Seasonal stratification and P. rubescens thin layer
Figure 1 shows the evolution of atmospheric forcing and lake temperature at the monitoring station (st0) for Lake Zurich in 2018. From January to March, the lake lost heat to the atmosphere (Fig. 1a). The water column was weakly stratified in January and the surface mixed layer (SML, defined as the depth where temperature was 0.5 °C lower than the near-surface value) deepened progressively. This continued until full mixing by mid-March (Fig. 1b) following a 10-day period of significant heat loss and relatively strong winds. The holomixis period was short with solar radiation dominating the heat budget after mid-March. As a result, a weak shallow thermocline had already developed by early April. Thereafter, surface temperature and water column stratification progressively increased to 26.5 °C, as observed on 8 August. During this warming period, a strong thermocline, with a temperature gradient ranging between 1.0 and 3.0 °C m\(^{-1}\), occurred just below the SML and showed a deepening trend from 2 to 10 m depth. Net cooling prevailed from August onwards and SML temperatures progressively decreased. The SML deepened steadily from 10 to 20 m depth in December, but the maximum thermal stratification remained strong (2–3 °C m\(^{-1}\)) until the end of September. It then declined gradually as the SML expanded through the deeper part of the metalimnion, which was more weakly stratified.
Planktothrix rubescens was observed throughout the SML as relatively low chl-a concentrations (chl-a \(<4\) μg L\(^{-1}\)) during the mixing period in winter and occurred throughout the water column after holomixis (Fig. 1c). From May onwards, P. rubescens communities formed a thin layer located within the main thermocline between 10 and 17 m depth. Planktothrix rubescens regulate their vertical position according to the daily dosages of photosynthetically available radiation (PAR; Walsby et al. 2004). The records described here found P. rubescens mostly located between daily PAR isolines for which P. rubescens acquires neutral buoyancy (0.28 mol photon m\(^{-2}\) d\(^{-1}\)) and for which the net growth becomes zero (0.036 mol photon m\(^{-2}\) d\(^{-1}\); thin dashed lines in Fig. 1c; Walsby et al. 2004). The layer remained stable, with peak concentrations between 30 and 40 μg L\(^{-1}\), until October, when the thermocline deepened and approached the layer. From mid-October, P. rubescens concentration in the SML began to increase but the peak persisted until the end of the month, when the thermocline transgressed the layer, and the latter dispersed. For the rest of the year, the P. rubescens population was located exclusively in the SML at moderate concentrations of ~ 10 μg L\(^{-1}\).
Microstructure measurements
Seasonal changes in stratification and mixing environment
Our turbulence sampling detected three stages in the seasonal development of the P. rubescens layer. The first microstructure and HR-mooring survey was carried out between 24 and 26 April 2018 (blue, Fig. 1), shortly before formation of the thin layer. The second survey occurred between 17 and 19 July (orange), when the thin layer had been established for more than 2 months and water column stability approached its maximum value. Finally, the third sampling took place between 2 and 4 October (green), when some P. rubescens chl-a had been detected in the SML but the chl-a peak remained sharp and well defined in spite of its reduced amplitude.
During the sampling in April, heating outpaced nighttime cooling and hourly wind speeds were maximal (6 m s\(^{-1}\)) on the 25th, such that no microstructure profiles could be carried out on that day. Except for this day, wind remained \(<4\) m s\(^{-1}\) (Fig. 2a). Thermal stratification was still moderate (\(N_{max} \approx 0.02\) s\(^{-1}\)), with a shallow thermocline located above 5 m depth (Fig. 2d, e). Chl-a measured with the SCAMP was low (\(<5\) μg L\(^{-1}\)) and no thin layer was observed (Fig. 2f). In July, nighttime cooling intensified but daytime heating still dominated the net heat budget. Maximum wind speeds of \(>5\) m s\(^{-1}\) were observed on the 19th (Fig. 2b). The water column was thermally stratified from the surface (\(N\approx 0.02\) s\(^{-1}\)), and a strong thermocline extended from 7 to 17 m depth with maximum stratification (\(N_{max}= 0.075\) s\(^{-1}\)) at 9 m depth (Fig. 2d, e). A ~2 m thick, vertically symmetric thin layer of chl-a (max. 30 μg L\(^{-1}\)) occurred at 13 m, 4 m below the stratification maximum (Fig. 2f). In October, nighttime cooling was prominent and daytime heating had weakened. The relatively low wind speeds (2 m s\(^{-1}\)), increased on 4 October (6 m s\(^{-1}\), Fig. 2c). A homogeneous SML, not observed in the previous surveys, extended down to 10.5 m depth, and rested on an even sharper thermocline (\(N_{max} \approx 0.1\) s\(^{-1}\) at 11.5 m depth, Fig 2d, e). A weaker chl-a maximum (13 μg L\(^{-1}\)) was observed at ~12 m depth coinciding with maximum N. The chl-a peak had broadened (4.5 m) to become asymmetric with a sharp upper edge (Fig. 2f).
