Measured and predicted freeze-thaw days frequencies in climate change conditions in central Poland

Study area

Created in 1991 in central Poland on the Warta river, Jeziorsko is a typical retention reservoir, ranking second in terms of area and fourth in volume in Poland (Fig. 1). Located within an old river valley on the borderline between plateaus, the reservoir is elevated to 115–118 m in the Warta valley and to 130–150 m in the plateaus (Forysiak, 2005; Kaczmarek, 2018). The slopes limiting the reservoir to the west are low and gentle, while those to the east are steeper and higher, frequently reaching heights well above 10 m. The dynamics of the eastern slopes have been subject to our detailed research (Kaczmarek, 2018; Kaczmarek et al., 2019, 2021).

The shore zone develops within Quaternary deposits, which are mainly glacial tills and sands of Riss glaciation, and to a lesser extent, sands and silty deposits of the latest glaciation (Klatkowa & Załoba, 1992a, 1992b; Załoba, 1996; Forysiak, 2005).

The Jeziorsko reservoir is located in the temperate climate zone. The mean annual air temperature for the area in 1951–2015 was +8.0 °C with the minimum of +6.0 °C and the maximum of +9.9 °C (Kaczmarek, 2018; Kaczmarek et al., 2019). The length of the period with negative mean daily air temperatures is between 70 and 80 days (Limanówka & Niedźwiedź, 1994), while the soil maximum frost depth is one meter (Polish Standard PN-81 N-03020, 1981). The study area is characterised by the country’s lowest level of precipitation with the annual totals remaining below 550 mm, nearly half of which is recorded between May and August (Kaczmarek, 2018; Kaczmarek et al., 2019). The mean annual accumulated thickness of snow cover in 1950–1989 was 640 cm, however the share of winter days without snow amounts to 50% (Niedźwiecki, 1998).

The area where the reservoir is located is among those with Poland’s lowest annual total of freeze-thaw days (FTDs) amounting to 66–71 in 1951–2018 (Kaczmarek et al., 2021). What is more, their number in the area decreased by 4 FTDs/10 years (Kaczmarek et al., 2021) over the study period.

The Jeziorsko reservoir is characterised by an annual cycle of operation with substantial water level fluctuations of up to 5.5 m. Historically, these changes ranged from 2.6 m to 5.65 m per year. Spring-time meltwater causes the level in the reservoir to increase, which is maintained over the summer months (May–September). In the autumn and early-winter months the water level gradually decreases to reach the minimum in January and February (Kaczmarek, 2018). A 15.3 km stretch of the shoreline, out of the total of 45.8 km, i.e. over half of the unregulated shore, is subject to coastal erosion and retreat. The cliffline recession results from the combined impact of wave erosion and subaerial processes (Kaczmarek, 2018; Kaczmarek et al., 2019).

Our TLS monitoring-based study conducted in 2014–2015 on the west-facing, 124 m-long stretch of Jeziorsko cliff face with an average height of 3.9 m, developed in frost-vulnerable silt and clay-rich sediments (the content of silt (0.002–0.075 mm) and clay (finer than 0.002 mm) reaches 73–85%; plastic limit PL = 12%, liquid limit LL = 26–29%, and plasticity index PI = 14–16%), indicates that the magnitude of recession within the studied cliff caused by freeze-thaw processes was max. 10 cm with the mean value of approx. 3 cm (Kaczmarek et al., 2019).

The 2014–2015 study coincided with the first season when, due to a changed reservoir operating regime, the level of water did not reach the cliff base. It enabled the authors to perform the assessment of the transformations within the cliff and the amount of the material accumulated at its toe during the summer period. The volume of the material deposited at the cliff toe in the winter of 2014–2015 and in the other seasons of the year suggests that freeze-thaw processes were responsible for 70% of the annual cliff recession in the absence of wave action. At the same time, this value makes up 20% of the annual cliff recession recorded in previous years when wave erosion took place (Kaczmarek et al., 2019). The studied shore stretch is not subject to transformation caused by slides or solifluction, nor are there any groundwater seeps. In the winter season, snow cover does not appear on the surface of the vertical or nearly vertical cliff face. In terms of precipitation, the study period can be classified as typical (Kaczmarek, 2018).

