Estimating or predicting the thickness of river ice and timing of ice breakups in polar regions is made difficult due to the multitude of processes in ice formation, growth and breakup that are highly dependent on local river morphology and hydrology. River freezing tends to start with skim and border ice formation along the river banks and the edges of bars as soon as the water has cooled down [1
]. The main parameters affecting the lateral growth of border ice are heat loss and flow velocity, with field studies showing a positive relationship between the cumulative number of days below 0 °C (Accumulated Freezing Degree-Days: AFDD) and the lateral extent of border ice. However, flow velocities also affect border ice development; a study done on the Nelson River in northern Manitoba showed flow velocities exceeding 1.2 m/s to decrease noticeably the lateral growth rate of border ice [1
]. Frazil ice, slush or floe formation may also take place prior to stable ice cover formation in turbulent rivers [2
]. Once a stable ice cover has formed, it thickens thermally downward due to heat transfer processes based on meteorological conditions.
Downward thermal thickening of stable ice can be relatively well described by the degree-day method using the Stefan equation [3
]. However, this method is not suitable for estimating very thin ice i.e., <10 cm thicknesses [5
]. Michel [6
] defined coefficients to be used in the thermal ice growth equation by Stefan when the river is snow covered. Ashton [7
] concluded that the ice thickening equation provides accurate predictions assuming that there is no formation of snow-ice. When a snow cover exists, snow-ice may form if the snow becomes saturated with water, either by river water overflowing the ice surface through cracks [8
], or from rain during a freeze-thaw cycle. Thus, the freezing of snow and water mixture can result in upward thickening of ice, which is not described with the basic Stefan equation.
] has developed site specific statistical ice growth models for several hydrometric river stations and found that accumulated freezing degree-days (AFDD) had a significant influence on observed river ice thicknesses, whereas the cumulative snow thickness and density had a relatively lower influence. Significant literature exists where Stefan’s equation has been applied to match the simulated ice thicknesses with observations (e.g., [10
]). Zhang et al. [13
] applied the ice thickness calculation method by Ashton [14
] and developed a simple model for snow wetness determination which was used to define the thermal conductivity of snow. Thus, the input parameters of their ice thickness calculation framework consisted of air temperature, snow thickness and the modeled thermal conductivity of snow in addition to constant values. The method used by Zhang et al. [13
] resulted in better thickness estimates than the original Stefan [3
] equation, which ignores the thermal resistance of snow on heat transfer between water and air. However, the equations of Zhang et al. [13
] and Ashton [14
] require a greater number of parameters for their calculation compared to the Stefan equation [6
], which may hinder their application.
Two sources of the break-up of river ice are thermal break-up and mechanical break-up. The main driver of thermal break-up is meteorological conditions, with this break-up generally occurring where there is no strong spring runoff event [15
]. A spring runoff event occurs due to rapid snow melt caused by rising temperatures and/or significant rainfall, with the resultant river flows resulting in a mechanical break-up. Temperatures are influenced by the solar radiation absorption of ice; thus, the albedo of snowpack and ice play a role in the ice decay process rate. While different ice decay equations have been developed, there lacks a universal method for estimating the ice cover break-up. However, hinge resistance at river banks could be applied to determine the onset of ice cover break-up in relatively straight rivers [16
In addition, Bilello [17
] used river ice decay data from Canada and Alaska and found reasonable site-specific relationships between incremental ice thinning and thawing degree-day parameters. Furthermore, Shen and Yapa [18
] developed a modified method to estimate river ice growth and thinning by applying degree-day method. The capability of the degree-day method to estimate the timing of ice breakups has been analyzed, e.g., by [19
], showing that the modeling of ice breakup dates and changes in ice thickness is possible in large rivers. Despite that previous studies analyzing for the changes in the river ice break-up dates within Europe, or fine-tuning of equations based on the data from North-American rivers, the previous studies have not fully analyzed how accurate the simple ice growth and decay equations (which are based on air temperature) work during hydrologically variable years in rivers of northern Europe. These rivers can be considered relatively small (e.g., few tens of meters wide) and are under the hydro-climatic influence of the Gulf stream [21
The polar region is warming faster than any other region on Earth [22
]. However, northern Europe is experiencing a greater sensitivity to warming when compared to areas of similar latitudes in North-America [23
]. Klaviņš et al. [24
] have already shown a clear decreasing trend in the duration of ice cover during the last 150 years in the River Daugava, which has become more intense during the last 30 years. Altogether, Klaviņš et al. [24
