1 Introduction

A number of previous studies have found a positive relationship between temperature and the incidence of acts of interpersonal violence such as assault (see reviews by Anderson 2001; Anderson et al. 2000). If increasing temperatures precipitate violence, then anthropogenic climate change might be expected to result in higher rates of violence (Anderson and DeLisi 2011). This research area is therefore one of potential interest to researchers concerned with the impacts of climate change.

1.1 Geographical variation in temperature and interpersonal violence

One way to study the relationship between temperature and the incidence of interpersonal violence is to compare hotter and colder geographical regions. A positive relationship between geographical variation in temperature and homicide rate was found across countries in two international studies (Robbins et al. 1972; Rotton 1986). Anderson et al. (2000) also that temperature was a significant predictor of violent crime (with murder, rape and assaults as indicators) across 260 US cities. This relationship had a standardised effect size of 0.43 when controlling for socio-economic status, population level, and sociocultural “Southernness”.

1.2 Temporal variation in temperature and interpersonal violence

Another way to study the relationship between temperature and interpersonal violence is to examine the relationship between the incidence of interpersonal violence and variation in temperature within a region (temporal variation in temperature). Temporal variation in temperature can be broken down further into sub-components including seasonal and irregular (random) variation in temperature. In terms of seasonal variation in temperature, Anderson et al. (2000) reported a comparison of assault rates across seven Northern Hemisphere datasets, finding that monthly assault rates were higher in warmer months: More than 40 % higher in the hot month of August than in the cold month of January. Hipp et al. (2003) also found that violent crime rates in the United States were about 35 % higher at the summertime peak than at the winter nadir.

Another type of temporal variation in temperature is irregular variation: Random variation, not explained by regular seasonal fluctuations. Irregular variation in temperature can be studied in several different ways. One method is to aggregate data (e.g., at the annual level), such that the effects of seasonal variation are removed. A series of studies using this approach and data from the United States found a positive relationship between temperature and violent crime (Anderson et al. 1997, 2000; Anderson and DeLisi 2011; Rotton and Cohn 2003). Another way in which irregular variation in temperature can be examined is by using data at a finer temporal level of aggregation (e.g., by using days or even shorter intervals), but using temporal control variables (e.g., for the months of the year) to remove seasonal variation. Positive effects of temperature on assault incidence have also been found by studies using this approach (Cohn and Rotton 1997; Harries and Stadler 1983).

A meta-analysis of the effect of temperature on interpersonal violence was conducted by Hsiang et al. (Hsiang et al. 2013). Hsiang et al. ensured that each study included in their meta-analysis controlled for any differences between geographical areas (if more than one region was included within a study), and for the effect of time, meaning that their study focused on the effect of irregular variation in temperature. In some cases, these controls were applied in re-analyses of the original studies’ data. Their meta-analysis found a mean effect of a 2.3 % increase in interpersonal violence for each standard deviation increase in temperature.

1.2.1 Experimentally manipulated temperature

As well as the aforementioned field studies, some laboratory studies have also found an effect of temperature on aggressive behaviour. For example, a Dutch study found that police officers were more likely to draw weapons and shoot suspects in a simulated burglary when the temperature in the simulation room was hotter (Vrij et al. 1994). However, the effect of temperature on aggressive behaviour in experiments is not consistent enough to result in a significant effect when synthesised in a meta-analysis (Anderson et al. 2000). One explanation for the inconsistent findings in this area is that the mechanism via which temperature affects violence in the real world cannot operate in the laboratory: For example, if temperature increases precipitate violence by providing increased opportunities for interactions between potential offenders and victims (Cohn and Rotton 2000).

Given the lack of firm experimental evidence, it is worth considering whether the generally positive relationship between temperature and violence could be attributable to some confounding variable. The fact that an apparent effect of temperature has been observed regardless of whether the component of temperature variation examined is geographical, seasonal or irregular greatly reduces the list of plausible confounds. Cultural or demographic variables might explain a relationship between geographical variation in temperature and violence (as in Hipp et al. 2003), and changes in human activity patterns due to calendar events (e.g., increased vacationing in summer) might explain the relationship between seasonal variation in temperature and violence. However, neither of these potential confounds can explain why irregular variation in temperature is related to violent crime rates. Overall, a causal effect of temperature on violence is probably the most plausible reason for the relationship between temperature and interpersonal violence, although the specific mechanism of this relationship is subject to much uncertainty.