Meteorological data and terminology

Depending on the scope of analysis, its purpose, timespan and data availability, various kinds of data are adopted to characterise the thermal conditions of freeze-thaw processes (Gatto, 1995; Kreyling & Henry, 2011; Nilsen et al., 2021; Kaczmarek et al., 2021).

Our analysis was performed based on the 1951–2018 mean, minimum and maximum daily air temperatures 2 meters above the ground level obtained from three weather stations closest to the studied reservoir (41 to 46 km away), and belonging to the measurement network of the Institute of Meteorology and Water Management-National Research Institute (IMWM-NRI) in Warsaw (Poland) (Fig. 1, Table 1). The selection of the weather stations was dictated by their location, the quality of the existing data and the comparability of time series.

Based on available daily air temperatures, days with zero-crossings were identified. A day with a freeze-thaw event, referred to as a freeze-thaw day (FTD), is defined as the one on which the maximum daily air temperature is >0 °C and the minimum one is ≤0 °C. An FTD indicates the occurrence of at least one event of zero-crossing during a given day. The term “days with zero-crossings”, abbreviated DZC (Kjellström et al., 2016; Nilsen et al., 2021), is also frequently used to denote the same phenomenon. To ensure full coverage of the period in which such fluctuations appeared (autumn, winter, spring) the analysis encompassed one year from 1 August to 31 July.

Methodology

In order to determine the characteristics of frost action conditions at the cliff surface and to test the relationship between the air temperature at 2 meters above the ground level obtained from the IMWM-NRI weather stations and the temperature at the cliff face, the authors performed their own temperature measurements in the winter season of 2014–2015. The task was carried out with a HOBO temperature logger placed on the active, plant and snow cover-free, nearly vertical cliff surface, 0.3 m below a dense herbaceous plant cover. The measurements, taken with the frequency of 10 min and accuracy of ±0.2 °C took place from 11 Dec. 2014 to 17 Mar. 2015, which coincides with two cliff face morphometry measurement series performed with a Terrestrial Laser Scanner (TLS).

The study of the direction of changes in air temperature and FTD (estimation and significance) was carried out with the non-parametric Mann-Kendall (MK) test (Hirsch, Slack & Smith, 1982) commonly used to detect a monotonic trend in environmental, climate or hydrological data series. The null hypothesis of the test assumes that when no trend is present, the measurements (data) over time are independent (i.e. are not serially correlated over time) and identically distributed. The alternative test hypothesis assumes that the data show a monotonic trend. The significance of the MK test was assessed at the significance level of 0.05. The analysis also used the linear trend function to make a measurable assessment of the decrease or increase in the studied indicators per unit of time (e.g. 1 year, 10 years). A t-test was used to assess the significance of the regression coefficient in the linear trend function. The significance of the t-test was assessed at the significance level of 0.05.

Polynomial regression was used to describe the non-linear relationship between the studied features. The least-squares polynomial approximation can easily be considered as an example of multiple linear regression.

Due to a possibly high degree of relationship between polynomial regression coefficients, it was reduced with the orthogonal polynomial method. For ease of interpretation, the results are presented in the form of a polynomial equation in its usual form. The application of polynomials results both from their properties (any continuous function on a half-open interval can be approximated with any accuracy using polynomials) and the lack of assumption on the specific functional form of the relationship being studied. The relationship between mean monthly air temperature and the monthly number of freeze-thaw events has been described with polynomial functions as had been successfully done by Ho & Gough (2006) to study similar relationships in Toronto, Canada. In our research, we applied functions of degree two to six. To assess the fit of the polynomial regression, we used the adjusted R-squared and the information criteria: Akaike Information Criterion (AIC) (Akaike, 1974) and Bayesian Information Criterion (BIC) (Schwarz, 1978). Moreover, the statistical significance of the parameters of polynomial models was checked. The fitting of data and the significance of regression were checked with the t-test. For all the tests, p-values smaller than or equal to 0.05 were accepted as statistically significant.

The estimated polynomial model, based on data sets from 1951/52–2017/18, provided the foundation for sketching scenarios about the future number of FTDs at a specific change in mean air temperature.