] analyzed river ice break-up dates from 17 stations in the Baltic States and Belarus. The climatic variables (i.e., North-Atlantic Oscillation (NAO) and Arctic Oscillation (AO)) have been stated as the reason for variation in freeze-up and break-up dates in Nemunas River, Lithuania, during the last 150 years [25
]. NAO and AO, which impact on thermal anomalies, have shown positive correlations with freeze-up dates during mid-November to early January period [25
]. However, statistically significant negative correlations during the period of early January to late March have indicated earlier than normal break-up dates in positive AO/NAO phases [25
]. Šarauskienė and Jurgelėinė [26
] have studied data from 13 water measurement stations (within eight rivers) in Lithuania and found that there has been a negative trend in ice duration and positive trend in freeze-up dates. Records from the Northern Hemisphere from 1846 to 1995 indicate a reduction in the ice season by 12.1 days per 100 years; however, records extending to 2005 indicate a further reduction of the ice season to 19.5 day per 100 years [23
The expected future changes in discharges/flooding, sediment transport and channel morphology [27
] in areas within cold climate region, such as northern Europe, are ultimately controlled by these river-ice characteristics, which will be affected by future shortening of the frozen period, earlier ice break-up, diminishing seasonally frozen ground, increasing freeze-thaw cycles and increased frazil ice occurrences [12
]. To be able to predict these future changes in river ice characteristics, and further their impacts on river hydro-morphodynamics and related flood and erosion hazards, analysis of thermal ice growth and decay equations based on observations of hydro-climatically varying years are needed from rivers of the polar region.
Therefore, the aims are to (1) investigate the impacts of hydro-climatically varying years on the river ice development in a subarctic meandering river and (2) parameterize and analyze the accuracy of realistic ice thickness growth and decay models to examine climate-induced changes in river ice. This includes analyses of whether the existing ice thickness growth models, and decay equations can sufficiently describe the reality at present. Ice growth and decay equations are applied for estimating the river ice development during 2013–2019 years of varying hydro-climatic conditions (i.e., from mild to severe winters). The established methods, namely, the Stefan’s ice growth equation (version by Michel et al. [6
]) and the Bilello [17
] decay equation, are now for the first time applied for detecting multi-annual ice growth and decay processes of a subarctic river, within the polar region of Northern Europe. The novelty of the approach is in the climatic aspect, in particular in showing how the freeze-thaw cycle impacts on the ice growth and ice decay processes. The performance of these equations has not been tested previously by using multi-annual freeze-thaw data from hydro-climatically varying years. Thus, these modeled results are for the first time compared against multi-annual field observations (e.g., ice thickness and snow depth) measured during the mid-winters, time-lapse camera pictures throughout autumn-winter-spring periods, and hydro-climatic observation data from the Finnish Meteorological Institute.
2. Study Area
The study area is located at the meandering Upper Pulmanki River (Northern Finland), which is a tributary of the Tana River (Figure 1
). The Pulmanki River is within the polar region (circa 70° N latitude) and belongs to the cold climate category without a dry season and with a cold summer (Dfc category of [33
]) (Figure 2
and Figure 3
). The hydro-climatic conditions, particularly the generation of low pressure systems, are affected by the Gulf stream heating the North Atlantic Ocean [21
]. The study site has large seasonal hydro-climatic variations, below 0 °C winter air temperatures, and annual maximum discharges during spring snowmelt events. Furthermore, the region is predicted to experience warmer winter seasons in the future [22
]. The study site has the advantage of no upstream lakes, which has been previously found to be an influential parameter for the malfunction of the ice growth analyses [12
]. The temperatures often reach below 0 °C in early October (Figure 2
and Figure 3
), and begin rising back above zero in early April. Thus, the freezing period lasts approximately seven months a year. The mid-winter ice bottom roughness was classified visually as smooth–rough, following the definition of [34
]. Similar ice roughness occurred each winter from 2013–2019, as seen from photos taken from drill holes. Summer discharges are typically around 4 m3
/s, but during spring the discharges can be around 50 m3
]. However, less than 2 m3
/s discharges have been observed in autumn and winter [36
]. Thus, this river represents a typical subarctic river with its hydro-climatological characteristics and ice cover processes.
When summing up the findings, the overall best performance of both equations (Stefan and Bilello) was in 2016–2017, when the maximum snow thickness values were high, the number of freeze-thaw days was closest to the long-term average of freeze-thaw days, and when there was both slow snow-melt and air temperature increases in the spring. Lind et al. [12
] have also found that the stability of the ice cover depends mainly on the number of freeze-thaw days and the length of the cold period. Thus, our findings are in line with their study, as the most unpredictable years were those with the parameters furthest away from the long-term average number of freeze-thaw days. In addition, the greater the AFDD values were, the less well the decay processes were possible to be defined.
