 18 December 2014This manuscript was handled by AndrasBardossy, Editor-in-Chief, with theassistance of Peter F. Rasmussen, AssociateEditor

Keywords:Canadian PrairiesStreamflowFrequency distributionTransformation

Hydrological processes alter the states and/or locations of water, and so they can be regarded as beingtransformations of the properties of the time series of input variables to those of output variables, suchas the transformation of precipitation to streamflow. Semi-arid cold regions such as the Canadian Prairieshave extremely low annual streamflow efficiencies because of high infiltration rates, large surface waterstorage capacities, high evaporation rates and strong climate seasonality. As a result snowfall producesthe majority of streamflow. It is demonstrated that the probability distributions of Prairie spring stream-flows are controlled by three frequency transformations. The first is the transformation of snowfall bywind redistribution and ablation over the winter to form the spring snowpack. The second transforma-tion is the melt of the spring snowpack to produce runoff over frozen agricultural soils. The third isthe transformation of runoff to streamflow by the filling and spilling of depressional storage by connect-ing fields, ponds, wetlands and lakes. Each transformation of the PDF of the input variable to that of theoutput variable is demonstrated at a number of locations in the Canadian Prairies and is explained interms of the hydrological processes causing the transformation. The resulting distributions are highlymodified from that of precipitation, and the modification depends on which processes dominate stream-flow formation in each basin. The results demonstrate the need to consider the effect of the interplayamong hydrological processes, climate and basin characteristics in transforming precipitation frequencydistributions into those of streamflow for the design of infrastructure and for water management.

� 2014 Elsevier B.V. All rights reserved.

1. Introduction

Hydrological processes alter the state and/or location of matterand/or energy. Because matter and energy are conserved, a givenhydrological process is also a transformation, whereby an inputtime series is transformed to that of an output, and the propertiesof the input time series (temporal distribution, probability density,autocorrelation) are transformed to those of the outputs. In tem-perate regions, streamflow can be regarded as the transformationof rainfall and the probability density function (PDF) of a givenstream’s flow could theoretically be computed analytically fromthat of the rainfall and from the transformations caused by theriver basin (Eagleson, 1972), although the effects of heterogeneity,non-stationarity, and thresholding make this difficult in practice(Struthers and Sivapalan, 2007). Transformation of precipitation

inputs to streamflow has been proposed as one approach forstreamflow prediction in ungauged basins where streamflow sta-tistical information is not available for design purposes(Sivapalan et al., 2003; Hrachowitz et al., 2013; Pomeroy et al.,2013).

In cold regions, an especially diverse set of hydrological pro-cesses is involved in the transformations of precipitation tostreamflow (Kuchment and Gelfan, 1991). Cold region streamflowsare the result of sequences of hydrological processes transformingthe input time series (snowfall and rainfall) to the output (stream-flow) through mass and/or energy transformation and storagefunctions. As shown in Table 1, these processes may share statevariables, and the outputs of some processes are inputs to othersbecause of temporal variations in energy inputs due to seasonalityand diurnal fluctuations. Computing the PDF of streamflows ana-lytically is more difficult in cold regions than in temperate regionsbecause of the larger number of hydrological processes and themany ways in which they inter-relate, the importance of phase

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396 K. Shook et al. / Journal of Hydrology 521 (2015) 395–409

change and energy budgets, the memory effects due to storage inthe state variables, the non-stationarity in the inputs and statevariables of the processes and the effects of thresholds in govern-ing many of the processes (Spence, 2010).

2. Study rationale and objectives

The rationale and objectives of this study are derived from itslocation in the Canadian Prairies (as shown in Fig. 1), the northernpart of the prairie pothole region of the glaciated plains of NorthAmerica (Shaw et al., 2012a). Most of the hydrological processesdiscussed are present in other cold regions of the world; othersare unique to the prairie pothole region. The reasons for the studyare connected to the requirement for estimating flows for thedesign and operation of hydraulic infrastructure in the region.Design flows are often determined by fitting historical peak annualflows to a frequency distribution which is extrapolated to thedesired return period (WMO, 2009). On the Canadian Prairies, fit-ting frequency distributions to streamflows is made difficult bythe relative scarcity of stream-gauges, by the region’s unusualhydrography, and by the usual issue of nonstationarity in hydro-logical processes.

2.1. Prairie hydrography and hydrology

The Canadian Prairies are recently-glaciated, flat, cold, andsemi-arid to sub-humid. The mean annual precipitation in theregion is approximately 454 mm (McGinn and Shepherd, 2003),with about 70% falling as rain and 30% falling as snow (Akinremiet al., 1998).

2.1.1. Prairie hydrographyMost of the land surface in the Canadian Prairies is not con-

nected to a conventional fluvial drainage system. Instead, localrunoff is often trapped in the multitudes of small, internallydrained depressional storage ponds present in many Prairie basins.These depressions are a legacy of the relatively recent glaciation ofthe region where ice sheets left moraines, glacial lake beds, sanddunes and knob and kettle topography that was not subsequentlyeroded by fluvial processes into traditional drainage basins. Thewater bodies in the depressions vary in size from ephemeral pud-dles to large closed-basin lakes. The term ‘wetland’ is often usedinterchangeably with ‘pond’, but actually refers to specific depres-sions whose soils are saturated or nearly saturated for most of theyear, include a dense ring of riparian vegetation, and which havefixed areas defined by their soils and vegetation (van der Kampand Hayashi, 2008). A pond is the water in a depression, whichmay be a wetland or may simply be a temporary puddle. The areaof a pond changes as the depth of water fluctuates. The uplandwhich drains into the pond comprises its drainage basin.

Table 1Important cold-regions hydrological processes responsible for the transformation of preci

Process Mass input

Infiltration Rainfall, melt waterEvaporation Surface water, soil moisture

Snowaccumulation

Snowfall

Snow melt Snowpack water equivalentDetention Direct precipitation, surface runoff

Subsurface flow InfiltrationStreamflow Direct precipitation, surface runoff, subsurface flow, upstream

flow

As the soils of the region are predominantly underlain by glacialtills which have very low hydraulic conductivities, groundwaterrecharge rates are very low, with the little recharge that does occurgenerally being focused from underneath wetlands (van der Kampand Hayashi, 1998). Consequently, baseflows are generally non-existent on small streams arising from glacial till substrates withinthe region.

In Canada, drainage basins are designated as being comprised ofthe ‘gross drainage area’, which is the plane area enclosed by thedivide, and the ‘effective drainage area’, which is defined as beingthe area which is expected to contribute flow to the stream oneyear in two (Godwin and Martin, 1975). That area which doesnot contribute flow with a return period of two years, i.e. the dif-ference between the gross and effective areas, may be consideredthe ‘non-effective’ area within a basin.

