Warming of Near-Surface Summer Water Temperatures in Lakes of the Conterminous United States

Abstract

Because warming water temperatures have widespread consequences for freshwater communities, we were interested in estimating the patterns and rates of change of near-surface summer water temperatures in United States lakes. We developed multiple regression models to relate daily surface water temperatures in lakes of the conterminous United States to 8-day average air temperatures, latitude, elevation, and sampling month and year using data from 5723 lake samples in the months of June-September during the period 1981-2018. Our model explained 79% of the variation with a root-mean-square error of 1.69 • C. We predicted monthly average near-surface water temperatures for 1033 lakes for each year from 1981 through 2018. Lakes across the conterminous United States have been warming for the period 1981-2018 at an average heating rate of 0.32 • C per decade for the summer months (June-September). The average summer warming from 1981-2018 would be the equivalent of a lake decreasing 259 m in elevation or moving 233 km south. On the basis of national air temperatures starting in 1895, it was inferred that lake water temperatures are variable from year to year and have been steadily increasing since 1964, but that maximum temperatures in the 1930s were just as warm as those in 2008-2018.

Full text

water
Article
Warming of Near-Surface Summer Water
Temperatures in Lakes of the Conterminous
United States
Roger W. Bachmann 1,* , Daniel E. Canfield, Jr. 1, Sapna Sharma 2and Vincent Lecours 1
1Fisheries and Aquatic Sciences, School of Forest Resources and Conservation, University of Florida,
Gainesville, FL 32653, USA; decan@ufl.edu (D.E.C.J.); vlecours@ufl.edu (V.L.)
2Department of Biology, York University, Toronto, ON M3J 1P3, Canada; sapna.sharma23@gmail.com
*Correspondence: rbach@ufl.edu
Received: 30 October 2020; Accepted: 27 November 2020; Published: 2 December 2020


Abstract:
Because warming water temperatures have widespread consequences for freshwater
communities, we were interested in estimating the patterns and rates of change of near-surface
summer water temperatures in United States lakes. We developed multiple regression models to
relate daily surface water temperatures in lakes of the conterminous United States to 8-day average
air temperatures, latitude, elevation, and sampling month and year using data from 5723 lake samples
in the months of June-September during the period 1981–2018. Our model explained 79% of the
variation with a root-mean-square error of 1.69
◦
C. We predicted monthly average near-surface water
temperatures for 1033 lakes for each year from 1981 through 2018. Lakes across the conterminous
United States have been warming for the period 1981–2018 at an average heating rate of 0.32
◦
C per
decade for the summer months (June–September). The average summer warming from 1981–2018
would be the equivalent of a lake decreasing 259 m in elevation or moving 233 km south. On the basis
of national air temperatures starting in 1895, it was inferred that lake water temperatures are variable
from year to year and have been steadily increasing since 1964, but that maximum temperatures in
the 1930s were just as warm as those in 2008–2018.
Keywords:
climate change; lake heating; air–water temperatures; heating rates of lakes; hindcasting
temperatures; lake temperature models; conterminous United States
1. Introduction
In recent decades, lakes have shown extensive responses to climate change including less
seasonal winter ice cover [
1
,
2
], warmer surface water temperatures [
3
], modified mixing regimes [
4
],
and decreases in water level and in surface water extent [
5
]. Warming water temperatures, in particular,
have impacts on the increased likelihood of algal blooms [
6
,
7
], shifts in fish species distributions [
8
,
9
],
declining fish productivity [
10
], and ecosystem functioning [
11
]. Because of the widespread importance
of surface water temperatures to lake ecosystem functioning and ecosystem services, here we explore
the patterns and trends in water temperatures across thousands of lakes distributed across the
conterminous United States.
Near-surface summer lake water temperatures are highly influenced by climate conditions, such as
air temperatures, shortwave and longwave solar radiation, cloud cover, and wind speed [
12
–
15
].
Generally, warmer lakes are found in regions with warmer air temperatures and higher solar radiation
inputs [
16
]. In addition, lake morphometry and water chemistry, such as surface area, lake depth,
and water clarity, can be important determinants of surface water temperatures. For example,
within the same region, smaller, shallower, and clearer lakes tend to be warmer [14,17,18].
Water 2020,12, 3381; doi:10.3390/w12123381 www.mdpi.com/journal/water

