Three morphometrically different lakes, Lake Mendota, Fish Lake, and Lake Wingra, located near Madison, Wisconsin, United States of America (USA), were selected for this study. These lakes are chosen for (i) their morphometry differences, (ii) their proximity to one another, and (iii) the availability of long-term data for model input and calibration.

Lake Mendota (43∘6′ N; 89∘24′ W; Fig. 1a; Table 1), is a dimictic, eutrophic drainage lake in an urbanizing agricultural watershed (Carpenter and Lathrop, 2008). The lake stratifies during the summer, and typical stratification periods last from May to September. Summer (1 June–31 August) mean surface water temperature is 22.4 ∘C, and hypolimnetic temperatures vary between 11 and 15 ∘C. Normal Secchi depth during the summer is 3.0 m (Lathrop et al., 1996). Fish Lake (43∘17′ N; 89∘39′ W; Fig. 1b; Table 1) is a dimictic, eutrophic, shallow seepage lake located in northwestern Dane County. From 1966 to 2001, the lake level rose by 2.75 m due to increased groundwater flow from higher-than-normal regional groundwater recharge (Krohelski et al., 2002). Krohelski et al. (2002) hypothesized that the increase in recharge may be the result of increased infiltration from snowmelt after increased snowfall and less frost-covered soil. Summer stratification lasts from the beginning of May to mid-September. Mean surface water temperature is 23.9 ∘C, and hypolimnetic temperatures are normally near 8 ∘C during the summer months; however, some years reach temperatures of only 5–6 ∘C in the hypolimnion due to shortened spring mixing durations. Average Secchi depth during the summer months is 2.4 m. Lake Wingra (43∘3′ N; 89∘26′ W; Fig. 1c; Table 1) is a shallow eutrophic drainage lake. It stratifies on short timescales of hours to weeks (Kimura et al., 2016) but does not experience sustained thermal stratification. Summer mean water temperature is 23.9 ∘C, and mean Secchi depth is 0.7 m. All three lakes have ice cover during the winter months, and a description of ice on the lakes can be found in Magee and Wu (2017).

To hindcast water temperature and stratification in the three study lakes, we use the vertical heat transfer model, DYRESM-WQ (DYnamic REservoir Simulation Model for Water Quality) by Hamilton and Schladow (1997), which employs discrete horizontal Lagrangian layers to simulate vertical water temperature, salinity, and density with input including inflows, outflows, and mixing (Imberger et al., 1978). The model has been previously used on a variety of lake types and is accepted as a standard for hydrodynamic lake modeling (Gal et al., 2003; Hetherington et al., 2015; Imberger and Patterson, 1981; Kara et al., 2012; Tanentzap et al., 2007). DYRESM-WQ adopts a one-dimensional layer structure based on the importance of vertical density stratification over horizontal density variations. A one-dimensional assumption is based on observations that the density stratification found in lakes inhibits vertical motions, while horizontal variations in density relax due to horizontal advection and convection (Antenucci and Imerito, 2003; Imerito, 2010). Surface exchanges include heating due to shortwave radiation penetration into the lake and surface fluxes of evaporation, sensible heat, longwave radiation, and wind stress (Imerito, 2010). Surface layer mixing is based on potential energy required for mixing, and introduction of turbulent kinetic energy through convective mixing, wind stirring, and shear mixing (Imerito, 2010; Yeates and Imberger, 2003). Layer mixing occurs when the turbulent kinetic energy (TKE), stored in the topmost layers, exceeds a potential energy threshold (Yeates and Imberger, 2003). To represent convective overturn, layers are checked for instabilities resulting from surface cooling, and if they exist, layers are merged and a fraction of the potential energy released becomes available as TKE. To represent wind stirring, wind stress is calculated from the wind speed and TKE is produced in the uppermost layer. Upper layers will mix with lower layers if TKE is greater than the energy required for mixing. Mixing by shear flow is determined by calculating the mean horizontal velocity of the uppermost layer, which is dependent on the critical wind speed and the shear period. Yeates and Imberger (2003) improved performance of the surface mixed layer routine within the model by including an effective surface area algorithm based on observations in five lakes of different size, shape, and wind forcing characteristics (see Eq. 32 in Yeates and Imberger, 2003) that reduced surface mixing in smaller, more sheltered lakes. The effective area is used to modify the transfer of momentum from surface stress, as described in detail in Yeates and Imberger (2003) and not reproduced here. Their analysis developed a strong inverse relationship between the lake number and lake-wide average vertical eddy diffusion coefficient, which configures a pseudo two-dimensional deep mixing within the code, found to significantly improve the simulation of thermal structures observed in lakes that experienced strong wind forcing (Yeates and Imberger, 2003). Details of the surface mixed layer algorithm are not reproduced here but can be found in Eqs. (27)–(34) of Yeates and Imberger (2003). Hypolimnetic mixing is parameterized through a vertical eddy diffusion coefficient, which accounts for turbulence created by the damping of basin-scale internal waves on the bottom boundary and lake interior (Yeates and Imberger, 2003). Detailed equations on the simulation of water temperature and mixing can be found in Imberger and Patterson (1981), Imerito (2010), and Yeates and Imberger (2003).

