modelling urban snowmelt runoff

Modelling urban snowmelt runoff

C. Valeo*, C.L.I. Ho

Department of Geomatics Engineering, University of Calgary, 2500 University Drive NW, Calgary, Alta., Canada T2N 1N4

Abstract

Few investigations have been made into modelling snowmelt in urban areas; hence, current urban snowmelt routines have

adopted parameters and approaches intended for rural areas that are not appropriate in an urban environment. This paper

examines problems with current urban snowmelt models and proposes a model that uses parameters developed from field

studies focusing exclusively on urban snow. The Urban Snow Model (USM) uses an energy balance scheme at an hourly time

step, changes in urban snow albedo, and incorporates eight different types of redistributed snow cover. USM is tested against

observed flow data from a small residential community located in Calgary, Alberta. The degree-day method for snowmelt, the

SWMM model, and a modified version of USM that incorporates a partial energy budget scheme relying only on net radiation,

are also tested against the observed flow data. The full energy budget version of USM outperformed all other models in terms of

time to peak, peak flowrate and model efficiency; however, the modified version of USM fared quite well and is recommended

when a lack of data exists. The degree-day method and the SWMM models fared poorly and were unable to simulate peak

flowrates in most cases. The tests also demonstrated the need to distribute snow into appropriate snow covers in order to

simulate peak flowrates accurately and provide good model efficiency.

q 2004 Elsevier B.V. All rights reserved.

Keywords: Urban hydrology; Snowmelt; Distributed modelling; Energy balance

1. Introduction

Studies of urban hydrology have concentrated

mainly on the response of urban catchments to rainfall

events. Generally, high intensity rainfalls are assumed

to be the major flood-generating events in urban areas

(Buttle and Xu, 1988); however, in the northern

hemisphere, flooding is observed during snowmelt in

urban environments in Scandinavia, Canada and the

northern USA (Bengtsson and Westerstrom, 1992;

0022-1694/$ - see front matter q 2004 Elsevier B.V. All rights reserved.

doi:10.1016/j.jhydrol.2004.08.007

* Corresponding author. Tel.: C1-403-220-4112; fax: C1-403-

284-1980.

E-mail address: [email protected] (C. Valeo).

Semadeni-Davies and Bengtsson, 1998; Thorolfsson

and Brandt, 1996; Farrell et al., 2001). A flooding

situation can be aggravated by high levels of receiving

waters or reduced outfall drainage capacity. In these

cases, it may be necessary to consider seasonal design

events in urban flood analysis for stormwater manage-

ment system design. Traditionally, waste and storm-

water systems have been constructed according

to standards set for rainfall dominated climates

(Marsalek, 1991; Matheussen and Thorolfsson,

1999; Semadeni-Davies, 2000).

Snowmelt intensities are much lower than rainfall

intensities, but it has been assumed that the processes

and factors governing both urban and rural snow

Journal of Hydrology 299 (2004) 237–251

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http://www.elsevier.com/locate/jhydrol

C. Valeo, C.L.I. Ho / Journal of Hydrology 299 (2004) 237–251238

hydrology are the same. Thus, snow receives little

interest in urban hydrological research. However,

there are differences between the factors that control

snowmelt and runoff generation in the two environ-

ments (Bengtsson and Westerstrom, 1992); and

therefore, snowmelt modelling approaches in each

area should also differ. Accurate modelling of urban

snowmelt can assist efforts to study winter pollutant

transport (Buttle and Xu, 1988). Snow has been shown

to store high levels of various pollutants including

lead, hydrocarbons, polychlorinated-biphenyls and

other metals and solids (Marsalek et al., 2000).

Suzuki (1990) noted high levels of SO42– in urban

snow due to anthropogenic emission sources in urban

areas.

1.1. Factors affecting melt and winter runoff in urban

areas

The major causes of differences between urban and

rural snow are the snow removal practices employed

in urban areas. Snow in urban areas is usually

removed from the impervious surfaces and much of

it is piled onto adjacent grassed banks. In highly

impervious urban areas, the snow can be trucked to a

dumpsite. Undisturbed, fairly uniform snow cover

similar to rural snow can usually be found only in city

parks and open grassed areas.

In urban areas, melt seems to be dominated by net

radiation fluxes, while contributions from sensible heat

flux, turbulent exchanges and heat exchange at the

snow–soil interface are minor (Westerstrom, 1981;

Sundin et al., 1999; Bengtsson and Westerstrom, 1992;

Semadeni-Davies and Bengtsson, 1998; Marks and

Dozier, 1992). Snowpack energy fluxes are greatly

influenced by the urban environment. Spatial varia-

tions in energy fluxes exist over the snowpack due to

factors such as longwave radiation from buildings,

full-sun/shadowed effect, the variability in snow

albedo, and atmospheric composition (Bengtsson

and Westerstrom, 1992; Semadeni-Davies, 1999;

Thorolfsson and Sand, 1991; Buttle and Xu, 1988;

Semadeni-Davies and Bengtsson, 1998). Snow albedo

(the reflectivity of a body to shortwave radiation) is

lower in the city than in rural areas due to pollution and

the rapid increase in iciness caused by ploughing

and packing (Bengtsson and Westerstrom, 1992;

Semadeni-Davies, 2000; Conway et al., 1996).

Compared to rural areas, urban soils suffer

heavy compaction due to activities such as construc-

tion and traffic, which tend to reduce the soil’s

infiltration capacity. Frozen soils with low soil

moisture contents may exhibit significant infiltration

capacities initially in the snowmelt period (Granger

et al., 1984), but infiltration tends to decrease

substantially as the snowmelt period progresses

(Buttle and Xu, 1988; Bengtsson and Westerstrom,

1992; Westerstrom, 1990; Ho, 2002). Hence, per-

meable areas can contribute to snowmelt induced

runoff. For rain-on-snow events, the area contributing

to runoff increases considerably, and can be greater

than for summer storms.

