Spatial heterogeneity of climate change as an experiential basis for skepticism

Significance

We develop a simple heuristic to measure local changes in climate based on the timing of record high and low temperatures. The metric shows local cooling and warming in the United States and captures two aspects of experiential learning that influence how the public perceives a change in climate: recency weighting and an emphasis on extreme events. We find that skepticism about whether the Earth is warming is greater in areas exhibiting cooling relative to areas that have warmed and that recent cooling can offset historical warming. This experiential basis for skepticism of climate change identifies obstacles to communicating ongoing changes in climate to the public and how these communications might be improved.

Abstract

We postulate that skepticism about climate change is partially caused by the spatial heterogeneity of climate change, which exposes experiential learners to climate heuristics that differ from the global average. This hypothesis is tested by formalizing an index that measures local changes in climate using station data and comparing this index with survey-based model estimates of county-level opinion about whether global warming is happening. Results indicate that more stations exhibit cooling and warming than predicted by random chance and that spatial variations in these changes can account for spatial variations in the percentage of the population that believes that “global warming is happening.” This effect is diminished in areas that have experienced more record low temperatures than record highs since 2005. Together, these results suggest that skepticism about climate change is driven partially by personal experiences; an accurate heuristic for local changes in climate identifies obstacles to communicating ongoing changes in climate to the public and how these communications might be improved.

Despite overwhelming scientific evidence, a significant fraction of the US population does not believe that climate is changing as proxied by a general warming, (1, 2), which we term skepticism. This skepticism is likely caused by many reasons, including two psychological phenomena: climate change is hard to perceive via everyday experience, and climate change is ancillary to everyday concerns (3–6). Under these conditions, experiential learning tends to be more powerful than statistical results (4, 7–10).

Here, we test the hypothesis that skepticism about climate change is partially caused by variations in the direction (warming or cooling) and magnitude of climate change over space (herein spatial heterogeneity), which expose experiential learners to climate heuristics that differ from the global average, by formalizing a simple index that measures local changes in climate and comparing this index with survey-based model estimates of county-level opinion about whether global warming is happening (1). Beyond the predictable impact of demographic factors (11–13), our results indicate that the index for local changes in climate (which may proxy an individual’s climate experience) can account for a significant fraction of county-level variations in the percentage of the population that believes that “global warming is happening.” These results are tempered by our finding that belief is shaped by more recent experiences. Specifically, belief is diminished by record low temperatures since 2005. Together, these results suggest that skepticism about climate change is driven partially by personal experiences; an accurate heuristic for local changes in climate identifies obstacles to and potential solutions for communicating ongoing changes in climate to the public.

Previous analyses calculate climate heuristics by comparing temperature during a given day (14, 15), week (16), season (3, 17, 18), or year(s) (19, 20) with a long-run average for the corresponding period and classifying this anomaly as either warmer or cooler than average. However, these daily, weekly, seasonal, or annual differences from the mean do not represent a change in climate, which is a change in the long-run weather means. Furthermore, the anomalies are not compared with natural variability, and therefore, they are moot about their probability. As such, these anomalies do not proxy changes in climate, which suggests that poor heuristics could bias previous results regarding the effect of experiential learning on the degree to which the public accepts climate change (3, 14, 18, 20–22).

To evaluate how the spatial heterogeneity of climate change affects the public’s willingness to accept scientific results that the climate is changing, we propose an index that accurately measures local changes in climate based on the number of days per year for which the year of the record high temperature is more recent than the year of the record low temperature. The index (23) is calculated as follows:

$$TMa{x}_i={\displaystyle \sum }_{D=1}^{365}\left(Hig{h}_{Di}>Lo{w}_{Di}\right)\times 1,$$ [1]

in which High_Di is the year of the record high temperature and Low_Di is the year of the record low temperature for weather station i on day D. If the year of the record high is more recent, the statement in parentheses is true, and day (D) has a value of one (otherwise, it has a value of zero). For instance, if, for January 1st, the record high occurred at station i in 1998 and the record low occurred in 1950, TMax_i would take the value of one, or zero if the record low had occurred after 1998. Daily values of zero or one are summed over the year to calculate TMax_i. Because TMax can be affected by the minimum sample period (e.g., 30, 40, or 50 years [i.e., 1961 (or earlier) through 2010 or later]) and missing observations (e.g., 5, 10, or 15 observations), these criteria are varied to test how including/excluding weather stations affects our results (SI Materials and Methods, 1. Datasets).

TMax is used as a heuristic for local changes in climate with values that can be interpreted relative to a null hypothesis of no change in climate. Under this null, the probability that a day’s temperature will be a record high is equal to the probability that it will be a record low. If local climate is warming, the probability that a day’s temperature will be a record high is greater than the probability that the day’s temperature will be a record low. Under these conditions, there will be more days on which the record high is more recent than the record low (TMax > 182). Deviations from 182 can be evaluated against a binomial distribution; the probability that random chance generates values of TMax greater than 201 (207) or less than 163 (157) is less than 5% (1%).

Beyond being an accurate heuristic for local changes in climate, TMax captures two aspects of experiential learning that influence how the public perceives a change in climate: recency weighting and an emphasis on extreme events. Record high and low temperatures are rare events that are featured by the local media. This attention is critical because rare events are given more weight in human decision-making (4). The importance of extreme events may be one reason that the public can perceive droughts, floods, and long periods of warmth more accurately than shorter-term temperature anomalies (17, 19). Recognition of record temperatures is reinforced by an emphasis on recent events, which is termed recency weighting (6, 24, 25). Because TMax is determined by the most recent records, a high value is consistent with record warmth being more recent than record cold.

