Layout 1 INTRODUCTION Ice cover in lakes has a significant impact on various air-water exchange processes. It reduces the sunlight pen- etration into water, which is necessary for photosynthesis; it also hinders heat transmission and water oxygenation. Ice conditions on lakes determine the duration of naviga- tion period as well as the possibility of transporting people and/or cargoes over the stable ice (Karetnikov and Nau- menko, 2008; Salo and Nazarova, 2011; Assel et al., 2004). The data on ice regime characteristics is applicable to climate models and can be used to predict the periods of freeze-up and break-up phases of lakes (Salo and Nazarova, 2011; Baklagin, 2017). The formation and break-up of ice cover on large lakes depend greatly on the complex of meteorological processes, which occur over the water area of lakes (Salo and Nazarova, 2011; Dibike et al., 2011); therefore, research related to the influence of climate factors on long-term variability of ice regime of lakes is of high interest. Reduction of ice phenomena duration due to global warming observed over the past few decades is the main tendency in the long-term variability of ice regime of large lakes (Brown and Duguay, 2010; Latifovic and Pouliot, 2007; Efremova et al., 2013; Magnuson et al., 1990). Ac- cording to Livingstone (1997), the ice of large lakes serves as a sensitive indicator of climate change that is even more reliable than air temperature. With the water surface area of 9720 km2, Lake Onego is one of the biggest lakes in Europe. Identifying the pat- terns of ice regime formation of Lake Onego is of great importance for issues connected with organizing water transport between such settlements as Petrozavodsk, Med- vezhyegorsk, Kondopoga, Povenets, Vytegra, Vozne- senye, as well as on White Sea-Baltic Canal and Volga-Baltic Canal (Salo and Nazarova, 2011). Long-term variability of ice regime of large lakes on the territory of the Republic of Karelia, including Lake Onego, has been described by Efremova et al. (2013). The authors observed that during the years 1950-2009, the duration of ice phenomena on Lake Onego reduced by more than 20 days. Identified variability patterns of air temperature influence on the formation and break-up of ice cover show that for Lake Onego, in particular, freeze-up dates are most accurately indicated by Novem- ber-December average air temperature, and break-up dates by that of April-May. Furthermore, a ±1°C fluctu- ation of average air temperature leads to a ±4-6 days shift of the freeze-up dates and a ±3-4 days shift of the break-up dates (Efremova et al., 2013). It is important to note that these results were derived from visual ice cover data at the observation stations of the Russian me- teorological service and that they are relevant for small lakes, which can visually inspected by the observers. In case of Lake Onego, the observation is focused on the ice cover condition of Petrozavodsk Bay. Its surface area is less than 2% of the total surface area of Lake Onego, which is not sufficient for estimating the indicative pe- riods of the ice regime. Long-term variability of the ice regime on Lake Onego was described by Salo and Nazarova (2011) based on air observations of ice for the period of 1955-1990 per- formed by air research office of the North-West, the Fed- eral Service for Hydrometeorology and Environmental Monitoring. Based on the data, the correlation between indicative periods, the duration of ice phenomena, air tem- perature (Weather station Petrozavodsk), and NAO (Northern Atlantic Oscillation) index was traced. It is worth noting that the data obtained from ice sur- face mapping of Lake Onego used in the study (Salo and Nazarova, 2011) lacks sufficient time interval for proper evaluation of indicative dates of ice regime and the analysis of chronological ice coverage progress (5- 10 air observations within the period of ice formation). ARTICLE Variations of indicative dates of ice regime on Lake Onego based on ground air temperature Vyacheslav N. Baklagin Northern Water Problems Institute, Karelian Research Centre, Russian Academy of Sciences, Aleksander Nevsky st. 50, 185030 Petrozavodsk, Republic of Karelia, Russia ABSTRACT The paper shows the changes in the dates (complete freeze-up, ±5 days/°C and complete ice clearance, ±3 days/°C) of the ice regime in Lake Onego depending on changes in average air temperature within the preceding two-month periods (autumn and spring). The regression equations for their calculation based on previous three- and four-month periods according to the 2000- 2018 data are also provided. Indicative dates of ice regime based on accumulated