Outdoor Ice Rinks in Ontario, Canada—An Oversimplified Model for Ice Water Equivalent and Operational Duration to Evaluate Changing Climate

Abstract

Outdoor ice rinks have long been a staple for inexpensive exercise and entertainment in cold environments. However, the possible deterioration of or impact on outdoor ice rinks from a changing climate is poorly understood due to no or little monitoring of data of such facilities. To investigate long-term changes in ice rinks over recent decades, an energy-balance-based ice rink model (with three versions considering precipitation and melt) was applied to a simulated ice rink for two representative area—Dorset of south-central Ontario and the Experimental Lakes Area (ELA) of northwestern Ontario, Canada. The model was calibrated and tested using four-year ice rink data (since limited data are available) and applied to a 40-year period starting in 1978 to reproduce the dates of rink-on and rink-off, rink duration in a season, and ice water equivalent under daily climate inputs, and to illustrate any changing trend in these variables, i.e., the ice rink responses to changed climate. Results showed no clear trend in any ice rink features over four decades, attributed to winter temperature that did not increase substantially (a weak driver), no change in events of rain-on-ice and snowfall-on-rink, and reduced wind speed (possibly slowing ice melting). This is the first trial of a physically based rink model to evaluate outdoor ice rinks. More in situ monitoring and in-depth modelling are necessary, and this model can help guide the monitoring.

1. Introduction

People’s love for outdoor skating is extensive in Canada and many other regions, dating back hundreds of years [1,2,3,4,5,6]. Outdoor ice skating is a part of Canada’s culture and identity [2,3,4]. Notable hockey players like Gordie Howe [7], Maurice Richard [8], Wayne Gretzky [9,10], and Sidney Crosby [11] all sharpened their skating skills on frozen ponds and backyard rinks in Canada [12,13]. Outdoor ice skating is not just a sport; it provides a sense of community. Skating often acts as a place for social gatherings and events [2,5].

For ice on natural lakes or rivers, there have been a few studies on their changes. For example, small lakes across southern Quebec, Ontario, Manitoba, and Saskatchewan are breaking up earlier and freezing up later [14]; river ice has been breaking up earlier across all of Canada from 1950 to 2016 [15]; and ice cover duration has decreased in most regions of the world [16]. However, it is largely unknown how the ice condition (thickness or depth) and operation duration length of an outdoor ice rink have been affected by climate change, as there is no systematic or routine measurement or monitoring of the ice rinks to provide in situ data. Further, there are few analyses or simulation studies that evaluate climate change’s impact on ice rinks.

The few ice rink studies that assessed the impacts of climate change used a temperature threshold to determine the beginning time of ice rink season (e.g., the mean temperature of consecutive 3 days being below −5 °C) and suggested that ice rink condition or skating availability is affected by climate warming [17,18,19]. Although the ice rink season is controlled by air temperature to a certain extent, the rink thickness (growth and decay process) and operation duration are also influenced by other factors such as snowfall and rainfall during the winter season. The actual responses of an ice rink to climate change are likely more complicated, which requires more analysis and investigation.

Since there are limited observation data on operating outdoor ice rinks, such as their duration, to directly reveal the actual rink deviations due to climate change, a physically based ice rink model was developed and then run to evaluate the responses. Even though an ice rink model may not be able to fully reproduce the real ice rink processes, it can assist in assessing the response or trend under climate change. To our best knowledge, this is the first such model developed. Thus, we conducted a physically based simulation of the ice rink process (from its beginning to termination) to understand the possible effects of climate change on ice rink operation and to provide initial quantitative information and modelling tools for researchers and ice rink managers.

2. Study Area and Methods

A typical outdoor ice rink, targeted in this study, is one that is built and managed by a family, small residential community, or township, using simple and local resources (not necessarily by a professional engineer or big association; Figure 1). A basic approach of set-up and operation of an ice rink is to first find a relatively lower and flat area, maybe restrict the area by wood framing or earth containment, spray or pour water onto the area at the beginning of the winter season when the air temperature is cold enough to formulate the first ice layer/rink, then start to use the ice layer as a rink, and maintain it through the winter. It is maintained by shovelling off fresh snow, adding water to relevel the surface and cover skate marks, and removing ice bumps, if needed.

