Numerical analysis of the relationship between mixing regime, nutrient status, and climatic variables in Lake Biwa

Model validation

Based on the time-series validations of water temperature and DO concentration, model accuracy improved gradually, despite several discrepancies at the beginning of the simulation (Supplementary Fig. S1). The model is primarily driven by a set of boundary data, including wind speed, solar radiation, and precipitation data^24,25. From this perspective, more high-quality boundary data promotes better numerical reproducibility. However, meteorological data collection was challenging due to the early observation equipment limitations and low observational accuracy compared to current data. The temporal inconsistency of accuracy in observational data has been eliminated to a large extent by fitting a regression curve²⁴. Spatial resolution is the other issue. Possessing spatially constant values for all boundary conditions complicates the numerical reproducibility of variations on finer scales.

The relationship between turnovers and the curve shape of water temperature versus DO concentration is theoretically sound^27,28. In the last stage of stratification in the lake, water temperature and DO concentration near the bottom are more likely to slightly increase due to thermal diffusion and DO supplies from the upper water. If a turnover occurs, the whole column of water is mixed strongly (Supplementary Fig. S3). Bottom water temperature decreases due to surface water cooling, and DO concentration increases, due to surface water replenishment and increased oxygen solubility. If the turnover fails, only the partial column of water is mixed, causing a delay in the timing of deep-water renewal (Supplementary Fig. S3). However, the upper water in later months, like that in March, has been rapidly warmed, resulting in an increase in the bottom water temperature. For example, in 2007 and 2016, the simulated water temperature and DO concentration fluctuated within a limited range in February and then skyrocketed in March, after mixing with the warmed surface water (blue points in Supplementary Fig. S4). On the other hand, explicit definitions of turnover timing are challenging. The threshold used to judge turnover timing is reliable because the results matched the observation. The turnover timing varied by 36 days in Lake Biwa during the simulation period, which is comparable to that observed in other lakes, such as approximately 21 days in Heiligensee, Germany over a 17-year timespan²⁹, 16 days in Lake Washington over a 40-year timespan³⁰, and 28 days in Blelham Tarn over a 41-year timespan³¹.

Variables affecting the mixing regime

Determining variables that affect the mixing regime is essential to improve understanding and enable future projections^16,17,18. Air temperature, wind speed, cloud cover, precipitation, water density, and lake transparency are all potential variables. We, here, compared the above variables to the turnover timing in Lake Biwa. The meteorological inputs in this study provided data for air temperature, wind speed, cloud cover, and precipitation. Water density and particulate organic carbon (POC) concentration representing lake transparency were the model’s outputs. The annual averages and cold season (November–April) values of the above variables were calculated over the simulation period (Supplementary Fig. S6). Annual averages illustrate general long-term warming trends¹⁸, while cold season values particularly determine the timing of turnover¹⁷. However, in Lake Biwa, air temperature during the cold season fluctuated greatly compared to the annual averages. A random forest analysis¹⁷ has been conducted between the turnover timing and the above two variable sets (cold season values versus annual averages) in Lake Biwa, and the cold season values better explained the turnover timing (35.39% versus 18.48%). The results agree with the conclusion drawn from the previous sensitivity tests, which indicated the relative importance of air temperature and solar radiation during winter based on 40 scenarios³².

The importance of variables was estimated based on the random forest analysis using the cold season data (Fig. 4a). Wind speed dominates the timing of turnover, which is consistent with the previous studies^17,25. The POC concentration, the difference in water density between the surface and bottom, and cloud cover have moderate effects on the timing of turnover. However, air temperature is less important, which is contrary to the turnover mechanism^17,24,32. A re-confirmation was conducted of the relationship between turnover timing and air temperature (Fig. 4b and Supplementary Fig. S7). The cool air generally encourages an early turnover, albeit with several anomalies. The turnover timing between 1976 and 1990 remained constant independent of climate change, and the period coincidently had a substantial nutrient fluctuation (Fig. 3). As a result, it is essential to investigate the nutrient status further.