air temperatures within the ice period of Lake Onego were also established (early formation of ice phenomena, complete freeze-up phase, beginning of the break-up phase and complete ice clearance). Together with the data on expected air temperature above the lake’s surface, these dependencies enable us to predict the indicative dates of the ice regime. No n- co mm er cia l u se on ly Variations of indicative dates of ice regime on Lake Onego based on ground air temperature 25 The maximum alternation rate of ice coverage of Lake Onego per 24 hours for the years 2000-2018 is 62.5% (registered by MODIS sensor, from 8th to 9th January, 2016). More reliable information on the ice cover of lakes is obtained from satellite observations (Karetnikov and Naumenko, 2008; Assel et al., 2004; Baklagin, 2018). For the last few years, daily satellite surveys of the Earth using various ranges (visual, infrared, microwave), have collected large amounts of data including the data about snow and ice cover of the planet. For this reason, it is necessary to update previous studies (Salo and Nazarova, 2011; Efremova et al., 2013) based on present satellite data and to confirm previously identified corre- lations. Besides that, we need to analyze the potential influence of temperature conditions and some other me- teorological factors (such as wind and snow cover depth) on ice cover formation and break-up on Lake Onego, since these issues have not been fully described in the available studies. The purpose of this study is to identify statistical cor- relations between meteorological parameters and the ice regime characteristics of Lake Onego calculated on the basis of satellite data within the years 2000-2018. METHODS Identification of the ice regime in Lake Onego Given the possible quick changes in areas of ice phe- nomena on Lake Onego (up to 63% per 24 hours), the ice regime characteristics of Lake Onego for the years 2000- 2018 were calculated on the basis of daily time series of ice coverage obtained from satellite observations. In this study we used satellite data provided by National Aero- nautics and Space Administration, USA, NASA (device MODIS – The Moderate Resolution Imaging Spectrora- diometer, with a spatial resolution of 250 m), National Snow and Ice Data Center, NSIDC (4-6 km), Center for Satellite Applications and Research, NOAA NESDIS (4- 6 km). The technique described by Bakalgin (2018) was used to develop daily time series of ice cover of Lake Onego on the basis of these data series with minimizing faulty proportion while identifying ice cover (Fig. 1). For the purposes of comprehensive assessment of the change of ice cover during the period of ice phenomena, sums of daily values of ice coverage for each period of ice phenomena were calculated using the formula: ∑ice=∑n(k=1)icek , where icek is ice coverage value (ice cov- Fig. 1. Dates of the beginning and the ending of phases and the duration (number of days) of ice freezing (1), complete freeze-up (2) and break-up (3) on Lake Onego for the period 2000-2018. No n- co mm er cia l u se on ly V.N. Baklagin26 erage is defined as the ratio of the ice cover area to the total lake area) in k-day of the period of ice phenomena, n –duration of the period of ice phenomena. Values ∑ice and RICI, i.e. the calculation technique that was used to estimate the ice regime of Lake Ladoga (Karetnikov and Naumenko, 2008) are similar, since values RICI for each year were obtained by normalizing of value ∑ice to mean value ∑̅̅i̅c̅e̅ for multiyear period. However, in this study there is no need in normalizing values ∑ice for identifi- cation of statistical correlation. Estimation of meteorological conditions above Lake Onego In this study we used daily data of mean air tempera- ture, precipitation, and snow-cover depth for the years 2000-2017 from meteorological observation points near Petrozavodsk and Vytegra provided by All-Russia Re- search Institute of Hydrometeorological Information - World Data Centre (RIHMI-WDC) (http://meteo.ru). Data on daily mean air temperature and wind speed for the years 2000-2018 from meteorological observation points near Petrozavodsk, Medvezhyegorsk, Vytegra, and Pu- dozh were provided by National Oceanic and Atmos- pheric Administration, USA, NOAA (NCDC NOAA) (ftp://ftp.ncdc.noaa.gov/pub/data/noaa/). Meteorological conditions above Lake Onego were estimated by averaging of parameters measured at four observation points around the lake (Fig. 2): near Petroza- vodsk (22820), Medvezhyegorsk (22721), Vytegra (22837), and Pudozh (22831) (with index of the World Meteorological Organization, WMO). Several observa- tion points for estimating