RE S EARCH ART I C L E

On the relationship between the risk of hoar frost on roadsand a changing climate in Sweden

Tinghai Ou | Yumei Hu | Torbjörn Gustavsson | Jörgen Bogren

Department of Earth Sciences, University ofGothenburg, Gothenburg, Sweden

CorrespondenceYumei Hu, Department of Earth Sciences,University of Gothenburg, Guldhedsgatan 5 A,413 20 Gothenburg, Sweden.Email: gusyumhu@gmail.com

Hoar frost, one of the most common types of road slipperiness, can reduce roadsurface friction thereby adversely affecting traffic safety. The two main causes ofhoar frost are warm air advection and radiative cooling. This paper investigates theimpact of a changing climate on the formation of hoar frost in Sweden during thewinter months due to warm air advection and radiative cooling. The analysis isbased on in situ observations from 244 stations in the Swedish Road WeatherInformation System. The results show that in northern Sweden, hoar frost wasmainly caused by warm air advection, while radiative cooling was the main causeof hoar frost in southern Sweden. Given the increase in the air temperature overland due to climate change during the period 2000–2016, the relative frequency ofhoar frost due to warm air advection has significantly decreased, while the relativefrequency of hoar frost due to radiative cooling has significantly increased. Furtheranalysis showed that the weakened temperature gradient between land and ocean,which leads to weakened warm air advection, is the main cause of the changes.

KEYWORDS

changing climate, hoar frost risk, radiative cooling, road surface temperature,temperature gradient, warm air advection

1 | INTRODUCTION

In cold regions with a long winter season, road slipperinessduring the winter is a common problem for the road trans-port system. The frequent presence of snow and ice on theroad surface reduces road surface friction (Wallman andÅström, 2001; Haavasoja and Pilli-Sihvola, 2010) and influ-ences the road users in terms of both safety and mobility.For instance, Norrman et al. (2000) indicated that about 50%of traffic accidents that occurred in three winter periods inHolland, Sweden were related to slippery road conditions.

There are about 24 different types of slipperiness basedon ice-forming processes and the characteristics of snowcover (Lindqvist and Mattsson, 1979). Of these types, hoarfrost is generally associated with high accident rates(e.g., Wallman and Åström, 2001). The influence of hoarfrost on traffic safety has been reported in many countries inthe Northern Hemisphere, such as United States (Takle,

1990; Greenfield and Takle, 2006; Toms et al., 2017),Canada (Crevier and Delage, 2001), United Kingdom(Hewson and Gait, 1992; Andersson and Chapman, 2011b),Russia (Bulygina et al., 2015), Poland (Gałek et al., 2015)and Sweden (Gustavsson and Bogren, 1990; Karlsson, 2001;Andersson et al., 2007). Of these countries, Sweden sufferssevere hoar frost problems (Gustavsson and Bogren, 1990;Hewson and Gait, 1992). For instance, of all traffic accidentscaused by severe weather in Sweden in winters between2004 and 2006, about 24% were caused by the presence ofhoar frost on the road (Andersson and Chapman, 2011a),and 31% in southwest Sweden between 1991 and 1996(Norrman, 2000).

In order to ensure the safety and mobility of road users,winter road maintenance (WRM) activities are often carriedout to increase road surface friction and reduce slipperiness.WRM expenditure in cold regions with long winters can bevery high. For instance, the annual winter expense in WRM

Received: 26 May 2018 Revised: 30 November 2018 Accepted: 20 December 2018 Published on: 13 January 2019

DOI: 10.1002/joc.5974

Int J Climatol. 2019;39:2601–2611. wileyonlinelibrary.com/journal/joc © 2018 Royal Meteorological Society 2601

for Sweden is around 0.2 billion USD (Swedish TransportAdministration, 2015, 2016, 2017). Improvements inmethods for predicting the occurrence of hoar frost can leadto more efficient WRM activities, thereby making consider-able savings in energy and costs (Riehm and Nordin, 2012).

