Shallow lakes are widely distributed across the globe [1
], which is reflected in the low global average depths of 3.5 m for lakes in the smallest size class of 0.1–1 km2
and generally low average depths across different continents [2
]. Given their low average water depth, the water column of shallow lakes heats up faster compared to a deeper lake with the same surface area in the same climatic region [3
]. This results in both larger diurnal temperature fluctuations as well as larger seasonal temperature ranges in shallow lakes. The morphological characteristics make shallow lakes generally more susceptible to atmospheric forcing like irradiance, air temperature and wind friction [5
]. This does not only refer to variables related to hydro- and thermodynamics but also affects water quality variables. For example, higher water temperatures combined with high nutrient concentrations lead to the frequent occurrence of persistent cyanobacteria blooms [6
]. Usually, surface scums of cyanobacteria are not distributed homogeneously, but are constantly transported by wind and occur at a spatially-variable severity (e.g., [8
]). This can result in larger horizontal than vertical gradients in shallow lakes [9
]. Pronounced spatial patterns also have been observed for the occurrence of hypoxic zones, which lead to the dissolution of reduced metals and, thus, water quality deterioration (e.g., [11
This spatial variability, which is primarily caused by hydrodynamics, is difficult to cover through observations alone: ground-based measurements by moorings or ship-based measurements cannot be implemented in the required spatial and temporal resolution. While remote sensing develops into a promising technology to support the monitoring of lake surfaces (see the reviews by [13
], the special issues [15
] and the overview by [17
]), it does not resolve the vertical dimension in the water column. In order to complement local measurements and to expand information along spatial and temporal scales, numerical models have been proven useful [18
]. Depending on the question, they can be designed from one-dimensional models that resolve the vertical dimension to rather complex three-dimensional models. The latter have the benefit that they resolve both horizontal and vertical heterogeneity, as well as three-dimensional circulation patterns.
In oceanography, three-dimensional models have a long history of application (see e.g., [19
]). They became more popular in limnological studies in the early 2000s [20
]) and are now used frequently to understand physical (e.g., [23
]) and biological (e.g., [25
]) processes in lakes and to assess the effects of lake management on oxic conditions [27
] or phytoplankton dynamics [28
]. In shallow lakes, three-dimensional models are commonly applied to analyze the occurrence of anoxia [29
], resuspension events [30
], cyanobacteria blooms [31
] and to support management, e.g., by identifying critical nutrient loads [32
]. Lake Taihu, a shallow lake similar to Lake Chaohu, has a long history of three-dimensional model applications (for an overview, see [34
]). Three-dimensional lake models have the advantage being able to resolve most physical processes in the water body, e.g., long internal waves, upwelling and to analyse spatial phenomena like the distribution of surface scums (e.g., [35
]) or the flux of nutrients through the benthic boundary layer [20
] under pre-defined conditions. One open-source and publicly available three-dimensional hydrodynamic model is the General Estuarine Transport Model (GETM). GETM was originally developed for coastal ocean applications (see the review by [37
]), but was also successfully applied to lakes (e.g., [38
]). Important features for lake modelling are adaptive terrain-following coordinates [40
]. This facilitates a proper vertical resolution of boundary layers. Within GETM, non-hydrostatic effects [41
], which are required for high-resolution studies, can optionally be included. State-of-the-art vertical turbulence closure is provided via an interface to the General Ocean Turbulence Model (GOTM; [42
Three-dimensional models require a large amount of data for forcing and validation. In countries with a large territory or areas that are not easily accessible due to a lack of infrastructure (e.g., in some tropical countries or arctic regions), the high demand of input data is hard to satisfy since the necessary data to drive a complex model are in many cases not easily available at the required spatial and temporal resolution (e.g., [43
]). Alternatively, local forcing data could be obtained from e.g., high-resolution atmospheric models (e.g., [44
]). However, these local atmospheric models need to be nested into large-scale global models [45
] or are often specific for a certain meteorological variable and developed for a specific region (e.g., [47
]). The question arises, whether coarse meteorological and hydrological data from global models can be used directly for driving local lake models. This methodology would be easily transferable to other water bodies worldwide and would help to apply lake models in regions with scarce monitoring data.
