A simple model for predicting oxygen depletion in lakes under climate change

ABSTRACT

The advent of climate change has placed aquatic ecosystems at risk for potential declines in water quality, including an increase in the number of lakes experiencing substantial dissolved oxygen (O₂) depletion. Through its influence on the thermal structure of lakes via elevated water temperatures and alterations in stratification phenology, climate change intensifies biogeochemical and ecological processes involved in O₂ consumption, giving rise to conditions like hypoxia/anoxia. However, predicting O₂ dynamics is difficult, with in situ O₂ depletion rates showing considerable lake-dependent variability, underpinned by distinct underlying mechanisms. Our study attempts to overcome these lake-specific features and targets distilling key components of O₂ depletion into a simple and transferable conceptual model applicable across a diverse array of lakes and at large scales. Using O₂ depletion rates from literature reflecting variability in trophic state, we quantified the typical O₂ depletion rate ranges for oligotrophic, mesotrophic, and eutrophic lakes and assessed their temperature sensitivity for a broader climate impact assessment. Our model gave reasonable estimates for O₂ depletion and risks of anoxia through 3 explanatory variables: trophic state, stratification duration, and hypolimnion temperature. We validated our model predictions using data from 5 German lakes and assessed the relative importance of the 3 influencing factors. This easy-to-use approach has potential for lake management to attain rapid assessments of possible future problems with O₂ dynamics in a given lake, even in the absence of in situ data. Moreover, it allows scaling of O₂ dynamics continentally/globally without lake-specific hydrological or morphological details.

KEYWORDS:

• anoxia
• climate change
• hypolimnion temperature
• oxygen depletion model
• stratification duration
• water quality

Introduction

Dissolved oxygen (O₂) is a crucial component of aquatic environments that governs the functions of ecosystems (Wetzel 2001). The reliance on dissolved O₂ by biological (Spoor 1990, Plumb and Blanchfield 2009) and biogeochemical processes (North et al. 2014) occurring in lakes has long been viewed as a fundamental aspect in limnology (Hutchinson 1957), thus highlighting the importance of this critical parameter in lake water quality and management (European Commission 2000, Cooke et al. 2016). However, bottom water deoxygenation, documented in recent studies (Jones et al. 2008, Jenny et al. 2016, Jane et al. 2021), detrimentally affects aquatic biodiversity (Marcus 2001, Pollock et al. 2007, Jones et al. 2008), potentially increasing both greenhouse gas emissions (Encinas Fernández et al. 2014, Marotta et al. 2014) and internal nutrient loading (Brothers et al. 2014, North et al. 2014). Consequently, dissolved O₂ thresholds have been widely adopted to describe critical concentrations for bottom waters (Vaquer-Sunyer and Duarte 2008). The definition of such threshold values depends on their context in management strategies and intended human water uses (Nürnberg 2002). For example, dissolved O₂ concentrations in lake hypolimnia are said to foster detrimental biogeochemical developments when <0.5 mg L⁻¹ (anoxic; Encinas Fernández et al. 2014, North et al. 2014, Jane et al. 2022), be unsuitable for a majority of fish species when <2.0 mg L⁻¹ (hypoxic; Turner et al. 2005, Vaquer-Sunyer and Duarte 2008, Roberts et al. 2009), and be uninhabitable for cold-dwelling trout species when <5.0 mg L⁻¹ (Spoor 1990).

In monomictic and dimictic lakes, climate change manifests its influence on O₂ dynamics through multiple process chains involving its effects on lake stratification, vertical mixing processes, and biogeochemical processing. During stratification, the distinct detachment between the epilimnion and the hypolimnion render the latter inaccessible to atmospheric exchange, therefore restricting its O₂ replenishment (Livingstone 2003, Jankowski et al. 2006, Boehrer and Schultze 2008, Woolway and Merchant 2019). Climate warming leads to milder winters (Livingstone 1997, Straile et al. 2003), warmer lakes (Woolway et al. 2020), and enhanced thermal stability (Kraemer et al. 2015, Pilla et al. 2020), with dire consequences for hypolimnetic O₂ concentrations (Fang and Stefan 2009, Mi et al. 2020, Woolway et al. 2021). Long-term studies have shown that stratification phenology in individual lakes is altered (Livingstone 2003, Coats et al. 2006, Foley et al. 2012), starting earlier and ending later than previously observed (Foley et al. 2012), therefore prolonging the duration of O₂ depletion. Thus, with a prolonged stratified period (Adrian et al. 1995) and lower chances of O₂ replenishment during the shortened spring mixing timeframe (Pilla and Williamson 2022), lakes can be exposed to critical O₂ thresholds (Van Bocxlaer et al. 2012, North et al. 2014, Palmer et al. 2014). However, the effects of stratification phenology on O₂ concentrations are lake specific, influenced by morphometry (Livingstone and Imboden 1996), hypolimnion temperatures, local climate, and trophic characteristics (Rippey and McSorley 2009, Rhodes et al. 2017).

Trophic characteristics of a lake not only directly influence O₂ depletion rates, with higher depletion occurring in more eutrophic waters (Steinsberger et al. 2020), they are also predicted to be indirectly affected by climate change (Moss et al. 2011, Trolle et al. 2011, Kong et al. 2022). For example, climate warming-induced changes to precipitation patterns and evaporation rates (Huntington 2006, Knutti and Sedláček 2013) may result in altered watershed hydrological processes, thus heightening external nutrient loading (Jeppesen et al. 2009, Carey et al. 2012) or accelerating internal nutrient loading by intensifying sediment release (North et al. 2014). In general, eutrophication of lake systems is closely associated with anthropogenic activities, driving increased nutrient inputs (Jeppesen et al. 2009, Gregersen et al. 2022) into aquatic systems stemming from industrialization, agricultural intensification, and urbanization (Dubois et al. 2018). Ultimately, these human pressures have led to increased productivity in lake epilimnia (Maheaux et al. 2016, Beaulieu et al. 2019, Gregersen et al. 2022), resulting in heightened hypolimnetic O₂ demand (HOD) for organic matter decomposition (Moss et al. 2011).

Lake trophic status is well represented by hypolimnetic O₂ consumption (Borowiak et al. 2011, Steinsberger et al. 2021), and widely accepted frameworks for determining HOD related to lake trophy include the areal hypolimnetic O₂ depletion rate (AHOD; Lasenby 1975, Beutel 2003, Matthews and Effler 2006) and volumetric hypolimnetic O₂ depletion rate (VHOD; Rosa and Burns 1987, LaBounty and Burns 2007). Previous models of O₂ depletion required detailed O₂ measurements for parameterization and were lake-specific (Couture et al. 2015). However, implementing the interactions of trophic characteristics and climate change on hypolimnetic O₂ depletion dynamics in a transferable, simple predictive tool is advantageous for multi-lake applications and is needed for upscaling studies targeted at continental/global scales. Therefore, a simple approach integrating water temperature increases, prolonged stratification, and trophic state effects is crucial to quickly and universally assess the climate-driven pressures on hypolimnetic O₂ concentrations and the threat of hypoxia/anoxia, without requiring extensive local data.

Many existing ecological models for lake O₂ dynamics are complex and lack the required ease of use for widespread applications in lake management and global-scale studies. Hence, this study aimed to formulate a simple O₂ depletion model in lake hypolimnia, emphasizing trophic characteristics, hypolimnetic temperatures, and stratification duration effects. The model parameters were identified from a literature survey and have a solid empirical basis. We also validated our model using independent data from yearly observations in 5 German lakes with varying stratification regimes, hypolimnion temperatures, and trophic statuses. Furthermore, we implemented the model on actual lake systems by utilizing data from 13 German lakes. Subsequently, we assessed the sensitivity of the model by examining the interplay of trophic state, hypolimnion temperature, and the duration of stratification in attaining critical O₂ thresholds.