The least correspondence between the estimated (Stefan [6
]) and observed ice thicknesses (underestimation) was during the years which had the thinnest snow-cover and the thickest maximum and average ice cover at the Pulmanki River. The ice thickness development was not possible to observe continuosly from 2013–2019, but only from the mid-winter conditions. However, visual inspection of the ice type was made in winter 2013–2014 through the bore holes and a 10–20 cm thick layer of snow ice was detected on top of the thermally formed black ice [11
]. It is likely that river water had inundated on top of the ice cover at some point during the winter since the amount of snow was low on the river ice during field work in February–March 2014, despite snow having been accumulated in the nearby forested areas. As the Stefan equation [6
] does not account for snow-ice formation, the underestimation of the ice thickness would be at least partly explained by the snow-ice in the 2013–2014 winter. Contrary to the present study, Ma et al. [20
], found overestimation of ice thickness calculations during the years with snow on the ice. They had applied Stefan’s equation without any correction coefficient. Their four observation sites located along the large Lena River, in Siberia. However, Ma et al. [20
] do not state where the measurement locations of the maximum ice-thickness values were. As the cross-sectional variation of the ice-thickness can be expected to be greater in the wide and large Lena River compared to the 20 m wide Pulmanki River, the possible difficulties in measuring the representative maximum ice thickness could also explain the overestimation of the model applied by [20
] in a large river. The empirical coefficient applied in the Stefan equation (from [6
]), which was used in the present study, took into account the temperature difference between air and surface and insulating effect of snow. The next step further would be to test with the Ashton [7
] equation, which takes into account the thermal resistance of the surface to air boundary layer [7
]. However, these parameters are not available from as many study sites as the air temperature parameters for Michel equation [6
], and therefore, the lack in data sets hinders the spatially wide applicability of the Ashton [7
] equation. In any case, further studies in areas with longer and continuous snow pack thickness time series data are suggested. The application of ice thickness estimation methods, which require contiuous information on snow depths, such as by [13
], would then also be possible.
The thermal ice growth equation is not expected to work in the future in the areas of polar region, which are similar to the cold climate category area [33
] of Northern Fenno-Scandinavia, as there is expected to be less snow and a higher number of freeze-thaw days in the future [22
], in addition to the increased frazil ice appearance [46
]. Persson et al. [43
] has stated that the average number of freeze-thaw days would increase from the average 10 to 30 by year the end of the 21st century in northern Scandinavia. The 2018–2019 winter had 20 freeze-thaw days at the Pulmanki River, which would be in line of the predictions that Persson et al. [43
] had mentioned more than a decade ago. Furthermore, the maximum ice thickness values had a linearly decreasing trend during the observation period 2013–2019. The changes in air temperature and increased number of freeze-thaw days could be a possible explanation for this. Thus, overestimations of ice thickness estimates are expected in years when the number of freeze-thaw days differs from the long-term averages, and underestimations during years with diminishing snow depths.
In addition, adjustments to the ice decay equation and the applied parameter values would be needed for predicting ice decay processes in future hydro-climatic conditions, because earlier snow-melt floods [30
] are expected, which also indicates an earlier and more intensive rise in air temperature than at present. Turcotte et al. [48
] have stated that future earlier spring snowmelt periods influence the break-up process as the ice cover is less exposed to short-wave radiation (the sun angle increases over time) when the discharge begins to rise. Based on long-term data sets, changes towards earlier break-up dates have also been observed in Northern (polar/subarctic region) and Southern Finland (boreal region) [49
]. Thus, an increasing potential for mechanical break-ups and higher ice-jam-induced water levels are expected [48
]. As the ice decay equation of Bilello [17
] did not explain the mechanical break-up timing at present, it is not either expected to predict those in the future. During springs, with rapid and intensive temperature rise, the results of this study indicated better performance of the equations when applying the average mid-winter ice thickness value. Therefore, we suggest that these average mid-winter ice-thickness values may also work in the future with changed hydro-climatic conditions (i.e., early and rapid melting). Thus, the applied ice thickness value (i.e., whether applying average or maximum value) in ice decay equation would require adjustment based on the observed hydro-climatic characteristics of each year. This need for analyzing the hydro-climatic characteristics of each spring season first, i.e., before calculating the ice decay with Bilello [17
] equation, makes it difficult to predict the ice decay processes of the coming years.