Fig. 1 plots the non-effective areas of river basins in WesternCanada, which generally coincides with the Prairie ecozone in Can-ada, 71% of the Prairie ecozone being non-effective. The effectivefraction of each basin (the effective area divided by the gross area)is indicated by the color of the dots identifying the gauges plottedin Fig. 1 for streams having gross areas smaller than 1000 km2

within the region. This maximum gross area value was selectedto exclude large rivers (the Saskatchewan River and its tributaries)which are sourced in the Rocky Mountains and their foothills,rather than the Prairies. The means of the annual unit dischargesof these streams over their periods of record, as computed fromthe gross and effective areas, are 19.5 and 29.3 mm, respectively.Despite the low mean annual flow depths, floods do occur on Prai-rie streams.

The fraction of the area of a Prairie basin which contributes flowto the stream (the contributing fraction) is dynamic and dependson the storage of water in the depressions (Stichling andBlackwell, 1957). Filled depressions allow additional water to spilloverland to other depressions and may connect to a stream chan-nel. This process, denoted ‘fill and spill’ (Spence and Woo, 2003)has been studied extensively by hydrologists in the Canadian andAmerican Prairies (Spence, 2007; Shook and Pomeroy, 2011;Leibowitz and Vining, 2003; Zhang et al., 2009; Shaw et al., 2012b).

Declining water levels cause depressions to disconnect, reduc-ing the fraction of the basin contributing flow to the stream chan-nel. Because the connection and disconnection are controlled bydiffering processes, there can be hysteresis between the total quan-tity of water stored in depressions and the fraction of the basincontributing to flow from the basin (Shook and Pomeroy, 2011;Shook et al., 2013). The existence of hysteresis in the contributingfraction is evidence that the state of depressional storage (andtherefore the contributing area) displays ‘memory’, being influ-enced by the history of prior inflows and outflows.

In a storage-dominated Prairie basin, the probability distribu-tion of the discharge of a stream is the product of the distributions

pitation to streamflow.

Mass output State variables governing process

Soil moisture Soil moisture, ice content, soil temperatureWater vapor Depressional storage, soil moisture, state of

plantsSnowpack water equivalent Snow depth, density, vegetation states

Melt water Snowpack water equivalent, temperatureDetention, depressionalstorage

Soil saturation, surface water storage

Streamflow Soil moisture, groundwaterDownstream flow Streamflow

Fig. 1. Location of Water Survey of Canada gauges within the Prairie ecozone (shown in gray) for uncontrolled basins smaller than 1000 km2. The Cypress Hills are indicatedby the 1000 m elevation contour. Projection is UTM 13. The non-contributing area for the one in two year flow is shown in blue. The effective fraction for each gauged basin isshown by a colored dot scheme. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

K. Shook et al. / Journal of Hydrology 521 (2015) 395–409 397

of the depth of runoff and of the contributing area. Large stream-flow events require large magnitudes of both runoff and of the con-tributing area (i.e. full depressions). As Canadian Prairie streamstypically have short observation records, there may be bias in therepresentations of infrequent large events which depend on theunknown frequency distributions of the contributing fractions oftheir basins. Like most parts of the planet, the Canadian Prairiesare experiencing the effects of changing climates (Shook andPomeroy, 2012) with the resulting increasing evidence of non-sta-tionarity in streamflow.

The periods of record of Prairie streams coincide with large-scale trends toward the reduction of agricultural tillage, whichhas been shown to affect the quantities of surface runoff (Elliottet al., 2001). The periods of record also coincide with large-scaledrainage of Prairie wetlands. Up to 71% of Prairie wetlands wereestimated to have been lost to drainage by 1986 (EnvironmentCanada, 1986), although as the areas of Prairie ponds generallyapproximate Pareto distributions (Shook et al., 2013), and smalldepressions are most likely to be drained, the fraction of the wet-land area drained is much smaller than the fraction of drained wet-lands. Watmough and Schmoll (2007) found that 5% of the wetlandarea in the Canadian Prairies was drained for agriculture over theperiod 1985–2001. Drainage of depressions increases the contrib-uting areas for streamflow. Model simulations and analyses ofstreamflow and precipitation records show that it has stronglyaltered the responses of storage dominated Prairie basins(Pomeroy et al., 2010; Ehsanzadeh et al., 2014). Therefore methodsof estimating future streamflows from historical data, which aresubject to non-stationarity from both climate and land usechanges, are even less valid on the Canadian Prairies than theyare in other regions of the world.

2.1.2. Prairie hydrologyOn the Canadian Prairies, large streamflows are generally due to

runoff from the spring melt of the winter snow pack, which isresponsible for the majority of annual surface runoff (Gray et al.,1988). The winter snowpack is reformed from accumulated snowwhich is redistributed by wind and ablated by sublimation andmid-winter melts Pomeroy and Li (2000). Blowing snow transportand sublimation result in losses from exposed snowcovers of 30%to 75% of annual snowfall in Prairie environments (Tabler, 1975;Pomeroy et al., 1993). The disposition of this eroded snow eitherto sublimation or to transport and subsequent deposition is impor-tant to surface water budgets (Pomeroy et al., 1997), as transportedsnow is available for snowmelt, whilst that sublimated is returnedto the atmosphere. Blowing snow fetch, or the downwind distanceof uniform terrain that permits snow transport, determines thedisposition between sublimation and transport, longer fetchespromoting greater sublimation per unit area (Tabler, 1975).Vegetation height over the fetch is also very important to seasonalblowing snow redistribution and sublimation; taller crop stubblepromotes reduced redistribution and sublimation of snow. Snowis preferentially redistributed to Prairie depressions (Fang andPomeroy, 2009) due to the effect of vegetation and topographicdepressions in reducing wind speeds and causing divergence intransport rates.

Without snowmelt inputs, many Prairie depressions would notform ponds in most years due to the semi-arid climate of theregion. Snowmelt is driven primarily by solar radiation and is usu-ally characterized by a substantial and rapid melt period in Marchor April. The rate of snowmelt is controlled by energy inputs and bythe previous redistribution of the snowpack, which controls thespatial distribution of snow water equivalent (SWE) within the


original snow pack. High surface runoff from the major springsnowmelt event is a result of the frozen state of soils at the timeand the relatively rapid release of water from snowpacks (Grayet al., 1985). After snowmelt, most rainfall occurs in spring andearly summer from large frontal systems and the most intenserainfall rates occur in summer from convective storms over smallareas (Gray, 1973; Shook and Pomeroy, 2012). In summer and fall,thawed soils with high infiltrability and high water storagepotential, rapid plant growth and concomitant transpiration of soilmoisture along with sparse rainfall produce little or no runoff buthigh evapotranspiration rates (Granger and Gray, 1989; Elliott andEfetha, 1999). The histogram of historical annual peak flows for thePrairie stream gauges in Fig. 3 indicates that the majority of thepeak runoff events occur during the months of March and April,i.e. when the melt of the Prairie snowpacks typically occurs.

