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Overview
In earlier work34, epidemiological models are broadly divided into two large categories, called forecasting and mechanistic. The former models fit a specific curve to the data and then attempt to predict the dynamics of the quantity under consideration. The most well known mechanistic models are the SIR-type models. As noted by Holmadahl and Buckee34, the mechanistic models involve substantially more complicated mathematical machinary than the forecasting models, but they have the advantage that they can make predictions even when the relevant circumstances change. In our case, since our goal is to make predictions after the situation changes due to the lifting of the lockdown measures, we need to consider a mechanistic model. However, it is widely known that the main limitation of mechanistic models is the difficulty of determining the parameters specifying such models. In this direction, a methodological advance was presented by the authors35, filling an important gap in the relevant literature: it was shown in35 that from the knowledge of the most reliable data of the epidemic in a given country, namely the cumulative number of deaths, it is possible to determine suitable combinations of the constant parameters (of the original model) which specify the differential equation characterizing the death dynamics. Furthermore, a robust numerical algorithm was presented for obtaining these parameters. One of these constants, denoted by c, is particularly important for the analysis of the effect of easing the lockdown conditions, because it is proportional to the number of contacts between asymptomatic individuals that are infected by SARS-CoV-2 and susceptible ones. Specifically, as the equations presented below will indicate, this coefficient is measured in units of inverse population (where the population represents the number of individuals to which we assign no units) times inverse days. This constant reflects the probability of infection given a contact which is proportional to the viral load (i.e., the viral concentration in the respiratory-tract fluid) of expelled respiratory droplets36. Easing the lockdown will lead to an increase of the value of this constant. Thus, in order to quantify this effect we assumed that the post-lockdown situation could be described by the same model but with c multiplied by an integer number (zeta), such as (zeta =2), or 3, etc. Assuming a fixed viral load emission (i.e., no face mask or similar protective measures), this would be tantamount to doubling or tripling the number of contacts per day. To put things into perspective, it is relevant to mention here that in the relevant literature a ballpark estimate for daily contacts of an individual is about 13.437.
We first applied the above algorithm to the case of the COVID-19 epidemic in Greece. However, the novelty and the main interest of the present work consists of the extension and application of the above methodology to two subpopulations. This situation is significantly more complicated than that of2 and is described by 12 ODEs involving 18 parameters (details are discussed in the “Methods” section). Using this extended formulation, we analysed the effect of easing the lockdown measures under two distinct possible scenarios: in the first, we examined what would happen if the interactions between older persons, namely persons above 40 years of age, as well as between older and younger persons, namely those below 40, continue to be dictated by the same restrictions as those of the lockdown period. However, we assumed that the interaction among the young was progressively more free. In the second case, we analysed the effect of easing the lockdown measures in the entire population without distinguishing the older from the young. In principle, the effect on deaths in the above two scenarios could be analyzed by the extension of the rigorous results of35. However, due to the sparsity of the deaths data (especially for the younger population), this approach is practically not possible at present. Thus, we supplemented the data for deaths for the two subpopulations with data for the cumulative numbers of reported infected.
Using four sets of data, namely the number of deaths and the number of reported infected for the older and the younger population we found that the above two alternatives would result in very different outcomes: in the first case, the total number of deaths of the two sub-populations and the number of total infections would be relatively small. In the second case, these numbers would be prohibitively high. Specifically, in the case of Greece, if the lockdown was to be continued indefinitely, our analysis suggests that the total numbers of deaths and infections would finally be around 165 and 2550, respectively. These numbers would remain essentially the same even if the lockdown measures for the interaction between the young people were eased substantially, provided that the interactions of older-older and older-young would remain the same as during the lockdown period. For example, even if the parameter measuring the effect of the lockdown restrictions on the young-young interactions were increased fourfold, the number of deaths and infections would be (according to the model extrapolation) 184 and 3585, respectively. On the other hand, even if the parameters characterizing all three interactions were increased only threefold, the relevant numbers would be 48144 and 1283462. It is clear that the latter numbers are prohibitive, suggesting that a generic release of the lockdown may be catastrophic.
In our view, the explanations provided in the “Methods” section for the assumptions of our model, which show that these assumptions are typical in the standard epidemiological models, substantiate the qualitative conclusions (and notes of caution) regarding the impact of the above two different types of exit policies. This may provide a sense of how a partial restoration of regular life activities can be achieved without catastrophic consequences, while the race for pharmacological or vaccine-based interventions that will lead to an end of the current pandemic is still ongoing. Importantly, we also offer some caveats emphasizing the qualitative nature of our conclusions and possible factors that may substantially affect the actual outcome of the lifting of lockdown measures.
Model setup: single population versus two age groups
We divide the population in two subpopulations, the young (y) and the older (o). In order to explain the basic assumptions of our model we first consider a single population, and then discuss the needed modifications in our case which involves two subpopulations. Let E(t) denote the exposed (but not infectious) population. An individual in this population, after a median 4-day period (required for incubation — see e.g.38) will either become sick or will be asymptomatic; an interval of 3-10 days captures 98% of the cases. The sick (infected) and asymptomatic populations will be denoted, respectively, by I(t) and A(t). The rate at which an exposed person becomes asymptomatic is denoted by a; this means that each day aE(t) persons leave the exposed population and enter the asymptomatic population. Similarly, each day sE(t) leave the exposed population and enter the sick population. These processes, as well as the subsequent movements are depicted in the flowchart of Fig. 1.
Figure 1