April data gave elevated \(\varepsilon\) values of \(2 \times 10^{-7}\) W kg\(^{-1}\) in the upper 8 m. Below this depth, \(\varepsilon\) dropped sharply to very low values (\(\le 10^{-10}\) W kg\(^{-1}\); Fig. 3a). In July and October, \(\varepsilon\) showed a similar vertical distribution, with larger values between \(4\times 10^{-9}\) and \(4\times 10^{-8}\) W kg\(^{-1}\) in the upper 14 m, and a second maximum in the depth range of the main thermocline (10–13 m). From the base of the main thermocline, \(\varepsilon\) decreased to \(10^{-10}\) W kg\(^{-1}\) at 25 m depth.
The Thorpe scale, \(L_T\), describing the size of turbulent overturns, was 1–3 cm in the upper 10 m during April and gradually increased with depth to up to 10 cm at 20–25 m depth (Fig. 3b). In this deeper layer, \(L_T\) was similar to the Ozmidov scale (\(L_O\)), but \(L_O\) was 10 times larger than \(L_T\) in the upper 10 m. In July, \(L_T\), was ~3 cm in the upper 5 m but exhibited smaller thickness below (\(L_T = 1\) mm to 1 cm). During this sampling, \(L_O\) was also about one order of magnitude larger than \(L_T\) throughout the water column. October data gave relatively large \(L_T\) and \(L_O\) values (10 cm to 1 m) that resembled each other in the upper 12 m. These declined sharply below 12 m to the order of \(\sim\)1 cm with \(L_T\) being generally smaller than \(L_O\).
April data gave a buoyancy Reynolds number of \(Re_b>100\) in the upper 8 m indicating energetic turbulence (Fig. 3c). At greater depths, \(Re_b<15\), except for a local peak at 12 m. Smaller values of \(Re_b<15\) indicate that turbulence is buoyancy-suppressed (Ivey and Imberger 1991; Bouffard and Boegman 2013). In July, \(Re_b\) exceeded 100 in the upper 5 m but declined rapidly below this depth to \(Re_b<15\) in deeper layers. October data showed a sharp transition for \(Re_b\) at 11 m depth from high values (\(Re_b \approx 1000\)) in the SML to molecular values within the thermocline.
The turbulent heat diffusivity (\(K_T\) in Eq. 2) followed the same vertical distributions as those exhibited by \(Re_b\) for the three sampling dates (Fig. 3d). \(K_T\) approached (April) or fell below (July, October) molecular levels in the depth range where \(Re_b \lesssim 15\), including the metalimnion. April and July data gave moderate \(K_T\) values (\(10^{-5}\) m\(^2\) s\(^{-1}\)) in the upper ~ 7 m, while October data gave large values (~10\(^{-2}\) m\(^2\) s\(^{-1}\)) in the SML.
Turbulence statistics in the plankton layer
Figure 4 and Table 1 show probability distributions and mean values for turbulence-related parameters derived from the microstructure profiles within the chl-a maximum during July and October 2018. The vertical extent of the layer was defined as the depth range where chl-a exceeded the e-folding fraction of the maximum (chl-a > max (chl-a)/e). This range should contain \(85\%\) of the layer biomass assuming a Gaussian distribution.