A previous study (Hu et al., 2018) found that warmingclimate has led to an increase in winter hoar frost risk daysin central Sweden from 1999/2000 to 2015/2016 due to theincrease in the humidity. The increased risk of hoar frostmay lead to a higher risk of traffic accidents. However, thereis a strong regional difference in the trend of winter hoarfrost risk days, while the cause is still unknown. Therefore,more attention is required to improve the understanding ofthe impact of changing climate on the formation of hoarfrost. That understanding can be used to assess the quality ofprediction models, which will contribute to improvements inthe accuracy and reliability of methods for predicting theoccurrence of hoar frost, thereby reducing the cost of WRMactivities and improving road safety.

Theoretically, hoar frost forms on a road when (a) roadsurface temperature (RST) is equal to or less than the freez-ing point (RST ≤ 0�C); and (b) RST is less than dew pointtemperature (Td) (RST < Td) (Takle, 1990; Karlsson, 2001).The first condition ensures that frost rather than dew willform in association with any moisture deposition; the secondcondition ensures that moisture flux is directed towards theroad surface. Meteorological parameters, including windspeed (Hewson and Gait, 1992; Karlsson, 2001), previousweather conditions (Gustavsson and Bogren, 1990; Takle,1990; Hewson and Gait, 1992) and the difference betweendew point and road surface (Karlsson, 2001), influence thedeposition rate and depth of hoar frost. A substantial amountof frost has to be deposited to create slippery road conditions(Knollhoff et al., 2003). Karlsson (2001) reported that roadsurface friction can decrease to 0.4 (below which traffic isadversely affected) (Al-Qadi et al., 2002) 2 hr after the firstoccurrence of a hoar frost. Therefore, in this study, an occur-rence of hoar frost is only recorded if RST is less than Td forat least 2 hr in order to cover all the possibly dangerous con-ditions caused by hoar frost thoroughly, same as the defini-tion used by Hu et al. (2018).

There are three conditions under which hoar frost canform: (a) warm air advection which is characterized by awarm front passing over a cold surface; (b) radiative coolingwhich leads to road surface cooling faster than the airdirectly above it; and (c) morning heating of air temperaturewhich is associated with increasing temperature but coldroad surfaces (Lindqvist, 1979; Lindqvist and Mattsson,1979). Of them, warm air advection and radiative coolingare often observed (e.g., Gustavsson and Bogren, 1990;Bogren et al., 2001; Karlsson, 2001) and used to parameter-ize the forming of hoar frost (e.g., Toms et al., 2017). How-ever, little attention has been paid to the third condition inthe literature.

In the long winter season in Sweden, December, January,and February (DJF) are the most severe months and experi-ence the greatest number of occurrences of hoar frost(e.g., Norrman, 2000; Eriksson and Norrman, 2002). Theaims of this study, then, are to (a) characterize winter (DJF)hoar frost formation on Swedish roads under the three condi-tions, (b) examine the changes in the occurrence of hoarfrost under the three formation conditions identified aboveduring the period 2000–2016, and (c) investigate the impactof changing climate on the changes in the causes of hoarfrost.

2 | DATA AND METHODS

2.1 | Data

In situ observations from the road weather information sys-tem (RWIS), provided by the Swedish Transport Adminis-tration (STA), were used to investigate the way in which therisk of hoar frost in Sweden may have changed. The RWISstations are located by the sides of roads and record meteoro-logical information every 30 min. Data recorded at244 RWIS stations with RST, air temperature at 2 m level(Ta), relative humidity (RH) at 2 m level, precipitation, andTd (calculated from Ta and RH by the STA), for the winterseason from 2000 to 2016 were used in the analysis

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Centers of geos. wind

k-means clusters

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Central

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Upper Northern

FIGURE 1 Locations of in situ RWIS stations and their respective clusters(triangles), and the centres of geostrophic wind calculated for the threeregions (stars). The background shows the four traditional Swedish climatezones as shown in Wallman (2004) [Colour figure can be viewed atwileyonlinelibrary.com]

