Introduction
Many studies have shown that lake temperatures and ice cover can strongly
affect water chemistry, individual organism physiology, population
abundance, community structure, and food-web dynamics (King
et al., 1997; Schindler et al., 1990). Air temperature (Findlay et al.,
2001; Lynch et al., 2015), wind speed (Brown et al., 1993; Lynch et al.,
2015), and water clarity (Arhonditsis et al., 2004b; Lathrop et al., 1996)
are important factors driving these lake ecosystem properties. Understanding
how lakes respond to changes in these drivers is of great interest to
predict how lakes may change in the future (Fang
and Stefan, 2009; Magnuson et al., 1997; Robertson, 1989). The response of
lake ice and water temperature to long-term changes in air temperature and
wind speed is integral to assess potential impacts of climate change on lake ecology.
Over the past 100 years, climate has been changing and will continue to
change (IPCC, 2013). Globally averaged combined land
and ocean surface temperature data show a linear warming trend of
0.85 ∘C from 1880–2012 (IPCC, 2013). This
warming was most pronounced from 1979–2012, greater than 0.25 ∘C per
decade (Hartmann et al., 2013). Increases in air temperature alter the ice cover of lakes
(Butcher et al., 2015; Magnuson et al., 2000; Robertson et al., 1992) and affect
their thermal structures (Robertson and
Ragotzkie, 1990), evidenced by increasing epilimnetic temperatures (Arhonditsis
et al., 2004a; Dobiesz and Lester, 2009; Schindler et al., 1990), warming of
the lake surface temperature (Schneider and Hook, 2010; Shimoda et al., 2011), increasing temperature gradient
across the thermocline (Robertson and Ragotzkie,
1990; Wilhelm and Adrian, 2008), changing thermocline depth (King
et al., 1997; Schindler et al., 1990), advancing the onset of summer
stratification (Austin and Colman, 2007), delaying
fall turnover (King et al., 1997),
increasing the strength of thermal stratification (Rempfer
et al., 2010), and prolonging the stratified period (Robertson and Ragotzkie,
1990; Wilhelm and Adrian, 2008).
Trends in wind speed over the last 30–50 years have been reported in
several studies that have analyzed historical wind speed records across the
globe (Jiang et al., 2009; Wan et al.,
2010). Klink (2002) examined 22- to 35-year records
(ranging between 1959 and 1995) of wind speed at seven stations in and around
Minnesota and found decreasing annual wind speeds at five of the seven
stations. Pryor et al. (2009)
reported that the 50th and 90th percentile annual wind speeds over
the period 1973–2005 across most of the US have also decreased. Decreased
wind speeds increase thermal stratification and can reduce whole-lake
average temperature (Tanentzap et al., 2008).
Interestingly, an opposing trend (increasing wind speed) has been observed
in Lake Superior, North America, where the lake surface temperatures have
been warming faster than air temperatures (Austin and
Colman, 2007). Desai et al. (2009) suggest that the
larger increase in water temperatures than air temperatures reduced the
air–water temperature gradient and destabilized the atmospheric surface
layer above Lake Superior, which resulted in increasing wind speed at a rate
of nearly 5 % per decade. Differences in wind-driven mixing may explain
different temperature responses of hypolimnetic waters in large and small
lakes (Winslow et al., 2015). While the importance of wind in lake heat transfer
(Fu et al., 2009; Read et al., 2012), mixing, and thermal structure (Desai et al.,
2009; Schindler et al., 1990) has been recognized, studies on the effects of
wind speed alterations on seasonal ice cover and thermal structure of lakes
are still rare.
Water clarity, which controls the amount of solar radiation penetrating into
a lake, plays an important role in heat budgets in lakes. Increased water
clarity can result in warmer deep waters (Stefan
et al., 1996), while reduced light penetration can result in decreased
mixing depth and cooler deep waters (Hocking and Straškraba,
1999; Tanentzap et al., 2008). Previous studies have also shown that
increased water clarity was correlated with deeper mixed-layer depth (Fee et al., 1996;
Mazumder and Taylor, 1994; Schindler et al., 1996) and increased
hypolimnetic heating rate (Yan, 1983). Water
clarity has important consequences for photosynthesis and vertical
distribution of biota. Accompanied by a warming climate, increased
evaporation and changes in precipitation patterns can alter the inputs of
nutrients and dissolved organic carbon (DOC) into lakes, resulting in
changes in water clarity (Schindler et al., 1990, 1996).
Abrupt shifts, rather than linear changes, can occur in both climate and
lake variables over long timescales. In the past, the majority of
referenced studies used some form of linear regression analysis to look for
changes, which assumes that lakes undergo monotonic changes over time
(Van Cleave et al., 2014). This assumption can mask the occurrence of step changes
(Liu et al., 2013; North et al., 2013)
and can hide the underlying mechanisms that are responsible for the changes
(North et al., 2014). As noted in other studies (Mueller et
al., 2009; Van Cleave et al., 2014), long-term changes in lake thermodynamic
variables can be associated with a pronounced, nonlinear step change that
indicates a rapid switch between stable states or regimes
(North et al., 2013; Rodionov, 2004; Scheffer et al., 2001). Identifying this type of abrupt change in climate
drivers and corresponding abrupt or gradual change in lake variables may
shed light on the role of changing climate on the corresponding ecosystem.