Air temperature in the Stevenson screen vs. ground temperature on the cliff surface

The comparison of mean daily air temperatures at the three selected IMWM synoptic stations closest to the studied reservoir with the cliff surface temperature data for the period of the research in the 2014–2015 season shows a high level of similarity both in the trend and the recorded values (Fig. 2). On the other hand, the comparison of the number of FTDs determined on the basis of the maximum and minimum daily temperature on the cliff face and air temperature measurements at a height of 2 meters above ground level shows that out of 48 FTDs identified on the cliff, 30 to 39 FTDs were also recorded in Stevenson screens, i.e. 64–81% of those on the cliff (Fig. 2).

The notably higher number of FTDs recorded on the cliff face means that the surface layer of the ground experiences no fewer FTDs than is indicated by the air temperature measurements performed at the other stations concerned. The Kalisz-based readings display the highest level of similarity in trends and values to the results of the cliff surface temperature measurements. Additionally, each FTD identified on the basis of air temperature measurements in Kalisz was confirmed by the cliff face temperature check (Fig. 2).

Air temperature

Mean annual air temperature for the entire study period ranged from +8.1 °C to +8.5 °C (Table 2, Fig. 3A). The results obtained from the MK test and t-test indicate a statistically significant growing trend (Fig. 3A) with the rate of change amounting to +0.27 °C/10 years in Koło, +0.28 °C/10 years in Łódź and +0.33 °C/10 years in Kalisz. During the operation of the reservoir i.e. 1991/92–2017/18, the mean air temperature at all these stations, was higher by approx. 1 °C as compared to the preceding period (1951–1990) (Table 2).

Number of freeze-thaw days

Considering the study period, the mean annual number of days with a freeze-thaw action was similar in Koło and Kalisz i.e. 64.2 and 65.6, respectively. In Łódź, this figure was slightly higher and averaged 71.4 days (Table 2).

The annual totals of FTDs varied throughout the study period with a higher number recorded in the early years (Fig. 3B). The first nine of them, (1951/52-1959/60) saw a significant positive deviation from the average in the incidence of FTDs. On the other hand, the closing years (2006/07–2017/18), in the same respect, were marked by a negative deviation. The mean from the first period was 85 FTDs in Kalisz, 84 FTDs in Łódź and 79 FTDs in Koło. At the other end, in 2006/07–2017/18, the number of FTDs averaged 49 (Kalisz), 55 (Koło) and 63 (Łódź) which makes 57.6%, 69.6% and 75.0% of the initial period values respectively.

This variation is also made evident by comparing the periods before and after Jeziorsko reservoir was created. Initially, i.e. 1951–1990, the number of FTDs averaged 66–74, while in 1991–2018 it amounted to 58–68 (Table 2).

The change in the annual number of FTDs over the full period was significant at all the stations (Table 3), yet it was most pronounced in Kalisz (−4.2 days/10 years). In Łódź and Koło it was similar and amounted to −2.5 days/10 years and −2.1 days/10 years, respectively.

The distribution of the mean number of FTDs in the annual cycle (August–July) is similar for all the stations involved. One peak is visible in March (Fig. 4), which is the month accounting for 20–21% of the annual number of FTDs in 1951–2018.

In Kalisz and Łódź the number of FTDs in individual months considerably decreased in November, December and January. All the stations also indicated a significant drop in April when the rate of change equalled −0.5 days/10 years in Łódź and Koło and −0.8 days/10 years in Kalisz (Table 3).

Beginning, end and duration of time with FTDs

In 1951/52–2017/18, all the stations recorded the earliest FTDs in the second decade of September, and the latest in November. The days with the 0 °C transition ended the earliest in April (Łódź) and May (Koło and Kalisz), and the latest in May (Koło and Kalisz) or early June (Łódź) (Table 4).

The beginning and end dates of the FTDs changed significantly (Fig. 5, Table 5). Table 5 summarises the MK test and t-test p-value of the series of start and end dates of the occurrence of FTDs.

