THERMAL AND ICE PROCESSES IN LADOGA LAKE AT POSSIBLE CLIMATE CHANGES (ON THE SIMULATION RESULTS) (28-34)

28 Национальная ассоциация ученых (НАУ) # 59, 20 20
ФИ ЗИКО -МАТЕМАТИЧЕСКИЕ НАУКИ

ТЕРМИЧЕСКИЙ И ЛЕДОВЫЙ РЕЖИМЫ ЛАДОЖСКОГО ОЗЕРА В УСЛОВИЯХ
ВОЗМОЖНЫХ КЛИМАТИЧЕСКИХ ИЗМЕНЕНИЙ
(ПО РЕЗУЛЬТАТАМ МОДЕЛИРОВАНИЯ)

Зверев Илья Сергеевич 1
канд. физ. -мат. наук, научный сотрудник
Шипунова Екатерина Александровна 1
младший н аучный сотрудник
Голосов Сергей Дмитриевич 1
канд. физ. -мат. наук, старший научный сотрудник 1Санкт -Петербургский Федеральный научно -исследовательский центр
Российской академии наук, Институт озероведения
Российской академии наук (ИНОЗ РАН – СПбФИЦ РАН)
г. Санкт -Петербург , Российская Федерация

THERMAL AND ICE PROCESSES IN LADOGA LAKE AT POSSIBLE CLIMATE CHANGES
(ON THE SIMULATION RESULTS)

Zverev Ilia Sergeevich 1
Candidate of Science, research scientist
Shipunova Ekaterina Alexandrovna 1
Junior research scie ntist
Golosov Sergey Dmitriyevich 1
Candidate of Sciemces , senior research scientist 1St. Petersburg Federal Research Center
of the Russian Academy of Sciences, Institute of Limnology
of the Russian Academy of Sciences (SPC RAS)

Аннотация
Представлены ре зультаты трехмерного математического моделирования термического и ледового
режимов Ладожского озера в условиях климатических изменений. Показано, что п редполагаемое к концу
XXI века потепление климата скажется, в первую очередь, на скорости нарастания и та яния льда. Быстрое
таяние льда привед ет к раннему очищению озера от ледового покрова. При этом сроки начала ледовых
явлений в озере не изменятся. Раннее исчезновение ледового покрова приведет к временному сдвигу в
термических процессах в озере, что скажетс я на химико -биологическом режиме озер а.
Abstract
Results of 3D mathematical modeling of the thermal and ice conditions in Ladoga Lake at possible climatic
changes are presented. It is shown that the expected climate warming by the end of the XXI century w ill affect,
first of all, the rate of growth and melting of ice. The fast melting of the ice will lead to the early disappearance of
the ice cover that, in turn, will cause a temporal shift in the thermal processes in the lake. This will affect the
tempera ture dependent chemical and bi ological processes in the lake.
Ключевые слова: Ладожское озеро, температурный и ледовый режимы, изменение климата,
трехмерное моделирование
Key words: Ladoga Lake, thermal and ice processes, climate change, 3D modeling

Intro duction
Among the numerous fac tors that determine the
status and functioning of the aquatic ecosystems in
natural and artificial reservoirs and the quality of water
resources, the thermal regime of the water body, mixing
conditions and ice phenomena are of paramount
importance. Therefo re, practically all chemical and
biological processes in reservoir, such as formation and
decay of organic matter, dissolution of atmospheric
gases (primarily of oxygen and carbon dioxide), red –
ox reactions, vital activity o f almost all aquatic
organisms are temperature dependent [3, 6, 11].
In turn, thermohydrodynamic (THD) processes
that occur in the water bodies arise as a result of
atmospheric effects on them and therefore are subject
to fluctuations in the regional clim ate. In order to assess
the re sponse of the aquatic ecosystem to possible
changes in the regional climate, it is necessary, first of
all, to understand what changes can occur in THD
processes under the impact of climate change.
In the present study on the basis of 3D model
simulations the effect of possible changes of regional
climate on THD processes in the Ladoga Lake is
assessed.
Materials and methods
A three -dimensional (3D) mathematical model of
the inland sea hydrodynamics (MISH) developed at the
Institute of numerical mathemat ics RAS was used to
perform the calculations [2]. To describe the water
mass circulation in a water object of any configuration