The purpose of this study is to investigate how long-term changes in air
temperature, wind speed, and water clarity affect the ice cover and thermal
structure of a dimictic Lake Mendota, Wisconsin, USA during the past century
using a long-term 104-year simulation model. We hypothesize that changes in
lake ice cover (ice-on and ice-off dates, ice cover duration, and maximum
ice thickness) and thermal structure (stratification onset, fall turnover
date, stratification duration, water temperatures, and hypolimnetic heating)
variables may be characterized by periods of abrupt change rather than
gradual trends, based on observations of rapid change in the climate drivers
of air temperature and wind speed. To address this, a one-dimensional
hydrodynamic model with ice cover is employed to simulate long-term
(1911–2014) ice cover and water temperature in the lake. With the knowledge
of lake responses to these past conditions, we aim to reveal how lakes might
respond to future changes in air temperature, wind speed, and water clarity.
Methods
Hydrodynamic model
An ice and snow model was added to the DYRESM-WQ model (Hamilton and
Schladow, 1997), a physically based one-dimensional hydrodynamic model for
simulating vertical mixing and advective transport in lakes and reservoirs.
The resulting model, DYRESM-WQ-I (Hsieh, 2012), is used to
simulate daily changes in the vertical distribution of water temperature and
ice cover in Lake Mendota from 1911–2014. In this model, the lake is
represented by a series of Lagrangian horizontal layers with uniform
properties that may change in elevation and thickness in response to
inflows/outflows and surface mass fluxes (evaporation and precipitation).
Layer thickness is updated using an algorithm to give appropriate vertical
density resolution at each time step. Mixing in the model is represented by
merging the layers when the sum of available turbulent kinetic energy (TKE)
produced by wind stirring, convective turnover, and shear stress exceeds the
potential energy required to mix the adjacent layer below. Hypolimnetic
mixing is modeled with an eddy diffusivity coefficient, which is a function
of the dissipation of TKE and strength of stratification. More detailed
descriptions of the simulation of water temperature and mixing are provided
by Imberger and Patterson (1981).
The ice model is based upon the MLI model of Rogers et
al. (1995) with alterations to two-way coupling of the water-column
dynamics to the ice model and the addition of time-dependent sediment heat
flux for all horizontal layers. Ice growth in the model is based upon a
quasi-steady state assumption 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). This assumption is valid under a Stefan number < 0.1 (Hill and Kucera,
1983). The ice module is applied when the simulated surface water
temperature first drops below 0 ∘C; the initial ice thickness is set to
a value of 5 cm to address effects of partial ice cover
(Patterson and Hamblin, 1988; Vavrus et
al., 1996). Upward conductive heat flux between ice/snow cover and the
atmosphere, q0, is determined by numerically solving the
quasi-steady state heat conduction equations (Rogers et
al., 1995) and assigning appropriate boundary conditions to the water, ice,
and atmospheric interfaces. At the ice (or snow) surface, a heat flux
balance provides the condition for surface melting, and accretion or
ablation of ice is determined through the heat flux at the ice–water
interface. Imbalance between heat conduction through ice and the heat flux
from the water to the ice gives the rate of change of ice thickness at the
ice–water interface. Snow conductivity is estimated from its density using
an empirical equation (Ashton, 1986), and snow compaction is based
on an exponential decay formula (McKay, 1968), with snow compaction
parameters based on air temperature and snowfall/rainfall
(Rogers et al., 1995). Snow (white) ice is generated in
response to flooding, when the mass of snow that can be supported by the ice
cover is exceeded. The uppermost solid layer of ice or snow is adjusted in
thickness at the end of each 1 h model time step according to the balance
of the heat budget. When ice thickness decreases to less than 5 cm, open
water conditions are restored.
Sediment heat flux, the main external source of heat after freezing, is
important to water temperatures beneath ice cover (Ellis et al., 1991). Sediment heat flux
(Fang and Stefan, 1996a) is included as a source/sink
term for each Lagrangian layer to closely simulate under-ice water
temperatures. A simple diffusion relation (Rogers et
al., 1995) is used to estimate heat transfer from the sediments to the water
column, qsed:
qsed=KseddTdz,
where Ksed is the sediment conductivity (= 1.2 W m-1 ∘C-1).
dT/dz, the temperature gradient across the sediment–water interface, is estimated as
dTdz≈Ts-Twzsed,
where Ts is the sediment temperature, Tw is the water temperature
adjacent to the sediment surface, which varies hourly and with depth, and
zsed is the distance beneath the water–sediment interface at which the
sediment temperature becomes largely invariant. From data collected at four
locations on Lake Mendota (Birge et al., 1927), it
was found that sediment temperatures varied little at 5 m depth below the
sediment–water interface, so zsed is set to be 5 m. In addition, data
from Birge et al. (1927) are used to fit a curve to describe the seasonal
variation of Ts
Ts=9.7+2.7sin2π(D-151)TD,
where D is the number of days from the start of the year and TD is the total
number of days for the year of interest (365 or 366). The vertical transfer
of heat in the water column beneath the ice is regulated by an assigned
thermal diffusion coefficient. The formulation is the same as that
originally used in DYRESM-WQ (Hamilton and Schladow, 1997) to simulate heat transfer throughout the open water period.
This produced diffusivities that were within the range of measurements by
Ellis et al. (1991) of 1–3 times greater than molecular values.
