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4th International Conference on Integrating GIS and Environmental Modeling
(GIS/EM4):
Problems, Prospects and Research Needs. Banff, Alberta, Canada, September
2 - 8, 2000.
Mean daily spatial surface temperature at Lake Ladoga:
a new approach from thermal informative-diagnostic system
GIS/EM4 No. 246
Mikhail Naumenko
Sergey Karetnikov
Vadim Guzivaty
Abstract
Recognition and understanding of the characteristics of the temperature
regime of the largest European lake - Lake Ladoga - are key to successful
interpretation of information on its physics, chemistry and biology. The
created thermal database was used for calculation of statistics of water
temperature. We have made the quantitative analysis of a seasonal course
of water temperature for the regions in connection with their depths. The
model of seasonal cycle of surface temperature as a functional representation
is presented . For the analysis of daily water temperature distribution,
the lake surface was divided up by means of a grid with area of about 10
x10 km.
Approximation functions were found for all 235 squares and the temporal
limits of their applicability defined. As the last step, a solution was
created using an information-diagnostic system (IDS), which allowed "typical"
water surface temperatures for each square to be obtained for any given
date (D). The spatial distributions of daily mean temperatures are
performed. Mean position of the vernal thermal front and schemes of "biological
summer" duration have been obtain.
Keywords
Spatial variability, functional representation of the seasonal surface
temperature cycle, Lake Ladoga, vernal thermal frontal zone, "biological
summer" duration.
Introduction
Environmental temperature is one of the most important defining parameters
in large lakes ecosystems. The water temperature is the most important
environmental variable for lakes in general, including Lake Ladoga.
Lake Ladoga, the largest lake in Europe, is situated at the periphery
of the Baltic Crystalline Shield near St.-Petersburg is about 61°
N, 31.5° E. The surface area is 17700 km,
mean depth 47 m. Depths of the northern part are from 60 up to 200 m, maximum
depth is 230 m., while depths of the southern part are as a rule among
10-50 m (Fig.1).
Lake Ladoga is an important public and industrial water supply and
serves as a source of drinking water for more than 4.5 millions people.
It is also important for fisheries and is used for commercial shipping
and as a recipient for urban sewage and industrial effluent (main from
paper and pulp mills).
Recognition and understanding of the characteristics of the temperature
regime of a lake are key to successful interpretation of information on
its physics, chemistry and biology. The rates of limnological processes
usually temperature dependent, besides the spatial and temporal variation
of that property strongly influence patterns of currents and density structure,
and hence affect the rate of vertical mixing or of exchange between the
nearshore zone and midlake, and influence the flushing characteristics
of regions or the lake as a whole (Boyce 1974). Thus water quality concerns
cannot be properly addressed without reference to thermal characteristics.
Furthermore, the large lake is an heat accumulator related to surrounding
land.
Lake temperature cycles are important for studies of most aquatic processes,
especially for numerical models that are intended to simulate annual bio-geochemical
cycles. Changes in lake temperatures, possibly resulting from changes in
global climate, may have significant impacts on Lake Ladoga and for evaluations
of climatological departures from typical conditions.
This paper focuses on the model of seasonal cycle of surface temperature
as a functional representation for Lake Ladoga and the spatial distribution
of daily mean temperatures based on it.
Material and methods
Spatial-temporal variability is a common feature of large lakes both physical
and biological processes. Theoretical and empirical studies show that the
analysis of large (i.e. regional) scale patterns must integrate processes
occurring at the small (i.e. local) scale (Levin 1992).
Owing to its large area and basin morphology, there is considerable
horizontal and vertical heterogeneity in the temperature of Lake Ladoga
in all seasons except the ice cover period.
The mean Lake Ladoga thermal features were determined by A.I.Tikhomirov
on the base of data for 50-60 years of our age (Tikhomirov 1982).
The bank of Lake Ladoga limnological information, created in Institute
of Limnology RAS (www.limno.org.ru), was
used for investigation of thermal region peculiarities. At present time
the database capacity has reached 140,000 records, and covers the period
of 71 years. The information density is more 150 measurements per km3.
Lake Ladoga computer thermal database has allowed to study the statistically
significant changes in spatial thermal structure in the lake throughout
the open water period (Guzivaty et al. 1998).
Thermal regionalization of Lake Ladoga
The principal among factors affecting temperature is the bathymetry
which partitions the lake into six distinct compartments. These physiographic
areas exhibit markedly different temporal and spatial distributions of
temperature.
Based on the new Lake Ladoga bathymetrical model (Naumenko 1995) the
lake was divided into six regions with uniform bottom slope (Fig.1).