Sediment heat flux is included as a source/sink term for each model layer. A diffusion relation from Rogers et al. (1995) is used to estimate qsed, heat transfer from the sediments to the water column. qsed=KseddTdz, where Ksed represents the sediment conductivity with a value of 1.2 Wm-1 ∘C-1 (Rogers et al., 1995), and dT/dz is estimated as dTdz=Ts-Twzsed, where dT/dz is the temperature gradient across the sediment–water interface, Tw is the water temperature adjacent to the sediment boundary, and zsed is the distance beneath the water–sediment interface at which the sediment temperature becomes relatively invariant and is taken to be 5 m (Birge et al., 1927). Ts is derived from Birge et al. (1927) and seasonally variant as follows: Ts=9.7+2.7sin⁡2πD-151TD, where D is the number of days from the start of the year and TD is the total number of days within a year.

The ice component of the model, DYRESM-WQ-I, is based on the three-component MLI model of Rogers et al. (1995), with the additions of two-way coupling of the hydrodynamic and ice models and time-dependent sediment heat flux for all horizontal layers. The model assumes that the timescale for heat conduction through the ice is short relative to the timescale of meteorological forcing (Patterson and Hamblin, 1988; Rogers et al., 1995), an assumption which is valid with a Stefan number less than 0.1 (Hill and Kucera, 1983). The three-component ice model simulates blue ice, white ice, and snow thickness (see Eq. 1 and Fig. 5 of Rogers et al., 1995). Further description of the ice model can be found in Magee et al. (2016) and Hamilton et al. (2017). Details on ice cover simulations in response to changing climate for the three lakes can be found in Magee and Wu (2017).

Model inputs include lake hypsography, initial vertical profiles for water temperature and salinity, Secchi depth, meteorological variables, and inflows/outflows. The model calculates the surface heat fluxes using meteorological variables: total daily shortwave radiation, daily cloud cover, air vapor pressure, daily average wind speed, air temperature, and precipitation. Water temperature, water budget, and ice thickness are calculated at 1 h time steps. Snow ice compaction, snowfall, and rainfall components are updated at a daily time step, corresponding to the frequency of meteorological data input. Cloud cover, air pressure, wind speed, and temperature are assumed constant throughout the day, and precipitation is assumed uniformly distributed. Shortwave radiation distribution throughout the day is computed based on lake latitude and the Julian day (Antenucci and Imerito, 2003). Parameters relevant to the open-water period are provided in Table 2. Ice cover model parameters can be found in Hamilton et al. (2017), Magee and Wu (2017), and Magee et al. (2016). During the entire simulation period, all model parameters and coefficients are kept constant. Simulations were run for all three lakes starting on 7 April 1911 and ending on 31 October 2014 without termination.

Model calibration consisted of two processes: (1) closing the water balance to match simulated and observed water levels and (2) adjusting the minimum water level thickness to match simulated and observed water temperatures for each lake. Water balance for all three lakes was closed using the method described in Sect. 2.3.5 to match measured water levels to known values and to long-term average water levels when elevation information was unknown. Model evaporation rates were not validated; we assume that evaporative water flux and heat flux were properly parameterized by the model. Model parameters were derived from literature values (Table 2). Within the model, the minimum layer thickness sets the limit for how small a water layer can become before it is merged with the smaller of the layers above or below. If the minimum layer thickness is too large, the model may not have the desired resolution to accurately capture changes in temperature and density that occur over small changes in depth. To calibrate this parameter, the minimum layer thickness was varied from 0.05 to 0.5 m in intervals of 0.025 m for the period 1995–2000 for all three lakes, similar to the method in Tanentzap et al. (2007) and Weinburger and Vetter (2012). One minimum layer thickness was chosen for all three lakes to keep model formulation and implementation identical among the three lakes, and the final thickness was chosen to be 0.125 m, as it minimized the overall deviation between simulated and observed temperature values for the three lakes.

