Stratification stability of tropical lakes and their sensitivity to climate

Abstract

Tropical lakes experience less thermal convection than temperate lakes and can be stably stratified by temperature gradients alone. Deep tropical lakes are often presumed meromictic, but conditions for sustained meromixis are poorly constrained. Here, we investigate the stratification stability of a deep (200 m) tropical Lake Towuti (Indonesia) and analyze its sensitivity to meteorological and climatic parameters using exploratory hydrodynamic simulations. The inferred effects on water chemistry are further evaluated with a reactive-transport biogeochemical model. In contrast to the previous assumption of meromixis, our results suggest that in 2008 Lake Towuti experienced mixing over most of its water column, with the attendant weak oxygenation of the previously anoxic lower strata. The lake likely remained stratified afterwards, but the chemical distributions measured after the episode, particularly during the International Continental Scientific Drilling Program in 2015, were out of steady state, and may be still evolving in time. We find the thermal stratification to be most sensitive to average air temperatures and wind speeds and predict further stabilization of the lake by climate change. We also describe a negative feedback mechanism that can stabilize oligomictic tropical lakes for a number of years after the episodes of mixing and cooling, and infer that such episodes should be significantly less frequent in deeper lakes.

Most water bodies stratify vertically some of the time (Boehrer and Schultze 2008). The developed density gradients restrict vertical movements of chemicals, as well as organisms, and restrict oxygen supply to bottom waters (Schultze et al. 2017). Permanent stratification (meromixis) in lakes is a special case of this phenomenon. Prolonged stratification leads to anoxic conditions at depth. This allows reduced chemical compounds to build up in bottom waters, eliminates sediment reworking by macrofauna, slows down microbial degradation of organic material, and affects the way minerals and biomarkers are preserved in sediments. Under sulfate-replete conditions, accumulated reduced substances are dominated by hydrogen sulfide (euxinia). In a subset of meromictic lakes, however, notably including the Indonesian Lake Matano (Crowe, Jones, et al. 2008), anoxic conditions lead instead to the accumulation of dissolved ferrous (Fe²⁺) iron and methane (CH₄) (Crowe et al. 2011). The relationship between meromixis and iron accumulation has historically captivated the interest of limnologists (Kjensmo 1962). These lakes have recently acquired importance as analogue systems for studying the biogeochemistry of early Earth (Swanner et al. 2020). Iron-rich (ferruginous) conditions are rare today, but were the dominant feature of the world's oceans through most of the Earth's geologic history (Poulton et al. 2004).

Deep tropical lakes are more likely than their temperate counterparts to stabilize based on their thermal gradients alone (thermogenic meromixis; Katsev et al. 2010, 2017). At temperatures much higher than the temperature of maximum density (4°C), strong density gradients can be generated by relatively small temperature differences. Lakes such as the East African lakes Malawi (Li et al. 2018) and Tanganyika (Verburg and Hecky 2009), or the Indonesian Lake Matano (Katsev et al. 2010), maintain stratification at only a few degrees difference between surface and bottom waters, with only minor contributions from salinity gradients (Wüest et al. 1996; Katsev et al. 2017). The weak thermal stratification could permit some exchange of substances, making it challenging to classify the lake as either traditionally holomictic or meromictic—a concern raised by Boehrer et al. (2025) in describing tropical Lake Bosumtwi. With weak seasonal and inter-annual variability, thermally driven whole water-column convection is relatively rare in the tropics (Katsev et al. 2017). The strongest mixing usually happens during the dry season, when cooler air temperatures, stronger winds, lower solar radiation, and greater evaporation cool the surface waters of the lake, creating thermal convection and homogenizing temperatures in the upper layer, which in those times of the year may extend down to 100 m in depth (Katsev et al. 2017). The waters below a permanent thermocline at the base of the surface mixed layer, however, remain mostly isolated from the atmosphere.

Some of the key questions surrounding tropical lakes revolve around the quantitative controls on lake stratification. When does a lake become permanently stratified? What magnitudes of changes in climate or other parameters may cause a lake to mix episodically or regularly? Besides the immediate applications in physical limnology, answers to such questions inform paleolimnological studies in these lakes and the corresponding inferences about contemporary environmental conditions. Ancient deep lakes located in tectonic depressions accumulate thick piles of sediments, which contain valuable records of past climates. Lake Malawi and the Indonesian Lake Towuti, in particular, have been sites of the International Continental Scientific Drilling Program, which recovered hundreds of meters of sediment, from hundreds of thousands of years ago (Russell et al. 2016). The kinds of mineralogical and biological signals preserved in sediments often strongly depend on the physical stratification of the lake at the time of sediment deposition and on the redox conditions at the lake's bottom. While it is generally acknowledged that greater depths and smaller surface-to-depth ratios increase the probability of meromixis (Swanner et al. 2020), tropical-lake-specific predictions generally have not been possible. Further questions pertain to the responses of tropical lakes to climate change. Though climate warming may be increasing surface temperatures of tropical lakes to a lesser degree than in temperate lakes (Kraemer et al. 2015), such temperature increases are predicted to significantly strengthen stratification. Higher water temperatures also decrease oxygen solubility (Jane et al. 2021), exacerbating anoxia.

