Relative impacts of increases of solar radiation and air temperature on the temperature of surface water in a shallow, eutrophic lake

We monitored lake surface water temperatures from 1992 to 2019 in Lake Kasumigaura, a shallow lake in Japan. We hypothesized that increases of shortwave radiation had increased surface water temperatures and heat fluxes more than had the increases of air temperature. We used the heat flux analyses and the sensitivity analyses to test the hypothesis. The fluxes of solar radiation gradually increased during the study period in a manner consistent with the phenomenon of global brightening. The increase was especially apparent in the spring. The rate of increase of surface water temperature was especially significant in May. Air temperature did not significantly increase in May, but it increased significantly in June (0.40 °C decade (cid:1) 1 ). A sensitivity analysis of the heat fluxes at the lake surface (shortwave radiation, longwave radiation, latent heat flux, and sensible heat flux) revealed that surface water temperature was more sensitive to changes of shortwave radiation than to air temperature during the spring. Although other factors such as inflows of groundwater and river water may also have impacted surface water temperatures, the increase of solar radiation appeared to be the major factor responsible for the increase of surface water temperature during the spring in Lake Kasumigaura. the rate of increase of the atmospheric temperature in spring. (cid:129) We clarified that increases of solar radiation had affected the surface water temperature more than the increases of atmospheric temperatures.


INTRODUCTION
The International Panel on Climate Change (IPCC) has predicted a global temperature increase of 4.8°C by 2100 based on scenario RCP 8.0 (Stocker et al. 2013). This increase in air temperature could substantially affect lacustrine environments (Woolway et al. 2020). Previous studies have analyzed the effects of the climate change on deep lakes, such as changes in stratification pattern, but shallow lakes should also be affected by the climate change. Previous studies have experimentally predicted the effects of increases of surface water temperatures on aquatic ecosystems (Meerhoff et al. 2012;O'Reilly et al. 2015), such as macrophytes (Feuchtmayr et al. 2009) and phytoplankton blooms (Bucak et al. 2018).
Global air temperature increase could cause an increase of surface water temperatures, but some studies have already reported that the rate of increase of surface water temperatures has exceeded the rate of increase of air temperature in lakes (Schmid & Köster 2016;Woolway et al. 2019). The implication is that the increase of surface water temperatures has been determined by more than the increase of air temperature. A variety of factors affect the flux of heat through the surface water of a lake and hence the temperature of the water (e.g., shortwave radiation, longwave radiation, sensible heat flux, latent heat flux). For example, the global increase of solar radiation (Wild et al. 2005(Wild et al. , 2007 has increased the flux of shortwave radiation (Schmid & Köster 2016). The direction and speed of the wind associated with, for example, local land-sea breezes also change surface water temperature via sensible and latent heat fluxes through the lake surface (Yoshikado 2013). Differences in the changes of lake surface water temperatures have therefore reflected how much and what kind of heat fluxes through the water surface have changed during the last couple of decades.
Shallow lakes with mean water depths of less than 5 m are very common in Japan (78% of the total number of lakes). Whether and how much increases of air temperature are affecting lake surface water temperatures should be clarified because changes of surface water temperature can be expected to have impacts on lake biology [e.g., phytoplankton blooms; Tomioka et al. (2011)] and chemistry [e.g., colored dissolved organic matter; Weyhenmeyer et al. (2016)]. Previous studies of climatic effects on lake surface water temperatures have focused mostly on subarctic lakes and high-altitude lakes (Fink et al. 2014;Schmid & Köster 2016;Niedrist et al. 2018). Such lakes are especially sensitive to an increase of surface water temperature because of the associated reduction of ice cover (Benson et al. 2012;Magee & Wu 2017;Chikita et al. 2019). However, most temperate lakes are ice-free, and little information is currently available about the effect of meteorological changes on heat fluxes.
The objective of the current study was to clarify (1) how surface water temperatures have been changing in a shallow, eutrophic lake and (2) whether heat fluxes during the last 28 years in Lake Kasumigaura, a shallow, eutrophic lake in Japan, have increased more because of changes of solar radiation or air temperature. First, we documented the relationship between surface water temperature in Lake Kasumigaura and meteorological conditions. Second, we calculated heat fluxes (i.e., shortwave radiation, longwave radiation, sensible heat flux, and latent heat flux) through the lake surface. We then analyzed the sensitivity of the heat fluxes to solar radiation and air temperature. Third, because the surface water temperature is also altered by river inflow, ground storage, and groundwater inflow, we analyzed how much changes of the heat flux through the lake surface could explain changes of surface water temperature in Lake Kasumigaura. We have been monitoring the surface water temperature of Lake Kasumigaura and meteorological conditions over the lake since 1992. Because the monitoring data have been obtained at intervals of 1 h, we could carry out detailed analyses of heat fluxes. We tested the hypothesis that increases of solar radiation had affected the surface water temperature more than the increases of air temperatures.