1.3 The mechanism of the temperature-violence relationship

A number of theories have been invoked to explain a relationship between temperature and the incidence of interpersonal violence. The general affective aggression model (Anderson et al. 1995) suggests that uncomfortable temperatures can increase aggressive cognitions and emotions and thereby increase the incidence of aggressive behaviour. Similarly, the negative affect escape model (Bell and Baron 1976; see also Bell and Fusco 1989) suggests that unpleasant situational variables such as uncomfortable temperatures can increase negative affect, and that negative affect increases aggressive behaviour. However, in the negative affect escape model this relationship is hypothesised to hold only up to an (unspecified) inflection point, beyond which extremely high levels of negative affect prompt escape from the situation. Whether non-linearity in the temperature-assault relationship exists such that very high temperatures prompt a decrease in assaults is a subject of some debate (Bell and Fusco 1989; Bushman et al. 2005; Cohn and Rotton 2005).

An alternative sociological theory is that warmer weather precipitates violent crime by increasing the probability that potential offenders and victims come into contact (Cohn and Rotton 2000). Finally, it is possible that warmer temperatures provoke violence by eliciting greater alcohol consumption (Harries and Stadler 1988). Indeed, alcohol sales tend to be highest in summer (Uitenbroek 1996), and there is strong evidence that alcohol consumption increases the risk of aggressive and violent behaviour (Bennetts and Seabrook 2008; Bushman and Cooper 1990; Ray et al. 2008).

1.4 Consideration of climate change

Most studies concerned with the relationship between temperature and interpersonal violence have been completed without an explicit consideration of what their findings imply for a future that involves a warming climate. One notable study that did pay explicit attention to climate change was Anderson and DeLisi (2011; see also similar earlier studies by Anderson et al. 1997, 2000). Anderson and DeLisi correlated national annual rates of serious and deadly assault in the United States for 1950–2008 with temperatures averaged across the 50 largest cities in the country. The authors estimated that were an extra 7.54 murders and assaults per 100,000 for each 1 °C temperature increase when controlling for year, autoregressive effects, and the proportion of the population in prison. They reported that this implied that an 8 °F (4.4 °C) temperature increase would lead to more than 100,000 extra serious and deadly assaults per year in a population of 305 million.

Another study that did explicitly consider climate change was Rotton and Cohn (2003). Cohn and Rotton analysed both US national data as well as cross-sectional time series assault data aggregated at state level (for 1960–1998). On the basis of this analysis they calculated a smaller effect of an extra 2.18 additional assaults per 100,000 p.a. for each 1 °C temperature increase. Finally, using a series of temperature anomalies from St. Louis, Missouri, Mares (2013) found that each 1 °F increase in temperature was associated with a 0.69 % increase in violent crime (1.25 % per 1 °C), and concluded that climate change may have a substantial effect on crime rates.

Of course, anthropogenic climate change is likely to comprise not just temperature increases but changes to other meteorological variables such as precipitation, wind, and tropical storm intensity. In this study we focus on the effects of temperature, primarily because future changes to other meteorological variables are subject to more uncertainty and are expected to be differ widely across geographical regions (see Reisinger et al. 2014 for projections for New Zealand). The large body of existing literature concerned with the relationship between temperature and violence also provides a basis for a concern that temperature increases in specific might have a detrimental effect on assault incidence. This said, we also briefly examine the effects of humidity, given the effect of humidity levels on thermoregulation and apparent temperature for humans.