The beginning of the occurrence of FTDs was being pushed further at a rate of about −1.6 days/10 years in Koło. At the remaining stations, the mean rate of change is statistically insignificant (Table 5, Fig. 5A). On the other hand, the end of FTDs occurred sooner at a rate of approx. 3 days/10 years (Table 5, Fig. 5B).

The maximum duration of FTDs taking place was 240 days in Koło and Łodź and a similar 239 days in Kalisz. The corresponding minimum amounted to 132 days in Kalisz, 140 days in Koło and 156 days in Łódź (Fig. 5C). The change in the dates of the beginning and end of FTDs resulted in a natural consequence of narrowing down the time window in which they occurred.

Relationship between mean monthly temperature and the number of FTDs

Figure 6 depicts the relationship between mean monthly air temperature and the monthly number of FTDs, as well as two to six-degree polynomial functions describing such a relationship as exemplified by the weather station in Koło (Fig. 6).

The spread of the number of FTDs is not symmetrical. Higher values are characteristic of the months with the mean monthly air temperature in the positive rather than negative areas. As the monthly FTDs number increases, the range of the mean monthly air temperature decreases. FTDs were recorded in the following brackets of mean monthly air temperature: −11.2 °C to +15.4 °C (Kalisz), −11.6 °C to +15.4 °C (Koło), and −11.6 °C to +17.3 °C (Łódź).

The outer “fringes” of the temperature ranges gather the months with the lowest number of FTDs, i.e. 1–4 in a month, which tend to be the early autumn ones, i.e. September, October and November, as well as the early spring months like April and May. This observation is true for all the weather stations involved in the study (e.g. Kalisz, Fig. 6A).

The highest monthly numbers of FTDs occur at the mean monthly air temperature oscillating around 0 °C. The highest monthly FTDs number of 24 was recorded in Łódź at the mean monthly temperature of −0.1 °C. In Kalisz and Koło, this figure counted 23 at the mean monthly temperature of +0.3 °C and 22 at −1.8 °C, respectively.

The results of polynomial fitting for the studied stations proved the 5-degree polynomial to most adequately describe the relationship between the mean air temperature and the monthly number of FTDs (Table 6). At the same time, it must be noted that the parameter of the six-degree polynomial function at the highest power was statistically insignificant at all the weather stations. Table 7 presents the polynomial equations applied to describe the relationship.

Projection of the change in the number of FTDs

Projections of changes in the annual number of FTDs have been presented for specific climate change scenarios according to all six polynomial models considered (Fig. 7). Calculations for each polynomial were performed in the range of mean monthly temperatures at which there were days with a freeze-thaw event. The X axis (Adjusted Mean Temperature) presents the temperature shifted by a given number of degrees and the Y axis presents corresponding projected number of FTD for given changes in temperatures. For example, the value of +1.0 °C means that in each month of the analysed period we adjusted the temperature by +1.0 °C, and for given data we calculated the corresponding projection on the number of FTDs. The value of 0 in Fig. 7 means that the mean air temperature in the model corresponds to the mean annual temperature from the 1951/52–2017/18 real data for each analysed station. Thus, the number of FTDs resulting from the model corresponds to or is close to the actual number of FTDs from the same period.

Table 8 presents mean annual numbers of FTDs recorded at the analysed stations as calculated in the period 1951/52–2017/18, as well as mean numbers of FTDs calculated with two to six-degree polynomials. Using the prepared five-degree polynomial model we calculated the annual number of days with a freeze-thaw event for the above scenario. The same procedure was repeated until the annual number of days with 0 °C transition reached the value of zero.

Changes in air temperature and the number of FTDs

The information and data published in IPCC or WMO (2019) reports indicate changes in the global air temperature. The special IPCC Global Warming of 1.5 °C report (IPCC, 2018) informs that the mean global air temperature in the period 2006–2015 increased by 0.87 °C compared to 1850–1900 (pre-industrial period). However, the temperature growth varies geographically.

Poland (Central Europe) is in the transition zone of temperate climate, where cool continental air masses flowing in from the east clash with considerably milder maritime air masses from the west and northwest. The mean annual area air temperature in Poland in 1951–2008 was 7.9 °C (7.6 °C in the eastern part and 8.2 °C in the western one) (Limanówka et al., 2012).