Lake Kasumigaura
Lake Kasumigaura, the second-largest freshwater lake in Japan, is 60 km northeast from the Tokyo metropolitan area (Figure 1; 36°00.22 0 N, 140°22.85 0 E). The water depth of the lake averages 4 m, and the maximum water depth is 7 m. The lake has a surface area of 172 km 2 and a watershed area of 1915 km 2 . Water retention time in Lake Kasumigaura is about 200 days. More than 944,000 people in 2018 live in the watershed. The lake is a source of drinking water and is used for fishing and recreation. Lake Kasumigaura is ice-free even in winter; its minimum recorded surface water temperature has been ∼4°C since 1992. The water level of the lake is controlled and is almost constant. Lake Kasumigaura is very turbid; Secchi depths in the lake are ∼50 cm. Our research team from the National Institute for Environmental Studies has been monitoring Lake Kasumigaura for more than 40 years as a part of the Global Environmental Monitoring System Water Trend Monitoring Program.

Data collection and analyses
The hourly monitoring data are available at the website of the Lake Kasumigaura Water Research Station of the National Institute for Environmental Studies (Figure 1). The water depth at the study site was ∼1.7 m. We collected hourly surface water temperature, wind speed, and air temperature data at the monitoring station ( Figure 1); temperature and humidity data were collected at an adjacent weather station on the rooftop of our laboratory at a height of 13 m above the ground. Surface water temperatures were collected at a depth of 0.2 m. The data are opened online at National Institute for Environmental Studies (http://www.cger.nies.go.jp/db/kasumi/index.html). If data were missing for more than 60 h during a given month, monthly averages were not calculated for that month.
Concentrations of suspended particulate matter (SPM) in the atmosphere were collected from the database of the Atmospheric Measurement and Experiment Laboratory (Air Quality Research Station), National Institute for Environmental Studies (NIES; Figure 1). Solar radiation and atmospheric pressure data were collected from the website of the Japan Meteorological Agency (https://www.jma.go.jp/jma/menu/menureport.html). We used data from the Japan Meteorological Agency (JMA) Automated Meteorological Data Acquisition System at Tsukuba for solar radiation and atmospheric pressure. Longwave radiation data were also checked from the website of the JMA. The data were downloaded from the website of JMA and used for the analyses.

Heat flux model at the lake surface
We analyzed heat fluxes at the water surface from 1992 to 2019. Positive values indicate downward fluxes, and negative values indicate upward fluxes. The net heat flux through the water surface was expressed with the following equation: where R n is the net heat flux through the water surface (W m À2 ), R s is the flux of shortwave radiation (W m À2 ), R l is the flux of longwave radiation (W m À2 ), R la is the latent heat flux (W m À2 ), R sn is the sensible heat flux (W m À2 ), and R prec is the heat flux associated with precipitation (W m À2 ).
The shortwave radiation was calculated with the following equation: where ref is albedo, and S d is the flux of solar radiation (W m À2 ). We calculated ref based on the zenith angle (Kondo 1994;Woolway et al. 2015).  The flux of longwave radiation was calculated with the following equation: where R ld is the flux of downward longwave radiation (W m À2 ) and R lu is the corresponding upward flux (W m À2 ). Downward longwave radiation was calculated by using the following equation: where ε a is emissivity, σ is the Stefan-Boltzmann constant (¼5.67 Â 10 8 W m À2 K À4 ), and T a is air temperature (K). Emissivity (ε a ) was calculated with the following equation ( (5) where CC is the cloud cover function (0-1), e a is the air vapor pressure, and AT is the air temperature (°C). The values were also verified with data collected by the JMA. Cloud cover (CC) was calculated with the following equation (Quaas 2012) : where r is relative humidity (0-1), and r c is the critical relative humidity (¼0.1). Upward longwave radiation was calculated by the following equation: where 1 is emissivity [¼1.0; dimensionless; Sugita et al. (2020)], and T w is the surface water temperature (K). Sensible and latent heat fluxes were calculated with the following bulk formulae: where c p is specific heat under constant pressure (J kg À1 K À1 ), ρ a is the density of air (kg m À3 ), C H and C E are the bulk coefficients for sensible and latent heat (dimensionless), respectively, U is wind velocity (m s À1 ), l is latent heat (J kg À1 ), q sat is saturation-specific humidity (dimensionless), and q is specific humidity (dimensionless). The bulk coefficients of the latent (C H ) and sensible heat fluxes (C E ) were calculated in accord with (Kondo 1994) as follows: The heat flux associated with precipitation was calculated with the following equation (Chikita et al. 2019): where ρ w is the density of water (kg m À3 ), c w is the specific heat of water (J kg À1 K À1 ), d is precipitation (m s À1 ), T p is the temperature of the rainwater, and T o is the standard temperature. The temperature of rainwater was assumed to be the same as the air temperature, and the standard temperature was the annual mean air temperature, 15°C.