1.2. Modelling urban snowmelt

Accurate snowmelt modelling requires an energy

budget scheme (Anderson, 1968) and this requires

good measurements of incoming solar radiation,

albedo, incoming longwave radiation, wind speed,

air vapor pressure, air temperature, and precipitation.

Due to the lack of available data, many practical

operational procedures for snowmelt predictions

generally rely on air temperature as the index of the

energy available for melt (Gray and Male, 1981; Watt

et al., 1989; Westerstrom, 1990). In these cases, the

temperature index or degree-day method replaces the

full energy budget scheme. It is physically sound in

the absence of shortwave radiation when much of the

energy supplied to the snowpack is atmospheric

longwave radiation, such as in heavily forested areas

(Semadeni-Davies, 2000). In its simplest form, the

relationship between snowmelt and air temperature

can be expressed as

M Z MfðTi KTbÞ (1)

where M is the snowmelt generated (mm dayK1); Mf

is the melt factor (mm 8CK1 dayK1); Ti is the index air

temperature in 8C (commonly the mean temperature

of the day or some derivative of the daily minimum

and maximum temperatures); and Tb is the base

temperature in 8C (commonly 0 8C).

Snowmelt runoff simulated with the degree-day

method assumes both a homogeneous snowpack and

snow cover. Bengtsson (1984) showed that snowmelt

from the heterogeneous urban environment cannot be

C. Valeo, C.L.I. Ho / Journal of Hydrology 299 (2004) 237–251 239

adequately determined from temperature indices.

Urban snow tends to be plowed into piles having a

wide range of characteristics depending on location

and landuse. Thus, the presence of snow piles can both

reduce the maximum volume of melt and extend the

melt period (Semadeni-Davies, 2000). Without modi-

fications to the method, its application is not

theoretically suitable for urban snow runoff simu-

lations (Semadeni-Davies, 2000). In addition, only the

full energy budget method can simulate rain-on-snow

conditions.

Semadeni-Davies (2000) and Ho (2002) conducted

reviews of various computer models that are often

used to simulate snowmelt in urban areas. Available

computer-based models for snow accumulation and

melt range from simple temperature index models to

full energy balance schemes. The snowmelt models

are generally components of more comprehensive

runoff models intended for large rural or urbanizing

watersheds. It should be noted that all snowmelt

routines have two basic components: (1) the method

of snowmelt generation (i.e. the degree-day method or

the energy budget method); and (2) the method of

handling snow cover accumulation and depletion

(Watt et al., 1989). Semadeni-Davies (2000) and

Ho (2002) reviews included the NWSRFS model

(NWSHL, 1996) which incorporates SNOW-17;

SWMM (Huber, 1995); MOUSE RDII (DHI, 2000);

HSPF (Donigian et al., 1995); and SSARR (Speers,

1995). They all offer equations ranging from the

temperature index method to the energy budget

method and hybrids in between those two extremes.

NWSRFS SNOW-17, SWMM, MOUSE RDII and

SSARR use the degree-day method to simulate melt,

but SWMM, SSARR and HSPF also offer a full

energy budget scheme option.

The degree-day method has been proven to be

valuable in rural and alpine areas (WMO, 1986),

but transferring the model to an urban environment

is questionable. Various types of snow cover can

be found in urban areas with the most dominant

types being snow piles and natural snow cover on

pervious areas. Other types include snow on road

shoulders, snow on rooftops, and snow near

building walls. Snow piles are normally located

near roads and pavements and are compacted and

icy with low albedos. These factors will influence

local melt conditions. Given the small catchment

size and extreme spatial variability of snowpack

location, albedo, depth, density, and energy avail-

ability, the use of a single melt rate factor in urban

areas is questionable (Semadeni-Davies, 2000). In

their investigation of simulation errors due to

insufficient temporal resolution in urban snowmelt

models, Matheussen and Thorolfsson (1999) deter-

mined that snowmelt induced runoff in urban areas

should be measured and modeled with a 1-h time

resolution or less. Bengtsson (1984, 1986) noted

that because degree-day melt routines make melt

calculations only once daily, it masks the dynamics

of runoff generation over impervious urban

surfaces.

Energy balance models for each type of snow

cover in urban areas is different due to characteristics

of the snow such as initial density values, the initial

snow albedo values and the rate of change of the snow

properties. There has been no attempt to apply

separate energy models to the different snow cover

types to achieve accurate modelling of snowmelt in

urban areas. In addition, none of the current models

simulate ground frost. Thorolfsson and Brandt (1996)

and Westerstrom (1984) showed that urban soils can

become seasonally impervious, which suggests that a

soil frost/thaw routine could be important.

1.3. Objectives

The objectives of this research are to develop and

demonstrate an efficient and accurate model for

urban snowmelt, which accounts for at least some of

the shortcomings observed in currently used models.

Comparisons between a full-energy budget method, a

modified energy-budget method, and the degree-day

method are investigated. The models developed in

this research use information on snow properties

observed during a field campaign at the University of

Calgary in the winter of 2001 (Ho, 2002). This

information will be used to construct appropriate

time-dependent albedo curves, snow depletion

curves, and a latent heat transfer coefficient, in

order to create the best model possible. The models

will be tested to show the impacts of simulating the

redistribution of snow due to urban snow removal

practices versus undistributed snow. A popular

model for urban hydrology, SWMM, will also be

used in the comparisons.