For many tropical lakes where aquatic monitoring data are scarce, inferring physical dynamics of the lake is only possible from indirect markers, such as sediment records. In contrast to in-lake data, however, meteorological data are more widely available or, in the absence of direct on-site measurements, can be approximated from climate reanalysis products. Hydrodynamic lake models can potentially link the meteorological conditions at the water–air interface to the ensuing conditions within the water column. Such usage of hydrodynamic models has been rare so far. In a typical application, simulations are tethered to an observational time series, which are often used to iteratively correct model parameters to obtain a better fit to the data. In the absence of instrumental data, however, using the model in an exploratory fashion can help develop qualitative knowledge of the system behavior. Performing a sensitivity analysis on a spectrum of model solutions is a way to elucidate the likely responses of the lake to environmental forcing.

Here, we investigate the physical stratification and dynamics of the 200 m deep tropical Lake Towuti using a hydrodynamic model, and further explore the model outputs to infer the sensitivity of tropical lakes to climate change. We then couple the physical model to a reaction-transport biogeochemical model to analyze the effects of physical dynamics on chemical distributions, and test the inferred dynamics against the geochemical data in Lake Towuti.

Background on Lake Towuti

Lake Towuti (2.75°S, 121.5°E) is the largest lake in the Malili Lake system on the Sulawesi island of Indonesia (Vaillant et al. 2011), which also includes Lake Matano. Lake Towuti is more than 1 million years old (Vuillemin et al. 2022). With an area of 560 km² and maximum depth of 200 m (Fig. 1), it lies in ophiolitic rocks and is surrounded by lateritic soils (Lehmusluoto and Machbub 1997). The catchment area is around 4500. Despite significant rainfall, annual fluctuations in the water level of the lake are within 1 m (Sulistioadi et al. 2015). Lake Towuti's equatorial climate is characterized by nearly constant air temperatures of around 25°C. The dry season lasts from July to October and typically has higher wind speeds and lower air temperatures. The wet season lasts from November to May and is hotter and more humid (Russell et al. 2020). Located in the center of Indo-Pacific Warm Pool, the Sulawesi Island is highly likely to be influenced by decadal climate variations, including the El Niño–Southern Oscillation (Russell and Bijaksana 2012).

Fig. 1

Relative location of the Malili lake system in Sulawesi and Lake Towuti and Matano bathymetry. Modified from Russell et al. (2020).

Like Lake Matano (Katsev et al. 2010), Lake Towuti is stratified primarily by the temperature gradient of only a few degrees Celsius. The temperature difference between surface and bottom waters varies seasonally between 0.5 and 3.5°C (Costa et al. 2015), with only a weak salinity gradient, as indicated by conductivity, temperature, and depth measurements (see Supporting Information Fig. S1). This weak salinity gradient has a minimal impact on the density gradient in Lake Towuti (see Fig. S2) A persistent thermocline is located at around 70 m depth. The physical separation of the bottom waters leads to a strong chemical stratification. Oxygen is depleted below 120 m, and dissolved iron accumulates below 180 m (Costa et al. 2015). Iron concentrations ($$$ \sim $$$ 10 μM) in Lake Towuti are notably lower than in Lake Matano ($$$ \sim $$$ 140 μM). The maximum measured concentrations of hydrogen sulfide were similar in the two lakes (at low μM level), but the available vertical profiles in Lake Towuti show a significant overlap between the depth intervals containing Fe²⁺ and H₂S (Bauer et al. 2020), whereas in Lake Matano they appear to be better separated (Crowe, Jones, et al. 2008).

The Lake Towuti Drilling Project provided information on the paleoenvironment of the lake (Russell et al. 2016). Paleoclimate proxies suggest that the lake has experienced a substantially lower water level during the Last Glacial Maximum between c.a. 29 and 16 kya (Vogel et al. 2015), which reduced the hydrological connectivity with other Malili lakes (Costa et al. 2015). Abundant red siderite clay suggested that the lake was mixing regularly during that period and had abundant oxygen throughout the water column (Russell et al. 2020). Other evidence of the lake's change in mixing status includes variation of the biota. Ageli et al. (2022) suggests that Lake Towuti was once dominated by productive planktonic communities. However, under modern conditions, the primary production is strongly limited. Physical stratification plays a role in this phenomenon. The abundance of iron (hydr)oxides limits surface phosphorus concentration, and the stable stratification blocks nutrient supply towards surface plankton communities, thus limiting the primary production. Lake Towuti's surface primary production is probably similar to that of Lake Matano, where it is estimated at around $$$ 3.8\times {10}^{-3}\ \mathrm{mol}\;\mathrm{C}\ {\mathrm{m}}^{-2}{\mathrm{d}}^{-1}\ \left(16.6\ \mathrm{g}\ \mathrm{C}\ {\mathrm{m}}^{-2}\ {\mathrm{yr}}^{-1}\right) $$$ (Crowe, Jones, et al. 2008), an unusually low value for an equatorial lake (Alin and Johnson 2007).

Methods

Temperature and chemical measurements

Temperature and conductivity distributions in the water column of Lake Towuti were measured on several occasions between 2000 and 2014 using profiling instruments RBR XL-200 (1997), RBR XL-410, and Sea-and-Sun 90M. The XL-200X instrument was calibrated to be accurate within 0.1°C with the National Institute of Standards and Technology-traceable temperature standard. The 12-bit analogue-to-digital converter caused the temperature readings to be measured in steps of 0.072°C. The XL-410 instrument had similar accuracy and precision but measured temperature in steps of 0.01°C. XL-410 conductivity measurement had accuracy of $$$ \pm $$$ 0.003 mS cm⁻¹ with a resolution of 0.001 mS cm⁻¹. The instruments were programmed to take measurements at 3-s intervals as the probes were lowered and brought back up through the water column resulting in readings at every 2 m depth on average. Temperature measurements were also available between August 2012 and March 2015 from a mooring deployed in the lake during that period (Costa et al. 2015).