Input for the model includes lake morphometry (lake volume and surface area
as a function of elevation), 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. During the
simulation, all parameters/coefficients in the model are kept constant. The
time step in the model for calculating water temperature, water budget, and
ice thickness was set to 1 h. Snow ice compaction, and 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 air temperature are assumed to be constant throughout the day,
and precipitation is assumed uniformly distributed. Shortwave radiation
distribution throughout the day is computed based on the lake latitude and
the day or year. The DYRESM-WQ-I model is calibrated using measured lake
variables including water level, temperature profiles, ice thickness, and
ice-on and ice-off dates. The overall simulation period was 104 years,
starting with an isothermal (measured) water column temperature of
3.1 ∘C on 7 April 1911 and ending on 31 October 2014.
Model calibration
The model was calibrated for the period 1995–2014 by varying the minimum
layer thickness over values ranging from 0.05 to 0.5 m at 0.025 m
intervals. Layer thickness values were evaluated for the least amount of
deviation between predicted and observed temperature values for Lake Mendota
over the period. Based on this analysis, a minimum layer thickness of
0.125 m was chosen as the best setting to predict water temperature at all depths.
Other parameter values in the hydrodynamic and ice cover models were
obtained from literature values (Table 1). To evaluate the performance of
the model, root mean square error (RMSE) was used to compare simulated and
observed ice cover and water temperature values for the full model period
(1911–2014; see Sect. 4.2). Simulated and observed values are compared
directly, with the exception of aggregation of water temperature
measurements to daily intervals where subdaily intervals were available.
Values of DYRESM-ICE parameters and model simulation specifications
for both hydrodynamic and ice cover portions of the model.
Parameter
Value
Hydrodynamic model parameters
Albedo
0.08i,ii
Bulk aerodynamic momentum transport coefficient
0.00139ii
Critical wind speed (m s-1)
4.3ii
Effective surface area coefficient (m2)
1 × 107 iii
Emissivity of water surface
0.96iv
Potential energy mixing efficiency
0.2i,ii
Shear production efficiency
0.06i,ii,iii
Vertical mixing coefficient
200iii
Wind stirring efficiency
0.8ii
Minimum layer thickness
0.125
Maximum layer thickness
0.6ii
Vertical light attenuation coefficient
variablev
Ice model parameters
Waveband 1, snow ice light extinction (m-1)
3.8vi
Waveband 2, snow ice light extinction (m-1)
20vi,vii
Waveband 1, blue ice light extinction (m-1)
1.5vi,vii
Waveband 2, blue ice light extinction (m-1)
20vi,vii
Waveband 1, snow light extinction (m-1)
6vi,vii
Waveband 2, snow light extinction (m-1)
20vi,=vii
Distance of heat transfer, ice–water (m)
0.039viii
Density, snow ice (kg m-3)
890vi
Density, blue ice (kg m-3)
917vi,vii
Density, snow (kg m-3)
variableix
Compaction coefficient
variablevi
Thermal conductivity, snow ice (W m-1 ∘C-1)
2.0vi
Thermal conductivity, blue ice (W m-1 ∘C-1)
2.3vi,vii
Thermal conductivity, snow (W m-1 ∘C-1)
variablex
Thermal conductivity, sediment (W m-1 ∘C-1)
1.2vi
Thermal conductivity, water (W m-1 ∘C-1)
0.57vi,vii
Sources: i Antenucci and Imerito (2003);
ii Tanentzap et al. (2007); iii Yeates and Imberger (2003);
iv Imberger and Patterson (1981); v Williams et al. (1980);
vi Rogers et al. (1995); vii Patterson and Hamblin (1988);
viii Vavrus et al. (1996); ix McKay (1968); x Ashton (1986).
Piecewise regression algorithm
Breakpoints in the air temperature trend over the study period were
determined using a piecewise linear regression (PLR) method (Tomé and Miranda, 2004;
Toms and Lesperance, 2003; Ying et al., 2015) that assumes continuity in the
trendlines across the breakpoint. The piecewise linear regression model
finds the breakpoint, B, that minimizes the residual sum of squares (RSSPLR)
of the model between the two phases (Ying et al., 2015)
RSSPLR=∑i=1nyi-α-k1xi-k2-k1maxxi-B,02,
where xi and yi are the time and air temperature data corresponding
to the ith data point, respectively, and k1 and k2 are the slopes
of the linear fit to data before and after the breakpoint B. The parameter
α is the intercept of the linear fit to data below the estimated
breakpoint B, and n is the series length.
An F test was used to compare the residual sum of squares of an ordinary
linear regression model with the piecewise linear regression model with a
level of α = 0.05 used to indicate significance, and the
breakpoint year was determined to pass with p = 0.0016.
Sequential <inline-formula><mml:math display="inline"><mml:mi>t</mml:mi></mml:math></inline-formula> test analysis of abrupt changes
Abrupt changes in mean annual wind speeds and lake ice cover and temperature
variables were detected using the sequential t test STARS
(Rodionov, 2004), which can automatically detect multiple
change points. A shift occurs when a statistically significant difference
exists between the mean value of the variable before and after a certain
point based on the t test. The variables were tested using a threshold
significance level p = 0.05, a Huber weight parameter, h = 1
(North et al., 2013; Rodionov, 2006), and a cut-off length L = 15 years
(North et al., 2013).
Model input data
Bathymetry
Lake Mendota (43∘40′ N, 89∘24′ W) has a surface area of
39.4 km2 and maximum fetch of 9.8 km (Kitchell,
1992). The mean depth is 12.7 m, and maximum depth is 25.3 m. For detailed
bathymetry refer to Kamarainen et al. (2009).