2. Methodology and field study area

2.1. The USM model

The Urban Snow Model (USM) was created and

programmed in Matlab to simulate generation of

snowmelt runoff from an urban catchment. Although

flowrates for urban winter runoff are typically low,

they can be sustained over several days and a

significant fraction of winter pollutants may be

removed by snowmelt. The basic melt computations

in USM are based on routines developed by the US

National Weather Service (Anderson, 1973). The

program uses hourly time steps, allows redistribution

of snow from impervious areas to pervious areas, and

applies different snow albedo values for the different

snow cover types found in urban areas. All snow

depths throughout the model are treated as depths of

snow water equivalent (SWE). Thus, the model serves

to demonstrate the impact of incorporating snow

redistribution and urban snow characteristics on

snowmelt generation, which is important for urban

areas that receive high snowfall amounts.

2.1.1. Redistribution of snow by landcover type

Redistribution refers to the removal of snow from

the original area to its new location. The model

assumes eight different types of snow cover are

possible in an urban area and these are related to

landcover type. These types are shown in Table 1.

Redistribution occurs for roadways when SWE reaches

depths above 6.5 mm, for driveways/sidewalks when

Table 1

Area characterization

Type Perviousness Snow cover and extent

1 Impervious Normally bare



4 Pervious Covered with large snow piles

5 Pervious Covered with small dirty snow

6 Pervious Covered with small cleaner sn

7 Pervious Uniform snow cover

8 Pervious Uniform snow cover

SWE is above 10.0 mm, and for rooftops when the

SWE is above 8.5 mm. Generally in the City of

Calgary, snow removal occurs when SWE is greater

than 5 mm. But in new residential areas, not all the

roads are ploughed, thus, the SWE for this snow cover

type was elevated to 6.5 and 10 mm for driveways and

sidewalks. Snow on rooftops is redistributed to

simulate effects of drifting, blowing snow and sloping

roofs, but the SWE redistribution threshold of 8.5 mm

for this snow cover type was arbitrarily chosen.

2.1.2. Energy balance method

The energy balance equation for a snowpack is

expressed as follows

DQ Z Qsw CQlw CQe CQh CQg CQm (2)

where DQ is the change in heat storage in the

snowpack; Qsw is the net shortwave radiation entering

the snowpack; Qlw is the net longwave radiation

entering the snowpack; Qe is the latent heat transfer;

Qh is the sensible heat transfer; Qm is the advection of

heat into the snowpack by rain; and Qg is the

conduction of heat into the snowpack from the

underlying ground. Units for each energy balance

term are in W/m2 h. It is assumed that if the condition

is right for melt than all heat added to the snowpack

will produce liquid melt. For a melting snowpack,

heat conduction from the ground, Qg is negligible

compared to the energy exchange at the snow surface.

Thus, that term is neglected. It requires about 80 cal to

melt 1 g of water (the latent heat of fusion) or

93 W/m2 h per 1 mm of melt. The melt rate is thus

Examples of land

surface

%Area

Parking lots –

All level roads 11.8

Driveways and

sidewalks

8.9

Perimeter area of

parking lots

–

piles Road shoulders 0.6

ow piles Driveways/

sidewalk edges

3.6

Rooftops 23.9

Parks, lawns,

open areas

51.2


calculated as follows

Msr ZDQ

93(3)

where Msr is the melt rate (mm/h); and DQ is the

change in heat storage of the snowpack (W/m2 h).

2.1.3. Shortwave radiation

The net shortwave radiation is calculated as

follows

Qsw Z Qið1 KAÞ (4)

where Qsw is the net shortwave radiation (W/m2 h);

Qi is the incoming shortwave radiation (W/m2 h);

Fig. 1. Albedo

and A is the snow albedo. Snow albedo values were

measured in a field study conducted at the University

of Calgary over the winter of 2001–2002 (Ho, 2002).

From that study, eight snow albedo curves were

developed and are shown in Fig. 1. The Type 1 curve

(snow in parking lots) was derived from the Type 4

curve, but ultimately never used. The Type 2 curve is

a combination of albedo for snow on road shoulders

(Type 5) and sidewalk edges (Type 6). It was created

by combining all the measurements made for Types 5

and 6 areas in the University of Calgary field study

and fitting a curve to the data. The Type 3 curve is the

same as the Type 6 curve. The Types 4–6 and 8 albedo

curves were all produced from fitting curves to

curves.


measurements made in the field study. The Type 7

curve is a combination of curves of Types 5 and 6;

however, unlike the Type 2 curve, this curve was

delayed by 5 days in order to keep the snow on

rooftops fresher for an initially longer period of time.

The curve used for Type 8 was not used for rooftops

because most roofs are asphalt based; hence, albedo is

lower and decreases more rapidly as compared to the

albedo of snow in open areas.

2.1.4. Longwave radiation

The net longwave radiation is calculated as follows

Qlw Z Qa KEt (5)

where Qlw is the net longwave radiation (W/m2 h); Qa

is the incoming longwave radiation (W/m2 h); and Et

is the total emitted longwave radiation (W/m2 h).

The total emitted longwave radiation is given by the

Stefan–Boltzman law

Et Z 3sT4 (6)

where Et is the total emitted longwave radiation

(W/m2); 3 is the emissivity in the longwave portion of

the energy spectrum; s is the Stefan–Boltzman

constant (5.67!10K8 W mK2 KK4); and T is the

snow surface temperature (K). For ambient air

temperature ! 0 8C, the snow surface temperature

is assumed to equal the air temperature. For ambient

air temperature R0 8C, the snow is assumed to be

melting, and TZ273 K. Hence, assuming that the

emissivity 3 is 0.97 melting snow emits longwave

radiation at EtZ305 W/m2.