Methods

Literature survey on O₂ depletion data

To obtain realistic VHOD rates for our O₂ depletion model we conducted a literature search of empirical VHOD rates from previous studies. For this, we used search terms VHOD, HOD, oxygen depletion, and hypolimnion oxygen rate to find peer reviewed articles through the Google Scholar electronic database (https://scholar.google.com/). The lake VHOD rates obtained from these search terms, after inspection of the detected publications, are denoted as method A (Table 1). For most lakes, VHOD rates were reported according to the year the field measurements were performed, and as such, the individual yearly VHOD rates of a lake were treated as independent from one another. This approach is justified because our dataset lacks oligomictic lakes, ensuring complete annual mixing, and thus, subsequent years remain uninfluenced by prior years. When VHOD rates were given as a range, we derived the median of that range as a suitable rate to represent the study.

Table 1. Empirical estimates of VHOD rates obtained from literature for corresponding lakes, years, and trophic status.

Method	Lake name	Year	VHOD (mg L^−1 d^−1) (TREF = 4°C)	Trophic status	Source
A	Twin City South	1989	0.0148	eutrophic	(Axler et al. 1992)
	Sherman	1989	0.0109	oligotrophic
	Twin City South	1990	0.0374	eutrophic
	Sherman	1990	0.0304	oligotrophic
	Twin City South	1991	0.0436	eutrophic
	Sherman	1991	0.0374	mesotrophic
	Lower Crystal Springs	1999	0.0296	oligotrophic	(Beutel 2003)
	Lafayette	1967–1968; 1998–1999	0.1145	eutrophic
	Mathews	1997–1999	0.0265	oligotrophic
	Upper San Leandro	1997–1999	0.0787	mesotrophic
	San Antonio	1999–2000	0.0273	mesotrophic
	Muskegon	2011	0.222	mesotrophic	(Biddanda et al. 2018)
	Muskegon	2012	0.1651	mesotrophic
	Muskegon	2013	0.2072	mesotrophic
	Eerie	2005	0.0658	eutrophic	(Conroy et al. 2011)
	Otisco	2002	0.109	eutrophic	(Denkenberger et al. 2007)
	Onondaga	2002	0.1511	eutrophic
	Otisco	2003	0.1106	mesotrophic
	Otisco	2004	0.0974	mesotrophic
	Onondaga	2004	0.1768	eutrophic
	Blelham Tarn	1968–2008	0.2555	eutrophic	(Foley et al. 2012)
	Borabey	2013	0.0888	mesotrophic	(Göncü and Albek 2019)
	Porsuk	2013	0.1846	eutrophic
	Borabey	2014	0.0569	mesotrophic
	Porsuk	2014	0.1838	eutrophic
	Zurich	2003	0.1116	eutrophic	(Jankowski et al. 2006)
	Greifensee	2003	0.0857	eutrophic
	Rotorua	—	0.4518	eutrophic	(Rutherford et al. 1996)
	Rotorua	—	0.4673	eutrophic	(Vant 1987)
	Rotoiti	1981–1982	0.3505	eutrophic	(Vincent et al. 1984)
B	Sammamish	1965	0.0439	eutrophic	(Bella 1970)
	Clarke	1968	0.0112	oligotrophic	(Cornett 1982)
	Brewer	1968	0.0157	oligotrophic
	Costello	1968	0.0163	oligotrophic
	Kearney	1968	0.0179	mesotrophic
	Bob	1976	0.0327	oligotrophic
	Brompton	1978	0.0165	oligotrophic
	Central	1978	0.041	oligotrophic
	Lyster	1978	0.0203	oligotrophic
	Stukley	1978	0.0162	oligotrophic
	Lovering	1978	0.0169	oligotrophic
	Brompton	1979	0.021	oligotrophic
	Lovering	1979	0.0175	oligotrophic
	Lyster	1979	0.0207	oligotrophic
	North	1979	0.0274	oligotrophic
	Orford	1979	0.0254	oligotrophic
	Stukely	1979	0.0178	oligotrophic
	Truite	1979	0.0255	oligotrophic
	Central	1979	0.0279	oligotrophic
	Fitch	1979	0.021	mesotrophic
	Massawippi	1979	0.0499	oligotrophic
	Magog	1979	0.0239	eutrophic
	Brompton	1980	0.0209	oligotrophic
	Petite Brompton	1980	0.038	oligotrophic
	Lovering	1980	0.0205	oligotrophic
	Lyster	1980	0.0248	oligotrophic
	Orford	1980	0.0326	oligotrophic
	Stukely	1980	0.0212	oligotrophic
	Truibe	1980	0.0237	oligotrophic
	Central	1980	0.0376	mesotrophic
	Fitch	1980	0.0297	mesotrophic
	Massawippi	1980	0.0599	oligotrophic
	North	1980	0.0277	oligotrophic
	Magog	1980	0.0317	eutrophic
	Esrom	1969	0.0269	eutrophic	(Jónasson et al. 1974)
	Michin	1969	0.0293	oligotrophic	(Kerekes 1974)
	Bluehill	1969	0.0065	oligotrophic
	Skeleton	1969	0.0192	oligotrophic	(Michalski et al. 1973)
	Dudley	1969	0.0209	oligotrophic
	Gravenhurst	1969	0.0244	eutrophic
	Gravenhurst	1970	0.0173	eutrophic
	Gravenhurst	1973	0.0183	eutrophic
	Gravenhurst	1974	0.0281	eutrophic
	Harp	1973	0.0329	mesotrophic	(Nicholls 1976)
	Jerry	1973	0.0437	mesotrophic
	Stoney	1971	0.028	mesotrophic
	Washington	1957	0.0244	eutrophic	(Shapiro 1960)
	Washington	1958	0.025	eutrophic
	Kamloops	1974	0.0047	oligotrophic	(St John et al. 1976)
	Lake Lucerne, Horwer Bucht	1969	0.0259	eutrophic	(Stadelmann 1971)
	Walensee	1972	0.0138	oligotrophic	(Von Zimmermann and Suter-Weider 1976)
	Walensee	1973	0.0307	mesotrophic
	Walensee	1974	0.0269	mesotrophic
	Lake Lucerne, Horwer Bucht	1966	0.0259	mesotrophic	(Von Zimmerman 1969)
	Lake Lucerne, Horwer Bucht	1967	0.0301	mesotrophic
C	Aegerisee	1950–1951	0.0115	mesotrophic	(Livingstone and Imboden 1996)
	Aegerisee	1968–1983	0.0159	mesotrophic
	Constance	1977–1987	0.0334	eutrophic	(Rhodes et al. 2017)
	Constance	1988–1999	0.0285	mesotrophic
	Constance	2000–2010	0.028	oligotrophic

Acquisition of VHOD rate involved (A) literature searches, (B) conversions from AHOD, and (C) conversions from the oxygen consumption rate associated with the pelagic (J_V) and benthic (and J_A) zones.

The VHOD rates obtained from the literature search were further supplemented by applying conversions of areal hypolimnetic O₂ depletion (AHOD) rates of lakes (Cornett 1982) into VHOD rates. Here, we retrieved VHOD rates by dividing the individual AHOD rates of each lake by their corresponding mean hypolimnion thickness values, $z_h$, using equation 1: (1) $\mathrm{VHOD}={\displaystyle \frac{\mathrm{AHOD}}{z_h}.}$(1) VHOD rates for lakes acquired through equation 1 are denoted as method B (Table 1).