1.5 Research aims

In this study, we aimed to investigate the relationship between geographical, seasonal, and irregular variation in temperature and the incidence of one important type of interpersonal violence—assault—in New Zealand. In order to further assess the plausibility of the hypothesis that global meteorological changes can affect assaults in New Zealand, we also examined the relationship between the El Niño Southern Oscillation (ENSO) and assaults in New Zealand. We aimed to use the information produced in our analyses to predict how rising temperatures may affect the incidence of violence in New Zealand in the coming decades. We present investigations of two separate datasets relating to the incidence of assault in New Zealand: Recorded assault data from the NZ Police, and assault hospitalisation data from the Ministry of Health.

Like those of most other studies in this research area, our empirical analyses are restricted for practical reasons primarily to observations about the relationship between human behaviour and the weather (i.e., relatively short term variation in meteorological conditions, particularly temperature). Our overarching goal is nevertheless to make tentative inferences about the effects of climate change on assaults (the term climate referring to the mean and variability of meteorological variables over a long period of time, classically 30 years; Planton 2013). Such inferences are necessarily subject to significant uncertainty: Humans may react differently to sustained climate changes than they do to short-term temperature variation.

2 Methods

2.1 Recorded assault data

Data listing daily recorded assaults from 1 July 1994 to 31 July 2009 within five police districts (Auckland City, Waitematā, Counties Manukau, Wellington, and Canterbury) were obtained from the New Zealand Police. The Auckland City, Waitematā, and Counties Manukau police districts all cover different areas of the wider Auckland region, and were thus combined into a single Auckland region.

2.2 Assault hospitalisation data

The New Zealand Ministry of Health provided a listing of all public hospital admissions in New Zealand with a discharge date between 1 January 1993 and 31 December 2009 where at least one of the causes of hospitalisation was assault. These data were collated by date of injury (not necessarily the date of admission) and the patient’s territorial authority area of domicile. Territorial authority areas are hereafter referred to as “districts”. Excluding the offshore Chatham Islands, there are currently 66 districts in New Zealand. Where assaults on multiple dates contributed to a hospitalisation, the most recent date of assault was utilised as the date of injury. Furthermore, where the same assault appeared to have caused multiple hospitalisations (i.e., when the patient and the most recent date of injury listed for two hospitalisations matched), only the first admission was counted.

The original source of the hospitalisation data was the national minimum dataset for hospital events. A problem with this dataset was the presence of inconsistencies in terms of whether or not short emergency department stays were recorded, with different reporting practices used by different district health boards, as well as changes in reporting practices occurring over time (see Ministry of Health 2012 for a discussion). We therefore followed the practice of the Ministry of Health in excluding emergency department stays of less than 2 days from analysis, resulting in the exclusion of 19,356 incidents. A further 703 hospitalisations with a district of “overseas/other” listed were excluded, as were five hospitalisations of patients living on the offshore Chatham Islands.

2.3 Population estimates and demographic data

Annual population estimates by police area and by district were obtained from Statistics New Zealand and interpolated to produce daily estimates. Ethnicity and age data by district were obtained from Statistics New Zealand as at the census years 1996, 2001, and 2006. Deprivation index (NZDep) values by area for the same three censuses were obtained from the University of Otago (Salmond et al. 2014). NZDep values were aggregated into a single average value for each district over these three time points. The NZDep is a measure of socioeconomic deprivation scaled to have M = 1000 and SD = 100.

2.4 Meteorological data

Meteorological data was obtained from the virtual climate network of the National Institute of Water and Atmospheric Research (NIWA 2015). This network uses a thin plate smoothing spline model to interpolate meteorological measurements on a regular 5 km grid across New Zealand (see Tait et al. 2006). Use of the virtual climate network avoided any problems with missing data or changing station locations that could arise from the use of physical stations. The virtual station used to represent each region or district was the closest station to the town centre of the largest town within that region or district. Southern Oscillation Index (SOI) values were obtained from the Australian Bureau of Meteorology (2015). The SOI is a measure of ENSO variability based on the seasonally adjusted mean sea level pressure difference between Tahiti and Darwin.

2.5 Ethical approval

The study received ethical approval from the Massey University Human Ethics Committee.