Water 2020,12, 3381 2 of 17
In a recent study, we found that 8-day average air temperatures, latitude, longitude, elevation,
and month of sampling were important predictors of near-surface summer lake water temperatures
for lakes distributed across the conterminous United States and southern Canada and then developed
an empirical model to predict summer near-surface water temperatures of unsampled lakes [
16
].
The overall purpose of this study was to use those or similar equations to hindcast near-surface water
temperatures in lakes across the United States for past years in order to quantify to what extent lakes
have been warming. Our study involved six objectives: (1) test how well the Bachmann et al. [
16
]
models predicted water temperatures across a broader temporal period (1981–2018), because the
original models were developed with data from 2007 and 2012; (2) develop predictive models to
hindcast water temperatures for any day for any lake in the conterminous United States for the months
of June through September in the years 1981–2018; (3) calculate average summer water temperatures
for each of 1033 United States lakes for the years 1981–2018; (4) use the calculated water temperatures
for each year to determine summer warming trends for United States lakes over the period 1981–2018;
(5) examine
national average air temperature data for 1895–2018 to identify temporal patterns that
might reflect changes in average lake water temperatures; and (6) use changes between average
summer lake water temperatures with latitude and elevation to express lake heating rates in equivalent
changes in latitudinal position and lake elevation. The 1033 lakes associated with the third objective
had been selected as a part of a statistically based sampling program in the 2007 National Lakes
Assessment (NLA) of the United States Environmental Protection Agency (USEPA) [
19
,
20
] that made it
possible to use the results of those samples to find annual average values of water temperatures that
are representative of 49,803 lakes in the conterminous United States.
2. Materials and Methods
2.1. Testing Predictive Equations of Bachmann et al.
For the purposes of this study, near-surface lake water temperatures are defined as the water
temperatures measured at a depth of 1 m sometime during the daylight hours and hereafter will be
referred to simply as water temperatures. In an earlier study [
16
], we developed predictive models
that showed water temperatures in the summer months of lakes in the conterminous United States and
southern Canada were quantitatively related to their 8-day average air temperature, sampling month,
latitude, longitude, and elevation above sea level. The best model explained 81% of the variation in
water temperature. However, the models of Bachmann et al. [
16
] were based on data collected in 2007
and 2012. Piccolroaz et al. [
21
] had cautioned about the use of air–water regression models when
applied to air temperature ranges beyond the limits of the time series used in developing the equations.
This raised the question of how well Bachmann et al.’s 2019 models [
16
] would perform for hindcasting
temperatures outside of the 2007/2012 study years. We, therefore, devised a test of the ability of the
equations to hindcast water temperatures in each of the 38 years in the period 1981–2018 by expanding
our data collection for lakes sampled within the conterminous United States between 1981 and 2018.
We extracted water temperature data on lakes (natural and manmade) from the United
States Geological Survey’s (USGS’s) Water Quality Portal (https://www.waterqualitydata.us/),
which aggregates
access to multiple databases, including the USEPA’s Storage and Retrieval Data
Warehouse (STORET) and the USGS National Water Information System (NWIS). We filtered the
data to obtain water temperatures measured at 1 m depth in the months of June through September.
The obtained water temperatures were measured by a variety of government agencies and universities
and we assumed them to be accurate. However, in many cases, stringent quality control programs
like those of the USEPA’s NLA were not associated with the measurements. Our search also provided
the geographic coordinates of each of the selected lakes. Ultimately, we obtained from 49 to 207 lake
water measurements for each year in the 1981–2018 period with an average of 133 lakes per year.
Data were obtained for lakes in 36 states as not all states contributed data to the Water Quality Portal.
Most measurements came from lakes in Minnesota, Michigan, Wisconsin, North Carolina, and Vermont.

Water 2020,12, 3381 3 of 17
Because most of the sampled lakes were from low elevations, we added data from several lakes with
elevations greater than 500 m that were collected as a part of the NLA [
20
,
22
]. Our final dataset
included 5078 lake temperature measurements from the Water Quality Portal and 645 lake temperature
measurements from the NLA for a total of 5723 samples in the period 1981–2018. In some cases,
temperature measurements were obtained from the same lake for 1 to 4 months in the same year or
for more than one year. A flow chart of the data sets and analyses used in this study is presented in
Figure 1. Mean air temperatures at each lake for the day of sampling and for each of the preceding
seven days were obtained from the website of the PRISM Climate Group, Oregon State University
(http://prism.oregonstate.edu, created 23 May 2019). Their website allows one to obtain mean daily
air temperatures, other meteorological data, and lake elevations based on a grid of 30-arcseconds of
latitude and longitude. The cells are about 900 m
×
700 m in size [
23
]. We tested the four predictive
models developed by Bachmann et al. [
16
] on the 5723 lake temperature samples collected in this study
to calculate estimated water temperatures for each of the samples. The measured water temperatures
at each lake were subtracted from the calculated water temperatures to evaluate how well the models
developed by Bachmann et al. [
16
] could hindcast past temperatures. Regressions were run of the
differences between calculated and measured values versus the year of sampling.
Water 2020, 12, x FOR PEER REVIEW 3 of 17
from several lakes with elevations greater than 500 m that were collected as a part of the NLA [20,22].
Our final dataset included 5078 lake temperature measurements from the Water Quality Portal and
645 lake temperature measurements from the NLA for a total of 5723 samples in the period 1981–
2018. In some cases, temperature measurements were obtained from the same lake for 1 to 4 months
in the same year or for more than one year. A flow chart of the data sets and analyses used in this
study is presented in Figure 1. Mean air temperatures at each lake for the day of sampling and for
each of the preceding seven days were obtained from the website of the PRISM Climate Group,
Oregon State University (http://prism.oregonstate.edu, created 23 May 2019). Their website allows
one to obtain mean daily air temperatures, other meteorological data, and lake elevations based on a
grid of 30-arcseconds of latitude and longitude. The cells are about 900 m × 700 m in size [23]. We
tested the four predictive models developed by Bachmann et al. [16] on the 5723 lake temperature
samples collected in this study to calculate estimated water temperatures for each of the samples. The
measured water temperatures at each lake were subtracted from the calculated water temperatures
to evaluate how well the models developed by Bachmann et al. [16] could hindcast past temperatures.
Regressions were run of the differences between calculated and measured values versus the year of
sampling.
Figure 1. Flow chart for most analyses made in this study. Boxes enclosed with solid lines represent
data sources or results of analyses. Boxes enclosed with dashed lines indicate calculations and
Figure 1.
Flow chart for most analyses made in this study. Boxes enclosed with solid lines represent
data sources or results of analyses. Boxes enclosed with dashed lines indicate calculations and
analyses made with the data. NLA =National Lakes Assessment, NOAA =National Oceanic and
Atmospheric Administration.

