-
Journal of Hydrology 521 (2015) 395–409
Contents lists available at ScienceDirect
Journal of Hydrology
journal homepage: www.elsevier .com/ locate / jhydrol
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
http://crossmark.crossref.org/dialog/?doi=10.1016/j.jhydrol.2014.12.014&domain=pdfhttp://dx.doi.org/10.1016/j.jhydrol.2014.12.014mailto:[email protected]://dx.doi.org/10.1016/j.jhydrol.2014.12.014http://www.sciencedirect.com/science/journal/00221694http://www.elsevier.com/locate/jhydrol
-
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
-
398 K. Shook et al. / Journal of Hydrology 521 (2015)
395–409
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
K. Shook et al. / Journal of Hydrology 521 (2015) 395–409
399
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.
400 K. Shook et al. / Journal of Hydrology 521 (2015)
395–409
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.
K. Shook et al. / Journal of Hydrology 521 (2015) 395–409
401
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.
402 K. Shook et al. / Journal of Hydrology 521 (2015)
395–409
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).
K. Shook et al. / Journal of Hydrology 521 (2015) 395–409
403
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.
404 K. Shook et al. / Journal of Hydrology 521 (2015)
395–409
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.
K. Shook et al. / Journal of Hydrology 521 (2015) 395–409
405
-
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
406 K. Shook et al. / Journal of Hydrology 521 (2015)
395–409
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.
-
K. Shook et al. / Journal of Hydrology 521 (2015) 395–409
407
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.
References
Akinremi, O.O., McGinn, S.M., Cutforth, H.W., 1998.
Precipitation trends on theCanadian Prairies. J. Clim. 12,
2996–3003.
http://www.qgis.org/http://www.ec.gc.ca/rhc-wsc/default.asp?lang=En&n=894E91BE-1http://www.ec.gc.ca/dccha-ahccd/http://www.ec.gc.ca/dccha-ahccd/http://www.environment.alberta.ca/forecasting/WaterSupply/historical/histwsindex.htmlhttp://www.environment.alberta.ca/forecasting/WaterSupply/historical/histwsindex.htmlhttp://refhub.elsevier.com/S0022-1694(14)01025-7/h0005http://refhub.elsevier.com/S0022-1694(14)01025-7/h0005
-
408 K. Shook et al. / Journal of Hydrology 521 (2015)
395–409
Alberta Environmental Protection, 1999. Stormwater Management
Guidelines forthe Province of Alberta. Edmonton, Alberta,
Canada.
Bonsal, B.R., Zhang, X., Vincent, L.A., Hogg, W.D., 2001.
Characteristics of daily andextreme temperatures over Canada. J.
Clim. 14, 1959–1976.
http://dx.doi.org/10.1175/1520-0442(2001)0142.0.CO;2.
Conly, F.M., Su, M., van der Kamp, G., Millar, J.B., 2004. A
practical approach tomonitoring water levels in prairie wetlands.
Wetlands 24 (1), 219–226.
Cryer, J.D., Chan, K.-S., 2008. Time Series Analysis. With
Applications to R, seconded. Springer, 487p. ISBN
978-0-387-75958-6.
Eagleson, P.S., 1972. Dynamics of flood frequency. Water Resour.
Res. 8, 878–898.Ehsanzadeh, E., Spence, C., van der Kamp, G.,
McConkey, B., 2012. On the behaviour
of dynamic contributing areas and flood frequency curves in
North AmericanPrairie watersheds. J. Hydrol. 414–415, 364–373.
http://dx.doi.org/10.1016/j.jhydrol.2011.11.007.
Ehsanzadeh, E., van der Kamp, G., Spence, C., 2014. On the
changes in long termstreamflow regimes in the Prairies. Hydrol.
Sci. J., 58. http://dx.doi.org/10.1080/02626667.2014.967249.
Elliott, J.A., Efetha, A.A., 1999. Influence of tillage and
cropping system on soilorganic matter, structure and infiltration
in a rolling landscape. Can. J. Soil Sci.79, 457–463.
http://dx.doi.org/10.4141/S98-075.
Elliott, J.A., Cessna, A.J., Hilliard, C.R., 2001. Influence of
tillage system on waterquality and quantity in prairie pothole
wetlands. Can. Water Resour. J. 26, 165–181.
http://dx.doi.org/10.4296/cwrj2602165.