2.1.5. Latent and sensible heat transfer

Latent and sensible heat transfers are turbulent

transfer processes. Latent heat is either energy lost

from the snowpack due to evaporation and sublima-

tion or energy gained from condensation. Sensible

heat is attributed to the heat content of the air. A

common equation for the latent heat transfer is

(Eagleson, 1970)

Qe Z 2359:9!8:5keðztzbÞK1=6Ubðea KesÞ (7)

where Qe is the latent heat transfer (W/m2 h); zt is

the height above the surface at which the air

temperature measurements are made (ft); zb is the

height above the surface at which the wind speed

measurements are made (ft); Ub is the wind speed

(miles/h); ea is the vapor pressure at height zt (mb);

and es is the saturation vapor pressure at the snow

surface (mb). The factor 2359.9 converts inches to

W/m2 h, and the factor 8.5 accounts for the fact that

when the snowpack is ripe, the latent heat of

condensation will supply latent heat of fusion to

melt the snow. Due to the ratio of these latent heats

(600/80Z7.5), each inch of condensate will result

in 8.5 (that is, 7.5C1) inches of melt. This applies

to the evaporation process as well. In this study, the

coefficient ke is obtained through calibration to

snow evaporation measurements made in the field

study. Values of za, zb, Ub, ea, and es were obtained

from the University of Calgary’s weather station,

and used in the calculation of latent heat transfer.

The resultant values were compared to snow

evaporation loss measured in the field study.

Hence, the resultant ke coefficient is equal to

0.000035 in./h ft1/3 mi/h mbK1.

During snowmelt periods, heat is usually trans-

ferred from the air to the snowpack, because of the

snowpack’s colder temperature compared to the air

(sensible heat transfer term is positive). Similar to

latent heat transfer, sensible heat transfer depends on

the turbulence of the air. Assuming turbulent transfer

coefficients for heat and vapor are equal, sensible heat

transfer can be obtained using the Bowen ratio

(Anderson, 1973), expressed as

Qh

Qe

Z gTa KTo

ea Keo

(8)

where Qh is the sensible heat transfer (W/m2 h); Qe is

the latent heat transfer (W/m2 h); g is the psycho-

metric constant (mb 8CK1) (gZ0.00057Pa, where Pa

(mb) is the atmospheric pressure); To is the snow

surface temperature (8C); Ta is the temperature of

the air at za (8C); ea is the vapor pressure of the air at

zt (mb); and eo is the vapor pressure at the snow

surface (mb) (assumed equal to the saturation vapor

pressure at the snow surface temperature).

2.1.6. Advected heat from rain

The amount of heat transferred to the snow by

rainwater is directly proportional to the quantity of

rainwater and its temperature excess (O0 8C). For

every degree (8C) the rainwater is in excess of


the snow temperature (0 8C), and for every gram of

rainwater, 1 cal heat is available. It takes 80 cal to

produce 1 g of meltwater from ice. Hence, the

advected heat transfer from rain is

Qm Z 93c

80PxðTa KTsÞ (9)

where Qm is the advected heat from rain (W/m2 h);

c is the specific heat of water (cZ1.0 cal/g 8C); Px is

the rainfall intensity (mm/h); Ta is the air temperature

(8C) and Ts is the snow surface temperature (8C). The

factor 93 converts mm to W/m2Kh.

2.1.7. Areal depletion curve

Areal depletion curves are used to determine the

areal extent of the snow cover at any given time. The

areal extent of snow cover on a catchment is

determined by the fraction of area covered by snow,

ASC, on the areal depletion curve. It is assumed that

for all areas there is a depth, SnowD, above which

there is always 100% cover. In this study, the value of

SnowD is arbitrarily fixed at 5 mm. The SWE depth

present on the catchment at any time is indicated by

the parameter Swe. This depth is nondimensionalized

by SnowD to calculate ASC. Thus, patches of bare

ground will only appear after snowmelt reduces Swe

to less than 5 mm. The fraction ASC is used to adjust

the volume of melt that occurs, since heat transfer

occurs only over the snow-covered areas. Snow depth

at time step 2 is then reduced from time step 1

according to

Swe2 Z Swe1 K ðMsr !ASCÞ (10)

Because of the heterogeneous nature of snowpack

in urban areas, melt rates are rarely uniform within the

urban catchment. Thus, five different areal depletion

curves are used in this study to determine ASC

for the different snow cover types. The curves used

in this study were developed through calibration

(see Section 2.2) as insufficient field data did not allow

for the development of actual areal depletion curves

as a function of landcover type.

2.1.8. Liquid water routing in the snowpack

Snowpack is a porous medium that has a certain

‘free water holding capacity’ at any given time. Thus,

not all melt immediately results in runoff. Following

the computer model SWMM (Huber and Dickinson,

1988), the free water holding capacity is assumed to

be a constant fraction, Fr, of the variable snow depth,

Swe at each time step. The value of Fr is normally less

than 0.10 and usually between 0.02 and 0.05 for deep

snowpacks (Huber and Dickinson, 1988). Anderson

(1973) reported that a value of 0.25 is not unreason-

able for shallow snowpacks. The free water holding

capacity for each subcatchment is computed as

follows (Huber and Dickinson, 1988)

FWC Z Fr !Swe (11)

where FWC is the free water holding capacity (mm); Fr

is a fraction of snow depth; and Swe is the snow depth

at any time step in water equivalent (mm). Values were

estimated from the sources quoted above and even-

tually calibrated (see Section 2.2). The volume of the

snowpack’s free water holding capacity must be

satisfied before runoff can be produced. By including

the free water holding capacity of the snowpack in the

simulation, runoff can be delayed and attenuated. Cold

content accounting of the snowpack, which may

further delay melt, is not conducted by the model as

it is assumed that the snowpack is fully primed and ripe

before any significant snowmelt runoff is observed.

