The currents of gyre (circulation) flow play an important role in the transportation and mixing of dissolved or suspended nutrients and chemical substances. In recent years, climate change has affected the flow field in Lake Biwa. However, how much climate change can influence the flow field has not been clarified enough yet. In the present study, using a three-dimensional hydrodynamic model, we investigated the effect of changes in air temperature, wind speed, and precipitation on the change of the flow field in Lake Biwa. For sensitivity analysis, numerical simulations were performed for a baseline case using realistic meteorological data from 2007 to 2012, as well as hypothetical cases using meteorological data. The analysis revealed that the changes in air temperature and precipitation changed stratification and vorticity in the surface layer in each season. The strength of the stratification affected the gyre strength in the surface layer. The change in wind speed, on the other hand, changed the wind stress acting on the lake's surface, influencing the strength of gyre significantly. Increased wind speed lengthened the radius of the gyre in Lake Biwa, while decreased wind speed made it weaker above and below the thermocline.
The currents of gyre flow play an important role in the transportation and mixing of dissolved or suspended nutrients and chemical substances.
The significant feature of the flow field in Lake Biwa, Japan is the system of several gyres formed in the surface layer of the lake.
The change in wind speed altered the wind stress acting on the surface of the lake, which significantly influenced the strength of the gyre.
The study of the flow field is essential for understanding the transport and dispersion of nutrients from river inflows and lakes. Advection and diffusion of water also affect the distribution of the sediment in large lakes, and the variation in water temperature is significantly influenced by the flow field in lakes (Vincent et al. 1991). Hydrodynamics in large lakes is complicated and can change on hourly, daily, and seasonal timescales (Fischer et al. 1979). Hydrodynamics in lakes includes gyres (horizontal circulations), overturning (vertical circulation), wind-driven currents, gravity currents, and periodic flows such as internal waves and inertial oscillations. Internal waves generated by wind and gravity currents produced by river flow are important factors related to changing the flow field in lakes (Morales-Mar'n et al. 2017; Chen et al. 2020) and contributing significantly to the transportation of materials in Lake Kinneret (Stocker & Imberger 2003; Shilo et al. 2007) and Lake Grevelingen (Haren 2019). The currents of gyre in particular play an important role in the transportation and mixing of dissolved or suspended nutrients and chemical substances in lakes and enclosed oceans (Dipper 2022).
Global warming (IPCC 2021) can cause a shift from dimictic lakes to monomictic lakes, resulting in insufficient vertical overturning in Swiss lakes (Vinna et al. 2021). In other instances, in Lake Constance (Germany), the overturning of water ordinally occurred once a year, but due to the prolonged increases in air temperature, overturning in winter has become insufficient in recent years, according to observations (Rhodes et al. 2017). Previous research has shown that thermal stability in lakes influences the inter-annual variation of winter bottom conditions (Peeters et al. 2002; Arhonditsis et al. 2004; Yoshimizu et al. 2010).
The water quality in Lake Biwa due to climate change has been deteriorating since the 1950s (Kumagai & Vincent 2003; Kumagai et al. 2021). The reason for the decrease in dissolved oxygen is considered to be the strengthening of stratification caused by climate change in recent years. Climate change, such as the increase in air temperature, the decrease in wind speed, and the decrease in precipitation over the last 30 years, is a contributing factor to changing the flow field in the lake (Woolway et al. 2021). In particular, the rise in air temperature and the decrease in wind speed weaken the mixing of the water mass and can be the cause of low oxygenation and water contamination in the bottom layer.
Lake Biwa is the largest freshwater lake in Japan, which is located in Shiga prefecture. It is approximately 64 km long from north to south and covers an area of 672 km2. A total of 119 rivers drain from the surrounding mountains into Lake Biwa, and its main outlet is the Seta River, flowing into the Seto Inland Sea at Osaka Bay. Its average depth is approximately 41 m, and the deepest point is approximately 104 m. The total volume of water restoration is 27.5 billion m3. The lake provides an abundance of aquatic life and industry for the surrounding area in Japan.