SI Materials and Methods

1. Datasets.

We obtained data on the daily high and low temperatures for 18,713 stations located in the United States (28). Each station is classified according to the number of years for which data are available and the number of observations that are missing. These criteria affect the values for TMax, High2005, and Low2005 as well as their interpretation. The minimum number of years included affects the probability of observing a new record. If there is no change in climate (i.e., temperature is stationary), the likelihood of a new record declines asymptotically with a probability given by 1/N, where N is the number of observations (33). The length of the sample also may affect the public’s perception of a new record. A temperature that breaks a 50-y record may be viewed as a more extreme event than a temperature that breaks a 30-y record. If there is no change in climate, differences in the sample length do not affect the probability of a record high vs. record low (34). To ensure that TMax measures changes in climate and represents climate norms, the minimum sample length is 30 y (35).

The number of observations missing affects the ability to identify record high or low temperatures. Only a complete set of data allows us to identify the highest and lowest temperatures for a given day. Missing values introduce uncertainty. That is, we can identify the highest and lowest temperatures on a given day for which observations are available, but we cannot be sure that the records identified have temperatures that are higher or lower than the temperatures on the day and year for which observations are missing. This uncertainty increases with the number of missing observations. We could “fill in” missing observations by interpolating between observations. However, this method is inappropriate for calculations of TMax, which emphasizes record highs and lows. Instead, we chose to retain missing observations and limit their effects by including stations with small numbers of missing observations.

Applying these two criteria to include/exclude stations creates samples for Eq. 2 that include 313–2,318 stations. Because there is no a priori reason to choose a minimum sample size and/or a maximum number of missing observations, nine datasets are used to determine the degree to which the results are robust. The results do not vary significantly among datasets as indicated in Table 1.

Table 1.

Spatial lag results (y = $\rho$ Wy + xβ + e)

Years	Miss	Stations	Spatial autocorrelation $\rho$	TMax (β1)	Low2005 (β2)	Low2005 (β3)	High2005 (β4)	High2005 (β5)	Average High2005	Average Low2005	Pseudo-R2
30	5	383	0.670**	0.010**	0.012	−0.003	−0.007	−0.016**	60.6	26.3	0.38
30	10	1,507	0.670**	0.010**	−0.012	−0.007	−0.013*	−0.014**	55.2	27.0	0.38
30	15	2318	0.663**	0.013**	−0.005	−0.011***	−0.012*	−0.012*	48.9	24.4	0.38
40	5	344	0.674**	0.010**	0.017***	−0.003	−0.007	−0.015*	59.0	23.7	0.38
40	10	1,268	0.668**	0.012**	−0.016	−0.009	−0.022**	−0.019**	52.2	23.2	0.38
40	15	2,013	0.658**	0.015**	−0.003	−0.012*	−0.015*	−0.015*	46.15	21.21	0.382
50	5	313	0.668**	0.010**	0.015	−0.005	−0.011	−0.020**	57.24	22.46	0.376
50	10	1,121	0.664**	0.011**	−0.014	−0.007	−0.021**	−0.020**	49.85	21.75	0.378
50	15	1,826	0.661**	0.013**	−0.006	−0.013*	−0.017**	−0.015*	43.93	19.91	0.380

Levels of significance (*5%; **1%; ***10%).

2. A Local Measure of Climate Change.

For each of nine sets of stations described in SI Materials and Methods, 1. Datasets, we calculate a local measure of climate change for weather station i by calculating TMax_i, which is constructed using Eq. 1. If the year of the record high is more recent, the statement in parentheses is true, and day (D) has a value of one (otherwise, it has a value of zero). Daily values of zero or one are summed over the year to calculate TMax_i.

To illustrate, suppose that TMax is calculated from a weather station that has 40 y of observations and 10 or fewer missing observations. For January first (D = 1), we identify the year of the highest and lowest temperatures from 40 observations of daily maximum and minimum temperatures. Suppose that the highest temperature on January 1 during the sample period occurs in 2008, whereas the lowest temperature on January 1 occurs in 1987. Under these conditions, the record high is more recent than the record low (i.e., High₁ > Low₁), and the statement in parentheses in Eq. 1 is assigned a value of one. If the highest temperature on January 2 during the sample period occurs in 2001, whereas the lowest temperature on January 2 during the sample period occurs in 2009, Low₂ is more recent than High₂, and the statement in parentheses of Eq. 1 is assigned a value of zero. This process is repeated for each day of the year, and the values of zero or one are summed to calculate TMax. TMax_i, therefore, provides a measure of local climate change based on record high temperatures.

Experiential learners emphasize recent events, which psychologists term recency weighting. We highlight recency weighting by tracking record temperatures since 2005, which is consistent with the 5-y mean residence time during which individuals are assumed to live at their current address (36, 37). To capture recent warming, High2005 is calculated as follows:

$$High{2005}_i={\displaystyle \sum _{D=1}^{365}}[1\times (Hig{h}_{Di}>Lo{w}_{Di})\times 1\times \left(Hig{h}_{Di}\ge 2005\right)].$$ [S1]

In this case, High2005 on day D has a value of one if the year of the highest temperature on day D is more recent than the year of lowest temperature on day D and if the year for that high temperature is 2005 or later. To illustrate, suppose that the warmest temperature on January 1 during the sample period occurs in 2008, whereas the coolest temperature on January 1 during the sample period occurs in 1987. Under these conditions, High₁ is more recent than Low₁, and the high temperature occurs in 2008, which is more recent than 2005. Because the second condition is also true, the statement in brackets is assigned a value of one. Conversely, if the warmest temperature on January 1 occurs in 1998, the second condition is false. As such, the entire statement in brackets has a value of zero.