Furthermore, we modified the O₂ depletion rates established for both Lake Aegeri (Livingstone and Imboden 1996) and Lake Constance (Rhodes et al. 2017), which were in the form of the Livingstone and Imboden devised morphometry-based O₂ depletion model (Livingstone and Imboden 1996), to obtain their VHOD rates. This process involved retrieving the area of the whole hypolimnion of each lake from the upper boundary of the hypolimnion, $A_h$ (Imboden 1973, Imboden and Joller 1984): (2) $A_h=A_0{\left({\displaystyle \frac{1-z_{h2}}{z_m}}\right)}^q,$(2) where ${\mathit{A}}_0$ represents the lake surface area, $z_{h2}$ the depth of the upper boundary of the hypolimnion, $z_m$ the maximum depth of the lake, and a nondimensional exponent $q$ (0.73) as explained in Livingstone and Imboden (1996). With the values of the area of hypolimnion from both lakes, the calculation of the hypolimnetic volume, $V_H$, of each lake was conducted by multiplying $A_h$ by $z_h$: (3) $V_H=A_h{z}_h.$(3) Using the reported volumetric and areal O₂ consumption rates associated with the pelagic zone, $J_V$, and the benthic zone, $J_A$, respectively, of both lakes (Livingstone and Imboden 1996, Rhodes et al. 2017), we calculated the VHOD rates for each respective lake: (4) $\mathrm{VHOD}={\displaystyle \frac{J_A{A}_h+J_V{V}_h}{V_h}.}$(4) One $J_V$ value (3.9 g O₂ m⁻³ yr⁻¹) and 2 $J_A$ values (47 g O₂ m⁻² yr⁻¹ corresponded with 1950–1951 and 113 g O₂ m⁻² yr⁻¹ with 1968–1983) for mesotrophic Lake Aegeri (Livingstone and Imboden 1996), resulting in 2 VHOD rates for the lake aligned with each $J_A$timeframe. In the case of Lake Constance, the $J_V$ and $J_A$rates were reported for 3 separate timeframes associated with the different trophic states the lake underwent. Lake Constance was eutrophic from 1977 to 1987 ($J_V$ = 0.00543 g O₂ m⁻³ d⁻¹, $J_A$ = 0.0750 g O₂ m⁻² d⁻¹), mesotrophic from 1988 to 1999 ($J_V$ = 0.00458 g O₂ m⁻³ d⁻¹, $J_A$ = 0.0640 g O₂ m⁻² d⁻¹), and oligotrophic from 2000 to 2010 ($J_V$ = 0.00393 g O₂ m⁻³ d⁻¹, $J_A$ = 0.0640 g O₂ m⁻² d⁻¹) (Rhodes et al. 2017). Given the distinctions in the depletion rates aligned with the trophic states of Lake Constance, we obtained 3 VHOD rates for the lake across the 3 timeframes. VHOD rates associated with Lake Aegeri and Lake Constance are shown as method C (Table 1).

We obtained 90 VHOD estimates from individual lakes or different time periods within a lake. We matched each VHOD estimate with the trophic state using total phosphorus (TP) concentrations based on Carlson’s trophic state index (Carlson 1977). For cases lacking TP data, we conducted additional literature searches to find lake-specific TP values for the observed VHOD timeframe. In the absence of TP concentrations, we categorized VHOD rates using chlorophyll a concentrations, adhering to Carlson’s indexing guidelines, resulting in 28 eutrophic, 24 mesotrophic, and 38 oligotrophic VHOD rates (Table 1). All the lakes included here were either dimictic or monomictic.

Given varying hypolimnion temperatures in the lakes, we standardized the VHOD estimates to a common temperature for accurate comparison and model application. Thus, we utilized a well-documented temperature standardization equation (Salisbury and Ross 1978) that follows the Q10 rule, commonly applied in temperature-dependent biological processes such as microbial mineralization (Gudasz et al. 2010): (5) $\mathrm{VHO}{D}_T=\mathrm{VHO}{D}_{T_{\mathrm{REF}}}{k}^{(T-T_{\mathrm{REF}})},$(5) where $\mathrm{VHO}{D}_T$ corresponds with the VHOD rate at a given temperature $T$ and $\mathrm{VHO}{D}_{T_{\mathrm{REF}}}$ is associated with the VHOD rates from the empirical studies at their respective reference temperatures, $T_{\mathrm{REF}}$ (in this case 4 °C). The value for the temperature coefficient $k$ used was 1.0869 (Gudasz et al. 2010). By rearranging equation 5 we calculated the estimated VHOD, referenced to 4°C, the temperature of maximum density of water and a widespread hypolimnion temperature in cold deep temperate lakes: (6) $\mathrm{VHO}{D}_{@4^{o}C}={\displaystyle \frac{\mathrm{VHO}{D}_T}{k^{(T-T_{@4^{o}C})}}.}$(6) Afterward, the same temperature correction was applied to analyze temperature sensitivity of the VHOD estimates for different trophic states over a range of temperatures between 0 and 20°C, based on the reference temperature of T_REF= 4°C according to equation 5.

A simple model of hypolimnetic O₂ depletion

We defined the O₂ concentration (mg L⁻¹) at the start of the stratification period $t_0$ (d) to be at 100% saturation, making the initial O₂ concentration, $O_2(t_O)$, a sole function of hypolimnetic water temperature in Kelvin (K). First, the temperature-dependent Henry coefficient for O₂, $k_{H{O}_2}$ (mol L⁻¹ bar⁻¹) was calculated using a Taylor expansion equation (Boehrer et al. 2021): (7) $k_{H{O}_2}=\exp \left(A_1+A_2{\displaystyle \frac{100}{T}+A_3\ln \left({\displaystyle \frac{T}{100}}\right)}\right)u,$(7) where $A_i$ are O₂-specific coefficients ($A_1$ = −58.3877, $A_2$ = 85.8079, and $A_3$ = 23.8439), temperature is $T$ (K), and $u$ (= 986.9/22391) is a unit conversion factor incorporated to account for the variations in solubility units. The O₂ concentration at 100% saturation at a given temperature, $O_{2_{\mathrm{SAT},T}}$, then defined the initial O₂ concentration, $O_2(t_0)$, as: (8) $O_2(t_0)=O_{2_{\mathrm{SAT},T}}=k_{H{O}_{2,}T}{P}_{i,O_2},$(8) where the partial pressure of O₂ in the atmosphere is represented by $P_{i,O_2}$ (bar) and is dependent on the altitude of the lake.

Finally, a simple difference equation calculated the O₂ concentration at end of stratification using the stratification period and VHOD. Assuming no O₂ fluxes from the atmosphere into the hypolimnion, this end-of-stratification O₂ concentration constitutes the minimum O₂ in a lake, characterized by a given trophic state and hypolimnion water temperature: (9) $O_2(t_{\mathrm{end}.\mathrm{strat}})=O_2(t_0)-t_{\mathrm{stratification}}\mathrm{VHO}{D}_{T,\mathrm{trophic}.\mathrm{state}},$(9) (10) $\mathrm{VHO}{D}_{T,\mathrm{trophic}.\mathrm{state}}=\mathrm{VHO}{D}_{@4^{o}C}{k}^{(T-T_{@4^{o}C})},$(10) where the O₂ concentration (mg L⁻¹) in the hypolimnion at the end-of-stratified period $(t_{\mathrm{end}.\mathrm{strat}})$ (d) is represented by $O_2(t_{\mathrm{end}.\mathrm{start}})$, $O_2(t_0)$ is the initial O₂ concentration at the start of stratification influenced by hypolimnetic water temperature (K) as described in equation 8, and $t_{\mathrm{stratification}}$ (d) denotes the duration of the stratification period. The $\mathrm{VHO}{D}_{T,\mathrm{trophic}.\mathrm{state}}$value is based on the median of corresponding literature survey estimates for the respective trophic state and adjusted to the relevant hypolimnion temperature according to equations 5 and 6 (Supplemental Table S1) as outlined in equation 10. Note that equation 9 can deliver negative O₂ concentrations, which were then set as 0. Although negative O₂ concentrations are unrealistic, they nevertheless contain meaningful information because they correspond to a chemical O₂ demand of the respective lake as reflected by the presence of reduced substances such as, for example, NH₄⁺, H₂S, Fe²⁺, and Mn²⁺ (Müller et al. 2012). In that sense, negative O₂ concentrations could be interpreted as a deficit with that amount of O₂ required to oxidize these reduced substances in the water. In a real lake, this interpretation would imply the O₂ deficit has to be filled (e.g., by atmospheric imports during circulation) before positive O₂ concentrations can be achieved.