Национальная ассоциация ученых (НАУ) # 59, 20 20 29
the 3D THD equations are incorporated in the model.
The interaction between the atmosphere and the water
body is described throu gh the fluxes of momentum,
heat and moisture. The ice module of MISH is activated
when the temperature at the water surface reaches the
freezing point. The module calculates the ice
temperature and thickness as well as the dyn amics of
ice fields within the water object. Herewith, over the
water area where the ice cover is present the fluxes of
momentum, heat and moisture at the air -water interface
are replaced by similar fluxes across the air -ice and ice -
water boundaries. The w ater exchange through the
late ral and air - water boundaries are explicitly
prescribed taking into account the properties of water
(heat content and mineralization). Also the model
explicitly assigns precipitation and evaporation at the
air -water interface . The model has been successfu lly
tested through calculation of the THD of the Caspian
Sea, which is a typical representative of the inland seas.
Taking into account the spatial scale of Ladoga
Lake, up to 230 km in length and 125 km in width with
a depth difference of several meters in the southern part
to 250 meters in the North -the lake can be considered
rather as a freshwater inland sea than as a lake.
Therefore, MISH was chosen to perform the
calculations for Ladoga Lake. Before the calculations,
MISH was adapted for use in the fr esh water conditions
[1]. In particular, taking into account the fact that the
mineralization of water in Ladoga Lake and its
tributaries differs from each other and its values are
much less than the typical salinity in the oc ean, the
equation of state for salty water was replaced by the
equation of state of slightly mineralized water [5].
Parameters of the computational grid were 600x600
meters horizontally and 30 levels in vertical direction.
The time step of calculations was 6 minutes.
The data of the r eanalysis, a joint project of the
National Centers for Environmental Prediction (NCEP)
and Atmospheric Research (NCAR) [7] were used to
assign initial meteorological conditions for calculation
of the current "medium -climatic" state of the THD
processes. As a scenario of possible climate change the
scenario MPI B2 developed at the Max Planck Institute
(Hamburg, Germany) was chosen [8]. This scenario is
characterized by the following main parameters: 1)
moderate emission of green house gases into the
atmospher e; 2) it is assumed that the main climate
warming will occur in winter, which corresponds to the
data of long -term field observations made over the last
40 -50 years; 3) the General trends of emissions are also
close to those o bserved over the past 40 years ; 4) the air
temperature on the planet at the end of the century can
increase by up to 3 –5 °C. According to its main
parameters the MPI B2 scenario can be considered as a
scenario of maintaining the current warming trend [8,
9, 10].
Initial conditions at t he MISH calculations were
set for the conditions of early October. The fact is that
in October the thermal structure of the lake is
homogeneous over the entire area [4]. This is the only
month in the year when the initial cond itions can be set
up correctly . The inflow from the main tributaries of the
lake, the rivers Volkhov, Svir’ and Vuoksa, as well as
the runoff of the Neva River, were taken into account
during the calculations. The results of numerical
experiments and their brief discussion are presente d
below. The data of calculations obtained using the
NCEP/NCAR meteorological reanalysis are shown at
the left (a) panels of the figures. The results of
simulations corresponding to the climate scenario MPI
B2 are presented at the right panels (b). Color s cale
stands for water temperature (°C), the white -grey -black
one for ice thickness (m).
Results and discussion
The initial distributions of the lake surface
temperature on October, 1 of the middle climatic year
and at the end of the XXI century are shown in Fig. 1a,
b respectively.

Figure 1. Initial spatial distribution of the water temperature in the Ladoga Lake

As follows from the data in figure 1 a, b, the lake
at this time is thermally homogeneous; the water
temperature t hroughout the entire ar ea is close to 7 -8
°C [4]. October is the time of year when density
convection prevails over all dynamic processes in the
lake. Due to intensive vertical mixing caused by the
convection, the water column becomes thermally
homogeneous .
Further cooling lead s to the formation of spatial
temperature heterogeneity. At this time the most cooled
are the shallow areas of the lake, localized mainly in the
South -Eastern, Southern and South -Western regions.
At the end of October – early Novembe r the fall thermal

30 Национальная ассоциация ученых (НАУ) # 59, 20 20
fron tal zone (thermal bar) starts to develop. In the case
of "medium -climatic" year the thermal bar is formed
earlier and the rate of its moving towards deeper sites
is higher (Fig.2). That takes place due to lower values
of the air temp eratures, and hence, th e larger heat losses
through the free surface of the lake.