Three statistical measures were used to evaluate model output against observational data (Table 3): absolute mean error (AME), root mean square error (RMSE), and Nash–Sutcliffe (NS) efficiencies were used to compare simulated and observed temperature values for volumetrically averaged epilimnion temperature, volumetrically averaged hypolimnion temperature, and all individual water temperature measurements for unique depth and sampling time combinations. Simulated and observed values are compared directly, except for aggregation of water temperature measurements to daily intervals where subdaily intervals are available. Water temperatures were evaluated for the full range of available data on each lake.

Modeling results were analyzed using linear regression, sequential t test, and Pearson correlation coefficient. Linear regression was used to determine the trend of long-term changes in lake variables. Breakpoints in variables were determined using a piecewise linear regression (Magee et al., 2016; Ying et al., 2015). A sequential t test (Rodionov, 2004; Rodionov and Overland, 2005) was used to detect abrupt changes in the mean value of lake variables. The variables were tested on data with trends removed using a threshold significance level of p= 0.05, a Huber weight parameter of h= 2, and a cut-off length of L = 10 years. Coherence of lake variables (Magnuson et al., 1990) for each lake and between lake pairs was determined with a Pearson correlation coefficient (Baron and Caine, 2000). The three lakes were paired to compare coherence of lake variables with surface area difference (Mendota/Fish pair), depth differences (Fish/Wingra pair), and both surface area and depth differences (Mendota/Wingra). Additionally, temperature, stratification, and heat flux pair variables for all three lakes are correlated to air temperature and wind speed drivers, ice date and durations, and temperature, stratification, and heat flux variables within each lake.

To determine the sensitivity of lake water temperature and stratification in response to air temperature and wind speed, we perturbed these drivers across the range of -10 to +10 ∘C in 1 ∘C temperature increments and 70 to 130 % of the historical value in 5 % increments, respectively. For each scenario, meteorological inputs remained the same as for the original simulation and snowfall (rainfall) conversion if the air temperature scenarios increased (decreased) above 0 ∘C. Similarly, the water balance and water clarity are maintained so that the long-term values in both lakes matches the historical record. This limits our analysis, as it may exclude changes in water temperatures as a result of increased evapotranspiration, increased precipitation, or altered water clarity under future climate scenarios. Inflow temperatures are recalculated for each lake to account for increases or decreases in temperature because of air temperature changes.

Yearly average air temperatures (+0.145 ∘C decade-1; p < 0.01) and seasonal air temperatures (winter: +0.225 ∘C decade-1; spring +0.165 ∘C decade-1; summer +0.081 ∘C decade-1; fall +0.110 ∘C decade-1; p < 0.05) increased from 1911 to 2014 (Fig. 2a). Additionally, yearly average air temperatures, but not seasonal temperatures, showed a significant change in slope occurring in 1981 based on a breakpoint analysis and an F test at a 0.05 significance level (Magee et al., 2016), and summer air temperatures showed three significant abrupt changes in mean value (Fig. 2a). Yearly (-0.073 m s-1 decade-1; p < 0.01) and seasonal average (winter: -0.083 m s-1 decade-1; spring -0.071 m s-1 decade-1; summer: -0.048 m s-1 decade-1; fall: -0.088 m s-1 decade-1; p < 0.01) wind speeds decreased from 1911 to 2014 (Fig. 2b). A change in air temperatures also occurred in the 1980s in central Europe (Woolway et al., 2017b), which may indicate that changes in air temperature were a global phenomenon rather than local occurrence. Significant shifts (p < 0.01) in the mean occurred in the mid-1990s for all seasons, but there were no changes in rate of wind speed decreases.

Simulated temperatures agreed well with observations for all three lakes (Fig. 3, Table 3). The model was validated with all available data for all three lakes during the period 1911–2014. AMEs and RMSEs for all variables were low and less than the standard deviations. NS efficiencies of the daily time bases were high (> 0.85) and most above 0.90, indicating high model accuracy.

