Heat Waves Can Cause Hypoxia in Shallow Lakes

We assessed how warm air temperatures, high solar radiation, and weak wind speeds might induce hypoxia in a shallow lake during a heat wave. We simulated bottom‐water dissolved oxygen concentrations and compared concentrations in 2022 with the average for the previous 30 years. We found that hypoxia was most sensitive to wind speeds. When the wind speed was low, convection was insufficient to prevent hypoxia, but there was no hypoxia if the wind speed equaled the average speed during the previous 30 years. However, if solar radiation and air temperatures equaled the respective averages during the previous 30 years, hypoxia did not occur, even if wind speeds were low. We conclude that the combined effects of weak winds and either high solar radiation or air temperatures induced hypoxia during the heat wave of 2022.

Tracking the effects of these physical changes on oxygen dynamics requires high-frequency monitoring of water temperatures and DO b concentrations (Wells & Troy, 2022).
Japan experienced a heat wave from June to July of 2022. During that time, we monitored DO concentrations, water temperatures, and phytoplankton biomass every 10 min in Lake Kasumigaura, a shallow, eutrophic lake 60 km northeast of Tokyo, Japan ( Figure S1 in Supporting Information S1). Our goal was to clarify whether and how the heat wave affected DO b concentrations. By integrating the results of high-frequency monitoring of meteorological conditions, water temperatures, DO concentrations, and phytoplankton biomass into a simulation, we were able to analyze how heat waves could impact the thermal stability of the water column and the DO b concentration. We used a one-dimensional numerical simulation model to investigate how meteorological conditions affected the DO b concentrations (Antonopoulos & Gianniou, 2003;Dong et al., 2020;Fang & Stefan, 2009;Ladwig et al., 2022;Stefan & Fang, 1994). We also collected meteorological data from 1992 to 2022 and estimated how heat waves affected stratification and the supply/consumption of DO b . We tested the hypotheses that (a) high air temperatures and solar radiation lead to increased stratification of the water column during heat waves; and (b) slack winds limit the supply of DO to bottom water and thereby cause DO b depletion, even in shallow water.

Study Site and Buoy System
Lake Kasumigaura has a surface area of 172 km 2 and maximum and mean water depths of 7 and 4 m, respectively. The sediments of Lake Kasumigaura are highly polluted, and organic matter has accumulated in the sediments. The water depth at the study site was ∼4 m and the water level was controlled artificially. Because stream inflow from the northern part of the study site is only ∼5 m 3 s −1 , the effects of stream inflow on the DO b concentration are negligible.
We developed a new buoy observation system ( Figure S2 in Supporting Information S1) that uses sensors to record water temperatures at depth intervals of 0.5 m. We monitored the water temperatures (HOBO U22, Onset, Cape Cod, MA, USA) and the DO concentrations (HOBO U26 DO logger, Onset) every 10 min. The DO concentration was measured at the lake surface (∼60 cm depth: DO s ), at the bottom of the buoy (350 cm depth: DO 350 ), 30 cm above the lake floor (DO 30b ), and 10 cm above the lake floor (DO 10b ). Chlorophyll a data were recorded by a sensor (EXO3, Xylem Japan, Kanagawa, Japan). The sensor was calibrated with Rhodamine dye and corrected based on the values measured via a UNESCO protocol ( Figure S5 in Supporting Information S1). We serviced the sensors every month to minimize fouling and to check the calibration.

Meteorological Data Set
We used two kinds of meteorological data to (a) analyze heat wave conditions in 2022 compared with the previous 30 years; and (b) carry out a numerical simulation. To compare the heat wave conditions in 2022 with the previous 30 years, we downloaded data from the Japan Meteorological Agency (https://www.data.jma.go.jp/obd/stats/ etrn/index.php) collected at Tateno, Tsukuba ( Figure S1 in Supporting Information S1). We collected data during the period 23 June-5 July from 1992 to 2022. We calculated hourly averages of air temperature, solar radiation, and wind speed from 1992 to 2021 and compared them with the data from 2022.
For numerical simulation, meteorological data were collected at a station near the water quality sensors ( Figure  S1 in Supporting Information S1). Solar radiation, air temperature, atmospheric pressure, and wind direction/ speed were collected via a meteorological data-collecting system (Vantage Pro2, Davis Instruments, Hayward, CA). The data were collected at ∼2 m above the water surface. The data were recorded every 5 min for inclusion in the simulation model.