Oxygen was measured in 2013 with the Sea-and-Sun 90M probe with a clarc electrode, which has accuracy of $$$ \pm $$$ 0.003% saturation, and resolution of 0.1% oxygen saturation.

Samples for Fe measurements were collected using a syringe directly from a Niskin bottle spigot without exposure to the atmosphere to avoid Fe oxidation, and were filtered immediately through a 0.2 μm pore size (Supor membrane, Acrodisc) syringe filter into HCl for a final acid concentration of 2%. Fe(II) concentrations were determined according to a modified version of the classic spectrophotometric ferrozine method (Viollier et al. 2000).

Samples for sulfide and sulfate measurements were collected using a syringe directly from a Niskin bottle spigot without exposure to the atmosphere to avoid sulfide oxidation, and were filtered immediately through a 0.2 μm pore size (Super membrane, Acrodisc) syringe filter into zinc acetate for a final zinc acetate concentration of 0.1%. Sulfide concentrations were determined spectrophotometrically (Cline 1969). Sulfate concentrations were determined by ion chromatography using a Dionex ICS-2100 instrument equipped with a Dionex AS 18 analytical and MFC-1 trap column.

Hydrodynamic modeling

We investigate the physical properties of Lake Towuti with a dynamic one-dimensional hydrodynamic model Simstrat 3.0 (Goudsmit et al. 2002). This $$$ k-\epsilon $$$ model previously generated adequate results for vertical temperature profiles and thermocline positions in deep stratified lakes, in temperate (Gaudard et al. 2019) as well as tropical settings (Thiery et al. 2014; Bärenbold et al. 2022). Lake-specific input parameters include bathymetry, initial distributions of temperature and salinity, light attenuation, and hydrological flows (see Supporting Information section “Simstrat simulations setup”). Some model parameters, such as the ratio of wind energy going into seiche energy, $$$ {\alpha}_S $$$, and the fractionation coefficient for seiche energy, $$$ {q}^{NN} $$$, could not be directly determined from observations in Lake Towuti, due to lack of long-term continuous observational data in the water column; default Simstrat values were used (Lake Zurich 2021 test case).

Meteorological forcing data at the lake surface were obtained at hourly resolution from ERA5 reanalysis (Hersbach et al. 2020), for 121.4°E, 2.75°S. Forcing variables included wind velocity, surface air temperature, incoming solar radiation, vapor pressure (calculated from relative humidity, air temperature, and air pressure), and cloud cover. In the absence of direct meteorological measurements at the lake, a comparison was made against the weather stations in Kendari (166 km away) and Palu (approx. 300 km away) (see Supporting Information Fig. S4). Model parameters $$$ {p}_{\mathrm{sw}\hbox{-} \mathrm{water}} $$$ and $$$ {p}_{\mathrm{lw}} $$$ for the absorption of shortwave and longwave radiation were used as adjustment parameters to make the simulated surface temperatures approximate the conductivity, temperature, and depth data (see Supporting Information Table S1). This was similar to the process used by Bärenbold et al. (2022) in Lake Kivu and Gaudard et al. (2019) in Swiss lakes to correct for differences between the weather over the lake and at measurement stations. In our study, the adjustment compensated for differences between the over-lake weather and the ERA5 reanalysis data.

The outcomes of the hydrodynamic simulations were characterized with several calculated quantities that describe the strength of stratification and the propensity of the lake to whole-water-column mixing:

The weakest temperature difference ($$$ \mathrm{WTD} $$$) was defined as the smallest temperature difference in the water column in the entire simulated time series:

$$$$ \mathrm{WTD}=\underset{t}{\min}\left[\underset{z}{\max}\left(T\left(z,t\right)\right)-\underset{z}{\min}\left(T\left(z,t\right)\right)\right] $$$$ (1)

The quantity in the square brackets is the difference between the maximum and minimum temperatures in the water column at any given time, typically between the lake surface and bottom. A $$$ \mathrm{WTD} $$$ of zero would correspond to a homogeneous temperature distribution throughout the water column at least once during the simulation, indicative of whole-water column mixing.

The maximum buoyancy frequency ($$$ \mathrm{MBF} $$$) is the maximum Brunt–Väisälä stability frequency squared ($$$ {N}^2 $$$) anywhere in the water column. It characterizes the strength of the density gradient in the thermocline achieved during the simulation run:

$$$$ \mathrm{MBF}=\underset{z,t}{\max}\left[{N}^2\left(z,t\right)\right] $$$$ (2)

Resistance of lakes to mixing is often characterized by Schmidt Stability, which is commonly defined as the difference in potential energy between the lake with its current density gradient and a hypothetical fully mixed lake (Idso 1973). For our purposes, we define a depth-dependent stability, $$$ S\left({z}_d\right) $$$, which corresponds to a similarly defined difference in potential energy per unit area in a depth range between the lake surface and some depth $$$ {z}_d $$$ (Katsev et al. 2014, 2017).