Lake Mendota and Lake Wingra had similar increasing epilimnetic water temperature trends, while Fish Lake had a larger increase (Table 4). All three lakes have statistically significant (p < 0.01) abrupt changes in mean epilimnion temperatures over the study period. For Lake Mendota, a change occurs after 1930 from 22.09 to 22.99 ∘C. For Fish Lake, three changes were detected: after 1934, from 21.68 to 22.50 ∘C; after 1995, from 22.50 to 24.26 ∘C; after 2008, from 24.26 to 22.14 ∘C. Lake Wingra has an abrupt change after 1930 from 23.13 to 24.02 ∘C. These increases in epilimnetic temperatures are similar to those found for European lakes (Woolway et al., 2017b) in response to regional climate changes, although Woolway et al. (2017b) demonstrated a substantial increase in annually averaged lake surface water temperatures in the late 1980s in response to an abrupt shift in the climate, which is not apparent in epilimnion water temperatures for our study lakes. Additionally, Van Cleave et al. (2014) showed a regime shift in July–September Lake Superior surface water temperatures after 1997, driven by El Niño in 1997–1998; however, we do not find a similar regime shift in our study lakes, which may be due to geographical differences in meteorology or morphometric differences from the larger Lake Superior.

Lake Mendota and Fish Lake hypolimnions were defined as 20–25 and 13–20 m, respectively, based on the long-term bottom depth of the metalimnion. Lake Mendota has a larger decrease in hypolimnetic temperature than Fish Lake (Table 4), and neither has an abrupt change in temperature nor a significant breakpoint in linear trend during the study period (Fig. 4). Change in summer (15 July–15 August) hypolimnetic heating was an order of magnitude larger for Mendota than for Fish Lake (Table 4).

We characterize summer stratification by stratification onset, fall overturn, and duration of stratification (Fig. 5). Onset of stratification and fall turnover were defined as the day when the surface-to-bottom temperature difference was greater than (for stratification) or less than (for overturn) 2 ∘C (Robertson and Ragotzkie, 1990). Lake Wingra experienced only short-term stratification (timescale of days–weeks) and is excluded from this analysis.

Lake Mendota has larger trend in earlier stratification onset, fall overturn, and stratification duration than Fish Lake (Table 4), with most of the difference in stratification duration caused by larger change in stratification onset date for Lake Mendota. For both lakes, a significant (p < 0.01) shift in onset date occurred at similar times, with a shift to 13.3 days earlier for Lake Mendota after 1994 and 15.1 days earlier for Fish Lake after 1993. No change in trend occurred for stratification onset or overturn, but stratification duration shifted from +0.067 to +4.5 days decade-1 after 1940 for Lake Mendota and from -0.19 days decade-1 to +9.6 days decade-1 after 1981 for Fish Lake (Fig. 5).

We quantify resistance to mechanical mixing with a Schmidt number (Idso, 1973). Lake Mendota showed greater stability in general than Fish Lake (Fig. 6) and had a larger trend of change than Fish Lake (Table 4), possibly due to a larger change in stratification and hypolimnion temperature, increasing stability. There was no significant abrupt shift or change in trend for any of the three lakes during the study period.

Modeled surface heat fluxes included net shortwave, net longwave, sensible heat, latent heat, and total heat fluxes (Fig. 7). Magnitudes of shortwave, longwave, and sensible heat fluxes are similar for all three lakes, but Lake Wingra has a larger magnitude of both latent and net heat fluxes. Net longwave is negative for all three lakes and increased in magnitude (Table 4), and sensible heat flux decreased in magnitude (it became less negative; Table 4). There is no significant trend in other surface heat flux variables. Lake Wingra has a much smaller change in trend for longwave radiation than Mendota or Fish, but a larger change in trend for sensible heat flux, indicating that depth likely influences the response of those heat fluxes to air temperature and wind speed changes.

Pearson correlations for all variables and lake pairs are significant (Table 5). Shortwave, longwave, sensible, and latent heat fluxes show high correlation for lake pairs, suggesting that morphometry has little impact on variability among lakes. Similarly, epilimnion temperatures have high temporal coherence. However, Fish Lake pairs have lower correlations, which may be a result of changes to lake depth (Krohelski et al., 2002) compared to stable water levels in Mendota and Wingra. Low coherence between the Mendota/Fish pair for hypolimnion temperature and stratification dates suggests that fetch differences impact variability. Stability, however, is lower for pairs with Lake Wingra, indicating that lake depth plays a role in temporal coherence of stability. Similarly, Lake Wingra pairs have lower coherence of net heat flux although the coherence of heat flux components is relatively high. Depth may be influencing a non-linear response of net heat flux that is not present in the components of the flux.