In July, energy dissipation rates ranged over three to four orders of magnitude (\(\varepsilon\) from \(10^{-10}\) to \(10^{-6}\) W kg\(^{-1}\)) within the depth range of the thin layer (11.75–14.25 m, Table 1; Fig. 4a). This parameter followed a lognormal distribution slightly skewed towards high values. As a consequence, the mean values for \(\varepsilon\) of \(1.8 \,[1.6-3.4] \times 10^{-8}\) W kg\(^{-1}\) (\(90\%\) confidence intervals in brackets) exceeded median values (\(0.99 \times 10^{-8}\) W kg\(^{-1}\)). It is worth noting that only about \(42\%\) of the fits to the Kraichnan spectrum met the quality criteria. This indicates that the shape of the temperature gradient spectra was possibly influenced by fine structures under the strongly stratified conditions (Gregg 1977; Luketina and Imberger 2001). In October, the \(\varepsilon\) distribution centered on smaller values (median \(0.12 \times 10^{-8}\) W kg\(^{-1}\), mean \(0.25 \,[0.21-0.78] \times 10^{-8}\) W kg\(^{-1}\)) but also exhibited a small number of outlying peaks of large values (\(>10^{-8}\) W kg\(^{-1}\)). These suggest a sharp vertical gradient for \(\varepsilon\) within the plankton layer (Fig. 3a). Nearly half of the fits (\(47\%\)) from the October data failed to meet the goodness of fit criteria.
The Ozmidov length-scale (\(L_O\)) exhibited a tight symmetrical distribution for July and October with respective median values of 1.3 and 0.60 cm, and respective mean values of \(1.4\,[0.70-1.50]\) cm and \(0.66\,[0.31-0.68]\) (Table 1; Fig. 4b). However, \(L_T\) was 0 for ~90\(\%\) of the datapoints indicating that overturning motions were undetectable (the median of \(L_T\) was zero in both samplings). When detectable, the Thorpe scale tended to fall below the Ozmidov scale, i.e., \(L_T<L_O\). For typical overturns detected (\(L_T>0\)) in July and October, \(L_T\) equaled \(0.23\,[0.14-0.35]\) cm and \(1.5\,[0.7-2.8]\) cm, respectively. The \(\varepsilon \approx 10^{-8}\) W kg\(^{-1}\) gives a Kolmogorov length-scale on the order of 3 mm. This estimate approaches the size of the detected overturns in July suggesting effective damping by viscous forces.
Within the thin layer, \(Re_b <15\) was found for \(87\%\) and \(99\%\) of the samples for July and October, respectively (Fig. 4c). July and October data gave median values of 4.8 and 0.86 and mean values of \(8.2 \,[7.1-14.9]\), and \(1.3 \,[1.2-2.8]\) indicating that non-turbulent, molecular fluxes prevailed. Estimated \(K_T\) distributions for July (median: \(0.04 \times 10^{-7}\) m\(^2\) s\(^{-1}\), mean: \(0.12 \,[0.10-0.31]\times 10^{-7}\) m\(^2\) s\(^{-1}\)) and October (median: \(0.06 \times 10^{-7}\) m\(^2\) s\(^{-1}\), mean: \(0.71 \,[0.39-7.40]\times 10^{-7}\) m\(^2\) s\(^{-1}\)) agreed with the former estimates indicating that turbulent mixing did not enhance molecular heat fluxes.\(^2\)
Short-term variability
Microstructure profiles measured on a repeated basis established patterns of some short-term temporal variability in turbulence and chl-a profiles. Figure 5 shows this variability for the days of 19 July and 4 October, when winds reached relatively high speeds (~5 m s\(^{-1}\), Fig. 5a, f). For the July date, the isothermals remained mostly flat during the 5 h of sampling (Fig. 5a–e) indicating weak internal wave activity. The P. rubescens layer persisted unperturbed between the 8 and 18 ºC isotherms of the thermocline (Fig. 5e). Despite moderate wind speeds, the Monin–Obukhov length-scale (\(L_{MO}\)) characterising the penetration of wind mixing below the surface remained shallow (\(<5\) m) due to the stabilizing heat flux. The \(\varepsilon\) distribution showed little variation around the mean estimate for the profile (Fig. 5b; blank spaces represent rejected fits for the theoretical temperature-gradient spectrum). The upper 10 m showed some variability with turbulent patches having \(\varepsilon \approx 10^{-7}-10^{-6}\) W kg\(^{-1}\). The \(L_T\) record illustrates the scarcity and small size of overturns within the main thermocline (empty bins represent \(L_T = 0\) in Fig. 5c). In the upper 10 m, estimates of \(L_T \approx 10\) cm showed very little variation. Below 15 m depth, intermittent turbulent patches with \(L_T \gtrsim 10\) cm occasionally appeared. Vertical diffusivity (Fig. 5d) approached or fell below molecular levels throughout the day except in the relatively turbulent patches of the upper SML, but none the turbulent patches reached the P. rubescens layer (Fig. 5d). The profiles collected on 18 July, a day of lower wind speeds, showed even weaker variability (Fig. S3).