Physical and DO Models
We used a one-dimensional numerical simulation model based on Henderson-Sellers (1985). The details are shown in Supporting Information S1 (Table S1). The model simulated the effects of wind turbulence on the vertical distribution of water temperature. Because wind is the major external force on Lake Kasumigaura, we used the model to analyze the vertical structure of water temperature (Fukushima et al., 2022). We used vertical eddy diffusion coefficients based on Munk and Anderson (1948). When the square of the buoyancy frequency (N 2 ) was negative, we assumed that the water column was well mixed and that the water temperature was the same as the temperature of the surface water at all depths (convective mixing (Dake & Harleman, 1969)). The heat flux at the lake surface was calculated based on a previous study of Lake Kasumigaura (Shinohara et al., 2021). We took into consideration shortwave, longwave, sensible, and latent heat fluxes to calculate the exchange of heat at the surface (Text S1 in Supporting Information S1).

DO Model
We used a diffusion equation (Table S2 in Supporting Information S1) to calculate DO concentrations. The mass balance (R) of DO in the water column was calculated using Equation 1: where P DO is the supply of DO from phytoplankton photosynthesis, R DO is the respiration rate of the phytoplankton, and BOD is the DO consumption associated with other biological oxygen demand (Table S2 in Supporting Information S1). To calculate the rate of photosynthesis, we used the chlorophyll a concentration measured every 10 min by the water quality sensor.
The boundary conditions for the DO fluxes at the surface and bottom were aeration and DO b uptake by the sediments (sediment oxygen demand (SOD)), respectively (Robson & Hamilton, 2004): where K DO is the vertical eddy diffusion coefficient of DO, C DO is the DO concentration, z is the water depth, w is the coefficient in Wanninkhof's equation for the exchange of oxygen (=7.22 × 10 −2 s 2 m −1 d −1 ; Wanninkhof, 1992), O a is the oxygen-saturated DO concentration, DO top is the DO concentration at a depth of 0-0.1 m below the lake surface, S c is the Schmidt number of DO, s up is the DO uptake rate by the sediments (=0.90 g m −2 d −1 ; Shimotori et al., 2021), and θ s is the temperature acceleration (=1.2; dimensionless). The oxygen-saturated DO concentration (O a ; gO 2 m −3 ) depends on the water temperature (Saito et al., 1983). Table S3 in Supporting Information S1 shows the parameters.

Calculation Conditions and Flux Analyses
We used an implicit finite volume scheme to integrate the model. The calculation period was 9 June-31 July 2022. We started the calculation 31 days before 9 June (9 May 2022) to allow the model to spin up and to create a homogeneous vertical distribution of DO concentrations and water temperatures as the initial conditions. The width of each layer was 0.1 m, and the time interval was 60 s.
We equated bottom water to water less than 0.5 m above the sediment surface (depth of 3.5-4.0 m in the water column). We calculated the oxygen fluxes in and out of a parcel of water as a function of water depth. We used Equation 4 to calculate the diffusive flux (F diff , g m −2 s −1 ) across a depth of 3.5 m: where K DO is the diffusion coefficient of DO (g m −2 h −1 ; Table S2 in Supporting Information S1), C DO is the DO concentrations (g m −3 ) at a depth of 3.5 m, and z is the water depth (m). We equated the flux due to convective mixing (F conv , g m −2 h −1 ) to the difference of the DO concentrations before and after convection: where dz is the grid size (dz = 0.1 m). We calculated Equation 5 at water depths of 3.5-4.0 m at each 60-s time step.