meteorological parameters were chosen to cover the variability of climatic conditions caused by the large dimensions of Lake Onego (from north to south, 248 km; from west to east, 96 km). For in- stance, the average air temperature according to RIHMI- WDC and NCDC NOAA for the period of 2000-2017 at Medvezhyegorsk is 3.11°С, in Petrozavodsk -3.89°С, and in Vytegra -4.06°С. The dates of the beginning and end of the periods of accumulated positive temperatures ∑T+ and negative tem- peratures ∑T– were derived from the condition: ∑tt 21 |Tt |→max, where t1, t2 are the dates of beginning and end of the periods during the current hydrological year, Tt is the average air temperature for the date t. Method of determining the indicative dates of ice regime based on accumulated air temperatures This study assumes that accumulated negative air tem- peratures over the lake required for beginning ice phe- nomena formation ∑Tfreezing and the complete freeze-up on the lake ∑Tice, probably depend on thermal reserve of the lake before the beginning of the cold season in question. This thermal reserve of the lake depends on accumulated positive air temperatures ∑T+ of previous warm season. Moreover, accumulated negative air temperatures over the lake required for the beginning break-up ∑Tbreaking and the complete ice clearance on the lake ∑Tfree, depend on ac- cumulated negative air temperatures ∑T– of previous cold season. In the study, regression analysis was used to de- termine the dependencies of the accumulated air temper- atures required for changing the phases of ice regime (indicative date) on accumulated air temperatures of pre- vious period, i.e. the accumulated air temperatures re- quired for changing the phases of ice regime (indicative date) is function from accumulated air temperatures of previous period ∑Tind date (∑T). We can calculate the in- dicative date of the ice regime dateind based on a forecast of air temperatures for a period (for example, a week) and the calculated value ∑Tind date (∑Tfreezing, ∑Tice, ∑Tbreaking, ∑Tfree). The indicative date of ice regime is determinate: Fig. 2. The location of meteorological observation points on the coast of Lake Onego. No n- co mm er cia l u se on ly Variations of indicative dates of ice regime on Lake Onego based on ground air temperature 27 dateind = datecur + x (eq. 1) where datecur is the current date; x is the duration of the period from current date to the indicative date of the ice regime (days). Value x can be determined based on the condition: ∑Tind date ≈∑Tcur date +∑xj =1 Tj, (eq. 2) where ∑Tcur date) is the accumulated air temperatures for period from the date of air temperature transition over 0°С to current date (°С); j is the counting number of days from current date; Tj is the daily predicted air temperature of jth days (°С). The method of calculation resides in searching the value x where eq. 2 will be true. RESULTS For the analyzed range of years 2000-2018, the dura- tion of ice phenomena period varied from 132 to 203 days with the average value of 171 days (from November to May), coefficient of variation is 10%, complete freeze-up period - from 11 to 137 days, with the average value of 90 days, coefficient of variation is 36%. Statistical characteristics of accumulated positive and negative air temperatures over Lake Onego are repre- sented on Fig. 3. For the years 2000-2018, the accumu- lated sums of positive air temperatures over the Lake Onego ∑T+max ranged from 1932°С to 2527°С, absolute values of negative air temperatures ∑T– max from 553°С to 1520°С. It is noteworthy that the average daily air tem- perature over Lake Onego in the years 2000-2018 was 0.9°С higher than in 1936-1999 (data provided by RIHMI-WDC) (Tab. 1). In addition, this increase in the average air temperature was mainly caused by frequent warm winters over the last years. Over the years 2000- 2018, the cold seasons differed from one another in terms of temperature conditions more considerably (variation coefficient of ∑T– max 32%) than the warm seasons (vari- ation coefficient of ∑T+max 7%). According to the calculations for the years 2000-2018, the dates of air temperature transition over 0°С to negative values over Lake Onego were within the range from 14th October to 25th November, and to positive values - from 4th March to 21st April. The average period with positive air temperatures (warm season) lasted 220 days, and with negative air temperatures (cold season) 144 days. Correlation analysis showed, that the following val- ues: ∑ice, the duration of freeze-up D (days) and the total period of ice phenomena L (days) on the Lake Onego have close correlation (L to a lesser extent) with annual average air temperature over the lake T̅ (paired correlation coeffi- Fig. 3. Integral curves of positive (a) and negative (b) air temperatures over Lake Onego with the range of sample for the period 2000-2018. Tab. 1. Temperature conditions over Lake Onego at different time periods. Period Average air temperature (°С) Difference (°С) 1936-1999 2000-2018 Year 2.7 3.6 0.9 Warm season 9.6 10.4 0.8 Cold season –8.2 –6.8 1.4 No n- co mm er cia l u se on ly V.N. Baklagin28 cients -0.89, -0.83 and -0.50, respectively). The regression analysis revealed polynomial relationships of ∑ice and D with annual average air temperature over the lake T̅ : ∑ice= –0,548 ∙ T̅ 2–17,566 ∙ T̅ +188,649 (R2=0.8; P<0.05) (eq. 3) D= –3,894 ∙ T̅ 2–3,782 ∙ T̅ +157,531 (R2=0.7; P<0.05) (eq. 4) Updating air temperature – ice regime relationships The starting date of ice phenomena formation on Lake Onego was calculated by multiple regression from monthly average air temperatures: Dfreezing= 0,249 ∙ T̅XII2 – 0,061 ∙ T̅XI2 – 0,444 ∙ T̅X2 + 4,253 ∙ T̅IX2 + 3,579 ∙ T̅XII + 1,974 ∙ T̅XI + 4,122 ∙ T̅X – 79,643 ∙ T̅IX + 422,458 (R2=0.81; P<0.05) (eq. 5) where Dfreezing is the duration of the period from 1st October to the beginning of ice phenomena formation, (days); T̅i is the average air temperature of ith month over the lake in °С. Strong correlation (r= 0.76; P<0.05) was also identi- fied between the average air temperature for a two-month period - from November to December T̅XI-XII and the dates of ice complete freeze-up on the lake for 2000-2018. The dependency of changing of these dates from the value T̅XI-XII was obtained (Fig. 4). The slope factors of dependences are coherent with the results of a similar study on the ice regime of Lake Onego for the period of 1950-2009 (Efremova et al., 2013) (Tab. 2). The average air temperature over the lake from December to January (T̅XII-I) had the strongest correlation (r=0.88; P<0.05) with the ice complete freeze-up on Lake Onego for the period of 2000-2018. (Tab. 2). However, values T̅XI-XII were used to define relationships in the study by Efremova et al. (2013). Considering air temperatures of a 4-month period (Oc- tober-January) instead of a 3-month period (October-De- Fig. 4. Dependences of indicative dates of ice regime on Lake Onego on air temperature for the years 2000-2018, where a) dates of complete freeze-up depending on the average air temperature for period from November to December; b) dates of complete freeze-up depending on the average air temperature for period from December to January; c) dates of complete ice clearance depending on the average air temperature for period from April to May; d) dates of complete ice clearance depending on the average air temperature for April. 1, actual values; 2 linearly regression function. No n- co mm er cia l u se on ly Variations of indicative dates of ice regime on Lake Onego based on ground air temperature 29 cember) as used by Salo and Nazarova (2011) for estimat- ing the complete freeze-up on Lake Onego for 1955-1990, as well as applying the polynomial multiple regression helped to improve the explanatory power of the regression model (R2 rose from 0.74 to 0.89): Dice=0,380 ∙ T̅I2+ 0,073 ∙ T̅XII2 + 0,267 ∙ T̅XI2 + 0,692 ∙ T̅X2 + 10,295 ∙ T̅ I + 3,466 ∙ T̅XII + 2,109 ∙ T̅XI – 3,881 ∙ T̅X + 187,491 (R2=0.89; P<0.05) (eq. 6) where Dice is the duration of the period from 1st October to the beginning of complete freeze-up phase, days. The beginning of ice cover break-up could be deter- mined by air temperature from January to March: Dbreak = –0,089 ∙ T̅III2 – 0,385 ∙ T̅II2 – 0,130 ∙ T̅I2 – 2,344 ∙ T̅III – 8,701 ∙ T̅II – 4,412 ∙ T̅I – 27,842 (R2=0.63; P<0.05) (eq. 7) where Dbreak is the duration of the period, starting with 1st of March, until the beginning of ice cover break-up, days. A lower negative correlation (r=-0.52; P<0.05) was found between the dates of the complete ice clearance on Lake Onego and the April-May average air tempera- ture T̅IV-V. Considering April air temperatures only slightly strengthened the correlation (Tab. 2). The best multiple regression model for estimating the dates of complete ice clearance included air temperatures from March to May: Dfree = 0,328 ∙ T̅V2 – 0,096 ∙ T̅IV2 – 0,126 ∙ T̅III2 – 6,910 ∙ T̅V – 2,925∙ T̅IV – 2,370 ∙ T̅ III + 79,620, (R2=0.71; P<0.05) (eq. 8) where Dfree is the duration (in days) of the period from 1st April to complete ice clearance. Averages of the absolute deviations of the calculated values from the actual values were as follows: determin- ing the date of the beginning of the ice formation: 3-4 days; determining the date of freeze-up