Water 2020,12, 3381 4 of 17
2.2. Development of New Predictive Equations for 1981–2018
We found that when we applied the equations of Bachmann et al. [
16
] to our sample values
over the period 1981–2018, the calculated values tended to overestimate the measured temperatures
early in the time period (see Results). We, therefore, developed a new set of predictive equations.
We randomly split our data set into a training group (4723 observations) and a testing group (1000
observations). With the training group, we used multiple regression models for each month using a
forward stepwise multiple regression of water temperatures as the dependent variable and 8-day air
temperature, latitude, elevation, and year as independent variables. When each variable was added to
the regression, we recorded the probability that the variable was statistically significant, the coefficient
of determination (R
2
), the root-mean-square error (RMSE), and the Akaike information criterion (AIC).
In our final equations, we only included variables that were statistically significant (p<0.05) and
reduced the AIC when they were added. We used the observations in the testing group to determine
how well the new equations predicted the water temperatures. We also calculated standardized
beta coefficients to compare the importance of the independent variables in the predictive equations.
We used the JMP software, v14.0 [24] for all of our statistical summaries and analyses.
2.3. Calculation of Near-Surface Water Temperatures
We used the new multiple regression equations which included sampling year as a variable to
calculate the daily summer water temperatures in a representative sample of United States lakes in
order to calculate an average summer near-surface water temperature for each year. For this objective,
we used the locations of the 1033 lakes sampled by the USEPA during the 2007 NLA [
20
]. These lakes
had been selected as a part of a statistically based sampling program designed to find national average
values for various chemical and biological variables. The lakes were identified using the National
Hydrography Dataset as a basis and selected with a stratified random sampling technique [
19
,
25
].
This design was necessary because lakes are found mostly in the few states that had been impacted
by the Wisconsin glaciation, but we wanted to sample lakes in all 48 contiguous states. Likewise,
we wanted to obtain information on larger lakes, even though most lakes are of smaller size. In this
process, each lake was given a numerical weight to represent a number of similar lakes in terms of size
and location. In the NLA, the measured chemical or biological variables in each lake were multiplied
times their numerical weights to find average values that are representative of 49,803 lakes in the
conterminous United States. In our case, we used the calculated daily temperatures in each of the 1033
lakes and their weights to find a weighted national daily near-surface water temperature for each
summer day for each of the 38 years using the new equations developed from the multiple regressions
for each month. Data on air temperatures were again obtained from the PRISM website, and latitude
and elevation were obtained from the NLA data set. We used the calculated daily water temperatures
to calculate an average near-surface water temperature for each summer month for each lake for each
of the 38 years in our study. We also calculated an average annual summer water temperature using
the average annual monthly temperatures for the months of June, July, August, and September.
2.4. Calculation of Rates of Change of Lake Water Temperatures
For each of the 38 years of study, we calculated the average annual water temperatures for the
months of June, July, August, and September and for the summer period of June through September.
For each month and the summer period, the annual average near-surface water temperatures were
regressed against years to determine if the slopes of the regressions were statistically different from 0.0
(p<0.05). Thus, the slopes would represent the rates of change in near-surface water temperatures for
the population of lakes in the United States in the period 1981 through 2018.
An alternative approach was to look for changes in annual average temperatures in each of the
1033 individual lakes by finding the slopes of the regressions of annual average water temperatures for
the months of June, July, August, and September individually and for the summer period versus years.

Water 2020,12, 3381 5 of 17
The slopes also would represent the rates of change in water temperatures in the period 1981–2018.
We then determined the means, standard deviations, and the frequency distributions of the slopes
for the summer and each of the summer months. To determine if the rates of temperature change in
individual lakes were related to geographical locations of the lakes, we plotted the monthly slopes on
maps of the conterminous United States to identify spatial patterns.
To determine if rates of changes in average water temperatures in individual lakes were related to
rates of change in average monthly air temperatures over the lakes, we again used the PRISM website
to find the average monthly air temperatures in the summer for each of the 1033 lakes for each of the
years 1981–2018. For each lake, we ran regressions of average annual air temperatures by month and
the summer against years to find the slopes of the rates changes in average air temperatures over the
period 1981–2018. The rates of change of average air temperatures were plotted on maps to compare
with the distributions of rates of change of water temperatures.
2.5. Finding Annual Average Summer Lake Temperatures
The process we have used to find the estimated average water temperatures of United States
lakes works well, but it is limited to recent years as the detailed mean air temperatures data for each
lake do not start on the PRISM website until 1981. To look for relationships that might indicate trends
in water temperatures for years prior to 1981, we extracted the average annual national summer
air temperatures for the contiguous United States for the period 1 June through 30 September for
each of the 38 years using the website of the National Oceanic and Atmospheric Administration
(NOAA, https://www.ncdc.noaa.gov/cag/). We then ran a regression for our calculated average annual
estimated summer water temperatures versus the annual national summer average air temperatures.
Because we found that there was a close relationship between the average annual national summer air
temperatures and the average annual water temperatures, we plotted the national summer average
air temperatures in United States lakes during the period 1895–2018 against time as an indication of
how lake temperatures might have changed in that time period. We used Locally Weighted Scatterplot
Smoothing (LOWESS) to fit a non-parametric curve of temperatures versus time using the method of
Cleveland [26] in the JMP statistical package [24].
2.6. Effects of Latitude and Elevation on Water Temperatures
Because it was known that summer lake temperatures decrease with increases in latitude and
elevation [
16
], we wished to relate the average rates of change in summer water temperatures over time
to the changes in averaged water temperatures observed with latitude and elevation because of the
effects such changes could have on lake biota. For the effect of latitude, we used the averages of summer
water temperatures for the 1033 individual lakes in the period 1981–2018 and removed lakes with
elevations greater than 500 m in order to reduce the known effects of elevation on water temperatures.
We then ran a regression of average summer water temperatures versus latitude and found the slope
of the regression in units of changes in water temperatures divided by changes in latitudes in degrees.
We used the common conversion factor of 111 km per degree of latitude [
27
] to convert the slope
to change in temperature per kilometer. For the analysis of the effects of elevation, we used lakes
with elevations of 500 m or greater. To further reduce the possible effects of latitude we only used
lakes whose latitudes were in the range of 37 to 42 degrees north latitude. We regressed average
summer temperatures versus elevation and found the slope in units of degrees of water temperature
per meter of elevation. This information was used to convert rates of change in temperature with time
to equivalent decreases in distances moved south for lowland lakes and in decreases in elevation for
high elevation lakes.