Flowchart of the populations considered in the model and the rates of transformation between them. The corresponding dynamical equations are Eqs. (1)–(6).

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The asymptomatic individuals recover with a rate (r_1), i.e., each day (r_1A(t)) leave the asymptomatic population and enter the recovered population, which is denoted by R(t). The sick individuals either recover with a rate (r_2) or they become hospitalized, H(t), with a rate h. In turn, the hospitalized patients also have two possible destinations; either they recover with a rate (r_3), or they become deceased, D(t), with a rate d.
It is straightforward to write the above statements in the language of mathematics; this gives rise to the equations (1)–(5) below:

$$begin{aligned} frac{dA}{dt}= a E – r_1 A end{aligned}$$
(1)

$$begin{aligned} frac{dI}{dt}= s E – (h + r_2) I end{aligned}$$
(2)

$$begin{aligned} frac{dH}{dt}= h I – (r_3+d) H end{aligned}$$
(3)

$$begin{aligned} frac{dR}{dt}= r_1 A + r_2 I + r_3 H end{aligned}$$
(4)

$$begin{aligned} frac{dD}{dt}= d H end{aligned}$$
(5)

$$begin{aligned} frac{dE}{dt}= c left[ T – (E+I+A+H+R+D)right] left( A + b Iright) – (a+s) E end{aligned}$$
(6)

It is noted that our model is inspired by various expanded versions of the classic SIR model adapted to the particularities of COVID-19 (such as the key role of the asymptomatically infected). It is, in particular, inspired by, yet not identical with that of14. In order to complete the system of equations (1)–(6), it is necessary to describe the mechanism via which a person can become infected. For this purpose we adopt the standard assumptions made in the typical epidemiological models, such as the SIR (susceptible, infected, recovered) model: let T denote the total population and let c characterize the number of contacts per day made by an individual with the capacity to infect (c is thought of as being normalized by T). Such a person belongs to I, A or H. However, for simplicity we assume that the hospitalized population cannot infect; this assumption is based on two considerations: first, the strict protective measures taken at the hospital, and second, the fact that hospitalized patients are infectious only for part of their stay in the hospital. The latter fact is a consequence of the relevant time scales of virus shedding in comparison to the time to hospitalization and the duration of hospital stay. The asymptomatic individuals are (more) free to interact with others, whereas the (self-isolating) sick persons are not. Thus, we use c to characterize the contacts of the asymptomatic persons and b to indicate the different infectiousness (due to reduced contacts/self-isolation) of the sick in comparison to the asymptomatic individuals.
The number of people available to be infected (i.e., the susceptible population) is (T-(E+I+A+H+R+D)). Indeed, the susceptible individuals consist of the total population minus all the individuals that are going or have gone through the course of some phase of infection, namely they either bear the infection at present ((E+A+I+H)) or have died from COVID-19 (D) or are assumed to have developed immunity to COVID-19 due to recovery (R). Hence, if we call the total initial individuals T, this susceptible population is given by the expression written earlier. The rate by which each day individuals enter E is given by the product of the above expression with (c(A+bI)). At the same time, as discussed earlier, every day ((a+s)E) persons leave the exposed population. It is relevant to note here that within this simpler model, it is possible to calculate the basic reproduction number (R_0), which is a quantity of substantial value in epidemiological studies32,33. In this model, this can be found to be33:

$$begin{aligned} R_0=frac{c T}{a+s}left[ frac{a}{r_1} + frac{b s}{r_2+h} right] . end{aligned}$$
(7)

