=Paper=
{{Paper
|id=Vol-3006/67_short_paper
|storemode=property
|title=Spatial-temporal analysis of temperature in Lake Shira based on long-term observations
|pdfUrl=https://ceur-ws.org/Vol-3006/67_short_paper.pdf
|volume=Vol-3006
|authors=Olga S. Volodko,Lidiya A. Kompaniets,Lyudmila V. Gavrilova
}}
==Spatial-temporal analysis of temperature in Lake Shira based on long-term observations==
https://ceur-ws.org/Vol-3006/67_short_paper.pdf
Spatial-temporal analysis of temperature in Lake
Shira based on long-term observations
Olga S. Volodko1 , Lidiya A. Kompaniets1 and Lyudmila V. Gavrilova2
1
Institute of Computational Modeling SB RAS, Krasnoyarsk, Russia
2
Siberian Federal University, Krasnoyarsk, Russia
Abstract
Long-term in-situ measurements of temperature were conducted in lake Shira during 2013-2015. The
principal component analysis of temperature time series allowed to identify period of generation and
propagation of internal waves. The spectral analysis revealed the dominance of the oscillations with
periods of 21.3, 10.6 and 5.3 h.
Keywords
In-situ measurements, internal waves, spectral analysis, isotherms.
1. Introduction
The dynamics of water currents are studied intensively in order to analyze the distribution of
impurities and phytoplankton and, thus, to determine characteristics of water systems.
Lake Shira located in the Republic of Khakassia, Eastern Siberia, is an enclosed saline lake
with only a small tributary of the Son River. In the period of summer stratification, the wind
stress is a main factor induced the water currents.
The observations on many stratified lakes confirm that one of the most common wind
reactions is the occurrence of internal waves [1], which determine the intensity of mixing in
the coastal zone, and therefore biological processes and water quality in lake.
In present work, the periods of internal waves has been determined using spectral estimates
of temperature of 2013–2015.
2. Long-term temperature measurements
In summer of 2013–2015 in lake Shira long-term temperature measurements were carried out
at several stations of the lake, as shown in Figure 1. The temperature measurements were
performed using thermal circuits. The temperature were measured with interval of 1–1.5 m and
with accuracy of 0.5 ∘ C in 2013–2014, and the accuracy of 0.1 ∘ C in 2015.
The temperature data of 2013–2014 of four stations T2, T3, T4, T5 were analyzed from
03.07.2013 to 05.08.2013 and from 01.07.2014 to 21.07.2014. The data of 2015 were analyzed from
SDM-2021: All-Russian conference, August 24–27, 2021, Novosibirsk, Russia
" osv@icm.krasn.ru (O. S. Volodko); lv.gavrilova@gmail.com (L. V. Gavrilova)
© 2021 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
Workshop
Proceedings
http://ceur-ws.org
ISSN 1613-0073 CEUR Workshop Proceedings (CEUR-WS.org)
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Olga S. Volodko et al. CEUR Workshop Proceedings 567–574
Figure 1: The stations of temperature measurements in 2013 (left), in 2014–2015 (right).
seven stations T1, T2, T4, T7, T8, T9, T10 with depth 15.7, 23.6, 24.4, 13.8, 17.5, 17 and 12.9 m
correspondingly of two periods from 8.07.2015 to 11.07.2015 and from 01.07.2015 to 01.08.2015.
3. Spectral analysis
The spectral estimates of temperature were found using the method of averaged periodogram
with Blackman – Harris window and the Welch’s method [2]. In the last method signal is split
up into eight overlapping segments and then averaged windowed using Blackman – Harris
window. On the each segment the periodorgam is calculated by computing discrete Fourier
transform
𝑁 −1
1 ∑︁
𝐷𝑛 = 𝑓𝑚 𝑊 𝑚𝑛 , 𝑛 = 0, 1, 2, . . . , 𝑁 − 1,
𝑁
𝑚=0
where {𝑓𝑚 , 𝑚 = 0, 1, 2, . . . , 𝑁 − 1}, 𝑊 = 𝑒−2𝜋𝑖/𝑁 is discrete exponential functions. The
discrete Fourier transformation is computes using fast Fourier transformation, that allows to
obtain result in time of 𝑂(𝑁 log 𝑁 ).