Meteorological variables
Daily meteorological data required to run the DYRESM-WQ-I model include
solar radiation, air temperature, vapor pressure, wind speed, cloud cover,
rainfall, and snowfall. Daily air temperatures are computed as the average
of daily maximum and minimum temperatures. Vapor pressure, wind speed, and
cloud cover are also entered as daily average values while solar radiation,
rainfall, and snowfall are daily accumulation values.
Meteorological data for the Madison area have been continuously recorded
since 1869, however, the station and techniques have changed several times.
Robertson (1989) constructed a continuous, homogeneous daily
meteorological data set from 1884 to 1988 by adjusting for changes in site
location and observation time, and resultant changes in the surface
roughness (e.g., height of surrounding trees and buildings). These data were
appended with data from the most recent weather station of the National
Climate Data Center (NCDC, NOAA) located in Madison (MSN) Dane County
Regional Airport (Truax Field), approximately 4.5 km east from the
simulation location, the same site as that used in 1988. All data except
solar radiation can be obtained for MSN from
http://www.ncdc.noaa.gov/, except solar radiation which can be obtained from
http://www.sws.uiuc.edu/warm/weather/ (approximately 150 km southeast of
Lake Mendota). Since Robertson (1989) adjusted all historical data to that
collected in 1988, no adjustments are applied to the recent data except for
wind. In 1996, a discontinuity in the wind record was caused by change in
observational techniques and sensor locations (McKee et
al., 2000). To address the nonclimatic changes in wind speed, data from MSN
are carefully compared with those collected from the tower of the
Atmospheric and Oceanic Science Building at the University of
Wisconsin-Madison (http://ginsea.aos.wisc.edu/labs/mendota/index.htm),
approximately 4 km south of simulation location. Hourly data from both sites
(UMSN,hourly and UAOS,hourly) during 2003–2010 were used to
form a 4 × 12 (four components of wind direction × 12 months)
matrix (K4,12) of wind correction factors, yielding
UAOS,daily = Ki,j × UMSN,daily. A comparison of
results indicated that the MSN weather station measured a higher magnitude
in winds out of the east by 5 % and lower magnitude in winds out of the
west and south by 30 and 10 %, respectively. The adjusted wind data
(= Ki,j × UMSN,daily) are used in the model simulation.
Overall the adjusted wind data show a decline in mean wind velocities of
16 % from 1988–1993 to 1994–2014) compared to 7 % at a nearby weather
station with no known observational changes (St. Charles, Illinois; 150 km
southeast of Lake Mendota).
Light extinction
Seasonal Secchi depths can be used to determine the light extinction
coefficient for DYRESM-WQ-I. Lathrop et al. (1996) compiled
Secchi depth data for Lake Mendota between 1900 and 1993 (1701 daily Secchi
depth readings from 70 calendar years), and summarized the data for 6
seasonal periods: winter (ice-on to ice-off date), spring turnover (ice-off date to
10 May), early stratification (11 May to 29 June), summer (30 June to 2 September),
destratification (3 September to 12 October), and fall turnover
(13 October to ice-on date). After 1993, Secchi depths were obtained from the
North Temperate Lakes – Long Term Ecological Research (NTL-LTER)
(https://portal.lternet.edu/nis/home.jsp#). For years with no Secchi
data, the long-term mean seasonal Secchi depth was used to estimate light
extinction. Light extinction coefficients are calculated as a function of
Secchi depth using the equation, k = 1.1/zs0.73 (Williams et al., 1980), where k is the
light extinction coefficient and zs is the measured Secchi depth, in meters.
River inflow and outflow
Daily inflow measurements have been made on selected Lake Mendota
tributaries since 1974, and daily outflow from the lake has been measured
since 1975. Streamflow for the tributaries were obtained from
http://waterdata.usgs.gov/wi/nwis/sw/. Daily outflow from 1975 to 1997 were
calculated from gate/lock/bypass pipe USGS ratings and local governmental
daily operational records. Daily outflow from 1998 to 2003 were estimated from
monthly outflow estimates from downstream Lake Waubesa and Mendota outlet
data from earlier years. Daily outflow from 2003 to the present, were
obtained from http://waterdata.usgs.gov/wi/nwis/uv/?site_no=05428000.
These measurements were used to calculate total daily inflow
and outflow. Total daily inflow and outflow from 1930 to 1974 were estimated
from measurements made at the gauging station downstream of the lake using
the drainage-area ratio method (Maidment, 1993). Prior to 1930,
total inflow and outflow were calculated using a water budget
approach, i.e., the balance of inflow/outflow, precipitation, evaporation,
and lake level changes. The inflow/outflow is the residual unknown term of
the water balance where other terms include evaporation, rainfall, and water
level. The calculation is performed at the interval of water level
measurements and the residual term is then distributed evenly across the
number of days between water level measurements. Water level of Lake Mendota
has been recorded since 1916 at the Yahara River inlet in the north of the
lake (http://waterdata.usgs.gov/wi/nwis/dv). Prior to 1916, the
long-term mean lake level was assumed in water budget calculations. River
water temperature has been recorded at the Yahara River inlet since 2002
(US Geological Survey, http://waterdata.usgs.gov/nwis). To estimate daily
river temperatures prior to 2002, river temperatures were estimated from air
temperatures (Hsieh, 2012). A linear regression was used to
correlate river temperatures and weekly average air temperature data during
2002–2009 for air temperatures above the freezing temperature (r2 = 0.86),
and a separate polynomial regression analysis was performed for air temperatures
below the freezing temperature (r2 = 0.68).
