Spectral properties of the horizontal irradiance vertical distribution in Lake Teletskoye in August 2023: processing methodology and regional features

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1. Introduction

Sunlight penetrating into the water column is weakened by absorption and scattering by optically active substances (phytoplankton pigments, dissolved organic matter, suspended particles of various origins). The spectral variability of the optical properties of these components determines the resulting spectrum of underwater irradiance at different depths. The vertical distribution of irradiance is important for the phytoplankton functioning and, therefore, for the aquatic ecosystem as a whole. Estimation of the vertical distribution of underwater irradiance and the vertical attenuation coefficient of irradiance is required to model the photosynthesis processes of a specific reservoir. This is especially important for bounded water bodies, such as lakes, which are sensitive to both climate change and anthropogenic influence (Akulova et al., 2017; Aslamov et al., 2020; Churilova et al., 2020; Suslin et al., 2020).

In August 2023, comprehensive hydrooptical studies were performed on Lake Teletskoye, which included measurements of underwater irradiance spectra and the reflectance coefficient of the water column. Lake Teletskoye is located in the north-eastern part of the Altai Republic (Fig. 1a). It has an elongated shape and consists of two parts: a meridional part with a length of 50 km and a latitudinal (northern) one with a length of 28 km. Lake Teletskoye is a flowing lake, with more than 150 permanent rivers and temporary streams flowing into it, the largest of which is the Chulyshman River, which provides up to 70% of the total water inflow, and the Biya River flows out (Selegey et al., 2001).

 

Fig.1. Geographical location of (a) Lake Teletskoye and (b) stations at which measurements of the spectral irradiance profile were carried out in August 2023.

 

Previous optical measurements on Lake Teletskoye were presented by spectra of underwater irradiance and light attenuation coefficient (Sutorikhin et al., 2020; Akulova et al., 2022). The aim of this work was to calculate the spectrum of the vertical light attenuation coefficient using spectral measurements of the horizontal irradiance profile, estimate the spectral slope of the total light absorption coefficient in the shortwave part of the spectrum and identify regional features characteristic of Lake Teletskoye. As an additional task, based on synchronous measurements of the photosynthetically active radiation (PAR) profile and the horizontal irradiance spectrum, to develop a method for constructing the attenuation profile of the horizontal irradiance spectrum in physical units.

2. Materials and methods

The stations positions at which synchronous spectral measurements of the horizontal irradiance profile and the PAR profile were carried out are shown in Fig. 1b. The figure shows that the measurements cover the northern, central and southern parts of the lake, including its estuary areas. Thus, we have representative station coverage of all major areas of the lake.

To study the light spectra at different depths, a new instrument made on a modern elemental basis was used (Latushkin and Kudinov, 2019). The instrument performed synchronous measurements of irradiance profiles in seven spectral bands with central wavelengths of 380, 443, 490, 510, 555, 590 and 620 nm. The bandwidth in the first spectral band is 30 nm, in all others – 10 nm. An example of measuring horizontal irradiance profiles in all seven spectral bands at the station 002 is shown in Fig. 2.

 

Fig.2. Example of measuring horizontal irradiance profiles at the station 002 in seven bands with a central wavelength: 380 nm (a), 443 nm (b), 490 nm (c), 510 nm (d), 555 nm (e), 590 nm (f) and 620 nm (g). Straight line is the result of approximation by Equation 4 for the corresponding band.

 

To solve one of the listed problems, measurements of the PAR profile were used with the “CONDOR” instrument (Lee, 2012; Hydrobiophysical multiparametric submersible autonomous complex “CONDOR”. URL: https://dent-s.narod.ru/kondor.html), which were carried out synchronously with the measurement of horizontal irradiance. An example of measurements a PAR profile at station 002 by “CONDOR” instrument is shown in Fig. 3.

 

Fig.3. An example of measuring the PAR profile with the “CONDOR” instrument at station 002

1 – symbol “+”;

2 – result of approximation of variation with depth by equation (1);

3 – PAR(0^-) value, as a result of interpolation of equation (1) at 0 when z→0.

 

Let us describe a method for determining the integral value of photosynthetically active radiation immediately below the water surface using direct measurements of the PAR(z) profile, where z is the depth. From the definition of vertical attenuation coefficient (K_d) it follows that PAR(z) = PAR · exp(−K_d · z). After taking logarithms, the solution is reduced to finding the constants a and b in the linear equation (1):

y=a+b·z, (1)

where a = ln(PAR(0^-)) and b = – K_d.