There are many kinds of flows in Lake Biwa in Japan, which have various spatiotemporal scales. Wind-generated internal waves in Lake Biwa have also been studied using field observations (Saggio & Imberger 1998), modal analysis (Shimizu et al. 2007), and numerical simulation (Kitazawa et al. 2010; Koue et al. 2018). Internal waves, as demonstrated by Kitazawa et al. (2010), influenced the transport of hypoxic waters in the flow field in Lake Biwa. Gravity currents on the sloping boundary appeared to contribute to the gyre in the surface layer and lead to the restoration of oxygen and rich nutrients in the deep waters of Lake Biwa, according to Fer et al. (2002) and Akitomo et al. (2009a, 2009b). This phenomenon could have an impact on the ecosystem of the lake (Brooks & Zastrow 2002; Livingstone 2008).
Realistic flow conditions are generated as a result of the complicated superposition and interaction of these flows, but the flow conditions show significantly different aspects depending on the water area, depth, and season. These flows play an important role in the transportation and mixing of dissolved or suspended nutrients and chemical substances horizontally and vertically. The gyre in Lake Biwa especially changes the horizontal and vertical transportation of nutrients, algae, and dissolved oxygen. Therefore, in order to understand the actual distribution of nutrients and dissolved oxygen, the mechanism of generation of gyre should be elucidated, and at the same time, how much the change of meteorological conditions contributes to the gyre in Lake Biwa needs to be clarified.
The currents of gyre especially play an important role in the transportation and mixing of dissolved or suspended nutrients and chemical substances in lakes and enclosed oceans. The gyres in Lake Biwa were reproduced by the three-dimensional hydrodynamic model (Akitomo et al. 2009a, 2009b; Kitazawa et al. 2010; Koue et al. 2018). In recent years, climate changes have had an impact on the flow field in Lake Biwa. The effects of climate change on the structure of the stratification in Lake Biwa were analyzed by Koue (2022), who showed that the effects of wind speed were stronger than those of air temperature and precipitation on the structure of stratification. The effects of climate change on the vertical material circulation were discussed previously, but those of climate change on the horizontal circulation have not been evaluated. There is little research about the effect of climate change on the gyre in Lake Biwa. How much each meteorological element can influence the gyre has not yet been clarified. Therefore, it is critical to quantify the effects of each meteorological element on the flow field. In the present study, we examined the effect of changes in air temperature, wind speed, and precipitation on the change of gyre in Lake Biwa in the surface layer by using a three-dimensional hydrodynamic model.
HYDRODYNAMIC MODEL IN LAKE BIWA
|.||Name of river .||Mean annual flow rate (m3 s−1) .|
|.||Name of river .||Mean annual flow rate (m3 s−1) .|
The governing equations
In this study, the three-dimensional hydrodynamic model, developed by Koue et al. (2018), was used to figure out thermocline and vorticity in detail. This model was validated for reproducibility of the structure of the thermal stratification and flow field in Lake Biwa, compared with the observed data. The origin of the coordinate axes is in the southwestern edge of the domain on the horizontal plane. The x and y axes are set to west–east and south–north directions, respectively, and the z-axis directs upward.
As for the initial condition, the current velocity of each component (x, y, z) was all set to be 0 m s−1. The initial conditions of water temperature were set to be the data on the 1st of April, which was linearly interpolated by using the observed data on the 20th of March and that on the 10th of April in the year 2006. The water temperature was observed by the Lake Biwa Environmental Research Institute twice a month at the monitoring point Imazu-oki as shown in Figure 1(b), the depth of which is 0.5, 5, 10, 15, 20, 30, 40, 60, 80, and 90 m.
The numerical simulation was carried out during the period from April 1st, 2006 to March 31st, 2012 within the spin-up period from April 1st, 2006 to March 31st, 2007. In the three-dimensional hydrodynamic model, the boundary conditions for the water volume and temperature of each river were assumed by the results, which were calculated by the hydrological model. By using this initial condition, the direction of the water flow, the current velocity, and the water temperature were calculated.
The boundary conditions used were the same conditions described by Koue et al. (2018). Grid point value data from the Japan Meteorological Agency Meso-Scale Model (GPV MSM) were used to calculate the heat flux and wind stress on the water surface. The meteorological data were collected on air temperature, atmospheric pressure, wind direction and speed, and relative humidity. GPV MSM data had a spatial resolution of 0.0625° longitude by 0.05° latitude (horizontally 5 km) and a temporal resolution of 1 h. In order to reflect the GPV data into each mesh on the surface correctly, the meteorological data were given by interpolating the value which was averaged inversely proportional to the square of the distance. Since each data were updated every hour, it is possible to reproduce the heat balance and water flow on the surface of the lake. The air temperature and wind velocity at the Hikone Local Meteorological Observatory were used as the representative values in Lake Biwa. The location of the Hikone Local Meteorological Observatory is shown in Figure 1(b). Short-wave solar radiation was derived from hourly observation data at the Hikone Local Meteorological Observatory.