$$$$ S\left({z}_d\right)=\frac{g}{A_0}\kern0.5em {\int}_{z={z}_d}^{z=0}\left(z-{z}_g\right)\kern0.5em A(z)\kern0.5em \left(\rho -\overline{\rho}\right)\kern0.5em dz $$$$ (3)

Here, $$$ {A}_0 $$$ is the lake surface area, $$$ A(z) $$$ is the areal extent at depth $$$ z $$$, $$$ {z}_g $$$ is the depth of the center of the mass:

$$$$ {z}_g=\frac{\int_{z={z}_d}^{z=0}\rho \kern0.5em A(z)\kern0.5em z\kern0.5em dz}{\int_{z={z}_d}^{z=0}\rho \kern0.5em A(z)\kern0.5em dz} $$$$ (4)

and $$$ \overline{\rho} $$$ is the average density of the water column:

$$$$ \overline{\rho}=\frac{\int_{z={z}_d}^{z=0}\rho \kern0.5em A(z)\kern0.5em dz}{\int_{z={z}_d}^{z=0}\kern0.5em A(z)\kern0.5em dz} $$$$ (5)

Similarly, depth-dependent heat content, $$$ \mathrm{HC}\left({z}_d\right) $$$, is defined as the thermal energy stored from a certain depth $$$ {z}_d $$$ to the surface.

$$$$ HC\left({z}_d\right)=\frac{1}{A_0}{\int}_{z={z}_d}^{z=0}\rho \kern0.5em {c}_w\kern0.5em \left(T-{T}_0\right)\kern0.5em A(z)\kern0.5em dz $$$$ (6)

Here, $$$ {T}_0 $$$ is an arbitrary reference temperature (e.g., the temperature at $$$ z={z}_d $$$), and $$$ {c}_w=4200\kern0.5em \mathrm{J}\kern0.5em {\mathrm{kg}}^{-1{}^{\circ}}{\mathrm{C}}^{-1} $$$ is the specific heat of water.

These two quantities, $$$ S\left({z}_d\right) $$$ and $$$ \mathrm{HC}\left({z}_d\right) $$$, have units of kJ m⁻², and show the minimum mechanical energy required to mix the water column till depth $$$ {z}_d $$$, and the total heat content between surface and $$$ {z}_d $$$, respectively. By comparing these two quantities with the surface heat fluxes and mechanical energy fluxes, we can identify whether the lake is mixed by mechanical energy or by heat removal. To eliminate the effects of the initial spin-up period for the model, the first year of the simulation was excluded from the calculations of all stratification indicators.

Sensitivity analysis

The sensitivity of the lake stability to climate variables was tested using a Monte Carlo method. Multiple climate variables on model input were varied randomly and simultaneously, for 100 model realizations. Meteorological forcing variables were drawn from normal distributions that reflected their realistic ranges (see Supporting Information Table S2). We did not attempt to account for co-variations of the variables, which would cause deviations from independently chosen normal distributions. Individual simulation runs were characterized by their $$$ \mathrm{WTD} $$$ and $$$ \mathrm{MBF} $$$ values, which were then compared.

Biogeochemical modeling

To elucidate the effects of mixing dynamics on lake biogeochemistry, the simulated hydrodynamic solutions were used in a reaction-transport chemistry model. A one-dimensional dynamic reactive-transport model was constructed as described in Pu (2023). The physical transport in the model was described by the vertical eddy diffusivity ($$$ {K}_z $$$) computed by Simstrat. As coupling the biogeochemical model with the time- and depth-varying $$$ {K}_z $$$ proved to be computationally challenging, we investigated two contrasting simpler scenarios (Fig. 2) that reveal the characteristic time scales of the chemical dynamics, though not its exact evolution. The “stable stratification” scenario used a typical time-averaged profile of $$$ {K}_z $$$ over a period of prolonged stratification. The corresponding $$$ {K}_z $$$ values were approximated to match the observed ranges during the 2003 dry and wet seasons (Fig. 2). The “mixing scenario” used the $$$ {K}_z $$$ profile characteristic of the brief period of enhanced mixing, such as during the inferred 2008 mixing event. The values of $$$ {K}_z $$$ for this scenario were approximated after the 2008 dry season simulation. To avoid excessive numerical stiffness, the obtained profiles of $$$ {K}_z $$$ were further approximated using analytical expressions (see Supporting Information Eq. 7), which spanned over the range of temporal variability in $$$ {K}_z $$$, as shown in Fig. 2.

Fig. 2

Typical stratification (left) and mixing (right) $$$ {K}_z $$$ profiles extracted from the hydrodynamic model (square and circular markers) and their corresponding analytical approximation (solid line) used in the biogeochemical model.

To mimic the dynamic changes in lake stratification using time-constant $$$ {K}_z $$$ profiles, simulations were performed as follows. First, the “stable stratification” scenario was applied starting from oxic initial conditions for 36 yr, which was sufficient for the bottom water to become anoxic for at least 10 yr and for reduced chemical species to accumulate there. Then, the “mixing” scenario was applied for 2 months (corresponding to the typical duration of mixing in hydrodynamic simulations). The “stable stratification” scenario was then applied again for 7 yr. This allowed us to obtain the typical temporal and concentration scales for the accumulation and consumption of oxygen in the deep waters of Lake Towuti, and the accumulation and reoxidation of the reduced chemical species, such as H₂S and Fe²⁺.