To capture recent cooling, Low2005 is calculated as follows:

$$Low{2005}_i={\displaystyle \sum _{D=1}^{365}}[1\times (Hig{h}_{Di}<Lo{w}_{Di})\times 1\times \left(Lo{w}_{Di}\ge 2005\right)].$$ [S2]

In this case, Low2005 on day D has a value of one if the year of the lowest temperature on day D is more recent than the year of highest temperature on day D and if the year for that low temperature is 2005 or later. To illustrate, suppose that the lowest temperature on January 1 during the sample period occurs in 2008, whereas the highest temperature on January 1 during the sample period occurs in 1987. Under these conditions, Low₁ is more recent than High₁, and the low temperature occurs in 2008, which is more recent than 2005. Because the second condition is also true, the statement in brackets is assigned a value of one. Conversely, if the lowest temperature on January 1 occurs in 1998, the second condition is false. As such, the entire statement in brackets has a value of zero.

It is possible to represent recency effects with a continuous variable, but we do not think that this specification would generate reliable results. Recency effects could be specified using variables that represent the number of record highs and lows in given year, such as 2005, 2006, 2007, etc. However, this specification poses two challenges. At any station, the number of record highs or lows in any given year tends to be very small, with many stations having a value of zero. These small numbers would make it difficult to generate statistically measurable effects. Furthermore, under the null hypothesis, the likelihood of new records declines over time as the sequence of observations grows (SI Materials and Methods, 1. Datasets). This decline opposes the effect of recency weighting, which should strengthen as time moves toward the current date, and these countervailing effects make it difficult to specify the sign a priori.

3. Assigning Climate Observations to Political Boundaries.

We assign all portions of US counties to their nearest weather station as follows. Thiessen polygons (Fig. S1, gray polygons) around each weather station define the area nearest to it (Fig. S1, white dots). We use a spatial union between these Thiessen polygons and all US census tracts (Fig. S1, dark gray) to cut tracts boundaries based on its nearest weather station (Fig. S1, union of white and gray lines). The voting age population of each tract is reassigned to these newly divided census tracts based on each portion’s percentage of total geographic area. Population data are compiled from ref. 30. For instance, if Census Tract A is divided evenly between two weather stations, one-half of its population would be assigned to each portion. These new census tract boundaries define both the area and the population associated with a weather station.

Fig. S1.

Assignment of climate observations to political boundaries.

To link climate data with the estimated percentage of a county’s adult population that agrees that global warming is happening, we translate station-level values of TMax_i and (High2005_i and Low2005_i) to county-level values for TMax_c and (High2005_c and Low2005_c) using a weighted average that is based on voting population. This weighted average is calculated as follows:

$${\overline{TMax}}_{C}weighted={\displaystyle \sum }_{i=1}^n{w}_{ci}{X}_{ci},$$ [S3]

in which the county-level weighted average is the sum of all weighted climate indicators, $w_{ci}$ is the percentage of voting age county-level population that lives in each station split tract i in county c, $X_{ci}$ is the TMax value assigned from the nearest station to station split tract i in county c, and n is the total number of station split tracts in county c.

4. Econometric Specification.

To assess the relation between local changes in climate as measured by TMax_c, High2005_c, and Low2005_c and the percentage of the population that answers yes to the question “do you think that global warming is happening?,” we estimate the following equation (with the addition of a spatial lag term), which is identical to Eq. 2:

$$\begin{array}{l}\%Belie{f}_c=\alpha +{\beta }_{1}TMa{x}_c+{\beta }_{2}High{2005}_c\times (TMa{x}_c\le 163)\\ +{\beta }_{3}High{2005}_c\times (163<TMa{x}_c\le 182)+{\beta }_{4}Low{2005}_c\\ \times (182>TMa{x}_c\le 201)+{\beta }_{5}Low{2005}_c\\ \times (TMa{x}_c>201)+{\mu }_c,\end{array}$$ [S4]

in which %Belief is the estimated percentage of the county c adult population that answers yes to the question “do you think that global warming is happening?” (1); TMax_c, High2005_c, and Low2005_c are as defined previously; α and β values are regression coefficients, and μ_c is the regression error.

The interpretation of ${\beta }_1$ (in absence of a spatial lag term) (SI Materials and Methods, 7. The Experiential Effect of Climate Change discusses the interpretation in a spatial context) is straightforward. Ceteris paribus, a high value of TMax_c indicates that local climate is warming and provides experiential evidence in favor of climate change. As such, we would expect ${\beta }_1$ to be positive, because personal experience with a warming climate is likely linked to increased confidence that global warming is happening.

Rather than reinforce the effect of TMax, Eq. S4 specifies the recency effects proxied by High2005_c and Low2005_c in a way that contradicts the sample-wide values of TMax_c. For counties that experience sample-wide cooling (as measured by values of TMax_c less than 182), Eq. S4 allows two effects by which recent warming may increase the public’s belief that climate is warming. One effect is associated with counties that cool strongly over the sample period. In this case, strong cooling is defined by a small likelihood (P < 0.05) that the low value of TMax (TMax < 163) over the sample period is generated by random chance (based on a binomial distribution). The other effect is associated with counties that cool over the sample period (163 > TMax ≤ 182), but this cooling is consistent with random chance (P > 0.05). For both, we expect ${\beta }_2$ and ${\beta }_3$ to be positive, because recent warming in these counties should offset the tendency to disagree with the statement that global warming is happening that is associated with the cooling experienced over the sample period.