Our modelling trial does not consider all the details of ice rink building and operation, as it is not possible to cover all the details in a model. We only focus on the major and common features of the ice rink process. We aim to build an initial ice rink model so that it can be used to assess the impacts of climate change for a selected region.

2.1. Study Area

An ice rink is simulated for Dorset, Ontario, Canada, so that the 41-year period of meteorological data (1978–2018, observed at the DESC (Dorset Environmental Science Centre) meteorological station, the red triangle in Figure 2a) was used to run the model. Daily IWE (ice water equivalent) and ice depth of the rink are simulated for each winter season (1 November 1 to 31 May). The rink operation duration of each year is obtained from the simulated IWE results, and any changing trend or pattern in the dates of rink-on, rink-off, and rink duration is found out by statistical analysis for each model version. The Dorset site represents an area east of Lake Huron, with frequent snowfall events and substantial “rain-on-ice” events.

To have an increased representation of landscape or weather condition for the simulation work, a second site—the Experimental Lakes Area (ELA) in northwestern Ontario—was chosen to conduct a similar ice rink simulation, which represents a colder area with less rain-on-ice events (north of the Great Lakes; Figure 2a). The ice rink was simulated for 39 years (1978–2016), using local climate data as inputs [20]. The local meteorological station was located at ELA (red circle in Figure 2a).

Daily input data for ice rink models were prepared from observed meteorological data of two study areas (listed in

Table 1. Items of input data for models.

Input Item	Unit	Remark
Precipitation	mm/day
Mean temperature	°C
Minimum temperature	°C
Relative humidity	%
Wind speed	km/h
Shortwave radiation	KJ/day
Longwave radiation	KJ/day	measured or estimated
Snowfall	mm/day	estimated
Rainfall	mm/day	estimated

). Among the nine input items, the precipitation, temperature, relative humidity, wind speed, and shortwave radiation were obtained directly from sensor data, the longwave radiation was either measured onsite or estimated from other climate items, and the daily snowfall or rainfall was estimated from the precipitation by using a threshold mean temperature of 0.0 °C, i.e., rainfall occurs when warmer than 0.0 °C.

2.2. Initial Testing of the Ice Rink Model

The commonly operated or used outdoor rinks in communities or personal properties are rarely monitored on a regular basis or documented for scientific research. There are very limited data of ice rink dates (start, end) and ice conditions (thickness, hardness, snow status) which could be used for model testing or calibration. RinkWatch https://www.rinkwatch.org/ (last accessed 7 May 2025) [21] is a citizen science-based initiative to provide rink information; this resource provided access to several years of ice rink data in North America.

The Dorset area of Ontario, Canada (Figure 2a), was selected as an example site in this study since the necessary meteorology data were available as inputs for the model from the climate station operated by the Ontario Ministry of Environment, Conservation and Parks [22]. More importantly, the area is cold enough in the winter to have ice outdoors (Figure 3). We found two nearby ice rinks with daily rink data, but only for the winter of 2012–2013: the Annie Williams Park rink is in Bracebridge, Ontario, and operated by the township, and Port Sydney Ontario rink (Huntsville Township) is operated by Stephenson Lions Club; a third ice rink further away from Dorset (Parkview NIR, North York, Ontario) has 4 years (2012–2016) of data. The first two rinks are about 30–40 km west of Dorset, and the third rink is about 200 km southwest of Dorset (Figure 2b). The simulated end date of the rink model is compared with the recorded end date at two rinks (5 March 2013 at Stephenson Lions Club rink and 13 March 2013 at Annie Williams Park; five dates of five winters at Parkview NIR) for basic model testing.