Environment Canada, 1986. Wetlands in Canada: A Valuable
Resource, LandsDirectorate, Environment Canada. 73-686-4E.
Fang, X., Pomeroy, J.W., 2007. Snowmelt runoff sensitivity
analysis to drought onthe Canadian prairies. Hydrol. Process. 21,
2594–2609. http://dx.doi.org/10.1002/hyp.6796.
Fang, X., Pomeroy, J.W., 2009. Modelling blowing snow
redistribution to prairiewetlands. Hydrol. Process. 23, 2557–2569.
http://dx.doi.org/10.1002/hyp.7348.
Godwin, R.B., Martin, F.R.J., 1975. Calculation of gross and
effective drainage areasfor the Prairie Provinces. In: Proceedings
of Canadian Hydrology Symposium.pp. 219–223.
Granger, R.J., Gray, D.M., 1989. Evaporation from natural
nonsaturated surfaces.J. Hydrol. 111, 21–29.
Granger, R.J., Male, D.H., 1978. Melting of a prairie snowpack.
J. Appl. Meteorol. 17,1833–1842.
Granger, R.J., Gray, D.M., Dyck, G.E., 1984. Snowmelt
infiltration to frozen prairiesoils. Can. J. Earth Sci. 21,
660–677. http://dx.doi.org/10.1016/0148-9062(85)92399-X.
Gray, D.M., 1973. Handbook on the principles of hydrology: with
special emphasisdirected to Canadian conditions in the discussions,
applications, andpresentation of data. Water Information Center,
Inc., Huntingdon,New York.
Gray, D.M., Steppuhn, H., Abbey, F.L., 1979. Estimating the
areal snow waterequivalent in the prairie environment. In: Canadian
Hydrology Symposium: 79– Cold Climate Hydrology, Vancouver,
B.C.
Gray, D.M., Landine, P.G., Granger, R., 1985. Simulating
infiltration into frozenprairie soils in streamflow models. Can. J.
Earth Sci. 22, 464–472.
Gray, D.M., Landine, P.G., Gray, M., Synthesis, S., 1988. An
energy-budget snowmeltmodel for the Canadian Prairies. Can. J.
Earth Sci. 25, 1292–1303.
Hayashi, M., van der Kamp, G., 2000. Simple equations to
represent the volume-area-depth relations of shallow wetlands in
small topographic depressions. J.Hydrol. 237, 74–85.
Hayashi, M., Hirota, T., Yukiyoshi, I., Takayabu, I., 2005.
Snowmelt energy balanceand its relation to foehn events in Tokachi,
Japan. J. Meteorol. Soc. Jpn. 83, 783–798.
http://dx.doi.org/10.2151/jmsj.83.783.
Helgason, W.D., Pomeroy, J.W., 2005. Uncertainties in estimating
turbulent fluxes tomelting snow in a mountain clearing. In: 62nd
Eastern Snow Conference.Waterloo, ON, Canada, pp. 129–142.
Hrachowitz, M., Savenije, H.H.G., Blöschl, G., McDonnell, J.J.,
Sivapalan, M., Pomeroy,J.W., Arheimer, B., Blume, T., Clark, M.P.,
Ehret, U., Fenicia, F., Freer, J.E., Gelfan,A., Gupta, H.V.,
Hughes, D.a., Hut, R.W., Montanari, A., Pande, S., Tetzlaff,
D.,Troch, P.a., Uhlenbrook, S., Wagener, T., Winsemius, H.C.,
Woods, R.a., Zehe, E.,Cudennec, C., 2013. A decade of predictions
in ungauged basins (PUB)—areview. Hydrol. Sci. J. 58,
1198–1255.
Kittson, K., Bonti-Akomah, S., Zafiriou, M., Gao, S., Islam, N.,
2007. An Overview ofthe Canadian Agriculture and Agri-Food System,
Agriculture. Research andAnalysis Directorate Strategic Policy
Branch Agriculture and Agri-Food Canada,Ottawa, Ontario,
Canada.
Kuchment, L.S., Gelfan, A.N., 1991. Dynamic-stochastic models of
rainfall andsnowmelt runoff formation. Hydrol. Sci. J. 36, 153–169.
http://dx.doi.org/10.1080/02626669109492496.
Leibowitz, S.G., Vining, K.C., 2003. Temporal connectivity in a
prairie potholecomplex. Wetlands 23, 13–25.
http://dx.doi.org/10.1672/0277-5212(2003)023[0013:TCIAPP]2.0.CO;2.