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(Figure 1). Winter is defined as being from December toFebruary inclusive: the winter of 2000, for example, is fromDecember 1999 to February 2000. RWIS does not recordthe occurrence of hoar frost directly, so the above variableswere used to infer an occurrence of hoar frost. For the pur-poses of this study, a hoar frost event occurs when RST ≤ 0�C and RST < Td (Takle, 1990; Karlsson, 2001) for at least2 hr (no precipitation should be detected during the sameperiod) same definition as the one used by Hu et al. (2018).A day with a hoar frost event detected is called a hoar frostrisk day. The other days are called non-hoar frost risk days.

In order to examine the link between changes in theoccurrence of hoar frost risk days and changes in large-scale(e.g., continent-scale) climate and circulation, data from theModern-Era Retrospective analysis for Research and Appli-cations, Version 2 (MERRA-2) (Gelaro et al., 2017) werealso used to analyse the changes in regional wind directionand temperature and to understand the changes in the hoarfrost. Hourly temperature at 2 m and 850 hPa, and sea levelpressure were retrieved from MERRA-2 with a horizontalresolution of 0.5 × 0.625� (latitude × longitude).

2.2 | Methods

In order to find the typical climate zone based on the occur-rence of hoar frost, K-means method, which is the mostwidely used non-hierarchical clustering approach (Wilks,2011), is utilized in the current work. For a given vectors ofobservation (x1, � � �, xn), the centres of a given number ofclusters k (v1, � � �, vk) will be determined by the followingexpression:

f K −means ¼ minXk

i¼1

X

x2Six− vik k2, ð1Þ

in which Si means the observations belong to the cluster i.A random initial centre will be given for a specified

number of clusters. Then, the centres are changed so that thedistance (fK − means) between observation and the k centres isreduced. By iteration, the final centre of the k cluster will bedetermined when there is no or small change in cluster cen-tres. The member of each cluster is then determined.

Geostrophic wind can provide a good approximation ofthe dominant wind direction of a large area. Westerly (zonal)and southerly (meridional) components of the geostrophicwind are calculated using the Jenkinson and Collison (1977)method. The direction of the geostrophic wind is then calcu-lated based on the two wind components. Further details ofthis method for calculating geostrophic wind can be found inthe work by Ou et al. (2011). This method was used in thisstudy to calculate the dominant wind direction for a largearea on an hourly basis based on sea level pressure. Thedirection of the geostrophic wind for each of the threeregions at hourly intervals was calculated using the sea levelpressure. The wind direction was calculated for the centre of

each region to represent the major wind direction for thatregion (the locations of the regional centres are indicated inFigure 1).

3 | RESULTS

3.1 | Hoar frost climate zones

By definition, the occurrence of hoar frost is affected byRST, Ta, and humidity (specified by RH or Td). In order tounderstand the prevailing climatic conditions when hoarfrost occurs, the differences in the values of these variableson hoar frost risk days and non-hoar frost risk days wereexamined. Figure 2 summarizes differences in temperatureand RH for hoar frost risk days and non-hoar frost risk days.In general, it is warmer in the northern part of Sweden dur-ing hoar frost risk days (compared to non-hoar frost riskdays), and colder in the southern part. RH is generally higherwhen hoar frost occurs. However, the results for Ta and RSTin central Sweden are more ambiguous, with Ta tending tobe higher on hoar risk days and RST tending to be lower.These results suggest it is necessary to consider the occur-rence of hoar frost in Sweden on a regional basis.