Note that because of the simplifications we included in our model approach, we made the following assumptions. The model (1) treats the hypolimnion as a single compartment without vertical gradients, (2) assumes a linear O₂ decrease over time, (3) operates with one VHOD value per lake, and (4) does not distinguish sediment O₂ demand from pelagic O₂ depletion and hence does not explicitly account for morphometric features of the hypolimnion.

Model validation

Model performance was evaluated using observed hypolimnion O₂ concentrations from 5 dimictic German lakes. The measurements from these lakes represented the average hypolimnion O₂ concentrations over the season and hence contain information about O₂ concentration at the end-of-stratified period, compatible to our model output. This validation dataset (Supplemental Table S2) included 27 individual observations from the 5 lakes, with 1 measurement per year for any given lake treated as an independent measurement (described earlier). Because average hypolimnion concentrations were measured a few days before, we utilized our model to predict O₂ concentrations corresponding to the actual measurement date in the field. Note that the validation dataset was independent from the data used to parameterize the model.

Model application

We tested the model suitability for real lake systems using 13 dimictic German lakes (Fig. 1, Table 2), a dataset completely independent of the literature data used to parameterize the model (Table 1). We used 45 different yearly datasets from 2 oligotrophic lakes, 6 mesotrophic lakes, and 5 eutrophic lakes (Table 2). Using aggregated daily water surface and bottom (i.e., 5 m) temperatures, we defined stratification duration based on temperature differences. The start of stratification was regarded as the first day the temperature difference between the surface water and the deep water was ≥2 K, considered the end-of-stratification period. For the period bounded by these established stratifications start and end dates, the difference in temperatures between the top water and bottom water had to exceed the 2 K threshold to be considered truly stratified. When the predicted final O₂ concentration was ≤0, anoxia was assigned/assumed.

Figure 1. Study lakes in Germany (black points) denoting where stratification duration and mean hypolimnion temperature data were observed. Points for Breiter Luzin, Schmaler Luzin, and Feldberger Haussee overlap.

Table 2. Mean hypolimnion temperature, stratification duration, and model-based VHOD estimates in 13 German lakes.

Trophic state	Name	Year	Hypolimnion temperature (°C)	Stratification duration (d)	VHOD (mg L^−1 d^−1)
Oligotrophic	Titisee	2019	4.40	221	0.0216
	Titisee	2020	4.50	235	0.0218
	Rappbode	2016	4.09	224	0.0211
	Rappbode	2017	4.19	213	0.0212
	Rappbode	2018	3.99	223	0.0209
	Rappbode	2019	4.06	229	0.0210
Mesotrophic	Laacher See	2017	4.51	257	0.0344
	Laacher See	2018	4.30	248	0.0338
	Tollensesee	2021	7.09	191	0.0427
	Groß Glienicker See	2018	9.35	176	0.0516
	Groß Glienicker See	2019	10.50	183	0.0567
	Schmaler Luzin	2021	5.52	227	0.0375
	Illmensee	2018	5.87	225	0.0386
	Illmensee	2019	6.28	228	0.0399
	Breiter Luzin	2003	4.72	225	0.0350
	Breiter Luzin	2004	4.33	224	0.0339
	Breiter Luzin	2005	4.46	230	0.0343
	Breiter Luzin	2006	4.06	250	0.0332
	Breiter Luzin	2010	4.41	223	0.0341
	Breiter Luzin	2011	4.61	228	0.0347
	Breiter Luzin	2012	4.86	225	0.0355
	Breiter Luzin	2015	4.64	232	0.0348
	Breiter Luzin	2016	4.44	231	0.0343
	Breiter Luzin	2018	4.39	228	0.0341
	Breiter Luzin	2019	4.49	251	0.0344
	Breiter Luzin	2020	5.08	239	0.0361
Eutrophic	Arendsee	2013	4.29	217	0.0422
	Arendsee	2014	5.07	243	0.0451
	Arendsee	2015	5.17	225	0.0455
	Arendsee	2016	5.06	230	0.0450
	Arendsee	2017	4.86	239	0.0443
	Arendsee	2018	4.50	224	0.0430
	Arendsee	2019	4.87	243	0.0443
	Arendsee	2020	5.52	233	0.0468
	Arendsee	2021	5.43	218	0.0464
	Scharmützelsee	2020	7.72	220	0.0562
	Scharmützelsee	2021	8.71	191	0.0610
	Feldberger Haussee	2018	8.08	195	0.0579
	Feldberger Haussee	2019	9.37	193	0.0645
	Feldberger Haussee	2020	9.08	190	0.0629
	Feldberger Haussee	2021	10.11	165	0.0686
	Großer Plöner See	2021	5.99	223	0.0486
	Tegeler See	2018	8.95	198	0.0623
	Tegeler See	2019	10.99	174	0.0738
	Tegeler See	2021	10.80	153	0.0726

We considered the application to empirical lake data important to identify the most relevant parameter space in the hypolimnion temperature versus stratification duration for typical Central European lakes. In other climates and regions, this area of interest varies; for instance, subtropical lakes often have warmer hypolimnion temperatures. Given the extensive empirical data from our literature survey, which covered diverse lakes in terms of trophic state, hypolimnion temperatures, and climates, our model should apply effectively across various climates and regions.

Additionally, we used the yearly mean deep-water temperatures of the lakes during stratification as an estimate of hypolimnion temperatures by averaging temperatures 3 m above the bottom for lakes <20 m deep and 5 m for lakes >20 m deep during stratification, assuming this mean temperature represented the entire hypolimnion. Ultimately, we used lake-specific stratification duration, hypolimnion temperature, and trophic state (characterized by TP concentrations using Carlson’s trophic state index; Carlson 1977) to estimate end-of-stratification O₂ concentrations for each lake on a given year using our model.

Furthermore, we utilized 3 critical O₂ concentration thresholds identified in literature (5, 2, and 0.5 mg L⁻¹) to interpret the predicted end-of-stratification O₂ concentrations concerning their impact on the ecosystem (Jane et al. 2022). Oxygen concentrations below ∼5 mg L⁻¹ affect sensitive, cold-adapted fish species like brook trout (Spoor 1990), whereas a concentration of O₂ <2–3 mg L⁻¹ has been associated with a hypoxic state (Diaz and Rosenberg 2008, Vaquer-Sunyer and Duarte 2008). O₂ concentrations <0.5 mg L⁻¹ are commonly seen as indicators of the onset of anoxia in lakes (Vaquer-Sunyer and Duarte 2008, North et al. 2014), affecting the production of reduced substances and massive losses of higher organisms, and even representative of actual anoxia (Jane et al. 2022).

Relative importance of stratification duration, hypolimnetic temperature, and trophic state with respect to critical O₂ concentrations and climate adaptation potential

As a synthesis, we analyzed the sensitivity of our model to examine the influence of hypolimnion temperature, stratification duration, and trophic state for reaching critical end-of-stratification O₂ concentrations. By rearranging the model equation, we computed stratification durations for the applied critical O₂ concentrations thresholds (5, 2, and 0.5 mg L⁻¹, discussed earlier) as a function of a given hypolimnetic temperature and trophic state: (11) $t_{\mathrm{stratification}}={\displaystyle \frac{O_2(t_{\mathrm{end}.\mathrm{strat}})-O_2(t_0)}{\mathrm{VHO}{D}_{T,\mathrm{trophic}.\mathrm{state}}}.}$(11) The resulting sensitivity diagram reveals how enhancing trophic state impacts the climate adaptation potential of a lake. In this context, a decrease in productivity (such as transitioning from eutrophic to mesotrophic conditions) allows the tolerance of a certain stratification prolongation and hypolimnetic warming without deteriorating O₂ conditions. It therefore informs decision makers about lake management targets and tolerable increases in hypolimnetic temperature and stratification duration that a lake can withstand without reaching critical O₂ concentrations, provided a targeted improvement of trophic state of a lake is implemented.