Results

Stratification dynamics in Lake Towuti

Hydrodynamic simulations reproduced the general features of stratification in Lake Towuti: a permanent thermocline around 60–80 m depth and a seasonal thermocline during the wet season around 20–30 m depth (Fig. 3). The simulated temperatures at the lake surface ($$$ <{31}^{{}^{\circ}}\mathrm{C} $$$) and near the bottom (around 28°C) were within 1°C of their observed values, which we deem to be sufficiently in agreement, given the uncertainties in the input meteorological data and the absence of continuous calibration data to correct for any numerical drift. Compared to the observations from a 2012–2015 mooring deployment (Costa et al. 2015), the model slightly underestimated surface water temperatures and overestimated the depth of the thermocline (Fig. 4).

Fig. 3

Temperature distributions and evolution in Lake Towuti simulated using the unmodified ERA5 reanalysis meteorological data as model input. Contour lines emphasize temperature differences that are challenging to discern with the color gradient alone. Black dotted lines represent the 28.5°C contour, highlighting the seasonal thermocline. The gray dashed contour (28.12°C) illustrates the temperature evolution of the bottom water between 2003 and 2007, a period when no prominent permanent thermocline was present. The white solid contour, representing 27.85°C, marks the establishment of a permanent thermocline following whole-water column mixing in the lake.

Fig. 4

Temperature measurements (blue dots) from conductivity, temperature, and depth (CTD) and mooring instruments, and the simulated temperatures (red lines) for the same dates. Error bars represent the mooring instruments accuracy of 0.2°C. The two mooring profiles were selected to represent typical wet (e.g., February) and dry (e.g., July) seasons. A comprehensive mooring comparison is provided in Fig. S3.

Simulated dynamics reveal the possibility of one or more full water column mixing events over the period from 2000 to 2009, indicated in Fig. 3 by homogenized temperature distributions extending over most of the water column. Based on the model results, mixing events may have occurred in 2001 and 2002. The strongest mixing event is predicted to have happened during the 2008 dry season: The lake started to experience mixing during the 2007 dry season. After a period of stratification during the 2007–2008 wet season, the lake experienced strong circulation during the 2008 dry season. The water temperature significantly decreased, including in the deep waters, driven by strong removal of heat at the lake surface. The bottom water temperature during the 2008 dry season may have decreased by almost half a degree, from 28°C to 27.5°C. Following the event, stratification remained stable until the end of the simulated period, with surface temperatures exhibiting a warming trend and the downward diffusion of heat leading to gradual deepening of the permanent thermocline to around 100 m.

Conductivity, temperature, and depth (CTD) and mooring profiles (Fig. 4) record a similar decrease in bottom water temperature between 2006 and 2009. Bottom water trends recorded at discrete times by instrumental data indicate cooling from 2000 to 2002 (consistent with mixing suggested by the model), warming from 2002 to 2006, a strong cooling between 2006 and 2009, and slow subsequent warming until at least 2013. Differences between the absolute values of the simulated and measured temperatures (Fig. 4) suggest that the model, while capturing the overall qualitative dynamics, may be underestimating the rate of heat transfer from mixolimnion to the deep waters.

In the sensitivity analysis, full water column mixing occurred during the simulated 2001–2008 time period in 68% of the randomized simulation runs, as indicated by zero $$$ \mathrm{WTD} $$$ values (Fig. 5). Significantly higher stability was predicted for the subsequent 2009–2016 period (Fig. 5). Air temperature had the strongest effect on the stability of stratification, followed by wind speed. Full water column mixing was predicted to happen for average wind speeds exceeding 2 m s⁻¹, or when the average air temperature dropped below 23°C (Fig. 5). For average air temperatures exceeding 27°C, the stratification was likely to persist for the entire simulation period. Higher air temperatures also led to stronger thermoclines (indicated by greater $$$ \mathrm{MBF} $$$) during peak wet seasons.

Fig. 5

Sensitivity of Lake Towuti stratification to atmospheric conditions. Maximum buoyancy frequency ($$$ \mathrm{MBF} $$$, squares) characterizes the maximum strength of the thermocline; the weakest temperature difference ($$$ \mathrm{WTD} $$$, circles) characterizes the minimum temperature difference achieved in the water column in a simulation run. They are plotted against the mean values of the meteorological variables of each simulation, whose values were randomixed in Monte Carlo simulations. Filled darker symbols correspond to the simulation period 2001–2008 and open lighter symbols correspond to 2009–2016.

Biogeochemical dynamics

Biogeochemical simulations indicate that, to establish anoxic conditions after a hypothetical complete oxygenation of the water column, stratification would need to persist for several decades (Fig. 6a). Following the depletion of oxygen, reduced substances (first H₂S, then Fe²⁺) begin to accumulate below the thermocline, reaching high μM levels in about a decade. The rates of downward oxygen transport during a weak mixing scenario, such as suggested by the hydrodynamic simulations for 2008 in Lake Towuti, however, do not lead to full oxygenation. While water is transported to deep strata from the surface, the transport is slow enough to support only minor oxygenation of the deep anoxic layers (Fig. 6b). Reduced substances decrease in concentrations, but do not necessarily disappear. The depth of oxygen penetration increases, but concentrations remain low. Upon restratification, concentrations of reduced substances increase, but the rate of their accumulation is slow enough for the concentrations to not exceed tens of micromolar for at least several years or even decades (Fig. 6c). Concentrations of hydrogen sulfide are predicted to not exceed low μM levels, while ferrous iron can eventually accumulate to higher concentrations, similar to the situation in neighboring Lake Matano (Bauer et al. 2020).