Traditionally, Sweden is divided into four climatezones—southern, central, lower northern, and upper northernSweden—based on the lengths of the winters in each zone(Wallman, 2004). However, as can be seen in Figure 2, thedifferences in average temperature and RH during hoar frostrisk days, compared to that of non-hoar frost risk days, aresimilar for both lower northern and upper northern Sweden.The traditional division of Sweden into climate zones is notbased on the occurrence of hoar frost. Thus, a new divisionof climate zones with a focus on the occurrence of the occur-rence of hoar frost is needed. In order to determine the num-ber of cluster, an R package, NbClust (Charrad et al., 2014)is utilized. Here only Ta and RST are considered in the clus-ter analysis for its significant difference in the average asshown in Figure 2. According to the majority rule, threeclusters are determined as the best number of clusters basedon the 17-year data. Then, a station will be classified as clus-ter i (i = 1, 2, 3) if the station is classified to the clusteri (i = 1, 2, 3) when the majority years of the station is classi-fied as cluster i (i = 1, 2, 3). For example, a station is classi-fied as cluster 1 if more than 1/3 of the 17 years the stationis classified as cluster 1. By doing this, the RWIS stationsare grouped into three appropriate regions (clusters) (shownin Figure 1). The identified three regions correspond roughlyto the geographic location of the traditional climate zones,with cluster 1 being similar to lower northern and uppernorthern Sweden combined, cluster 2 to central Sweden, andcluster 3 to southern Sweden.

Changing in temperature has a great impact on the regionof the three clusters. For instance, as shown in Figure 3, theregion of cluster 3 expanded northwards, which covers the

OU ET AL. 2603

classified regions of both cluster 2 and 3, in a warm winter.This has pushed cluster 2 to even north with almost no sta-tions in cluster 1 left. On the other hand, in a cold winter,the region of cluster 1 expanded southwards. Cluster2 moved even south with almost no station in cluster 3 left.

3.2 | Temporal variations in temperature prior tooccurrence of hoar frost

For each classified climate zone, changes in mean tempera-tures (RST, Ta, and Td) over time with respect to the occur-rence of hoar frost were further investigated. Specifically,the differences between the temperature at the point the hoarfrost occurred, t0, and the temperature at times between

24 hr before and 4 hr after t0 (at 30-min intervals) were cal-culated for each hoar frost event. The means of those differ-ences are shown in Figure 4. Here, it is assumed that Td isclose to RST at t0. Ta is also comparable to RST at that timesince RH is generally quite high (average RH is above 95%)when a hoar frost occurs. So, information of the differencebetween the three temperatures for each hour can beretrieved from Figure 4 as well.

The results for northern Sweden show that the value ofall three temperature variables increased until the occurrenceof hoar frost, as expected from Figure 2. This is a typical ofthe way in which temperature fluctuates prior to the forma-tion of hoar frost due to warm air advection(e.g., Gustavsson, 1991). In southern Sweden, however,

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FIGURE 2 Spatial distribution of differences in observed daily mean (a) Ta, (b) Td, (c) RST, and (d) RH between days with and without a hoar frost risk(t test has been utilized, the black circles indicate the difference is significant at 0.01 level) [Colour figure can be viewed at wileyonlinelibrary.com]

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RST decreases a few hours before the occurrence of hoarfrost, with Ta either following the decrease in RST or exhi-biting no obvious change, but Td increasing. The increase inTd is due to the increase in RH, which, in turn, is caused bya decrease in Ta and an increase in water vapour transporta-tion. These patterns of temperature change are typical ofhoar frost formation due to radiative cooling (e.g., Karlsson,2001). The results for central Sweden are less clear, demon-strating effects associated with both the other regions.

The rate of temperature change before the occurrence ofa hoar frost event is an important factor in determining thespatial distribution of hoar frost in a region(e.g., Gustavsson, 1991). Gustavsson (1991) found that dur-ing warm air advection, the rate of temperature change 5 hrbefore the occurrence of hoar frost (TT5 hereafter) influ-ences the reaction time, the period from the moment temper-ature starts to rise to the moment when slipperiness occurs,at different stations. Furthermore, the results in this studyshow that TT5 values are similar for a particular cause ofhoar frost formation and for a particular region (Figure 4).Therefore, TT5 was further utilized to classify the cause ofhoar frost in each climate zone.