2.2. Problems with estimating return-period streamflows in thePrairies

Currently, there is no viable method for estimating designstreamflows for ungauged basins on the Canadian Prairies. Waterresources assessments in ungauged basins require a method forestimating the probability density function (PDF) of streamflowsfrom input variables and parameters that can be perturbed forchanging hydrological processes due to land use and climatechange. Despite the importance of snowmelt runoff, many of themethods used by operational hydrologists on the Canadian Prairiesassume that peak streamflows are caused by rainfall. Because of itswidespread use, simplicity and very modest data requirements, theRational Method is often specified for use for hydraulic design inthe Prairie Provinces of Canada (Alberta EnvironmentalProtection, 1999). The Rational Method is essentially a linear trans-formation of rainfalls having a desired return period, under theassumption that the resulting streamflows will have a similarreturn period. As the Rational Method does not incorporate snow-melt, it is physically invalid for estimating peak flows on the Cana-dian Prairies despite its specification in current practice. TheRational Method is also statistically invalid in the region. Regionalresults show that peak streamflows are best fitted by a two-param-eter lognormal distribution (Spence, 1973), and that the annualmaxima of daily rainfalls in the Prairies are well described by theGeneralized Extreme Value distribution (Shook and Pomeroy,2012). Linear functions like the Rational Method are unable totransform the distributions of extreme rainfalls to those of stream-flows largely caused by snowmelt runoff.

Hydrological models developed for more temperate and welldrained environments are typically unable to simulate streamflowsin the region, as they typically do not incorporate the processeswhich generate runoff in the region. Neither can conventionalmodels reproduce the effects of the region’s unique hydrographyon streamflows.

2.3. Research objectives

The objective of this research is to determine the causes of theobserved frequency distributions of annual streamflows on theCanadian Prairies by quantifying the transformation of the PDFsof winter precipitation inputs to those of the spring streamflowoutputs. Three major transformations are to be considered: ofsnowfall to the spring snowpack, of the spring snowpack to runoff,and of runoff to streamflow. The causes of each transformation arealso to be identified. Improving the understanding of the transfor-mation processes will allow their simulation by physically-basedmodeling, with the benefit of finally providing a method for esti-mating return-period streamflows in the region.

3. Data analyzed

Hydrological and meteorological data are sparse on theCanadian Prairies and no location examined in this study has allof the variables used by all three of the frequency transformations.Consequently, it was necessary to evaluate each of the frequencytransformations individually, with each transformation beingapplied to differing datasets.

3.1. Streamflow data

Historical streamflow data were obtained from the Water Sur-vey of Canada (WSC) for gauges on the Prairies. The locations ofthe streamflow datasets are mapped in Fig. 1.

3.2. Snowfall data

The snowfall data locations are mapped in Fig. 2. Monthly pre-cipitation totals were obtained from the Adjusted and Homoge-nized Canadian Climate Data (AHCCD). These datasets have beencorrected for the effects of wind on gauge undercatch and changesin the collection procedures as described by Mekis and Vincent(2011). The minimum, maximum and mean lengths of the 39 datasets within the Prairie ecozone were 40, 134 and 75.9 years,respectively. The starting years of the datasets varied between1872 and 1957, and the ending years varied between 1994 and2011.

The total accumulation of snowfall at the end of winter is ofinterest, as it represents the water available for spring runoff.Because the annual melt of the Prairie snowpack generally occursin March or April, accumulated winter precipitations were deter-mined by summing the monthly precipitations over the periodNovember-February, and November-March, to estimate the totalaccumulated snowfalls on March 1, and April 1.

3.3. Snow-course data

The locations of the snow-course sites are mapped in Fig. 2. TheAlberta snow-course data were obtained from Alberta Environ-ment and Sustainable Resource Development. Of 56 Alberta plainssnow-courses, 26 were within the Prairie ecozone. The Prairiesnow-course records were generally short, having minimum, max-imum and mean lengths of 23, 36 and 33.2 years, respectively. TheAlberta snow survey sites are categorized as being open, closed(surrounded by trees) or mixed. Snow-course data were alsoobtained for the Agriculture and Agri-Food Canada (AAFC) Semi-arid Prairie Agricultural Research Centre (SPARC) at Swift Current,SK. The station is described at http://www4.agr.gc.ca/AAFC-AAC/display-afficher.do?id=1180634963149. Snow course data werealso available at the St. Denis National Wildlife Area (SDNWA),which is described at http://www.ec.gc.ca/ap-pa/default.asp?lan-g=En&n=CF62237A-1, over the period 1994–2012.

The identity of the AHCCD precipitation station nearest to eachsnowcourse was determined. The distances between each Albertasnowcourses and its associated precipitation measurements variedbetween 4.3 and 86 km (mean = 42 km). The Swift Current snow-courses were located within 1 km of their respective precipitationmeasurements. Winter precipitation data were not available forSDNWA.

3.4. Upland runoff data

The only source found for gauged historical upland runoff datais a set of three runoff plots at the AAFC SPARC. Runoff data wereavailable over the period 1962–2009.

http://www4.agr.gc.ca/AAFC-AAC/display-afficher.do?id=1180634963149http://www4.agr.gc.ca/AAFC-AAC/display-afficher.do?id=1180634963149http://www.ec.gc.ca/ap-pa/default.asp?lang=En&n=CF62237A-1http://www.ec.gc.ca/ap-pa/default.asp?lang=En&n=CF62237A-1

Fig. 2. As Fig. 1 but with locations of Alberta snow course, monthly snowfall measurement, and wetland sites.

0

200

400

600

Jan Feb Mar Apr May Jun Jul Aug Sep Oct

Num

ber

of p

eak

flow

s

Fig. 3. Monthly histogram of peak annual flows from Water Survey of Canadagauges for uncontrolled basins having gross areas smaller than 1000 km2.

Table 2Location, number of ponds sampled and period of record of pond depths.

Location Number of ponds Period

St. Denis, SK 74 1968–2010Swift Current, SK 46 1962–2010Floral, SK 25 1962–2010Melfort, SK 12 1962–2010


Spring inflow data were available for four wetlands (numberedas 25–26, 50, 90 and 109) at SDNWA, each of which did not spill tolower elevations during the period of record. Estimated inflow val-ues were available over the period 1969–2009.

