URBAN THERMAL CLIMATE EFFECTS ON STORMWATER IN COLD REGIONS?
A.F. Semadeni-Davies*, L. Bengtsson**, A. Lundberg*** and W. Schilling*
*
Department of Hydraulic and Environmental Engineering, Norwegian University of
Science and Technology, S.P. Andersens vei 5, N 7491 Trondheim, Norway. E-mail:
annette.davies@bygg.ntnu.no and wolfgang.schilling@bygg.ntnu.no
** Department of Water Resources Engineering, Lund University, Box 118, 22100 Lund,
Sweden. E-mail: lars.bengtsson@tvrl.lth.se
*** Division of Water Resources Engineering, Luleå University of Technology, 971 87
Luleå, Sweden. E-mail: angela.lundberg@sb.luth.se
ABSTRACT
In cold regions spring
causes high water loading at a time when the drainage system is
least able to cope. Floods in Norway have prompted a call for improved winter simulations of
water delivery (i.e., snowmelt) and runoff generation for planning and management
applications. Snowmelt and runoff data from Luleå, Sweden, are used to illustrate how the
town climate can influence stormwater. A literature based discussion of snowmelt and
infiltration processes is followed by a modelling exercise to show how uneven melt and
runoff conditions could be handled in an urban drainage model. Five index models for
snowmelt ranging from estimates made from the average daily air temperature to one that
simulates hourly melt from hourly temperature and net allwave radiation are tested. A simple
soil water accounting scheme is altered to mimic changes in storage that can be expected in
frozen soil. Further work is outlined and a forum for discussing the special modelling needs of
urban catchments is suggested.
KEYWORDS: Cold regions, flood, snowmelt indices, net all wave radiation, soil frost,
infiltration, runoff
INTRODUCTION
Recently UNESCO / IHP (2001) initiated a report into the special nature of urban drainage in
cold regions in response to a growing awareness that different climatic zones have different
drainage needs. Flooding, poor water quality, wastewater overflow, low hydraulic capacity,
system failure and treatment plant overloading are all associated with snow and ice (e.g.,
Marsalek, 1991; Oberts, 1994; Viklander, 1997). Drainage systems have been designed and
constructed with technology developed in temperate regions were most drainage problems are
caused by short bursts of intense rain. In cold regions, freezing on the ground surface and in
soil, inlets and pipes changes the hydraulic behaviour of drainage pathways while snowmelt
represents a high total volume of water. Although the instantaneous rate of delivery of melt
water is slow, persistent flow causes available storage facilities to remain at full capacity for
days to weeks.
In Norway, urban flooding is often linked to snowmelt or winter rainfalls or both, particularly
when ground frost has limited infiltration into soil. There is an increase in contributing area
despite impermeable surfaces normally associated with runoff being snow-free. Non-extreme
rain or snowmelt events can lead to extreme runoff events. Winter flooding including a major
event in Trondheim during January 1999 and continuing specific drainage problems have lead
to the inclusion of snow and ground frost in a new joint German and Norwegian project
(Risursim,Risik Management of Urban Drainage Systems by Simulation) for urban flooding
modelling and consequence analysis. The influence of radiation on snowmelt and soil freezing
on infiltration and stormwater generation is illustrated here using runoff plot data collected at
the Luleå University of Technology, Sweden. Although the more continental climate differs
from maritime coastal Norway, these data represent some of the few available. They are
presented along with results of traditional snowmelt and infiltration routines and several
alternatives for a new wintertime modelling strategy are discussed.
SNOWMELT
Snowmelt dynamics are dependant on the location and condition of the snow as well as
thermal and radiative characteristics of the town. These are highly variable in time and space.