2.3. Assumptions or Prior Settings for the Ice Rink and Its Modelling

The proposed model is applied to numerous years for two locations. For any given year or season, a criterion is used to set the beginning day of an ice rink. A similar definition as used by Damyanov et al. [17] is utilized to define the beginning of the outdoor ice rink: the last day of the first three consecutive winter days with a daily mean air temperature below −5 °C, which is based on the requirement of several consecutive cold days to lay the initial ice foundation of a rink. That beginning day usually occurs in December in Ontario, Canada, where the model is applied. On that first day, a large enough volume of water is sprayed over the selected rink area using a water pipe, sprinkler, etc. For consistency in comparing model results, an initial layer thickness of 30 mm is assumed to appear (or formulize) on the area, which is the first ice depth of the artificially formulated ice rink. The situation of a natural pond or a bay of lake being frozen into an ice rink is not considered in our modelling work.

2.4. Physically Based Ice Rink Model

A daily time-step ice rink model was developed by slightly modifying the water-balance- and energy-balance-based process model utilized for a snowpack [23]. The main changes are the consideration albedo for the ice surface, ice sublimation, and ice melting (e.g., shifting from snowpack to ice rink body). The water volume as contained or stored in the ice rink was defined as ice water equivalent, just as the widely used concept of snow water equivalent. Calculations of daily ice water equivalent (IWE) are simplified and described below.

A daily IWE balance equation is as follows:

IWE_i+1 = IWE_i + Spray + Snow + Rain − Subl − Melt,

(1)

where IWE_i+1 is the IWE value (mm) at the end of any calculation day i (for a year under calculation); IWE_i is the value at the end of the previous day; Spray is the artificially sprayed water on the first day to formulize the rink foundation and so its value is 30 mm for the first calculation day but 0.0 for any other day in a rink season (thus a first ice of 30 mm IWE was formulized); Snow is the volume of snowfall (if any, in mm·d⁻¹) in the day which is supposed to stay on the ice and transform into ice (depending on model version and the specific method to determine its value; see below Section 2.5); Rain is the rainfall (if any, in mm.d⁻¹) within the present day and is supposed to become part of the ice rink (depending on model version or treatment method); Subl is the ice loss (in mm·d⁻¹) through ice sublimation (solid ice changes to vapour); and Melt is the ice loss (in mm·d⁻¹) through ice melting into liquid water. The melting mainly happened on the surface or upper portion of the ice rink, due to warmer temperature, radiation, or rain-on-ice. The melted water is supposed to flow away from the ice rink in our model.

It is acknowledged that the present model structure as represented by Equation (1) is largely simplified, without considering or detailing some sub-processes. For example, the rain during ice rink operation was supposed to become ice in a day, as the season is basically cold, so rainwater would be frozen in short time; however, its actual process (maybe taking a few days) was not considered. As a result, the process (or energy needed) to freeze rainwater (or refreeze meted ice water) was not considered. The snow fallen during ice rink season was supposed to either become ice or be blown away (depending on model version) because frequent use of the ice rink by skaters would make the snow firmly attached to the ice, compacted to or changed to ice, or swiped away. The real process of interactions of snow and ice was not included. Unlike the situation of natural lake ice where a layer of snowpack is usually designed in a lake ice model, for the ice rink model (usually the snow layer is not present for a long-time during operation) the snow layer might be ignored here or considered not so important as in the lake ice case. These simplifications may influence model performance and would be improved in the future.

The outflowing of water from melted ice may not be easy to estimate. Our first option is to assume that the ice-melted water will flow out of the rink without staying. This may shorten the simulated ice rink duration because the refreezing of melted water would again become ice and prolong the ice rink duration. However, a second option (not evaluated) of letting the melted water stay on ice will definitely extend the ice rink duration. Then, the only way for ice to decay in this situation is ice sublimation that is quite slow, while ice melting plus the melted water flowing away is much faster to decay the ice rink. A trial model test of letting the melted water stay on ice without flowing out indicated a substantial delay in ice rink termination and could not meet the observed rink ending date badly; thus, this option was not considered.

For each day, the ice depth is obtained by converting the IWE to depth by using the ice density (917 kg·m⁻³; for example, 30 mm of IWE has an ice depth of 32.7 mm).

