2.1 The hydrodynamic lake model

GLM is a one-dimensional hydrodynamic model simulating the vertical profiles of temperature, salinity, and density at one spatial point in a lake over time (Frassl et al., 2016; Robertson et al., 2018). It applies the Lagrangian layer structure adapting the thickness and volume of layers with uniform properties from each simulation step (Bueche et al., 2017). The underlying equations and hydrodynamics closures are documented in Hipsey et al. (2014, 2017). The hydrodynamic model can also easily be coupled with the Aquatic Ecodynamics library (AED2) to simulate water quality simulations (Weber et al., 2017; Bruce et al., 2018).

GLM simulations are based on parameterizations of mixing processes, surface dynamics, and the effect of inflows and outflows. The model performance for simulating the lake thermal dynamics as well as the water balance can be improved by a calibration of lake-specific parameters. The model documentation of Hipsey et al. (2017) includes also a description of the lake-specific parameters and the default values for GLM simulations. The model requires meteorological and hydrological input data (see Table A1 in Appendix A). Field data of water temperature should be available in a suitable temporal and spatial (several depths) resolution to enable a reliable calibration process.

2.2 R package glmGUI

The R package glmGUI written by the authors interacts with the functionality of GLM. It provides two basic application functions – the logical elements of model-fit criteria calculations and graphical user interfaces for data visualization. The package requires a software version of R of ≥3.4 and the version of rLakeAnalyzer ≥1.8.3. All required R packages are automatically installed during the first installation of glmGUI.

2.3 Graphical user interface

The graphical user interface is constructed as a window-based design using functions of the R package gWidgets (Verzani, 2014), which provides several toolkits for producing user interfaces by creating, for example, labels, buttons, containers, or drop lists. The GUI is organized in a main menu with five sections. Submenus and result messages are opened in separate windows (Fig. 1).

Figure 1Window-based structure of glmGUI with examples of the submenu “Calculate SI-value” and of the result message “Temperature RMSE” created after a model run.

2.3.2 Plots and output visualization

Plot options are provided by glmGUI for the input time series in part 2 (Fig. 1) and for all output variables generated by GLM (csv and netCDF file formats, part 5 Fig. 1). This includes simple line plots (e.g., for lake level or evaporation) and contour plots for a parameter varying with lake depth, such as water temperature or density. In addition, two types of contour plots of the vertical profile can be created. First is the visualization of observed and modeled water temperatures in one plot above each other with the option of the measured data as point overlay to mark where and when field data are available (areas in between are interpolated to draw the plots, Fig. 2). The second plot visualizes the temperature differences between the interpolated measured values and the modeled data. This plot type is a new feature, enabling a quick overview on the spatial and temporal errors and deviations of the simulation (Fig. 9). The displayed deviations are fixed to nine classes in the range of the errors between −5 and +5 ^∘C, and all values beyond these limits are shown in one color ($\le -\mathrm{5}$ in dark blue and ≥5 in red), summarizing and highlighting extreme errors. The spatial reference in both plots is the lake surface, but lake-level variations are represented by changes in depth, which become visible at the “bottom” of this plot type.

The generation of the contour plots is based on functions provided by glmtools. The default settings to scale the color bar legend for water temperature plots take into account the range of temperatures and also erroneously the range of lake depth. This method is adopted in glmGUI, while discarding the consideration of the lake depth, and the temperature range is adjusted explicitly to the plotting method to provide well differentiated color ranges in the legend.

Figure 2Example of a contour plot of observed (a) and modeled (b) water temperatures for lake Ammersee. Black dots mark the availability (time/date and depth) of observed water temperatures.

Download

3.1 Study site

Lake Baratz is located in the northwest of Sardinia (Fig. 3), Italy, and it is the only natural lake of the island. The elevation of its bottom is 18.6 m a.s.l., and the lake level suffered significant changes in the last 2 decades with a maximum lake depth of 11 m and a minimum of 3 m (Giadrossich et al., 2015; Niedda et al., 2014). The overflow spillway of the lake is at 32.5 m a.s.l. (Niedda et al., 2014). At this maximum level the lake has a surface of about 0.6 km² and volume of 5.1×10⁶ km³ (Giadrossich et al., 2015). As lake-overflow events to the sea were extremely rare in the past century, the catchment area is considered to be a closed basin (Niedda and Pirastru, 2013). The lake watershed is about 12 km² with a maximum elevation of 410 m (Pirastru and Niedda, 2013). The only significant tributary inflowing the lake is in the northeast and drains a subcatchment area of 8.1 km². Due to a very dry summer season, the water inflow starts usually in December and ends in May (Giadrossich et al., 2015).

The lake can be classified as eutrophic and the water is brackish. Thermal stratification usually establishes in February or early March and lasts until early autumn (Giadrossich et al., 2015). Lake mixing occurs all throughout winter, and thus it can be classified as a warm monomictic lake.

Figure 3(a) Lake Baratz and its hydrological catchment area and observation station; (b) observation stations outside of the lake watershed (gray area); (c) contour lines of the lake basin. The blue area indicates the lake surface at a lake level of 8 m (equal to an elevation of 26 m a.s.l.) observed in November 2012. Brown lines display dry terrain and cyan isobaths at this lake level (Source DEM © Regione Autonoma della Sardegna).