The R 4.1.2 statistical programming environment (R Core Team 2021) was used in all analyses, model calculations, and figure generation.

Results

O₂ depletion rates for different temperatures and trophic states

Literature-based VHOD rates provided a clear pattern with increasing VHOD from oligotrophic to mesotrophic and eutrophic lakes (Fig. 2). The variability in VHOD among different studies or lakes and years, respectively, increases with rising trophic state. Eutrophic lake VHOD values partially overlapped with high values observed in mesotrophic lakes. Notably, temperature had a nonlinear effect on VHOD (Fig. 2), causing larger differences in VHOD between trophic states at higher temperatures. Hence, shifting from mesotrophic to eutrophic trophic states had more pronounced effects on hypolimnion O₂ concentrations in warmer conditions than colder conditions. For example, at 4.00°C, mean VHOD estimates for mesotrophic and eutrophic states are 0.0412 and 0.104 mg L⁻¹ d⁻¹ (a difference in VHOD of 0.0628 mg L⁻¹ d⁻¹), respectively. However, at a hypolimnion temperature of 12.00°C, these values increase to 0.0802 and 0.203 mg L⁻¹ d⁻¹, respectively, (a difference in VHOD of 0.123 mg L⁻¹ d⁻¹). This temperature effect is important, not only for model applicability across lakes of different morphologies and climates that exhibit significant hypolimnion temperature variations, but also because hypolimnion temperature is an influential variable over the further progression of climate warming.

Figure 2. Mean (black lines) VHOD rates as a function of hypolimnetic temperature for different trophic status. The shaded regions illustrate the 99% confidence interval of each trophic state VHOD mean.

Model validation

To evaluate our O₂ depletion model, we conducted a linear regression between predicted and in situ O₂ concentrations. The estimated O₂ concentrations during stratification showed a significant linear correlation with the in situ measured O₂ concentrations. Values of R² (0.6) and RMSE (1.50 mg L⁻¹; Fig. 3) attest to good model performance in predicting O₂ concentrations (Santhi et al. 2001, Pilla and Couture 2021) given the simplicity of our approach. The regression line had a slope of 0.9 ± 0.1, suggesting it is not significantly different from 1. Furthermore, the intercept was 1.1 ± 0.5 mg L⁻¹, indicating no significant deviation from 0 (Fig. 3). In summary, the regression line between predicted and observed O₂ concentrations was closely aligned with the 1:1 line (Fig. 3). Ultimately, these validation results demonstrate the satisfactory performance of our model and documents its transferability and potential to predict O₂ concentration dynamics in stratifying lakes, particularly in larger-scale applications.

Figure 3. Validation of predicted O₂ concentrations from our model with in situ measured O₂ concentrations from 5 German lakes (Arendsee, Feldberger Haussee, and Tegler See are eutrophic; Breiter Lutzin and Groß Glienicker See are mesotrophic). The regression line (red) is shown with 95% confidence interval (shaded grey area). Blue and dotted line indicates the 1:1 line.

Model application: predicting hypolimnion O₂ concentrations for lakes of diverse trophic states

Model-based predictions for hypolimnetic O₂ depletion showed a strong dependence on both hypolimnion water temperature and stratification duration. Essentially, O₂ depletion speeds up with rising hypolimnion temperatures, and the response is nonlinear because of the exponential effect of water temperature on VHOD (discussed earlier; Fig. 2). Concurrently, extended periods of stratification inherently lead to increased O₂ depletion, following a linear scaling pattern (equation 8). In co-action, higher hypolimnion temperatures and the prolongation of the stratified period, as expected in a warming climate, will further increase hypolimnetic O₂ depletion in lakes, thus markedly increasing the risk of anoxia/hypoxia. The specific quantitative outcomes vary significantly based on the trophic state.

The trophic state-dependent nomograms (Fig. 4) enable the determination of O₂ concentration estimates at the end-of-stratified period when the hypolimnion temperature, stratification duration, and trophic state of a lake are known. A prolongation of stratification duration (e.g., by climate warming) will shift the lake farther to the right (i.e., parallel to x-axis). Any increase in hypolimnion temperatures shifts the lake upward (i.e., parallel to y-axis). The combined effects of hypolimnion temperature (acting nonlinearly) and stratification duration (acting linearly; Fig. 4) induce a concave curvature in the isolines for final hypolimnetic O₂ concentration. In cases where hypolimnion temperature and stratification both increase—likely when warming is intense—a shift along the diagonal (i.e., towards the upper right corner) occurs, and isolines are crossed perpendicularly, representing a fast drop in final hypolimnetic O₂ concentration. Moreover, we stress that hypolimnion temperature acts via a second chain because it also determines the starting conditions for hypolimnetic O₂ conditions seen as O₂ concentrations along the y-axis (i.e., at duration of 0 days). The warmer the hypolimnion, the lower the initial concentration because of the decrease in O₂ solubility with increasing temperatures.

Figure 4. Contour plots displaying the predicted O₂ concentration (color scale) in (a) oligotrophic, (b) mesotrophic, and (c) eutrophic lakes as a function of stratification and hypolimnion temperature. Points denote separate years in a respective lake. Isolines represent O₂ concentrations.

Model application for oligotrophic lakes

In oligotrophic lakes, the model predicts relatively low VHOD, but anoxia can nevertheless be reached if temperatures rise to, for example, >10.00°C (Fig. 4a). If the hypolimnion temperature gets warmer, for example >20.00°C, as in many tropical lakes, anoxic conditions in the hypolimnion can even be expected under oligotrophy if stratification persists only for a few months. Consequently, as the hypolimnion temperature rises, the VHOD increases and the availability of O₂ for ecological and biological processes decreases, thus reinforcing the occurrence of low O₂ concentrations.

Nevertheless, oligotrophic lakes have a high resistance against loss of O₂ and never reach anoxia when stratification remains <300 days and the hypolimnion temperature <10.00°C. But lakes with high hypolimnion temperature, for example ≥15.00°C, can indeed become anoxic if stratification lasts >7 months. The example data for German oligotrophic lakes clearly show they are never at risk of anoxia, even if the hypolimnion temperature and stratification duration rise considerably (Fig. 4a). The 2 oligotrophic lakes, Rappbode and Titisee, with a stratification period of 213–235 days and hypolimnion temperatures 3.99–4.50°C (Table 2), were predicted to reach O₂ concentrations of 6.67–7.99 mg L⁻¹ at end-of-stratification (Fig. 4a; Supplemental Table S3), well above the 3 thresholds identified as indicative of lakes facing threats to their ecological functioning.

Model application for mesotrophic lakes

The rate of O₂ depletion is more pronounced in mesotrophic lakes, resulting in a more rapid depletion of hypolimnetic O₂ concentrations as the stratification period progresses (Fig. 4b). The depletion of O₂ concentrations influenced by hypolimnion temperatures for mesotrophic lakes is shown to occur much faster than in oligotrophic lakes, a logical consequence from the higher median VHOD rates for mesotrophic lakes (0.0330 mg L⁻¹ d⁻¹) than for oligotrophic lakes (0.0209 mg L⁻¹ d⁻¹; Fig. 2, Supplemental Table S1). However, mesotrophic lakes remain resistant against anoxia and reach this condition only if stratification goes >300 days and hypolimnion temperature is >9.00°C. But in warmer lakes the risk of anoxia becomes real. For example, if a hypolimnion temperature of 15.00°C is assumed, a mesotrophic lake becomes anoxic when stratification persists longer than 5 months (Fig. 4b), which could be a typical situation in a subtropical lake.