phase: 4-5 days; determining the date of the beginning break-up phase: 2- 3 days; determining the date of complete ice clearance on the lake: 7-8 days (Fig. 5). The effect of the accumulated positive and negative air temperatures on ice regime The values ∑Tice, ∑Tfree for the years 2000-2018 showed a wide variation (Tab. 3). No correlation was de- tected between ∑Tice and ∑T+max (r = –0.01). ∑Tice and ∑Tfreezing had strongest correlations (corre- spondingly, r = 0.70; P<0.05 and r = -0.57; P<0.05) with the accumulated positive air temperatures for the last 55 days of the warm season (before the transition to negative values), ∑T55. On the basis of regression analysis, equations were ob- tained connecting ∑Tfreezing and ∑T55, and ∑Tice and ∑T55 for Lake Onego: ∑Tfreezing = 7,195 ∙ 10–5 ∙ ∑T552 – 0,092 ∙ ∑T55 – 7,768. (R2=0.33; P<0.05) (eq. 9) ∑Tice = 1,1311 ∙ 10–3 ∙ ∑T552 – 1,218 ∙ ∑T55 – 116,855. (R2=0.53; P<0.05) (eq. 10) The analysis connecting ∑T– max and ∑Tfree , ∑T– max and ∑T–break showed a close statistical correlation (by the Cheddok scale), with pair correlation coefficient between ∑T– max and ∑Tfree and ∑T– max and ∑T–break equal to -0,75 and -0,78, respectively. Regression analysis connecting ∑T– max and ∑T–break , and ∑T– max and ∑Tfree showed the following results: ∑T–break = – 4,8389 ∙ 10–7 ∑T– max3 – 0,0016 ∙ ∑T– max2 – 1,6623 ∙ ∑T– max – 527,852 (R2=0.72; P <0.05) (eq. 11) ∑Tfree = – 1,9775 ∙ 10–7 ∙∑T– max3 – 0,0008 ∙ ∑T– max2 – 1,1202 ∙ ∑T– max – 268,835 (R2=0.66; P<0.05) (eq. 12) The mean values of the absolute deviations of accu- mulated air temperatures from the actual values were as Tab. 2. Changes in indicative dates of the ice regime (complete freeze-up and complete ice clearance dates) on Lake Onego per ± 1°C change in average air temperature in different periods. Period Pair correlation coefficient Date changes per ± 1°C change in mean air temperature, days 1950-2009 2000-2018 November-December 0.76 ±4-6 ±5 December-January 0.88 - ±5 April-May -0.52 ±3-4 ±3 April -0.59 - ±3 No n- co mm er cia l u se on ly V.N. Baklagin30 follows: 5-6°C at the beginning of the period of formation of ice phenomena; –38-39°C at the time of complete freeze-up; 12-13°C at the beginning of the period of ice break-up; –27-28°С at the moment of complete ice clear- ance of the lake from ice. DISCUSSION Calculation results of average durations of warm and cold seasons corresponds to the results of the research (Nazarova, 2013). It is important to note that the average duration of ice phenomena period of Lake Onego (171 days) is longer than the period of negative air tempera- tures over the lake. Prediction of indicative dates of the ice regime of Lake Onego using the regression equations (5)-(8) for calcula- tions Dfreezing, Dice, Dbreak, and Dfree is not justified because, in most cases, the predicted date precedes the periods used as input data for which average air temperatures are cal- culated. For example, the average statistical date for the complete freeze-up phase on Lake Onego over the period 2000-2018 is January 16th, but in some years the complete Fig. 5. Actual (1) and predicted on the basis of the provided regression models (2) indicative dates of the beginning of the ice phenomena formation (a); complete freeze-up phase (b); beginning of ice cover break-up (c); and complete clearing of ice (d) on Lake Onego for the period 2000-2018. Tab. 3. Accumulated air temperatures over the water area of Lake Onega within the indicative dates of the ice regime for different time periods. Data for 1955-1990 are from the study by Salo and Nazarova (2011). Values Periods 1955-1990 2000-2018 Accumulated air temperatures over the waters of Lake Onego At the beginning of the formation of ice cover ∑Tfreezing (°С) - –43 - –15 At the complete freeze-up phase ∑Tice (°С) –490 - –290 –500 - –275 At the beginning of break-up phase ∑Tbreak (°C) - 0-115 At the moment of complete ice clearance on the lake ∑Tfree (°C) 200-310 87-294 No n- co mm er cia l u se on ly Variations of indicative dates of ice regime on Lake Onego based on ground air temperature 31 freeze-up phase occurred in mid-late December (Fig. 1), while the equation for calculating the Dice value includes the average value of January air temperatures, which ob- viously do not affect the Dice value. The strong correlation (0.88) in this case can probably be explained by the re- verse effect of the ice cover on the air temperature over its surface. The calculated intervals of the values ∑Tice , ∑Tfree for the period of 2000-2018 were consistent with the results by Salo and Nazarova (2011) (Tab. 3). Probably strong correlations between ∑Tice with ∑T55 