This will be useful below for the purposes of finding the change in c (under lockdown) needed in order for transmission to cross the threshold of (R_0=1) and thus to lead to growth of the epidemic. In the particular case of the data shown in Table 1, (R_0=0.4084), in accordance with the lockdown situation associated with a controlled epidemic.
It is straightforward to modify the above model so that it can describe the dynamics of the older and younger subpopulations. Each subpopulation satisfies the same set of equations as those described above, except for the last equation which is modified as follows: the people available to be infected in each subpopulation are described by the expression given above where T, E, I, A, H, R, D have the superscripts (^o) or (^y), denoting older and young, respectively; (A+bI) is replaced in both cases by (A^o+A^y+b(I^o+I^y)) where for simplicity we have assumed that the infectiousness of the older and the young is the same. We have already considered the implications of the generalisation of the above model by allowing different parameters to describe the interaction of the older and young populations; this will be discussed in the “Methods” section. In what follows, we will discuss the results of this simpler “isotropic” interaction model.
Quantitative model findings
The parameters of the model are given in the flowchart of Fig. 1. Naturally, for the two-age model considered below, there is one set of such parameters associated with the younger population and one associated with the older one. The optimization routine used for the identification of these parameters is explained in detail in the “Methods” section. The parameters resulting from this optimization for the single population model are shown in Table 1, whereas for each of the two populations are given in Table 2. Clearly, many of these parameters are larger for the older population in comparison to the young, leading to a larger number of both infections and deaths in the older than in the young population.
Table 1 Optimized model parameters for the single population model, and the variation interval of each parameter within the optimization process (for further details, see “Methods” section).
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Table 2 Optimized (isotropic) model parameters for the young and older populations, and the variation interval of each parameter within the optimization process (for further details, see “Methods” section).
Full size table

Support for the validity of our model is presented in Fig. 2, which depicts its comparison (using the above optimized parameters) with the available data. The situation corresponding to keeping the lockdown conditions indefinitely, is the one illustrated in Fig. 2. In this case, the number of deaths and cumulative infections rapidly reaches a plateau, indicating the elimination of the infection. Here, we have optimized the model on the basis of data used from Greece39 between April 3rd and May 4th. It is noted that daily updates occurred at 3pm for the country of Greece, hence it is not clear up to what time the data are collected that are included in the daily report. We have assumed that the data reflect the infections and deaths present on that particular day. This possibly shifts the starting point of our count by a few hours, but should not change the overall result trends.
We next explain the implications of the model when different scenarios of ‘exit’ from the lockdown state are implemented. The relevant results are illustrated in Figs. 3, 4 and the essential conclusions are summarized in Table 3 for the numbers of deaths and cumulative infections, respectively. First, we need to explain the meaning of the parameter (zeta) appearing in the above tables: this parameter reflects the magnitude of the easing of the lockdown restrictions. Indeed, since the main effect of the lessening of these restrictions is that the number of contacts increases, we model the effect of easing the lockdown restrictions by multiplying the parameter c with a factor that we refer to as (zeta). The complete lockdown situation corresponds to (zeta)=1; the larger the value of (zeta), the lesser the restrictions imposed on the population. By employing the above quantitative measure of easing the lockdown restrictions, we consider in detail two distinct scenarios. In the first, which corresponds to the top rows of the Figures 3 and 4, we only allow the number of contacts of “young individuals with young individuals” (corresponding to the parameter (c^{yy}) mentioned in the “Methods” section) to be multiplied by the factor (zeta). This means that the lockdown measures are eased only with respect to the interaction of young individuals with other young individuals, while the interactions of the young individuals with the older ones, as well as the interactions among older individuals remain in the lockdown state. In the second scenario, corresponding to the bottom rows of the Figures 3 and 4, the restrictions of the lockdown are simultaneously eased in both the young and the older population; in this case all contacts are increased by the factor (zeta). It is noted that while we change c by this factor, we maintain the product cb at its previous value (i.e., we concurrently transform (crightarrow zeta c) and (brightarrow b/zeta)) considering that the sick still operate under self-isolation conditions and thus do not accordingly increase their number of contacts.
Table 3 Deaths D(t) and cumulative infections C(t) in the case of increasing of the number of contacts by (zeta). The second and fourth columns refer to the case for which the lockdown measures are eased for the young population, whereas the third and fifth column refer to the one where this occurs for both the young and older populations.
Full size table