The ice sublimation rate (mm·d⁻¹) is calculated by an empirical formula [23]:

Subl = 0.1 + 0.09 · U_z (e_sat − e_a),

(2)

where U_z is wind speed (m·s), e_sat is saturated vapour pressure (mb), and e_a is the actual vapour pressure (mb) in present day with e_a = e_sat · RH (RH is relative humidity). The coefficient constants 0.1 and 0.09 were selected for local application. Over water, e_sat is estimated with the Buck equation [24]:

e_sat = 6.1121 · exp [(18.678 − T_a/234.5) (T_a/(257.14 + T_a))],

(3)

where the T_a is the mean daily air temperature (in °C).

Daily ice melt (mm·d⁻¹) was determined by the total available energy of separate energy sources as follows:

Melt = [(1 − α) H_K + H_L* + H_C + H_A + H_R]/(λ∙ρ_w),

(4)

where α is ice albedo of shortwave radiation and is taken as a fixed value that is to be calibrated for this study, H_K is shortwave radiation (MJ·m⁻²·d⁻¹), as measured on site at a climate station, H_L* is net longwave radiation, measured on site or estimated from temperature data (e.g., [25]), H_C is convective energy (diffusion or convection of heat), calculated from air temperature and wind speed, H_A is advective energy (transport of heat by bulk motion of a fluid), calculated from temperature and wind, H_R is energy coming from rainfall, calculated from temperature and precipitation, and λ and ρ_w are the latent heat coefficient and water density, respectively. The total available energy in a day was converted to melted water thickness by using the λ and ρ_w.

The convective and advective melting energy are calculated as follows:

H_C = C_C ∙ T_a ∙ U_z ∙ R_M,

(5)

H_A = C_A ∙ T_min ∙ U_z ∙ R_M,

(6)

where T_a is air temperature, U_z is the wind speed, R_M is a reduction factor, and T_min is the minimum temperature in a day (in °C); the coefficients C_C (0.12) and C_A (0.08) are considered constants. The value of R_M is a function of atmospheric stability and is estimated from Richard’s Number RI:

R_M = 1.0 − 7.7 RI for (0 ≤ R_M ≤ 1.6),

(7)

where RI is a linearized estimate as follows:

RI = 0.095 ∙ T_a/U_z ²,

(8)

The last component in Equation (4), the melting energy due to rainfall, is calculated as follows:

H_R = C_R ∙ T_a ∙ P_R,

(9)

where P_R is the rainfall in a day and C_R is a coefficient (a value of 47.0 was given for local area [23]).

With daily input data of air temperature, precipitation, relative humidity, short-wave radiation, longwave radiation, and wind speed, the ice rink process is calculated by running Equations (1)–(9) for each day of the ice rink season (from the beginning day until the last day when the ice depth reduces to zero).

2.5. Model Versions with Varying Scenarios

Although actual ice rinks have had different management/maintenance practices, a few simplified treatments or management measures must be presumed for the purpose of modelling. In terms of the snow and rain components in Equation (1), three different versions of the model are created and evaluated. The assumptions for each version are stated below.

2.5.1. Version I: Adding Rain as Ice and Ignoring Snow

In this scenario, it is assumed that after the start of an ice rink, any rain falling on the ice would become ice and therefore join to the ice rink body without flowing out of the rink. The volume of Rain in Equation (1) is converted to ice or IWE. Any fresh snowfall would be assumed to be completely blown away by wind or swept/scoped away by operators, not staying on the rink surface. As a result, the melting of the fresh snow and its contribution to the ice body are ignored in the process modelling (Snow in Equation (1) is zero). The interruption of the snow layer with the energy balance calculation of the ice rink is thus ignored, too. For convenience and simplicity of phase converting, the density of water, ice, and new snow were fixed at 1000, 917, and 100 kg/m³.

