Freshwater ice occurs in many forms on rivers and lakes. There are particular differences between the process of ice evolution on lakes, with static ice formation, and rivers, which are dynamic in terms of ice formation (Barry and Gan, 2011). However, the common point is that, after the water cools to below 0 ∘C, frazil ice can develop. The other ice forms are then built up from frazil ice particles (Carlson, 1981). The regular freshwater ice observations include the monitoring of the following ice phenomena.

Border ice: ice attached to the shores along shallow river banks (Hicks, 2009) or adjacent to the lakeshore (Barry and Gan, 2011). At certain places border ice zones can merge, forming ice bridges.

The ice regimes of rivers and lakes can be characterized by the dates of appearance and disappearance, duration, and frequency of the different ice phenomena during the winter seasons (Leppäranta, 2010; Smith, 2000). The following ice phenology records were extracted for each winter.

Ice-on: the start date of the first occurrence of floating ice

There are few stations around the Globe with records of freshwater ice phenology reaching back more than 100 years (Prowse et al., 2007b). However, in Hungary lake/river ice has traditionally been observed for more than 140 years. In eastern–central Europe knowledge of river and lake ice regimes has been important in relation to fishing, transportation (navigation and crossing possibilities of rivers and lakes), or river ice jam floods (Herman, 1887; Lukács, 1934; Rácz, 2016).

There are three major sources of freshwater ice phenology:

regular monitoring;

For statistical evaluation and long-term trend detection, the raw version of freshwater ice phenology records underwent some pre-processing.

The calendar dates of ice phenomena appearances and disappearances were converted to numbers: 1 November was designated as 1 and the other dates were assigned numbers up to 160, that is, 10 April.

We investigated the freshwater ice time series for the Danube and Lake Balaton for a long-term, linear trend. We applied two methods:

linear regression, a parametric method for trend testing in which the trend magnitude can be estimated from the regression slope, and

Ice occurrence is in general to be expected between late December and late February; ice cover usually builds up from mid-January to mid-February over the investigated section of the Danube, but in extreme cases these dates can vary as far as covering the period from November to March (Fig. 2, Table 2). On the basis of the observations, the earliest date of ice-on was 14 November 1888, and the latest date of ice-on was 26 February 1986. The earliest and latest freeze-up times were recorded on 9 December 1925 and 21 February 1887, respectively. In the case of break-up, the earliest date was 20 December 1902, while the latest was 26 March 1895. The earliest observed ice-off date was 30 November 1915, while the latest was 28 March 1940. In the case of the extended observations from Budapest, the mean and extreme dates are similar; earlier ice-on and freeze-up were only recorded on 11 November 1876 and 7 December 1774, respectively.

Considering the entire section of the Danube, ice-on occurs earlier at the upper stations because of the ice-drifting arriving from upstream. However, freeze-up starts at the lower sites and then the ice cover is built up in an upstream direction. Break-up also occurs earlier in the direction of flow, while ice-off takes place later on the lower sites (Fig. 2). There is an apparent contradiction between the mean dates of break-up and ice-off, so that the break-up occurs later than the ice-off on average. The explanation for this odd feature is the presence of winters with no ice cover at all (only drift ice appears). If ice cover is formed, the date of ice-off is to be found much later compared to years without any ice cover formation (Table 3).

The interannual variability of ice phenomena based on the standard deviation of the dates for the appearance of ice phenomena and their disappearance are similar at all of the observation sites along the investigated section of the Danube. In the case of ice-on and freeze-up, this is 15–21 days, while for break-up and ice-off it is somewhat higher, 20–25 days.

Over the investigated section of the Danube, the length of the ice-affected season – excluding the ice-free winters – is 26–35 days on average, which increases in the direction of flow (Fig. 3). The longest ice-affected season was observed in 1894/1895, when 100 days of ice phenomena were recorded. The duration of ice cover is 29–36 days on average (omitting winters without ice cover), which also leads to an apparent contradiction (Fig. 3). Here, the explanation is similar, with the shift in mean statistics being caused by the presence of ice-cover-free winters, when the duration of the ice-affected season is much shorter than when ice cover develops as well. The longest duration of ice cover was recorded in 1946/1947, when ice cover lasted for 83 days. The extended historical observation dataset of Budapest contains only one longer record, in 1829/1830, when the ice cover lasted for 99 days. The interannual variability of the ice-covered and ice-affected seasons is 20–23 and 22–28 days, respectively.