3.3 | Variations in the causes of hoar frost formation inSweden

The three conditions leading to the formation of hoar frostwere further analysed based on the TT5 of each hoar frost

event. In total four groups were identified by the clusteringalgorithm, including the three groups that correspondedclosely to known causes of hoar frost plus one unclassifiedgroup. The characteristics of each group are summarized inTable 1. The relative frequencies with which each of thesefour groups occur within in each of the three regional clus-ters are shown in Figure 5. It can be seen that the majority ofhoar frost in Sweden is due to warm air advection (IAIR)and radiative cooling (DADR). The second group (IADR),which may be caused by morning heating of air but coldroad surface, only accounts for about 10% of the occurrencesof hoar frost in each of the three regions. However, about30% of the occurrences of hoar frost in each region are inthe unclassified group (UC), which will be discussed later.

The results show that hoar frost in northern Sweden(cluster 1) is mainly due to warm air advection, confirmingthe results in Figure 4. Hoar frost in southern Sweden(cluster 2) is mainly caused by radiative cooling, followedby warm air advection. The results for central Sweden(cluster 3) display effects associated with both northern andsouthern Sweden.

3.4 | Influence of changing climate on the causes ofhoar frost

The graphs in Figure 6 illustrate how the occurrences of hoarfrost (according to the above classification) are linked withchanges in temperature. The results show a consistent trend

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k-means clusters 2007/2008Cluster 1

Cluster 2

Cluster 3

Traditional climate zonesSouthern

Central

Lower Northern

Upper Northern

0 190 38095 km

k-means clusters 2010/2011Cluster 1

Cluster 2

Cluster 3

Traditional climate zonesSouthern

Central

Lower Northern

Upper Northern

Case winter 2007/2008 Case winter 2010/2011 (a) (b)

FIGURE 3 The geographic location of stations in the three clusters (triangles) for a warm (a) and a cold (b) winter [Colour figure can be viewed atwileyonlinelibrary.com]

OU ET AL. 2605

for the occurrence of hoar frost in the three groups both intotal number and the relative frequency of occurrences ofhoar frost in each group (Figure 6), while no clear change inthe total occurrence of hoar frost for the whole of Sweden isfound with changes in temperature. The relative frequencyof hoar frost due to warm air advection significantlydecreased in relation to an increase in the large-scale Ta (themean temperature of a grid from MERRA2, 0.5� latitude

× 0.625� longitude, containing an RWIS), while the fre-quency due to radiative cooling significantly increased. It isbelieved that the weakened temperature gradient betweenland and ocean caused the decrease in the number of occur-rences of hoar frost due to warm air advection, since the landtemperature increases faster than over the ocean (e.g., Suttonet al., 2007). No clear trend is found for the occurrence ofhoar frost in the second group (IADR), which may be causedby morning heating of air but cold road surface. In the cur-rent work, the link between the changing climate and theoccurrence of hoar frost due to warm air advection and radi-ative cooling is the main focus.

Changes in the temperature gradient, in relation to thechanges in the large-scale temperature over Sweden, werethen examined to test the above hypothesis. In order todetermine the source of the warm air, the major wind direc-tions of the three regions were first investigated. Resultsshow that the dominant wind directions for all three regionsare west and southwest (Figure 7). The temperature gradi-ent along four directions was further analysed, includingthe two dominant wind directions and the northwest andsouth direction so that the most of the possible wind trans-ports were considered. For each direction, the air

Time to the occurrence (Hr)

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FIGURE 4 Average of anomalies of Td, RST, and Ta from 24 hr before to 4 hr after the first occurrence of a hoar frost (w.r.t. the first occurrence of a hoarfrost) for stations in (a) cluster 1, (b) cluster 2, and (c) cluster 3 (colour bands and vertical bars indicate the ±0.5 standard deviation of the three variables)[Colour figure can be viewed at wileyonlinelibrary.com]