Generally, direction and magnitude of Pearson correlation between lake variables are similar for each of the three lakes; however, there are some notable exceptions (Fig. 8). Ice-off dates are significantly correlated with stratification onset dates and hypolimnetic temperature on Fish Lake, but those correlations do not exist for Lake Mendota. Stratification onset is significantly correlated with hypolimnetic temperature and stability in Lake Mendota but not significantly correlated on Fish Lake. Summer air temperatures are more highly correlated with stability than summer wind speed for Lake Mendota and Fish Lake, but the opposite is true for Lake Wingra, where summer air temperature is not significantly correlated. Additionally, hypolimnion temperature is more highly correlated with stability in Lake Mendota, whereas epilimnion temperature is more highly correlated with stability in Fish Lake.

Responses of simulated stratification onset, fall overturn, and hypolimnetic temperature to air temperature and wind speed perturbation scenarios for Lake Mendota and Fish Lake are discussed in the following. Other variables are omitted for brevity and Lake Wingra did not experience prolonged stratification under any sensitivity scenarios, so they are excluded from the analysis. In our analysis, we refer to the “base case” as the meteorological values that represent the historical period from 1911 to 2014 and refer to perturbations in air temperature and wind speed from that base case.

Stratification onset generally occurs earlier on Fish Lake than Lake Mendota for all scenarios (Fig. 9). Simulations show that the response of median onset dates to changes in air temperature is the same for both increases and decreases from the base case (-2.0 days ∘C-1) for Lake Mendota, but for Fish Lake the magnitude of change is larger for air temperature decreases (-1.5 days ∘C-1 for temperature increases and +2.7 days ∘C-1 for temperature decreases). Variability in Lake Mendota onset remains consistent across scenarios but decreases for Fish Lake as air temperatures increase. This may be from interaction between ice cover and stratification onset on Fish Lake but not on Lake Mendota. For Lake Mendota, stratification onset dates have a larger change for wind speed increases than decreases (-3.4 days (m s-1)-1 for decreases and +10.5 days (m s-1)-1 for wind speed increases), as is the case for Fish Lake (-3.6 days (m s-1)-1 for decreases and +8.1 days (m s-1)-1 for wind speed increases). Variability in onset dates decreases with lower wind speeds and increases with higher wind speeds.

Fall overturn typically occurs slightly early on Lake Mendota than on Fish Lake for all scenarios (Fig. 10). For Lake Mendota, stratification overturn dates change at a rate of +0.68 days ∘C-1 with positive and negative perturbations in temperature, while Fish Lake has a larger change for air temperature increases (+1.81 days ∘C-1 for temperature increases and -0.77 days ∘C-1 for temperature decreases) from the historical condition. Standard deviation in overturn dates decreased slightly for Lake Mendota as air temperature increased but remained consistent for Fish Lake. For stratification overturn dates on Lake Mendota, the change is +13.9 days (m s-1)-1 for wind speed decreases and -17.1 days (m s-1)-1 for wind speed increases. For Fish Lake, the change is +16.4 days (m s-1)-1 for wind speed decreases and -8.5 days (m s-1)-1 for wind speed increases. Like onset dates, variability in overturn dates decreases with lower wind speeds and increases with higher wind speeds.

For both lakes, increases in air temperature increase hypolimnetic temperatures, while decreases in wind speed decrease temperatures (Fig. 11). Simulations show that the response of median hypolimnetic temperatures to changes in air temperatures is consistent for Lake Mendota (+0.18 ∘Chypolimnion Cairtemperature-1) for both increases and decreases from the base case but not so for Fish Lake (+0.25 ∘Chypolimnion Cairtemperature-1 for air temperature increases and -0.18 ∘Chypolimnion Cairtemperature-1 for air temperature decreases). Standard deviations under varying air temperature scenarios remain consistent for both lakes. Hypolimnion temperatures change inconsistently with increases and decreases in wind speed for both lakes. For Lake Mendota, the change is -1.1 ∘C (m s-1)-1 for decreases and +1.8 ∘C (m s-1)-1 for wind speed increases. For Fish Lake, the change is -1.2 ∘C (m s-1)-1 for decreases and +0.8 ∘C (m s-1)-1 for wind speed increases. Variability decreases for lower wind speeds in Lake Mendota but remains constant for Fish Lake.