3.5. Soil moisture data

Historical fall soil moisture data were obtained for researchplots at the AAFC SPARC over the interval 1971–2010. Soil mois-ture was measured gravimetrically before freeze-up at depths to120 cm.

3.6. Pond depths

Depth measurements of ponds, including the spring-time great-est depths, are available for SDNWA (Conly et al., 2004), near the

AAFC SPARC and near the towns of Floral (now part of CormanPark, SK) and Melfort, SK. The locations of these sites are plottedin Fig. 2. Although the Melfort site lies slightly outside the Prairieecozone, it is in an agricultural zone well within the Prairie potholeregion. The number of ponds sampled and the period of record ateach site are given in Table 2.

4. Methods

The changes in the properties of the input variables (snowfall,snow accumulation, runoff) to those of the output (snow accumu-lation, runoff and streamflow) are examined for each of the trans-formations. The PDFs of the input and output variable areillustrated by plotting their kernel densities, which are similar tohistograms except that the total area under each curve is equalto 1 (Venables and Ripley, 2002). The four statistical moments(the mean, variance, skewness and kurtosis) allow the PDFs ofthe input and output variables, and therefore their transforma-tions, to be quantified. To separate changes in the variability fromchanges in the mean, the coefficient of variation (CV), which is thestandard deviation divided by the mean, was used in this study asthe second moment. The calculation of the skewness and kurtosisis described by Cryer and Chan (2008). The input and output timeseries were also tested to see if the transformation process affects

0.000

0.005

0.010

0.015

0 50 100 150

March 1 SWE and Snowfall (mm)

Den

sity Variable

Snowfall

SWE

Fig. 5. Kernel densities of March 1 SWE (Morinville, Alberta) and cumulative wintersnowfall (November–February) (Edmonton City Centre Airport) over the interval1974–2009.


autocorrelation, by calculating their autocorrelation functions(ACFs) as described by Venables and Ripley (2002). If a time seriesdoes not display statistically-significant autocorrelation, then itmay be modeled by a random process. The presence of significantautocorrelation in an output time series, when the input time ser-ies is not significantly autocorrelated, is an indication of memory inthe transformation processes.

Where statistics are available for several locations, their alter-ation is examined to determine the variability of the transforma-tion process. Each of the transformations is also examined todetermine its underlying physical causes, i.e. the hydrological pro-cesses that are responsible, so it may can be modeled any location.The degree to which the processes are affected by nonstationarityin climate and landuse are also examined. The presence of nonsta-tionarity in the transformations would prevent their being consid-ered as purely statistical processes, and would require their beingsimulated by physically-based models of hydrological processes.

5. Results and discussion

5.1. Transformation of winter precipitation to spring snowpack

The frequency distributions of the total winter precipitationaccumulations, over both periods (to 1 March, and 1 April), arewell-described by normal distributions. For all datasets, over bothintervals, the null hypotheses that the data fit a normal distribu-tion were accepted, according to Kolmogorov–Smirnov tests atthe 5% significance level. The annual winter precipitation accumu-lations at a single location, over both intervals, typically displayvirtually no significant autocorrelation. As an example, Fig. 4 plotsthe autocorrelation function (ACF) of March 1 accumulated snow-fall at the Edmonton Centre Airport over the interval 1896–2004.For lag lengths between 1 and 20 years, only a single ACF valueexceeds the 95% confidence level for random data, as would beexpected to occur by chance.

As with the winter accumulated snowfall datasets, each of thesets of spring SWE values fit a normal distribution (null hypothesisaccepted by Kolmogorov–Smirnov tests at the 5% significancelevel). Fig. 5 demonstrates a typical frequency transformation fromwinter precipitation to snowfall as is illustrated by the change inkernel density. Fig. 6 plots the statistical moments (mean, coeffi-cient of variation, skewness and kurtosis) of the Alberta March 1snowcourse SWE, against those of the nearest November-FebruaryAHCCD snowfall accumulations. For each pair of sites analyzed,only those years having values in both datasets were used to deter-mine the SWE and snowfall statistics. The minimum, mean and

0.00

0.25

0.50

0.75

1.00

0 5 10 15 20

Lag (years)

AC

F

Fig. 4. Autocorrelation function of cumulative snowfall to March 1 for theEdmonton City Centre Airport. The blue lines represent the 95% confidence intervalfor random data. (For interpretation of the references to color in this figure legend,the reader is referred to the web version of this article.)

maximum number of years in the combined datasets were 20,25.9, and 33, respectively.

The closed snowcourse sites generally capture a greater fractionof the falling snow than do the open sites, with the mixed sitesbeing in between. Shook and Pomeroy (2010) demonstrated adecrease in the mean of snow accumulation, relative to winter pre-cipitation, for an open Prairie site, and an increase in the meansnow accumulation for a closed mountain site. The general reduc-tion of the mean SWE from the mean accumulated snowfall forPrairie landscapes was initially noted by Gray et al. (1979) andwas shown to be largely due to ablation from blowing snow ero-sion and in-transit sublimation in cold mid-winter periods(Pomeroy et al., 1993) with the additional effect of mid-wintermelting in relatively warm years (Fang and Pomeroy, 2007).Granger and Male (1978) found that the rates of sublimation mea-sured from in situ Prairie snowpacks were less than 0.2 mm/dayand peaked during the spring melt period, with very low sublima-tion losses over the winter.

The coefficients of variation of the SWE plotted in Fig. 6b aregenerally greater than or equal to those of the snowfall, with theopen sites displaying the greatest increase. The skewness and kur-tosis plots show little systemic variation, but a great deal of scatter.All of the time series of March 1 snowcourse SWE values displayedno significant temporal autocorrelation. Evidently the processestransforming snowfalls to SWE are not sufficiently serially-corre-lated to overcome the lack of autocorrelation in annual snowfallaccumulations.

5.1.1. Transformation processThe transformation of the accumulated snowfall PDF to that of

the snowcourse PDF is due to: (1) wind transport leading to redis-tribution of snow amongst landscape elements, (2) the sublimationof blowing snow and (3) the ablation of snowpacks by melt/subli-mation events during the winter. The processes of blowing snowtransport and sublimation and their effects on snow redistributionare explained in great detail in Pomeroy et al. (1993,1995,1998),Pomeroy and Li (2000), while Fang and Pomeroy (2009) describedthe effects of the processes on the accumulation of snowpacks atbasin scales including SDNWA wetland basins.