Figure 2

Evolution of the current situation of deaths D(t) (left) and cumulative infections C(t) (right) in Greece, under the case of an indefinite continuation of the lockdown conditions. In this and all the figures that follow, the blue curve corresponds to the young population, while the red curve to the older population. The data for Greece from the 3rd of April to the 4th of May 2020 are depicted by dots. For the latter, alternate colors have been used (i.e., blue dots for the older population and red for the younger for clearer visualization).

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Fig. 3 corresponds to the case where the parameter (zeta) associated with the number of contacts between susceptible and asymptomatic individuals doubles. In this case, as also shown in Table 3, the situation does not worsen in a dramatic way. In particular, the number of deaths increases by 1, whereas the cumulative infections only increase by the small number of 58. In the second scenario where the number of contacts is doubled for both the young and the older populations, we find slightly larger (but not totally catastrophic) effects: the number of deceased individuals increases by 58 and the total number of infections grows by 1550.
Figure 3

Again the deaths D(t) and the cumulative infections C(t) are given for the case where the c factor (characterizing the number of contacts) amongst young individuals is doubled, but those of the older individuals (and of the young-older interaction) are kept fixed. This is shown in the top panels. In the bottom panels, the c’s of both young and old individuals are doubled.

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The situation becomes far more dire when the number of contacts is multiplied by a factor of 3 for both the young and older populations, meaning that the lockdown restrictions are eased significantly for the entire population. As shown in Table 3 and in Fig. 4, if the c’s of the young population only are multiplied by a factor of 3, then the deaths are increased by 3 and the infections by 198 (black line in the Figure and 3rd row of the Tables). This pales by comparison to the dramatic scenario when the c’s associated with both the young and older sub-populations are multiplied by 3; in this case, the number of deaths jumps dramatically to 48144, while the number of infections is a staggering 1283462, growing by about 500 times.
Figure 4

Same as reported in Fig. 3 but now where the contacts are multiplied by factors 3, 4 and 5. Full (dashed) lines hold for the young (older) population.

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An example corroborating the above qualitative trend can also be found in Fig. 4 and in the 4th and 5th rows of Table 3. Here, for e.g. (zeta =5), even the effect of releasing solely the young population leads to very substantial increases, namely to 6044 deaths and 306219 infections although of course it is nowhere near the scenarios of releasing both young and older populations. In the second scenario, the numbers are absolutely daunting: using the parameters of Table 2 we find that the number of deaths jumps to 83274 and the number of cumulative infections to 2221296.
Figure 5

Hospitalizations when only the young population (left) or both the young and older (right) population are released. Full (dashed) lines hold for the young (older) population.

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Finally, we show the prediction of the easing measures in the hospitalizations (i.e. daily occupied beds in hospitals). This is a crucial point to assess in order that the health system does not collapse because of COVID-19 patients. Figure 5 shows these trends for the above mentioned values of (zeta). In the case of releasing solely the young population (see left panel of the Figure), it is observed that the number of hospitalizations decreases monotonically except for (zeta =5), where the hospitalization peak is 523 for the young population and 1426 for the older one (values that are affordable by Greek health system); however, if both the young and older population are released (see right panel of the Figure), there is a monotonically decreasing behaviour only for (zeta =1) and 2. For higher (zeta) we observe that the height of the peak obviously increases with (zeta), while this peak also occurs earlier when the number of contacts is increased; for instance, for (zeta =3), the hospitalization peak number of the young population is 3844 whereas this value is 37030 for the older one, numbers that are, unfortunately, unaffordable for the Greek health system. These figures grow even further to 16869 and 163648 if (zeta =5).
In light of the above results, the significance of preserving the lockdown restrictions of the sensitive groups of the older population is naturally emerging. It can be seen that in the case where the number of contacts is roughly doubled, the behavior of release of young or young and older individuals is not dramatic (although even in this case releasing only the young population is, of course, preferable). Nevertheless, a more substantial release of the young population is still not catastrophic. On the other hand, the higher rates of infection, hospitalization and proneness to death of senior individuals may bring about highly undesirable consequences, should both the young and older members of the population be allowed to significantly increase (by 3 times or more) their number of contacts. More