TABLE 1 The characteristics of four groups of hoar frost identified byclustering algorithm

Groupidentifier

Correspondingcause Conditions

IAIR Warm air advection Positive TT5 of RST and Ta, with theTT5 of Ta larger than that of RST(Ta increases faster than RST)

IADR Morning heating ofair but cold roadsurface

Positive TT5 of Ta, with negative orno change in the TT5 of RST

DADR Radiative cooling Negative TT5 of RST and Ta, with theTT5 of Ta larger than that of RST

UC Not applicable Not applicable

Note. TT5: the rate of temperature change 5 hr before the occurrence of hoarfrost.

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temperature gradient at 850 hPa was calculated, based on alinear regression of the temperature from the target grid onland to about 1,000 km away from the target grid in theselected direction.

As shown in Figure 8, the temperature gradient alongeach of the two dominant wind directions is generally weak-ened with an increase in the large-scale temperature of thegrid. In the winter season, the temperature over the ocean to

IAIR IADR DADR UC0

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FIGURE 5 Box-whisker plot of the relative frequency of the four different groups for hoar frosts of the stations in the three clusters (a) cluster 1, (b) cluster2, and (c) cluster 3

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Cluster 3 - IAIR (R = 0.44(0.50)) Cluster 3 - IADR (R = 0.05(0.18)) Cluster 3 - DADR (R = 0.42(0.13)) Cluster 3 - UC (R = 0.01(0.09))

FIGURE 6 Scatter plot of the winter mean grid temperature (units: K) from MERRA2 and the relative frequency (ratio between the occurrence of eachgroup and the total occurrence) of hoar frost for the stations in the MERRA2 grid during the 17 winters for group 1 (IAIR: a, e, i), group 2 (IADR: b, f, j),group 3 (DADR: c, g, k), and group 4 (d, h, l) in cluster 1 (a–d), cluster 2 (e, f, g, h), and cluster 3 (i, j, k, l). The link between the occurrence and thetemperature is shown in the small figure to the top-right of each figure

OU ET AL. 2607

the west and southwest of a given grid on land is generallyhigher than that of the grid. The temperature gradient willdecrease when the land temperature increases faster than thatof the ocean. This will then lead to weakened warm air

advection and a weaker influence on the local temperatures,which may reduce the likelihood of hoar frost. This will thencontribute to the significant decrease in the frequency ofhoar frost due to warm air advection.

North

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FIGURE 7 Rose diagrams of wind directions for (a) cluster 1, (b) cluster 2, and (c) cluster 3 based on hourly MERRA2 sea level pressure

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FIGURE 8 Scatter plot of the winter mean grid temperature from MERRA2 and temperature gradient in along northwest (a, e, i), west (b, f, j), southwest (c,g, k), and south (d, h, l) at 850 hPa for 17 winters for each grid, with at least one RWIS station located in that grid, in cluster 1 (a, b, c, d), cluster 2 (e, f, g, h),and cluster 3 (i, j, k, l). Positive temperature gradient indicates the mean temperature at the grid is lower than that of the grid upwind

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4 | DISCUSSION

In the present work, in order to investigate occurrences ofhoar frost in Sweden, three climate regions (clusters) wereidentified by using data obtained from RWIS stations andthe K-means clustering algorithm. The classified regionsroughly match the traditional Swedish climate zones(Wallman, 2004). However, a number of stations geographi-cally close to the centre of cluster 2 (central Sweden) wereclassified as belonging to cluster 3 (southern Sweden), asshown in Figure 1. These misclassifications may be due tothe influence of local climatological factors, such as screen-ing (Bogren, 1991; Gustavsson, 1991; Hu et al., 2016), lati-tude (e.g., Andersson et al., 2007), and topography(e.g., Gustavsson and Bogren, 1990; Bogren, 1991), whichmay lead to a different microclimate thus affecting the wayin which hoar frost forms at that location. For instance, coldair pooling in a valley may affect the forming of hoar frost(e.g., Gustavsson and Bogren, 1990). No big difference inresults would be observed if the geographical location hadbeen considered in the classification, since the focus is thecause of the occurrence of hoar frost. As shown, on averagethe temporal variations in temperature (Figure 4b,c), domi-nant wind direction (Figure 7b,c), and temperature gradientare similar between clusters 2 and 3.