2.1.9. Infiltration into frozen ground

Analysis from the University of Calgary field study

revealed that frozen ground acts as a near impervious

surface regardless of the condition of the initial soil

moisture content (Ho, 2002). Thus, infiltration of

snowmelt into frozen ground is minimal and assumed

negligible in this study and hence, was not pro-

grammed into the model. Instead, all pervious areas

can possibly contribute to runoff.

2.1.10. Net runoff

Runoff from snowmelt is produced after the free

water holding capacity of the snowpack is fulfilled.

Net runoff is a combination of areal weighted

snowmelt runoff from snow covered areas, and

rainfall falling on bare grounds.

NRunoff Z ASC!Msr C ð1:0 KASCÞPx (12)

where NRunoff is the net runoff (mm/h); and Px is the

rainfall intensity (mm/h).


2.2. Study area and calibrations

The study area used in this research is the

McKenzie Lake community in South East Calgary.

It is a residential area that drains into the Bow River.

Flow data were measured at a manhole located in the

study area shown in Fig. 2. The distribution of landuse

was determined manually and is shown in Table 1.

The catchment did not include any commercial

centers, therefore, area Types 1 and 4 are not

simulated. Residential areas were selected as 40%

impervious, commercial and industrial areas were

selected as 75% impervious, and institutional areas

were selected as 70% impervious. These values are in

the upper part of the imperviousness ranges as

suggested by Chow (1964). The total catchment area

is 254,800 m2 while the pervious area amounts to

55.4% and the impervious area amounts to 44.6%.

Total impervious area measured is slightly higher than

values established from the literature because the

study area is a fairly new residential area, and

the ratios of house area to lot size is higher than in

slightly older communities.

Hourly meteorological data including precipi-

tation, temperature, relative humidity, vapor pressure,

wind speed, incoming shortwave radiation and long-

wave radiation were obtained from the University of

Calgary’s weather station. The University’s weather

station is less than 20 km of the study site. Flow data

measured at the outlet of the McKenzie watershed

were provided by the City of Calgary at hourly time

steps for the period between January 26 and February

28. A custom designed weir built to the dimensions of

the storm sewer pipe in conjunction with an ultrasonic

level sensor and a flow datalogger was used to

measure flow. An area–velocity sensor helped to

measure flows at times when overtopping of the weir

was possible. This time period was chosen because it

begins with a significant snowfall event of 15.3 mm

SWE in depth and calibrations were conducted over

this period. The study area in this research receives

fairly low snowfall amounts in general, but other

Canadian cities such as Quebec and Winnipeg receive

very high snowfall amounts. Advected heat from rain

was not simulated in this study as this event did not

occur in the study period.

A calibrated version of the complete USM model

predicted flowrates are compared to observed

flowrates. In addition, a modified USM model that

only uses short and long-wave radiation is also

assessed. This scaled down version of the model

was chosen as net radiation fluxes are quoted as the

dominant processes in urban areas. In this case,

Eqs. (7)–(9) are not used and Qe, Qh, Qg and Qm are

neglected and considered near zero in Eq. (2). In

addition, the degree-day method is tested along with

the SWMM model.

The SWMM model was selected because it is a

very popular model for use in urban areas. No rain on

snow events occurred during the study period so

SWMM was executed using only its internal degree-

day method at a daily time-step (the only time-step

allowed). In SWMM, snow is redistributed from

impervious areas to either: snow covered impervious

areas; snow covered pervious areas; snow covered

pervious areas in another subcatchment; snow trans-

ferred out of the watershed; and snow converted

immediately to melt on normally bare impervious

areas. There is a calibrated fraction of snow associated

with each redistribution type and the five fractions

should sum up to 1.0. In these tests, redistribution

from impervious areas to snow covered pervious areas

was the only type used as it was the only one that was

truly applicable, and thus, the fraction of snow

redistributed to pervious areas from impervious

areas was 1.0. SWMM also uses a variety of melt

coefficients for each cover type and a sinusoidal curve

to interpolate these coefficients to daily values over

the year. These are calibrated by the user. In each

case, except for SWMM, the models are tested using

redistributed and undistributed snowpacks according

to covers shown in Table 1. In the undistributed case,

the snow is homogenous throughout the catchment,

but the same albedo curves are used for each snow

cover type.

The full USM calibration involved manually

adjusting the areal depletion curves for each snow

cover type present in the catchment (see Fig. 3), and

adjusting the values of Fr. The initial values of Fr were

estimated from the literature and the calibrated Fr

values are shown in Table 2. Note that they are

slightly higher than those shown in the literature.

These values also apply to the modified USM model

application. Calibrated melt rate factors for each snow

cover type used in the application of the degree-day

method are shown in Table 3. Note that these values

Fig. 2. Study area (produced using 1:5000 City of Calgary digital aerial survey section map).