Scenario Analyses of Physical Effects on DO b Concentrations-Sensitivity Analysis
To quantify the contributions of physical factors to the DO 10b concentrations, we calculated the sensitivities of the DO 10b concentration to air temperature, wind speed, and solar radiation. We analyzed the differences of meteorological conditions (air temperature, wind speed, and solar radiation) during the heat wave and the conditions during 23 June-5 July of 2022 and the 30 years prior to 2022. We then calculated whether the average meteorological conditions during the previous 30 years could have mitigated the low DO b concentration simulated by the model during the heat wave. Based on this simulation, we assessed the individual or combined effects of the three meteorological variables (Table S4 in Supporting Information S1). During the heat wave, we multiplied the values in 2022 by factors of 0.83 for air temperature, 1.47 for wind speed, and 0.69 for solar radiation. These multiplication factors were based on the observed meteorological conditions and the average values during the previous 30 years and during 2022. Figure 1 shows the observed and simulated water temperatures and DO concentrations at the surface (60 cm below the water surface: DO s ), 350 cm below the surface (DO 350 ), 30 cm above the sediment surface (DO 30b ), and 10 cm above the sediment surface (DO 10b ). The observed DO 10b and DO 30b concentrations were low, despite the high concentration of DO 350 and DO s . The observed temperature stratification was simulated well by the model (Figures 1a and 1b; r = 0.95, p < 0.001; RMSE = 0.95°C). The observed DO concentrations were also simulated well at all depths where observations were made (Figures 1c-1e; r = 0.58, p < 0.001, RMSE = 2.1 mg L −1 ).

DO Concentrations and Meteorological Conditions During the Heat Wave
The DO 10b concentration gradually decreased, and the water became hypoxic (DO < 2.0 mg L −1 ) during the heat wave ( Figure 2a). The air temperatures during the heat wave of 23 June-5 July 2022 in Tsukuba City were ∼10°C above the average air temperature for that time interval during the previous 30 years (maximum air temperature in 2022: 33.3 ± 3.0°C; previous 30 years: 25.6 ± 1.1°C; paired t-test, p < 0.001; Figure 2b). Solar radiation during 23 June-5 July, 128 W m −2 , was 1.47 times the analogous solar radiation during the previous 30 years (maximum solar radiation in 2022: 837 ± 159 W m −2 ; previous 30 years: 516 ± 59.5 W m −2 ; paired t-test, p < 0.001; Figure 2c). The wind speed was greater between 23 and 27 June, but it was lower after 28 June. Wind speeds from 23 June to 5 July in 2022 were 0.69 times the analogous average wind speeds during the previous 30 years (paired t-test, p < 0.05; Figure 2d).
There was a significant positive correlation between daily mean solar radiation (W m −2 ) and air temperatures (Figure 2e). There was also a significant positive correlation between daily solar radiation and air temperatures in 2022 (Figure 2e). There was a significant correlation between wind speed and air temperature, but the correlation was weak (Figure 2f). There was no significant correlation between solar radiation and wind speed (Figure 2g).

Simulation During the Heatwave: Sensitivity of DO
The conditions to which the DO concentrations were sensitive in descending order of sensitivity were wind speed (46.4%) > combined effects of air temperature and solar radiation (37.5%) > air temperatures (22.9%) > solar radiation (18.8%; Figure 3a). Either average air temperature or average solar radiation led to hypoxic bottom waters (Figure 3a). The diffusive flux did not differ much between the default and other conditions (Figure 3b).
The DO 10b concentrations were most sensitive to wind speed. The default conditions were remarkably associated with no convective flux of DO across a depth of 3.5 m during 28-30 June and during 3-4 July (Figure 3c). During those periods, the mixing depth due to thermal convection did not reach 3.5 m under default conditions and the effects of only solar radiation and air temperature (Figure 3d). When wind speed was increased by 46%, there was always a flux associated with convective mixing during 23 June-5 July (Figure 3c), and DO reached the bottom of the lake (Figure 3d, Figure S6 in Supporting Information S1). This difference was caused by the flux of heat into the atmosphere.
Decreases of both solar radiation and air temperatures contributed to the dissipation of hypoxia (Figures 3c  and 3d). The effects included convective mixing and the suppression of SOD by the decrease of water temperatures ( Figure 3e, Table S5 in Supporting Information S1).