and ∑Tfreezing with ∑T55 is caused by the fact that high positive air tempera- tures over Lake Onego in autumn (on the average during the period 2000-2018 September-October) inhibit water cooling in the lake, keeping the heat accumulated during the summer. Therefore, the bigger value of accumulated negative air temperatures ∑T– is required for further drop of the water surface temperature to 0°С and for ice for- mation. The described phenomenon can occur in autumn in case of a sudden winter which is followed by transition from moderate positive temperatures (5-10°С) to negative ones, omitting small positive temperatures (0-5°С). The obtained equations for calculating ∑Tfreezing, ∑Tice, ∑T–break, ∑Tfree taking into account data on expected air temperature, can potentially be used to predict the indica- tive dates of the ice regime of Lake Onego. It should also be noted that this study notes a shift in the period affecting the date of formation of ice cover of Lake Onego for the years 2000-2018, a month ahead com- paring with the periods in question (Efremova et al., 2013; Salo and Nazarova, 2011) (three months and two months, respectively). Perhaps this phenomenon is associated with the late dates of the freeze-up phase on Lake Onego in 2000-2018 (on average - January 16th) than in previous years, as a result of this tendency towards a reduction in duration of the period of ice phenomena on large lakes due to global warming (Brown and Duguay, 2010; Lati- fovic and Pouliot, 2007; Efremova et al., 2013, Magnuson et al., 1990). In addition, as already noted, calculations of the characteristics of the ice regime of Lake Onego in this paper (Efremova et al., 2013) were made on the basis of observations of the condition of the ice cover of the Petrozavodsk Bay, which due to its morphological struc- ture is covered with ice much earlier than the water area of the lake as a whole. Moreover, significant differences in the values of the lower limit of the interval of value ∑Tfree (Tab. 3) is due to the presence of abnormally low ∑T+ values in 2013 and 2014, when a complete ice clear- ance of Lake Onego was recorded (∑Tfree, respectively, 87°C and 92°C). In these years, abnormally warm winters preceded the break-up phase - the accumulated negative air temperatures during the cold season ∑T– max had mini- mum values for the years 2000-2018 (about 555°C), with an average value of -970°C over this period. CONCLUSIONS The dependences of the indicative dates of the ice regime of Lake Onego on air temperature are generally consistent with the results obtained earlier in (Efremova et al., 2013; Salo and Nazarova, 2011). However, in 2000- 2018 there was one-month ahead shift in the period af- fecting the date of the formation of ice cover in comparison with the second half of the 20th century, con- sidered in the studies by Efremova et al. (2013) and Salo and Nazarova, 2011). This indicates climate change in re- cent decades, which contributes to the late winter onset and, as a consequence the shift in the freeze-up dates, which is consistent with the concept of global warming. Therefore, it can be concluded that the models of the for- mation of the ice cover of Lake Onego presented in papers (Efremova et al., 2013; Salo and Nazarova, 2011) require some adjustment to be applicable nowadays. The equations for calculating the indicative dates of the ice regime (5)-(8) are hardly applicable for forecast- ing, but can be used for diagnostic purposes, for example, to re-design the long-term time series of the characteristics of the ice regime of Lake Onega based on the available daily data on air temperature. This is particularly true for the first half of the 20th century, when there are only frag- mentary data on the condition of the ice cover of the Petrozavodsk Bay of Lake Onego and rare air observa- tions due to the lack of appropriate technical means (satel- lite observations). The indicative dates of the ice regime of Lake Onego are potentially predictable on the basis of the equations derived in the paper. This may be of practi- cal use in planning the navigation period and the organi- zation of waterways. ACKNOWLEDGMENTS The study was fulfilled with the financial support of the Grant of the President of the Russian Federation MK- 3379.2018.5. 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Received: 2 April 2019. Accepted: 14 June 2019. This work is licensed under a Creative Commons Attribution Non- Commercial 4.0 License (CC BY-NC 4.0). ©Copyright: the Author(s), 2019 Licensee PAGEPress, Italy Advances in Oceanography and Limnology, 2019; 10:8198 DOI: 10.4081/aiol.2019.8198 No n- co mm er cia l u se on ly