Taking the effect of the river inflow to Lake Biwa into account, not only the observed data but also the simulated data were given as boundary conditions. This is because the hydrodynamic model is assumed to be integrated into the Yodo River Basin Water System Model (Shrestha & Kondo 2015) in the future. The water temperature and the water volume, which were calculated by the hydrological model, were interpolated each day for 56 rivers. The only outflowing river was located at the southernmost part of Lake Biwa. Furthermore, the grid size of the area of the simulation was 1 km, and the total number of meshes was 7,557. The data of the river inflow were updated every day for the analysis in detail. The location of six main rivers and the mean annual river inflow rates are shown in Figure 1(a) and Table 1. The total mean amount of annual river inflow rate was 177.5 m3 s−1.
Baseline case simulation
|JFY .||2007 .||2008 .||2009 .||2010 .||2011 .|
|WS (m s−1)||2.8||2.6||2.7||2.6||2.8|
|JFY .||2007 .||2008 .||2009 .||2010 .||2011 .|
|WS (m s−1)||2.8||2.6||2.7||2.6||2.8|
Numerical simulations were carried out for a baseline case using realistic meteorological data from 2007 to 2012 and hypothetical cases using meteorological data with modified air temperature, wind speed, and precipitation for sensitivity analysis. For sensitivity analysis, the coefficients of variation (σ/μ) were obtained from the mean value (μ) and standard deviation (σ) of the mean annual air temperature, wind speed, and precipitation for 30 years from 1981 to 2010 at the Hikone Local Meteorological Observatory. The coefficient of variation (σ/μ) was 0.21% for air temperature, 4% for wind speed, and 21% for precipitation. All pseudo-weather data were generated by multiplying 1 + σ/μ, 1 − σ/μ by the air temperature, wind speed, and precipitation of GPV MSM data. The simulation cases named as AT + (AT−), WS + (WS−), and Pre + (Pre−) indicate the increase (decrease) in air temperature, wind speed, and precipitation, respectively. The pseudo-weather data of air temperature, wind speed, and precipitation data are shown in Table 2. The air temperature was calculated by the absolute temperature.
Evaluation of the strength of stratification and vorticity
The buoyancy frequency (Brunt–Väisälä frequency) is calculated to determine the strength of the stratification more precisely in each case in detail. The buoyancy frequency is a measure of stratification strength and is expressed in terms of the frequency N of oscillations caused by buoyancy in a fluid under the influence of gravity and with density stratification. Since it is proportional to the square root of the vertical change in density, it is used as a parameter to represent the stratification strength.
ω > 0 indicates the counterclockwise gyre, and ω < 0 indicates the clockwise gyre.
RESULTS AND DISCUSSION
The first gyre appeared above the thermocline and existed from spring to autumn. The flow speed was approximately 10–30 cm/s, peaking in summer as shown in Figure 3. Since the 1980s, the details of the flow field have been clarified by the development of mooring equipment and flow velocity measuring equipment attached to the bottom of the ship. It was pointed out that the second and third gyres do not exist steadily and the first main gyre steadily exists according to the observation (Endoh et al. 1995; Kumagai & Vincent 2003) and simulation (Akitomo et al.2009a, 2009b; Koue et al. 2018). These surface gyres were also observed in other large lakes (Rueda et al. 2009). Counterclockwise gyres have also been observed in Lake Michigan, Lake Superior, Lake Erie, Lake Constance, etc., and the gyre is affected by the shape of the basin, the difference in water depth, and the size of the lake (Bennington et al. 2010; Beletsky et al. 2013; Morales-Mar'n et al. 2017). In Lake Biwa, the effect of topographic heat storage effects is more pronounced due to the smaller gradient of the eastern shore.