Conversely, for counties that experience sample-wide warming (as measured by values of TMax greater than 182), Eq. S4 allows two effects by which recent cooling may reduce the public’s belief that climate is warming. One effect is associated with counties that warm strongly over the sample period. In this case, strong warming is defined by a small likelihood (P < 0.05) that the high value of TMax (TMax > 201) over the sample period is generated by random chance. The other effect is associated with counties that warm over the sample period (201 ≥ TMax > 182), but this warming is consistent with random chance (P > 0.05). For both, we expect ${\beta }_4$ and ${\beta }_5$ to be negative, because recent cooling in these counties should offset the tendency to agree with the statement that global warming is happening that is associated with the warming experienced over the sample period.

The OLS estimate for Eq. S4 does not account for the nature of %Belief, which is a proportion observed on the interval (0,1). As a robustness check, we also estimate the models by applying a logit transformation to the dependent variable now mapped to the real line, noting that no observation of $\%Belie{f}_c$ in our sample is equal to exactly zero or one:

$$\begin{array}{l}Logit[\%Belie{f}_c]=\alpha +{\beta }_{1}TMa{x}_c+{\beta }_{2}High{2005}_c\times (TMa{x}_c\le 163)\\ +{\beta }_{3}High{2005}_c\times (163<TMa{x}_c\le 182)\\ +{\beta }_{4}Low{2005}_c\times (182>TMa{x}_c\le 201)\\ +{\beta }_{5}Low{2005}_c\times (TMa{x}_c>201)+{\mu }_c,\end{array}$$ [S5]

where $Logit\left[y_c\right]=\text{ln}(y_c/[1-y_c])$, such that any predicted values of $y_c$ will fall within the (0,1) interval:

$$\begin{array}{l}\%Belie{f}_c=Logi{t}^{-1}[\alpha +{\beta }_{1}TMa{x}_c+{\beta }_{2}High{2005}_c\times (TMa{x}_c\le 163)\\ +{\beta }_{3}High{2005}_c\times (163<TMa{x}_c\le 182)+{\beta }_{4}Low{2005}_c\\ \times (182>TMa{x}_c\le 201)+{\beta }_{5}Low{2005}_c\\ \times (TMa{x}_c>201)+{\mu }_c].\end{array}$$ [S6]

The coefficients in the transformed model (Eq. S6), which are interpreted relative to the log odds, are consistent with the findings in the original model (Eq. S4). The signs of the estimated coefficients ${\beta }_1$ to ${\beta }_5$ in Eq. S6 coincide with those of Eq. S4: ${\beta }_1$ is positive and significant for all sample specifications (varied minimum of observations and maximum missing observations per station).

5. Spatial Regression.

To account for the possible effects of spatial autocorrelation, Eq. S4 is estimated as a spatial simultaneous lag model of the form:

$$y_c=\rho W{y}_j+X_c\text{'}\beta +{\epsilon }_c,$$ [S7]

in which $W$ is a K nearest neighbor row standardized weights matrix (K = 5), $W{y}_j$ is the spatial lagged values of c neighbors j, $\rho$ is a spatial autoregressive slope coefficient, $\beta$ is a vector of regression coefficients for all independent variables for observation c ($X_c$), and $\epsilon$ is an N × 1 vector of white noise error. Residuals from all OLS estimates show signs of significant spatial autocorrelation (P < 0.01) using the lm.morantest from R’s spdep package (30–32). The use of a spatial lag is validated (P < 0.01) for all datasets through robust versions of the Lagrange Multiplier test for spatially dependent linear models (31).

As described in the text, the residual from estimates of Eq. S4 shows significant levels of spatial autocorrelation (P < 0.01). If left uncorrected, the presence of significant positive autocorrelation in the residual would cause OLS to underestimate SEs, leading to potential problems with inference (38). To avoid such difficulties, we use a spatial lag model to account for spatial dependence. The method chooses between the use of spatial lag and spatial error models based on robust Lagrange multiplier diagnostics for spatial dependence (38). All sets of station data point to the use of a spatial lag model (P < 0.01) as described by Eq. S7. This spatial lag model is analogous to autoregressive time series models that control for temporal autocorrelation, except that $W{y}_j$ accounts for the impact of neighboring counties. As such, findings presented in Table 1 should be both conservative and robust to spatial autocorrelation.