Water 2020,12, 3381 6 of 17
3. Results
3.1. Developing Predictive Equations for the Period 1981–2018
We found the differences between the measured water temperatures and those calculated with
the four predictive models developed by Bachmann et al. [
16
] for the 5723 lake temperature samples
collected in this study between 1981 and 2018. When regressions were run on the differences between
measured and calculated water temperatures, we found that the slopes of these regressions, though
relatively small, were significantly different from 0.0 (Figure 2a, p<0.05). This indicated that the
year of sampling needed to be included in the predictive equations to account for changes in the
relationships between air and surface water temperatures in the period 1981–2018. We developed four
new predictive relationships for hindcasting water temperatures in United States lakes in the period
1981–2018. The equations for the months of June, July, August, and September are:
Water 2020, 12, x FOR PEER REVIEW 6 of 17
3. Results
3.1. Developing Predictive Equations for the Period 1981–2018
We found the differences between the measured water temperatures and those calculated with
the four predictive models developed by Bachmann et al. [16] for the 5723 lake temperature samples
collected in this study between 1981 and 2018. When regressions were run on the differences between
measured and calculated water temperatures, we found that the slopes of these regressions, though
relatively small, were significantly different from 0.0 (Figure 2a, p < 0.05). This indicated that the year
of sampling needed to be included in the predictive equations to account for changes in the
relationships between air and surface water temperatures in the period 1981–2018. We developed
four new predictive relationships for hindcasting water temperatures in United States lakes in the
period 1981–2018. The equations for the months of June, July, August, and September are:
Figure 2. (a) Average annual difference between predicted [16] and measured water temperatures
versus years. (b) Measured daily water temperatures versus calculated water temperatures for United
States lakes found in the National Water Quality data set for the years 1981 through 2018. Calculated
temperatures were found with Equations (1)–(4).
TempJune = -8.93+ 0.620 Air - 0.114 Lat - 0.00158 Elev + 0.0122 Year (1)
TempJuly = -15.42+ 0.513Air - 0.132 Lat - 0.00254 Elev + 0.0178 Year (2)
TempAugust = -11.69+ 0.542 Air - 0.209 Lat - 0.00205 Elev + 0.0170 Year (3)
TempSeptember = -23.09 + 0.538 Air - 0.315 Lat - 0.00158 Elev + 0.0239 Year (4)
where TempMonth is the calculated daily water temperature in the subscripted month (°C), Air is the 8-
day average mean daily air temperature (average of daily maximum and minimum) at a lake ending
on the day of sampling (°C), Lat is the latitude of the lake (°), Elev is the elevation of the lake above
sea level (m), and Year is the year of sampling. When we applied the equations to the lakes in our
testing data set, we found good agreement between measured and calculated summer daily water
temperatures for 1000 lakes sampled between 1981 and 2018 Figure 2b. The R2 was 0.79 and the RMSE
was 1.69 °C. Using the averages of the standardized beta coefficients in the multiple regressions for
the months of June, July, August, and September, we found that the 8-day air temperatures were
most important with a value of 0.63. Next in importance were elevation with −0.29, latitude with
−0.18, and years with 0.07.
3.2. Trends in Average Summer Water Temperatures in the Period 1981−2018
Figure 2.
(
a
) Average annual difference between predicted [
16
] and measured water temperatures
versus years. (
b
) Measured daily water temperatures versus calculated water temperatures for United
States lakes found in the National Water Quality data set for the years 1981 through 2018. Calculated
temperatures were found with Equations (1)–(4).
TempJune =−8.93+0.620 Air −0.114 Lat −0.00158 Elev +0.0122 Year (1)
TempJuly =−15.42+0.513Air −0.132 Lat −0.00254 Elev +0.0178 Year (2)
TempAugust =−11.69+0.542 Air −0.209 Lat −0.00205 Elev +0.0170 Year (3)
TempSeptember =−23.09 +0.538 Air −0.315 Lat −0.00158 Elev +0.0239 Year (4)
where Temp
Month
is the calculated daily water temperature in the subscripted month (
◦
C), Air is the
8-day average mean daily air temperature (average of daily maximum and minimum) at a lake ending
on the day of sampling (
◦
C), Lat is the latitude of the lake (
◦
), Elev is the elevation of the lake above
sea level (m), and Year is the year of sampling. When we applied the equations to the lakes in our
testing data set, we found good agreement between measured and calculated summer daily water
temperatures for 1000 lakes sampled between 1981 and 2018 Figure 2b. The R
2
was 0.79 and the RMSE
was 1.69
◦
C. Using the averages of the standardized beta coefficients in the multiple regressions for the
months of June, July, August, and September, we found that the 8-day air temperatures were most
important with a value of 0.63. Next in importance were elevation with
−
0.29, latitude with
−
0.18,
and years with 0.07.

Water 2020,12, 3381 7 of 17
3.2. Trends in Average Summer Water Temperatures in the Period 1981−2018
We found that the near-surface summer water temperatures of United States lakes on average
have been warming during the period 1981–2018. Our regressions of monthly weighted average water
temperatures developed by the application of Equations (1)–(4) to our sample of 1033 lakes against
year of sampling showed statistically significant positive slopes for each of the summer months and
the 4-month summer, see Figure 3a–e and Table 1.
Water 2020, 12, x FOR PEER REVIEW 7 of 17
We found that the near-surface summer water temperatures of United States lakes on average
have been warming during the period 1981–2018. Our regressions of monthly weighted average
water temperatures developed by the application of Equations (1)–(4) to our sample of 1033 lakes
against year of sampling showed statistically significant positive slopes for each of the summer
months and the 4-month summer, see Figure 3a–e and Table 1.
Figure 3. Calculated average water temperatures for United States lakes in June (a), July (b), August
(c), September (d) and for the entire summer (e) for each year in the period 1981–2018. Fitted linear
regression lines are shown. The slopes are all statistically significantly different from zero (p = 0.05).
Figure 3.
Calculated average water temperatures for United States lakes in June (
a
), July (
b
), August
(
c
), September (
d
) and for the entire summer (
e
) for each year in the period 1981–2018. Fitted linear
regression lines are shown. The slopes are all statistically significantly different from zero (p=0.05).