Sensitivity of heat fluxes through the lake surface on solar radiation and air temperature
We used a sensitivity analysis to determine how solar radiation and air temperature had changed heat fluxes through the lake surface. The default values of solar radiation, air temperature, and surface water temperature were the values from January to June in 2000. Because solar radiation and air temperature were both expected values on the regression line (solar radiation or air temperature vs. year) in 2000, we chose the year as the default year. For the sensitivity analysis, we determined the magnitude of the increase in solar radiation and air temperature based on the slope of the regression line between the solar radiation/air temperature and years during the observation period. We set the magnitude of the increase in solar radiation from about À3% (À5.1 W m À2 ) and þ8% (þ13.5 W m À2 ) based on the values in 2000. The magnitude of the increase in air temperature was set to about À2.0% (À0.21°C) and þ4.0% (þ0.43°C) from the values in 2000. The sensitivities of air temperature and solar radiation were calculated with the following equation: where β is the calculated value of each heat flux, and α is the default value of each heat flux.

Statistical analysis
We used the Pearson product-moment correlation to determine the significance of long-term increases or decreases. A type I error rate (a) of less than 0.05 was regarded as significant. We used the software Microcal Origin ver. 8.5.1.J for the calculations.

RESULTS AND DISCUSSION
3.1. Long-term changes of surface water temperature and meteorology We first analyzed monthly meteorological data from 1992 to 2019 ( Figure 2 and Table 1). Surface water temperature increased markedly during the study period, especially in May. The rate of increase in May was 0.74°C decade À1 (Table 1). In June, increases of both atmospheric and surface water temperature were observed (air temperature: 0.40°C decade À1 ; surface water temperature: 0.56°C decade À1 ). The rate of increase of the surface water temperature was much greater than that of air temperature. The higher rate of increase of surface water temperature than air temperature was consistent with results of previous studies , and the increase of surface water temperature in spring was also consistent with previous studies in shallow lakes in China ). An increase of air temperature was also observed in August, but surface water temperature did not increase significantly during that time. Many studies have analyzed the water temperature increase in summer, but our study showed the clear increases during the springtime. Solar radiation increased in May and June by ∼25% between 1992 and 2019 (Figure 2(c)). The reason for the increase in solar radiation could be the decrease in SPM in the atmosphere (Tanaka et al. 2016). The SPM concentrations decreased from  (Figure 3(a)). There was a negative correlation between solar radiation and SPM concentrations in the atmosphere during spring (Figure 3; in May and June: r ¼ À 0.56, p , 0.01). This correlation is consistent with previous studies that have shown that a decrease of aerosol concentrations can increase the flux of solar radiation to Earth's surface around the world (Tanaka et al. 2016).
Changes in wind velocity were observed only in October (Table 1); wind velocity can be changed by global warming and urbanization (Shen et al. 2019). In the Kanto Plain of Japan, where Lake Kasumigaura is located, land-sea breezes, which are dominant from spring to autumn (Yoshikado 2013), affect water quality in the area (Shinohara & Isobe 2010, 2012. The other factors that affect the heat flux through the water surface changed only a little from 1992 to 2019. The precipitation and humidity during each month exhibited no significant increase during that time.

Heat fluxes and sensitivity analyses
The surface energy flux was calculated ( Figure 4); the calculated values were comparable to those in the previous Lake Kasumigaura report (Masunaga & Komuro 2019). We also verified the downward longwave radiation flux with that observed at Tsukuba ( Figure 5). The high correlation coefficient (r ¼ 0.91, p , 0.001) and the slope of the regression line (slope ¼ 1.0) suggested that the simulated values were realistic.

Uncorrected Proof
To determine whether surface water temperature was more sensitive to changes in solar radiation or air temperature, we calculated the effects of solar radiation and air temperature on R n values at the lake surface (Tables 2 and 3). The initial air temperatures and solar radiation fluxes are shown in Figure 6(a) and 6(b).
Because the mean values of air temperature and solar radiation during January and June were the expected values on the regression line ( Figure S1), the values of 2000 were set to the default value for the analyses of their sensitivities on net heat flux (R n ). The magnitudes of the increase in solar radiation and air temperature were determined by the slope of the regression lines: air temperature was set to a value between 10.4°C (À2.0% from the default value in 2000) and 11.1°C (þ4.0% from the default value in 2000). Similarly, the flux of solar radiation was set to a value between 164 W m À2 (À3.0%) and 183 W m À2 (þ8.0%).
Increases of air temperature were associated with increases of downward longwave radiation (∼1.0%), sensible heat flux (∼28.6%), latent heat flux (∼3.1%), precipitation (∼92.0%), and R n values (31.1%). Increases of solar radiation affected the net heat flux (R n ), which increased from the default value by 88.4%. Surface water temperature at the lake surface was therefore more sensitive to increases of solar radiation. The greater sensitivity of surface water temperature to the increase of solar radiation was consistent with the conclusion of a previous study of temperate lakes . The increase of solar radiation has been observed globally (Wild 2009) and has been associated with an increase in the volume of hypoxic water in coastal areas (Tanaka et al. 2014).