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Climate change has increased water temperature and altered wind-driven water movements in aquatic systems1,2. This applies not only to the mean conditions3,4, but also to the frequency of extreme events (i.e., near the upper ends of the range of observed values5,  > 80th percentile). For example, high air temperature or powerful winds5,6,7,8,9 has affected the behaviour of surface gravity waves10. Understanding the changes in wind and wave climate provides insight into the prediction and management of climate change impacts related to coastal dynamics, such as coastal erosion and sediment budgets, water motions, and biological responses6,11,12. Several studies on the impacts of climate change on oceanic waves12,13,14,15 have been undertaken, including a recent study16 that shows a 0.41% annual increase in global wave power (WP; the transport of energy by waves, which represents the temporal variations of energy transferred from the atmosphere to the ocean surface motion over cumulative periods of time16,17 (Eq. 2) due to stronger winds caused by increases in sea surface temperature. The oceanic wave climate also responds to global atmospheric phenomena (e.g., El Niño Southern Oscillation and the Atlantic Multidecadal Oscillation), in which sea surface temperature modifies wind patterns and storm cyclogenesis12,18,19,20. A systematic long-term assessment of climate warming impacts on waves in lakes remains to be undertaken, but should include winds, which are one of the principal sources of mechanical energy for lake circulation and interbasin coupling (e.g., exchange)21,22,23,24.
The Laurentian Great Lakes, which consist of lakes Superior, Michigan, Huron, Erie, and Ontario (Fig. 1a), are the largest group of freshwater lakes on Earth; they contain 21% of the world’s volume of fresh surface water. These lakes have been affected by climate change in several ways including increased surface water temperature, longer summer stratification related hypoxia (i.e., dissolved oxygen [DO] concentrations  0.05); all the black bars are significant (i.e., p  8 m s−1) from the south and southwest that are the common wind directions over the Great Lakes23, tilt the thermocline upward in the western and northern part of the central basin due to Ekman transport of surface water southward22,38,42,43,44,45. As this hypolimnetic water upwells into shallower depths it can be transported counter clockwise by the alongshore surface currents moving to the west32. If there is a calm period following the high winds, the upwelled water in the northwestern part of the central basin will flow southward because of the pressure gradient and also in a clockwise direction (to the west) because of the Coriolis effect, and so will intrude into the western basin (i.e., a geostrophic flow) opposite to the hydraulic flow from the Detroit River (Fig. 1c)22,32,46. This causes the rapid (on the order of hours) formation of a thermocline within the northeastern portion of the western basin (Pelee Passage) due to the intrusion of low temperature bottom water22,42, which can also be hypoxic22 or anoxic (i.e., DO (approx) 0) at the sediment surface22 and contain high soluble reactive phosphorus concentrations (SRP; 0.02–0.05 mg L−1)47,48,49. Low values of sediment oxygen uptake are observed during these events in the western basin due to stratification and weak bottom shear and turbulence, which results in thicker diffusive sublayer22.
Interbasin exchange has been observed in lakes with multiple basins elsewhere (e.g., Lake Geneva50, Nechako Reservoir51) as well as in the Great Lakes region (e.g., Muskegon Bay52, Green Bay53, Kempenfelt Bay54, Pere Marquette River55). In Lake Michigan, for example, high winds can lead to coastal upwelling into Muskegon Lake causing episodic hypoxia52. In case of Lake Erie, interbasin exchange was identified as the dominant cause (63%) of hypoxia in the northeastern portion of the western basin during biweekly fishing trawls in August over the past 30 years22. However, there are no long-term continuous water quality observations to assess the occurrence and historic trends in these hypoxic events. Extreme winds prevailing from upwelling favourable directions (i.e., from the south and southwest) can generate strong surface waves and water currents through momentum flux at the air–water interface. Therefore, WP can be used as an indicator or proxy (but not the cause) of interbasin exchange. Here, we examine the historical trends in water temperature, winds and resultant waves in the context of climate change in the summer in the Great Lakes (Fig. 1a) with an emphasis on the western basin of Lake Erie (Fig. 1b). We examine data for August, which is the month when hypoxia is most likely to occur in dimictic north temperate lakes before the fall turnover, and when large HAB have