Water 2020,12, 3381 8 of 17
Table 1.
Slopes (
◦
C decade
−1
) with standard errors of average near-surface water temperatures in lakes
of the conterminous United States versus years for different time periods in the summers of 1981–2018.
The summer temperatures represent the average summer temperatures for the months of June through
September each year. Slopes for other combinations of 2 or 3 months are also presented.
Time Period Rate of Change in Temperature
(◦C Decade−1)Standard Error of the Mean (◦C)
June 0.31 0.08
July 0.31 0.06
August 0.22 0.08
September 0.49 0.07
Summer
(June–September) 0.32 0.05
June–August 0.29 0.06
July–September 0.34 0.05
July–August 0.26 0.06
August–September 0.36 0.05
For the four-month summer period, the warming rate was 0.32
◦
C decade
−1
. The fastest warming
rate was for the month of September with 0.49
◦
C decade
−1
followed by the months of June and July both
with rates of 0.31
◦
C decade
−1
, and August (0.22
◦
C decade
−1
). We also calculated our results for different
combinations of three or two months for comparisons with the results of other studies (Table 1).
When we examined the distribution of rates of change in water temperatures in the period 1981 to
2018 among individual lakes, see Table 2, we found that the mean and median rates were very similar to
each other and ranked the same as the rates calculated on the basis of average annual water temperature
for United States lakes, see Table 1. The highest rates of warming were in September followed by June,
July, and August, see Table S1. There was considerable variation among lakes for each time period as
shown by the coefficients of variation that ranged from 22% in September to 46% in August.
Table 2.
Summary statistics for the distributions of rates of temperature change (
◦
C decade
−1
) in the
period 1981–2018 for 1033 lakes in the conterminous United States.
June July August September Summer
Descriptive Statistics
Mean 0.34 0.34 0.24 0.46 0.34
Standard deviation 0.14 0.14 0.11 0.07 0.08
Standard error 0.004 0.004 0.003 0.010 0.003
Coefficient of variation
41 41 46 22 22
N 1033 1033 1033 1033 1033
Frequency Distributions
Minimum −0.07 0.01 −0.03 0.04 0.02
10th% 0.17 0.19 0.09 0.32 0.26
20th% 0.23 0.23 0.14 0.37 0.28
30th% 0.27 0.25 0.18 0.41 0.30
40th% 0.30 0.28 0.22 0.44 0.32
Median 0.35 0.30 0.25 0.47 0.34
60th% 0.38 0.34 0.28 0.49 0.36
70th% 0.42 0.39 0.31 0.51 0.38
80th% 0.45 0.45 0.34 0.54 0.41
90th% 0.51 0.56 0.38 0.58 0.44
Maximum 0.78 0.87 0.78 0.81 0.75

Water 2020,12, 3381 9 of 17
There was an uneven distribution of the rates of temperature change in the individual lakes across
the contiguous United States depending on the period of sampling, see Figure 4. For example, the lakes
with the highest rates of temperature change (indicated by red dots showing >0.40
◦
C decade
−1
) are
clustered southwest of the center of the map in June. In July, the greater rates of change extended across
most of the western states, but by August there were small numbers of lakes with changes >0.40
◦
C
decade
−1
in the northwest and northeast United States. For September, there were large clusters of lakes in
the north-central states and in the eastern states warming rapidly, while for the entire summer the highest
rates tended to cluster in the western states with warming rates >0.40
◦
C decade
−1
. For the summer,
the five highest average rates were found in the states of New Mexico, Colorado, New Jersey, Delaware,
and Wyoming while the five lowest average rates were in the states of South Dakota, North Dakota,
Florida, Minnesota, and Indiana, see Table S2. Variations in the lake water heating rates were related to
variations in the rates of increase in average air temperatures in the period 1981–2018, see Figure 5.
Water 2020, 12, x FOR PEER REVIEW 9 of 17
There was an uneven distribution of the rates of temperature change in the individual lakes
across the contiguous United States depending on the period of sampling, see Figure 4. For example,
the lakes with the highest rates of temperature change (indicated by red dots showing >0.40 °C
decade
−1
) are clustered southwest of the center of the map in June. In July, the greater rates of change
extended across most of the western states, but by August there were small numbers of lakes with
changes > 0.40 °C decade
−1
in the northwest and northeast United States. For September, there were
large clusters of lakes in the north-central states and in the eastern states warming rapidly, while for
the entire summer the highest rates tended to cluster in the western states with warming rates >0.40
°C decade
−1
. For the summer, the five highest average rates were found in the states of New Mexico,
Colorado, New Jersey, Delaware, and Wyoming while the five lowest average rates were in the states
of South Dakota, North Dakota, Florida, Minnesota, and Indiana, see Table S2. Variations in the lake
water heating rates were related to variations in the rates of increase in average air temperatures in
the period 1981–2018, see Figure 5.
Figure 4. Rates of temperature change in 1033 United States lakes during the time period 1981–2018.
Figure 4. Rates of temperature change in 1033 United States lakes during the time period 1981–2018.

Water 2020,12, 3381 10 of 17
Water 2020, 12, x FOR PEER REVIEW 10 of 17
Figure 5. Rates of temperature change in average air temperatures at the locations of 1033 United
States lakes during the time period 1981–2018.
3.3. Trends in Average National Summer Air and Water Temperatures
The average rates of change in water temperature for United States lakes in the summer for the
years 1981–2018 were strongly related to the average annual summer national air temperatures for
the contiguous United States with an R
2
of 0.88 and an RMSE of 0.17 °C, see Figure 6. The relationship
is given by:
WT = 4.57+ 0.857 Air
National
(5)
Figure 5.
Rates of temperature change in average air temperatures at the locations of 1033 United States
lakes during the time period 1981–2018.
3.3. Trends in Average National Summer Air and Water Temperatures
The average rates of change in water temperature for United States lakes in the summer for the
years 1981–2018 were strongly related to the average annual summer national air temperatures for the
contiguous United States with an R
2
of 0.88 and an RMSE of 0.17
◦
C, see Figure 6. The relationship is
given by:
WT =4.57+0.857 AirNational (5)
where WT is the predicted average summer water temperature for conterminous United States lakes
and Air
National
is the average annual summer national air temperatures for the contiguous United
States. This finding was important because data on national average summer air temperatures on