6. Interpreting the Regression Coefficients.

The interpretation of the regression coefficients (${\beta }_1$ to ${\beta }_5$) in Eqs. S4 and S6 is based on the equations used to generate county-level values for the fraction of the population that answered yes to the question “do you think that global warming is happening?” As described in ref. 1, the sample size of the original national survey is not sufficient to generate county-level values. Instead, these county-level values are generated via a downscaling procedure using multilevel regression and poststratification. Following this procedure, the authors of the work in ref. 1 use the national sample to estimate an equation that has the following general specification:

$$\%Belie{f}_{jc}={\alpha }_c+{\displaystyle \sum _{k=1}^n{\beta }_k{R}_{kj}}+{\eta }_j,$$ [S8]

in which %Belief is the yes or no answer to the question “do you think that global warming is happening?” that is given by respondent j who lives in county c, R is a vector of n individual-level demographic variables k (i.e., gender, education, and race/ethnicity) that is used to classify respondent j, ${\beta }_k$ represents the effect that demographic variable k has on the probability that respondent j will answer yes to the question “do you think that global warming is happening?,” ${\alpha }_c$ is a county-specific intercept that represents the effect of county-level observed (e.g., aggregate socioeconomic variables, such as election results) and unobserved variables (a random effect accounting for differences not explained by individual- or county-level observed variables) on the probability that respondent j will answer yes to the question “do you think that global warming is happening?,” and ${\eta }_j$ is an error term specific to individual j. As such, the county-level estimate for %Belief includes two components: the effect of socioeconomic variables based on the population of that county and unobserved effects through ${\widehat{\alpha }}_c$.

The final multilevel regression poststratification models that are used to project the average opinion in county c have the following general specification:

$$\%Belie{f}_i=\frac{{\displaystyle \sum _{cei}{N}_c{\vartheta }_c}}{{\displaystyle \sum _{cei}{N}_c}},$$ [S9]

in which $\vartheta$ is the projected opinion of each demographic type (e) indexed over cell c, and N gives the population count for that cell.

We postulate that the unobserved county-level effects ${\widehat{\alpha }}_c$ include experiential learning of county residents, which is influenced in part by local changes in climate as proxied by TMax_c, High2005_c, and Low2005_c. As such, the relation between %Belief_c and TMax_c, High2005_c, and Low2005_c goes beyond the effect of demographic and socioeconomic variables. The county-level downscaled measure on the belief that global warming is happening, therefore, contains variation through the county-level effects ${\widehat{\alpha }}_c$.

To test whether this unexplained variation can be attributed to individual experience as captured through TMax_c, High2005_c, and Low2005_c, we test whether TMax_c has information about %Belief_c beyond demographic and socioeconomic variables by estimating (Eq. S10)

$$\%Belie{f}_c=\alpha +\lambda \%Vot{e}_c+\xi TMa{x}_c+{\mu }_c,$$ [S10]

in which %Vote is the fraction of county c’s population that voted for President Obama in the 2012 election. Statistically significant positive values for $\xi$ would suggest that our measure for local changes in climate has information about belief in climate change that goes beyond the important effects of the voting variable, which summarizes county-level information on political affiliation, race, gender, education, income, etc. (39).

Results indicate that the coefficient associated with TMax always is statistically significant and positive when Eq. S10 is estimated from each of nine datasets for TMax. This statistical significance suggests that our measures for local changes in climate have information about county-level opinion regarding climate change that extends beyond demographic and socioeconomic variables and that this interpretation is robust to the criteria used to include stations.

Nonetheless, the coefficients in the downscaling regressions (Eq. S8) may be biased because of the omission of TMax_c, High2005_c, and Low2005_c—indeed, one could argue that local changes in climate affect a person’s decision about party affiliation (i.e., experiential learning in counties that have warmed may increase the likelihood that a person would affiliate with the Democrat Party). Conversely, it is difficult to conceive a mechanism by which the socioeconomic characteristics of a county’s population influence our local measures of climate. However, the inclusion of a county-specific intercept should alleviate the majority of these concerns.

7. The Experiential Effect of Climate Change.

The results summarized in Table 1 (Table S1) indicate that the coefficients associated with TMax and TMin2005 are statistically different from zero and that these coefficients, along with the spatial autocorrelation, can account for about 38% of the total variation in %Belief as indicated by the values for the Nagelkerke (40) pseudo-R² in Table 1 and Table S1. Beyond statistical significance of the independent variables, here, we assess the effect of our measures for experiential learning on %Belief.

Table S1.

Model results for the logit-transformed dependent variable ($logit\left[y\right]\hspace{0.17em}=x\beta +e$)

Years	Miss	TMax (β2)	Low2005 (β2)	Low2005 (β3)1	High2005 (β4)	High2005 (β5)	${\overline{R}}^2$
30	5	0.002**	0.002**	0.001**	0.003	−0.001**	0.044
30	10	0.002**	0.0001	−0.0004*	−0.0002	−0.0005**	0.055
30	15	0.002**	−0.00001	−0.001**	−0.0002	−0.0004**	0.083
40	5	0.002**	0.002**	0.001**	−0.0001	−0.001**	0.046
40	10	0.002**	−0.0001	−0.0003	−0.001**	−0.001**	0.068
40	15	0.002**	0.0002	−0.001**	−0.0003	−0.0003***	0.088
50	5	0.002**	0.002**	0.0002	−0.001**	−0.002**	0.062
50	10	0.002**	−0.0003	−0.0005**	−0.001**	−0.001**	0.073
50	15	0.002**	−0.0001	−0.001**	−0.001**	−0.001**	0.092

Levels of significance (*5%; **1%; ***10%).

We quantify the effect of the independent variables on %Belief in two ways. First, we consider the individual effect of every independent variable. Second, we consider the total sum of effects of all relevant independent variables. Because of the spatial lag term in the estimated model, the regression coefficients cannot directly be interpreted as effects on the dependent variable. To compute the impact while accounting for spatial autocorrelation, we calculate the direct, indirect, and total effects for each independent variable using the implementation in the R-package spdep (41), where the direct effect is the impact given by the coefficient values in Table 1, the total effect is the total change in response to the direct effect and neighbor spillovers, and the indirect (spatial) effect is the difference between the total and direct effects. We report the results here for the spatial lag model with 40 y of data and at most, 10 missing observations, noting that there is little difference in the magnitude of effects for other sample datasets.