K_d was considered independent of z and was determined from PAR(z) measurements for an area just below the surface (z > 2–3 m) to avoid the influence of the ship’s shadow. The measurements were carried out over several minutes to minimize errors associated with variable illumination of the water surface, such as cloudiness. Having determined the coefficient a, we find the photosynthetically active radiation immediately below the water surface PAR(0^-). In Fig. 3 the blue dot shows an example calculation for station 002.

The method for calibrating horizontal irradiance measurement bands using synchronous measurements of the PAR(z) profile consists of three stages. For both instruments, we assumed that the following conditions were met: linearity of the scales and stability of the measuring scales during the expedition cycle.

2.1. Stage 1

We have initial telemetry measurements O^T(λ_i, z), where λ_i is the central wavelength of the spectral band in nm, i is the number of the band from 1 to 7, z is the horizon depth in meters. Let’s find the average value for each band for depths greater than 30 m $⟨O^T({\lambda }_i,z>30m)⟩$ – dark signal. Note that $⟨O^T({\lambda }_i,z>30m)⟩$ was determined for depths almost twice as large as the photosynthesis layer, i.e., at the lower boundary of which the radiance incident on the water surface in the range from 400 to 700 nm was attenuated 100 times

$⟨O^T({\lambda }_i,z>30m)⟩=\frac{1}{N}\cdot {\sum }_{z=30}^{z=z_{\max }}{O}^T({\lambda }_i,z)$, (2)

where z is the measurement depth, starting from 30m; z_max – maximum measurement depth for the corresponding station; N – number of measurements from 30m to z_max.

To test the hypothesis of the stability of the “dark” telemetric signal of horizontal irradiance for seven bands, measurements were used at the station 002 and 021. The time difference between measurements at these stations was 2 days. The results are presented in Fig. 4 and Table 1. Table 1 shows the average value of $⟨O^T({\lambda }_i,z>30m)⟩$, their standard deviation (SD) and the number of measurements N. From Fig. 4 it is clear that the calibrations are stable.

 

Fig.4. Test for the stability of calibrations during the expedition in seven bands using the example of station 002 and 021, separated by two days.

 

Table 1. Statistical characteristics of the “dark” telemetric signal of horizontal irradiance for seven bands at the station 002 and 021

Station number	$\mathbf{⟨}{\mathit{O}}^{\mathit{T}}\mathbf{(}{\mathit{\lambda }}_{\mathit{i}}\mathbf{,}\mathit{z}\mathbf{>}\mathbf{30}\mathit{m}\mathbf{)}\mathbf{⟩}\mathbf{ }\mathbf{\pm }\mathbf{ }\mathbf{SD}$							N
	380 nm	443 nm	490 nm	510 nm	555 nm	590 nm	620 nm
002	16462±91	12855±90	12625±112	15373±99	19883±88	14937±101	14600±95	333
021	16281±90	12751±79	12469±98	15393±96	19714±103	14770±98	14438±97	88

 

2.2. Stage 2

The calculation of the signal taking into account the dark current O^u(λ_i,z) is performed according to the expression:

$O^u({\lambda }_i,z)=O^T({\lambda }_i,z)-⟨O^T({\lambda }_i,z>30m)⟩$ (3)

where $⟨O^T({\lambda }_i,z>30m)⟩$ – dark current values (see Table 1). Calculation of a(λ_i) and b(λ_i) was carried out for each station and for each of the seven bands according to the formula:

$\ln \left(O^u\right({\lambda }_i,z\left)\right)=b\left({\lambda }_i\right)\cdot z+a\left({\lambda }_i\right)$, (4)

where the horizontal irradiance in the band with a central wavelength λ_i, immediately below the water surface was as $O^u\left({\lambda }_i{\mathrm{,0}}^{-}\right)=\underset{z\to 0^{-}}{\lim }\left(O^u\right({\lambda }_i,z\left)\right)$ or $a\left({\lambda }_i\right)=\ln \left(O^u\right({\lambda }_i{\mathrm{,0}}^{-}\left)\right)$, and the vertical light attenuation coefficient in the corresponding band λ_i as K_d(λ_i,0^-)=–b(λ_i). The results of calculations of coefficients a(λ_i) and b(λ_i) according to equation (4) for all seven stations are summarized in Table 2.