been observed in the western basin of Lake Erie. August is also the time when the spatial extent of hypoxia in the central basin is the largest and when the aforementioned upwelling into the western basin is likely to occur22,40,56. The data examined are from buoys with the longest historical records (Fig. 1a and Table S1). We examine winds from the south and southwest directions, which are the common wind directions over the Great Lakes during August, and which are favourable for upwelling into the western basin of Lake Erie. The results show that the WP in Great Lakes has increased in the past 40 years. A pattern in WP (a proxy for hypoxic upwelling events into the western basin of Lake Erie) has also increased in frequency over this time, which has implications for the water quality (e.g., dissolved oxygen and total phosphorus) of the lake. The increased frequency of interbasin upwelling was confirmed using historical records of lake bottom water temperature (LBT), as well as dissolved oxygen and total phosphorus concentrations. This is the first time that WP has been identified as an indicator of climate change-driven biogeochemical responses in lakes.
Long-term trends in WP and LST in the Great Lakes
First, we investigate the historical trends in average lake surface temperature (LST), wind, and waves in the Great Lakes during August. Results show that LST and LSTw (hereinafter subscript ”w” is used to denote the variables measured during upwelling favourable winds from 180° to 270°, clockwise from north) have both increased significantly (p  0.2% year−1) since 1980, although lower trends were observed in lake Erie and Michigan (Figs. S1–S5 ((a) and (b)) and Table S1). These changes in the LST correspond to a warming trend in air temperature (Tair); the average Tair over the Great Lakes increased significantly by ~ 0.4 (pm) 0.2 ((pm) standard error) oC decade−1 since 1980 (Fig. S6a,b). There was an associated significant increase in wind speed (W) over the Great Lakes during August (Ww) of ~ 0.4 (pm) 0.1 m s−1 decade−1 for winds from the south and southwest (Figs. S1–S5 ((c) and (d)) and Table S1). Consequently, the wind stress associated with wind from the south and southwest over the water surface of the Great Lakes (({tau }_{w}=0.0012{rho }_{air}{W}_{w}^{2}), where ({rho }_{air})=1.22 kg m−3 is the density of air57, and the wind speed is measured 10 m above the water) increased significantly by 0.006 (pm) 0.002 Pa decade−1 during August (3.0 (pm) 0.9% year−1; Figs. S1–S5 ((e) and (f)) and Table S1).
The effects of increased wind stress can also be seen in wave power, which is a function of the square of significant wave height (the mean value of the largest third of the wave heights during typically 1 h, SWH) and the wave period (({T}_{p}); i.e., (WP propto {{T}_{p} times SWH}^{2})); and changes in wind are reflected in wave power ((WP propto {W}^{2.4}) and (propto {W}^{5}) for developing and fully developed waves, respectively; see “Materials and methods”). The average SWH and SWHw in the Great Lakes during August have increased significantly by 0.03 (pm) 0.02 and 0.04 (pm) 0.03 m decade−1, respectively (i.e., ~ 1.0 (pm) 0.8% and ~ 1.7 (pm) 1.5% year−1, respectively), and this is largely driven by the increase in the frequency of extreme surface winds58 (Figs. S1–S5g and h; WP responds to changes in mean values, but it is more sensitive to extreme events because WP (propto { SWH}^{2})16). Consequently, the average WP and WPw in the Great Lakes during August have increased by ~ 0.04 (pm) 0.02 and ~ 0.06 (pm) 0.03 kW m−1 decade−1, respectively (i.e., ~ 1.0 (pm) 0.6% and ~ 2.0 (pm) 0.9% year−1, respectively; Fig. 2). In Lake Erie, WPw during August increased significantly by 0.02 (pm) 0.01 kW m−1 decade−1 (1.4 (pm) 0.2% year−1; Fig. 2 and Table S1; the increasing trend in WP = 0.02 (pm) 0.02 or 0.5 (pm) 0.1% was not statistically significant). It is relevant to note that these results are based on observations from a single buoy per lake; the one with the longest available data records (Fig. 1a and Table S2). However, the wind records and historical wave trends between buoys Sta. NDBC 45005 and Port Stanley in Lake Erie (Fig. 1a), which are ~ 130 km apart, are consistent based on the available records. Specifically, wind speed and direction in 2018 have Pearson correlation coefficients, r  > 0.6 (Fig. S7a,b, respectively); Ww and WPw are also correlated with r = 0.51 and 0.67, respectively, during August of 1990–2018 and the buoys show similar temporal increases in WPw (~ 0.025 (pm) 0.02 and 0.02 ± 0.01 kW m−1 decade−1 in Port Stanley and Sta. NDBC 45005, respectively). The trends in historical LSTw and WPw are related statistically (i.e., higher mutual information; Fig. S8) similar to the relationship described for global sea surface temperature and oceanic WP used as an indicator of climate change16.
Figure 2