In the absence of warm air advection, snowmelt is largely due to incoming long- and
shortwave radiation. The “canyon” configuration of buildings and roads blocks incoming
direct beam shortwave radiation at some sites while causing multiple reflections between the
snow and walls to enhance it at others. At the same time, walls limit the sky-view so that
diffuse shortwave and atmospheric longwave radiation received at the ground lessen
progressively with proximity to buildings. Observations of strong radiative enhancement in
full sun over urban snowpacks have been made in Sweden and Canada (Bengtsson and
Westerström, 1992; Xu & Buttle, 1987). Enhancement is largely due to solar radiation
incident on walls causing warming and increased longwave radiation emmittence. Buildings
have the greatest influence over the radiation budget on sunny days when there is obvious
shading to the north and heating of walls to the south. Under cloudy skies, shortwave
radiation is restricted to diffuse radiation and incoming radiation is similar both to the north
and south of buildings. A physically-based snowmelt model (Semadeni-Davies & Bengtsson,
1998) showed that melt rates are highly dependent on location. Snow to the south of buildings
begins to melt earlier and with a greater melt rate than shaded snow. Figure 1 (SemadeniDavies et al., unpubl) shows how radiation inputs near a purpose built black plastic-clad 3 m
high wall differ from open site conditions under clear and cloudy skies. Disparities in energy
could be expected on slopes with different steepnesses and aspects. Also of great importance,
but not discussed here is the huge spatial variation in albedo of urban snow which determines
how much solar radiation can be absorbed (Bengtsson & Westerström, 1992, SemadeniDavies & Bengtsson, 1998).
GROUND FROST AND INFILTRATION
The hydrology of frozen soils has been investigated by a number of researchers over the last
30 years (see Kane and Stein, 1983; Kane & Chacho, 1990; Williams and Smith, 1991).
Characteristics of frozen soil can be described in terms of thermal (thermal conductivity, heat
capacity) and hydraulic (hydraulic conductivity, K, water storage capacity) properties.
Infiltration capacity depends largely soil moisture before freeze-up. Dry frozen soil initially
allows infiltrations and will warm to isothermal at 0ºC as latent heat is released by water
freezing on contact with the soil. Little ice is produced in pores by this mechanism (latent heat
of fusion for water >> specific heat of soil), but impervious ice lenses can form on the
surface. In saturated frozen soil, K is controlled by the grain-size of the soil and the pore ice
content; pores become blocked with ice-grains leaving only a thin film of water around the
soil particle. Some soil water can remain unfrozen despite below freezing temperatures, finer
300
300
300
200
200
0
-2
Radiation (Wm )
-2
Radiation (Wm )
-2
Radiation (Wm )
soils have greater specific surface area and a higher content of liquid water is possible. The
colder the soil the less liquid water storage possible and the lower K - K can drop as much as
-6
10200
m s-1 between 0 and –1C – due to ice build-up in pore.spaces. Daytime thaw followed by
subfreezing nights can cause the infiltration capacity to be lowered by both saturation and
freezing. Snow cover mitigates frost penetration as its thermal conductivity of snow can be an
order of magnitude less than for soils.
100
100
0
0
a)
100
-100
a)
-100
8:00
9:00
8:00
9:00
11:00
10:00
10:00
11:00 12:00
13:00 14:00 15:00 16:00 17:00 18:00
12:00
South, 1m
b) -100 14:00
13:00
10:00
11:00
19:00
South, 3m
North, 1m
15:00
13:00
12:00
16:00
15:00
14:00
17:00
18:0019:00 19:00
17:00
18:00
16:00
SMHI, open site
Figure1. Net allwave radiation measured over a snow pack on two sides of a purpose built wall for a)
clear sky (16 April, 1998) and b) cloudy sky (18 April, 1998) compared to and an open site
at the Swedish Meteorological and Hydrological Institute metrological station 5 km distant.
Moisture migration and heat transfer occur simultaneously in soil and are directly linked.
Water in unsaturated soil has a tension lower than the atmospheric pressure (i.e. suction).