Lake ice cover and water temperature
Observed ice cover data from 1911–2014 (available at NTL-LTER website:
https://portal.lternet.edu/nis/home.jsp#), showed that Lake Mendota, on
average, freezes on 22 December (ice-on date), breaks up on 31 March
(ice-off date), and has an ice duration of 98 days. Ice thickness and snow
depth during the study period were compiled from various sources: 1911–1916
(unpublished data from E. Birge, University of Wisconsin); daily ice
thickness during 1961–1962, 1962–1963, and for part of the winter
1963–1964 (Stewart, 1965); 1975–1995 (unpublished data,
D. Lathrop, Wisconsin Department of Natural Resources); after 1995, ice
thickness and snow depth were sampled once or twice every winter by the
NTL-LTER Program (https://portal.lternet.edu/nis/home.jsp#). In addition,
during winters of 2008–2009 and 2009–2010, blue ice, snow ice, total ice
(blue ice + snow ice), and snow cover depth were measured weekly at
multiple locations on the lake (Hsieh, 2012). In total, there are
251 measurements of total ice, 21 for blue ice, 21 for snow ice, and 49 for
snow depth during 1911 to 2014.
Long-term water temperature records were obtained from Robertson (1989) and the NTL-LTER data set
(https://portal.lternet.edu/nis/home.jsp#). The frequency of water
temperature data varied widely from only one or two profiles per year to
several profiles for a given day, while there were no data collected in some
years between 1931 and 1970. The vertical resolution of the water profiles
varied from 0.5 to 2 m and sometimes 5 m when the water column was weakly stratified.
Historical record of annual average (a) air temperature and
(b) wind speed in Madison, WI, USA, and (c) Secchi depth in Lake Mendota.
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Discussion
Significance of lake drivers
Changes in long-term simulated ice cover and thermal variables in Lake
Mendota from 1911–2014 appear to occur over short time frames within this
period, synchronous with rapid changes in measured drivers (i.e., air
temperature, wind speed, and water clarity). The variables examined included
ice-on/ice-off dates, maximum ice thickness, freeze-over water temperature,
midsummer epilimnetic and hypolimnetic temperatures, summer hypolimnetic
heating, and dates of stratification onset and fall turnover. To identify
the relationship between the drivers and each of these variables, we
employed Pearson correlation analysis on the detrended driver and simulation
data. While using this method does not allow us to directly determine
causality, we may identify possible related drivers to changes in lake
variables and the relative importance of relationship of three drivers (i.e.,
air temperature, wind speed, and water clarity) to the lake variables. To
calculate correlation coefficients, each lake driver was averaged over a
fixed period (e.g., April–May or November–December) and then paired with each
of the simulated lake variables from the same period. The averaging period
for air temperature and wind speed was chosen based on the fixed period that
yielded the best correlation. We chose to employ fixed periods because
thorough testing indicated that using a dynamic period introduced seasonal
meteorological variations into the analysis. For instance, the correlation
coefficient between onset date and the mean air temperature averaged over
the prior month is expected to be high simply due to the seasonal variations
over the course of the year, i.e., the later in the spring, the warmer air
temperature. Seasonal Secchi depths were compiled for six seasonal periods:
winter, spring turnover, early stratification, summer, destratification, and
fall turnover (Lathrop et al., 1996), and the period closest
to the averaging period used for air temperature and wind speed was used for
correlation analysis. The averaging periods used for calculating correlation
coefficients of each pair of variables are listed in Table 3. We discuss
below the correlations for each pair of variables, shown in Fig. 12.
Averaging periods for lake drivers used for calculating correlation
coefficients of each pair of variables.
Lake variables
Air temperature/
Secchi depth*
wind speed
Ice-on date
November–December
13 October – ice-on
Ice-off date
February–March
ice-on – ice-off
Max. ice thickness
January–March
ice-on – ice-off
Freeze-over water temperature
November–December
13 October – ice-on
Date of stratification onset
April–May
ice-off – 10 May
Summer epilimnetic temperature
16 July–15 August
30 June–2 September
Summer hypolimnetic temperature
May
ice-off – 30 June
Hypolimnetic heating
July–August
30 June–2 September
Date of fall turnover
September
3 September–12 October
* Six seasonal periods defined in Lathrop et al. (1996).
Correlation coefficients between lake variables and drivers. The
critical value (dashed lines) for significant correlation (p < 0.05)
is 0.193 (n = 104).
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Ice cover variables
Ice-on and ice-off dates have been shown to be sensitive to climate
conditions (Livingstone, 1997; Magnuson et al., 2000; Robertson et al., 1992). For both air
temperature and wind speed, the averages from 1 November to 31 December
(N–D) give the highest correlation with ice-on date; in agreement with the
results of Assel and Robertson (1995) and similar to Gao
and Stefan (1999). Averaged air temperature and
wind speed over the period from 1 February to 31 March (FM) provide the
highest correlation with ice-off date, consistent with the study by Gao and
Stefan (1999), who found that ice-off dates for 10 Minnesota lakes
correlated significantly with February–April air temperatures. The strong
positive correlation (r = 0.82) between ice-on date and N–D air temperature
indicates a relationship between warmer N–D air temperatures and later
freezing dates. Strong negative correlation between ice-off date and F–M air
temperature (r = -0.70) indicates a relationship between earlier ice
breakup and warmer F–M air temperatures. In contrast to air temperature, ice
cover is only weakly related to the seasonal average wind speed.