Fig. 6

Biogeochemical dynamics simulated for (a) Development of chemical stratification starting from fully oxygenated initial condition. A typical “stable stratification” $$$ {K}_z $$$ was applied over 36 yr. (b) After stratification was established, a weak mixing scenario was applied for 2 months. (c) Restratification after weak mixing. A typical “stable stratification” K_z was applied again for 7 yr. Red circles are observational data measured in 2013, several years after the hypothesized weak mixing event in 2008.

Discussion

Dynamics of stratification in Lake Towuti

If judged only by the available physical and chemical evidence in its water column, Lake Towuti seems to be meromictic: the vertical distribution of water temperature shows little variation from year to year, and the deep waters contain reduced substances, indicating persistent anoxic conditions. Even the absence of a salinity gradient—a hallmark of meromixis—is not necessarily a sign of recent mixing: a tropical lake may remain stably stratified by its weak temperature gradient for a long time, such as the neighboring 600 m deep Lake Matano (Crowe, O'Neill, et al. 2008). Salinity can also be maintained low by slow basin-scale circulation, such as in some large deep lakes (Katsev et al. 2017). The density gradient induced by the temperature differences can remain stable if heat diffusing into the deep waters from the surface is transferred into the sediments or consumed by colder groundwater inflows. Nevertheless, our simulations indicate that Lake Towuti may have experienced one or more mixing events at the beginning of the 21^st century. The strongest such event is implicated for the dry season of 2008 (Fig. 7). Toward the end of the dry season, the surface of the lake has cooled down sufficiently to sustain slow vertical circulation over the entire water column, which would promote slow exchange between the oxygenated surface waters and anoxic deep waters over a period of several weeks. Further evidence for such deep circulation in Lake Towuti is provided by conductivity, temperature, and depth profiles, which record a decrease in the bottom water temperature from 2006 to 2009 (Fig. 4). Because in a stably stratified lake without a salinity gradient heat constantly diffuses downward, the temperature of the bottom waters may decrease only through an intrusion of colder water, such as during a thermally induced mixing event from overlying waters.

Fig. 7

Stability and thermal fluxes in Lake Towuti. (a) Net heat flux across the lake surface, as simulated by the model. (b) Depth-dependent stability $$$ S\left({z}_d\right) $$$; (c) depth-dependent heat content $$$ \mathrm{HC}\left({z}_d\right) $$$. At each moment of time, HC values represent the excess heat needed to be removed to thermally mix the water column down to a given depth, while $$$ S\left({z}_d\right) $$$ characterizes the resistance to mechanical mixing due to density stratification. Note the difference in the colorbar scales between $$$ \mathrm{HC}\left({z}_d\right) $$$ and $$$ S\left({z}_d\right) $$$. (d) The time integral of the net heat flux in (a) (solid line, starting from the minimum during the 2001 dry season, set as zero), and its comparison to the resultant maximum $$$ \mathrm{HC} $$$ (the lake bottom values in (c); dash line, zero values correspond to homogeneous temperature distributions). Deviation during the 2008 dry season corresponds to cooling of the entire water column.

Simulations indicate that the 2008 mixing became possible because of a sequence of meteorological conditions that led to the removal of heat from lake surface, coupled with a relatively low heat content of the lake at that time (Fig. 7). Notably, monthly air temperatures during the 2008 dry season were substantially (by nearly half a degree) lower than typical (Fig. 7a). Humidity and wind speeds, however, were not outside of their normal range. Crucially, the period of time over which the net heat flux across the lake surface remained negative was longer that year (Fig. 7a). It also came after a sequence of two preceding years over which the overall heat content of the lake declined (Fig. 7d). Deep mixing in a deep lake like Towuti is predicated on thermal convection, with the mechanical energy of the wind becoming important only when the thermal gradient becomes very weak. The potential energy of thermal stratification is reflected by Schmidt stability, which in a typical wet season in Lake Towuti is around 5–10 kJ m⁻² (based on Fig. 7b). This is two orders of magnitude greater than the energy that can be supplied to the lake surface by wind over a period as long as a month ($$$ \sim $$$ 0.03 kJ m⁻²). In contrast, the net amount of heat removed during a typical dry season ($$$ \sim $$$ 0.3 GJ m⁻²) is very similar in Lake Towuti to the total heat content that creates the thermal gradient (Fig. 7d). In 2008, strong negative heat fluxes, persisting for somewhat longer than usual, not only have cooled the surface enough to eliminate the thermal gradient, but also persisted for long enough after that point to cool down the thus homogenized water column (Fig. 7d). In a good illustration of the importance of the integrated, rather than instantaneous, energy fluxes, the net heat fluxes during the 2010 and 2012 dry seasons reached similar strongly negative values (Fig. 7a), but that did not lead to full mixing because of the greater heat content of the lake in those years and the shorter durations of the 2010 and 2012 cooling seasons.