The DYRESM-WQ-I model reliably simulated water temperatures over long-term (1911–2014) simulations (Fig. 3, Table 4). Generally, simulated temperatures were lower than observed values. Some may be attributed to timing of observations, which in most instances occur during midday, when water temperatures may be slightly higher than daily averages, as output from the model. Slight deviation is also expected due to averaging of air temperature and wind speeds. In general, thermocline depths were within 1 m of observed values, but some years differ by as much as 2.5 m, contributing additional error in water temperature comparison for depths near the thermocline.

The performance of the DYRESM-WQ-I model was within those of other studies. Perroud et al. (2009) performed a comparison of one-dimensional lake models on Lake Geneva, and RMSEs for water temperatures were as high as 2 ∘C for the Hostetler model (Hostetler and Bartlein, 1990), 1.7 ∘C for DYRESM (Tanentzap et al., 2007), 2 ∘C for SIMSTRAT, and 4 ∘C for the Freshwater Lake Model (FLake) (Golosov et al., 2007; Kirillin et al., 2012). Similar to this study, errors in the upper layers were lower than those in the bottom of the water column (Perroud et al., 2009). Fang and Stefan (1996) gave standard errors of water temperature of 1.37 ∘C for the open-water season and 1.07 ∘C for the total simulation period for Thrush Lake, MN, similar to those here. Nash–Sutcliffe efficiency coefficients for all three study lakes were within the ranges found in Yao et al. (2014) for the Simple Lake Model (SIM; Jöhnk et al., 2008), Hostetler, Minlake (Fang and Stefan, 1996), and General Lake Model (GLM; Hipsey et al., 2014) for Harp Lake, Ontario, Canada, water temperatures.

Model parameters used to characterize the lake hydrodynamics were taken from literature values. These values may be expected to have small variability between lakes; however, previous studies have shown that many of the hydrodynamic parameters are insensitive to changes of ±10 % (Tanentzap et al., 2007). Here, the model was validated against an independent dataset for each lake to determine if the model fits measured data and functions adequately, with errors within the range of those from other studies. Adjustments were made to limit uncertainty and errors associated with changes in location and techniques of meteorological measurements. Inflow and outflow measurements were assessed by the USGS for quality assurance and control, but uncertainty for both quantity and water temperature is unknown. The effects of these uncertainties may not be large as the inflow and outflow are small in comparison to lake volume. The combination of uncertainties in parameters and observed data may be high; however, as all parameters and observational methods were kept consistent among the three lakes, the validity of the model in predicting differences among the three lake types is adequate.

The main limitation in the model and resulting simulations is the assumption of one-dimensionality in both the model and field data. Quantifying the uncertainty from this limitation can be difficult (Gal et al., 2014; Tebaldi et al., 2005) Small, stratified lakes generally lack large horizontal temperature gradients (Imberger and Patterson, 1981), allowing the assumption of one-dimensionality to be appropriate. However, short-term deviations in water temperature and thermocline depth may exist due to internal wave activity, especially in larger lakes (Tanentzap et al., 2007), and spatial variations in wind stress can produce horizontal variations in temperature profiles (Imberger and Parker, 1985). To address the role of internal wave activity and benthic boundary layer mixing, the pseudo two-dimensional deep mixing model by Yeates and Imberger (2003) is employed here. This mixing model has been shown to accurately characterize deep mixing that distributes heat from the epilimnion into the hypolimnion, thus weakening stratification, and the rapid distribution of heat entering the top of the hypolimnion from benthic boundary layer mixing, which strengthens stratification (Yeates and Imberger, 2003). Tributary inflows may also contribute to enhanced diffusion due to inflow momentum; however, lakes used in this study are seepage-dominated lakes with little to no tributary contribution, so this phenomenon does not prevent the one-dimensional model from being applicable in this study. This one-dimensional assumption here and corresponding model results may not apply elsewhere for lakes with large inflow volumes.

Additionally, light extinction significantly impacts thermal stratification (Hocking and Straškraba, 1999) and light extinction estimated from Secchi depths can have a large degree of measurement uncertainty (Smith and Hoover, 2000), which may result in uncertainty in water temperatures. To address this uncertainty, where available, we use measured Secchi depth values, which have been shown to improve estimates of the euphotic zone over fixed coefficients (Luhtala and Tolvanen, 2013). Secchi depths were unavailable for portions of the simulation period, and average values for the season were used. Analysis comparing using the method of known Secchi depths to both seasonally varying average Secchi depths and constant Secchi depths for the lakes indicates that seasonally varying averages do not significantly decrease model reliability when compared to year-specific values but do show improvement over constant Secchi depths.