Figure 2. The thermal bar localization (blue line) by November 2 corresponding to “medium -climatic” (a) and
scenario -based (b) atmospheric impact

At the end of November, t he localization of the
thermal bar in both versions of the calculations is
almost the same. The main differences are observed in
the thickness of the ice and the area of the lake covered
by ice: both parameters are greater at the "average
climatic" atmosph eric exposures (Fig. 3 a, b).

Figure 3. The thermal bar localization and the ice cover by the end of November

At the end of December, the thermal bar ceases to
exist in both versions of the calculations (Fig. 4 a, b).
At the same time, it should be noted that in the case of
"scenario" atmospheric effect, the ice -free surface of
the lake cools faster, compared with the "medium -
climatic" conditions. The fact is that corresponding to
scenario B2, the temperature of air boundary layer is
higher during this pe riod, which leads to more intensive
evaporation at the water surface and, accordingly, to
accelerated surface co oling. Due to the higher air
temperature, the rate of ice growth in the "scenario"
version is lower, and the ice thickness is less than in the
case of "medium -climatic" impact.

Figure 4. The thermal bar disappearance and ice cover by the end of December

Национальная ассоциация ученых (НАУ) # 59, 20 20 31
In both versions of atmospheric impact the lake is
completely frozen by the middle of February. Intense
evaporation in the case of scenario imp act has one more
additional effect. The earlier formation of the ice cover
on the entire surface of the lake lea ds to the fact that in
the central part the ice thickness becomes even greater
compared to "average climatic" case (Fig. 5 a, b). At
the same ti me, the maximum ice thickness for the
"average climatic" year can reach 1 meter in the
southern regions of the l ake. In the same areas, if
calculated according to the climate scenario, the ice
thickness will be less by about 25%. In the North -
Western part of the lake the ice is practically absent in
both versions of calculations.

Figure 5. The ice cover in the lak e by the mid February

In mid -March, the differences in the state of the
ice cover become much more significant. In case of
"average climatic" at mospheric impact, the lake
remains completely covered by ice, although its
thickness in the North -Western deep -water area is
about 10 – 15 cm. In the case of climate scenario
calculation, a significant part of the North -Western
water area is ice -free. More over, ice becomes thin in
most of the central areas of the lake, reaching only 10 –
15 cm (Fig. 6 a, b).

Figu re 6. The ice cover in the lake by the mid March

By the end - April and in the first days of May (Fig.
7 a, b) in the case of "average" year the lake becomes
completely ice -free. At the same time, in the case of the
climate scenario the thermal bar has been already
formed in the Bay of Petrokrepost', partly in the
Volkhov Bay, in the area of Priozersk and it started to
spread towards the central pa rts of the lake (Fig. 7b).
This means that in these areas the water masses have
already warmed up to the tempera ture of the maximum
density of slightly mineralized water.

32 Национальная ассоциация ученых (НАУ) # 59, 20 20
Figure 7. Distribution of the temperature in Ladoga Lake by May 3 for mean -climati c (a) and scenario (b)
atmospheric impacts. Blue line marks the location of 4°C isotherm characterizing the posi tion of the thermal bar

By mid -June (Fig. 8 a, b), the THD processes in
Ladoga Lake, determined by the "average climatic"
atmospheric effects, l ag behind the "scenario" ones by
one month on the average. The thermal frontal zone is
only approaching the cent ral areas of the lake from the
Southern side. From the Eastern direction the thermal
bar slightly moved to the center of the lake. In the North
and North –West thermal bar is still close to the
coastline. The water temperature is close to 20 °C only
in the Bay of Petrokrepost’ and partly in the Volkhov’s
Bay. The pattern is quite different in the case of THD
processes defined by the climate scenari o. Thermal bar
ceased to exist, and an intense warming up of the whole
lake is started. The water temperature in the Bay of
Petrokrepost’, in the Volkhov’s and in the Svir’s Bays
has already exceeded 20 °C, or is close to this value.
The same temperature i s observed in the skerries. Over
the rest of the lake the water temperature varies from 7 -
8 to 15°C.