Water 2020,12, 3381 11 of 17
NOAA’s website (https://www.ncdc.noaa.gov/cag/) start in 1895, so the long-term changes in national
air temperatures should give an indication for the long-term changes in lake temperatures for United
States lakes over 122 years, see Figure 7. Because Equation (5) was developed for the period 1981–2018,
we cannot use it to directly calculate past temperatures in the period 1895–1980 as there may have
been changes in the exact relationship between air and water temperatures in that time period. We do
expect that in general the trends will be similar with years of high air temperatures being years of high
lake water temperatures, see Figures 4,5and 7.
Water 2020, 12, x FOR PEER REVIEW 11 of 17
where WT is the predicted average summer water temperature for conterminous United States lakes
and AirNational is the average annual summer national air temperatures for the contiguous United
States. This finding was important because data on national average summer air temperatures on
NOAA’s website (https://www.ncdc.noaa.gov/cag/) start in 1895, so the long-term changes in
national air temperatures should give an indication for the long-term changes in lake temperatures
for United States lakes over 122 years, see Figure 7. Because Equation (5) was developed for the period
1981–2018, we cannot use it to directly calculate past temperatures in the period 1895–1980 as there
may have been changes in the exact relationship between air and water temperatures in that time
period. We do expect that in general the trends will be similar with years of high air temperatures
being years of high lake water temperatures, see Figures 4, 5 and 7.
Figure 6. The calculated average annual summer water temperatures for the lakes of the conterminous
United States for the years 1981–2018 plotted against the average of the national summer air
temperatures during the same years.
Figure 7. National average summer air temperatures for the conterminous United States for the period
1895 through 2018 with a non-parametric (Locally Weighted Scatterplot Smoothing (LOWESS)) line.
The upper red line represents the average summer water temperatures.
There is great variability in the average national air temperatures from year to year, see Figure
7, during the 1895 to 2018 period. Using LOWESS regression analysis, we found a small reduction in
Figure 6.
The calculated average annual summer water temperatures for the lakes of the conterminous
United States for the years 1981–2018 plotted against the average of the national summer air temperatures
during the same years.
Water 2020, 12, x FOR PEER REVIEW 11 of 17
where WT is the predicted average summer water temperature for conterminous United States lakes
and AirNational is the average annual summer national air temperatures for the contiguous United
States. This finding was important because data on national average summer air temperatures on
NOAA’s website (https://www.ncdc.noaa.gov/cag/) start in 1895, so the long-term changes in
national air temperatures should give an indication for the long-term changes in lake temperatures
for United States lakes over 122 years, see Figure 7. Because Equation (5) was developed for the period
1981–2018, we cannot use it to directly calculate past temperatures in the period 1895–1980 as there
may have been changes in the exact relationship between air and water temperatures in that time
period. We do expect that in general the trends will be similar with years of high air temperatures
being years of high lake water temperatures, see Figures 4, 5 and 7.
Figure 6. The calculated average annual summer water temperatures for the lakes of the conterminous
United States for the years 1981–2018 plotted against the average of the national summer air
temperatures during the same years.
Figure 7. National average summer air temperatures for the conterminous United States for the period
1895 through 2018 with a non-parametric (Locally Weighted Scatterplot Smoothing (LOWESS)) line.
The upper red line represents the average summer water temperatures.
There is great variability in the average national air temperatures from year to year, see Figure
7, during the 1895 to 2018 period. Using LOWESS regression analysis, we found a small reduction in
Figure 7.
National average summer air temperatures for the conterminous United States for the period
1895 through 2018 with a non-parametric (Locally Weighted Scatterplot Smoothing (LOWESS)) line.
The upper red line represents the average summer water temperatures.
There is great variability in the average national air temperatures from year to year, see Figure 7,
during the 1895 to 2018 period. Using LOWESS regression analysis, we found a small reduction in
average air temperatures until about 1910. Air temperatures then tended to rise to a high point in the
early 1930s, followed by a decrease until about 1964, after which national air temperatures began an
increasing trend through 2018. The greatest air temperatures calculated for the 1930s are similar to the