1. Individual effects.

To quantify the impact of TMax, we consider the effect of spatial heterogeneity in belief as to whether global warming is happening by estimating the counterfactual %Belief in the absence of spatial heterogeneity by calculating the TMax effect as:

$$Effec{t}_{Jc}={\beta }_j\times (V_{jc}-\overline{V}),$$ [S11]

where V is the value of TMax for county c, $\overline{V}$ is the mean value of TMax across all counties, and ${\beta }_j$ (j = [direct, indirect, total]) captures the direct effect (regression coefficients from Table 1), the indirect effect from spatial spillover (neighboring counties affecting their neighbors), and the total effect as the sum of both direct and indirect effects. This specification measures the effect of TMax on %Belief if there was no spatial heterogeneity in climate change as measured through TMax. In other words, Effect_Jc measures the response in the belief variable if TMax was moved to its sample mean for every county. We quantify the impact of the recency variables by considering their effect on each county if the condition on TMax is satisfied (e.g., TMax < 163, TMax > 201, etc.). The resulting distribution of effects across all counties is shown as histograms in Figs. S3–S7. The individual effect of TMax on %Belief ranges from −4 to +4% (Fig. S3) across all counties. Of four recency effects, recent cooling (Low2005) has a larger effect on %Belief (Fig. S7) than recent warming (High2005) (Figs. S4 and S5).

Fig. S3.

Histogram of the direct, indirect, and total effects associated with TMax on %Belief across all counties.

Fig. S7.

Histogram of the direct, indirect, and total effects associated with $Low{2005}_c\times (TMa{x}_c>201)$ on %Belief across all counties.

Fig. S4.

Histogram of the direct, indirect, and total effects associated with $High{2005}_c\times (TMa{x}_c<163)$ on %Belief across all counties.

Fig. S5.

Histogram of the direct, indirect, and total effects associated with ${\mathit{High}2005}_c\times ({\mathit{TMax}}_c<163)+{\beta }_3{\mathit{High}2005}_c\times (163<{\mathit{TMax}}_c<182)+{\beta }_4{\mathit{Low}2005}_c\times (182>{\mathit{TMax}}_c<201)+{\beta }_5{\mathit{Low}2005}_c\times ({\mathit{TMax}}_c>201)$ on %Belief across all counties.

2. Overall effect.

The total effect of experiential learning on %Belief is calculated by summing the effect of TMax in absence of spatial heterogeneity (TMax moved to the county average for all counties) and the associated recency effect. Because only one of four variables for recency effects applies to a county, the sum of this variable and TMax represents the total effects of experiential learning on %Belief as quantified by the spatial lag model (Eq. S7).

The total effects of experiential learning increase/decrease %Belief between −5 and +3% points (Fig. S8). Of these percentage points, about one-half are associated with TMax (Fig. S5). The other one-half of these percentage points are associated with recency weighting (Fig. S7).

Fig. S8.

Histogram of the direct, indirect, and total (TMax and recency) effects associated with experiential learning on %Belief across all counties.

Together, these results suggest that experiential learning can account for a significant portion of county-level variations in %Belief. This interpretation is consistent with the effect of experiential learning on %Belief relative to county-level variations in %Belief. A histogram of %Belief (Fig. S2) indicates that one-half of all county values are within ±3% points of the mean (and median) of 59% (the interquartile range covering one-half of the sample spans from 56 to 62%). The total range of %Belief spans from 45 (minimum) to 84% (maximum), with an SD of 4.9% points. This range establishes total variation in %Belief, which is roughly comparable with the effects of experiential learning.

Fig. S2.

Histogram of variation around mean value for %Belief.

8. Model Performance.

Fig. 2 summarizes the spatial relation between TMax and %Belief. However, this figure does not represent the effects of recency weighting on %Belief, and interpreting chloropleth maps is subject to perceptual bias. To provide information about the effect of TMax and recency weighting on %Belief, Fig. S9 plots county-level values of the observed values of %Belief as a function of county-level values for $\%\widehat{B}elief$ generated by the statistical model given by Eq. 2. A perfect fit would have the points fall along the black dashed 45° line. Although naturally, we do not observe a perfect fit, the predicted values of $\%\widehat{B}elief$ are strongly correlated with the observed values of %Belief (the estimated coefficient when regressing fitted values on actual values is $\beta$ = 0.410, P < 0.01). The estimated regression coefficient between the fitted and observed series is indicative of the model fit; however, the coefficient here does not directly correspond to the R² of the original regression, such as is the case in OLS. The fitted values are obtained through maximum likelihood estimation of the spatial lag model, for which the R² is not formally defined. The predicted values range from 50 to 73%, closely matching the range of observed %Belief, which ranges from 45 to 85%.

Fig. 2.

Belief in climate change and heuristics for local changes in climate. The fraction of a county’s population that answered yes to the question “do you think that global warming is happening?” (1) is indicated by shading. Station values of TMax_i are indicated by colored circles. Red and blue circles identify stations with values that are higher and lower, respectively, than expected by random chance as indicated by a binomial distribution.

Fig. S9.

Values of %Belief simulated by Eq. 2 as a function of observed values of %Belief.