There are two main causes of gyres in Lake Biwa: one is thermally driven and the other is wind-driven current. The first thermally driven one is also called the topographical heat storage effect. Due to the difference in the amount of heat storage in the water column, a density gradient is formed, so that the flow is generated. In summer, water masses are less likely to warm up in deep water than in shallow water, and water masses with relatively low water temperatures accumulate offshore and have a relatively high density, so they sneak into the lower layers and serve as a compensation flow. As a result, a flow is generated from the coast to the offshore, and the Coriolis force acts on the right side of the northern hemisphere in the direction of travel, forming the first counterclockwise gyre.
As for the other wind-driven one, wind stress curl generates a counterclockwise gyre. In order for the first gyre to become a geostrophic current, the difference depending on the location of the wind direction must be a counterclockwise rotation by subtraction. Endoh et al. (1995) calculated the wind stress curl on Lake Biwa using meteorological observation data. It is reported that the wind stress curl tends to strengthen the first gyre in each season from spring to autumn. Once the gyre is formed, the geostrophic current is maintained even under the influence of the topographical heat storage effect, so it is difficult to quantitatively evaluate which the cause is.
The strength of the gyre was calculated by averaging the vorticity as described in Section 2.6. The increase and decrease in air temperature changed the stratification on the surface slightly (Figure 3(a)). Moreover, the increase and decrease in precipitation tended to strengthen and weaken the counterclockwise gyre on the surface, respectively (Figure 3(c)). The change in wind speed altered the wind stress acting on the surface of the lake, respectively, so that it significantly influenced the strength of the gyre. That is, the increase in wind speed made the radius of the gyre in Lake Biwa longer and the decrease in wind speed made it shorter both above and below the thermocline (Figure 3(b)).
The horizontal convergence of the lake water on the surface associated with the gyre plays an important role in the transportation of suspended nutrients and chemical substances. The flow speed of the gyre is a critical factor for the transportation of materials leading to the water environment. Therefore, it is important to maintain the gyre in Lake Biwa.
In winter, the counterclockwise gyre flow was considered to remain in the case of the warm winter, while the clockwise gyre flow existed in the case of the severe cold winter. In fact, in the winter of 2010, the air temperature was cooler than usual, the wind speed was lower, and the amount of precipitation was less (Figure 5), resulting in a flow of snowmelt water from the coast to the bottom of the lake along the slope because the density of water in the coast was heavier than the surrounding water. Circulating currents formed from the lake center to the lakeshore but turned to the right under the influence of the earth's rotation in the northern hemisphere and the clockwise gyre occurred due to the topographical heat storage effect. Hence, only in 2010, a clockwise gyre flow was formed in the simulation (Figure 4(d)), and it was also observed in February 2011.
In the surface layer, the Brunt–Väisälä frequency was positive with increasing temperature and decreasing wind speed during the spring when the stratification began, and the stratification was stable. For the vorticity, it took a positive value (approximately 2.0 × 10−7) with increasing temperature and wind speed, thus strengthening the counterclockwise gyre. The change in air temperature and precipitation affected the counterclockwise gyre more than the change in wind speed. In summer, when the thermocline was stable, the Brunt–Väisälä frequency and vorticity had a wider range of values than in spring, and as wind speed increased, the Brunt–Väisälä frequency also became negative, the stratification was unstable, and the counterclockwise gyre tended to be stronger. In autumn, when the air temperature decreased and stratification began to collapse, the order of the strength of vorticity increased from 8.0 × 10−7 to 1.6 × 10−6, which was approximately twice that of the summer season. The fluctuations in vorticity were large due to the change in air temperature, wind speed, and precipitation. In winter, when the entire layer was mixed, the vorticity tended to be negative and less than that in autumn.
In the thermocline, both vorticity and the Brunt–Väisälä frequency did not change much in spring due to the change in each meteorological factor unlike in the surface layer. In summer, the Brunt–Väisälä frequency was reversed, and vorticity tended to be similar to that of the surface layer because the stratification structure was stable. In autumn, the fluctuation of vorticity due to the change in each meteorological element was similar in the surface layer and the thermocline, and the Brunt–Väisälä frequency was more variable in the thermocline than in the surface layer. In winter, the surface layer and the thermocline showed almost the same level of fluctuation due to each meteorological element. In the deep layer, the direction of vorticity was opposite to that of the surface layer and the layer shallower than the thermocline, and the clockwise vorticity was stronger. In terms of changes in each meteorological element, from spring to summer, the increase in wind speed caused the stronger counterclockwise vorticity, while the decrease in wind speed caused the weaker counterclockwise vorticity. From autumn to winter, for each climatic factor, the order of the strength of vorticity increased from 8.0 × 10−7 to 1.6 × 10−6 in the deep layer as well as in the surface layer and the layer shallower than the thermocline, which was approximately twice as large as that in summer, and the flow tended to be opposite to that in the layer shallower than the thermocline.