Nevertheless, the correlation between ice-on date and wind speed (r = -0.26)
is significant, indicating a relationship between decreasing wind speed and
earlier ice-on dates. Since large wind events prevent ice formation by breaking up
skim ice, decreased wind speeds allow ice cover to form slightly earlier in
the year. In the Madison area, the decreasing wind speeds may act to
slightly mitigate the effects of increasing air temperature in later ice
freezing. Correlation between ice dates and Secchi depths is low (r = 0.24
for ice-on dates and r = -0.22 for ice-off dates), indicating that water clarity has only
a minor relationship with ice dates, in agreement with the simulation
results of Fang and Stefan (1997). For both ice-on and ice-off dates, correlations with wind speed and Secchi
depth are much less significant than with air temperature, indicating that
air temperature has a more significant relationship with ice-on and ice-off
dates and may be a more significant indicator of ice cover dates and
ultimately ice cover duration.
Annual maximum ice thickness is negatively correlated with the 1 January–31 March
(J–F–M) averaged air temperature (r = -0.77) and weakly correlated
with J–F–M wind speed (r = 0.21), indicating a better relationship between
annual maximum ice thickness and air temperature than for wind speed. The
relationship of air temperatures on ice phenology is consistent with
previous findings for lakes in northern Wisconsin, Canada, and Maine
(Gao and Stefan, 2004).
The strong correlations between air temperature and ice cover variables
agree with several earlier studies (Anderson
et al., 1996; Gao and Stefan, 2004; Livingstone, 1997; Vavrus et al., 1996;
Williams et al., 2004). Snowfall has also been shown to be related to
ice-off date (Jensen et al., 2007) and ice thickness (Duguay et al., 2003; Vavrus
et al., 1996) because snowfall changes surface albedo and isolates ice cover
from the atmosphere. We found that simulated number of snow days (number of days
when the lake has snow cover) is strongly correlated with ice-off date
(r = 0.70) and maximum ice thickness (r = 0.75), indicating snowfall is also
significantly related to ice cover.
Water temperature and stratification
Figure 10 shows that the simulated water temperatures in Lake Mendota at the
time of freezing have been increasing since 1911. The correlation between
freeze-over water temperature and lake drivers during 1 November and
31 December (N–D) is significant but with low rvalues for wind speed
(r = -0.37) and air temperature (r = -0.24) and insignificant for Secchi depth
(r = 0.18). This result indicates that wind mixing is related to cooling of
the water column before Lake Mendota freezes.
The simulated onset dates of stratification are negatively correlated with
April–May (A–M) air temperature (r = -0.55) and positively correlated with
A–M wind speed (r = 0.35). In Lake Mendota, the combination of increasing
air temperatures and decreasing wind speeds are both related to earlier
onset of stratification. Austin and Colman (2007) suggested that the
declining ice cover combined with higher air temperatures cause the earlier
onset of stratification in Lake Superior at a rate of 0.5 day yr-1.
However, no correlation between ice-off date and the onset of stratification
was found for Lake Mendota in this study.
Midsummer (16 July–15 August) epilimnetic temperatures are most strongly
correlated with the air temperature averaged over the corresponding period.
Epilimnetic temperature is highly correlated with air temperature (r = 0.77)
and not significantly correlated with wind speed averaged over the
corresponding period (r = -0.11) and Secchi depth (r = 0.09). Midsummer
hypolimnetic temperatures depend on the timing of stratification (how long
the near-bottom water is heated before the onset of stratification) and the
amount of heat mixed into hypolimnion before and during the stratification
period. Hypolimnetic temperatures are weakly correlated with air
temperatures (r = -0.23) and not significantly correlated with wind speed
(r = 0.11) and Secchi depth (r = -0.02). Summer hypolimnetic heating
(temperature change between 1 July and 31 August, J–A) is most strongly
correlated with J–A wind speed (r = 0.49), moderately correlated with Secchi
depth averaged over 30 June–2 September (r = 0.35), and not
significantly correlated with J–A air temperature (r = -0.02). This
indicates a relationship between stronger winds and clearer water and deeper heat mixing.
Fall turnover occurs when the lake water cools, driven largely by colder air
temperature and wind-induced mixing. The date of fall turnover is
significantly negatively correlated with September wind speed (r = -0.43) so
that higher wind speed is related to earlier fall turnover. Air temperature
(r = 0.11) and Secchi depth (r = -0.15) are not significantly correlated
with the timing of fall mixing. Interestingly, the midsummer
epilimnion–hypolimnion temperature difference has a higher correlation with
turnover date (r = 0.62) than any of the three lake drivers. This finding
suggests that the influences of spring conditions may be transmitted to the
following summer and fall seasons. In other words, the cooler hypolimnion
and the greater epilimnion–hypolimnion temperature difference after a warmer
and less windy spring may be related to later fall turnover and a longer
stratification period.
Abrupt changes in lake variables
To investigate the effects of abrupt changes in air temperature and wind
speed on lake ice cover and water temperatures, we used the hydrodynamic
model DYRESM-WQ-I to describe changes in several lake variables during
1911–2014. Simulation results were used to examine differences in mean
values of these lake variables between specific periods (see Sect. 4.1). For
each period of the selected periods, mean lake variables were calculated and
the differences between periods were analyzed with t tests to determine if
they were significantly different. Table 2 lists the mean values and
differences for the nine lake variables during the three selected periods.
Comparison of period 1 (1911–1980) to period 2 (1981–1993) of lake variables
shows a shift to warmer air temperature, period 2 to period 3 (1994–2014)
represents an abrupt change to lower wind speed, and period 1 to period 3
represents a shift to warmer air temperature combined with an abrupt change
to lower wind speeds.
