CanRCM4 is developed by the CCCma of Environment and Climate Change Canada (ECCC). It has the same dynamical core as the Global Environmental Multiscale (GEM) model, which is an integrated numerical weather forecasting and data assimilation system developed by ECCC (Côté et al., 1998). CanRCM4 shares the same package of physical parameterizations with the fourth-generation Canadian atmospheric global climate model (CanAM4) of CCCma (von Salzen et al., 2013), which forms the atmospheric component of CanESM2. In particular, CanRCM4 uses the deep-convection scheme of Zhang and McFarlane (1995), the shallow-convection scheme following von Salzen et al. (2005), and the Canadian Land Surface Scheme version 2.7 (Verseghy, 2012). Scinocca et al. (2016) provide further details of the main characteristics and physical parameterizations of this RCM and its relationship with its parent global model CanESM2.

The experimental domain of CanRCM4 covers North America (NA) and adjoining oceans at a 0.44∘ resolution. This study uses an ensemble of 50 initial-condition simulations (Fyfe et al., 2017) driven by CanESM2 (Arora et al., 2011) at the lateral boundaries under the historical (1950–2005) and RCP8.5 (2006–2100) scenarios. Simulations share the same forcings, differing only in initial conditions specified at the beginning of the historical simulation period. RCP8.5 is a high-emission scenario corresponding to radiative forcing of 8.5 W m-2 by the end of the 21st century compared to pre-industrial values (IPCC, 2013); therefore, it is an appropriate scenario for business-as-usual and non-climate policy conditions. Moreover, RCP8.5 has closely matched recent emissions (Sanford et al., 2014). From each simulation, 3-hourly temperatures at the surface (2 m) and three upper levels (i.e., 500, 850 and 1000 hPa), surface air pressure, precipitation, and surface (10 m) wind speed are used to calculate 3-hourly offline freezing precipitation (FP) and ice accretion.

The National Centers for Environmental Prediction (NCEP) North American Regional Reanalysis (NARR) dataset is used to evaluate CanRCM4. NARR is a long-term, consistent, high-resolution (approximately 0.3∘ grid) reanalysis dataset for the NA domain (Mesinger et al., 2006). An advantage of using this reanalysis is that its gridded output is more comparable to CanRCM4 output, representing spatial scales of a grid cell, compared to local point station measurements. NARR uses the Baldwin and Contorno (also called NCEP) algorithm to diagnose freezing-precipitation occurrence. All 3-hourly temperatures at the surface and 11 upper levels from 200 to 1000 hPa, surface air pressure, precipitation and surface wind speed are used to evaluate FP and ice accretion of CanRCM4. Reanalysis variables have differing levels of reliability, depending on the relative influence of observed data and the atmospheric model (Kalnay et al., 1996). In general, upper-air temperature and surface air pressure are most reliable (type A), as they are strongly influenced by observed data; surface air temperature and wind speed are less reliable (type B) compared to type A, as both observational data and the model have a strong influence on the variables. Precipitation should be used with caution (type C), as it is typically completely determined by the model (Kalnay et al, 1996). Unlike most reanalyses, however, Mesinger et al. (2006) reported that NARR could potentially provide more realistic precipitation fields, as it assimilates observed precipitation to adjust the accumulated convective and gridded precipitation based on the difference between the modelled and observed hourly precipitation. The reliability of NARR precipitation will thus be heavily influenced by the density of assimilated rain gauge information, which is low over Canada.

To evaluate the frequency and amount of freezing precipitation diagnosed from CanRCM4, precipitation and manually observed weather condition datasets are obtained from 588 meteorological stations over NA for the 1986–2016 period. In particular, daily freezing-precipitation series are prepared from 205 meteorological stations operated by ECCC over Canada, and a series from 383 observation stations is obtained from the National Climatic Database Center (NCDC) Integrated Surface Database (ISD) (Smith et al., 2011) over the US.

In addition to CanRCM4 simulations, 3-hourly surface temperature and 6-hourly 850 hPa temperature outputs from nine GCM simulations are used to investigate the mechanisms driving changes in FP occurrence in the future. The nine simulations considered in this study are obtained from six CMIP5 (Coupled Model Intercomparison Project phase 5) models.