Water 2020,12, 3381 12 of 17
maximum air temperatures found in the period 2008 to 2018. Because of the common finding that
lake water temperatures tend to follow air temperatures, the general trends in lake temperatures most
likely mirror those of the national air temperatures, see Figures 6and 7.
3.4. Temperature Changes with Changes in Latitude and Elevation
There were strong relationships between the average water temperatures and latitudes (R
2
=0.94)
and elevations (R
2
=0.91) such that temperatures decreased with increasing latitude and increasing
elevations, see Figure 8a,b. Temperatures increased by 0.58
◦
C per degree of latitude progressing in a
southerly direction, thus, the latitude effect would be 0.0052
◦
C km
−1
. For elevations, the slopes of the
regression lines indicated that average water temperatures increased by 0.0047
◦
C for every meter of
decrease in elevation. This value is close to the rate of 0.0038
◦
C m
−1
found by Lewis [
28
] for several
tropical lakes.
Water 2020, 12, x FOR PEER REVIEW 12 of 17
average air temperatures until about 1910. Air temperatures then tended to rise to a high point in the
early 1930s, followed by a decrease until about 1964, after which national air temperatures began an
increasing trend through 2018. The greatest air temperatures calculated for the 1930s are similar to
the maximum air temperatures found in the period 2008 to 2018. Because of the common finding that
lake water temperatures tend to follow air temperatures, the general trends in lake temperatures most
likely mirror those of the national air temperatures, see Figures 6 and 7.
3.4. Temperature Changes with Changes in Latitude and Elevation
There were strong relationships between the average water temperatures and latitudes (R2 =
0.94) and elevations (R2 = 0.91) such that temperatures decreased with increasing latitude and
increasing elevations, see Figure 8a,b. Temperatures increased by 0.58 °C per degree of latitude
progressing in a southerly direction, thus, the latitude effect would be 0.0052 °C km−1. For elevations,
the slopes of the regression lines indicated that average water temperatures increased by 0.0047 °C
for every meter of decrease in elevation. This value is close to the rate of 0.0038 °C m−1 found by Lewis
[28] for several tropical lakes.
Figure 8. (a) Average summer water temperatures of United States lakes located between latitudes of
26° N and 49° N and at elevation less than 500 m. (b) Average summer water temperatures of United
States lakes located between latitudes 37° N and 42° N and at elevations greater than 500 m.
4. Discussion
4.1. Predictive Equations for Summer Lake Temperatures
In this study, we developed models to predict near-surface summer water temperatures for
individual lakes across the conterminous United States. Multiple linear regression models including
air temperatures, latitude, elevation, and sampling year reliably predicted summer surface water
temperatures for 1000 lakes. The relationship between predicted and measured daily temperatures
yielded an RMSE of 1.69 °C. These models were an improvement on the earlier predictive equations
developed by Bachmann et al. [16] as we found that the predicted values in the earlier years tended
to overestimate the measured values in the period 1981–2018. By including year as a coefficient, we
have accounted for changes over time in the relationship between air temperatures and water
temperatures in this sample of lakes [8], because the Bachmann et al. [16] equations were developed
with data from 2007 and 2012. It is possible that other important climatic variables such as wind
velocity, humidity, cloud cover, and solar radiation inputs may have changed during this time
period.
Figure 8.
(
a
) Average summer water temperatures of United States lakes located between latitudes of
26
◦
N and 49
◦
N and at elevation less than 500 m. (
b
) Average summer water temperatures of United
States lakes located between latitudes 37◦N and 42◦N and at elevations greater than 500 m.
4. Discussion
4.1. Predictive Equations for Summer Lake Temperatures
In this study, we developed models to predict near-surface summer water temperatures for
individual lakes across the conterminous United States. Multiple linear regression models including
air temperatures, latitude, elevation, and sampling year reliably predicted summer surface water
temperatures for 1000 lakes. The relationship between predicted and measured daily temperatures
yielded an RMSE of 1.69
◦
C. These models were an improvement on the earlier predictive equations
developed by Bachmann et al. [
16
] as we found that the predicted values in the earlier years tended to
overestimate the measured values in the period 1981–2018. By including year as a coefficient, we have
accounted for changes over time in the relationship between air temperatures and water temperatures
in this sample of lakes [
8
], because the Bachmann et al. [
16
] equations were developed with data from
2007 and 2012. It is possible that other important climatic variables such as wind velocity, humidity,
cloud cover, and solar radiation inputs may have changed during this time period.
4.2. Trends in Average Summer Water Temperatures in the Period 1981–2018
We found that the annual average near-surface water temperatures of United States lakes in
the summer months of June through September in the period 1981–2018 warmed at an average
rate of
0.32 ◦C decade−1,
see Table 1. This is in agreement with O’Reilly et al. [
3
] who found an
average heating rate of
0.34 ◦C decade−1
in the period 1985–2009 for a global group of 235 lakes

Water 2020,12, 3381 13 of 17
for the months of July through September. Our heating rate for the same period (July through
September) was
0.34 ◦C decade−1.
For comparison, Adrian et al. [
29
] presented July heating rates
for 12 lakes for various periods between 1970 and 2009 and found an average rate of warming of
0.43 ◦C decade−1.
Specifically, the rates of warming for their lakes ranged from 0.00
◦
C decade
−1
(Lakes Baikal, Muggelesee, and Champlain and Blue Chalk Lake) to 1.57
◦
C decade
−1
(Lake Stensjon).
The value of 0.00 indicates no significant change in temperatures.
When looking at water temperature averages for United States lakes, we found September was
the fastest-warming month with a warming rate of 0.49
◦
C decade
−1
. Water temperatures in June
and July warmed at rates of 0.31
◦
C decade
−1
, while the August average rate was the slowest at
0.22 ◦C decade−1.
Other lake temperature studies focused on Wisconsin also found that for most of the
Wisconsin lakes they studied, the maximum heating rates were found in the fall months and resulted in
a delay in fall cooling [
30
,
31
]. Higher rates of warming in lakes in the fall season could be contributing
to delayed dates of ice formation in north temperate lakes [
32
]. However, we also found a high degree
of variability in warming rates among lakes with monthly coefficients of variation ranging from 22% to
46%, such that some individual lakes showed no or negative rates of temperature change.
The geographic distribution of rates of temperature change differed by month, see Figure 4. Areas
showing high or low rates of change in one month would not necessarily show the same patterns in
other months. For example, the fastest-warming lakes in June were found in the southern United
States typically below the 0
◦
C isotherm where lakes are unlikely to experience winter ice cover [
2
].
In contrast, lakes found in more northern regions of the United States exhibited the fastest rates of
warming in September.
4.3. Trends in Average Summer Air and Water Temperatures 1895–2018
The plot of national air temperatures versus years showed that since 1895 there has been large
variability in the average temperatures from year to year, see Figure 7. However, the application of
a LOWESS regression to the data suggested there were general patterns in the heating and cooling
of air temperatures over time. The greatest measured air temperatures found in the 1930s during
the Dust Bowl years [
33
] are similar to maximum air temperatures found in the period 2008 to 2018.
Given that we and others have found a close correspondence between air temperature and lake water
temperatures, we expect that average lake water temperatures will follow the same trends as air
temperatures over time. This expectation is in accord with the findings of Lathrop et al. [
31
] who found
that the summer epilimnetic temperatures in Wisconsin lakes during many years in the 1930s and
1940s were likely as warm as recent (up through 2017) epilimnetic temperatures.
Lathrop et al. [31]
also noted that the Wisconsin lakes they studied had unusually cool epilimnetic temperatures in the
summers of 1992 and 1993. This was attributed to solar dimming resulting from the eruption of
Mt. Pinatubo
in the Philippines in June 1991 that resulted in summer cooling in 1992–1993 in several
regions across the globe. We also note the decrease in the average national air temperatures in 1992
and 1993, see Figure 7, and the corresponding dips in lake water temperatures in 1992, see Figure 3a–e.
4.4. Implications of Lake Warming
Our summer warming rates of 0.032
◦
C year
−1
in the period 1981–2018 would be the equivalent
of a lake moving south about 6.1 km year
−1
or losing 6.8 m of elevation a year. Over the 38-year
period from 1981 to 2018, the summer warming of lake near-surface water temperatures would be the
equivalent of a lowland lake moving 233 km south or an average mountain lake decreasing 258 m in
elevation. These calculations give some perspective on how lake heating may influence lake properties
and distributions of aquatic organisms, such as macrophytes, invertebrates, and fish. For example,
the range of warmwater fishes, such as the smallmouth bass (Micropterus dolomieu), are expanding
northwards in direct response to the warming of near-surface summer water temperatures in north
temperate lakes [
34
,
35
]. Concurrently, the range of suitable thermal habitat for coolwater and coldwater
fishes, such as walleye (Sander vitreus), cisco (Coregonus artedi), and lake trout (Salvelinus namaycush),