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Consequently, for each of these regions a heating and cooling rate,
development of biological communities will have only it inherent values.
Regions are delimited by the isobaths. The depth distribution functions
for the regions obey a uniform law.
We have made the quantitative analysis of a seasonal course of water
temperature for the regions in connection with their depths.
Water temperatures and the main statistical characteristics of the
water body as recorded in 8 horizons (0,5,10,20,30,40,50 and 100 m) since
May 15 were calculated for each region of Lake Ladoga. The averaging period
was 10 days with shifting on 5 days, allowing for smoothing of the high-frequency
temperature fluctuations. The changes in water temperature and its variation
in all six regions are shown in Fig.2.
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Thus moving statistical characteristics calculations such as mean value, variance, mode, median etc., allowed temporal changes in water temperature to be investigated for the various limnological regions.
Spatial distribution of daily mean surface temperature
A.Tikhomirov (1982) calculated the spatial distribution of monthly
mean surface temperatures for Lake Ladoga over the period 1957-1963, but
it is known that during the warming season the mean daily increase in surface
temperature can reach 0.1° C.
The daily trend in temperatures is dependent on latitude and the bottom
morphology of the lake. Thus it is evident that spatial distribution of
daily mean surface water temperatures in Lake Ladoga should be determined
in order to obtain a more accurate description of thermal conditions in
the lake.
For the analysis of "typical" daily water temperature distribution,
the lake surface was divided up by means of a grid with side 10' in longitude
and 5' in latitude , giving a total of 235 grid squares to cover the lake
area, each having an area of about 10 x 10
km. The size of square was based on an analysis two-dimensional spatial
autocorrelation functions of Lake Ladoga water surface temperature (Naumenko
1994). Over a distance more than 10 km the correlation factor becomes
less then 0.5. This means that dependency
between water surface temperatures for the different points is insignificant.
All the available surface temperature data for May to November have
been taken together without regard to year of observation. The total number
of water surface temperatures measurements was more than 25000.
The water surface temperatures for each grid square were analyzed using
the STATISTICA software package and an approximation function for seasonal
changes. We present here a very accurate method (in terms of average conditions)
for estimating surface water as a continuous function of time. The main
requirements for a functional representation are:
1) A parametric function T°C must be sought with a limited number of parameters,
2) The function must be asymmetric on either side of a single peak.
Heating period has to be shorter than cooling one (Naumenko 1994, Naumenko
et al. 1996),
3) The function must exhibits asymptotic behavior when extrapolated
beyond the domain of the original data (T>0).
Different types of function were applied to the data, notably a third
degree polynomial; function, constructed from exponential and power-mode,
and compositional harmonic functions. The criterion for the determining
the best approximation function was the highest determination coefficient,
which shows a fraction of variance explained.
We obtained the best fit with a composite of exponential and power-mode
functions:
where T - a water temperature in °C;
D - a date in days from 1st
March;
a,b,c,d - empirical factors, selected for each square by the Newton
method.
A continuous parametric function with six parameters was fitted to
daily mean lake surface temperature measurements made at buoys in the Great
Lakes by Lesht and Brandner (1992). Our function has only 4 parameters
and accounts more than 70% of the variation in the data.
C. Mortimer (1988) reports about the different kinds of inshore and
deep-water warming regime of American Great Lake,
and a similar approach can be applied to Lake Ladoga. For deep-water squares
(bottom depth usually more than 50 ì) the initial period of warming
before 4° C (the free convection regime) was approximated by exponential curve:
The terms are the same as in equation (1) above.
The average value of determination factor for 235 squares is got 0.72,
and in only 5% of cases was this factor less than 0.5.
Results and discussion
Ultimately we perform a quantitative analysis of the seasonal course of
water temperature in all six regions in relation to their depths. We found
initially the variation in water temperature occurs regularly from month
to month and is dependent on depth. The largest variation is found during
the heating period, which is characterized by a short period of rapid rapid
energy exchange in the lake water mass.
Tests of the significance of the temperature differences between the
regions (Caulcott 1973) show that the distinction between the zones in
term of seasonal trends undergoes considerable changes. The differences
are statistically significant for periods only from May to July down to
the depth of 20 m.
Approximation functions for water temperature were found for all 235
squares and the temporal limits of their applicability defined. As the
last step, a solution was created using an information-diagnostic system
(IDS), which allowed "typical" water surface temperatures for each square
to be obtained for any given date (D). In Fig. 3 there are examples
of the spatial distribution of surface temperatures in Lake Ladoga water
on 15th May to 15th October.
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It is seen that the widest range of horizontal temperature changes occurs
from middle of June up to middle of July (magnitude of surface water temperature
exceeds 15° C) , i.e. in period of the
most intensive water surface heating. During the cooling period the horizontal
differences in surface temperature are less then 3-4° C.