2.5.2. Version II: No Rain Addition and Adding Some Snow as Ice

It is assumed that any rain-on-rink would not stay on ice and flow away from the rink, so the Rain in Equation (1) is zero for any day during ice rink operation. Fresh snowfall would not fully stay on the ice rink (at least some of it will be blown out by wind or swiped away by an operator). It is difficult to know or determine how much fresh snow stays and becomes ice (due to temporary snowmelt and then freeze on the same day). For simplicity, if the snowfall is less than 2.0 mm (water equivalent) (snow depth of 2 cm around), the snow will stick to ice and become ice, and the Snow in Equation (1) is given the value of snowfall; if the snowfall is larger than 2.0 mm, 2.0 mm of snow will stay on the ice (Snow = 2.0 mm) and all remaining snow will be blown out.

2.5.3. Version III: Neither Rain nor Snow Addition

It is assumed that neither snow nor rain in a day will stay, and both will not become ice (i.e., Rain = 0, Snow = 0). This scenario would probably not occur in reality. It is considered here as an “extreme” scenario to compare with the other two model versions and to help evaluate or explain the rink responses to climate change.

2.6. Trend Analysis

Trends in the modelled ice rink data were assessed using Theil–Sen’s Slope [26,27] to compute the rate of change, and the Mann–Kendall test [28,29] to determine the significance level. A significant trend was considered when p < 0.05. A moderately significant trend was considered when p < 0.1. Hydrometeorological input data was also evaluated for trends. These data (Figure 3) included annual mean winter temperatures (December through March) at Dorset and ELA (Figure 3a), mean wind speed at Dorset (Figure 3b), annual lake ice duration at Dorset (Figure 3c), snowpack duration at Muskoka airport (Figure 3c), and mean winter snow depth at Muskoka airport (Figure 3b) (see Figure 2b for the airport location). Muskoka snow data were obtained from Environment Canada and climate change [30]. These long-term changes in meteorology and lake ice could be potential drivers for the ice rink trends.

3. Results

3.1. Model Testing

Only one parameter was adjusted slightly: the ice albedo of shortwave radiation being set at 0.48 for the model. It was determined based on two considerations: the albedo of a rough-surface ice rink would be smaller than ocean ice (its albedo being 0.5–0.7), and a few trial-and-error tests with the ice rink model helped to find a proper value. For the 2012–2013 winter and by using model version I, simulated IWE in the Dorset area indicated a rink starting date of 24 December 2012 and an ending date of 8 March 2013 (Figure 4,

Table 2. Comparison of simulated and observed rink ending dates (numbers in the bracket are simulation errors in days: positive meant delayed, negative meant advanced).

Rink	Observed	Model I	Model II	Model III
Stephenson Lions	5 March 2013	8 March 2013 (3)	9 March 2013 (4)	22 February 2013 (−13)
Annie Williams	13 March 2013	8 March 2013 (−5)	9 March 2013 (−4)	22 February 2014 (−19)
Parkview NIR	8 March 2013	8 March 2013 (0)	9 March 2013 (1)	22 March 2013 (14)
	24 March 2014	28 March 2014 (4)	5 April 2014 (12)	20 February 2014 (−32)
	9 March 2015	11 March 2015 (2)	14 March 2015 (5)	1 March 2015 (−8)
	21 February 2016	26 March 2016 (33)	11 March 2016 (18)	19 February 2016 (−2)

). The modelled end date was very similar to the recorded end dates of 5 March 2013 at Stephenson Lions Club rink, 13 March at Annie Williams Park rink, and 8 March at Parkview NIR. For the four years 2012–2016 at Parkview, model version I gave small errors from the observation (<5 days, except for 2016). Although there was limited data for comparison, the first model is probably or tentatively acceptable for ice rink process simulation considering unknown factors such as actual operation style/action, site difference among rinks, and model assumptions.

The model version II gave a rink ending date of 9 March 2013, just a one-day difference from version I (Figure 4, Table 2), performing well for 2013. It had greater errors of ending date for the other three years (5–18 days). The IWE with version II had greater variations (up and down) in the season than version I. The model version III gave a much earlier ending date of 22 February 2013, with 19 days difference from the observed date March 13. Its ending dates in all years at three rinks had much greater mistakes (−32 to +14 days, except for Parkview 2016). The varying treatment approaches of snowfall and rain-on-ice in three versions produced quite varied ice rink thickness or rink dates. Although it is not proper or confident to conclude on the accuracy and applicability of the model versions only based on a limited few years of data, versions I and II would probably provide better performance than version III. More model tests are desired if monitoring data are available.