Fig. 3. Snow depletion curves.


are lower than those quoted by Westerstrom (1984)

for a single asphalted study plot (1.5–6.5 mm/8C day

depending on how long the temperature was above 8C,

with lower melt rates occurring earlier in the melt

period), and for a snowmelt event from the Porson

Table 2

Calibrated fraction of snow depth Fr versus cover type

Type Cover type Initial Fr Fr

2 All level roads 0.02 0.03

3 Driveways and sidewalks 0.02 0.08

5 Road shoulders 0.02 0.03

6 Driveways/sidewalks edges 0.10 0.15

7 Rooftops 0.10 0.23

8 Parks, lawns, open areas 0.25 0.30

residential area (with roughly 4 ha of impervious area)

in Lulea, Sweden (2.8 mm/8C day). Those melt

factors were obtained for areas much smaller than

the impervious area in this study (over 11 ha)

Table 3

Calibrated melt factors used in degree-day method

Type Cover type Melt factor,

Mf (mm/8C day)

2 All level roads 0.2

3 Driveways and sidewalks 2.0

5 Road shoulders 0.2

6 Driveways/sidewalks edges 0.2

7 Rooftops 0.02

8 Parks, lawns, open areas 0.11

Table 4

Calibrated melt factors used in SWMM

Day Cover type Melt factor

(mm/8C-h)

June 21 Snow covered impervious area 0.100

June 21 Snow covered pervious area 0.150

June 21 Normally bare impervious area 0.001

Dec 21 Snow covered impervious area 0.020

Dec 21 Snow covered pervious area 0.020

Dec 21 Normally bare impervious area 0.000

Note that values for June 21 are maximum melt factor values and

values for December 21 are minimum melt factor values.


and were not obtained for individual urban snow

cover types as they have in this study. Thus, a

comparison of melt rates between the studies is

difficult to make. The calibrated SWMM melt

coefficients are shown in Table 4.

The models were assessed in the period of

February 1–22 in order to remove biases caused by

long periods of baseflow. The criteria to evaluate the

model performances in this period are based on

the resulting Nash and Sutcliffe Efficiency (NSE)

measure (Nash and Sutcliffe, 1970) for the assessment

period; the total volumes; the ability to simulate peak

flowrates in four major peaks during the time period;

and the times to peak (measured from the start of the

rising limb to the peak flowrate value). Table 5 shows

the characteristics of the peak flowrates used to assess

the models and percent differences were computed as

(observedKpredicted)/observed.

3. Results and discussion

Fig. 4 shows the distribution of runoff type as

predicted by the full USM model for each snow cover

type. Runoff from roadways (Type 2 area) is intense

and starts early in the melt period. Due to traffic

activities, the runoff period is short as whatever little

Table 5

Observed peak characteristics

Day Time to peak (h) Peak flowrates (m3/h)

Feb 10 6 122

Feb 15 4 133

Feb 16 6 160

Feb 17 4 119

snow that is left from plowing/sanding melts off

quickly. Snow on roads is usually dirty and radiation

reflected or emitted from the asphalt back to the snow

can increase melt. Snow on driveways, sidewalks and

pathways (Type 3) melts in a similar manner as a

uniform snow cover. Snow is usually relatively clean

and assumes the albedo of a uniform snow cover in

this study. Snow on road shoulders (Type 5) is

simulated as a small dirty pile. Melt is intense, but the

magnitude of runoff is low, increasing with time as

snow albedo decreases, and runoff is sustained over a

long period. Although melt intensity is high, the area

covered by this snow cover is small, but contains a

high value of SWE; hence, flow remains low and is

sustained over several weeks. Snow on driveway/

sidewalk edges (Type 6) are simulated as small clean

piles. Snow is usually shoveled, but it does not contain

a high amount of dirt/sand. The start of runoff occurs

later in the melt period as snow albedo decreases

gradually. Similar to dirty snow piles, the runoff is

quite low, but sustained over a long period. Area

covered by this snow cover type is also relatively

small. Runoff from rooftops (Type 7) is intense and

lasts only several days. Snow on roofs is similar to

snow on roadways as most roofs are asphalt based.

Due to the relatively large area covered by this snow

cover type, the resulting magnitude of runoff is high.

Runoff in Type 8 areas (lawns, parks, and open

spaces) starts late in the melt period as the rate of

decrease of the snow albedo is lowest for this cover

type. When the snow albedo reaches a low enough

value so that energy for melt is available, the runoff is

intense and for only a relatively short period. The area

in the catchment covered by this snow type is quite

large.

Figs. 5–7 show the results of the simulations for the

various models. Tables 6 and 7 show the model

assessment results in the form of percent differences

in observed and predicted peak flowrates and

volumes, as well as Nash and Sutcliffe efficiencies.

From the graphs and tables, the full USM model

generally predicted both small and high peaks well,

although, the highest peak on the 16th is 10% lower

then the observed value. With the exception of the

degree-day method, this difference is small compared

to the other models.

The undistributed approach tends to overestimate

the small peaks that occur early in the melt period

Fig. 4. Predicted runoff from the different snow covered surfaces.


more greatly than the distributed approach’s estimates

of the same peaks. This is because the amount of snow

that would be normally moved to road shoulders and

sidewalk edges is now remaining on impervious areas

that have albedo curves that decrease rapidly with

time. This means more snow is melting earlier than

expected.

The degree-day method hydrographs for both the

distributed and undistributed cases look very similar

and hence, the undistributed case was not shown. For

the large peak on the 16th, the degree-day method

fairs better in its prediction then any other model. This

is because the majority of snow coverage for this

catchment is in the form of Types 7 and 8 and hence,

the time at which this cover contributes to runoff is

mostly on the 15th–17th. Considering the relatively

small area of catchment that is not of Types 7 and 8,

both the hydrographs and the results seen in Table 6

are greatly influenced by other cover types.