Shook and Pomeroy (2010) demonstrated that the temporal dis-tribution of Prairie daily snowfall influences the transformation ofthe accumulated winter snowfall to spring SWE, by affecting theincidence of blowing snow events. They also demonstrated thatdaily time series of snowfalls on the Prairies display multiscaling,and that the parameters of the multiscaling have changed signifi-cantly over interval 1895–2003 at 4 out of 6 locations examined.

Fig. 6. Mean, coefficient of variation, skewness and kurtosis of March 1 SWE at Alberta snow courses vs. corresponding values for annual winter snowfall (November–February) at nearest meteorological station.


Therefore, the process of transformation of snowfall to SWE byblowing must have been non-stationary at many locations duringthe period of record of Prairie streamflows.

Mid-winter snow ablation events in the south-western Cana-dian Prairies are often caused by Chinooks, which are warm, dryfoehn winds originating from the Rocky Mountains at the western(upwind) edge of the ecozone (Helgason and Pomeroy, 2005). Chi-nook winds are associated with high insitu sublimation rates(Hayashi et al., 2005) as well as rapid melting. The ‘Chinook belt’(the region most affected by these winds) is primarily withinsouthern Alberta (Nkemdirim, 1996) and southwestern Saskatche-wan. The northern Alberta sites are not generally affected by Chi-nooks, and although the southern Alberta snow surveys arelocated within the Chinook belt, they are located in the CypressHills, (shown in Fig. 2) where their altitude (~1200 m) reducesthe incidence of mid-winter snow ablation.

Positive trends in surface air temperatures have been found inthe Canadian Prairies during the winter and spring (Bonsal et al.,2001; Zhang et al., 2000) over the 20th century. Fang andPomeroy (2007) showed that increased air temperatures result inincreased mid-winter melts on the Prairies and so these trendsare consistent with increasing frequencies of mid-winter ablationevents. Thus, the transformations of snowfall to SWE due to snowablation may also have been non-stationary over the period ofrecord of Prairie streamflows.

The kernel densities of the snow-course SWE for Swift Currentand St. Denis are plotted in Fig. 7. Unlike the Alberta data, the Sas-katchewan SWE are peak annual values and cannot be compared

directly to accumulated precipitation. However, the highly-skewednature of the Swift Current SWE kernel density is self-evident. AsSwift Current, unlike St. Denis, is within the Chinook belt, theincreased skewness of the SWE distribution is believed to becaused by mid-winter snow ablations due to Chinooks.

5.2. Transformation of accumulated SWE to upland runoff

If the small effects of evaporation/sublimation and rainfall dur-ing the snow melt period are ignored, the depth of water runningoff an upland soil in the spring may be expressed as the differencebetween the accumulated winter SWE and the depth of water infil-trating the soil, i.e.,

RO ¼ SWE� INF ð1Þ

where

RO = spring runoff (mm),INF = total infiltration to frozen soil (mm), andSWE = snowpack pre-melt SWE (mm).

As the value of the mean annual INF is non-zero, the magnitudeof the mean annual RO will invariably be smaller than that of themean annual SWE.

Table 3 lists the moments of the distributions of the maximumannual accumulation and the spring runoff for Swift Current andSDNWA, whose kernel densities are plotted in Fig. 7. The momentsindicate that the spring runoff is more variable (as indexed by the

0.00

0.01

0.02

0.03

0 25 50 75 100 0 25 50 75 100Peak SWE, Spring runoff (mm)

Den

sity

VariablePeak SWE

Spring runoff

St Denis Swift Current

VariablePeak SWE

Spring runoff

Fig. 7. Kernel densities of peak seasonal SWE accumulation and spring runoff for St. Denis (1989–2009) and plot 3 at the Swift Current AAFC SPARC station (1962–2009).

Table 3Statistical moments of annual peak SWE and upland runoff for St. Denis (1989–2009) and plot 3 at Swift Current AAFC SPARC station (1962–2009).

Site Snowpack SWE Upland runoff

Mean (mm) CV Skewness Kurtosis Mean (mm) CV Skewness Kurtosis

St. Denis 61 0.37 0.17 0.00 17 0.96 0.83 �0.41Swift Current 33 0.70 0.90 0.45 24 1.03 1.09 0.59

0.00

0.01

0.02

0.03

0.04

0 25 50 75 100

SWE, RO (mm)

Den

sity

VariableRO, θp = 0.2

RO, θp = 0.4

RO, θp = 0.6

RO, θp = 0.8

SWE

Fig. 8. Kernel densities of March 1 SWE at Wetaskiwin Alberta, and of snowmeltrunoff simulated using the Gray et al. (1985) limited case infiltration to frozen soilfor various levels of soil saturation.


CV) and skewed than is the accumulated SWE at both locations.The magnitude of the kurtosis shows very little change in thetransformation from snow accumulation to runoff, at both loca-tions. The annual upland runoff depths at SDNWA and Swift Cur-rent showed no significant temporal autocorrelation.

5.2.1. Transformation processGranger et al. (1984) demonstrated that the fraction of the

accumulated snowpack infiltrating to a frozen soil beneath thepack is controlled by the state of the soil. Frozen soils which arecracked or have substantial macropores have unlimited infiltrationcapacity, with essentially all of the snow meltwater infiltrating.Under restricted conditions, when an ice-layer develops at thesoil-snow interface due to mid-winter melting or fall/spring rain-falls, virtually no snow meltwater infiltrates. In the most common,limited case, the depth of infiltration is related to the pre-meltsnowpack SWE and soil moisture (frozen and unfrozen) by (Grayet al., 1985)

INF ¼ 5 1� hp� �

SWE0:584 ð2Þ

where hp = premelt soil saturation of 0–30 cm soil depth(dimensionless).

The observed enhanced skewness of runoff relative to snowaccumulation is explained in part by Eqs. (1) and (2). The valueof the exponent (0.584) in Eq. (2) causes the PDF of the value ofRO to be positively-skewed relative to that of the SWE. As shownin Fig. 8, small values of hp increase the skewness of kernel densityplots of RO computed from measured values of SWE.

The value of hp for a given Prairie soil changes from year to year,due to variability in the atmospheric forcings (precipitation, airtemperature, humidity, wind speed, all-wave radiation), hydrolog-ical processes (evapotranspiration, infiltration) and agriculturalpractices. Under limited conditions, the transformation of the snowaccumulation PDF to that of runoff is predictable – if the PDF of hpis also known. Ravelo and Decker (1979) found that the PDF of an

index of soil moisture could be described well as a beta distribu-tion for unidentified soil plots at Swift Current. However the kerneldensity plots of fall soil moisture in Fig. 9 show evidence of bimo-dality, which is presumably due to the effects of crop rotation fromcultivation to summerfallow over the early part of the period ofrecord. The increasing use of conservation tillage and no-tillagein Prairie agriculture since the 1990s (Kittson et al., 2007), hascaused the PDFs of pre-melt soil moisture to continue to changeand macropores to develop as tillage is reduced. Macropore devel-opment may increase the prevalance of unlimited infiltrationconditions.