While many have addressed the importance of changing air temperatures on water temperatures and water quality (e.g., Adrian et al., 2009; Arhonditsis et al., 2004; O'Reilly et al., 2015; Shimoda et al., 2011), fewer have investigated wind speed as a specific driver of changes to lakes (Magee et al., 2016; Kimura et al., 2016; Snortheim et al., 2017). However, results here show that correlations between wind speeds and lake temperature variables are as high as, or higher than, correlations between air temperature and lake temperature variables (Fig. 8), highlighting the importance of considering wind speeds as drivers of lake temperature and stratification changes. For many variables (e.g., stratification dates, epilimnetic temperatures, stability), correlation is opposite for air temperature and wind speed variables, indicating that wind speed increases may offset the effect of air temperature increases, while locations with decreasing wind speeds may experience a greater impact on water temperature and stratification than with air temperature increases alone. This is further supported through sensitivity analysis on stratification onset and overturn (Figs. 9 and 10), which show that, for Madison-area lakes, increasing air temperatures and decreasing wind speeds have a cumulative effect toward earlier stratification onset and later overturn. Other studies have also found that wind speed can be as important as or even more important than air temperature for influencing lake stratification and water temperatures. For example, Woolway et al. (2017a) found that for polymictic Lake Võrtsjärv, wind speed is the key factor on the number of stratified days, and the influence of air temperature increases was minimal; Kerimoglu and Rinke (2013) found that a 30 % increase in wind speed can compensate up to a 5.5 K increase in air temperature, and Hadley et al. (2014) suggested that the combination of increased air temperature and decreased wind is the primary driver of enhanced stability in Harp Lake since 1979, although no significant change in the timing of onset, breakdown, or duration of stratification was observed. However, for hypolimnetic temperatures, correlations and sensitivity indicate that decreasing wind speeds may cool hypolimnetic temperatures, while increasing air temperatures warm hypolimnetic temperatures. Arvola et al. (2009) showed that hypolimnion temperatures were primarily determined by the conditions that pertained during the previous spring turnover and timing of stratification onset, which is consistent with our results showing significant (p < 0.01) correlation between hypolimnion temperatures and wind speed (Fig. 8) but no significant correlation with air temperature or summer conditions. This could explain the conflicting results of previous research showing both warming and cooling trends in different lakes (Gerten and Adrian, 2001). Hindcasted hypolimnion temperatures (Fig. 4) show decreasing trends for Lake Mendota and Fish Lake. Combining the effects of air temperature and wind speed, it suggests that wind speed decreases are a larger driver to hypolimnetic water temperature changes than increasing air temperatures for both lakes. This is particularly notable as current research has been dominated by studying air temperature effects and neglecting the role of wind speed changes.

Ultimately, lake warming or cooling may depend on the magnitudes and directions of changes of air temperature, wind speed, and other variables as climatic variables (humidity, cloud cover, solar radiation and water clarity) are important in determining lake water temperatures. Schmid and Köster (2016) demonstrated that 40 % of surface water warming in Lake Zurich was caused by increased solar radiation, and Wilhelm et al. (2006) showed that daily extrema of surface equilibrium temperature responded to shifts in wind speed, relative humidity, and cloud cover in addition to changes in air temperature. However, neither study looked at lakes with seasonal ice cover, which may not account for changes in ice sheet formation and the resulting influence on lake water temperatures (Austin and Colman, 2007). Other studies have demonstrated that ice cover changes do not directly influence summer surface water temperatures (Zhong et al., 2016), in agreement with our modeling results (Fig. 8). Changes in underwater light conditions from increased dissolved organic carbon concentrations combined with reduction in surface wind speeds can result in cooling whole-lake average temperatures despite substantial air temperature increases, as was the case for Clearwater Lake, Canada (Tanentzap et al., 2008). Water clarity has seen both increases and decreases since the early 1990s (Rose et al., 2017), with precipitation playing a critical role in year-to-year variability (Rose et al., 2017). Further investigation into the combined effects of these climatic and lake-specific variables is warranted.