3.2. Comparing Three Versions by Simulations of Six Winters (2011 to 2016)

Large differences are seen among the versions of the model (Figure 4 and Figure 5). The first two versions have quite similar results in ice duration (Figure 5b), with version II having the longest duration. However, the mean IWE over each season is quite different between the two versions (e.g., thinner vs. thicker in 2012–13, while thicker vs. thinner in 2015–16) (Figure 5c). Version III differed substantially from the other two versions, giving much shorter ice duration and thinner ice thickness (Figure 5). Similarly, as mentioned in Section 3.1, the results of version III for the six years seemed less reliable since IWE was too small and its rink duration was too short. On average of the six years, compared to version I, the percent difference in Version II was 6.9% in rink duration and −18.4% in IWE; the difference in Version III was −9.3% in rink duration and −50% in IWE (Figure 5).

The large discrepancies between versions I and II, particularly for the 2013–14 and 2015–16 winters, reflected the different treatments of rain-on-ice and snow-on-ice in the model versions and their effects. The small amount of rain in 2013–14 winter (56.5 mm) or less rain events vs. the large amount of rain in 2015–16 winter (215.9 mm) or more rain events caused a relatively thinner ice rink in 2013–14 vs. a thicker rink in 2015–16 under version I, as this version took rain to become ice. Similarly for version II, which took partial snow to become ice, the large snowfall in 2013–14 (223.0 mm) caused a thicker ice rink, while the small snowfall in 2015–16 (117.5 mm) caused a thinner rink. As a result, the different treatments of rain or snow determined different sensitivity or response to rain or snow contribution in the modelling and thus produced the discrepancy in IWE within the winter season.

3.3. Long-Term Simulation at Dorset and ELA

The simulated rink-on date for Dorset over the 40-year period of record (1978–2018) and for ELA over the 39-year period of record (1978–2016) showed substantial inter-annual variability (Figure 6a). The rink-on variability at Dorset was about one-third more than modelled for ELA. The variability increased by 52% and 41% over the last two decades compared to the first two decades at Dorset and ELA, respectively (

Table A1. Model summary statistics for the entire time series (mean, standard deviation) and the first two and last two decades (standard deviation) for Dorset and ELA.

Statistic	Rink-On	Rink-Off	Duration	Mean IWE	Total Rain-On	Total Snow-On
Dorset
Version I: mean	6 December	2 March	106	40.4	75.7	N/A
Std. Dev.	12.8	12.0	18.6	15.7	48.3	N/A
SD 1st 20 yrs	9.7	14.1	18.6	12.7	43.5	N/A
SD 2nd 20 yrs	14.8	9.6	19.3	18.2	54.3	N/A
Version II: mean	6 December	21 March	105.5	47.4	70.2	187
Std. Dev.	12.8	10.0	19.8	13.6	37.1	56.2
SD 1st 20 yrs	9.7	11.1	17.3	12.7	32.7	61.2
D 2nd 20 yrs	14.8	9.3	22.0	15.0	42.0	46.8
Version III: mean	6 December	28 February	84.5	19.8	48.8	N/A
Std. Dev.	12.8	18.8	22.4	3.9	32.4	N/A
SD 1st 20 yrs	9.7	11.9	18.1	4.0	35.4	N/A
SD 2nd 20 yrs	14.8	22.8	23.8	3.8	30.8	N/A
ELA
Version I: mean	17 November	6 March	108.7	20.9	3.0	97.7
Std. Dev.	9.5	13.1	14.3	4.0	5.8	33.3
SD 1st 20 yrs	7.3	15.0	13.8	3.5	2.8	33.0
SD 2nd 20 yrs	10.1	11.6	14.5	3.7	7.3	35.3
Version II: mean	17 November	21 March	2 May	45.7	5.0	111
Std. Dev.	9.5	13.3	16.2	9.1	6.8	35.2
SD 1st 20 yrs	7.3	13.7	13.3	8.4	6.0	32.1
SD 2nd 20 yrs	10.1	13.9	18.2	9.7	7.5	38.8
Version III: mean	17 November	5 March	107.7	19.7	2.5	97.4
Std. Dev.	9.5	13.4	14.7	3.6	4.1	33.3
SD 1st 20 yrs	7.3	15.1	14.1	4.0	2.8	33.0
SD 2nd 20 yrs	10.1	12.0	15.0	2.5	4.8	35.5