To avoid issues associated with perceptual bias, we calculate local Moran’s I bivariate clusters of the relation between anomalies in observed %Belief ($\%Belie{f}_c-\%\overline{B}elief$) and anomalies in predicted values of %Belief ($\%\widehat{B}elie{f}_c-\%\overline{B}elief$). The local Moran’s I bivariate clusters identify spatial clustering of similar and dissimilar values within a predefined spatial neighborhood, here defined as the five nearest neighbors. The values in Fig. 3 indicate that the model does a good job of matching observed anomalies in county levels of %Belief with the long- (TMax) and short-run (High2005 and Low2005) heuristics of local climate change that support high or low values of skepticism. There are 516 counties where the large fraction of the population that believes that climate is warming matches our heuristics for climate change (i.e., high values for TMax and low values for Low2005). Similarly, there are 718 counties where the large fraction of the population that does not believe that climate is warming matches our heuristics for climate change (i.e., low values for TMax and high values for Low2005). Conversely, the model generates relatively few “counterexamples.” That is, our heuristics for local changes in climate cause the model to predict large positive anomalies for %Belief in only 41 counties where the observed anomalies are large (in an absolute sense) and negative. Similarly, our heuristics for local changes in climate cause the model to predict large (in an absolute sense) negative anomalies for %Belief in only 30 counties where the observed anomalies are large and positive. Additionally, these 71 exceptions are a small fraction of 3,143 counties analyzed and reflect an “error rate,” which is a rate consistent with random chance (P < 0.05). As expected, most counties (1,838) have no significant local spatial clustering of either high or low %Belief with our heuristics for local changes in climate.

Fig. 3.

Local Moran’s I bivariate clusters of county anomalies for observed values of %Belief (%Belief − US average of %Belief) and the corresponding anomalies for the predicted values of %Belief (predicted %Belief − US average of predicted %Belief) from Eq. 2. Areas with above-average %Belief and above-average predicted values of %Belief (red), above-average %Belief and below-average predicted values of %Belief (pink), below-average %Belief and above-average predicted values of %Belief (light blue), below-average %Belief and below-average predicted values of %Belief (blue), and statistically insignificant local clustering (gray) are shown.

Results

Values of TMax indicate considerable spatial heterogeneity; local climate in the United States has both cooled and warmed in more locations than expected by chance (Fig. 1). Consistent with a warming climate, the number of stations with values of TMax that exceed 201 or 207 is greater than expected by random chance (red in Fig. 1). Nearly 49% of stations have values of TMax greater than 207; random chance generates such values for only about 0.5% of the sample. Conversely, there is considerable evidence for local cooling. About 10% of the stations have values of TMax below 157 (blue in Fig. 1); again, random chance generates such values for only about 0.5% of the sample. Findings for both warming and cooling are not sensitive to the criteria used to include/exclude weather stations in the calculation of TMax.

Fig. 1.

Distribution of TMax. The fraction of observations for a given value of TMax expected based on random chance (gray) in a nonchanging climate as given by the binomial distribution is shown together with a histogram of observed TMax calculated from stations that have at least 40 y of observations and 10 or fewer missing observations. Areas in red represent the fraction of stations where TMax indicates warming beyond that expected by the binomial distribution, whereas areas in blue represent the fraction of stations where TMax indicates cooling beyond that expected by the binomial distribution. Note that both the mean and the variance in the observations exceed those of the binomial reference distribution. The number of counties warming is higher than one would expect under a nonchanging climate. The overdispersion (higher variance) is likely the result of spatial heterogeneity in TMax—the probability of observing a record high relative to a record low is not constant across different counties because of geographic variation in warming. We use this spatial heterogeneity to explain some of the variation in %Belief.

We test the relation between how the public perceives climate change and the degree to which they believe that global climate is warming (Fig. 2) by regressing the estimated percentage of a county’s adult population who agree that global warming is happening (%Belief) against county-level values for TMax (Fig. S1) and the influence of recent record temperatures (recency weighting) as represented by the most recent record temperature, high (High2005) and low (Low2005) temperatures since 2005, which is chosen based on the mean residence time of US households (Materials and Methods). Regression results indicate that there is a statistically measureable positive relation between county-level values of TMax and the percentage of the population that believes that global warming is happening (Table 1). Estimation results suggest that spatial variations in TMax (comparing observed patterns of TMax relative to all counties experiencing TMax at its sample mean) lead %Belief to vary $\pm 4$% points (Fig. S2) across counties (positive if increased and negative if decreased). This effect suggests that the public’s willingness to believe that global warming is happening depends in part on the degree to which they personally experience a warmer or cooler climate. These results are robust to the differential criteria used to include/exclude weather stations in the calculation of TMax and the estimation method (SI Materials and Methods, 4. Econometric Specification and SI Materials and Methods, 5. Spatial Regression).

The effect of TMax on %Belief is strongly mediated by one component of recency weighting: record low temperatures after 2005. For counties that experience high warming over the entire sample period (TMax > 201), increases in the number of record low temperatures since 2005 reduce the percentage of the population that believes that global warming is happening by up to 4% (SI Materials and Methods, 7. The Experiential Effect of Climate Change). Conversely, record high temperatures since 2005 in counties that cool over the sample period (TMax < 182) have little effect on %Belief.