Reanalysis projects assimilate weather forecast models with local observations leading to global datasets of atmospheric circulation [48
]. The same data assimilation technique is applied over the whole time period considered, resulting in a historically coherent dataset that is independent of methodological changes [48
]. In addition, with the reanalysis approach being spatial, global coverage can be achieved [49
]. The European Centre for Medium-Range Weather Forecasts (ECMWF, [48
]) provides the ERA-Interim reanalysis consisting of a wide range of meteorological variables with a global coverage on a grid of 0.75 degrees (approx. 80 km) resolution. Only few lake-modelling studies have made use of reanalysis data. Layden et al. [50
] used data from ERA-Interim to drive a global model application and estimate lake surface temperatures with the model FLake. Schmid et al. [51
] used data from the NOAA NCEP-NCAR CDAS-1 reanalysis project to simulate CO2
concentrations and temperature dynamics in a lake that is located in a data-scarce region. Piccolroaz and Toffolon made use of the consistency of reanalysis products and ran a long-term simulation for Lake Baikal [52
]. Xue et al. [53
] applied wind input from different sources as driving data for a three-dimensional model of Lake Superior. They found that wind input from a weather forecast model or from reanalysis data produced better modelling results than wind derived from local observations. This was due to the fact that spatial wind patterns, especially at the shore of the lake, were not captured by the observations [53
In this study, we try to find an approach for modelling and analysing thermal and stratification dynamics in areas where only insufficient data is available. Sparse measurements often limit the validation of simulated overall circulation. This approach, therefore, requires some pragmatism in deriving information. It is our aim to explore the opportunities as well as the limits of using freely available reanalysis data for modelling seasonal to sub-daily temperature variability in large shallow lakes. The realistic reproduction of temperature dynamics and stratification periods is used as a criterion for evaluating the model performance. Analysing the hydrodynamic processes causing the stratification patterns remains out of the scope of the present study. As an exemplary test, we simulate the fifth-largest lake in China, Lake Chaohu, with the 3D hydrodynamic model GETM and spatially uniform atmospheric forcing extracted from the ERA-Interim reanalysis data set. We compare simulated with measured water temperatures at several locations within the lake over the course of one year.
In this paper, a three-dimensional coastal ocean model was applied to simulate thermal and stratification dynamics of a large shallow lake in the Yangtze River basin in China. The model was driven by ERA-Interim reanalysis data. Measured by common model fit metrics (NSE, RMSE, MAE), the seasonal dynamics in surface and bottom temperature were reproduced well. The combination of data and model succeeded in reproducing synoptic-scale cooling and warming events. However, diurnal stratification patterns predicted by the model were too regular compared to that observed: stratification occurred more often in the model and, on average, lasted longer compared to observations.
Stratification in shallow lakes is heavily affected by wind and by heat fluxes at the water surface [71
]. A comparison of wind data obtained from the reanalysis data and local measurements showed that wind speed was overestimated in the reanalysis data (0.27 m s−1
, i.e., 12%) and that wind directions diverged from each other. However, wind is unlikely to be responsible for the mismatch in stratification. Overestimations in wind speed would rather weaken instead of intensifying stratification in the model. Although wind directions in the reanalysis data differed from measured directions, they were similar to what has been denoted as the main wind direction in Chaohu by others [54
]. Huang et al. [60
] denote an eastern wind as the main wind direction between 2011 and 2013, which is comparable to the reanalysis from 2015 (Figure 2
). Chen and Liu [62
] state the main wind direction as south-east in summer. Dividing the reanalysis per month led to main wind directions either from south–south-west or east–north-east during the months June–August of the years 2014–2015 (data not shown). In winter, wind direction was more variable in the reanalysis with a stronger tendency towards the north-east as the main wind direction compared to the north-west stated as the main wind direction in winter by Chen and Liu [62
]. In general, wind was found to be a meteorological variable that is well represented by reanalysis data [53
] although the spatial resolution of the reanalysis does not account for local orography at small scale. It has to be noted that Xue et al. [53
] used reanalysis data to simulate Lake Superior, which is more than 10 times the size of Lake Choahu. Whether a bias in wind data from the reanalysis is causing the observed mismatch of longer stratification events in the eastern part of the lake (Figure 5
A, stations F and J) can only be clarified through local measurements at various stations on and around the lake. The paper by Zhang et al. [54
] hints at local differences in wind direction between Heifei and Chaohu City.
A difficulty in correctly simulating stratification in lakes arises from the surface-energy budget. Preliminary simulations revealed a high sensitivity of the model towards the equation used for calculating net longwave radiation fluxes. Furthermore, the model results showed a large diurnal fluctuation of surface water temperatures, which points to problems in the sub-daily energy budget. It is possible that cloud cover, which is part of the heat budget estimation, contributes a large error, since it is hard to simulate within global climate and forecast models [72
A direct assessment of sub-daily patterns in reanalysis data could not be achieved since local measurements were only available as daily averages. Furthermore, it has to be kept in mind that local weather conditions can also be very heterogeneous around the lake leading to further complications. Daily land–lake wind patterns can develop due to different warming and cooling rates of land and water surfaces, and evaporation from the large surface area can have a buffering effect on local temperatures as well as changing local cloud cover and thus incoming irradiance. These processes are not included in the reanalysis model and would improve model performance [73
Due to the unavailability of local data, we were not able to quantify the lake’s water balance and neglected in- and outflows in our simulation. Our assumption is strengthened by previous simulation studies, which have shown the negligible effect of discharge on the lake’s hydrodynamics [60
]. We cannot completely exclude local effects of river inflows on stratification. An assessment of small-scale patterns would need reliable discharge data and several thermistor chains deployed close to the main inflows. Changes in water depth can potentially affect stratification. The water level in Lake Chaohu rises mainly in summer due to the rainy season (see e.g., [60
]). If this had an effect, we would expect a strong seasonal bias in the model fit, which we did not observe. Other factors that could contribute to the spatial mismatch of longer stratification events are potential errors in the bathymetry used for the simulations, the spatial resolution of the model, the operation of the dam, and even ship traffic. The lake is deeper in the eastern part. Inaccuracies in the bathymetry could have caused the mismatch at station F. Station J is located in a narrow bay, close to Chaohu City. A higher resolution of the model, as well as data on the dam operation could result in a better prediction at this location. Finally, Lake Chaohu is strongly used for the transportation of goods, leading to continuous ship traffic that causes turbulence in the water column. Station J could especially be affected by ship and boat traffic, since it is located in a bay of the lake, near to Chaohu City.