The example dataset for German mesotrophic lakes shows they never reach anoxia but can be hypoxic and reach low O₂ concentrations of ∼0.90 mg L⁻¹ with a hypolimnion temperature markedly >4.00°C (Fig. 4b). The set of mesotrophic German lakes covered a range in stratification from 176 to 257 days and in hypolimnion temperature between 4.06 and 10.50°C (Table 2). At end-of-stratification, most mesotrophic lakes exhibited O₂ concentrations ranging from ∼0.87 to ∼5.37 mg L⁻¹. As a result, most had O₂ levels below the 5.00 mg L⁻¹ threshold, with the exception of Groß Glienicker See in 2019, where O₂ levels dropped to 0.87 mg L⁻¹ (Fig. 4b, Supplemental Table S3).

Model application for eutrophic lakes

When applying the model to eutrophic lakes, O₂ depletion during stratification significantly outpaces that in oligotrophic and mesotrophic lakes. The literature search yielded a median eutrophic VHOD rate of 0.0412 mg L⁻¹ d⁻¹ in hypolimnion temperatures of 4.00°C (Supplemental Table S1), markedly higher than both the oligotrophic and mesotrophic median VHOD rates. Evidently the risk of hypoxia and anoxia is higher in eutrophic systems, even at a temperature of 4.00°C, the typical hypolimnion temperature in deep dimictic lakes, when stratification persists for >10 months (Fig. 4c). Furthermore, the likelihood of a lake having O₂ concentrations below the 3 thresholds is higher in eutrophic lakes than in other trophic states, particularly in systems where hypolimnion temperatures are >5.00°C, underscoring the decisive influence of temperature on lake hypolimnion O₂ dynamics. For example, at hypolimnion temperatures ∼10.00°C, anoxia is reached after 5 months of stratification while conditions with O₂ <5.00 mg L⁻¹ are realized after 3 months (Fig. 4c).

In this context, we stress that the model delivers whole-hypolimnion averages for dissolved O₂ concentration and cannot resolve potential gradients within the hypolimnion. Under conditions of low average hypolimnion concentrations (i.e., 1.00 mg L⁻¹), an already large share of the initial O₂ is likely depleted. For example, at 5.00°C hypolimnion temperature, corresponding to an initial O₂ concentration of 12.00 mg L⁻¹, a critical O₂ concentration of 2.00 mg L⁻¹ is reached after 240 days, meaning that 83% of the initial O₂ storage is lost. In a real-world lake that loses >80% of hypolimnetic O₂, the occurrence of fully anoxic conditions in the deep hypolimnion is highly likely, whereas the upper parts of the hypolimnion probably retain O₂ concentrations above the average (details discussed later).

Eutrophic lakes in the dataset consistently ended stratification periods with O₂ concentrations <4.00 mg L⁻¹ (Fig. 4c). Stratification duration varied among these 5 lakes, ranging from 153 days in Tegeler See (2021) to 243 days in Lake Arendsee (2014 and 2019; Supplemental Table S3). Simultaneously, mean hypolimnion temperatures ranged from 4.29°C (Lake Arendsee 2013) to 10.99°C (Tegeler See 2019; Table 2). Feldberger Haussee and Tegeler See, owing to their relatively moderate depth (<20 m) and consequently shallower hypolimnion, exhibited higher average hypolimnion temperatures than the 3 deeper lakes. Furthermore, by end-of-stratification, the O₂ concentrations in these shallow lakes, including Scharmützelsee, had already dipped into the anoxic range.

Relative importance of stratification duration, hypolimnetic temperature, and trophic state with respect to critical O₂ concentrations and climate adaptation potential

Our model quantifies the sensitivity of end-of-stratification O₂ conditions with respect to all 3 influential variables; trophic state, stratification duration, and hypolimnetic temperature (Fig. 5). A hypothetical oligotrophic lake with a hypolimnion temperature of 6°C, for example, would take 294 days of stratification to reach an O₂ concentration of 5 mg L⁻¹. By comparison, at the same temperature a mesotrophic lake would require only 186 days and a eutrophic lake only 149 days. Raising the temperature of a mesotrophic lake from 6 to 7°C reduces the time to reach critical O₂ thresholds: 31 days less for 0.5 mg L⁻¹, 28 days less for 2 mg L⁻¹, and 21 days less for 5 mg L⁻¹ (Fig. 5; Supplemental Table S4). This difference reflects the high sensitivity of temperature on hypolimnetic O₂ conditions; an increase of only 1°C corresponds to changes in stratification duration on the order of a month. In warming lakes with increased hypolimnetic temperature and longer stratification, temperature effects can therefore become dominant. These results underscore the effectiveness of eutrophication control and trophic state reduction measures as climate adaptation strategy. For example, converting a eutrophic lake of 4°C and 200 days of stratification into a mesotrophic lake allows it to tolerate a hypolimnetic warming of 2°C or a 100-day extension in stratification without adversely affecting its hypolimnetic O₂ levels.

Figure 5. Stratification duration for a lake of a specific trophic state at a given hypolimnetic temperature to reach critical O₂ biological and ecological thresholds; anoxia = 0.5 mg L⁻¹ (solid line), hypoxia = 2 mg L⁻¹ (long dash), uninhabitable by cold dwelling fish species = 5 mg L⁻¹ (dot dash). Our reference temperature of 4°C is denoted by the black dotted line.

Discussion

Our model illustrates the impact both hypolimnetic water temperature and stratification duration have on lake O₂ concentration dynamics at the end-of-stratified period in conjunction with lake trophic level. Our approach proves reasonable in predicting yearly trends in end-of-stratification O₂ concentrations and assessing the risk of breaching 3 crucial biological and ecological thresholds. Furthermore, our model documents the susceptibility of lakes to future warming by indicating that critical O₂ thresholds will be reached earlier with rising hypolimnion temperatures and prolonged stratification periods unless measures to reduce trophic state are implemented.

Model assumptions

Neglecting vertical gradients in the hypolimnion and obtaining averaged O₂ concentrations leads to overlooking variations specific to different depths. First, when our model indicates an end-of-stratification O₂ concentration of 2.00 mg L⁻¹ in a lake, the actual O₂ distribution in the hypolimnion is probably not uniform. The upper hypolimnion probably has higher concentrations while the deep hypolimnion may already be in an anoxic state. Second, processes such as photosynthesis in the hypolimnion (Burns 1995, Burns et al. 2005), observed in studies by Lucas and Thomas (1972) and Mitchell and Burns (1979), could challenge our assumption of linear O₂ decrease over time and no O₂ inputs during stratification through the metalimnion following a first-order O₂ decrease. Other potential processes would be the delivery of O₂-rich water via lake inflows (Vincent et al. 1984, Gibbs 1992, Burns 1995) or diffusive fluxes through the thermocline becoming significant, either through internal wave activities (Bocaniov et al. 2014) or downward diffusion (Burns 1995). However, the transport through the thermocline depends on turbulent diffusion and lake morphometry and is usually small (Kreling et al. 2017, Dong et al. 2020), but it reached up to 18% in the relatively shallow Lake Erie with considerable Poincaré wave activity as a source of turbulence (Bouffard et al. 2013).

Unlike our VHOD-focused model, the widely used Livingstone and Imboden (1996) model (L&I model) in applied limnology accounts for lake morphometry and offers depth-dependent O₂ depletion rates. This depth resolution enables the L&I model to predict dynamic changes in vertical O₂ gradients during the stratified season. Although their assumption of vertically constant rates of sediment O₂ demand and pelagic O₂ depletion is a simplification (Schwefel et al. 2018, LaBrie et al. 2023), distinguishing between benthic and pelagic fluxes is advantageous because benthic fluxes often dominate the hypolimnetic O₂ depletion, unless the lake is exceptionally large with a high volume-to-area ratio. Because our model does not account for these morphometric features (i.e., the ratio of sediment area to hypolimnion water depth), it is simpler and requires fewer parameters. In addition to its simplicity, another reason to opt for our VHOD-based model over a morphometric approach like the L&I model is the broader availability of literature values for VHOD rates. This extensive literature evidence facilitated a comprehensive examination of the impact of various trophic states and allowed us to incorporate temperature as a crucial factor, which is not included in the L&I model.