2.6 Data analysis and computation

Data analysis was completed using R version 3.1.1 (R Core Team 2013). Generalised linear mixed models were estimated using the function glmmPQL in the MASS package version 7.3-34 (Ripley 2014). A Poisson distribution and log link were used for almost all the models reported. glmmPQL includes a freely estimated residual variance term when estimating Poisson models, avoiding any problems with overdispersion.

2.7 Electronic supplementary materials

Further information about this study’s methods and results is available in the electronic supplementary materials for this article.

3 Results

3.1 Analyses of assaults recorded by the police

In this first subsection of the results, analyses of assaults recorded by the police are reported. Over the study period, there were 162,219 recorded assaults in Auckland, 46,838 in Canterbury, and 58,958 in Wellington (combined total 268,015). The mean number of recorded assaults per 100,000 was 846 p.a. in Auckland, 891 in Wellington, and 616 in Canterbury (combined mean 803 per 100,000 p.a.). The mean temperature at the city centre of each region was 15.3 °C in Auckland, 13.2 °C in Wellington, and 12.0 °C in Canterbury.

3.1.1 Form of the temperature-assault relationship

Scatterplots displaying the relationship between temperature and assault rates are displayed in Fig. 1. Loess smoothing was used to indicate a line of best fit in each case. These plots indicate firstly that the relationship between temperature and assault (for both recorded assaults and assaults resulting in hospitalisation) is relatively small in comparison to the wide variation in daily assaults. Secondly, there is little evidence of any marked deviation from linearity: The small positive relationship between temperature and assault held regardless of whether temperatures were cold, moderate, or hot. Linear or log-linear relationships were therefore assumed in the models estimated in this study. The estimated effects of seasonal and irregular daily variation in temperature within each region are reported in the subsections that follow.

Fig. 1
figure 1

Scatterplots of temperature and recorded assaults in Auckland, Wellington, and Canterbury, and of temperature and assaults resulting in hospitalisation (nationally averaged). Lines of best fit shown using loess smoothing (span = 0.5, degree = 2)

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3.1.2 Seasonal variation in temperature and recorded assaults

In all three regions, assaults were least frequent in June (winter), as is visible in Fig. 2. The peak month was December for both Auckland and Wellington, and November in Canterbury.

Fig. 2
figure 2

Mean daily recorded assaults by month and region

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The effect of seasonal variation in temperature on recorded assaults was estimated using a generalised linear mixed model estimated within each of the three regions using a Poisson distribution. In this model, the predictor variable of interest was the mean temperature on each of the 365 days of the calendar year as averaged across the entire study period within each region (i.e., the seasonal norm temperature). The response variable was the summed number of assaults occurring in a region across each of the 15 occurrences of each day of the calendar year over the study period. In order to ensure that each day of the year had the same number of instances, the period analysed was restricted to 1 August 1994–31 July 2009, and February 29 was excluded. The intercept was free to vary randomly across regions, removing any effect of geographical variation in temperature. The effect of population was included as a control variable, following a log transformation; in combination with the log link function, this allowed population size to have an additive effect. One autoregressive term was specified for the error terms in order to deal with short-term residual autocorrelation.

When entered as the sole predictor apart from population, the coefficient for seasonal variation in temperature was positive, \( \widehat{\beta} \) = 0.014, 95 % CI [0.011, 0.017]. However, if daylength was controlled as an additional predictor, the estimated effect of temperature fell to nearly zero, \( \widehat{\beta} \) = −0.004, 95 % CI [−0.008, 0.0003]. The log of daylength (in hours) had a larger effect of \( \widehat{\beta} \) = 0.461, 95 % CI [0.378, 0.543], implying that every 10 % increase in daylength is associated with a 1.100.451–1 = 4.5 % increase in assaults. Seasonal variation in temperature and daylength were correlated an average r = 0.79 across regions.