).

The model versions produced varying rink-off results for Dorset (Figure 6b and Table A1) compared to ELA (Figure 6c and Table A1). At Dorset, versions I and II were on average the same date (with variance from 2.5 weeks earlier in 2015 to 5 weeks later in 1980). Version III rink-off results were on average 3 weeks earlier than versions I and II (Figure 6b), with a maximum difference of three months in 2007. For ELA, model versions I and III were on average almost the same (1 day different) with a maximum difference of 10 days (earlier for version III in 1984) (Figure 6c). Version II was on average 2 weeks later than versions I and III (almost 6 weeks later in 2001).

Deviation in rink duration reflects rink-off variation: shorter for version III at Dorset and longer for version II at ELA. For the model applied to Dorset, typically the mean modelled season IWE is mostly for version II, the average for version I, and almost always the least for version III (Table A1). For ELA, version II produced almost twice the mean IWE compared to versions I and III, which yielded quite similar mean IWE (Table A1).

3.4. Trend over Time

There are varying changes in the ice rink characteristics over the period of record (Figure 7a,b). The rink-on date is later at both locations (1 or 2 days/decade at Dorset and ELA, respectively), which corresponds to a warming temperature (Figure 7d); the trends for rink-on and winter temperature at ELA were moderately significant. The modelled rink-off dates were also later (about 2 days/decade), except for version II at Dorset. The modelled duration generally became shorter for the three model versions at the two locations, with version III at Dorset becoming much shorter (moderate significant; Figure 7a). The rain-over-ice amount was increasing in Dorset (moderately significantly for model version II; Figure 7a), and the snow-over-ice amount was increasing in ELA (Figure 7b). The snow-over-ice amount was decreasing in Dorset for version II. The snow cover duration was increasing in Muskoka (Figure 7c) and the wind speed at Dorset was significantly decreasing (Figure 7d). The lake ice duration over the same 40-year period monitored at Dorset [25,29] was decreasing (Figure 7c) but not significantly.

4. Discussion and Conclusions

Three versions of the outdoor ice rink model, as applied to two sites in Ontario, Canada (Figure 2b), illustrated the same result of ice rink changes (although some minor differences). There are limited changes for the trends in the rink-on, rink-off dates, rink operation duration or rink water equivalent over about 40 years since 1978 (Figure 6 and Figure 7; Table A1). These results should be taken with caution as they do not support an unproven image in public opinion—deteriorated ice rink condition due to warming climate [31]—while this opinion is not ubiquitous [32]. Although the proposed model is in an initial stage, this study is one of few trials related to outdoor ice rink changes.

The no-trend phenomenon of ice rink duration over 40 years was supported by the lack of trend in either the total sublimation in a winter season or the total ice melting, two key deterministic factors for ice rink duration (Figure 8). As the ice loss drivers, the seasonal sublimation was basically flat over time without any clear trend, and the seasonal ice melting fluctuated over time but had no trend (except an occasional increase in 2015–16).

A partial reason leading to the simulation result of limited changes is that while winter temperatures are warming over four decades (Figure 7d) with more rain-over-ice at Dorset (Figure 7a), wind speed did decrease significantly at Dorset (Figure 7d), leading to less convective and advective melting energy (Equations (5) and (6)). More data are necessary to evaluate trends and provide ground truth in situ observation of long-term operation of outdoor ice rinks. These currently have limited (hard to find) data; RinkWatch is a resource [21], and additional data would be useful. Further model evaluation with such data would be useful [23].