Overall, all models predicted flow volumes

relatively well and within acceptable limits. The

high values of NSE for both the USM and modified

USM model (in distributed cases) is a testament to the

overall performance of the model. The modified USM

model tends to underestimate high peaks, but may be a

reasonable trade-off when data are lacking. The

degree-day method hydrograph looks good at first

glance, however, the NSE value for this case is low.

This is because this model has great difficulty

predicting the time to peaks in all cases. This problem

will greatly skew NSE values. The full USM model

provided the best prediction of times to peak while the

modified USM and SWMM models were also fairly

good in predicting times to peak.

Fig. 5. Observed flow versus full USM.

Fig. 6. Observed flow versus modified USM.

Fig. 7. Observed flow versus predicted flow by Degree-day method

and SWMM model.

Table 6

Comparison in time to peak and peak flowrates

Model Day in

Feb

Time to peak (h) %Difference in

peak flowrates

Redist. Undist. Redist. Undist.

Full USM 10 4 6 29 23

15 4 4 1 12

16 6 5 10 14

17 4 3 6 11

Modified USM 10 4 4 45 26

15 4 4 16 26

16 4 4 21 27

17 4 4 K7 0

Degree-day 10 9 9 55 61

15 5 5 K23 K18

16 5 5 1 K3

17 7 6 44 40

SWMM 10 4 – 52 –

15 5 – 51 –

16 4 – 50 –

17 4 – 61 –


Table 7

Comparison in volumes and Nash and Sutcliffe efficiencies

Model Total volume

(m3)

%Difference NSE

Observed 5452.80 – –

Full USM and

redistributed

snow

5229.38 4.1 74

Full USM and

undistributed

snow

5257.31 3.6 57

Modified USM

and redistribu-

ted snow

5414.95 0.7 69

Modified USM

and undistribu-

ted snow

5543.98 K1.7 55

Degree-day and

redistributed

snow

5751.26 K5.5 57

Degree-day and

undistributed

snow

5412.59 0.7 52

SWMM 5459.20 0.1 12


The calibration of the SWMM model was the best

that could be obtained for this period. However, the

model performed poorly in terms of NSE values,

hydrographs, and peak flowrate values. This is

because SWMM’s degree-day method uses daily

estimates of minimum and maximum temperature

and an inadequate redistribution of urban snow. The

degree-day method applied by the authors used hourly

values of mean temperature.

4. Conclusions

This research shows that the manner in which

urban snow is redistributed can have a significant

impact on the timing and values of peak flowrates.

While most urban areas may have the majority surface

of area as pervious, the pervious area will contribute

directly to runoff with little infiltration. While piling

snow into piles and ploughing them along the sides of

roads delays their melt, this timing along with the melt

of open area snow can have significant impacts on the

resulting hydrographs.

The redistributed-full energy balance method of

USM fared the best in comparison to other models,

but the modified USM that only used net radiation

also fared respectably and can be used in areas

where a nearby meteorological station can at least

provide estimates of short and longwave radiation.

If the degree-day method must be used, then hourly

values of temperature are highly recommended.

Acknowledgements

The authors would like to thank Mr Charlie

Moxham from the Wastewater Division of the City

of Calgary for supplying the flow data, and Dr John

Yackel of the Department of Geography at the

University of Calgary for his insightful comments.

We would also like to thank Dr Jeffrey M. Rice and

an anonymous reviewer for their helpful comments

and suggestions. This work was supported by the

National Science and Engineering Council of Canada,

The Alberta Heritage Foundation, and the University

of Calgary.

References

Anderson, E.A., 1968. Development and testing of snowpack

energy balance equations. Water Resources Research 4 (1),

19–37.

Anderson, E.A., 1973. National Weather Service River Forecast

System—Snow Accumulation and Ablation Model. NOAA

Tech. Memo. NWS HYDRO-17. US Department of Commerce,

Silver Springs, MD, p. 217.

Bengtsson, L., 1984. Modelling snowmelt induced runoff with short

time resolution, Proceedings of the Third International Con-

ference Urban Storm Drainage. Chalmers University of

Technology, Gothenburg pp. 305–314.

Bengtsson, L., 1986. Snowmelt simulation models in relation to

space and time, Proceedings of the Budapest Symposium

Modelling Snowmelt-Induced Processes. International Associ-

ation of Hydrological Sciences, Wallingford, UK pp. 115–123.

Bengtsson, L., Westerstrom, G., 1992. Urban snowmelt and

runoff in northern Sweden. Hydrological Sciences Journal 37,

263–275.

Buttle, J.M., Xu, F., 1988. Snowmelt runoff in suburban

environments. Nordic Hydrology 19, 19–40.

Chow, V.T., 1964. Handbook of Applied Hydrology. McGraw-Hill,

New York.

Conway, H., Gades, A., Raymond, C.F., 1996. Albedo of dirty snow

during conditions of melt. Water Resources Research 32 (6),

1713–1718.


Danish Hydraulic Institute (DHI), 2000.Anon., 2000. MOUSE

RDII user guide. Danish Hydraulic Institute, Hørsholm,

Denmark, p. 41.

Donigian Jr., A.S., Bicknell, B.R., Imhoff, J.C., 1995. Hydrological

Simulation Program—Fortran (HSPF), in: Singh, V.P. (Ed.),

Computer Models of Watershed Hydrology. Water Resources

Publication, Colorado, USA, pp. 395–442.

Eagleson, P.S., 1970. Dynamic Hydrology. McGraw-Hill,

New York.