3.1.3 Irregular daily variation in temperature and recorded assaults

Irregular daily variation in temperature was captured by calculating the difference between the temperature observed in a region on a given date and the seasonal norm temperature (as defined above). Across dates and districts, the standard deviation of these temperature anomalies was 2.2 °C, with a range of −8.0 to 8.7 °C. The effect of irregular temperature variation was estimated again using a generalised linear mixed model, with a Poisson distribution, and population size controlled. Intercepts were free to vary across both regions and years (within regions), allowing for a flexible control for any omitted time-varying confounders. The response variable was simply the number of assaults occurring on a given date within a region. Dummy variables for month and weekday and a single autoregressive term for the error structure were included in order to account for residual autocorrelation. In this model, the estimated effect of temperature was \( \widehat{\beta} \) = 0.015, 95 % CI [0.012, 0.017], or around 1.5 % more assaults for every 1 °C increase in temperature. This coefficient also implies that a standard deviation (2.18 °C) increase in temperature anomaly was associated with an e 0.015*2.18–1 = 3.3 % increase in assaults.

If the effect of temperature was permitted to vary across regions, it was very similar in each case: \( \widehat{\beta} \) = 0.014 in Auckland and Canterbury, and 0.017 in Wellington. The lagged effects of temperature anomalies on recorded assaults were also investigated with lags up to 7 days in an alternative model, but all of the lagged effects were very small (\( \left|\widehat{\beta}\right| \) < 0.003) and not statistically significant. When the relative humidity anomaly (%) was added to the model along with temperature, it had a very small negative main effect \( \widehat{\beta} \) = −0.001, 95 % CI [−0.001, −2.3 × 10−4], while there was no evidence of an interaction between relative humidity and temperature, \( \widehat{\beta} \) = 2.0 × 10−4, 95 % CI [−1.4 × 10−5, 4.1 × 10−4].

3.1.4 Trends in recorded assaults and temperature

Year-to-year trends in recorded assaults and mean temperature (averaged across the three regions studied) are displayed for descriptive purposes in Fig. 3. There was a slight positive trend in assault rate, with an increase of 3.2 extra assaults per 100,000 per year.

Fig. 3
figure 3

Trends in recorded assaults and temperature; averaged across Auckland, Wellington, and Canterbury

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3.1.5 Recorded assaults and ENSO

High SOI values indicate La Niña conditions, which tend to be associated with warmer temperatures in most of New Zealand (Wratt et al. 2015). During the study period, the correlation between SOI values and monthly mean temperatures (averaged across Auckland, Wellington and Canterbury) was r = 0.17. The correlation between monthly SOI values and the mean number of recorded assaults per 100,000 per day (aggregated across Auckland, Wellington and Canterbury) was r = 0.24, 95 % CI [0.10, 0.37]. A linear mixed model was also estimated with the sum of assaults across Auckland, Wellington and Canterbury in each month as the response variable, a random effect for year to control for any omitted time-trending confounds, and a Poisson distribution with log link. In this model the coefficient for SOI remained positive, \( \widehat{\beta} \) = 0.002, 95 % CI [0.001, 0.004]. Given that SOI values are scaled to have a long-term standard deviation of ten, this coefficient suggests a 2 % increase in assaults for every 1σ increase in SOI.

3.2 Analyses of hospitalisation data

In this second subsection of the results, we report analyses based on nationwide assault hospitalisation data. The use of nationwide data allowed for the study of the effects of geographical variation in temperature as well as of irregular and seasonal variation. There were a total of 44,745 assaults resulting in hospitalisation over the study period of 1993 to 2009, or 67 incidents per 100,000 p.a. As mentioned previously, this dataset excludes short emergency department stays. It is nevertheless clear that the rate of assault resulting in hospitalisation is much smaller than that of recorded assaults. There was a moderately strong correlation, r = 0.52, between the number of daily recorded assaults across the Auckland, Wellington and Canterbury regions and the number of assaults resulting in hospitalisation in the 17 districts roughly comprising those regions.

3.2.1 Seasonal variation in temperature and assaults resulting in hospitalisation

As for recorded assaults, assaults resulting in hospitalisation were most common in the warmer months (with a peak of 0.21 daily assaults per 100,000 in December), and least common in the colder months—although the nadir was actually in the autumn month of April (0.16 per 100,000 per day).