Following the 2008 mixing event that cooled the bottom water, Lake Towuti became more stably stratified (Fig. 7). Our simulations suggest a continuous stratification from 2009 onward, with warming of the lake surface providing the necessary temperature gradient, and the downward diffusion of heat leading to a gradual deepening of the thermocline to about 100 m (Fig. 3). The overall heat content of the lake increased in 2009 relative to the bottom water temperature baseline, and remained substantially higher in subsequent years, relative to the 2001–2008 values (Fig. 7c,d). This suggests an increased stability of the lake. While it is impossible to rule out future sequences of weather conditions that would create low heat content and high rates of heat removal leading to mixing, continued warming of the lake surface would be expected to make mixing episodes less likely in the coming years. Tropical lakes have been suggested to warm at a rate similar to that of the atmosphere, at around 0.12° per decade suggested by Katsev et al. (2014). The warming trend is also observed in global lakes (O'Reilly et al. 2015). The rate of surface warming in Lake Towuti is hard to estimate for the lack of long-term observation series, but our simulations, as well as data of Costa et al. (2015) are consistent with a long-term trend of similar magnitude.

Chemical dynamics

Biogeochemical simulations in Lake Towuti further support the possibility of mixing prior to 2009. They indicate, in particular, that the chemical distributions measured in recent years may not have been at steady state. They also provide explanation for the seemingly unusual co-occurrence of dissolved ferrous iron and hydrogen sulfide in the same strata in deep waters, as Fe²⁺ did not accumulate in Lake Towuti to as high levels as in Lake Matano, and at low μM concentrations it is less likely to precipitate with H₂S (Rickard 2006).

While in temperate lakes a complete overturn (especially when driven by thermal convection) usually implies a complete oxygenation of the water column, a slow and relatively brief vertical exchange suggested by our hydrodynamic simulations allows for a more subtle effect. Whereas a full oxygenation (to 100% saturation) would require about 30 yr to return to anoxic conditions, a < 2-month mixing period in Lake Towuti might raise the oxygen concentrations only to sub μM levels. Such slow oxygenation would be further delayed by oxygen reacting with accumulated reduced substances (of which methane would probably have the highest concentration). The water near the lake bottom may even stay completely anoxic, though the concentrations of H₂S and Fe²⁺ there would decrease (Fig. 6b). The renewed rates of their accumulation predicted for the period after the 2008 mixing event are consistent with the chemical profiles observed in 2015: in 6–7 yr, the concentrations of Fe²⁺ would increase by about 10 μM, while H₂S concentrations would remain in the low μM range. Dissolved iron and hydrogen sulfide may co-exist at those low concentrations because of the solubility of FeS complexes (Rickard 2006). Further accumulation of Fe²⁺ under continued anoxic conditions would suppress H₂S to even lower concentrations, perhaps also limiting its presence to a narrower depth interval below the oxycline (mid-water euxinia, as in other lakes reported by Crowe, O'Neill, et al. 2008; Li et al. 2018), while Fe²⁺ concentrations in deeper waters could reach hundreds of micromolar. These patterns, predicted closer to steady state, would then resemble more closely the ones currently observed in Lake Matano.

These findings are consistent with the available evidence in Lake Towuti, including information from sediments. Iron reduction in sediments leads to elevated (100 s of μM) concentrations of Fe²⁺ in porewater (Vuillemin et al. 2022) supporting diffusive fluxes of ferrous iron into the water column. Likewise, high (mM) porewater concentrations of methane (Vuillemin et al. 2022) would support significant levels of methane in the anoxic bottom waters. In Lake Matano, methane concentrations exceed those of Fe²⁺ by about 10 times (Crowe et al. 2011). The water column methane data for Lake Towuti are unavailable, however. Despite the low concentrations of hydrogen sulfide and residual sulfate, our model indicates viable populations of sulfate reducers, consistent with detectable rates of potential sulfate reduction in sediments (Vuillemin et al. 2016) and significant presence of sulfate reducers (Vuillemin et al. 2018). Though quantitative information about the concentrations of iron sulfides in sediments is not available, their inferred scarcity (Vuillemin et al. 2022) is consistent with the very limited accumulation of sulfide predicted by our model. Most of the hydrogen sulfide in the water column is consumed by an abiotic reaction with Fe(III), which produces elemental sulfur. And in sediments, at the low concentrations of sulfide produced by S⁰ disproportionation or the reduction or residual sulfate, sulfurization of organic matter may provide a competitive sink for sulfide that can limit formation of iron sulfides (Phillips et al. 2023).

The borderline stability of stratification in Lake Towuti, with subtle changes in climate potentially leading to frequent mixing (Fig. 5), indicates that the redox regime of the lake's water column has likely experienced changes over the geological history of the lake. The cooler and drier conditions during the Last Glacial Maximum, in particular, accompanied by a decrease in lake level, would certainly lead to regular mixing and a full oxygenation of the water column, as the sedimentological evidence indicates (Russell et al. 2020). This result is readily confirmed by simulations, as shown in more detail in Pu (2023).