Although the simulation results may be opposite to general public thought, it is argued that prediction of ice rink change only based on air temperature [17,18,19] would not be practical. Rather, the effects of other climatic drivers, such as rain or snowfall over ice rink and wind conditions should be considered at the same time. Before further testing and new data become available, the simulation trials in this study still indicated a possible situation—the outdoor ice rink might have not really deteriorated in past decades under changed climate for some regions such as Ontario, Canada.

A drawback or limitation for this current study is the lack of sound model calibration and evaluation, as there is limited real ice rink data being monitored for ice condition or operation duration. Such a monitored rink may exist, but such data are not currently available. Even if such an ice rink is available, its operation procedure could be different from the assumptions set herein; these data need to be monitored and archived. Further, this simple model and its assumptions can be used to guide the collection of additional data to understand the processes and evaluate the assumptions.

The assumptions used in this modelling have not been tested, and they may be questionable. For example, the flow-away of ice-melted water may not accurately apply to real ice rink situations, as some melted water stays on the ice and becomes ice again via refreezing. The assumptions with various model versions, such as rainfall becoming ice immediately, is likely improper. If rain occurs in the winter [33], it is unlikely that all the rainwater would remain on the ice without partly flowing out. In either case, liquid water on the rink is not good for the maintenance of the rink if it remains in a liquid phase, and it is not good for skating which could end the rink ice skating season.

The creation and maintenance of an outdoor ice rink can be difficult, and the processes are not well measured. A real outdoor ice rink is often built with boards designed act as a boundary, like in indoor rinks, to contain the skaters and thus water (Figure 1). However, this is not always the case, as per the rink at Annie Williams that does not have an elevated boundary. The boards have an opening for the entrance; the boards can be cracked, allowing water to flow out. The boards are designed mostly as a boundary to define the extent of the rink, and they are rarely sealed to contain flowing water. Snow can be pushed to the boards (Figure 1(lower)) and that acts as a partial inhibitor of water flow. Often boards are only made of snow. So, does liquid water flow out of the rink? There would be a good possibility that the melted water flowed out of the ice rink. Thus, when we assumed the flowing out of melted water, the model version produced reasonable results that roughly matched the observed rink termination dates (Figure 4).

Outdoor ice rink caretakers usually go out at the end of the day and spray water onto the ice, like an ice resurfacer machine for indoors rinks. They only do this when the overnight temperature is expected to be substantially colder than freezing. This acts to smooth the surface that has been roughened by skating.

The distinction of rain vs. snow is important for the energy balance, and while a 0 °C threshold was used here, that varies by climate [34,35]. Further, the density of fresh snow is rarely 100 kg/m³ [36]. Although there are a few assumptions and simplifications, the simulations for a long-term period to detect trends and impacts are still realistic provided that the treatments remain consistent in the simulations for all years. More data and modelling are necessary, but the model and versions presented herein are a start and were used to assess how ice rinks may change due to a changing climate. These ice rinks (Figure 1) are part of the culture in cold climates [1,2,3,4,5,6]. This research is relevant for those who enjoy and thrive in such environments [37].

It was noted that the relative contribution of various meteorological parameters to the proposed model varied or differed. Air temperature, shortwave and longwave radiation, and precipitation (both rain and snow) are the more important/contributive parameters for ice rink formation/deterioration, while humidity and wind speed played a lesser role. Future work could include (i) improvement of the ice rink model by testing assumptions, adding more details in energy budget, and expanding calibration/validation; (ii) finding or establishing an ice rink monitoring programme which can provide ice depth recording and really support a comprehensive model testing; and (iii) investigating more sites and areas in different climate regions. It is concluded that the proposed model of an outdoor ice rink can be a tentative tool for analyzing ice rink duration and its driving factors, and it can be applied to different areas/regions in Ontario, Canada, for studies of climate change impacts on ice rink operation. It may be used for other regions with different climate features by applying certain caution or modification.