GFDL-ESM2G: Geophysical Fluid Dynamics Laboratory Earth System Model with Generalized Ocean Layer Dynamics component

The 3-hourly FP amounts are calculated offline by the Bourgouin algorithm from 50 CanRCM4 simulations using surface, 500, 850, and 1000 hPa temperatures; surface air pressure; and precipitation for the 1986–2100 period. When precipitation occurs, the Bourgouin algorithm calculates the rates of four precipitation types (i.e., snow, ice pellets, freezing precipitation and rain). FP is diagnosed when precipitation falls through warm layers (>0 ∘C) and then arrives at a sub-freezing near-surface layer. This vertical temperature profile is possible when strong warm-air advection at upper levels is accompanied by strong cold-air advection near the surface. The Bourgouin algorithm calculates areas of positive and negative energy from all possible pressure levels above the surface and then determines the rate of FP based on the positive and negative areas and specified thresholds (Bourgouin, 2000).

Before investigating future CanRCM4 projections, FP estimated from the 50 CanRCM4 historical simulations is evaluated for the 1986–2016 baseline period by comparing the annual frequency of FP days, annual total FP amounts and daily extremes (i.e., 20-year return value estimated by fitting the Gumbel distribution to annual maxima using the method of moments) with those from NARR and 588 stations. Depending on temperature, the Baldwin and Contorno (NCEP) algorithm used by NARR determines the initial phase of precipitation at the highest saturated layer as either ice crystals (<-4 ∘C) or supercooled liquid water (≥-4 ∘C). FP is diagnosed when supercooled water occurs in combination with a sub-freezing near-surface layer or when ice crystals occur in combination with the temperatures of the warm upper layers and the cold surface layer that exceed specified thresholds (Baldwin and Contorno, 1993).

As FP amounts in CanRCM4 are diagnosed based on offline calculations from a limited number of vertical levels, it is important to evaluate their robustness. Therefore, a sensitivity analysis is carried out to quantify the impact of different vertical temperature resolutions on FP using NARR outputs, which are provided at higher vertical resolution (at 11 upper levels from 200 to 1000 hPa), and the Bourgouin algorithm. Three selected combinations of vertical levels, including one with the three levels offered by CanRCM4, are considered: case (1) includes all 11 NARR levels, case (2) includes a subset of 6 levels (200, 400, 600, 800, 900 and 1000 hPa) and case (3) includes the 3 CanRCM4 levels. As case (1) employs high vertical resolution, it can be assumed to be the same as the online simulation. Therefore, comparison between case (1) and NARR permits an evaluation of differences in FP diagnosed by the Bourgouin and NCEP approaches.

The 3-hourly horizontal, vertical and radial ice accretions are calculated using the Chaîné approach (Chaîné and Skeates, 1974), which is the operational scheme used by ECCC. Ice accretion on a horizontal surface (Th; mm per 3 h), such as a road or a flat roof, assumes that all FP accretes as ice when the surface temperature is below freezing (i.e., horizontal ice accretion is the same as the FP amount). The 3-hourly ice accretion on a vertical surface (Tv; mm per 3 h), such as the sides of towers and bridges, is calculated based on FP amount and surface wind: 1Tv=0.6008VP0.88, where V is the wind speed (meters per second) and P is the FP rate (mm per 3 h). Ice accretion on a radial surface (R; mm per 3 h), such as transmission lines or cables, is also calculated based on FP amount and wind speed: 2ΔR=-r+r2+Kr2Th2+Tv21/21/2, where K is a correction factor, ΔR (mm) is the incremental change in ice thickness and r (mm) is the radius of the cylinder, including ice already on the conductor, at the start of the hour. Ice accretion continues until the end of the ice storm event, i.e., when the surface temperature increases to above 1 ∘C or 7 d have passed without FP (CSA, 2010).