Prairie soils often freeze before the formation of the seasonalsnowpack. Restricted infiltration conditions can develop as a resultof mid-winter melting or by freezing of fall rains near the soil sur-face before the winter snowpack forms. Winter air temperatures,indexed by the annual number of days having temperatures below0 �C, have been demonstrated to have increased on the Canadian

0

1

2

0.4 0.6 0.8Fall soil moisture fraction

Den

sity plot

26A

26B

26C

26D

Fig. 9. Kernel densities of fall soil moisture as fractions of the maxima over theperiod of record for AAFC SPARC (Swift Current, SK) Soil Moisture Plots (1971–2010).


Prairies over the twentieth century (Vincent and Mekis, 2006) andmany Prairie locations show upwards trends in winter daily max-imum air temperatures (Zhang et al., 2000). The fraction of precip-itation falling as rain in the winter and fall months has also beendemonstrated to have increased in many locations in the CanadianPrairies over the same period (Shook and Pomeroy, 2012). Giventhese changes, the transformation of snowcover to runoff isassumed to have been non-stationary over the period of recordof Canadian Prairie streamflows.

5.3. Transformation of upland runoff to streamflows

As shown in Table 4, the annual flows of Prairie streams arehighly skewed, and have very large kurtoses. Although the valuesare not directly comparable, the means of the CV, skewness andkurtosis for the annual flow depths are much greater than thoseof the spring runoff from uplands listed in Table 3, despite themeans having similar magnitudes to those of the runoff. It ishypothesized that the large values of the higher moments ofannual streamflows are due to the transformation of upland runoffto streamflow within Prairie basins.

The annual streamflows display little temporal autocorrelation.Of 63 sites tested, only 6 showed any ACF values greater than the95% confidence level for random data, for lag lengths greater thanzero years. The large magnitude of the mean kurtosis of annualstreamflows demonstrates the difficulty of using conventionalmethods to estimate design flows for long return periods using flowsfrom Prairie streams. As the distributions are heavy-tailed, errors infitting a distribution will be exaggerated for long return periods.

5.3.1. Transformation processThe transformation of upland runoff to streamflow is affected

by the fraction of the basin which contributes flow. For any runoffevent, the stream discharge is related to the runoff by

Q ¼ RO f c ð3Þ

where

Q = depth of stream discharge (mm), andf c= contributing fraction of basin.

Table 4Mean moments of annual flow depth at WSC gauges of uncontrolled Prairie basinshaving gross areas smaller than 1000 km2 (1975–2005).

Mean depth (mm) CV Skewness Kurtosis

16.7 1.2 1.5 5.6

The effect of fc on the shape of the PDF of annual peak flows of agiven stream depends on whether its magnitude is constant orvariable.

The statistical moments of the annual depths of discharge of thePrairie streams analyzed are plotted in Fig. 10, for those streamshaving records over the period 1975–2005, against theirbasins’ effective fractions. The interval was chosen because itprovides the largest number of continuous records over a 30-yearperiod. The very large degree of scatter in the plots is to beexpected, as the basins chosen represent a very wide variety oftopographies, vegetation types, basin sizes, and climatic forcings.What is of interest is the direction of the fitted trends, rather thanthe strength of the trends.

Fig. 10a demonstrates a direct relationship between the meanannual discharge and the basin’s effective fraction, which isconsistent with Ehsanzadeh et al. (2012) who found a strongrelationship between the runoff ratio and the effective fraction ofseveral small Prairie basins. A direct relationship between themean annual flow and the effective fraction of a basin would beexpected to occur regardless of whether the basin’s contributingfraction is static or dynamic. Shaw (2009) and Shaw et al.(2012a) demonstrated that the interconnections among pondscan cause thresholding behavior in the relationship between thevolume of water stored and the fractional contributing area, forsmall numbers of ponds. Therefore, the discharges of streams hav-ing small effective fractions (i.e. those having a large fraction of thebasin basin area occupied by depressional storage) should be morevariable than those with large effective fractions, if the magnitudeof the contributing fraction changes over time. As shown inFig. 10b–d, the higher moments of the annual discharges appearto be inversely related to the basins’ effective fractions, which isevidence that the contributing fractions of the basins are dynamic,and that the variability of the pond areas contributes tocontributing fraction variability and hence the variability in Prairiestreamflows.

The contribution of depressional storage to the variability ofPrairie streamflow by transforming upland runoff is illustrated byFig. 11, which plots the kernel densities of annual spring-timeinflow to four wetlands at SDNWA. The plots show that the runoffkernel densities have greatly differing shapes, which are hypothe-sized to be due to the differences in the depressional storagesupstream of the wetlands.

The area of upstream depressional storage for each wetland wasestimated using the Wetland DEM Ponding Model (WDPM), whichhas been developed at the Centre for Hydrology. Like theConnectivity of Runoff Model (CRUM) (Reaney et al., 2007), theWDPM simulates the runoff of water applied to a digital elevationmodel (DEM). Unlike CRUM, the WDPM was developed explicitlyfor Prairie landscapes, and does not use the FD8 algorithm. TheWDPM is described in detail by Shook and Pomeroy (2011),Shook et al. (2013).

The area contributing to each terminal wetland, and the totalarea of water within that area, obviously depend on the state ofwater storage. For each of the wetland basins, a small amount ofwater (10–40 mm) was applied and allowed to run into the depres-sional storage. The depth of water applied was sufficient to coverthe bottoms of the depressions in each sub-basin, which corre-spond to the water elevations when the LiDAR data were collected,while allowing each modeled terminal wetland to remain discrete.Thus the areas of the terminal wetlands, and of their basins, shouldcorrespond closely to those existing on the date when the LiDARwere collected.

The collection of the LiDAR data is described in more detail inShook et al. (2013). To reduce the computational effort, the originalDEM data, which were collected on a 1 m grid, were averaged to a

Fig. 10. Statistical moments of annual total depth of discharge vs. effective fraction for uncontrolled gauged streams in the Canadian Prairies, 1975–2005. The lines are fittedby least-squares, the shaded regions represent the 95% confidence interval of the regressions. The values of r2 for the regressions are 0.19, 0.12, 0.22, and 0.15, respectively.


5 m grid. The output of the WDPM runs, which is a map of themodeled spatial distribution of water, is plotted in Fig. 12.