Historical patterns in wave power in Great Lakes. 10 year moving average of wave power (WP) during the August (a) and during August with the wind from south and southwest and (WPw; b). The dashed lines show the linear regression (statistical results provided in Table S1).

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The long-term variations in WP and LST may be related to the global atmospheric phenomena. The LSTw anomaly in all the lakes show an increasing trend beginning in 1995 (Fig. S9a), which corresponds to the switch from the negative mode of the Atlantic Multidecadal Oscillation (AMO) to the positive mode (associated with increased tropical cyclone activity and stronger westerly winds) between the 1980s and the early 2000s (Fig. S9b)16. Both the WPw and LSTw anomaly are positively correlated with the AMO (r ~ 0.50 and ~ 0.55, respectively, since 1990). Similar to global oceanic wave power16, peaks in WPw in the Great Lakes are associated with strong El Niño years (i.e., Multivariate El Niño/Southern Oscillation (MEI) greater than 1.5; Fig. S9c,d), which can contribute to the enhanced wind energy due to increased cyclonic events16. MEI and WPw in Great Lakes are generally correlated by r  > 0.45 since 1990, however, the impacts of global atmospheric events on temperature and water dynamics of Great Lakes requires further study.
Episodic hypoxic upwelling events in the western basin of Lake Erie
We used historical records (Table S2) of long-term near-bottom water temperature (1998–2018) and dissolved oxygen (2007–2018) in the northeastern portion of the western basin of Lake Erie as well as wave observations in the western portion of the central basin (1980–2018 in Sta. NDBC 45005, Fig. 1) in August to determine the frequency of hypoxic upwelling events and the impacts of these events on the total phosphorus concentration in the northeast portion of the western basin. These analyses do not include the local hypoxia due to periods of calm and warm atmospheric conditions that may occur annually31 and, which are different than episodic upwelling events. Intrusion of cold hypoxic hypolimnetic water from the central basin into the western basin, following high winds from upwelling favourable directions, can cause a sudden drop (on the order of hours) in LBT and dissolved oxygen (DO) when the hypolimnetic water in the central basin is hypoxic22. The LBT time series in the western basin from 2017 to 2018 show that LBT decreased more than 3 °C in less than 12 h during upwelling events; e.g., 9–16, 18–22 and 26–31 August 2018 at Sta E (Fig. 3b) and 24–29 August 2017 at Leamington and Sta E (Fig. S10b). The records of LBT measured by the Ontario Ministry of Natural Resources and Forestry (MNRF) in August in Leamington Ontario between 1998 and 2018 detected 23 events of intrusion of cold water, which are consistent with upwelling (the blue symbols in Fig. 4a).
Figure 3

Wave power and bottom water temperature during August 2018 in the western basin of Lake Erie. (a) Time series of wave power (WP; black line), wave period (Tp; magenta), and significant wave height (SWH; blue) recorded at Sta. NDBC 45005. (b) Time series of dissolved oxygen (DO; red) and water temperature (LBT; blue dashed-line) in Sta. E at 1 m above the bed and bottom water temperature in Leamington (blue solid-line) in August 2018. The red triangles represent the observed hypoxic events in the western basin of Lake Erie. The wave power of the waves from south and southwest (i.e., favourable for upwelling) are positive preceding upwelling.