Water 2020,12, 3381 14 of 17
are rapidly disappearing from the northern United States [
36
,
37
]. The northern United States is at the
southern extent of the biological range for many coolwater and coldwater fish species, such as walleye
and lake trout, and the vulnerability of these fishes is further exacerbated by the loss of suitable thermal
habitat in direct response to climate change as well as competitive interactions with warmwater fishes,
such as smallmouth bass [
9
,
37
]. Continued accelerated warming of near-surface water temperatures
may continue to impact freshwater ecosystems across the United States in unexpected ways.
4.5. Methodology for Estimating Near-Surface Water Temperatures
There is an interest in knowing what lake temperatures were in the past. For example,
the distributions of many aquatic animals like fish are dependent on lake temperatures. Increases in
water temperatures may allow some species to expand their range northwards and force other species
to decline in an area because the waters are becoming warmer. The zoogeographer is hindered because
there are only a small number of lakes with temperature records that extend over several decades.
We were trying to find a way to extend our knowledge of lake warming to a broader range of lakes
that do not have a history of temperature records. One approach would be to construct numerical
models based on the physics involved in the determination of lake temperatures. Eindinger et al.
(1968) explained that one of the most important factors governing the temperature of a lake is the
exchange of heat across the air–water interface, and that the rate of heat exchange is the sum of the rates
that heat is transferred by radiative processes, evaporation, and conduction between water and the
overlying air. They discussed how a knowledge of meteorological variables could be used to estimate
temperatures in water bodies. As an example of this approach, Hondzo and Stephan (1993) developed
predictive models of temperatures for Minnesota lakes using solar radiation, air temperature, dew point
temperature, wind speed, wind direction, and precipitation.
There is a limit to the expansion of such physical models, however, since we do not have
historical data for many of those meteorological variables for a broad range of lakes. Of necessity,
we followed an alternative approach using relationships between air temperatures and near-surface
water temperatures in lakes. There have been many studies where relationships have been developed
between air temperatures and the surface water temperatures in the summer in a particular lake [
38
–
42
].
These empirical models yield fairly good results, even though they do not directly use all of the
important physical variables. Kettle et al. (2004) make the point that air temperatures are important in
calculating surface water temperatures because they are related to all heat exchange processes except the
absorption of solar radiation and the emission of long-wave radiation from the lake surface. They also
point out that air temperatures are often correlated with humidity and cloud cover. Thus, these models
work because the air temperatures are related to several of the factors that are directly involved in the
transfer of heat energy in and out of lakes. This is shown by the fact that an air-temperature-based
model cannot be applied directly to another lake that was not used in its calibration. Presumably,
the factors not measured like solar radiation and relative humidity vary enough across the United
States to alter the constants in the simple models. We found serendipitously in a previous study [
16
]
that we could develop models that could be widely applied to lakes in the conterminous United States
and southern Canada if we included information on geographic location like latitude and elevation
as well as summer month. Presumably, these variables accounted for alterations in the models from
place to place. In this study, we found that the relationships between air temperatures and water
temperatures in lakes of the conterminous United States changed slightly between 1981 and 2018.
These changes might reflect some basic changes in the factors that are directly involved in determining
lake water temperatures. Our empirical models are limited in their accuracy because they do not
directly measure many of the important physical variables; however, they did perform well (RMSE
1.69
◦
C) when applied to 1000 lake samples not used in the formulation of the models for the period
1981–2018. This study was designed specifically for the lakes in the conterminous United States. It was
dependent on the grid of historic temperature data obtainable from the PRISM website. The approach

Water 2020,12, 3381 15 of 17
might work in other geographic regions where there is comparable historic air temperature data as
well as water temperature data on lakes over time that could be used in a calibration.
5. Conclusions
Near-surface water temperatures in lakes of the conterminous United States vary from year to
year, but on average have been increasing at a rate of 0.32
◦
C decade
−1
during the summer months
of 1981–2020. Warming rates were greatest in September (0.49
◦
C decade
−1
) and lowest in August
(
0.22 ◦C decade−1
). For individual lakes, the monthly heating rates were not evenly distributed across
the United States and changed from month to month. The highest summer rates were found in lakes of
New Mexico, Colorado, New Jersey, Delaware, and Wyoming and the lowest in South Dakota, North
Dakota, Minnesota, and Oklahoma. The observed lake heating may influence lake properties and the
distributions of aquatic organisms, such as macrophytes, invertebrates, and fish.
Supplementary Materials:
The following are available online at http://www.mdpi.com/2073-4441/12/12/3381/s1,
Table S1: Calculated heating rates by month for each of the 1033 lakes in our statistical sample. Table S2: Average
monthly heating rates by state.
Author Contributions:
Conceptualization, R.W.B., D.E.C.J., and S.S.; methodology, R.W.B., D.E.C.J., and S.S.;
software, R.W.B.; formal analysis, R.W.B.; data curation, R.W.B.; writing—original draft preparation, R.W.B.,
D.E.C.J., and S.S.; writing—review and editing, R.W.B., D.E.C.J., S.S., and V.L.; visualization, V.L. All authors have
read and agreed to the published version of the manuscript.
Funding: There was no outside funding for this study.
Conflicts of Interest: The authors declare no conflict of interest.
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