The seasonal effects of air temperature, wind speed, and precipitation variations on the gyre in the lake are shown. In spring, as the stratification increased, the counterclockwise gyre occurred due to the topographical heat storage effect. The effect of air temperature change on the gyre was stronger than that of wind speed. In summer, when the thermocline was stable, the change in wind speed had a stronger impact on the gyre than changes in air temperature and precipitation. This indicated that the gyre was formed by the heat storage effect with the onset of stratification and that the wind curl continued to strengthen the gyre during the summer season. During autumn and winter, when stratification collapsed and vertical mixing occurred, vorticity orders were approximately twice as large as in summer. In winter, the gyre tended to remain counterclockwise if the winter was warm at the surface and came to be clockwise if the winter was severe. Especially in winter, the inflow from snowmelt water influenced the strength of the clockwise gyre, depending on the strength of the vertical mixing. The gentle slope of the eastern shore of Lake Biwa made the snowmelt water fall down, which contributed to the clockwise gyre, and the intensity of it also depended on the strength of vertical mixing in all layers of Lake Biwa.
Nutrients and anoxic water masses produced by the decomposition of organic matter deposited on the lake bottom are diffused into all layers by vertical mixing in winter and then spread throughout Lake Biwa by the horizontal gyre flow from spring to autumn. When the eutrophication caused a red tide or blue-green algae bloom in a certain area, or if water pollution occurred when the wind speed was strong, the pollution would spread over a wide area due to the effects of the gyre currents. In the spring season, the strength of the currents is also affected by the air temperature and precipitation because of the strong thermal influence. At the depths below the thermocline, the flow in the opposite direction to that of the surface layer is formed, so meteorological changes have a significant impact on the material circulation. In summer, when the stratification is strong, the change in wind speed has a greater impact on the gyre than air temperature and precipitation; therefore, water pollution can affect a wider area.
In the present study, the analysis revealed that the change in air temperature had an effect on stratification in the surface layer, and as a result, the strength of the gyre in the surface layer changed. The difference in the water temperature in the horizontal direction and the difference in volume for advection–diffusion due to the amount of heat depending on the water depth affected the gyre flow. The change in wind speed, on the other hand, altered the wind stress acting on the lake's surface, which had a significant impact on the strength of gyre. Increased wind speed lengthened the radius of the gyre in Lake Biwa, while decreased wind speed made it weaker above and below the thermocline. The change in precipitation had an effect on the strength of the gyre because the direction of river inflow from the Ane River and the Ado River enhanced the counterclockwise gyre. The water temperature of rivers was a few degrees Celsius lower than that of Lake Biwa, which affected the flow field at depths below the thermocline.
The first gyre flow existed in the center of the circle in the northern part of the lake during a stratified season as the observational studies showed. In addition, in order to compensate for the flow field in the surface layer, the clockwise gyre existed right under the thermocline. The overall results would help to understand the movement of the substances in all layers of the lake. By analyzing the effects of climate change on the gyre of Lake Biwa, it is possible to figure out the flow field of Lake Biwa and track the movement of nutrients and suspended sediments. The intensity of the gyre has a remarkably important effect on the material cycle because the gyre can converge offshore of nutrients and flora and fauna plankton. Predicting the intensity of gyre due to climate change would play an important role in the conservation of the ecosystem of large lakes in the future.
The meteorological data in Shiga Prefecture were provided by the Japan Meteorological Agency (https://www.data.jma.go.jp/obd/stats/etrn/index.php), and water quality data were given by the Lake Biwa Environmental Research Institute via Internet (https://www.lberi.jp/investigate).
The authors are grateful for this support.
DATA AVAILABILITY STATEMENT
All relevant data are included in the paper or its Supplementary Information.
CONFLICT OF INTEREST
The authors declare there is no conflict.