In article [3] were presented analysis of temperature data in period from 01.07.2015 to
01.08.2015 using method of empirical orthogonal functions (principal component analyses).
The analysis identified periods of generation and propagation of internal waves. During the
time-period from 08.07.2015 to 11.07.2015 the internal waves were observed with period 7
and 9 hours (Figure 2). Therefore, these 4 days and the entire measurement time period from
01.07.2015 to 01.08.2015 were chosen for spectral analysis.
The spectral estimations in period from 08.07.2015 to 11.07.2015 were found for original
data, in period from 01.07.2015 to 01.08.2015 the temperature data were pre-processed with
decimation every 15 minutes (Table 1). The Figures 3–8 shows temperature spectrums.
The spectral analysis of temperature showed the frequencies longwave oscillations for period
four days are include in frequencies longwave oscillations for period a month (see Table 1).
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Table 1
The spectral estimations of temperature of 2015.
Frequency, Period, Spectral power Frequency, Period, Spectral power
1/hr h density, W/(1/h) 1/h h density, W/(1/h)
Station T1 Station T2
08.07.2015–11.07.2015
0.04688 21.3 4.415 0.07031 14.2 0.00728
0.1172 8.5 0.2474 0.1172 8.5 0.004908
0.1875 5.3 0.08537 0.1875 5.3 0.002681
01.07.2015–01.08.2015
0.04688 21.3 0.9873 0.03125 32 0.2594
0.0625 16 0.9592 0.0625 16 0.2738
0.09375 10.6 3.091 0.09375 10.6 0.2059
0.1172 8.5 2.891 0.125 8 0.1107
0.1953 5.1 1.396 0.1484 6.7 0.1829
0.1953 5.1 0.07305
Station T4 Station T7
08.07.2015–11.07.2015
0.04688 21.3 0.04632 0.04688 21.3 0.04848
0.09375 10.6 0.002482 0.1172 8.5 0.003557
0.1875 5.3 0.0003167 0.1875 5.3 0.001335
01.07.2015–01.08.2015
0.04688 21.3 0.1065 0.03125 21.3 6.179
0.0625 16 0.4059 0.08594 11.6 3.486
0.08594 11.6 0.2201 0.1094 9.1 0.5561
0.1016 9.8 0.2497 0.1328 7.5 0.1603
0.1484 6.7 0.1335 0.1484 6.7 0.2788
0.1797 5.5 0.04446 0.1797 5.5 0.1763
Station T8 Station T9
08.07.2015–11.07.2015
0.09375 10.6 0.0007315 0.07031 14.2 0.001293
0.1406 7.1 0.001111 0.1406 7.1 0.001111
0.2109 4.7 0.001112
01.07.2015–01.08.2015
0.07031 14.2 0.3639 0.02344 42.6 1.399
0.08594 11.6 0.814 0.03906 25.6 0.522
0.125 8 0.1068 0.0625 14.2 0.6069
0.1406 7.1 0.1728 0.08594 11.6 0.8786
0.1563 6.3 0.1129 0.1563 6.3 0.08016
0.1953 5.1 0.06089 0.2031 4.9 0.1576
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Figure 2: The isotherms in the station T1 of period from 08.07.15 to 11.07.2015, 𝑇 = 10, 12, 14, 16, 18 ∘ C.
Figure 3: The spectral density of temperature in the station T1 in periods 08.07.2015–11.07.2015 (left)
and 01.07.2015–01.08.2015 (right).
Figure 4: The spectral density of temperature in the station T2 in periods 08.07.2015–11.07.2015 (left)
and 01.07.2015–01.08.2015 (right).
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Figure 5: The spectral density of temperature in the station T4 in periods 08.07.2015–11.07.2015 (left)
and 01.07.2015–01.08.2015 (right).
Figure 6: The spectral density of temperature in the station T7 in periods 08.07.2015–11.07.2015 (left)
and 01.07.2015–01.08.2015 (right).