Ice cover
Three simulated ice cover variables (maximum ice thickness, ice-on date, and
ice-off date) show no significant difference in means between periods 1 and 2.
In other words, the abrupt change in air temperature trend does not
result in a different ice period even though the ice cover variables are all
highly correlated with air temperature (r > 0.70). This may be
because the change in air temperatures was not of sufficient magnitude to
cause a particularly large change in ice cover or it may signify that other
drivers are contributing to changes in ice cover variables. Additionally, no
significant difference is observed between period 2 and period 3 for the ice
cover variables since the wind speed and ice cover variables are only weakly
correlated. The ice variables do show a statistically significant difference
in mean values between periods 1 and 3, indicating that a significant shift
in these variables occurs only after a sufficiently large increase in air
temperature and an abrupt shift in wind speed within the time between
periods 1 and 3. In other words, air temperature needs to increase
sufficiently to observe a statistically significant difference in ice cover.
Ice cover duration, however, shows a significant difference in the mean
between all periods (1–2, 2–3, and 1–3), indicating that distinct
differences in ice cover duration can be affected by both trends in air
temperature (i.e., there was a large-enough change in air temperature
between each period) and an abrupt shift in the wind speed. The combined
effects of slightly later ice-on dates and earlier ice-off dates during each
of the three periods resulted in statistically significant difference in
mean ice cover duration values between each of the three periods.
Analysis of simulated maximum ice thickness, ice-on date, ice-off date, and ice cover
duration using the method of Rodionov (2004) shows that the most
statistically significant timing of the shift in these ice cover variables
occurs in the winter of 1997–1998, but a major shift in the air temperature
or wind speed data was not observed at that time. The unusual winter of
1997–1998 strongly drove the statistically significant difference in mean
values between periods 1 and 3 rather than the abrupt shift in wind speed in
1994. Interestingly, similar results have been reported in Lake Superior,
where statistically significant step changes were found in winter ice
duration and maximum wintertime ice extent; these step changes account for
most of the long-term trends in ice cover for the lake (Van Cleave et al., 2014). The timing of
this step change may be attributed to a combination of the longer term
changes in meteorological conditions and the short-term annual change
occurring in the warm El Niño winter of 1997–1998 (Van Cleave et al., 2014).
Mueller et al. (2009) found that a similar climate shift between 1997 and 1998 initiated a
change in lake ice phenology from infrequent to frequent summer loss in
several high-Arctic lakes. Similarly, lakes in Poland show a considerable
statistical relationship between ice cover and the North Atlantic
Oscillation winter indexes (Skowron, 2009), indicating that ice
cover may be driven by other large oscillations as well.
Water temperature and stratification
Means of five simulated lake variables (under-ice water temperature,
freeze-over water temperature, epilimnion–hypolimnion temperature difference
(indicative of strength of stratification), and duration of stratification)
over the three periods have significant (p < 0.05) differences only
between period 1 and period 3. This change likely occurs because of the
combined effects of large changes in air temperature and a change in wind
speed. Both air temperature and wind speed are significantly correlated with
these five lake variables. Each driver alone may not be strong enough to
cause a major shift in the lake variables, but their combined effects may
reinforce the drivers of abrupt change in ice and thermal phenology. Further
work is required to examine how the major drivers may either reinforce or
dampen lake ice and temperature responses, particularly in relation to
directional shifts predicted under climate change.
Fall turnover date, highly correlated with wind speed, exhibits a
significant (p < 0.05) shift in the mean value in 1994, corresponding
with the abrupt shift in the wind speed. Interestingly, hypolimnetic water
temperatures, which are not significantly correlated with wind speed, but
are correlated with air temperatures, also show a significant (p < 0.05) shift
in the mean value in 1994. Hypolimnetic heating, significantly correlated
with wind speed (r = 0.49), does not exhibit a significant breakpoint, nor
are any of the mean differences among the three periods significant. Given
the high correlation between wind speed and hypolimnetic heating, it is
hypothesized that there should be a shift in hypolimnetic heating caused by
the abrupt shift in wind speed in 1994. The lack of statistically
significant step change may be explained by the simultaneous high
correlation between Secchi depth and hypolimnetic heating (r = 0.35),
indicating that water clarity may act to inhibit heating regardless of
changes in wind speed, or it may be acting to filter or mitigate the effects
of the wind speed shift. Finally, mean onset date of stratification and
midsummer epilimnetic temperature exhibit no difference among the three
periods. This may be due to two processes: (i) the climate signal is being
filtered out by the lake or (ii) the external perturbation of the system is
not yet strong enough to trigger a major shift in the system's internal dynamics.
Ecological significance of long-term changes in lake variables
Changes in lake ice cover and thermal structure are of great ecological
significance. Summer stratification inhibits the vertical transport of
oxygen and nutrients. The vertical temperature gradient in Lake Mendota
increased (Fig. 9b), which should decrease the depth of vertical mixing and
oxygen penetration and decrease the transport of nutrients from the
hypolimnion to the epilimnion (Fee et al.,
1994). Thus, increases in air temperature may increase the
epilimnetic–hypolimnetic temperature gradient and decrease the extent of
summer algal blooms in the Lake Mendota where internal loading of phosphorus
has been shown to be significant to its summer phosphorus budget (Lathrop et al., 1998; Soranno et
al., 1997). Additionally, phosphorus entrainment predominately occurs during
periods of high wind (Kamarainen et al., 2009; Stauffer and Armstrong, 1986). Algal blooms have been
associated with increases in epilimnetic phosphorus due to these high-wind
episodes (Robarts et al., 1998; Soranno
et al., 1997; Stauffer and Lee, 1973). Changes in the frequency of high-wind
episodic events may further impact the growth of algal blooms within Lake
Mendota (Kara et al., 2012). Elevated water
temperatures can affect plankton community composition and abundance (Elliot
et al., 2005; Findlay et al., 2001; Francis et al., 2014; Rice et al., 2015)
and fish populations (Carpenter et al., 1992; De Stasio et al., 1996; Gunn, 2002; Magnuson et al., 1990).