Stratification in tropical lakes

Deep tropical lakes stratify differently from their temperate counterparts. The relative stability of meteorological conditions near the equator leads to stable temperature gradients, with surface mixed layers extending tens of meters below the surface, and extended thermoclines persisting below, as deep as 100 m or even deeper (Katsev et al. 2017). Additional thermoclines form within the surface layer seasonally (30–50 m, typically during wet seasons) and diurnally (10–20 m, during the day time), in response to the corresponding variations in solar insolation and surface heat fluxes (Katsev et al. 2010). Specific features of these patterns, however, depend on local meteorological conditions and may become modified by changes in local climate. As thermal fluxes contribute more mixing energy than wind (Imboden and Wüest 1995; Pu 2023), the strongest responses are evoked by factors that regulate the exchanges of heat across the lake surface. Most obviously, those include the air temperature and relative humidity. While commonly associated with the mechanical energy of mixing, wind speed is also one of such factors (Fig. 5), as it affects the latent and sensible heat transfers. Light penetration and biological productivity can also affect stratification: eutrophic lakes tend to absorb light near their surface, resulting in warmer and shallower, and therefore more stable, epilimnia. The depth to which the seasonal mixing extends is determined by the balance between the heat content of the lake and the heat fluxes at the lake surface. Mixing is generated when negative heat fluxes persist for a sufficiently long time, so that the mixolimnion cools down to the temperature of the underlying deep waters, eliminating the thermal density gradient. Regular or episodic mixing (oligomixis) may ventilate the deep waters well enough to prevent a buildup of salts, leaving the thermal gradient as the main factor in density stratification.

The depth of the lake is important in whether a tropical lake can become stratified for a long period of time. With thermal influences extending from surface down to $$$ \sim $$$ 100 m (Katsev et al. 2017), in the absence of a stabilizing salinity gradient, lakes shallower than about 100 m may be presumed to be susceptible to whole water-column mixing. Tropical lakes deeper than 200 m are likely to be stable, as seasonal mixing by typical thermal fluxes and turbulent wind energies do not reach that deep.

The history of the lake is also important to its responses to weather events. As our simulations in Lake Towuti illustrate, the cold event of 2008–2009 was not particularly extreme in terms of local weather parameters, but the lake arrived at the event on the heels of a prolonged series of colder years (Fig. 7), creating conditions more favorable for mixing. The difference between the surface and bottom water temperatures is a strong function of past mixing events, and dictates how much heat needs to be removed from the lake to induce whole-water-column mixing. Although lakes Towuti and Matano share climate conditions and have similar surface water temperatures, the bottom waters of Lake Matano are much colder (25–26°C vs. about 28°C in Towuti), providing a much greater stability (Fig. 8).

Fig. 8

Importance of thermal conditions (a) and lake depth (b) for lake mixing. (a) Profile 2 has the same surface temperature as Profile 1 but cooler bottom temperature. Full mixing requires the removal of a greater amount of heat (H2 vs. H1), making it less likely. (b) For similar temperature variations in the surface mixed layer, a shallower lake has a smaller overall Schmidt stability, and is less stable.

The mechanism indicated by our simulations for the enhanced stability of Lake Towuti post 2009 reveals a negative feedback that may be important for other tropical lakes (Fig. 9). A strong cooling event that lowers the bottom water temperature establishes conditions for a stronger stratification in subsequent years, when heating of the surface layer to its regular temperature range would result in a stronger thermal gradient. Subsequent downward diffusion of heat would erode that gradient, warming the deep waters and setting up the conditions for a repeated mixing. For typical mixing intensities ($$$ {K}_z $$$) such as in Lake Towuti, this process takes multiple years or potentially decades (Pu 2023), ensuring the relative stability of the lake in the intervening periods. For moderate-size lakes where vertical heat transport is dominated by turbulent eddy diffusion, this period of the enhanced stability would be expected to increase nonlinearly with the depth of the lake, as the time scale of diffusion increases as the square of the distance. This also means that bottom conditions in the deeper lakes may be capable of reflecting cooling events significantly farther back in their histories than in shallower lakes. For $$$ {K}_z={10}^{-6}\ {\mathrm{m}}^2\ {\mathrm{s}}^{-1} $$$, for example, diffusion of heat to 100 m below the thermocline (such as in a 200 m deep lake) would take around 150 yr, whereas diffusion to 500 m below the thermocline (such as in a 600 m deep lake) would require close to 4000 yr. A warming trend in air temperatures, such as over the recent decades, would be expected to increase the period of lake stability, by increasing surface water temperatures and thereby maintaining (or increasing) the thermal gradient in the water column. Heat exchanges between lake surface and atmosphere could generally be expected to happen faster than the propagation of heat into the stagnant bottom waters. Sufficiently fast atmospheric warming then could lead to progressive strengthening of the water column density gradient, making mixing episodes progressively less likely.

Fig. 9

Conceptual diagram of the mixing-stratification dynamics. A weak thermal gradient allows a strong cooling event to cause a whole water mixing. Continued cooling during mixing decreases the temperature of the bottom waters. When the surface temperature is re-established, stratification stability is increased by the increased temperature difference. Subsequent diffusion of heat downwards warms up the bottom waters, repeating the cycle.

Author Contributions

Tongyao Pu and Sergei Katsev jointly designed the study; Tongyao Pu performed modeling, curated data, analyzed results, and drafted the manuscript. G. Douglas Haffner and Sean A. Crowe contributed field data and insights into specifics of Lake Towuti. Sergei Katsev wrote the biogeochemical model, supervised the project, and co-authored the manuscript.

Acknowledgments

Tongyao Pu received summer support from the Water Resources Science program and Large Lakes Observatory at the University of Minnesota Duluth. Sergei Katsev acknowledges partial support from NSF awards 1660873 and 1754061. We thank Martin Schmid and Fabian Bärenbold for help with the Simstrat model. We thank Celine Michiels, Carri Ayne Jones, Julia Maresca, Jens Kallmeyer, and Jan Axel Kitte for help with sample collection.

Conflicts of Interest

The authors declare no conflicts of interest.