McGinn, S.M., Shepherd, A., 2003. Impact of climate change
scenarios on theagroclimate of the Canadian prairies. Can. J. Soil
Sci. 83, 623–630.
Mekis, É., Vincent, L.a., 2011. An overview of the second
generation adjusted dailyprecipitation dataset for trend analysis
in Canada. Atmosphere-Ocean 49, 163–177.
http://dx.doi.org/10.1080/07055900.2011.583910.
Minke, A.G., Westbrook, C.J., van der Kamp, G., 2010. Simplified
volume-area-depthmethod for estimating water storage of prairie
potholes. Wetlands 30,
541–551.http://dx.doi.org/10.1007/s13157-010-0044-8.
Nkemdirim, L.C., 1996. Canada’s chinook belt. Int. J. Climatol.
16, 441–462.
O’Kane, J.P., Flynn, D., 2007. Thresholds, switches and
hysteresis in hydrology fromthe pedon to the catchment scale: a
non-linear systems theory. Time 11, 443–459.
http://dx.doi.org/10.5194/hess-11-443-2007.
Phillips, R.W., Spence, C., Pomeroy, J.W., 2011. Connectivity
and runoff dynamics inheterogeneous basins. Hydrol. Process. 25,
3061–3075. http://dx.doi.org/10.1002/hyp.8123.
Pomeroy, J.W., Li, L., 2000. Prairie and Arctic areal snow cover
mass balance using ablowing snow model. J. Geophys. Res. 105 (D21),
26619–26634.
Pomeroy, J.W., Gray, D.M., Landine, P.G., 1993. The prairie
blowing snow model:characteristics, validation, operation. J.
Hydrol. 144 (1–4), 165–192.
http://dx.doi.org/10.1016/0022-1694(93)90171-5.
Pomeroy, J.W., Marsh, P., Gray, D.M., 1995. Application of an
arctic blowing snowmodel. In: International GEWEX Workshop on
Cold-Season/RegionHydrometeorology. IGPO Publ. No. 15, pp.
56–60.
Pomeroy, J.W., Marsh, P., Gray, D.M., 1997. Application of a
distributed blowingsnow model to the Arctic. Hydrol. Process. 11,
1451–1464.
Pomeroy, J.W., Gray, D.M., Shook, K.R., Toth, B., Essery,
R.L.H., Pietroniro, A.,Hedstrom, N., 1998. An evaluation of snow
accumulation and ablationprocesses for land surface modelling.
Hydrol. Process. 2367 (September),2339–2367.
Pomeroy, J.W., Gray, D.M., Brown, T., Hedstrom, N.R., Quinton,
W.L., Granger, R.J.,Carey, S.K., 2007. The cold regions
hydrological model: a platform for basingprocess representation and
model structure on physical evidence. Hydrol.Process. 2667,
2650–2667.
Pomeroy, J., Fang, X., Westbrook, C., Minke, A., Guo, X., Brown,
T., 2010. PrairieHydrological Model Study Final Report. Saskatoon,
Saskatchewan. 126 pp.
Pomeroy, J.W., Fang, X., Shook, K., Whitfield, P.H., 2013.
Predicting in ungaugedbasins using physical principles obtained
using the deductive, inductive, andabductive reasoning approach.
In: Pomeroy, J.W., Whitfield, P.H., Spence, C.(Eds.), Putting
Predictions in Ungauged Basins into Practice. Canadian
WaterResources Association, pp. 41–62.
Ravelo, A.C., Decker, W.L., 1979. The probability distribution
of a soil moistureindex. Agric. Meteorol. 20, 301–312.
R Core Team, 2013. R: A Language and Environment for Statistical
Computing, RFoundation for Statistical Computing, Vienna, Austria.
.
Reaney, S.M., Bracken, L.J., Kirkby, M.J., 2007. Use of the
connectivity of runoff model(CRUM) to investigate the influence of
storm characteristics on runoffgeneration and connectivity in
semi-arid areas. Hydrol. Process. 21,
894–906.http://dx.doi.org/10.1002/hyp.6281.
Shaw, D.A., 2009. The Influence of Contributing Area on the
Hydrology of the PrairiePothole Region of North America. Ph. D.
Thesis. University of Saskatchewan, 169pp.