Ice-on and freeze-up can occur as early as late December on Lake Balaton, while the usual periods of break-up and ice-off usually take place just in late February and at the end of February, respectively (Fig. 2, Table 2). Based on long-term ice observations, the earliest ice-on was recorded on 20 November 1956, and the latest ice-on was observed on 11 February 1975. The earliest date of freeze-up was on 24 November 1914, while the latest was on 25 February 1902. In the case of break-up, the earliest and latest records were 26 December 1973 and 30 March 1929, respectively. Finally, the earliest date of ice-off was observed on 31 December 1926 and the latest ice-off date was recorded on 8 April 1940. The interannual variability of the dates of the appearance and disappearance of lake ice are 19–22 days in the case of Lake Balaton, which is close to that of the Danube.

The length of the ice-affected season on Lake Balaton – excluding the ice-free winters – is 58 days on average, which is 2–3 weeks longer than in the case of the Danube (Fig. 3). The longest ice-affected season was observed in 1962/1963, when 118 days with ice phenomena were recorded. The duration of ice cover is also longer, 47 days on average (discounting winters with no ice cover; Fig. 3). The longest duration of ice cover was observed in 1969/1970, when ice cover remained for 110 days. Compared to the River Danube, ice cover is a more frequent phenomenon on Lake Balaton, with only five winters in which no ice cover developed after ice-on since 1885. The interannual variability of the ice-covered and ice-affected seasons is 25 and 28 days, respectively, similar to that of the Danube.

On the basis of the observations, ice-on dates have shifted to a significantly later date over the entire section of the Danube. Similarly, freeze-up dates have also appeared later, but this change was not significant for all stations. In the case of break-up, some differences could be detected: at Komárom and Nagymaros practically no changes could be found, but at Budapest and Mohács break-up has shifted to an earlier point in time, although the trend magnitude was not significant (p>0.05). However, in the last 50 years, ice cover has occurred only once on this river section. Ice-off has also appeared consistently earlier, and in this case the change was significant (Figs. 4 and 5). As a result of later freeze-up and earlier break-up, the duration of ice cover has decreased.

An exception is Komárom, where a slight but not significant increase could be detected. Due to later ice-on and earlier ice-off, the ice-affected season was significantly shortened at all sites on the River Danube (Table 4).

The number of ice-free and ice-cover-free winters has increased over the investigated period on the Danube, and especially from the 1970s. Between 1885 and 1965 between 5 and 9 ice-cover-free winters occurred per decade at Komárom and Nagymaros, and 2–7 at Budapest and Mohács, but after 1975 the number of ice-cover-free winters rises to 9–10. Ice-free winters have also become more frequent, again, especially since 1975.

During the analyzed period anthropogenic interventions have intensified remarkably in the Hungarian section of the Danube and also farther upstream. This also affects the river ice regime, together with the more general phenomena of climate change and increasing winter temperatures (Takács et al., 2013). In the case of the Danube, river regulation works and increasing water pollution have affected the river ice regime. The changes were strongest after the 1960s, when the relative frequency and the duration of ice phenomena and winter air temperatures triggering ice occurrence significantly decreased compared to the previous periods (Takács et al., 2013). Therefore river regulation and pollution, together with increasing temperatures, may well be the cause of the long-term trends in the river ice regime of the Danube River.

On the basis of the observations, ice-on (11.56 days/100 years, p<0.05) and freeze-up (6.56 days/100 years, p>0.1) have shifted to later dates on Lake Balaton. The magnitude of trend in ice-on was less than half that of the Danube, while in the case of freeze-up, it is about half of that. The date of break-up remains practically unchanged, but ice-off has moved to a significantly earlier timing. The ice-off trend magnitude was also less than half that of the Danube (Fig. 6). The duration of ice cover has not changed, either, with only slight changes in freeze-up and break-up dates. The ice-affected season has shortened as a result of later ice-on and earlier ice-off dates, as on the Danube, but the magnitude of this change was much lower than on the Danube (Table 4).