Water moves from high to low total potential (the sum of the geometric height and the suction
- and
downwards. Ice content increases suction so that water flows along the temperature gradient
form warm to cold. Ice lenses can develop as liquid water accumulates and freezes at the
freezing front in soils. Water frozen in lenses is often sucked up from the groundwater. The
resultant effect of lenses on runoff is largely dependent on the depth of lens; when at or close
to surface high runoff is likely, but when lower down some storage and lateral flow is possible
in the above soil.
In rural soils, ground frost that allows unhindered infiltration at the catchment scale is most
usual (e.g. Buttle & Sami, 1992; Bengtsson et al., 1991; Espeby, 1990). Water is generally
able to infiltrate via unfrozen patches or macropores and spring flow peaks contain pre-event
rather than snowmelt water. In urban catchments, soils are compacted by heavy machinery,
topsoil is removed, horizons mixed and vegetation changed. Moreover, surface water flows
short distances to stormwater inlets (reducing opportunities for infiltration) and the response
time to rain or melt events is rapid. During spring, stream discharge and stormwater
observations suggest that a large portion of melt water flows overland to conduits and
channels rather than infiltrating the soil (Westerström, 1984; Buttle & Xu, 1988). Figure 2
illustrates that runoff from surfaces with different surfaces – asphalt and gravel - have similar
diurnal overland flow cycles despite their normally very different K.
4.00
Gravel
Asphalt
-1
Surface Runoff (mm h )
3.50
3.00
Figure 1. Snowmelt surface runoff
from two 200m2 runoff plots with
different permeabilities. Luleå,
Sweden, April 1980
(Bengtsson, unpublished).
2.50
2.00
1.50
1.00
0.50
0.00
5
10
15
20
25
MODELLING
One of the reasons that drainage systems are unable to cope with wintry conditions is that the
planning and design models available have been developed for temperate climates of North
America and Europe (Semadeni-Davies, 2000). The degree-day or daily temperature-index
routines commonly used for snowmelt in these models were developed for catchment scale
rainfall runoff modelling. They represent average melt and runoff generation and can neither
account for diurnal cycles of melt nor spatially varying melt conditions. Moreover, there are
discordant spatial and temporal scales between the daily melt estimated from the daily mean
air temperature and stormwater and pipe hydraulic routines. Mathussen and Thorolfsson
(1999) suggest that a time step of one hour is sufficient to capture winter and spring overflows
events. This time-step is also consistent with internal snowpack processes such as percolation
which delay melt water release. While some urban drainage models do attempt to simulate
diurnal changes in melt (e.g. EPA SWMM), there is an underlying assumption that air
temperature tracks solar radiation which might not be valid in urban areas where shading,
combustion and advection can raise temperatures independantly of irradiance.
The degree-day approach relates daily melt M (mm day-1)melt conceptually to the average daily
ambient air temperature Ta (°C):
Ta  0
M 0
M  CmTa Ta  0
Where Cm is the melt-rate factor (mm° C-1 day-1).
Radiation indices have been applied as an alternative to degree-day when shorter time steps or
spatially varying conditions are to be simulated, particularly in small catchments with fast
response. These models are structurally similar to the degree-day technique; typically:
Mh  Ct Tha   Cr Qr
Ta h  0
Where Mh is the melt water generated (mm h-1); Ct is the temperature melt rate factor (mm C1 -1
h ); Cr is the radiation melt rate factor (mm m2 W-1 h-1); Qr is radiation available to
snowmelt (Wm-2); and Tah is hourly air temperature. Sand (1990) applied an hourly net solar
radiation index to lysimeter data and found good agreement. Thorolfsson and Killingtveit
(1991) incorporated this routine into the HBV model structure. It was then applied to several
Norwegian urban or partly urbanised catchments with varying land-uses (commercial,
industrial and residential) and sizes (0.2 – 6.9 km2) located in Trondheim and Bergen. Plots
showed good agreement between observed and simulated runoff. However effect of shading
was not considered either in the data collection or the modelling stages.