Morphometry, coupled with climate, influences hypolimnion temperatures in lakes, with shallower lakes usually having a warmer hypolimnion. Our model indirectly considers this effect through hypolimnion temperature influenced by morphometry. Nevertheless, studies such as Molot et al. (1992) have documented the interplay of O₂ depletion with morphometry, suggesting that hypolimnetic O₂ depletion is largely influenced by lake morphometry. Lakes with a low hypolimnion volume-to-area ratio rely more on sediments for their O₂ dynamics, whereas those with a high ratio rely primarily on pelagic processes (Steinsberger et al. 2020). Rhodes et al. (2017) argue that pelagic respiration dominates O₂ consumption in lakes with hypolimnetic depths >20 m. Livingstone and Imboden (1996) acknowledge that in shallow eutrophic lakes, O₂ depletion is primarily driven by the benthic interface, whereas in deeper oligotrophic lakes it is largely governed by the pelagic zones. Although we did not follow the L&I model approach of explicitly separating pelagic from sedimentary O₂ demand, a factor clearly shown to impact O₂ depletion in stratifying waters (Burns and Ross 1972, Butts and Evans 1977, Butts 1978), our model has wider applicability because we included water temperature and trophic state. Also, our model has transferrable parameters and does not require local calibrations. Thus, our model is more applicable at larger scales (e.g., in global scale assessments), enabling the generation of generalized, conceptual conclusions and patterns rather than precise, depth-resolving predictions for specific lakes.

Impacts of trophic state and VHOD on O₂ concentration dynamics

We demonstrate that trophic state strongly influences lake O₂ depletion rates and hypolimnion O₂ concentrations at end-of-stratification. Our literature search shows distinct VHOD rate variations based on trophic state (Fig. 2), an observation aligning with prior research indicating that increased lake productivity correlates with higher organic matter mineralization rates in the water column (Beutel 2003), leading to greater O₂ consumption (Müller et al. 2012, Steinsberger et al. 2020, Jane et al. 2021). Hence, eutrophic lakes, with wider ranges of TP levels as per Carlson’s trophic index, have more VHOD variability than other trophic states. Despite numerous case studies and textbook definitions of eutrophic lakes with anoxic hypolimnia, we found no comprehensive literature review quantifying O₂ depletion variations across trophic states. Therefore, the data gathered in this study represent an unexplored and vital empirical foundation. The robust empirical basis of our model has several strengths: (1) it enhances transferability, (2) it transforms qualitative knowledge into a precise predictive tool, and (3) the literature survey not only provided characteristic VHOD rates for the different trophic states, but also their variability and uncertainty bounds.

Our model predicts all eutrophic lakes in our sample lakes have O₂ concentrations below some of the outlined biological and ecological O₂ thresholds. All these lakes had concentrations <4.00 mg L⁻¹ at end-of-stratification (Fig. 4c), with a majority characterized as experiencing either hypoxia or anoxia. Rosa and Burns (1987), Evans et al. (1996), and Rhodes et al. (2017) observed similar interactions of eutrophication with hypolimnetic O₂ concentration dynamics. The influence trophic status has on hypolimnetic O₂ concentrations is further shown in our observed mesotrophic lakes, which tended to have higher O₂ concentrations (0.85–5.40 mg L⁻¹). While some of these mesotrophic lakes had end-of-stratification O₂ concentrations below the 5.00 mg L⁻¹ threshold; Groß Glienicker See, by contrast, experienced hypoxia in 2019. Our oligotrophic lakes had O₂ concentrations 6.00–7.00 mg L⁻¹ at the end-of-stratified period. Hence, our model effectively links O₂ depletion rates to trophic state, as described by Edmondson (1961) and Vincent et al. (1984), offering a straightforward and broadly applicable predictive framework. Nevertheless, our study also documents that the simplified generalizations (e.g., in textbooks) of eutrophic lakes always experiencing anoxic hypolimnia and mesotrophic lakes tending not to are not always valid. Mesotrophic lakes can turn anoxic when stratification is long and temperature is high. Even oligotrophic lakes can become anoxic if the hypolimnion is sufficiently warm, such as in the tropics.

Model sensitivity analysis

In evaluating the significance of the input parameters of the model (stratification duration, hypolimnion temperature, and trophic state) in reaching the delineated critical O₂ thresholds, we found all 3 to be relatively important. For instance, our model indicates that increasing hypolimnion temperature or stratification duration of a lake leads to decreased O₂ levels at end-of-stratification. Importantly, the combined impact of hypolimnion warming and prolonged stratification rapidly accelerates deoxygenation. Although our model treats both factors as additive rather than synergistic, the nonlinear, 2-way (initial O₂ and O₂ depletion rate) effect from hypolimnion temperature renders the temperature effect particularly influential. Moreover, the trophic state of a lake influences the speed of O₂ concentration depletion, with depletion and arrivals of O₂ concentrations at critical thresholds occurring much quicker at higher trophic states (Fig. 5, Supplemental Table S4).

Climate change frequently functions like eutrophication (Moss et al. 2011), particularly in lakes with altered catchments that lead to increased nutrient loading and eutrophication (Rose et al. 2016, Woolway et al. 2020, Jane et al. 2021), which in turn leads to heightened lake productivity (Lee and Biggs 2015, Ho et al. 2019), increasing VHOD rates, and ultimately lower O₂ concentrations at end-of-stratification (Jane et al. 2021). Thus, trophic state, and its vulnerability to climate change, significantly influences lake O₂ concentration dynamics in response to warming climates (Rose et al. 2016, Rogora et al. 2018). Therefore, reduction of lake trophic levels through measures such as nutrient loading controls becomes a fundamental strategy in mitigating the effects of climate warming and should be exploited by decision makers for climate adaptation of lake and reservoirs.

The temperature effect on O₂ concentration dynamics

Our model emphasizes the significance of hypolimnion water temperatures in lake O₂ concentration dynamics. This temperature influence is first evident from the end of the spring turnover, when O₂ saturation at the water–air interface is dependent on the water temperature (Boehrer et al. 2021). During the vertical mixing periods (spring turnover), O₂ saturation is attained because lake temperatures are relatively homogeneous, allowing for uniform atmospheric exchange and equilibrium throughout the water column. Stratification renders the hypolimnion inaccessible for atmospheric gas exchange, preventing the replenishment of O₂ concentrations. Our model calculates the initial O₂ concentration based on the average hypolimnion temperature. The importance of temperature on initial O₂ concentrations in hypolimnion waters is well described in literature. Hanson et al. (2006) described the role of temperature in dissolved gas concentrations, observing a downturn in lake O₂ concentrations with rising water temperature.

Moreover, our model highlights the importance of hypolimnion water temperatures in O₂ consumption during stratification. Our model quantifies the temperature effect on VHOD rates, with higher hypolimnion temperatures resulting in higher O₂ consumptions. For example, an increase from 4.00 to 8.00°C in an oligotrophic lake increases the O₂ depletion rate by ∼40%. The temperature-related acceleration of biochemical processes, including O₂ depletion, is widely reported in literature (Rosa and Burns 1987, Burns 1995, Foley et al. 2005, Gudasz et al. 2010). Hence, in calculating the VHOD rates for our observational lakes according to their hypolimnion temperatures (Table 2), the highest rate within each trophic state corresponds to the lake with the highest average hypolimnion temperature, and the lake with the lowest hypolimnion temperature had the lowest rates. In eutrophic lakes, Tegle/r See in 2019, with an average hypolimnion temperature of 10.99°C, had a VHOD rate of 0.0738 mg L⁻¹ d⁻¹, whereas Arendsee in 2013, with an average hypolimnion temperature of 4.29°C, had a VHOD rate of 0.0422 mg L⁻¹ d⁻¹. The effect of hypolimnion temperature on biogeochemical activities and the eventual decline of O₂ concentrations in the compartment is also described in Blumberg and Di Toro (1990).