Marosz et al. (2011) reported that the mean annual temperature in Poland (Central Europe) in 1951–2008 exhibited a statistically significant growing trend with the step of growth of +0.24 °C/10 years.

Mean annual (August–July) air temperature in the period 1951/52–2017/18 at all the analysed stations in the vicinity of Jeziorsko reservoir demonstrated statistically significant, positive changes of about +0.3 °C/10 years. This increase has consequently narrowed the time window for the occurrence of days with freeze-thaw activity. They began later, and the end occurred sooner, by 1.5–2.2 and 2.6–3.3 days, respectively. Also, the number of days with freeze-thaw events had been decreasing for many years by a maximum of 4.2 days/10 years in Kalisz (Fig. 3B). The shortening of the period of the occurrence of negative air temperatures, mainly as a result of earlier spring warming and later autumn cooling in the central and western parts of Poland, are also reported by Wypych et al. (2017) based on the analysis of data from 1951–2010. Graczyk & Szwed (2020) arrived at very similar conclusions following their analysis of the recent spring frost trends. By examining the series of minimum air temperatures at a height of 2.0 m and at the ground surface (0.05 m) in the period 1961–2020, e.g. for the Kalisz station, from which we also used the data in our research, they found that regardless of the height, a clear and statistically significant trend indicating the earlier occurrence of the last spring frost existed, with the average rate of the process ranging from 1.6 to about 3.5 days per decade.

The number of days with freeze-thaw events in the annual cycle varies significantly depending on the latitude. Wexler (1982, 1984) explained how the number of FTDs changes in particular months of the annual cycle as the latitude increases. At stations located in polar areas (extremely cold), FTDs were recorded exclusively in the summer season while those in medium latitudes with a continental climate indicated a bimodal annual distribution of FTDs with two peaks in October/November and in April. Stations at medium latitudes in the transitional climate zone recorded a high number of FTDs from November to March, with the maximum in February. At low-latitude stations (deserts and highlands), there was one peak in January. The distribution of the mean monthly number of FTDs in the annual cycle at the stations included in our study complies with the regularity observed by Wexler (1982). At the studied stations in central Poland, the largest number of FTDs occurred in the months from November to March with one culmination in March.

The relationship between mean monthly air temperature and the number of freeze-thaw events was also described by Wexler (1982, 1984) with the use of a two-parameter sine function. Schmidlin, Dethier & Eggleston (1987) and later Baker & Ruschy (1995) described the same relationship with a two-degree polynomial. Subsequently, Ho & Gough (2006) described it using two and six-degree polynomial functions. Our analyses involved the application of polynomials of the two to six-degree looking for the best fit. The obtained results of the information criteria AIC and BIC indicate that for the area of our research the analysed relationship is best represented by the five-degree polynomial function (Table 6).

Both the number and the decline in FTDs around Jeziorsko reservoir within the studied period were uneven. When the reservoir was in operation the rate of decrease in freeze-thaw processes accelerated nearly twice the rate compared to the whole study period, i.e. 195–2018 (Fig. 2B).