Farrell, A.C., Scheckenberger, R.B., Guther, R.T., 2001. A case in

support of continuous modelling for stormwater management

system design, in: James, W. (Ed.), Models and Applications to

Urban Water Systems Monograph 9. CHI, , pp. 113–130.

Granger, R.J., Gray, D.M., Dyck, G.E., 1984. Snowmelt infiltration

to frozen prairie soils. Canadian Journal of Earth Sciences 21,

669–677.

Gray, D.M., Male, D.H. (Eds.), 1981. Handbook of Snow:

Principles, Processes, Management and Use. Pergamon Press,

Toronto p. 776.

Ho, C.L.I., 2002. Urban Snow Hydrology and Modelling. MSc

Thesis. Department of Geomatics Engineering, University of

Calgary, Calgary, Alta., Canada, p. 145.

Huber, W.C., 1995. EPA storm water management model SWMM,

in: Singh, V.P. (Ed.), Computer Models of Watershed

Hydrology. Water Resources Publication, Colorado, USA,

pp. 783–808.

Huber, W.C., Dickinson, R.E., 1988. Storm water management

model, version 4: user’s manual, EPA/600/3-88/001a NTIS

PB88-236641/AS. US Environmental Protection Agency,

Athens, Georgia, pp. 350–379.

Marks, D., Dozier, J., 1992. Climate and energy exchange at the snow

surface in the alpine region of the Sierra Nevada 2. Snow cover

energy balance. Water Resources Research 28 (11), 3043–3054.

Marsalek, J., 1991. Urban drainage in cold climates: problems,

solutions and research needs, in: Maksimovic, C. (Ed.),

Proceedings of the International Conference on Urban Drainage

and New Technologies (UDT 1991), Dubrovnik, Yugoslavia.

Elsevier, Amsterdam, pp. 299–308.

Marsalek, J., Oberts, G., Viklander M., 2000. Urban water quality

issue in Urban Drainage in Specific Climates Vol. II Urban

Drainage in Cold Climates. In: Maksimovic, C. (Chief Ed.). In:

Saegrov, S., Milina, J., Thorolfsson, T. (vol. Eds.), IHP-V

Technical Documents in Hydrology, vol. 40 (II). UNESCO,

pp. 97–117.

Matheussen, B.V., Thorolfsson, S.T., 1999. Simulation errors due to

insufficient temporal resolution in urban snowmelt models,

Proceedings of the Eighth International Conference on Urban

Storm Drainage, Sydney, Australia 1999, pp. 1–8.

Nash, J.E., Sutcliffe, J.V., 1970. River flow forecasting through

conceptual models, Part I—a discussion of principles. Journal of

Hydrology 10, 282–290.

National Weather Service Hydrology Laboratory (NWSHL),

1996.Anon., 1996. Overview of NWSRFS, NWSRFS User’s

Manual I.1.1, 2001 1996.

Semadeni-Davies, A.F., 1999. Urban snowmelt processes: model-

ling and observation. Report No. 1026. Department of Water

Resources Engineering, Lund Institute of Technology, Lund

University, Sweden.

Semadeni-Davies, A.F., 2000. Representation of snow in urban

drainage models. Journal of Hydrologic Engineering 5 (4),

363–370.

Semadeni-Davies, A.F., Bengtsson, L., 1998. Snowmelt sensitivity

to radiation in the urban environment. Hydrological Sciences

Journal 43 (1), 67–89.

Speers, D.D., 1995. SSARR model, in: Singh, V.P. (Ed.), Computer

Models of Watershed Hydrology. Water Resources Publication,

Colorado, USA, pp. 367–394.

Sundin, E., Andreasson, P., Viklander, M., 1999. An energy budget

approach to urban snow deposit melt. Nordic Hydrology 30,

39–56.

Suzuki, K., 1990. Influence of urban areas on the chemistry of

regional snow cover, in: Davies, T.D., Tranter, M., Jones, H.G.

(Eds.), Seasonal Snowpacks, Processes of Compositional

Change NATO ASI Series, Series G: Ecological Sciences,

vol. 28. Springer, Berlin, pp. 303–319.

Thorolfsson, S.T., Brandt, J., 1996. The influence of snowmelt on

urban runoff in Norway, Proceedings of the Seventh Inter-

national Conference on Urban Storm Drainage, Hanover,

Germany 1996, pp. 133–138.

Thorolfsson, S.T., Sand, K., 1991. Urban snowmelt research in

Norway: measurements and modelling approach, in:

Maksimovic, C. (Ed.), Proceedings of the International Con-

ference on Urban Drainage and New Technologies. Elsevier,

New York, pp. 309–316.

Watt, W.E., Lathem, K.W., Neill, C.R., Richards, T.L., Rouselle, J.

(Eds.), 1989. Hydrology of Floods in Canada: A Guide to

Planning and Design. National Research Council Canada,

Ottawa, p. 245.

Westerstrom, G., 1981. Snowmelt runoff from urban plot, Proceed-

ings of the Second International Conference Urban Storm

Drainage, Urbana, IL 1981 pp. 452–459.

Westerstrom, G., 1984. Snowmelt runoff from Porson residential

area, Lulea, Sweden, Proceedings of the Third International

Conference on Urban Storm Drainage, Chalmers. University of

Technology, Gothenburg, pp. 315–323.

Westerstrom, G., 1990. Snowmelt—runoff from small urban

catchments. Research Report, Series A No. 184, Water

Resources Engineering Lulea, Tekniska Hogskolan I Lulea,

Sweden, p. 9.

World Meteorological Organization (WMO), 1986. Intercompar-

isons of models of snowmelt runoff operational hydrology.

Report No. 23 (WMO No. 646), Geneva, p. 440.