Figure 8 . The same as in Fig. 7 by the mid -June

By mid -July (Fig.9 a, b) the thermal bar ceases to
exist in the case of mean -climatic year and the lake
starts to warm up. The temperature field approximately
corresponds to the "scenario" one month earlier. The
cent ral, Northern and North -Western parts of the lake
are exceptions. Around these regions the water
temperature is in the range of 7 -8 °C. In the c ase of a
climatic scenario, the intense warming up of the lake
continues. The water temperature in almost all co astal
areas has either reached 20 degrees or approaching it.
The entire central part is warmed up to 15 -16 °C, and
only in a small area in the N orth –West of the lake the
water temperature is about 10 – 12 °C.

Национальная ассоциация ученых (НАУ) # 59, 20 20 33
Figure 9. Distribution of water temperature in Ladoga Lake by mid -July

August (Fig. 10 a, b) is characterized by the fact
that in the case of the "average climatic" year, the
warming of th e lake is almost completed. Calculations
according to the climate scenario show that by mid -
August, almost the entire water area of the lake warms
up to 20°C and more.

Figure 10. Distribution of water temperature in Ladoga Lake by mid -August

In the secon d half of August and in the beginning
of September the rapid cooling of the lake begins.
Herewith, i n the case of calculations according to the
climate scenario, it occurs much faster compared to the
"average climate" year. By the mid -September only in
the Bay of Petrokrepost’ the temperature is about 20 °C
(Fig. 11 a, b).

Figure 11. Distribution of wa ter temperature in Ladoga Lake by mid -September Finally, as noted above,
in October the lake in both cases cools to 7 – 8 °C (see Figure 1 a, b).

Conclusion s
Preliminary conclusions about the impact of
possible climate change on THD processes in Ladoga
Lake are the following. The expected climate warming
will affect both the thermal and ice conditions in the
lake. Herewith the terms of formation of the ice co ver
will not change. Onset of freezing, both in the case of
the "average climatic" year and under the climate

34 Национальная ассоциация ученых (НАУ) # 59, 20 20
scenario, occurs in early November in the southern
areas of the lake. The main influence of warming can
have on the rate of ice growth and melting . In the
"scenario" case, the lake is completely covered by ice.
However, small ice thickness predetermines early
melting. On the average, it should be noted that the
complete ice melting may occur on 2 -3 weeks prior to
the conditions of the "average" atmo spheric impact.
Early disappearance of the ice cover may lead to a
temporary shift in the processes that determine the
thermal regime of the lake in spring and summer. So,
the formation of the thermal frontal zone (thermal bar)
will start earlier on the sa me 2-3 weeks and the speed
of its propagation offshore will be higher. As a result,
the spring –summer thermal bar will terminate in mid -
June, instead of the average climatic mid -July [4]. As a
result, the summer warming of the main water mass
will start al mo st 1 month earlier that inevitably will
affect the temperature regime of the whole lake. Under
the conditions of the climate scenario, almost the entire
area of the lake will warm up over 20 °C, which does
not happen under the conditions of the "average"
climate scenario. If the predicted B2 scenario fulfills, it
should be expected that climatic changes will lead to
drastic changes in THD processes in the lake and, as a
consequence, in the functioning of the aquatic
ecosystem. Among the latter we can expe ct changes in
the gas regime of the lake (see introduction), in the
species composition of aquatic organisms, the
emergence of new organisms at all trophic levels and
decrease/increase in biodiversity.
The study was performed in frames of the state
assignm ent of the St. Petersburg Federal Research
Center of the Russian Academy of Sciences (SPC
RAS), Institute of Limnology of the Russian Academy
of Sciences (section No. 1.6, theme no. 0154 -2019 -
0001.
Работа выполнена в рамках государственного
задания Федерал ьного государственного
бюджетного учреждения науки «Санкт -
Петербургский Федеральный исследовательский
центр Российской академии наук» (СПб ФИЦ
РАН), Институт озероведения Российской
академии наук» по разделу № 1.6 темы № 0154 -
2019 -0001.

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