While historical surface water temperature increases due to climate warming are well documented, the rate of temperature rise in bottom waters has been reported to be slower. Livingstone (2003), for example, found hypolimnion temperature increments of ∼0.13 K decade⁻¹ from 1950 to 1990 in Lake Zurich. Pilla et al. (2020) showed that changes in hypolimnion temperatures were lake specific, with trends ranging between −0.65 and 0.65 K decade⁻¹ in a global analysis of 102 lakes. Bottom water temperatures remain relatively stable throughout the year, shielded from the influence of warmer air temperatures during stratification, as long as winter conditions permit sufficient lake cooling (Livingstone 2003). Ultimately, the climate warming-mediated differential temperature increase in both surface and bottom waters influences stratification prolongation. Dokulil et al. (2006), and Richardson et al. (2017), however, observed that bottom temperature increases in the hypolimnion are not occurring congruently. For example, large and deep lakes have been observed to show increases in hypolimnion temperatures, probably stemming from heat carryover from previous years (Livingstone 2003, Dokulil et al. 2006, Arvola et al. 2010, Rogora et al. 2018, Anderson et al. 2021). By comparison, shallow lakes experience faster heat loss in autumn and lower winter temperatures (North et al. 2013, Winslow et al. 2015), resulting in weaker hypolimnion warming trends.

Studies incorporating future climate scenario modeling have, nonetheless, shown that bottom temperatures are projected to increase in temperate lakes under moderate scenarios (Shatwell et al. 2019, Mi et al. 2020). With warmer winter air temperatures projected in the future, Mi et al. (2020) suggested reduced occurrences of ice cover and inverse stratification during winter, resulting in Rappbode Reservoir experiencing a shift in lake mixing regime, transitioning from dimictic to monomictic. Such shifts from dimictic to warm-monomictic are predicted for many lakes worldwide (Woolway et al. 2021), demarcating a critical tipping point where any further warming will directly affect the hypolimnion temperature. This subsequent hypolimnion temperature increase will result in dire consequences to lake ecosystems by accelerating VHOD and lowering initial O₂ concentrations.

However, research on the importance of hypolimnion temperature on O₂ consumption is limited, with an overrepresentation of deep dimictic lakes. Hence, lakes with hypolimnion temperatures significantly above 4.00°C are often understudied. This approach is flawed because lakes in subtropical/tropical regions, which undergo stratification, have relatively warmer hypolimnia. Additionally, Central European lakes of intermediate depth (i.e., with shallower hypolimnion depths) have hypolimnion temperatures >4.00 °C (i.e., Lake Scharmützelsee in our dataset). Given the potential impacts of climate warming on lakes, a comprehensive understanding of the global-scale implications of deep-water temperatures increase on O₂ concentration dynamics is essential.

O₂ concentrations in relation to stratification duration

Stratification duration plays a crucial role in hypolimnion O₂ depletion dynamics. Prolonged stratification raises anoxia risk, especially in eutrophic lakes or warmer hypolimnia. We established a linear relation between O₂ decrease and stratification period length. When comparing 2 lakes/years with similar hypolimnion temperatures and VHOD rates, a longer stratification period led to a greater decline in O₂ concentrations. In our case studies, the stratification duration effect was evident when comparing O₂ concentrations between 2 relatively similar years in Arendsee. In 2014, with a 243-day stratification period (hypolimnion temperature = 5.07°C and VHOD = 0.0451 mg L⁻¹ d⁻¹), the O₂ concentration at end-of-stratification was lower than in 2016, which had a 230-day stratification period (hypolimnion temperature = 5.06°C and VHOD = 0.0450 mg L⁻¹ d⁻¹; Supplemental Table S3, Fig. 4c). Several studies have described the connection between longer stratification and increased O₂ depletion (Fang and Stefan 2009, Foley et al. 2012, Jane et al. 2021, Pilla and Williamson 2022). Furthermore, longer stratification periods can lead to shorter spring turnover times, reducing O₂ replenishment to bottom hypolimnetic waters (Pilla and Williamson 2022), therefore promoting O₂ concentrations below the critical thresholds (Fang and Stefan 2009, Foley et al. 2012).

Numerous observational and modeling studies have associated stratification prolongation with climate warming (Foley et al. 2012, Ficker et al. 2017, Shatwell et al. 2019) and the eventual decreased O₂ concentrations (Foley et al. 2012, North et al. 2014, Woolway et al. 2021). Changes in stratification patterns driven by climate warming have been observed in Heiligensee (Germany; Adrian et al. 1995), Lake Washington (Washington State, USA; Winder and Schindler 2004), Blelham Tarn (Foley et al. 2012), and Austrian lakes Irrsee, Mondsee, and Hallstätter See (Ficker et al. 2017), resulting in earlier onset. By comparison, the later stratification breakup has been observed and modeled in Lake Tahoe (California/Nevada, USA; 4.4 d decade⁻¹), Blehlam Tarn (UK; 18 d decade⁻¹), and in the upper North American Great Lakes (average 3.5 d decade⁻¹) (Woolway et al. 2021).

Practical relevance of our results for lake management

Our results also have implications for lake management by providing quantitative predictions for hypolimnetic O₂ concentrations, which are highly relevant for the ecological status of lakes (European Commission 2000) and at the same time heavily impacted by climate change. With ongoing climate warming, hypolimnetic O₂ concentrations will decrease, and currently oxic lakes (e.g., in a mesotrophic state) will face future anoxia. Eutrophic lakes already experiencing anoxia will nevertheless suffer as the biogeochemical O₂ deficit increases and the production of reduced substances (Müller et al. 2012), including greenhouse gases (Encinas Fernández et al. 2014, Steinsberger et al. 2019), intensifies. Oligotrophic lakes will likely remain oxic but may lose their habitat suitability for salmonids by undercutting the critical O₂ threshold of 5 mg L⁻¹. The degree of climate warming risk varies based on the context of a particular lake ecosystem, and therefore determining which type of lake is more vulnerable becomes subjective. However, the following points are pertinent for lake management:

1. Lakes susceptible to hypolimnetic warming are particularly sensitive, including stratified lakes of moderate depth (≤20–30 m) in temperate zones, warm-monomictic lakes predicted not to reach the temperature at maximum water density during winter mixing in the foreseeable future, and numerous reservoirs with deep water release.

2. Because lake managers cannot stop climate warming, adapting to its changes necessitates strategic approaches. The most efficient adaptation is to reduce the trophic state of a lake. Transitioning a eutrophic lake to a mesotrophic state, for instance, will substantially improve O₂ conditions. Thus, achieving the goals of the European Water Framework Directive will indeed mediate climate adaptation.

3. In systems where reductions of trophic state cannot be realized, technical interventions like aeration may offer a solution. Alternatively, decision makers may need to acknowledge and tolerate the impending ecosystem degradation as an unfortunate reality.

Acknowledgements

The authors thank our colleagues at the Helmholtz Centre for Environmental Research (UFZ) for their valuable exchanges during the course of the study. We also thank Dr. Ian Jones for his advice during the writing process.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Financial support for this work was provided through H2020 Marie Skłodowska-Curie Actions grant agreement ID: 956623 (inventWater ITN). We are grateful for the financial support to KR from the Deutsche Forschungsgemeinschaft grant ID:RI2040/4-1 (newMOM).