The frequency of ice-free or ice-cover-free winters has not changed over the analyzed period at Lake Balaton. Compared to the Danube, ice-free winters were very rare at Lake Balaton; only zero to two winters with no ice cover and zero to one winter with no ice have occurred per decade since 1885.

River ice regime trends relying on an observation period exceeding 100 years have been investigated in the case of some other water bodies in eastern–central Europe (Pawłowski, 2009, 2015; Takács, 2016; Bączyk and Suchożebrski, 2016; Takács and Kern, 2015), providing an opportunity for regional comparison. The investigated trends compared to the trend results of this study display a similar direction, but are of a different magnitude (Table 5). On the Danube, the trend of the ice-on date is similar to the changes detected on the Drava, but much faster than the Raba. Freeze-up dates and ice-off dates on the Danube have changed twice as fast as on the Drava and Raba. The duration of ice cover has decreased to a similar degree on both the Danube and Drava, and somewhat faster than on the Raba. The length of the ice-affected season has also changed most on the Danube. Only in the case of break-up could slower changes on the Danube than on the Drava or Raba be found (Table 5).

Regarding the Lower Vistula, in 1960–2016 the duration of ice phenomena showed a strong decrease ranging from 6.6 to 9.6 days decade-1. Duration of ice phenomena was found to be correlated with the pollution of the river water, especially as the (annual mean) concentration of chlorides increased from approx. 40 to 200 mg dm-3 between 1960 and 2014, possibly explaining ∼ 25–30 % of the decrease in ice cover (Pawłowski, 2017). Anthropogenic influences have been observed on ice formation in additional water bodies, e.g., Silesian Upland (southern Poland) monitored in the winter season of 2009/2010 (Solarski et al., 2011). These observations concur with the reported strengthening of anthropogenic impact on the ice regime of the Danube after the 1960s (Takács et al., 2013) and call for special attention when trends from the late 20th century are to be discussed in a regional context in future studies.

Soja et al. (2014) evaluated the ice regime trends of Lake Balaton over a shorter period (1926–2013) utilizing only the records available from the Central Transdanubian Water Authority, Székesfehérvár, Hungary. The results relating to the trends in ice phenomena were contrary to those observed in the present study: it was found that freeze-up has not changed, break-up has shifted earlier by 7 days/100 years, and the duration of ice cover has decreased by 12 days/100 years (Soja et al., 2014). This discrepancy calls attention to the importance of a common reference period in trend analysis and climate research.

However, long-term freshwater ice phenology data are available mainly for stations outside of eastern–central Europe (Benson and Magnuson, 2012). A detailed evaluation of the large-scale climatic information that may be hidden in the freshwater ice phenology records of the Danube and Balaton is beyond the scope of this study. Nevertheless, comparison with the longest records from Asia, North America, and Europe highlights the scientific value of these new cryophenological records (Figs. 7 and 8).

For the period of 1774–2017 the changes in freeze-up dates, break-up dates, and duration of ice cover of the Danube were compared to the Red River (Canada–USA), the Angara (Russia), and Tornionjoki (Finland–Sweden). To eliminate the bias of anthropogenic interventions, trend magnitude was calculated for the 1774–1960 period in the case of the Danube. The dates of freeze-up have shifted to later dates in all cases, but on the Danube and Angara the changes were slower than on the Red River. The dates of break-up have shifted to earlier dates except in the case of the Angara River, where later break-up was observed. The magnitude of trend in the Danube is lower compared to the Red and Tornionjoki rivers. The duration of ice cover decreased on the Danube and Red rivers, but on the Angara no significant changes could be detected (Fig. 7).

Freeze-up dates, break-up dates, and the duration of ice cover at Lake Balaton were compared to the corresponding records for Lake Mendota (USA), Lake Baikal (Russia), Lake Suwa (Japan), and Nasijarvi (Finland). In the period 1885–2017 the dates of freeze-up have shifted to a later date at all lakes, but the magnitude of the trend was lower at Lake Balaton than the other lakes. In the case of break-up dates, earlier shifts were observed, but no significant change was detected in the case of Lake Balaton. The duration of ice cover has not changed either at Balaton, but at the other lakes decreasing trends have been detected in both instances (Fig. 8).