Freeze-thaw processes as a factor intensifying cliff retreat

Frost weathering related to freeze-thaw cycles resulting from temperature fluctuations below and above 0 °C is one of the subaerial geomorphological processes influencing the rate of cliff retreat on the areas experiencing sub-zero temperatures. It causes frost-vulnerable silt and clay sediments on vertical or nearly vertical cliff faces to exfoliate and fall off exposing another layer of sediments to frost processes. Consequently, the frost front progresses into the sediments and the rate of the cliff retreat increases (Bernatchez, Jolivet & Corriveau, 2011; Day et al., 2013; Boucher-Brossard et al., 2017). This process can amount to up to 20–90% of the total annual lake or river cliff retreat being the joint effect of wave erosion and other subaerial geomorphological processes e.g. weathering by drying or linear erosion (Reid, 1985; Reid, Sandberg & Millsop, 1988; Gatto, 1995; Egorov & Gleizer, 2012). For Jeziorsko reservoir, this value was estimated at 20% based on the volume of sediments accumulated at the cliff toe. At the same time, the share of retreat resulting from frost processes in relation to that triggered by all the subaerial geomorphological processes at the studied cliff amounted to 70% (Kaczmarek et al., 2019). The vertical face, western exposition and the lack of the protective or insulating vegetation or snow cover on the studied cliff on Jeziorsko reservoir, along with the sediment lithology, greatly promote the efficiency of freeze-thaw processes (Isard & Schaetzl, 1998; Zhang, 2005; Wojkowski & Skowera, 2017). The influence of solar radiation on the ground, western exposure of the studied cliff, which on the northern hemisphere means more freeze-thaw cycles than is the case with eastern and northern exposures (Hall, 2004), as well as a large angle of the cliff face resulting in a greater angle of incidence of solar radiation bring about a higher number of FTDs on Jeziorsko reservoir cliff than that identified on the basis of air temperature measurements (Fig. 3). In such conditions at similar levels of moisture of the sediments subjected to freeze-thaw processes, the efficiency of each cycle is comparable, which means that greater numbers of freeze–thaw cycles may lead to greater erosion rates as they reduce cliff strength (Wynn & Mostaghimi, 2006; Thomas, Iverson & Burkart, 2009; Van Klaveren & McCool, 2010). Research has shown that in particular conditions, a single freeze-thaw cycle can reduce the soil shear strength by up to 50% (Formanek, McCool & Papendick, 1984; Van Klaveren, 1987; after Gatto, 1995). At the above assumptions, each subsequent FTD is directly translated into increased cliff face retreat, and vice versa a lower number of FTDs means slowing down of this process. It must be stressed, however, that the area where the reservoir is located experienced some of the lowest annual totals of FTDs in Poland in 1951–2018 (Kaczmarek et al., 2021). Moreover, during that period, their number decreased by a further 2–4 FTDs/10 years (Fig. 3B).

Projected changes in the number of FTDs in the vicinity of Jeziorsko reservoir

Piniewski, Okruszko & Kundzewicz (2020) presented projections of changes in seasonal and annual air temperature for the area of Poland for the years 2021–2050 and 2071–2100 in relation to the reference period 1971–2000. A high (RCP8.5) and an intermediate (RCP4.5) scenario were used (Van Vuuren et al., 2011). Assuming the intermediate one (RCP4.5), the mean annual temperature in Poland will increase by +1.1 °C in the 2021–2050 horizon and +2.0 °C in 2071–2100. Assuming the high scenario (RCP8.5), the mean annual temperature in Poland will go up by +1.3 °C in 2021–2050 and by an annual average of +3.6 °C in 2071–2100.

These anticipated changes in air temperature in central Poland will be systematically reducing the number of FTDs, leading to a decline in the role of geomorphological processes related to freezing and thawing of the surface soil layer in modelling slopes with high inclination, in particular, vertical or almost vertical walls. Consequently, other subaerial processes e.g. weathering by drying or linear erosion, despite their similar efficiency, will start to play a greater role in the cliff transformation. At the same time, the rate of cliff retreat caused by all the subaerial processes will diminish. Still, though, this will be a slow process. With a mean yearly temperature increase of +1.1 °C, which for the RCP4.5 scenario for the area of Poland is predicted for 2021–2050 (Piniewski, Okruszko & Kundzewicz, 2020), the number of mean annual FTDs in the vicinity of Jeziorsko reservoir will drop by 6–7% in relation to 1951–2018. When the mean yearly temperature increases by +2.0 °C, as predicted for 2071–2100, the decline will reach 13–15% (Fig. 7). The RCP8.5 scenario suggests a slightly greater decline in mean annual FTDs. At the temperature increase of +1.3 °C i +3.6 °C projected for 2021–2050 and 2071–2100 (Piniewski, Okruszko & Kundzewicz, 2020) the number of FTDs will decrease by 8–9% and 25–29% respectively. Only with an increase in the mean yearly air temperature by more than +15 °C compared to the currently recorded values, could a complete disappearance of FTDs in this area be expected (Fig. 7).

In terms of the number of recorded FTDs, the whole studied period (1951–2018) could be divided into two subperiods: 1951/52–1990/91 and 1991/92–2017/18 i.e. when the reservoir was in operation. It is the former one which is characterised by a markedly higher number of FTDs (Table 2).