Shaw, D.A., Pietroniro, A., Martz, L.W., 2012a. Topographic
analysis for the prairiepothole region of Western Canada. Hydrol.
Process. 27, 3105–3114. http://dx.doi.org/10.1002/hyp.9409.
Shaw, D.A., van der kamp, G., Conly, F.M., Pietroniro, A.,
Martz, L., 2012b. The fill-spill hydrology of Prairie wetland
complexes during drought and deluge.Hydrol. Process. 26, 3147–3156.
http://dx.doi.org/10.1002/hyp.8390.
Shook, K.R., Pomeroy, J.W., 2010. Hydrological effects of the
temporal variability ofthe multiscaling of snowfall on the Canadian
prairies. Hydrol. Earth Syst. Sci. 14,1195–1203.
Shook, K.R., Pomeroy, J.W., 2011. Memory effects of depressional
storage inNorthern Prairie hydrology. Hydrol. Process. 25,
3890–3898. http://dx.doi.org/10.1002/hyp.8381.
Shook, K., Pomeroy, J., 2012. Changes in the hydrological
character of rainfall on theCanadian prairies. Hydrol. Process. 26,
1752–1766. http://dx.doi.org/10.1002/hyp.9383.
Shook, K., Pomeroy, J.W., Spence, C., Boychuk, L., 2013. Storage
dynamicssimulations in prairie wetland hydrology models: evaluation
andparameterization. Hydrol. Process. 27, 1875–1889.
http://dx.doi.org/10.1002/hyp.9867.
Sivapalan, M., Takeuchi, K., Franks, S.W., Gupta, V.K.,
Karambiri, H., Lakshmi, V.,Liang, X., McDonnell, J.J., Mendiondo,
E.M., O’Connell, P.E., Oki, T., Pomeroy, J.W.,Schertzer, D.,
Uhlenbrook, S., Zehe, E., 2003. IAHS decade on predictions
inungauged basins (PUB), 2003–2012: shaping an exciting future for
thehydrological sciences. Hydrol. Sci. J. 48, 857–880.
Spence, E.S., 1973. Theoretical frequency distributions for the
analysis of plainsstreamflow. Can. J. Earth Sci. 10, 130–139.
Spence, C., 2007. On the relation between dynamic storage and
runoff: a discussionon thresholds, efficiency, and function. Water
Resour. Res. 43. http://dx.doi.org/10.1029/2006WR005645.
Spence, C., 2010. A paradigm shift in hydrology: storage
thresholds across scalesinfluence catchment runoff generation.
Geogr. Compass 4, 819–833.
http://dx.doi.org/10.1111/j.1749-8198.2010.00341.x.
Spence, C., Woo, M., 2003. Hydrology of subarctic Canadian
shield: soil-filledvalleys. J. Hydrol. 279, 151–166.
http://dx.doi.org/10.1016/S0022-1694(03)00175-6.
Stichling, W., Blackwell, S.R., 1957. Drainage area as a
hydrologic factor on theglaciated Canadian prairies. In: IUGG
Proceedings, vol. 111. pp. 365–376.
Struthers, I., Sivapalan, M., 2007. A conceptual investigation
of process controlsupon flood frequency: role of thresholds.
Hydrol. Earth Syst. Sci. 11,
1405–1416.http://dx.doi.org/10.5194/hess-11-1405-2007.
Tabler, R.D., 1975. Estimating the transport and evaporation of
blowing snow. In:Snow Management on the Great Plains. Great Plains
Agricultural CouncilPublication No. 73. University of Nebraska,
Lincoln, NE, pp. 85–105.