 

Table 2. Results of calculations of coefficients a(λ_i) and b(λ_i) according to equation (4) for seven stations

Station	a(λi)/b(λi)
	380	443	490	510	555	590	620
1 001	17.64 -2.733	15.17 -1.049	15.03 -0.705	14.67 -0.455	14.90 -0.393	14.80 -0.368	14.80 -0.453
2 002	19.15 -3.191	14.83 -1.116	14.23 -0.681	14.15 -0.483	14.32 -0.421	14.08 -0.400	14.00 -0.498
3 005	19.99 -3.491	16.27 -1.304	15.74 -0.815	15.32 -0.498	15.53 -0.465	15.29 -0.435	15.31 -0.559
4 005*	20.44 -3.211	16.48 -1.210	15.49 -0.703	14.99 -0.439	15.13 -0.386	14.99 -0.356	15.01 -0.458
5 021	17.90 -3.145	13.83 -1.023	13.42 -0.635	13.19 -0.438	13.29 -0.389	12.93 -0.361	12.96 -0.434
6 k1	19.87 -3.006	16.04 -0.966	15.95 -0.670	15.69 -0.473	15.80 -0.417	15.71 -0.398	15.79 -0.481
7 1s2	18.12 -2.789	15.01 -0.786	16.24 -0.655	16.38 -0.478	16.70 -0.431	16.38 -0.405	15.87 -0.451

* station 005 was performed with a time difference of 1 hour (3 – 13:00; 4 – 14:00 local time).

 

2.3. Stage 3

The conversion of O^P(λ_i, 0^-) into physical units of radiation was carried out using the expression:

$O^p\left({\lambda }_i{\mathrm{,0}}^{-}\right)=PAR\left(0^{-}\right)\cdot w_i$, (5)

where $w_i=\frac{1}{\Delta {\lambda }_i}\cdot {\int }_{{\lambda }_i-\Delta {\lambda }_i/2}^{{\lambda }_i+\Delta {\lambda }_i/2}w\left(\lambda \right)d\lambda$ is the fraction of photons in the corresponding spectral interval (Suslin et al., 2020), associated with the characteristics of the band λ_i±Δλ_i/2 (Lee, 2012); PAR(0-) – is found from measurements of the PAR profile using the “CONDOR” instrument. It is obvious that the form of w(λ) depends on the altitude of the Sun and cloud conditions. In our case, the choice of the functional dependence of w(λ) was taken from the work (Bartlett et al., 1998).

Then the conversion factor of telemetry into physical quantities is calculated using the formula

$p\left({\lambda }_i\right)=\frac{O^p\left({\lambda }_i{\mathrm{,0}}^{-}\right)}{O^u\left({\lambda }_i{\mathrm{,0}}^{-}\right)}$. (6)

Since we assumed that PAR is the integral of the number of photons lying in the spectral range from 400 to 700 nm, the band with a central wavelength of 380 nm was excluded from the calculation. The results of calculating p(λ_i) are presented in Table 3.

 

Table 3. The result of calculating p(λ_i) in bands with a central wavelength λ_i and O^P(λ_i, 0^-) for station k1

λi, nm	443	490	510	555	590	620
p(λi)	1.424e-06	1.967e-06	2.751e-06	2.731e-06	3.149e-06	2.978e-06
OP(λi, 0-)	1.321e+01	1.664e+01	1.786e+01	1.985e+01	2.098e+01	2.140e+01

 

3. Results and discussion

Figure 5 shows the K_d spectra and their difference from the average spectrum $⟨K_d⟩$ for all seven stations (Table 2) after processing according to the method (equations (2) – (4)).

The minimum values of K_d in the band with a central wavelength of 590 nm, together with its high values in the spectrum short-wavelength region, indicate the dominance of absorption, primarily by the colored component of dissolved organic matter.

To identify the geographical features of K_d, consider Fig. 5b. Values of the difference $K_d–⟨K_d⟩$ above average in the spectrum short-wave region are observed in the south of the lake (stations 002, 005 and 005*); minimum values – in the lake north of (stations 001 and 1s2); intermediate values in the center (st. k1 and 021). Thus, in the upper layer of the lake there is a tendency for water absorption to decrease from south to north (mainly related to the concentration of dissolved organic matter, since we are talking about a band with a central wavelength of 380 nm).