Conditions varied more in October when early morning profiles captured the transition from nighttime cooling to daytime heating and wind speeds increased during the morning (Fig. 5f). Over the 6 hours of sampling, the thermocline rose gradually by 2 m (Fig. 5g–j) indicating likely a basin-scale response to enhanced winds. The chl-a maximum appeared between the 8 and 18ºC isotherms and tracked a stable upwards movement (Fig. 5j). Estimates of turbulence remained relatively uniform between the upper part of the SML and the top of the P. rubescens layer until 9am. These indicated moderate levels of mixing with \(\varepsilon \approx 10^{-8}-10^{-7}\) W kg\(^{-1}\), \(K_T \approx 10^{-2}\) m\(^2\) s\(^{-1}\) and large turbulent overturns \(L_T>1\) m (Fig. 5g–l). With the onset of warming, \(L_{MO}\) diminished (\(<5\) m), overturns decreased (\(L_T<1\) m) and \(\varepsilon\) and \(K_T\) declined, particularly in the lower part of the SML. As a result of the relatively strong winds, \(\varepsilon\) and \(K_T\) remained large in the upper SML down to 7–8 m depth. This daytime wind-driven sub-surface mixing however did not reach the thermocline or cyanobacterial layer.
High-resolution mooring observations within the thermocline
The high-resolution measurements by moored instruments revealed high-frequency internal wave variability not captured by the profilers. The patterns detected included cm-scale vertical internal wave-driven isothermal displacements and velocities on cm s\(^{-1}\) scales (Fig. 6). In July, the sampling range (10.84–12.9 m depth) spanned a region included in the main thermocline with a relatively uniform and pronounced temperature gradient (roughly 3.5 °C over 2.5 m; Fig. 6a, b). The overall amplitude of fluctuations in current velocities and isothermal displacements varied little during the 8-h deployment. In October, the sampling range (10.13–12.19 m depth) included part of the SML at the beginning of the deployment. Measurements detected only the upper, sharper edge of the P. rubescens layer, located between the 18ºC and 15ºC isotherms (Fig. 6e, f). For the first two hours, background currents were relatively weak with no fluctuations of the isotherms. After 10:30, current velocities increased gradually, and high-frequency fluctuations commenced. The intensification (up to a maximum of 5 cm s\(^{-1}\) at about 13:00) coincided with an expansion of the pycnocline such that it occupied the whole sampling range by the end of the deployment. This event likely reflects rising winds that morning, which also appeared in the microstructure profiles.
Horizontal flow velocities documented vertical structure within a narrow, meter-scale range during both deployments. The shear in the mean flow (\(S^2 = (\partial u / \partial z)^2 + (\partial v / \partial z)^2\)) can trigger shear instabilities to drive turbulence and mixing if it overcomes the stabilizing effect of stratification. This situation occurs when the gradient Richardson number (\(Ri = N^2/S^2\)) falls below the critical value of 1/4 (Miles 1961). High-resolution measurements show that, despite the existence of background shear, unstable Ri were not often obtained, due to the strong stratification. Specifically, conditions in July and October met stable criteria (\(Ri>1\)) \(88\%\) and \(80\%\) of the time (Fig. 6c, g). Furthermore, most unstable values occurred in October within the weakly-stratified SML. These exerted little effect on the thermocline, where the P. rubescens layer occurred.