The total estimated effect of right-hand side variables, including TMax and recency weighting, is between −5 and +3% points for different counties (Figs. S3–S7) and comparable with the spatial variation in %Belief, which has an SD of 4.9% points, with one-half of all counties falling within 3% points of the mean (and median) of 59% (Figs. S2 and S8). As such, perceptions of local changes in climate can account for a significant portion of the county-level differences in %Belief (SI Materials and Methods, 6. Interpreting the Regression Coefficients) and suggest that personal experience is an important determinant of the public’s willingness to accept the scientifically established fact that Earth is warming (Figs. 2 and 3 and Fig. S9).

Fig. S6.

Histogram of the direct, indirect, and total effects associated with $Low{2005}_c\times (182>TMa{x}_c<201)$ on %Belief across all counties.

Discussion

The importance of experiential learning creates several challenges to a public consensus needed to implement meaningful climate change policy. Local cooling, as indicated by low values for TMax and high values for Low2005, identifies 718 counties where personal heuristics support experiential learning that is consistent with high levels of climate skepticism (Fig. 3). Here, contradictions between personal experiences with local changes in climate and the scientific evidence for climate change seem settled in favor of personal experience. Changing this weighting in favor of scientific evidence will be difficult given the importance of personal experience.

Adding to this difficulty, our result suggests that the public tends to ignore local conditions when they are inconsistent with their beliefs (18). A recent spate of record high temperatures does little to reduce climate skepticism among residents who live in counties that have a relatively large number of record low temperatures over the sample period. Conversely, climate skepticism in counties with high values for TMax rises in response to a relatively small number of record low temperatures since 2005 (Low2005 is about one-half High2005) (Table 1). Asymmetric effects suggest biases that distort logic by allowing skeptics to maximize the importance of the record cold temperatures, because its inconsistency with global warming reinforces their nonbelief (26). This asymmetry may be partially responsible for the relatively small number of counties (n = 514) where experiential learning is consistent with high levels of acceptance of climate change (Fig. 3).

Despite these obstacles, our results suggest a way to supplement the information used to communicate ongoing changes in climate. In addition to monthly temperature anomalies, agencies may want to report the number of new record high and low temperatures. To enhance public understanding, these records could be framed as a wager against the hypothesis that global temperature is warming, in which a dollar is won for each record low and a dollar is lost for each record high. Defining the wager against a warming climate is consistent with the null hypothesis of scientific inquiry (no change in climate) and biases in human perception; loss aversion holds that people perceive a dollar lost as more valuable than a dollar gained (27).

Materials and Methods

We obtain data on the 24-h daily high and low temperatures for 18,713 stations located in the United States (28). Each station is classified according to the number of years for which data are available and the number of observations that are missing. For each station that satisfies a set of selection criteria, we calculate the value of TMax using Eq. 1. We also record the number of most recent record high (High2005) and low (Low2005) temperatures between 2005 and the last observation, which is 2010 or later (SI Materials and Methods, 2. A Local Measure of Climate Change). To be included, stations must have a minimum sample of 30, 40, or 50 y and be missing at most 5, 10, or 15 observations (SI Materials and Methods, 1. Datasets).

Values for TMax, High2005, and Low2005 are assigned to counties based on spatial proximity. All or any portions of a county are assigned to its nearest weather station based on Thiessen polygons created for each station, which assign an area closest to each station relative to all other stations (excluding water bodies) (Fig. S1). Spatially assigned values of TMax, High2005, and Low2005 are aggregated to counties (_c) in two ways: (i) as a county-wide mean and (ii) as a population-weighted mean (29). Population weights are defined as the percentage of voting age population living in any portion of the county (that has been assigned to the nearest weather station).

Each dataset is used to estimate the following regression:

$$\begin{array}{l}\%Belie{f}_c=\alpha +{\beta }_{1}TMa{x}_c+{\beta }_{2}High{2005}_c\times (TMa{x}_c\le 163)+{\beta }_{3}High{2005}_c\\ \times (163<TMa{x}_c\le 182)+{\beta }_{4}Low{2005}_c\times (182>TMa{x}_c\le 201)\\ +{\beta }_{5}Low{2005}_c\times (TMa{x}_c>201)+{\mu }_c,\end{array}$$ [2]

in which %Belief is the fraction of a county’s population that answers yes to the question “do you think that global warming is happening?” (1), α and β values are regression coefficients, and μ is the regression error that is estimated using ordinary least squares (OLS) and a spatial simultaneous lag model. We expect β₁, β₂, and β₃ to be positive (record warmth increases belief), whereas β₄ and β₅ should be negative (record cold reduces belief).

Because %Belief is a proportion observed on the interval (0,1), we also estimate Eq. 2 by applying a logit transformation to $\%Belie{f}_i$ as a check for robustness (Table S1). To account for spatial autocorrelation, Eq. 2 is estimated as a spatial simultaneous lag model of the form (SI Materials and Methods, 5. Spatial Regression):

$$y_c=\rho W{y}_j+X_c^{\text{'}}\beta +{\epsilon }_c,$$ [3]

in which $W$ is a K nearest neighbor row standardized weights matrix (K = 5), $W{y}_j$ is the spatial lagged values of c neighbors j, $\rho$ is a spatial autoregressive slope coefficient, $\beta$ is a vector of regression coefficient for all independent variables for observation c ($X_c$), and ${\epsilon }_c$ is an N × 1 vector of white noise error. Residuals from all OLS estimates show signs of significant spatial autocorrelation (P < 0.01) using the lm.morantest from R’s spdep package (30–32). The use of a spatial lag is validated (P < 0.01) for all datasets through robust versions of the Lagrange Multiplier test for spatially dependent linear models (28).