High water temperatures have been also shown to enhance the dominance of
cyanobacteria (Huber et al., 2008; Jöhnk et al., 2008). Such changes in algal blooms, zooplankton
populations, and fish populations may have drastic effects on the overall
food web within Lake Mendota (Carpenter et al., 1998).
Variations in ice cover conditions have impacts on ecosystems by
dramatically changing habitat factors such as light and temperature (Adrian et al., 1999;
Quayle et al., 2002). Such changes impact the distribution, behavior,
community composition, reproduction, and evolutionary adaptations of
organisms (Sala et al., 2000). Previous studies have shown that climate change
will likely affect the biodiversity of freshwater ecosystems (Heino et al.,
2009; Mantyka-Pringle et al., 2014; Wrona et al., 2006). Climate change can
bring asynchronies in biotic communities that may result in a phenological
decoupling of trophic relationships (Stenseth and Mysterud, 2002).
Conclusions
The one-dimensional hydrodynamic ice model, DYRESM-WQ-I, is developed and validated,
then used to simulate the ice cover and thermal structure of Lake Mendota,
WI from 1911–2014. The model reliably reproduces the interannual
variations and long-term (104-year) changes in ice cover and thermal
structure. To our knowledge, this study presents the first attempt to
continuously model both ice cover and thermal structure of a lake over a
period as long as a century. Simulated ice cover over this period has
changed dramatically: freezing later (9.0 days per century), breaking up
earlier (12.3 days per century), resulting in shorter ice duration (21.3 days
per century), and thinner maximum ice thickness (12.7 cm per century).
These results agree well with the observed data and previous studies. For
lake thermal structure, results of the continuous model simulation indicate
an earlier onset of thermal stratification (12.3 days per century), later
fall turnover (14.6 days per century), and a longer stratification period
(26.8 days per century) during this period. In addition, simulated
midsummer hypolimnetic temperature decreased (-1.4 ∘C per century),
causing midsummer epilimnetic–hypolimnetic temperature differences
(strength of stratification) to increase (2.0 ∘C per century).
Interestingly, there is no significant trend in midsummer epilimnetic temperatures.
Correlations comparing simulated lake conditions with seasonally averaged
meteorological conditions indicate that, among the three drivers, air
temperature has the largest relationship with the ice cover variables
(ice-on and ice-off dates, and maximum ice thickness) and with three
stratification variables (date of the onset of stratification, epilimnetic
temperatures, and hypolimnetic temperatures). Freeze-over water temperature,
summer hypolimnetic heating, and date of fall turnover all have the largest
correlation with wind speed. Both air temperature and wind speeds are highly
correlated with the onset of stratification. Secchi depth does not appear to
have a strong relationship with interannual variability of these variables
for Lake Mendota, but in combination with wind speed may be related to
hypolimnetic heating.
Changes in meteorological factors over the past 104 years were examined to
determine if there have been abrupt shifts, rather than linear changes.
Based on a change in the trend of air temperature increase occurring in 1981
and a major shift in wind speed in 1994, the Madison climate is divided into
three distinct periods: 1911–1980, with relatively low air temperatures
and mean wind speeds of 4.44 m s-1; 1981–1993, with higher air
temperatures and mean wind speeds of 4.44 m s-1; and 1994–2014 with
still higher air temperatures and mean wind speed of 3.74 m s-1. Ice
cover duration exhibited a significant difference in the mean among all
three periods, while ice-on date, ice-off date, and maximum ice thickness only show a
significant difference between periods 1 and 3, indicating that only
with a large change in air temperature and an abrupt shift in wind speeds
are change in the ice cover variables statistically different. Midsummer
hypolimnetic temperature and fall turnover date both reveal significant
(p < 0.05) differences in the mean value in 1994, corresponding with the abrupt
shift toward lower wind speeds. Some lake variables (under-ice water
temperature, freeze-over water temperature, epilimnion–hypolimnion
temperature difference, and stratification duration) may not be driven by
either the change in air temperature trend or the abrupt shift in wind speed
alone, but a shift in the mean of the lake variables does occur in 1994 when
both the air temperatures are warmest and the wind speed experienced an
abrupt shift. The exact timing of shifts may be difficult to define because
of extreme changes in weather in specific years and it may mask the longer
term changes in meteorological conditions (i.e., abrupt shifts).
Linear trends from the extensive data collection may be misleading as they
masks these sudden shifts in the air temperature and wind speed drivers and
lake ice cover and thermal structure variables. Examining the mean
differences in lake variables in response to shifts in air temperature and
abrupt shifts in wind speeds provide a better understanding of how the
southern Wisconsin climate has changed and what impact those changes have on
shifts in the ice cover and water temperature of dimictic Lake Mendota. It
is shown that air temperature and wind speed changes have occurred in stages
and lake variables have responded in a nonlinear way to these changes.