Lake nutrient concentrations

Because phosphorus is the limiting nutrient in Lake Biwa and DIP concentrations can be effectively limited by regulating external loadings as practiced (Fig. 3), DIP concentrations become the focus of this discussion for nutrient status. However, the DIP concentrations disproportionately responded to the external loadings of total phosphorus (TP) in Lake Biwa. Although external TP loading itself fails to determine lake phosphorus concentrations due to the hydrodynamics of lakes³³, Lake Biwa exhibited insignificant changes in the inflow rate or the retention time (and see an example of the surface flow in Supplementary Fig. S8). Therefore, it can be assumed that the hydraulic loading remained constant, and the input nutrient concentrations were proportionate to the external nutrient loadings in Lake Biwa. This finding contradicts a recent meta-analysis that highlighted a deterministic relationship between input nutrient concentrations and lake nutrient concentrations, based on steady-state mass balance models⁶. The possible reason is the dynamics of the lake’s ecosystem²², which have been considered in this study. For example, the surface DIP concentrations were almost nonexistent regardless of the external TP loadings in Lake Biwa, supporting that phosphorus is the limiting nutrient in Lake Biwa^34,35. The low DIP concentrations at the surface may be caused by the rapid recycling of phosphorus because the amount of phosphorus available for phytoplankton is easily affected by the feedback mechanism between phytoplankton photosynthesis and the phosphorus released from the water^35,36.

Hypoxia and strategies

The variations in DO concentration are the public’s top concern as it relates to hypoxia, a key indicator of water quality. Lake bottom, among all water depths, is more sensitive to small changes in oxygen conditions¹². In Lake Biwa, the annual minimum DO concentrations ranged from 2 to 5.5 mg/L over the last 60 years (Supplementary Fig. S9). The decrease in DO concentrations in the early period, typically till the 1980s, was mainly caused by nutrient enrichments (Fig. 3). The nutrient enrichment-induced heavy eutrophication eventually accelerates the rate of DO depletion². After eutrophication was controlled in the 1980s, climate change became the dominant stressor²³. There remains much uncertainty surrounding the relationship between climatic variables-related turnover timing and hypoxia in Lake Biwa¹². We, therefore, first investigate the relationship between hypoxia and turnover timing, and then concentrate on nutrients to alleviate hypoxia.

Although the relationship between turnover timing and DO concentrations is quite weak (R² = 0.10), there is a general decrease in DO concentrations with increasing turnover timing (Fig. 5a). On the other hand, a linear relationship has been found between DIP concentrations and DO concentrations, with an R² of 0.67 (Fig. 5b). The slope of –0.841 μgP/mgDO means an increase in DIP concentrations by approximately 0.841 μgP/L causes a decrease in DO concentrations by 1 mg/L. Note that the simulation results were compared over the whole period, and eutrophication-induced hypoxia differs theoretically from climate-induced hypoxia. Additional testing has been conducted to distinguish the effects of two stressors (eutrophication- and climate-induced hypoxia; Supplementary Fig. S10). Before 1980 when eutrophication progressed, the annual minimum DO concentrations and the DIP concentrations had a stronger linear relationship (R² = 0.89). Although waste-water treatment has improved conditions in the lake, climate change induced alteration of turnover timing may adversely influence water quality. However, the relationship weakened dramatically with an R² of 0.10 after 1980, when climate change dominated hypoxia. The lower R² value indicates that climate-related hypoxia is more complex as concluded previously^37,38. The two possibilities are as follows. First, there can be a legacy of hypoxia related to eutrophication. The DO recovery at the bottom of Lake Biwa was complicated by the low DO concentration in 1980 and the delayed timing of turnover; similar phenomena have been observed in the Lake of Zurich²². Second, ecosystem dynamics could help explain the difficulty in predicting hypoxia at the bottom. Phytoplankton fully exploits phosphorus at the surface, as explained above, then the death and sinking of the surface phytoplankton are accompanied by the sedimentation of phosphorus to the bottom as modeled. Bacteria break down the sinking phytoplankton, releasing phosphorus and consuming DO in the process. Additional DO consumption lowers the bottom DO concentration, which in turn encourages phosphorus release from the sediment in a low DO environment²². Such unfavorable feedback between DIP and DO concentrations are strengthened by prolonged stratification and eventually accelerates the development of hypoxia. However, future research is necessary because this numerical model simplified the relationship between water and sediment. The sinking of organic carbon into sediment is integrated in the model, and due to the decomposition of organic carbon in the sediment, nutrients are released into and oxygen is depleted in the water. Despite that, the trends between DO and DIP concentrations stay the same under climate change (Fig. 5b), and thus controlling lake phosphorus is beneficial to the Lake Biwa hypoxia.

Source: Ecology - nature.com