 

Fig.5. Spectra of the vertical light attenuation coefficient K_d (a) and their deviations from the average (${\mathit{K}}_{\mathit{d}}\mathbf{–}\mathbf{⟨}{\mathit{K}}_{\mathit{d}}\mathbf{⟩}$), (b) for the sample (Table 2).

 

Let us note one more feature – the difference in K_d values in the band with a central wavelength of 443 nm at stations 001 and 1s2, located in the northern part of the lake. For station 001, located in Kamga Bay, this difference is significantly greater than at station. 1s2. This difference in K_d may be associated with additional absorption by phytoplankton, the concentration of which is significantly higher in the bay. However, this assumption requires additional verification.

The conclusion drawn from the analysis of Fig. 5a about the high value of the absorption coefficient by the upper layer of water in Lake Teletskoye is in good agreement with the results of measurements of the water reflectance spectra (R_rs) made by E.N. Korchemkina during this expedition (Sutorikhin et al., 2020). A reference to the description of the instrument and method for the water column R_rs measuring is given in work (Shybanov et al., 2023). It is known that the absorption coefficient by dissolved organic matter in the Black Sea is significantly higher compared to the waters of the open ocean (Suetin et al., 2002; Kopelevich et al., 2004). Figure 6 shows examples of R_rs spectra of the water column in the Black Sea in April 2021 and in Lake Teletskoye at station 002 and 021 in August 2023. Note that the measurements in the Black Sea were carried out in the absence of coccolithophorid blooms. It is clearly seen that the value of the R_rs of the water column at a wavelength of 400 nm in Lake Teletskoye is more than three times less than in the Black Sea, despite the fact that in the long-wave region of the spectrum (more than 600 nm) the R_rs of the water column in the lake is greater than in the sea. On the one hand, this confirms the conclusion that the light absorption coefficient in the short-wave part of the spectrum in the lake is significantly higher than in the Black Sea. On the other hand, it is obvious that the light backscattering coefficient by suspended particles is significantly higher in the lake than in the sea. This is especially noticeable for station 002, located in the south at the confluence of the river Chulyshman, which carries a significant amount of suspended matter.

 

Fig.6. Examples of measurements of the water column spectral reflectance coefficient in Lake Teletskoye in August 2023 at station 002 and 021 and in the deep-water part of the Black Sea in April 2021.

 

The obtained data on K_d(λ) (Table 2) can be used to assess the spectral dependence S_CDOM of dissolved organic matter coefficient (a_CDOM), assuming that it makes the main contribution to the total absorption (atot) in the short-wavelength region of the spectrum (λÎ350 – 450 nm), i.e. a_CDOM>>a_w, a_ph, a_tot>>b_b, and additionally a_tot>>b_b, where a_w and a_ph are the light absorption coefficients by pure water and phytoplankton, b_b is the total light backscattering coefficient by water, then:

$K_d\left(\lambda \right)\approx const\cdot \left(a_{tot}\right(\lambda )+b_b(\lambda \left)\right)\approx const\cdot \left(a_w\right(\lambda )+a_{ph}(\lambda )+a_{CDOM}(\lambda )+b_b(\lambda \left)\right)\approx const\cdot a_{CDOM}\left(\lambda \right)$. (7)

Taking into account that the functional relationship a_CDOM from λ has the form (Kopelevich, 1983):

$a_{CDOM}\left(\lambda \right)=a_{CDOM}\left({\lambda }_0\right)\cdot \exp (-S_{CDOM}\cdot (\lambda -{\lambda }_0\left)\right)$, (8)

and, having made elementary transformations of equation (7), taking into account equation (8) for two bands with a central wavelength λ=380 nm and λ₀=443 nm, respectively, we obtain the expression for S_CDOM:

$S_{CDOM}=\frac{1}{\lambda -{\lambda }_0}\cdot \ln \left(\frac{K_d\left({\lambda }_0\right)}{K_d\left(\lambda \right)}\right)$. (9)

The calculation results are presented in Table 4.