4.1. Applicability of Reanalysis Data in Hydrodynamic Lake Simulations
Within an initiative of the International Association of Hydrological Sciences (IAHS), the project Predictions in Ungauged Basins (PUB) was launched in 2003 (http://iahs.info/pub/index.php
). PUB aimed at developing methods to increase the process-understanding and reduce the uncertainty of hydrological predictions in ungauged basins. The group mainly evolved from the need to develop models that are capable of providing reliable and transferable prognoses for future changes and for areas with little measurement activity [74
]. Furthermore, new possibilities for data acquisition, e.g., remote sensing, were supposed to be explored [75
]. In essence, the lake modelling community is confronted with similar problems: several surface water resources around the globe are at risk concerning water quality and quantity. Where standards in environmental monitoring are below the input data requirements of the established models, an alternative approach enabling model applications to those lakes and reservoirs is needed.
Despite the restrictions mentioned above, the model results described seasonal and synoptic scale patterns of water temperatures well, both at the surface and bottom of the lake. The lake morphometry prescribes a strong influence of meteorology on water temperature dynamics so that changes in meteorological conditions induce a fast thermodynamic response of the lake. Due to the shallow water depth, the effect of thermal inertia in spring and autumn, as observed in deep lakes with a large water volume, is strongly reduced. A potential buffering effect may arise from heat storage in the sediments or from groundwater intrusions leading to cooling in early summer and warming in autumn. Our simulated and observed temperature, however, did not provide evidence that such buffering effects are important in Lake Chaohu. Also, inflow and outflow dynamics of the lake are obviously negligible for the thermodynamic budget since our model was able to simulate temperature dynamics accurately without including in- and outflows. In conclusion, the direct effect of local meteorological conditions will be the main driver of the lake thermal and stratification dynamics. The good fit between observation and simulation regarding seasonal patterns showed that reanalysis data are suitable for simulations unless sub-daily dynamics are of interest. Our approach of applying reanalysis data has the benefits of easy transferability and the potential for global applicability since reanalysis data are available worldwide.
An important measure for water managers are the currents in the lake. An accumulation of cyanobacterial scums in the western part of the lake has been observed in several studies (e.g., [54
]). It would be of interest to assess the feasibility of reanalysis data for simulating current patterns in lakes. However, we argue that a full assessment of currents in the lake requires local measurements for validation to give an indication on the reliability of those simulation results.
4.2. Water Temperature Data
Through our measurements of water temperatures at the surface and bottom of the lake, we showed that the large polymictic Lake Chaohu is frequently stratified. This contrasts with Huang et al. [60
], who assumed that the lake does not stratify. We observed that the lake was stratified on average in 22% of all observations. It has to be stressed that this number does not relate to the whole year, since large data gaps exist in our dataset. It is probable that the percentage per year is higher, because the largest data gap existed in summer when the water column is most likely to stratify. Stratification sometimes lasted over several days. As the lower layer of a stratified water body does not have direct contact with atmospheric oxygen, the huge oxygen demand of the sediment favors anoxic conditions in the bottom layer of the lake. The longer the stratification, the more likely the lake system develops anoxic bottom water. A precise simulation of stratification and the timing is, thus, mandatory for a realistic simulation of the bio-geochemistry of Lake Chaohu.
The frequent alteration between mixing and stratification could even increase the release of nutrients from the sediment to the overlying water. While the lake is stratified, nutrients may accumulate in the bottom layers. When the lake is mixed again, these nutrients will be diluted within the whole water column and can readily be taken up by primary producers. This “nutrient pump” can generate high pulses of nutrients, if the bottom waters approach anoxic conditions and low redox potentials persist [78
]. In several studies, the occurrence of large anoxic zones, so called “black blooms”, in the shallow lakes of the Yangtze basin has been identified [12
]. A three-dimensional modelling study would be useful for analysing hydrodynamic processes leading to these phenomena. However, this will require additional information from local meteorological and probably hydrological measurements in combination with a well calibrated bio-geochemical model. Coupling GETM to a biogeochemical model is straightforward via the Framework for Aquatic Biogeochemical Models (FABM; [79
]). The limiting factor of such a study remains the availability of water quality data to validate the bio-geochemical model thoroughly.