The depressional storage areas, as estimated by the water-cov-ered areas, were computed for each of the drainage basins of thefour SDNWA terminal wetlands. The total depressional storagearea upstream was divided by the area of the terminal pond, foreach of the basins, to produce the upstream depressional area ratio.Pond 25–26 is so named because it consists of two separate ponds(25 and 26) which frequently coalesce into a single pond.Accordingly, the depressional area ratio for pond 25–26 wascomputed for the separate pond (ratio = 0.68), and combined pondcases (ratio = 1.5).

Although the water state simulated was arbitrary, it allows thecomparison and ranking of the depressional area ratios of the fourwetland basins. As listed in Table 5, the basin of pond 25–26 is esti-mated to have the least upstream depressional storage area ratio(under both cases), followed by basins 50 and 109, while sub-basin90 has the greatest upstream depressional storage area ratio. Thestatistical moments of the distributions of the annual pond inflowlisted in Table 5 show that large magnitudes of the upstream

depressional storage depress the mean (by increasing abstraction),while also increasing the variability (as indexed by the CV, skew-ness and kurtosis) of the annual inflow.

Phillips et al. (2011) demonstrated that large lakes located inthe downstream part of Canadian shield basins can act as ‘gate-keepers’ controlling the outflows from uplands and smaller lakesupstream. This process also occurs among ponds on the CanadianPrairies Shaw et al. (2012a). In the basin of SDNWA pond 90, themajority of the drainage is constrained by a single linear sequenceof ponds, as shown in Fig. 12. In the other sub-basins, the directionof drainage towards the terminal pond is more radial, and there-fore less likely to be constrained by individual ponds. Thus, theresulting gatekeeping also contributed to the relatively large mag-nitudes of the CV, skewness and kurtosis of the inflow to pond 90shown in Table 5.

Where Canadian shield lake basins have a small number of flowpaths due to their geological controls and glaciological history,there can be many flow paths among Prairie ponds which drainto a stream channel (Shook and Pomeroy, 2011) which reducesthe effects of the gatekeeping action of any single pond. Thus the

1. Pond 25−26 2. Pond 109

3. Pond 50 4. Pond 90

0.00

0.01

0.02

0.03

0.000

0.025

0.050

0.075

0.000

0.025

0.050

0.075

0.0

0.2

0.4

0.6

0 20 40 60 0 20 40 60

Annual pond inflow (mm)

Den

sity

Fig. 11. Kernel densities of spring inflow depth for ponds at St. Denis National Wildlife Area.

5784

000

5784

000

5785

000

5785

000

5786

000

5786

000

5787

000

5787

000

5788

000

5788

000

5789

000

5789

000

421000

421000

422000

422000

423000

423000

424000

424000

425000

425000

426000

426000

427000

427000

428000

428000

429000

429000

0 1 2 kmBasin 109

Basin 90

Basin 50

Basin 25-26Water

Pond 90Pond 109

Pond 25-26

Pond 50

Fig. 12. Output of the WDPM simulations for St. Denis pond basins 25–26, 50, 90, and 109. The location of the terminal pond is shown for each sub-basin. Pond 25–26 isshown as a single pond. Projection is UTM13.


Table 5Statistical moments of annual pond runoff at St. Denis, 1969–2009. The upstream water areas for pond 25–26 were calculated for the cases with the ponds combined andseparated, respectively.

Pond Gross drainage area (km2) Upstream water area ratio Mean (mm) CV Skewness Kurtosis

25–26 0.55 0.68, 1.5 17.1 1.0 0.8 �0.550 0.61 3.2 5.8 1.1 1.2 0.2109 0.11 3.3 5.2 1.2 1.5 1.990 12.1 21.1 1.5 2.9 4.3 19.3


moments of the Prairie streamflows, as listed in Table 4, are inter-mediate between the inflows to ponds 50 and 109 and those ofpond 90.

5.3.2. Pond memoryFig. 13 plots the depths of spring inflows into ponds 50, 90, and

109 against those of pond 25–26, which are used as indices ofupland runoff. In all cases, the pond inflow depths are smaller thanthe upland runoffs, indicating that the areas upstream of the threeponds never contributed completely during the period of record.

The loops in the plots demonstrate the existence of hysteresisbetween the pond inflow and upland runoff, as suggested byShook and Pomeroy (2011) and Shook et al. (2013). The hysteresisloops appear to run both clockwise and counterclockwise, which iscounterintuitive but is explained by the fact that the runoffs are

Pond 50 Po

0

10

20

0 20 40 600 20

Pond 25−2

Inflo

w (

mm

)

Fig. 13. Spring inflow depths into ponds 109, 50 and 90 at St. Denis National Wildlifesequence of values.

Floral Melfort

0.0

0.2

0.4

0.6

0 1 2 3 4 5 6 0 1 2 3 4 5Memo

Den

sity

Fig. 14. Histograms of maximum length of significant

annual events. The state of storage in the ponds upstream of theterminal ponds is influenced by additions (due to direct rainfall,upland runoff and, where present, groundwater inflow) and remo-vals (due to evaporation and infiltration) of water occurringbetween the episodes of spring runoff. Therefore, the hysteresisloops can run in either direction, depending on whether the mag-nitude of the total change in storage over each interval is positiveor negative.

Hysteresis is caused by memory in a system, where the presentbehavior is controlled by previous states (O’Kane and Flynn, 2007).The memories of the ponds at all of the Prairie sites were estimatedby determining the length of significant autocorrelation (in years)of annual maximum depth, for lags greater than or equal to oneyear. The histograms of the pond memory lengths at all four loca-tions, as plotted in Fig. 14, demonstrate that the vast majority of

nd 90 Pond 109

40 600 20 40 60

6 inflow (mm)

Area plotted against those of pond 25–26. The arrowheads indicate the temporal

StDenis SwiftCurrent

6 0 1 2 3 4 5 6 0 1 2 3 4 5 6ry (years)

autocorrelation of maximum annual pond depth.


Prairie ponds have very short memories of zero or one years,although a few ponds have memories as long as five years.

The variability of memory among Prairie ponds is hypothesizedto be caused by the frequency distribution of the maximum ponddepths. Deep depressions will hold water longer than shallow onesduring a period when the sum of evaporation and infiltrationexceeds the sum of direct precipitation and upland runoff. Thiseffect is enhanced by the recession rates for small ponds exceedingthose of large ones van der Kamp and Hayashi (2008). The maxi-mum areas of ponds in a given Prairie basin generally approximatepower-law distributions (Shook and Pomeroy, 2011; Zhang et al.,2009), and because of the area-depth-volume relationships foundby Hayashi et al. (2000) and Minke et al. (2010), their maximumdepths must also be similarly distributed, with most ponds havingrelatively small maximum depths. Thus the shape of the maximumvolume frequency distributions influences the shapes of the histo-grams of pond memories plotted in Fig. 14. The highly positively-skewed distribution of the depressional memory explains the verysmall degree of autocorrelation found in the annual flows of ponddominated streams in the Canadian Prairies, as the annual dis-charges from the majority of ponds are unaffected by their statein previous years, and the inputs to the ponds (direct snow accu-mulation, upland runoff) also display virtually no annualautocorrelation.