The clustering algorithm failed to associate around 30%of the occurrences of hoar frost with a known cause. Thismay be due to large variations in temperature over shortperiods of time (e.g., Gustavsson, 1991), especially in thenorth of Sweden (e.g., Andersson et al., 2007). This maylead to the occurrence of hoar frost with a preceding periodshorter than 5 hr (e.g., a short reaction time), which cannot

be classified by the current scheme used in this study.Another reason could be that the RST was around 0 �Cbefore some of the identified hoar frost (e.g., Gustavssonand Bogren, 1990). In this study, the relevant conditionsmust hold for a minimum of 2 hr in order to identify anoccurrence of hoar frost. Thus, hoar frost will not bedetected if RST fluctuates above and below 0 �C within a2-hr period. The fluctuation of RST around 0 �C alsomakes it difficult to see any clear patterns in temperaturechange in the 5-hr period before an occurrence of hoarfrost, making it difficult to classify such an occurrence asone of the known categories of hoar frost. This may beassociated with different weather conditions, under whichchanges in temperature vary significantly. Further study isneeded to examine the link between weather condition andchanges in local temperature, in relation to the occurrenceof hoar frost.

The frequency of hoar frost due to warm air advectiondecreases following the increase in the large-scale tempera-ture over land, while the frequency due to radiative coolingincreases (Figure 6). The clear temperature gradient fromsouth to north in Sweden may affect these frequencies. Foreach station, the correlation coefficients between wintermean grid temperature from MERRA2 and the relative fre-quency of the occurrence of hoar frost in the IAIR andDADR groups were calculated separately. The results,shown in Figure 9, indicate (a) a clear negative correlationbetween temperature and the relative frequency of hoar frostdue to warm air advection, and (b) a clear positive correla-tion for radiative cooling. This supports the conclusion ofthe impact of climate on the occurrence of different hoarfrost groups.

12°E 14°E 16°E 18°E 20°E 22°E 24°E 12°E 14°E 16°E 18°E 20°E 22°E 24°E

56°N

58°N

60°N

62°N

64°N

66°N

68°N

56°N

58°N

60°N

62°N

64°N

66°N

68°N

> 0.7

0.5 to 0.7

0.3 to 0.5

0 to 0.3

< 0

> 0

–0.3 to 0

–0.5 to –0.3

–0.7 to –0.5

< –0.7

Cor (RFreq IAIR, T2m) Cor (RFreq DADR, T2m)(a) (b)

FIGURE 9 Spatial distribution of correlation coefficient between winter mean grid temperature from MERRA2 and the relative frequency of hoar frost in(a) warm advection (IAIR) and (b) radiative cooling (DADR) groups [Colour figure can be viewed at wileyonlinelibrary.com]

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Weakened warm air advection, in association with theincrease in the large-scale temperature over land, isbelieved to account for the decrease in the frequency ofhoar frost due to warm air advection (Figures 6 and 8). Theoccurrence of hoar frost is generally associated with a radi-ative cooling process since most hoar frosts occur duringthe night. Warm air moving from the ocean to the landmay lead to an increase in air temperature if the tempera-ture difference between the incoming warm air and thelocal cold air is large enough to exceed the cooling ratecaused by outgoing longwave radiation. This may then leadto the occurrence of a hoar frost due to warm air advection.However, the weakened warm air advection may reducethe temperature difference between the incoming warm airand the local cold air, so that the cooling process domi-nates. This may lead to the occurrence of hoar frost beingassociated with temperature decrease; that is, hoar frostcaused by radiative cooling. Hu et al. (2018) showed thatthe volume of water vapour transported from the southwestincreased in a warming climate, which may result in moreoccurrences of warm air advection. However, based on theabove analysis, some occurrences of warm air advectionmay not lead to an increase in temperature. The occurrenceof hoar frost under such conditions will still be classifiedinto the radiative cooling group.