Energy dissipation rates derived from turbulent velocity fluctuations using structure functions ranged between \(10^{-10}\) and \(10^{-7}\) W kg\(^{-1}\) in July and rose to values on the order of \(10^{-10}-10^{-6}\) W kg\(^{-1}\) during October (Fig. 6d, h). In July, \(\varepsilon\) exhibited intermittent structure between calmer (from 10:30 to 11:00 and between 12:00 and 13:00) and more dissipative conditions. The periods of lower dissipation took place under conditions of reduced vertical shear when \(Ri<1\) events were not detected (Fig. 6c). In October, \(\varepsilon\) began with weak values during the first 2 h, when internal wave activity was weak and strengthened thereafter. The average \(\varepsilon\) was \(1.4 \,[1.4-1.5] \times 10^{-8}\) W kg\(^{-1}\) (median: \(0.91 \times 10^{-8}\)) and \(6.8 \,[6.3-7.3] \times 10^{-8}\) W kg\(^{-1}\) (median: \(2.9 \times 10^{-8}\)) for July and October, respectively. Table 1 lists these values as well as their respective ranges. The values in July showed very good agreement with microstructure estimates for the same depth range (Fig. 3a). Values derived for \(L_O\) and \(Re_b\) also resembled those derived form profile observations (Table 1). In October, high-resolution velocities gave somewhat larger values for \(\varepsilon\), but, \(Re_b\) remained in the range indicating a molecular regime (mean \(21\,[19-23]\), median: 10).
Nighttime sampling: the role of convective mixing
The asymmetric vertical distribution of chl-a in October and enhanced turbulence during the early morning of 4 October 2018 (before solar heating outpaced heat lost) suggest that convective mixing in autumn could potentially disrupt the P. rubescens layer and cause the decline observed in the long-term data (Fig. 1). It was not possible to test this idea with the 2018 dataset, since daytime measurements do not capture layer dynamics during fully developed convective mixing.
To overcome this limitation, a nighttime survey was conducted with a microstructure profiler, a CTD and a FluoroProbe between 14:40 UTC (16:40 local) on 24 September 2019 and 10:40 on 25 September 2019 (Fig. 7). This field campaign occurred under conditions of low wind speeds (2 m s\(^{-1}\)) and moderate heat loss (Fig. 7a). Observations recorded a 10 m SML with \(T = 18\) °C and a sharp pycnocline between 10 and 15 m depth (Fig. 7b). Consistent with the previous results, data failed to provide good fits to the theoretical temperature-gradient spectrum for the thermocline. As a consequence, \(\varepsilon\) could not be determined in several instances (Fig. 7b). Turbulent overturns were rare (Fig. 7c), and vertical diffusivity approached or fell below molecular values (Fig. 7d). The SML, below the Monin-Obukhov depth gave initially low values for \(\varepsilon\) (\(10^{-10}\) W kg\(^{-1}\)) with \(L_T<1\) m and \(K_T\) approaching molecular scale. After 17:00, a mixing layer with enhanced \(\varepsilon\) (\(2\times 10^{-8}\) W kg\(^{-1}\)), \(L_T\) (\(>1\) m) and \(K_T\) (\(>10^{-4}\) m\(^{2}\) s\(^{-1}\)) penetrated beneath \(L_{MO}\). At about 21:00, the mixing reached the thermocline, which also deepened slightly overnight. The intensity and downward penetration of the convective mixing declined after 04:00 and completely ceased after sunrise when the heat flux was negative (into the lake).
Figure 8 shows effects of convective mixing on P. rubescens distribution as determined by the FluoroProbe measurements. The initial profiles in the early afternoon (14:40) are plotted in light blue in every panel for clarity, and bars representing the \(L_T\) are included to illustrate the vertical extent and intensity of mixing. Planktothrix rubescens appears as a well defined peak in the afternoon and at relatively low concentration in the SML. Overnight, convection reached the top of the thin layer. The maximum P. rubescens layer concentration progressively declined and the community’s concentration in the SML increased due to filament entrainment by convective plumes eroding the layer from above. These results clearly show the disruptive effect of nighttime convection on the structure of the P. rubescens metalimnetic layer in early autumn.