As mentioned previously, the effect of gatekeeping in the Prai-ries is less important than in some regions, but it does exist andit allows the few deep depressions to control the contributionsfrom upstream, which increases their effect on the hysteresis.The short memories of the shallow depressions are not necessarilyinsignificant as a source of hysteresis. Even a pond with a memoryof less than one year could allow a wet summer or autumn to affectthe contributing fraction in the following spring.

Because of their large infiltration capacities, Prairie soils rarelyexperience upland runoff due to rainfall, except during infrequent,intense, convective storms, which are generally too small to causechanges in the flows of Prairie rivers. Shook and Pomeroy (2012)demonstrated the existence of trends of increased depths andlengths of multi-day rainfalls on the Canadian Prairies over the20th Century, which are consistent with trends to increasinglylarge-scale frontal rainfalls. Although frontal rain events usuallyhave intensities too low to cause significant runoff, they may con-tribute to increased pond storage over comparatively large regions,which may lead to increased streamflows from snowmelt runoffvia increases in the contributing fractions of stream basins. There-fore, it is probable that the transformation of snowmelt runoff tostreamflow is also non-stationary over the period of record of Prai-rie streams, even omitting the effects of wetland drainage.

6. Summary and conclusions

The overall transformation of the PDF of winter and springtimeprecipitation to that of spring streamflow on the Canadian Prairiesis demonstrated to be comprised of three transformations that aredominated by distinctive sets of hydrological processes. The trans-formation from snowfall to snowpack accumulation is dominatedby snow redistribution and mid-winter ablation processes, thatfrom snow accumulation to runoff generation is dominated bysnowmelt and frozen soil infiltration processes, and that from runoffto streamflow generation is dominated by depressional storagedynamics. These processes are typical of cold regions hydrology,from the US northern Great Plains to the circumpolar Arctic, andso the transformations should have application outside of the regionof demonstration. In each transformation, the annual median of theflux term is reduced, while the coefficient of variation and skewnessare generally increased. The three transformations result in annual

stream discharges which are intermittent, with many years havingno flows, and which show little serial correlation.

Each of the transformations has multiple causes, each of whichis subject to non-stationarity, making a purely statistical calcula-tion of streamflow PDFs difficult or impossible. However, it ishypothesized that estimation of the PDFs of Prairie spring stream-flows can be accomplished using physically-based hydrologicalmodels that incorporate the relevant processes. It is necessary todo this because of the small fraction of annual precipitation thatforms the seasonal snowpack, the small fraction of the snowpackthat forms runoff and the small fraction of runoff that formsstreamflow. As streamflow is a residual of a cascade of all the coldregions hydrological processes, it requires their careful simulationin order to estimate this very transient output. On the CanadianPrairies, modeling streamflows is made difficult by the region’s dis-tinctive post-glacial hydrography and semi-arid cold regionshydrology. Consequently, hydrological models and tools developedfor better drained, more topographically complex landscapes, andfor warmer and wetter regions often fail when used in the Cana-dian Prairies (Pomeroy et al., 2007).

The Centre for Hydrology at the University of Saskatchewan hasdeveloped the Cold Regions Hydrological Modeling (CRHM) plat-form (Pomeroy et al., 2007), which is capable of modeling the pro-cesses which control the transformation of snowfall to SWE (winderosion, deposition and sublimation due to blowing snow, andsnowcover depletion by melting) and the transformation of SWEto upland runoff (infiltration to frozen soils). Models such as theWetland DEM Ponding Model (WDPM) and Pothole Cascade Model(PCM) developed at the Centre for Hydrology have been shown tobe capable of reproducing the hysteretic effects of pond water stor-age on contributing area (Shook et al., 2013). It is anticipated thatfurther research will allow the integration of these models withCRHM to produce a deterministic model which is capable of accu-rately simulating the PDF of the flows of a given Prairie stream.Streamflow PDFs resulting from this hybrid deterministic-stochas-tic approach, and which include the effects of nonstationarity inthe precipitation and the processes governing the transformations,might then be used in engineering applications for design of infra-structure and for water management.

Acknowledgements

Financial support from Canada Research Chair Programme,Natural Sciences and Engineering Research Council, Ducks UnlimitedCanada and the U of S Global Institute for Water Security isgratefully acknowledged. This research was done entirely withFree Open Source Software (F.O.S.S.). All maps were created usingQGIS (http://www.qgis.org/). All analyses were performed usingthe statistical language R (R Core Team, 2013). All graphs wereplotted in R using the package ggplot2 (Wickham, 2009).

The authors wish to thank all those who contributed data used inthis study. These include Randy Schmidt (SWE at St. Denis), BrianMcConkey (SWE, soil moisture and runoff at Swift Current), and JackMillar, Malcolm Conly and Bob Clark (St. Denis pond depth data).

Water Survey of Canada streamflow data are available online athttp://www.ec.gc.ca/rhc-wsc/default.asp?lang=En&n=894E91BE-1.The monthly AHCCD data are archived online at http://www.ec.gc.ca/dccha-ahccd/; daily values must be requested. The Albertasnow-course data can be found within the Historical Water SupplyOutlook reports at http://www.environment.alberta.ca/forecast-ing/WaterSupply/historical/histwsindex.html.

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The transformation of frequency distributions of winter precipitation to spring streamflow probabilities in cold regions; case studies from the Canadian Prairies1 Introduction2 Study rationale and objectives2.1 Prairie hydrography and hydrology2.1.1 Prairie hydrography2.1.2 Prairie hydrology

2.2 Problems with estimating return-period streamflows in the Prairies2.3 Research objectives

3 Data analyzed3.1 Streamflow data3.2 Snowfall data3.3 Snow-course data3.4 Upland runoff data3.5 Soil moisture data3.6 Pond depths

4 Methods5 Results and discussion5.1 Transformation of winter precipitation to spring snowpack5.1.1 Transformation process

5.2 Transformation of accumulated SWE to upland runoff5.2.1 Transformation process

5.3 Transformation of upland runoff to streamflows5.3.1 Transformation process5.3.2 Pond memory

6 Summary and conclusionsAcknowledgementsReferences

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