3.2 Sensitivity analysis and calibration

The simulation period for lake Baratz is determined to be 13 July 2011 to 31 December 2016. We assume the light extinction coefficient value, K_w=0.57 m⁻¹, is representative of the whole study period. K_w is calculated by dividing the Secchi-disk constant (in this case the minimum value of 1.44 was taken as it usually ranges between 1.44 and 1.80; Hornung, 2002; Holmes, 1970; Chapra, 2008) by the mean Secchi-disk depth of 2.50 m (data from June 2016 to June 2017). A similar value can be obtained considering a Secchi-disk average depth of 3 m (assumed when the lake had a higher water level) and Secchi-disk constant of 1.70 (Poole and Atkins, 1929). A further detailed description of the applied meteorological and hydrological model input data, the field data, and the data processing can be found in the Supplement.

The calibration process of the lake level was accomplished without hydrological parameters, as preliminary estimations of the water balance considering the seasonality of the inflow and subsurface outflow already exist (see the Supplement Sect. S1.3), which are also applied in this study. Thus, the sensitivity analysis was performed by considering only the parameters of surface dynamics and the wind_factor as wind can have an impact on the lake level due to its influence on evaporation. The options of 10 % increase and the RMSE as a measure of deviation were selected.

After Lenhart et al. (2002), only one of four parameters (cd) is found to have a negligible sensitivity as indicated by a SI value of below 0.01. The analysis revels a high sensitivity for the parameters ch (SI =0.234, see also Fig. 4) and ce (SI =0.334) and a medium sensitivity for wind_factor (SI =0.089).

The sensitivity analysis regarding water temperature was conducted for parameters of lake mixing, surface dynamics, and the wind_factor with the same options as selected for the lake level. Negligible SI values of 0.005 and below are found for all considered parameters, except for ce (SI =0.232) and wind_factor (0.290) with high sensitivities and ch (0.050) with a sensitivity at the threshold between medium and small (Fig. 4). According to both sensitivity analyses, the model is calibrated first for the lake level considering these three parameters with medium and high sensitivities. As the model is found to be sensitive to lake level and water temperature simulations for changes in the same parameters, the calibration for water temperature simulations was performed only considering ce and wind_factor to prevent a decline of the lake level reproduction by the water temperature calibration. Not considering parameter ch is plausible, as its SI value only matches just the threshold to be medium sensitive. In addition, small parameter value ranges of 10 % are applied. Within the calibration process, a total number of approx. 3000 simulation runs were conducted in 6 autocalibration runs.

Figure 4Sensitivity index (SI) after Lenhart et al. (2002) of GLM simulations of lake Baratz regarding the lake level (blue) and water temperature (cyan). The lower horizontal line (SI =0.05) marks the threshold between small and medium sensitivity and the upper line (SI =0.20) between medium and high sensitivity.

Download

Figure 5Observed (blue) and simulated (red) lake level of lake Baratz.

Download

3.3 Simulation results

The calibration processes for lake-level simulations of the lake model reveal the best fit when applying an unchanged parameter value for ch, an adjustment of ce to 0.001748, and an adjustment of wind_factor to 1.56. The simulated lake level of lake Baratz shows very good model fit criteria with an average RMSE =0.11 m and an average MBE =0.05 m. The seasonal pattern of the lake level, characterized by a strong increase during winter and a drop during summer, is represented well. Additionally, the general decrease of the water stage by about 3 m during the simulation period is simulated correctly, which proves the capability of the model to reproduce the water balance of the lake and its catchment area.

The modeled water temperatures simulated with the adapted lake parameters found by the (auto)calibration yield an overall average RMSE of 1.30 ^∘C. A period of remarkable deviation of simulated and observed lake level is induced in January 2014, which could be attributed to uncertainties in the discharge input data simulated by a hydrological model. The basin in that period of the year is still in an intermediate status of soil moisture. Probably the hydrological model overestimated the discharge on the base of rainfall events in January 2014, which in reality did not produce a significant lake-level variation (see Fig. 2 in Giadrossich et al., 2015). However, the observed and simulated lake levels in Fig. 5 have the same trend, and the error caused in January is propagated throughout the year.

The model reproduces stratified and isothermal conditions (Fig. 6). A detailed overview on the temporal and spatial differences between the observed and simulated water temperatures is given in Fig. B1. The simulation can be assessed as a robust fit (Bruce et al., 2018), especially when considering the high degree of thermal dynamics due to the shallow depth of the lake and an additional enhancement by highly variable lake level (Fig. 6). The results also approve GLM to be applicable for shallow lakes in warm climates with a high variety in lake level.

Figure 6Observed (a) and simulated (b) water temperatures of lake Baratz.

Download

4.1 Study site

The pre-alpine lake Ammersee (Fig. 7) has a maximum depth of 83.7 m (Fig. S8, the Supplement), a surface area of 46.6 km², and a volume of about 1.8×10⁹ km³ (Bueche and Vetter, 2014b). The mixing regime can be classified as dimictic, but also monomictic seasons occur (Bueche, 2016). The trophic status is currently mesotrophic (Vetter and Sousa, 2012).

