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: and
** Department of Water Resources Engineering, Lund University, Box 118, 22100 Lund, Sweden. E-mail:
*** Division of Water Resources Engineering, Luleå University of Technology, 971 87 Luleå, Sweden. E-mail:
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 (Semadeni-Davies 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, Semadeni-Davies & 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 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 10-6 m s-1 between 0 and –1C – 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.
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 of the water in the pores) The unsaturated water flux can thus be directed both up- 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.
/ Figure 1. Snowmelt surface runoff from two 200m2 runoff plots with different permeabilities. Luleå, Sweden, April 1980(Bengtsson, unpublished).
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):
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:
Where Mh is the melt water generated (mm h-1); Ct is the temperature melt rate factor (mm C-1 h-1); 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:
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 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 0C for the dark snow.
Melt index / A / B / C / D / ER2 / 0.13 / 0.37 / 0.61 / 0.23 / 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). Cm = 0.3 CR = 0.005 Ct = 0.009 and R=0.5