For NARR and CanRCM4 simulations, annual maximum ice thickness time series are prepared for all land grid points over NA. The 50-year return-level (RL) (also referred to as design or extreme) ice thicknesses are estimated by fitting the Gumbel distribution – the extreme value distribution used operationally by ECCC for extreme ice thickness analysis in Canada (CSA, 2010) – to the annual maxima. Projected changes are provided for 31-year future periods at specific levels (e.g., +1, +2 and +3 ∘C) of GMTC above the baseline temperature (1986–2016) as well as the PI (1850–1900) temperature. The statistical significance of changes in design ice thickness in terms of internal variability is assessed by applying two sample t tests at the 10 % two-sided significance level between 50 members of baseline and future period values.

FP storms that lead to extreme ice accretion are compound events with multiple physical drivers. The variables driving changes in FP and associated design ice thicknesses in CanRCM4 are investigated by comparing frequencies of 850 hPa temperatures (T850) greater than 3 ∘C and surface temperature (Ts) within the range of -10 to 0 ∘C, as well as the precipitation occurrence for the freezing season (i.e., from onset to offset of Ts < 0 ∘C) of each year, between the baseline and future +2 ∘C GMTC periods. The sensitivity of FP and ice accretion to changes in driving variables is also investigated by comparing precipitation intensity and surface wind speed for the freezing season between these periods. Finally, to evaluate model uncertainty, changes in frequencies of the upper-level and surface temperature conditions are assessed in nine CMIP5 GCMs.

When compared against station observations for the 1986–2016 period, the ensemble means of frequency and the amount of daily FP are underestimated by CanRCM4, whereas NARR generally overestimates FP over most of NA (Fig. 1a and b). Interestingly, CanRCM4 is generally more consistent with in situ data over Canada and NARR over the US. Biases of CanRCM4 (-0.45 d and 1.15 mm) are smaller than those of NARR (3.25 d and 8.02 mm) over Canada for annual FP days and amounts. The reverse is true over the US; biases of NARR (0.16 d and 2.12 mm) are smaller than those of CanRCM4 (-1.47 d and -3.04 mm). The large bias of NARR over Canada is supported by the findings of Mesinger et al. (2006), which reported that the reliability of NARR precipitation is highly related to the density of rain gauges (i.e., the precipitation is less reliable across Canada as fewer observations are assimilated). For annual extremes, despite the fact that FP in CanRCM4 is diagnosed based on only three vertical temperature levels, CanRCM4 yields similar performance to NARR for 20-year RL of daily maximum FP (Fig. 1c). The CanRCM4 ensemble exhibits relatively small 5th–95th percentile ranges for most of northeastern NA and parts of southwestern Canada, particularly for annual total amount and extreme FP, compared to ensemble means. However, it yields similar or larger values of the ranges for northwestern, north-central and southern NA compared to ensemble means, indicating high levels of internal variability in these regions. Large spatial variability in observed annual total and extreme FP are exhibited over the Great Lakes and western coastal regions, and the CanRCM4 model shows large internal variability (i.e., larger 5th–95th percentile ranges than ensemble means) over these regions.

Online and offline results from NARR show that simulated frequencies and amounts of FP are highly dependent on the diagnosis algorithm. Specifically, the online NCEP algorithm (presented in second column of Fig. 1) yields a much higher frequency of FP occurrence over northeastern regions of NA, relative to the offline Bourgouin algorithm using 11 vertical levels (Fig. 2, case 1), which should behave in a similar manner to the online Bourgouin simulation due to the large number of vertical levels used. The average of relative absolute bias, i.e., percentage of absolute bias to mean value, in annual FP days of the NCEP to Bourgouin algorithms is 55 % across NA. This result is consistent with the findings of Matte et al. (2018) in their study region in southeastern Canada. Larger values from the NCEP algorithm are possible because it can simulate FP when all vertical temperatures are below 0 ∘C if supercooled water is diagnosed at the highest saturated layer. Similar differences over the domain are also apparent for the 20-year RL of daily maximum FP; the average of relative absolute bias (systematic bias) of the online NCEP algorithm to the case (1) Bourgouin algorithm is 42 % (-1.24 mm) across NA, with a larger negative bias (smaller than -3 mm in many grids) over eastern and western Canada.