http://dx.doi.org/10.1175/1520-0442(2001)014<1959:CODAET>2.0.CO;2http://dx.doi.org/10.1175/1520-0442(2001)014<1959:CODAET>2.0.CO;2http://refhub.elsevier.com/S0022-1694(14)01025-7/h0020http://refhub.elsevier.com/S0022-1694(14)01025-7/h0020http://refhub.elsevier.com/S0022-1694(14)01025-7/h0025http://refhub.elsevier.com/S0022-1694(14)01025-7/h0025http://refhub.elsevier.com/S0022-1694(14)01025-7/h0030http://dx.doi.org/10.1016/j.jhydrol.2011.11.007http://dx.doi.org/10.1016/j.jhydrol.2011.11.007http://dx.doi.org/10.1080/02626667.2014.967249http://dx.doi.org/10.1080/02626667.2014.967249http://dx.doi.org/10.4141/S98-075http://dx.doi.org/10.4296/cwrj2602165http://dx.doi.org/10.1002/hyp.6796http://dx.doi.org/10.1002/hyp.6796http://dx.doi.org/10.1002/hyp.7348http://dx.doi.org/10.1002/hyp.7348http://refhub.elsevier.com/S0022-1694(14)01025-7/h0075http://refhub.elsevier.com/S0022-1694(14)01025-7/h0075http://refhub.elsevier.com/S0022-1694(14)01025-7/h0080http://refhub.elsevier.com/S0022-1694(14)01025-7/h0080http://dx.doi.org/10.1016/0148-9062(85)92399-Xhttp://dx.doi.org/10.1016/0148-9062(85)92399-Xhttp://refhub.elsevier.com/S0022-1694(14)01025-7/h0090http://refhub.elsevier.com/S0022-1694(14)01025-7/h0090http://refhub.elsevier.com/S0022-1694(14)01025-7/h0090http://refhub.elsevier.com/S0022-1694(14)01025-7/h0090http://refhub.elsevier.com/S0022-1694(14)01025-7/h0100http://refhub.elsevier.com/S0022-1694(14)01025-7/h0100http://refhub.elsevier.com/S0022-1694(14)01025-7/h0105http://refhub.elsevier.com/S0022-1694(14)01025-7/h0105http://refhub.elsevier.com/S0022-1694(14)01025-7/h0110http://refhub.elsevier.com/S0022-1694(14)01025-7/h0110http://refhub.elsevier.com/S0022-1694(14)01025-7/h0110http://dx.doi.org/10.2151/jmsj.83.783http://refhub.elsevier.com/S0022-1694(14)01025-7/h0125http://refhub.elsevier.com/S0022-1694(14)01025-7/h0125http://refhub.elsevier.com/S0022-1694(14)01025-7/h0125http://refhub.elsevier.com/S0022-1694(14)01025-7/h0125http://refhub.elsevier.com/S0022-1694(14)01025-7/h0125http://refhub.elsevier.com/S0022-1694(14)01025-7/h0125http://dx.doi.org/10.1080/02626669109492496http://dx.doi.org/10.1080/02626669109492496http://dx.doi.org/10.1672/0277-5212(2003)023[0013:TCIAPP]2.0.CO;2http://dx.doi.org/10.1672/0277-5212(2003)023[0013:TCIAPP]2.0.CO;2http://refhub.elsevier.com/S0022-1694(14)01025-7/h0145http://refhub.elsevier.com/S0022-1694(14)01025-7/h0145http://dx.doi.org/10.1080/07055900.2011.583910http://dx.doi.org/10.1007/s13157-010-0044-8http://refhub.elsevier.com/S0022-1694(14)01025-7/h0160http://dx.doi.org/10.5194/hess-11-443-2007http://dx.doi.org/10.1002/hyp.8123http://dx.doi.org/10.1002/hyp.8123http://refhub.elsevier.com/S0022-1694(14)01025-7/h0175http://refhub.elsevier.com/S0022-1694(14)01025-7/h0175http://dx.doi.org/10.1016/0022-1694(93)90171-5http://dx.doi.org/10.1016/0022-1694(93)90171-5http://refhub.elsevier.com/S0022-1694(14)01025-7/h0190http://refhub.elsevier.com/S0022-1694(14)01025-7/h0190http://refhub.elsevier.com/S0022-1694(14)01025-7/h0195http://refhub.elsevier.com/S0022-1694(14)01025-7/h0195http://refhub.elsevier.com/S0022-1694(14)01025-7/h0195http://refhub.elsevier.com/S0022-1694(14)01025-7/h0195http://refhub.elsevier.com/S0022-1694(14)01025-7/h0200http://refhub.elsevier.com/S0022-1694(14)01025-7/h0200http://refhub.elsevier.com/S0022-1694(14)01025-7/h0200http://refhub.elsevier.com/S0022-1694(14)01025-7/h0200http://refhub.elsevier.com/S0022-1694(14)01025-7/h0220http://refhub.elsevier