Heat fluxes other than fluxes through the lake surface: uncertainties and limitations
There are heat fluxes other than those through the water surface, such as heat fluxes associated with river/groundwater inflow and the heat flux through the bottom (Chikita et al. 2019;Masunaga & Komuro 2019;Sugita et al. 2020). The values of these heat fluxes were unknown at the time of this study. The heat flux through the bottom sediment can be calculated with the following equation (Hipsey et al. 2019): The default value was the value in 2000. The rates of increase or decrease are shown in parentheses. The slope (decade À1 ) means the slope of the regression line of mean air temperature/solar radiation during January and June vs. year ( Figure S1).   where R G is the heat flux through the bottom sediment (W m À2 ), K sed is the thermal conductivity of sediment (¼0.25 W m À1 K À1 ), T w is the surface water temperature (K), T sed is the sediment temperature (K), and δz is the thickness of the sediment (m). Our observations involved monitoring water and sediment temperature monthly (Shinohara et al. 2017). Based on the temperatures of the water and sediment at 0.0 m and 1.5 cm, we estimated the heat flux between the water and bottom sediment to be in the range of À4.0 to 8.0 W m À2 . The temperature of the groundwater was unknown during the current study. However, in the case of Lake Kasumigaura, groundwater seepage is only 10% of river inflow (Nakayama & Watanabe 2008). We have no information about the temperature of the inflowing river water, but the inflow of river water undergoes seasonal variations ( Figure S2). The inflow from the closest river (the Ono River; see Figure 1) during May and October (3.5 Â 10 7 m 3 ) was 1.3 times the inflow during November and April (4.5 Â 10 7 m 3 ) in 2017. However, because the water retention time in Lake Kasumigaura is ∼200 days and the level of the water surface of Lake Kasumigaura is controlled artificially, the heat flux associated with river inflow should be small. Sugita et al. (2020) have estimated that the net heat flux associated with river inflow/outflow is ∼3 W m À2 . Further detailed monitoring of heat fluxes associated with the heat stored in the sediment and inflows of groundwater and river water are needed to more accurately estimate the heat flux of Lake Kasumigaura.
The recent increase of cyanobacteria during the spring in Lake Kasumigaura could have resulted from the increase in solar radiation because photosynthetically active radiation controls the abundance of cyanobacteria in Lake Kasumigaura (Tomioka et al. 2011). Many studies have analyzed the effects of increases of surface water temperature on lake ecosystems (Czernecki & Ptak 2018), but more attention should be paid to light effects during the springtime. For example, the increase of solar radiation could accelerate the photolysis of organic matter and thereby affect water chemistry (Zhang et al. 2019). Both increases and decreases of solar radiation have been observed globally and in Japan (Tanaka et al. 2016). Because aerosol concentrations are expected to decrease in the future (Goto et al. 2016), solar radiation reaching Earth's surface will increase to the extent.

CONCLUSIONS
We have monitored surface water temperature and meteorological conditions as part of a study of Lake Kasumigaura during the past 28 years. Surface water temperature increased, during the springtime, in May and June by 0.74°C and 0.56°C decade À1 , respectively. In May, the increase of surface water temperature was significant, but the change of air temperature was not. The rate of increase of water temperature in June (0.40°C decade À1 ) exceeded that of air temperature. Solar radiation also clearly increased in May and June presumably because of the decrease in SPM as given the significant negative correlation between the concentrations of SPM and solar radiation. The result is consistent with Tanaka et al. (2016) that the brightening and dimming of solar radiation in Japan are caused by aerosols. A sensitivity analysis of changes in air temperature and solar radiation indicated that increases of solar radiation affected surface heat fluxes more than increases of air temperature. We observed increases in downward longwave radiation, precipitation, and sensible heat fluxes associated with the increase of air temperature. However, the impact of the increase of air temperature on the net heat flux (R n ) at the lake surface was smaller than the effect of the increase in solar radiation. If aerosols contribute to solar radiation, further investigation is needed to identify the future changes in the concentration of aerosols and the effects on heat flux on the lake surface including the seasonalities.