Here five melt indices are tested: a standard daily temperature index split into 24 even hourly
values (A); an hourly temperature index run with daily maximum (3 pm) and minimum (3
am) temperatures where intervening hours are interpolated according to a sine wave (B); and
hourly temperature index run with measured hourly temperatures (C); a solar radiation /
temperature index (D) and a net radiation / temperature index (E). Snow is said to store 4 %
by volume liquid water before runoff can be generated and refreeze is calculated as:
M cc  R Tat 
0.5
Ta  0
Where Mcc is the effective loss of water to melt due to refreeze (mm), R is a refreeze
coefficient (mm C-0.5 h-0.5); t is the number of hours where the air temperature is below
freezing and Ta is the average air temperature for period t.
Routines for infiltration within urban routing models, such as the Green-Ampt method, are
fairly robust when the only process leading to overland flow is saturation and infiltration is in
response to discrete rainfall events of known intensity. The complexity of modelling
infiltration into frozen soil was alluded to in the above discussion and there are a number of
sophisticated physically-based models which solve governing energy and mass balance
equations for soil layers at the point or plot scale. In a situation analogous to the use of daily
temperature indices for melt, simulating ground frost is not a pressing need for large rural
catchments as discharge represents the average soil conditions. Indeed, operational rainfall /
runoff models often include neither infiltration nor freezing; all surface water is said to flow
into the soil where it is apportioned between groundwater recharge, quick- and base-flow and
evapotranspiration. However, in urban catchments, there is arguably a need for frost routines.
Three runoff sets are given here: no infiltration, that is measured runoff over asphalt (I);
modelled runoff over gravel where infiltration is restricted only by saturation (II); and where
infiltration is restricted by ground frost and saturation (III). In cases II and III comparisons are
made with runoff measured over gravel. Water loss to runoff is conceptually related to water
storage using a routine based on the HBV (Bergström, 1995) soil moisture accounting
scheme. Overland flow is not explicitly modelled; instead, quick flow conceptually originates
from the upper soil. Note that the slow rate of snowmelt is unlikely to exceed the infiltration
capacity of unfrozen soil (case II) so that surface runoff is dependant only on available
storage. Parameters for unfrozen soil were taken from the literature. Williams and Smith
(1991) state that a seasonal 1 m snow cover reduces the annual range of soil surface
temperatures by 40 %. For a seasonal snow cover greater than 60 cm, a rule of thumb is that
the soil just prior to snowmelt will be at the winter-time average air temperature, thus, by
April it was assumed that the soil was frozen to at least 300 mm (see Gray et al., 1985) and
the porosity (0.480 mm3 mm-3) was halved to simulate reduced storage and K. The approach
is purely hypothetical and is meant to show how storage loss that can be reasonably be
expected when ice grains fill pore spaces effects modelled runoff. Evapotranspiration was
assumed to be negligible. In future work, such as in Trondheim where winter sees several
freeze thaw episodes and intermittent snow cover; a soil frost routine will need to be used.
Such a model could have a form such as the empirical model derived by Zhao and Gray
(1998). They determined statistical relationships between infiltration calculated with a
coupled soil energy and mass balance model and various parameters such as pre-melt soil
moisture storage. For instance, they suggest that infiltration drops as much as 25 (clay) to
41% (sandy loam) with a temperature decrease from –4 to –8 C. Alternatively, an existing
infiltration model could be calibrated separately for summer and winter conditions defined
according to the whether the soil is frozen or not. This approach is similar to that of Sand and
Kane (1986) who parameterised HBV soil seasonally for an Alaskan catchment. An obvious
shortfall of both methods is that ice lenses are not simulated.