Figure 7: The spectral density of temperature in the station T8 in periods 08.07.2015–11.07.2015 (left)
and 01.07.2015–01.08.2015 (right).
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Figure 8: The spectral density of temperature in the station T9 in periods 08.07.2015–11.07.2015 (left)
and 01.07.2015–01.08.2015 (right).
The spectral estimations of temperature of 2013–2014 are presented in Tables 2 and 3.
In summer 2013, 2014 and 2015, the spectral analysis of the temperature data showed the
presence of maxima at a frequencies corresponding to long-time periods of 32, 26.5, 21.3,
14.2 h. In 2015 in station T10 were identified maximum corresponding to period of 42.6 h, that
multiple 21.3 h. It should be emphasized the presence at the same time of maxima at frequencies
corresponding to long periods, and periods 2–4 times smaller: 42.6 h — 21.3 h, 32 h — 16 h,
26.5 h — 13.3 h, 14.2 h — 21.3 h.
Table 2
The spectral estimations of temperature of 2014.
Frequency, Period, Spectral power Frequency, Period, Spectral power
1/h h density, W/(1/h) 1/h h density, W/(1/h)
01.07.2015–21.07.2015 19.07.2014–30.07.2014
Station T3 Station T4
0.03906 25.6 0.4086 0.03125 32 0.5518
0.04688 21.3 0.2974 0.04688 21.3 0.3595
0.07031 14.2 0.1158 0.0625 16 0.9857
0.09375 10.6 0.9203 0.07813 12.8 0.6905
0.1172 8.5 2.522 0.1094 9.1 2.228
0.1382 7.2 0.2607 0.1563 6.4 1.394
0.1797 5.6 0.2284
Station T5
0.03906 25.6 12.52
0.0625 16 4.52
0.0859 11.6 6.148
0.1016 9.8 10.81
0.1406 7.1 4.645
0.1875 5.3 16.91
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Table 3
The spectral estimations of temperature of 2013.
Frequency, Period, Spectral power Frequency, Period, Spectral power
1/h h density, W/(1/h) 1/h h density, W/(1/h)
03.07.2013–05.08.2013
Station T2 Station T3
0.0375 26.6 60.74 0.0375 26.6 44.62
0.04688 21.3 22.77 0.06094 16.4 11.2
0.075 13.3 14.82 0.07031 14.2 18.49
0.08437 11.8 31.83 0.08437 11.8 26.12
0.1125 8.8 23.79 0.1125 8.8 17.67
0.1453 6.9 11.2 0.1453 6.9 2.913
0.1875 5.3 2.842 0.1828 5.4 2.894
Station T4 Station T5
0.0375 26.6 19.2 0.0375 26.6 25.89
0.06094 16.4 15.81 0.05156 19.4 3.271
0.075 13.3 24.26 0.075 13.3 7.235
0.08906 11.2 29.34 0.08437 11.8 20.77
0.09844 10.1 17 0.1078 9.2 24.13
0.1125 8.8 14.01 0.1266 7.9 16.67
0.1453 6.9 4.523 0.1453 6.9 4.009
0.1828 5.4 4.711 0.1828 5.4 5.497
2014 2015
Figure 9: The spectral power of current velocity in the summer of 2014 and 2015.
The spectral estimates of temperature are consistent with the spectral estimates of the current
velocity in lake Shira (Figure 9). These spectral estimates were presented in work [4].
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4. Conclusions
The spectral analysis of the temperature data of summer 2013, 2014 and 2015 were allowed
determining a period of internal waves in lake Shira. The spectral estimates of temperature are
consistent with the spectral estimates of the current velocity. Based on spectral analysis over
a period of three years, we can expect the presence of internal waves of such periods in lake
Shira in other years.
Acknowledgments
This work is supported by the Krasnoyarsk Mathematical Center and financed by the Ministry of
Science and Higher Education of the Russian Federation in the framework of the establishment
and development of regional Centers for Mathematics Research and Education (agreement
No. 075-02-2021-1384).
The authors thanks to Tatyana Schidlovskaya for the computation the spectral estimates of
temperature of 2015.
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