Winter mean temperature has increased in Sweden dur-ing the period 2000–2016 (Hu et al., 2018). Projections ofthe future suggest that winter temperature in Sweden willcontinue to rise for the rest of this century, especially in thenorthern part (Kjellström et al., 2016). Temperatures areforecast to be higher in comparison to the period1971–2000, by up to 4 �C until 2040. The resulting warmingof land may further reduce the temperature gradient betweenland and ocean, which may lead to a decrease in the relativefrequency of hoar frost caused by warm air advection. How-ever, the relative frequency of hoar frost due to radiativecooling may increase, especially in central Sweden wherethe number of occurrences of hoar frost has been found toincrease in a warming climate.

This study provides detailed insights into the formationof hoar frost on winter roads in Sweden, taking different cli-mate zones within Sweden and changes in a warming cli-mate into consideration. Results from this work may be usedto evaluate models for predicting the risk of hoar frost,which may help to improve the accuracy of hoar frost pre-diction. This in turn could improve the efficiency of WRMand reduce the costs associated with it. Moreover, WRMengineers can be better prepared for hoar frost risk in awarming climate. Proper preparation might reduce WRMexpenditure, protect the environment by reducing theamount of salt (Blomqvist and Folkeson, 2001) required forWRM activities, and enhance the safety of roads in Sweden.Nevertheless, further work is required to improve the under-standing of the formation circumstances of hoar frost in awarming climate, such as the impact of sudden changes in

atmospheric circulation/weather patterns on the occurrenceof hoar frosts.

5 | CONCLUSIONS

In this study, the different conditions that lead to the forma-tion of hoar frost are examined. The frequency with whichhoar frost occurs under these conditions and how these fre-quencies might be affected by changing climate has beenanalysed. Results show that hoar frost in northern Sweden ismainly due to warm air advection and days with hoar frostare generally warmer and wetter than days without hoarfrost. On the other hand, in southern Sweden, hoar frost ismainly caused by radiative cooling, meaning days with hoarfrost are generally colder than days without hoar frost.

Following the increase in large-scale temperature, therelative frequency of hoar frost due to warm air advectionhas significantly decreased, while the relative frequency ofhoar frost due to radiative cooling has significantly increasedin each climate zone of Sweden. This is due to a weakenedtemperature gradient between land and ocean as the tempera-ture of the land rises faster than that of the ocean in a warm-ing climate.

Over the next few decades, Sweden will continue to getwarmer, which is likely to further reduce the temperaturegradient between land and ocean, thereby further reducingthe frequency of hoar frost caused by warm air advection.However, the relative frequency of hoar frost caused by radi-ative cooling may increase, especially in centre Swedenwhere the total number of hoar frost is found to increase in awarming climate.

ACKNOWLEDGEMENTS

Prof. D. Chen and Dr. David Rayner in the Department ofEarth Sciences, Göteborgs Universitet are gratefullyacknowledged for the helpful discussions and revision of thetext. We thank PhD E. Almkvist in the same department fordownloading and reading the in situ observations. Thisresearch project was funded by the Swedish TransportAdministration.

ORCID

Yumei Hu https://orcid.org/0000-0002-5947-3430

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How to cite this article: Ou T, Hu Y, Gustavsson T,Bogren J. On the relationship between the risk of hoarfrost on roads and a changing climate in Sweden. IntJ Climatol. 2019;39:2601–2611. https://doi.org/10.1002/joc.5974

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