Discussion
Heatwaves have been observed more often in recent years than before (Woolway et al., 2020) and lake ecosystems have suffered from the increase in water temperatures (Woolway et al., 2022). The air temperatures and solar radiation between 23 June and 5 July 2022 are regarded as the highest during the last 30 years (Figure 2). During that time, depletion of DO b occurred, especially from 27 June to 5 July. Observations and simulations indicate that the effect of wind was larger than the effects of solar radiation, air temperatures, or both (Figures 2 and 3).
The effects of wind on hypoxia are plausible because hydrodynamics in shallow lakes are often controlled by the wind (Luettich Jr. et al., 1990;Niemistö et al., 2008). Thermal stratification in shallow lakes is increased by a decrease of wind speed more than an increase of air temperature (Woolway et al., 2017). However, it was surprising that wind speed affected thermal convection during the afternoon and night more than the diffusive flux of DO associated with sea breezes (Figure 3). Those results differ from the results of the study by Masunaga et al. (2022), which suggested that the contribution of sea breezes to DO b was more important than the contribution of convective mixing. Our simulation also revealed that the flux of DO by thermal convection was smaller than by diffusion, and hypoxia occurred unless there was an adequate flux of DO. During the heat wave, our results indicate that cooling by only latent and sensible heat fluxes was insufficient to mix the whole water column (Figure 3).
Information on wind speed during the night is limited, but winds have been slackening because of climate change in the northern hemisphere (Gulev et al., 2021;Shen et al., 2021;Wu et al., 2018). Within the Kanto area, where Lake Kasumigaura is located, land sea breezes are the dominant winds (Yoshikado, 1992(Yoshikado, , 2013, and wind speeds over the Kanto Plain have not changed in recent years (Shen & Zhao, 2020). To our knowledge, how future meteorological conditions will change during heat waves on the Kanto Plain is still unclear, but Li et al. (2016) have reported that there was little wind at night during a heat wave in Beijing.
Increases of air temperatures, solar radiation, or both are also needed to create hypoxic conditions. Even when solar radiation increases, air temperatures vary widely (Figure 2e), and the single effect of a change of either solar radiation or air temperature has a small impact on the dissipation of hypoxia (Figure 3a). Overall, we found that the combined effects of wind and either solar radiation or air temperatures impacted the creation of hypoxic conditions by limiting fluxes of DO via thermal convection (Figure 4, Figure S6 in Supporting Information S1). Furthermore, if the air temperature and solar radiation are at normal levels, hypoxia is dissipated because the SOD is low.
Our results are relevant to other lakes because DO b depletion in shallow lakes occurs in many lakes (Masunaga & Komuro, 2019), and many lakes throughout the world have physical characteristics similar to those of Lake Kasumigaura (e.g., land-sea breezes and thermal convection; (Imberger & Ivey, 1991)). In contrast, the implications of our study are limited by considerations such as the uncertainty of the factors responsible for SOD (e.g., organic matter (Collins et al., 2017) and the sizes of sediment particles (Lavery et al., 2001)). Furthermore, thermal stratification and mixing are controlled by the size of a lake (e.g., water depth relative to fetch length), water temperatures, and surface heat fluxes (Fischer et al., 1979;Read et al., 2012). In our study, we did not consider humidity because the humidity was lower than the average humidity during the previous 30 years ( Figure S7 in Supporting Information S1). However, heat waves are often accompanied by high humidity (Smith et al., 2013), and high humidity can also affect thermal stability and accelerate hypoxia. Future studies of the effects of heat waves will need to consider the physical characteristics of each lake (e.g., the DO fluxes due to convection and diffusion) coupled with modeling of SOD (Collins et al., 2017). The frequency of heat waves will increase in the future, and the results of our study indicate that the slackening of terrestrial wind speeds in response to climate change (Wu et al., 2018) will lead to more frequent occurrences of hypoxia, even in shallow lakes.
In summary, we investigated the meteorological factors responsible for creating hypoxic conditions similar to the conditions during the heat wave of 2022. We recorded higher air temperatures, higher solar radiation, and weaker winds during the heat wave. We found that weaker winds led to insufficient thermal convection and to hypoxia. Furthermore, the combined effects of increased solar radiation and air temperatures led to high SOD. It is generally thought that the water column of shallow lakes is easily mixed by the wind blowing over the lake, but we found that insufficient convective mixing by cooling of the surface water led to low DO b concentrations and hypoxia during the heat wave of 2022 in Lake Kasumigaura. . Conceptual model of conditions during a heat wave with hypoxia (black lines) and increased wind speeds with no hypoxia (blue lines). the model and two anonymous reviewers whose comments greatly helped us to improve the manuscript. This research was financially supported by the Environment Research and Technology Development Fund 5RF-2103 of the Environmental Restoration and Conservation Agency of Japan.