RESULTS WITH DISCUSSION
Case I represents total melt water available to runoff (Table 1). While giving good fit during
early melt, B and D overestimated the melt rate and exhausted the simulated snow pack
several days before the end of the actual melt period leading to poor overall fit. A model
which distributes the snowpack so that snow depth is uneven (such as the EPA SWMM user
defined snow cover depletion curve) could make this problem less apparent at the catchment
scale. Both radiation indices predicted melt, albeit minor, beginning two days too early and
peaks appeared an hour or so before those recorded. The difference can be explained by
percolation of surface melt water through the pack. If simulated runoff is lagged one hour, the
correlations for D and E rise to 0.33 and 0.67 respectively. The temperature indices do not
show this lag as air temperature itself tracks solar radiation. Although the results for the
degree hour and net allwave radiation indices are comparable, the latter has the advantage that
effects of buildings (Fig. 1) and, perhaps more importantly, slopes on snowmelt can be
simulated. For instance, in Fig. 1 a, index E predicts that no melt will occur 1 m north of the
wall but 9 mm will occur 1 m to the south. Index C predicts 4 mm irrespective of location.
Semadeni-Davies and Bengtsson (1998) developed a simple, but effective model to determine
changes in radiation with location which was tested by Semadeni-Davies et al. (unpubl.) and
could be coupled to an urban snowmelt model. Additionally, the amount of solar radation
absorbed by the snowpack can be taken into account. Lundberg and Beyrel (2000) show that a
combined radiation and temperature index gave much better fit than a temperature index when
applied to snow artificilally darkened by ash with an albedo similar to dirty urban snow. They
found, for instance, that melt was possible at air temperatures well below 0C for the dark
snow.
Melt index
R2
A
0.13
B
0.37
C
0.61
D
0.23
E
0.53
Table 1. Correlation coefficients, R2, for snowmelt simulated by three temperature (A, B, C) and two
radiation (D, E) indices against measured hourly runoff over asphalt (I). C m = 0.3 CR = 0.005
Ct = 0.009 and R=0.5
Recall that II (unfrozen) and III (frozen) represent hypothetical cases of flow over gravel and that they
differ only in porosity. When run with the asphalt runoff data (i.e., measured melt water), the R2
values against measured runoff over gravel are both 0.89. However, there are differences in the total
runoff; the measured runoff was 182 and 125 mm for asphalt and gravel respectively. Case I gives a
seasonal estimate of 106 mm and case II 127 mm. By the end of the melt season, when the soil is said
to be saturated, both I and II give the same estimates of runoff. While not being a true simulation of
ground frost, the change in simulated runoff gives an indication of how separately calibrated
parameters for summer and winter could change estimates of runoff. The question remains as to
whether flooding is due to ground frost or simply to soils becoming progressively saturated in the
absence of evapotranspiration. The next step will be to couple a ground frost routine with an urban
routing model to see whether there is a change in fit.
Interestingly, Gray et al. (1985) give a statistical relationship for seasonal infiltration that fits the
measured runoff over gravel very well on the assumption that the top layer of soil is saturated. Given
that the soil is frozen, the total infiltration of melt water, INF, can be related empirically to the snow
water equivalent, SWE, and the pre-melt water storage, S (mm3 mm-3) in the upper 300 mm of soil by:
INF=5(1-S)SWE0.584
This relationship yields 54 mm, so that spring runoff expected is 128 mm.
CONCLUSION
This paper has presented a literature review and field data to illustrate how the urban thermal
climate can influence stormwater generation. Five simple indices for simulating snowmelt are
given. While the degree-hour (C) and net allwave radiation (E) indices give comparable
estimates, the latter could be useful if spatial changes in energy availability are needed to
simulate, for instance, slopes or snow proximity to buildings.
A simple soil water accounting routine was used to show how recalibrating soil parameters for cold
conditions can alter estimates of quick flow. The next step is to include improved algorithms for melt
and wintertime infiltration into an existing hydraulic model for town drainage. The challenge remains
to collect data for further development and validation and to extend this scheme to the wider
environment. To this end, a forum for discussing data needs and availability as well as engineering
solutions to the unique problems posed by snow and ground frost should be initiated.
ACKNOLEDGMENTS
Annette Semadeni-Davies holds a joint NorFA / Helmuth Hertz post-doctoral scholarship at
the Norwegian University of Science and Technology (NTNU). The authors would like to
thank members of the Risursim project at SINTEF and NTNU for their help.
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