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Figure 4

Number of hypoxic upwelling events in the western basin. (a) The number of hypoxic upwelling events based on patterns in wave power at Sta. NDBC 45005 (dark grey: average WPw  > 0.44 kW m−1, light grey: 0.37  8 m s−1 from similar directions, which corresponds to the ~ 80th percentile of wind speeds and is greater than the sum of the average and standard deviation of the wind speed (~ 6 and 2 m s−1, respectively). This wind threshold is consistent with Rao et al.’s44 wind speed that led to upwelling, which resulted in a fish kill along the north shore of the central basin in 2012.
We used a least-square method to find a wave pattern (i.e., wave direction, duration, and power) that could be applied to predict the number of upwelling events that could be hypoxic between 1998 and 2018 based on LBT observations. A rapid decrease in the LBT at both Sta E and Leamington (12 km vs. 20 km from the Pelee Passage, respectively) occurred during events in which the average WP was  > 0.44 kW m−1 (i.e., 22–24 August 2017; Fig. S10a,b). The model predicted 25 upwelling events at Leamington (dark bars in Fig. 4a) of which 23 were observed (as stated above; no data were available for 2012; blue circles in Fig. 4a) for waves from south and southwest that lasted for at least 15 h with an average wave power greater than 0.37 kW m−1. Of the 23 observed events, the model predicted 21 events providing a root mean square error [RMSE] of 0.20 events. We validated the model predictions using the biweekly DO measurements from MNRF cruises between 2007 and 2018, which happened to sample 17 of the 23 observed events of low LBT. We note, however, that two hypoxic upwelling events were also recorded outside the study period, i.e., early September; this supports the study’s focus on August. Hypoxic conditions (DO  1.6 events year−1 in 2018 based on a 10-year moving average. Specifically, 21 of 49 (~ 43%) upwelling events in the last four decades have occurred in the past 10 years. Thirty-two of these were strong events with WP  > 0.44 kW m−1, 15 of which (~ 47%) occurred after 2009. Interestingly, this pattern in wave power (i.e., waves from south and southwest that last for  > 15 h with an average WP  > 0.37 kW m−1 from the historical data) was also observed in August 1980 (Fig. 4a), when the LBT dropped following rapid formation of a thermocline, which at the time was attributed to the upwelling of hypolimnetic water from the central basin40,42. These results indicate that an increase in extreme winds from south and southwest during August, over the last four decades, has resulted in more frequent upwelling from the central basin into the western basin and consequently a greater number of episodic hypoxic events in that part of Lake Erie.
The effect of upwelling on phosphorus concentrations was examined through an analysis of the water column-average total phosphorus (TP) observations from biweekly cruises conducted by the MNRF at station W5 (Fig. 1b). We examined the available data recorded between 15 July and 15 September from 2000 to 2018 (3–5 records year−1; 66 observations in total), which is a period in which linear patterns in TP vs. sampling date were not evident (p  >   > 0.05). The z-score (standard deviate) was determined for the data within a given year (({mathrm{Z}}_{mathrm{TP}}=left(mathrm{TP}-{mathrm{TP}}_{mathrm{mean}}right)/mathrm{SD}), where ({mathrm{TP}}_{mathrm{mean}}) is the annual average of TP and SD is the standard deviation). Positive ({mathrm{Z}}_{mathrm{TP}}) values (i.e., (mathrm{TP} >{mathrm{TP}}_{mathrm{mean}})) were observed in 11 cases in which the sampling occurred  1) observed during 5 August–8 September sampling (black solid circles in Fig. 4b). Statistical comparison revealed that the average ({mathrm{Z}}_{mathrm{TP}}) was significantly higher during upwelling vs. non-upwelling samples (i.e., 0.95 ± 0.18, n = 11 vs. − 0.26 ± 0.12, n = 25; ANOVA F1,34 = 29.64, p  More

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