 

Table 4. Results of calculations of the spectral absorption slope of SCDM inanimate organic matter in Lake Teletskoye using equation (9)

λ/ λ0 nm	Station number							$\mathbf{⟨}{\mathit{S}}_{\mathit{C}\mathit{D}\mathit{O}\mathit{M}}\mathbf{⟩}\mathbf{\pm }\mathit{S}\mathit{D}$ nm-1
	001	002	005	005	021	k1	1s2
380/443	0.015	0.017	0.016	0.015	0.018	0.018	0.021	0.017± 0.002

 

Presented in Table 4 results coincided with studies of the primary hydrooptical characteristics of Lake Teletskoye carried out a year earlier at the same time (Moiseeva et al., 2023), during which they directly measured the spectral variation of the colored component of dissolved organic matter for a similar stations grid and which showed that the variability of S_CDOM lies in the range of 0.017 – 0.019 nm^-1 in the wavelength range 350 - 500 nm.

Figure 7 shows an example of recovering the spectrum of horizontal irradiance in physical units, obtained using the method described above (equations (2) – (6)) from measurements at k1 station. The behavior of the irradiance spectrum with depth (a sharp fail in the short-wavelength region of the spectrum) indicates a high content of dissolved organic matter in the Lake Teletskoye waters (Fig. 7). Features in the short-wave region of the horizontal irradiance spectrum and its maximum, starting from 5 m depth and below, correspond to a wavelength of 590 nm, also coincides with the results obtained a year earlier by employees of the Institute of Biology of the Southern Seas of RAS (Churilova et al., 2023).

 

Fig.7. An example of recovery the horizontal irradiance spectrum in physical units for k1 station.

 

4. Conclusions

The spectrum of the vertical light attenuation coefficient in seven bands has been restored, the anomalies of which describe regional features in the upper layer of water and are consistent with direct measurements of the water column spectral reflectance coefficient.

It has been demonstrated that in the case of synchronous measurements of the PAR profile and horizontal irradiance, it is possible to obtain irradiance in physical units at any horizon in the photosynthesis layer.

The obtained values for the spectral absorption coefficient by colored dissolved organic matter and the maximum wavelength of the spectrum of underwater irradiation in the photosynthesis layer coincided with the previously obtained results by employees of the Institute of Biology of the Southern Seas of RAS.

Acknowledgements

The work was carried out within the frameworks of government assignments: for MHI RAS № FNNN-2024-0012, and for IWEP SB RAS №0306-2021-0001 agreements with the administration of the Altai State Nature Reserve. The expeditionary work used scientific equipment of the CSU “Research Vessels of the IWEP SB RAS”.

Conflict of interest

The authors declare no competing interest.

作者简介

V. Suslin

FSBSI FRC Marine Hydrophysical Institute of RAS

编辑信件的主要联系方式.
Email: slava.suslin@mhi-ras.ru
俄罗斯联邦, Kapitanskaya str., 2, Sevastopol, 299011

O. Kudinov

FSBSI FRC Marine Hydrophysical Institute of RAS

Email: slava.suslin@mhi-ras.ru
俄罗斯联邦, Kapitanskaya str., 2, Sevastopol, 299011

E. Korchemkina

FSBSI FRC Marine Hydrophysical Institute of RAS

Email: slava.suslin@mhi-ras.ru
俄罗斯联邦, Kapitanskaya str., 2, Sevastopol, 299011

A. Latushkin

FSBSI FRC Marine Hydrophysical Institute of RAS

Email: slava.suslin@mhi-ras.ru
俄罗斯联邦, Kapitanskaya str., 2, Sevastopol, 299011

I. Sutorikhin

FSBSI Institute for Water and Environmental Problems, Siberian Branch of RAS

Email: slava.suslin@mhi-ras.ru
俄罗斯联邦, Molodezhnaya str., 1, Barnaul, Altai region, 656038

V. Kirillov

FSBSI Institute for Water and Environmental Problems, Siberian Branch of RAS

Email: slava.suslin@mhi-ras.ru
俄罗斯联邦, Molodezhnaya str., 1, Barnaul, Altai region, 656038

O. Martynov

FSBSI FRC Marine Hydrophysical Institute of RAS

Email: slava.suslin@mhi-ras.ru
俄罗斯联邦, Kapitanskaya str., 2, Sevastopol, 299011

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