The impact of vertical temperature resolution on diagnosed FP is summarized in Fig. 2. When compared to the diagnosis based on all 11 vertical levels (case 1), using three vertical levels (case 3) generally displays larger differences in annual FP days than using six vertical levels (case 2) over most of northern NA. However, FP occurrence is generally less sensitive to differences in vertical temperature resolution compared to the choice of diagnosis algorithm. Averages of relative absolute bias between cases (2) and (1) and between cases (3) and (1) are 13 % and 20 %, respectively. Moreover, extreme FP amounts are less sensitive to vertical temperature resolution than frequency of FP; averages of relative absolute bias in 20-year RL between cases (2) and (1) and between cases (3) and (1) are only 9 % and 14 %, respectively. The three cases yield similar levels of performance to each other but perform slightly better than NARR in terms of root-mean-square error when they are compared to site observations, as the Bourgouin algorithm yields much better performance over Canada but slightly worse performance over the US compared to the NCEP algorithm. It is notable that FP types cannot be diagnosed over western high-altitude regions in case (3) with three vertical levels, as surface pressures are usually lower than 1000 hPa; this is also visible in the CanRCM4 simulations (Fig. 1), which use the same levels.

Investigation of vertical temperature profiles during heavy and light FP events over selected eastern and western regions (Fig. 3) provides some clues as to why a limited number of vertical levels (500, 850, 1000 hPa) leads to relatively large underestimation of FP frequency but good performance for extreme FP amounts. Strongly non-linear temperature profiles with the requisite warm layer are evident for both heavy and light FP events. When only a few vertical levels are considered, as in CanRCM4, the warm layer can be underestimated, which results in misdiagnosis of FP as ice pellets. However, the warm-layer temperature maximum occurs at around 850 hPa, which indicates that the strength of warm-air advection leading to FP can generally be resolved. Furthermore, over the eastern region, heavy FP events (>10 mm per 3 h) are associated with a deeper warm layer than light FP events (<0.2 mm), which means that there is less potential to misdiagnose FP as ice pellets.

Spatial distributions of design ice thickness (50-year RL) on horizontal, vertical and radial surfaces for NARR and the historical CanRCM4 large ensemble simulations (ensemble mean and 5th and 95th percentiles) are presented in Fig. 4. As explained above, 50-year RL of annual maximum horizontal ice thickness is identical to that for annual maximum daily FP accumulation. Therefore, spatial patterns for horizontal values are generally consistent with those for extreme FP presented in Fig. 1c. These spatial patterns also show good agreement with those reported for NARR and CRCM5 by Jeong et al. (2018). Furthermore, CanRCM4 shows better agreement with CRCM5 as compared to NARR, particularly over northeastern NA, because the CRCM5 also uses the Bourgouin approach to diagnose FP. The CanRCM4 ensemble yields larger 5th–95th percentile ranges for southeastern NA, indicating larger simulated natural variability in that region than elsewhere.

Vertical thickness values are generally larger than horizontal values, indicating that vertical ice extremes are generally associated with strong surface winds during ice storm events. For instance, based on Eq. (1), vertical thickness is larger than horizontal when 10 (20) mm FP with stronger than 5.2 (5.6) m s-1 winds occur. Regionally, CanRCM4 simulates larger values over south-central, north-central and northeastern NA, where higher wind speeds are reported based on site observations and reanalysis datasets (Pryor et al., 2009; Jeong and Sushama, 2018). NARR shows larger vertical thickness than CanRCM4 over southeastern NA, where an overestimation of the reanalysis in surface wind speed has been reported (Pryor et al., 2009). The CanRCM4 ensemble yields larger 5th–95th percentile ranges of vertical extremes in comparison to horizontal extremes, particularly over north-central and northeastern NA, due to added variability caused by wind speed to the variability originated from FP.