] has observed in Peace River, Canada, that despite a rise in winter air temperatures since the 1960s, solid-ice thickness has increased. They concluded that porous accumulation covers enhanced winter ice growth via accelerated freezing into the porous accumulation. They stated that together with the reduction in winter snowfall, this effect (i.e., freezing into the porous accumulation) could reverse the effect of warmer winters on ice thickness, thus explaining present conditions. We are not able to state, based on the Pulmanki River data, if this would be also observable in Pulmanki River in the long-term. However, it is important to note that the equations at present may not work in future changed conditions due to these changes in process magnitudes. Note also that the climatic region of the Pulmanki River is presently under the warming influence of the Gulf stream [21
], which makes it different to the rivers of more continental climate areas, such as Peace River in Canada.
Lind et al. [12
] had previously observed that there is great difference between inland and coastal river reaches (in Sweden) in how well the AFDD can be applied to predict river ice thicknesses. The inland reaches had a stable ice cover, but the coastal reaches had many melting periods during the winter, and differences in AFDD values. Thus, the performance of the Pulmanki River can be considered more similar to the studied inland reaches of Sweden regarding the AFDD values, even though the impact of the Arctic Ocean warms the area more than the areas further inland in Finland. However, the Pulmanki River resembled the coastal rivers of the study of Lind et al. [12
] in the freeze-thaw day amounts (average of 15.6 freeze-thaw days). When compared to the global river ice classification model by Turcotte and Morse [53
], it was found that some ice characteristics of the Pulmanki River differed from it. According to Turcotte and Morse, the riffle-pool meandering rivers which are in cold climates, may get the complete ice cover that remains in place all winter after the first freeze-up cold spell. In the Pulmanki River, despite being in subarctic region and a small meandering channel, many freeze-thaw periods occurred each year.
Recently automated image processing algorithms have been developed and used for detecting the timing of ice formation and break-up processes [2
]. This method would be worth testing in different sites. In addition, Park et al. [54
] have simulated with a land process model ice thicknesses, as well as changes in the river freeze-up and ice break-up dates, consistent with in-situ data and satellite observations over the pan-Arctic. Their study indicated that less insulating snow might introduce thickening ice cover in the region. Thus, the next step would be to analyses the temperature changes in other subarctic and arctic areas, and analyzing how simple equations based on thermal properties fit with the observed thermal melting and ice break-up timing (such as based on satellite or aerial data). If these equations also work in other locations during similar hydro-climatic years as we observed at the Pulmanki River, then future predictions of changes in ice melting would be possible. Hence, the timing of the spring snow-melt flood and its changes could also be predicted, and further studies of the impacts of river ice changes on hydro- and morphodynamics could be performed for varying hydro-climatic conditions.
Based on the results of this study, it was possible to get a more detailed picture of the annual variation of ice-growth and decay processes within a sub-arctic river. It was also possible to define how well the simple ice growth and decay equations, which are based on air temperature, work during hydrologically variable years.
The mid-winter maximum ice thicknesses decreased during the observation period, along with the decreasing average and minimum mid-winter (February, i.e., the field measurement period) temperatures. However, the maximum mid-winter temperatures had also increased at the same time, indicating that extreme air temperatures had increased. The ice clearance date varied greatly between years, with the last one in 2017. Each year, the freezing process included frazil and border ice formation prior to the full ice-cover development. The ice clearance was thermal in all but one year, when it was mechanical.
Overall, the best performance of the ice growth and decay equations was in 2016–2017 winter, when the maximum mid-winter snow thickness value was high, the number of freeze-thaw days was the closest to the long-term average of northern Scandinavia, and the rate of thermal snow-melt was slow during spring. Overestimations of ice thickness estimates are expected in those years, when the number of freeze-thaw days differs from the long-term averages, and underestimations are expected during years with diminishing snow depths. Thus, the thermal ice growth equation is not expected to work in future changed conditions as well as at present as less snow and a higher number of freeze-thaw days are expected. Due to an expected earlier snow-melt flood and earlier rise in spring-time air temperatures in the future, adjustments to the ice decay equation for its future application would be needed based on seasonal hydro-climatic conditions. It is suggested to apply the average mid-winter ice thickness value for calculating the ice clearance date when winter is short and a rapid spring temperature increase is experienced. Thus, future possibly changed hydro-climatic conditions will complicate the application of both ice growth and decay equations.