A vernal frontal zone associated with temperature 4°
C persists in Lake Ladoga exists for more than two months (Naumenko, Karetnikov
1998). This is a very important phenomenon for biological and chemical
processes in the lake. Using created Lake Ladoga information-diagnostic
system for each square, the date when a temperature of 4°
C was reached on the surface was defined and drawn (Fig.4). This represents
the development of the frontal zone, i.e. the thermal bar.
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"Biological summer" duration
For Lake Ladoga the "biological summer" can be determined as a period when the temperature of the surface water exceeds 10° C. This marks the time at which the summer plankton communities are actively developing (Petrova, Terzevik 1992). The IDS allowed us to calculate the spatial distribution of 10-degree isochrones for heating and cooling periods (Fig.5).
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According to the long-term average data, the earliest beginning of "biological summer" for surface occurs in Volkhov bay on the 25th May and the latest, in the deep water areas of Lake Ladoga, on 20th July. The cooling of the lake occurs under homogeneous temperature conditions in the surface water. The end of the "biological summer" in late September is a simultaneous event all over the lake. Thus the duration of the "biological summer" ranges from 130 days in southern part of Volkhov bay to 65 days in the deep waters of the northern parts of the lake.
Conclusion
The results are of climatic importance for the study of Lake Ladoga as
the permit thermal spatial-temporal differentiation characteristics to
be stated for the regions and allow field surveys to be planned correctly
in relation to season.
Thus, initially the developed technique has allowed to receive the
daily spatial distributions of Lake Ladoga water surface temperature for
open water period, which can serve as average background distributions
at synoptic variability analysis and interannual variations. Created information-diagnostic
system gives a new possibilities at a solution of the diverse tasks on
thermodynamic of Lake Ladoga and its simulation.
References
Boyce F.M. 1974. Some Aspects of Great Lakes Physics of Importance to Biological and Chemical Processes. J. Fisheries Research Board of Canada 31 (5): 689-730.
Levin S.A. 1992. The problem of pattern and scale in ecology. Ecology 73:1943-1967.
Tikhomirov A.I. 1982. Large lakes thermic. Leningrad: Nauka. 232 p. (in Russian).
Guzivaty V.V, Karetnikov S.G, Naumenko M.A. 1998. Experience of creation and using of Lake Ladoga thermal database. Geography and natural resources (3): 89-96 (in Russian).
Naumenko M.A. 1995. New estimation of Lake Ladoga morphometric characteristic. Reports of Russian Academy of Sciences 345 (4): 514-517. (in Russian)
Naumenko M. 1994. Some Aspects of Large lakes Thermal Regime (Ladoga, Onega). Water Pollution Res. J. of Canada 29 (2-3): 423-439.
Naumenko M.A, Karetnikov S.G, Tikhomirov A.I. 1996. Main features of the thermal regime of Lake Ladoga during the ice-free period. Hydrobiologia 322: 69-73.
Lesht B.M, Brandner D.J. 1992. Functional representation of Great Lakes Surface temperatures. J. Great Lakes Res. 18 (1): 98-107.
Mortimer C.H. 1988. Discoveries and testable hypotheses arising from Coastal Zone Color Scanner imagery of southern Lake Michigan. Limnol. Oceanogr. 33 (2): 203-226.
Caulcott E. 1973. Significance tests. Routledge & Kegan Paul London and Boston. 124 p.
Naumenko M.A, Karetnikov S.G. 1998. Velocity of movement of a spring thermal frontal zone speed in Lake Ladoga movement. Meteorology and Hydrology (4): 107-115. (In Russian).
Petrova N.A, Terzevik A.U. (eds). 1992. Lake Ladoga. Ecological system state criterion. Saint-Petersburg: Nauka.
Authors
Mikhail.A. Naumenko, Prof., Head, Laboratory of Hydrology,
Institute of Limnology Russian Academy of Sciences, Russia.
Email: lake@spb.org.ru Tel: +7 -812 -294-80-20 , Fax: +7 -812 -298-7327
Sergey G.Karetnikov, Ph.D., Research Scientist, Laboratory
of Hydrology,
Institute of Limnology Russian Academy of Sciences , Russia .
Email: lake@spb.org.ru Tel: +7 -812 -294-80-20 , Fax: +7 -812 -298-7327
Vadim V.Guzivaty, Research Scientist , Laboratory of Hydrology,
Institute of Limnology Russian Academy of Sciences , Russia .
Email: lake@spb.org.ru Tel: +7 -812 -294-80-20 , Fax: +7 -812 -298-7327