Radial thickness values are larger than horizontal values but smaller than vertical values. This occurs because radial ice accretion results from the combined effect of horizontal and vertical ice accretion (see Eq. 2). Radial extremes show larger values for the Atlantic and Hudson Bay coastal regions, as well as northern Quebec, but smaller values for western and central regions. The spatial pattern for CanRCM4 is consistent with the contour maps of historical ice accretion in CSA (2010, 2013), which were developed based on ice accretion values from the Chaîné approach and applied to about 200 Canadian meteorological stations for the period 1953–2006. These spatial patterns are also in good agreement with those of Jeong et al. (2018), which were obtained from the CRCM5 model and the simpler CRREL approach for ice accretion (Jones, 1998). Furthermore, the spatial distribution of CanRCM4 values over the US is consistent with contour maps in ASCE (2006), which were developed using the CRREL approach using data from 330 meteorological stations for the period since 1959.

It should be noted before discussing projections that the surface temperature response of CanESM2 is relatively sensitive to radiative forcings; this suggests higher GMTC compared to the other CMIP5 models (Schleussner et al., 2016). CanESM2 also yields larger GMTC for the 1986–2005 period, with respect to the PI period (0.79 ∘C), compared to global observations (0.61 ∘C) (IPCC, 2013). As CanRCM4 simulations driven by CanESM2 for the PI period are not available, projected changes associated with different future GMTC levels are calculated with respect to the 1986–2016 baseline period. However, it should be noted that, in terms of CanESM2, the +0.5, +1, +2 and +3 ∘C GMTC levels relative to the 1986–2016 baseline are the same as +1.5, +2, +3 and +4 ∘C levels relative to the PI period, as the GMTC from the PI to the 1986–2016 baseline period is +1 ∘C (i.e., an additional +0.21 ∘C warming from the 1986 to 2005 period used by IPCC, 2013).

CanRCM4 projects significant decreases in future design ice thickness values on horizontal, vertical and radial surfaces over most of southern NA and some northeastern coastal regions of NA (Fig. 5). The spatial extent and relative magnitude of the decreases tends to increase as GMTC levels increase. However, the CanRCM4 ensemble also projects significant increases in future extreme ice thickness values over northern NA, with the exception of some Atlantic and Hudson Bay coastal regions. When considering changes in relative terms, CanRCM4 projects larger increases in future design ice thickness values for northwestern NA and smaller increases for northwestern regions of NA. However, it must be noted that the absolute changes in the northeast are actually larger than those in the northwest (not shown), due to the differences in baseline amounts in the different regions. These spatial patterns of projected changes of CanRCM4 are broadly consistent with those found for the CanESM2-driven CRCM5 simulation over Canada by Jeong et al. (2018), as FPs of both RCMs are driven by the same GCM and precipitation-type diagnose algorithm. Although robust changing signals in the projected changes to design ice thickness are obtained from the ensemble mean, the CanRCM4 yields large 5th–95th percentile ranges in the variable due to the large natural variability of this extreme. It is notable that increases in vertical design ice thickness are larger than horizontal thickness over northeastern NA, mainly due to increases in future surface wind speed. Gastineau and Soden (2009), Kumar et al. (2015), and Jeong and Sushama (2018) reported modest increases in extreme surface wind speed for those regions by the end of the 21st century based on CMIP3, CMIP5 and CRCM5 ensembles, respectively, due to amplified baroclinicity and decreases in future surface pressure with associated changes in surface pressure gradient.

Zonal averages of projected changes in annual FP amount and 50-year RL radial ice thickness over 10∘ N latitude bands are given in Fig. 6 for different levels of GMTC relative to the baseline period. Horizontal and vertical values behave in a similar fashion to radial thickness and are not shown. Annual FP amount exhibits decreases (increases) for the 30–40 and 40–50∘ N (50–60 and 60–70∘ N) latitude bands as GMTC increases. Interestingly, median changes in radial design ice thickness at the 30–40 and 40–50∘ N bands increase until the GMTC reaches +1.5 and +3.0 ∘C levels relative to the baseline (i.e., +2.5 and +4.0 ∘C levels relative to PI), respectively. Increases in future precipitation intensity and/or surface wind speed could result in increases in future extreme design ice thickness in those latitudinal bands despite overall decreases in FP frequency and annual amount. It is also notable that radial design ice thickness is projected to increase more than the annual FP amount at the 50–60∘ N latitude band under the same level of warming. Changes in internal variability in annual FP amount and radial design ice thickness with global warming are also shown in the Fig. 6. For instance, the two variables show an increase (decrease) in the 5th–95th percentile range at the 60–70∘ N (30–40∘ N) band as GMTC increases. The 5th–95th percentile ranges of radial design ice thickness at the 30–40, 50–60 and 60–70∘ N bands exclude the zero change line when GMTCs are larger than +3.5, +1.0 and +1.0 ∘C levels relative to the baseline, respectively, indicating statistically significant changes from natural variability at the 10 % significance level.