The lake has a catchment area of about 994 km², and its outflow is in the north (Stegen gauge station). The main tributary is river Ammer, which contributes approximately 80 % to the total annual discharge to the lake (Bueche and Vetter, 2015). Several other streams and creeks inflow into the lake, but only the rivers Rott and Fischbach have a share of greater than 5 % of the total lake catchment area size (see Fig. 7). Additionally, groundwater is assumed to inflow to the lake, which has not been quantified yet (Bueche and Vetter, 2014a). The mean lake level is 532.9 m a.s.l. and usually varies about 1 m (Bay. LfU, 2018).

Figure 7Catchment area (with subcatchments) of lake Ammersee. Dots mark the locations of hydrological observation stations (Source DEM: elevation data from ASTER GDEM, a product of METI and NASA; Source geodata: Geobasisdaten © Bayerische Vermessungsverwaltung, http://www.geodaten.bayern.de, last access: 30 January 2020).

4.2 Sensitivity analysis and calibration

The simulation period for lake Ammersee was chosen to be 30 January 2014 to 31 December 2017, starting when reliable field data of the lake station are available consistently (see the Supplement Sect. S2). The initial profile of water temperatures is taken from the observations of that date. No water quality data were available for the simulation period, and the salinity values are derived from conductivity measurements of January 2004, when similar thermal conditions of a slight inverse stratification prevailed and equivalent salinity conditions can be assumed. As the trophic status has not changed since 2004, the average K_w value of 0.35 m⁻¹, determined for the period 2004 to 2008 from Secchi-disk observations (data surveyed and provided by Bavarian Environment Agency), is used for the GLM simulations in this study.

The calibration of the lake level considers the inflow_factor (i.e., simple factor for the discharge values of the inflows) of the four defined inflows of river Ammer; river Fischbach; groundwater inflow; and the sum of river Rott, river Kienbach, and all other unknown inflows. Thus, the adjustment of the representative inflow_factor includes the required correction of the available discharge data, considering the observations are not taken at the stream inlet to the lake but at an upstream location. This is especially relevant for river Ammer with its gauge at Weilheim (Fig. 7). Meteorological input data are taken by a raft station at the lake center, except for precipitation and cloud cover data (see the Supplement, Sect. S2, for a detailed description about the sources of the used meteorological and hydrological input data and the processing of the data).

The sensitivity analysis regarding the water temperature (increase: 10 %; measure of difference: RMSE) reveals seven parameters with an SI >0.05, indicating a medium sensitivity (after Lenhart et al., 2002, Table 1). In order to reduce the calculation time of the autocalibration runs, four parameters of high sensitivity with a SI above 0.2 are chosen for this process. In total approx. 50 000 simulation runs in 12 autocalibration runs were performed within the calibration process.

Table 1Values of sensitivity index (SI) for lake Ammersee water temperature simulations.

Download Print Version | Download XLSX

4.3 Simulation results

The calibration of the lake-level simulation yields its best fit for the combination of inflow factors for the defined tributaries: river Ammer of 1.10; river Fischbach of 0.72; groundwater of 1.07; and rivers Rott, Kienbach, and all other smaller and unknown inflows of 1.01. By using these adapted inflow factors instead of the default value of 1.0, overall RMSE reduced significantly from 1.10 to 0.20 m, the MBE changed from −1.00 to 0.09 m, and the achieved model fit can be assessed as very satisfactory. The simulation shows periods of general deviations of over 0.20 up to 0.55 m for some months, but it reproduces the short-term fluctuations well (Fig. 8). The remaining errors and differences can be ascribed to the uncertainties and lack of data for some inflows as assumptions and estimations for the unknown surface input and the groundwater inflow had to be made. More detailed hydrological data might explain remarkable dates, like during summer when the trend of simulated and observed lake level changes abruptly. No obvious explanation for these trend shifts could be found, although a detailed investigation of the existing hydrological data was conducted. An impact of a highly complex groundwater inflow system is likely to have a key role in the water balance of the lake, which is not considered by the applied input data sufficiently. Furthermore it cannot be ruled out that unknown alterations or errors in the observation setup of the gauges cause these “turning points” as some of them correspond to flood events, which might have implied problems with the measurements. However, it was possible to improve the lake-level simulation distinctively by considering only the parameter inflow_factor for multiple inflows within the calibration process.

Figure 8Observed (blue) and simulated (red) lake level of lake Ammersee.

Download

Simulated water temperatures reveal an overall RMSE of 1.172 ^∘C. The highest deviations occur within the metalimnion at a depth between 7 and 18 m (Bueche and Vetter, 2014b) during summer stratification, when the model underestimates the temperature (Fig. 9). This is accompanied by layers that are too warm in the upper epilimnion at a depth of about 20 m. However, the general seasonal pattern is reproduced adequately, and differences during winter are negligible.

Figure 9Contour plot of differences between simulated and observed water temperatures of lake Ammersee.

Download