.com/S0022-1694(14)01025-7/h0220http://www.r-project.org/http://www.r-project.org/http://dx.doi.org/10.1002/hyp.6281http://dx.doi.org/10.1002/hyp.9409http://dx.doi.org/10.1002/hyp.9409http://dx.doi.org/10.1002/hyp.8390http://refhub.elsevier.com/S0022-1694(14)01025-7/h0250http://refhub.elsevier.com/S0022-1694(14)01025-7/h0250http://refhub.elsevier.com/S0022-1694(14)01025-7/h0250http://dx.doi.org/10.1002/hyp.8381http://dx.doi.org/10.1002/hyp.8381http://dx.doi.org/10.1002/hyp.9383http://dx.doi.org/10.1002/hyp.9383http://dx.doi.org/10.1002/hyp.9867http://dx.doi.org/10.1002/hyp.9867http://refhub.elsevier.com/S0022-1694(14)01025-7/h0270http://refhub.elsevier.com/S0022-1694(14)01025-7/h0270http://refhub.elsevier.com/S0022-1694(14)01025-7/h0270http://refhub.elsevier.com/S0022-1694(14)01025-7/h0270http://refhub.elsevier.com/S0022-1694(14)01025-7/h0270http://refhub.elsevier.com/S0022-1694(14)01025-7/h0275http://refhub.elsevier.com/S0022-1694(14)01025-7/h0275http://dx.doi.org/10.1029/2006WR005645http://dx.doi.org/10.1029/2006WR005645http://dx.doi.org/10.1111/j.1749-8198.2010.00341.xhttp://dx.doi.org/10.1111/j.1749-8198.2010.00341.xhttp://dx.doi.org/10.1016/S0022-1694(03)00175-6http://dx.doi.org/10.1016/S0022-1694(03)00175-6http://dx.doi.org/10.5194/hess-11-1405-2007
-
K. Shook et al. / Journal of Hydrology 521 (2015) 395–409
409
van der Kamp, G., Hayashi, M., 1998. The groundwater recharge
function of smallwetlands in the semi-arid northern prairies. Gt.
Plains Res. 8, 39–56.
van der Kamp, G., Hayashi, M., 2008. Groundwater-wetland
ecosystem interactionin the semiarid glaciated plains of North
America. Hydrogeol. J. 17,
203–214.http://dx.doi.org/10.1007/s10040-008-0367-1.
Venables, W.N., Ripley, B.D., 2002. Modern Applied Statistics
with S. Springer, 868p.Vincent, L.A., Mekis, É., 2006. Changes in
daily and extreme temperature and precipitation
indices for Canada over the twentieth century. Sci. Technol. 44,
177–193.Watmough, M.D., Schmoll, M., 2007. Environment Canada’s
Prairie and Northern
Region Habitat Monitoring Program Phase II: Recent Habitat
Trends in thePrairie Habitat Joint Venture. Technical Report Series
No. 493. EnvironmentCanada, Canadian Wildlife Service, Edmonton,
Alberta Canada.
Wickham, H., 2009. ggplot2: Elegant Graphics for Data Analysis.
Springer, NewYork.
WMO, 2009. Guide to Hydrological Practices Volume II Management
of WaterResources and Application of Hydrological Practices, sixth
ed., Geneva.
Zhang, X., Vincent, L.A., Hogg, W.D., Niitsoo, A., 2000.
Temperature and precipitationtrends in Canada during the 20th
century. Atmosphere-Ocean 38,
395–429.http://dx.doi.org/10.1080/07055900.2000.9649654.
Zhang, B., Schwartz, F.W., Liu, G., 2009. Systematics in the
size structure of prairiepothole lakes through drought and deluge.
Water Resour. Res. 45. http://dx.doi.org/10.1029/2008WR006878.
http://refhub.elsevier.com/S0022-1694(14)01025-7/h0310http://refhub.elsevier.com/S0022-1694(14)01025-7/h0310http://dx.doi.org/10.1007/s10040-008-0367-1http://refhub.elsevier.com/S0022-1694(14)01025-7/h0320http://refhub.elsevier.com/S0022-1694(14)01025-7/h0325http://refhub.elsevier.com/S0022-1694(14)01025-7/h0325http://refhub.elsevier.com/S0022-1694(14)01025-7/h0335http://refhub.elsevier.com/S0022-1694(14)01025-7/h0335http://dx.doi.org/10.1080/07055900.2000.9649654http://dx.doi.org/10.1029/2008WR006878http://dx.doi.org/10.1029/2008WR006878
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