Radial thickness values are larger than horizontal values but smaller than vertical values. This occurs because radial ice accretion results from the combined effect of horizontal and vertical ice accretion (see Eq. 2). Radial extremes show larger values for the Atlantic and Hudson Bay coastal regions, as well as northern Quebec, but smaller values for western and central regions. The spatial pattern for CanRCM4 is consistent with the contour maps of historical ice accretion in CSA (2010, 2013), which were developed based on ice accretion values from the Chaîné approach and applied to about 200 Canadian meteorological stations for the period 1953–2006. These spatial patterns are also in good agreement with those of Jeong et al. (2018), which were obtained from the CRCM5 model and the simpler CRREL approach for ice accretion (Jones, 1998). Furthermore, the spatial distribution of CanRCM4 values over the US is consistent with contour maps in ASCE (2006), which were developed using the CRREL approach using data from 330 meteorological stations for the period since 1959.

Projected changes to design ice thickness in CanRCM4 are primarily driven by changes in the vertical temperature profile, which, as discussed by Jeong et al. (2018), affects the frequency of FP events. As illustrated in Fig. 3, FP typically occurs when T850 > 3 ∘C coincides with -10 ∘C < Ts < 0 ∘C. CanRCM4 projects a decrease in the future frequency of these temperature conditions over southern NA, mainly due to warming at the surface (Fig. 7a). In contrast, CanRCM4 projects an increase in the frequency of favourable temperature conditions over northern NA, due to warming at both upper levels and the surface. Despite decreases in the frequency of surface temperatures between -10 and 0 ∘C, some parts of southern Canada and the northern US are projected to experience an increase in FP events, due to the increase in frequency of upper-level temperatures warmer than 3 ∘C (Fig. 7b). Consequently, CanRCM4 projects significant increases (decreases) in FP occurrence hours over northern (southern) NA (Fig. 7c). In addition, increases in future precipitation intensity over most of NA (Fig. 7d) can accelerate increases (or delay decreases) in FP and associated design ice thicknesses over northern (southern) NA. Finally, as shown in Fig. 4b, increases in surface wind speed over northeastern NA (Fig. 7e) during the freezing season can increase vertical and/or radial extreme ice thicknesses.

For a given level of GMTC, projected CanRCM4 changes in upper-level and surface temperature conditions that favour FP occurrence (i.e., Fig. 7a and b) are generally in good agreement with those projected by nine CMIP5 GCMs (Fig. 8). However, the GCMs do display some regional differences, particularly over northwestern coastal, northeastern and central regions of NA. In particular, GFDL-ESM2G, GFDL-ESM2M, IPSL-CM5-MR, IPSL-CM4-LR-r2, IPSL-CM4-LR-r4 and NorESM1-M project decreases in the frequency of surface temperatures between -10 and 0 ∘C (Fig. 8a) and the associated frequency of favourable conditions for FP occurrence (Fig. 8b) over some regions in northwestern and/or northeastern NA. Note, however, that some of the regional differences can be attributed to internal variability, rather than structural uncertainty, as the four IPSL-CM5-LR realizations show different patterns of change. As a further indication of structural uncertainty, GCMs have differing levels of climate sensitivity and hence respond differently to the same forcing scenario (e.g., Schleussner et al., 2016). For instance, the most sensitive (IPSL-CM5-LR and -MR) and least sensitive (GISS-E2-R) GCMs reach the +2 ∘C GMTC level of warming in the 2036–2066 and 2070–2100 periods, respectively.