The effect of seasonal variation in temperature was estimated using a generalised linear mixed model. Seasonal variation in temperature was operationally defined as the seasonal norm (mean) temperature of each of the 365 days of the calendar year within each district, across the entire study period. The response variable was the number of assaults resulting in hospitalisation for each of the 365 days of the calendar year, also across the entire 17-year study period (i.e., the sample size was 365 calendar days*66 districts = 24,090). Population size was controlled, and the intercept was free to vary across districts to account for geographical differences in assault rate. There was little evidence of autocorrelation in these analyses (e.g., average lag 1 r = 0.03 across districts), so error correlations were not included in the model.

The resulting estimate of the effect of seasonal variation in temperature was fairly large, \( \widehat{\beta} \) = 0.023, 95 % CI [0.020, 0.026]. However, when daylength was added as a control variable, the effect of seasonal variation in temperature again seemed to nearly disappear, falling to \( \widehat{\beta} \) = 0.004, 95 % CI [−0.001, 0.009]. Seasonal variation in temperature and daylength were correlated an average r = 0.82 across districts.

3.2.2 Irregular daily variation in temperature and assaults resulting in hospitalisation

The effect of irregular variation in temperature on assaults resulting in hospitalisation was estimated using a generalised linear mixed model. A Poisson distribution was specified, with population size controlled, and the intercept again free to vary across both districts and years within districts. The response variable was the number of assaults resulting in hospitalisation occurring on a given date within a district, resulting in a sample size of 6209 dates*66 districts = 409,794. Inspection of the residuals indicated that virtually no autocorrelation was present in these analyses, so neither autoregressive terms nor dummy variables for month and weekday were included.

The estimated effect of temperature in this analysis was \( \widehat{\beta} \) = 0.017, 95 % CI [0.013, 0.021], suggesting about 1.7 % extra assaults for every 1 °C increase in temperature. The potential lagged effects of temperature anomaly on assaults resulting in hospitalisation were again investigated with lags up to 7 days in an alternative model. There was a statistically significant positive effect at lag 1, \( \widehat{\beta} \) = 0.007, and a significant negative effect at lag 6, \( \widehat{\beta} \) = −0.008. However, the lagged effects were all small in size and mixed in sign, suggesting little evidence of a substantial lagged effect of temperature. When the humidity anomaly was added to the model, it had no substantial main effect, \( \widehat{\beta} \) = −0.0007, 95 % CI [−0.0017, 0.0003], although there was a positive interaction between temperature and humidity, \( \widehat{\beta} \) = 0.0006, 95 % CI [0.0002, 0.0010], implying a greater effect of temperature at higher humidity levels (or vice versa).

3.2.3 Geographical variation in temperature and assaults resulting in hospitalisation

The mean temperature by district varied from 9.5 °C at Queenstown-Lakes to 15.8 °C in the Far North District. The correlation between mean temperature and the rate of assaults causing hospitalisation by district was positive, r = 0.41, 95 % CI [0.18, 0.59]. A generalised linear model was also used to estimate the effect of geographical variation in temperature on assaults resulting in hospitalisation by district, as summed across the study period. Using a similar method to the models reported previously, albeit without the need for any random effects, a quasi-Poisson model was estimated. The effect of population size was controlled.

This simple model resulted in a large positive coefficient for temperature, \( \widehat{\beta} \) = 0.113, 95 % CI [0.053, 0.175]. However, a second model was also estimated including demographic controls: The percentage of each district’s population that were European, the percentage Māori (European and Māori being the two largest ethnic groups in NZ), the percentage aged 15–39, the percentage 40–64, and the percentage 65+. After these controls, there was no evidence of a positive effect of temperature, \( \widehat{\beta} \) = −0.029, 95 % CI [−0.089, 0.031]. The only demographic control with a statistically significant coefficient was the percentage Māori, \( \widehat{\beta} \) = 0.022, 95 % CI [0.009, 0.035].

We also estimated a third model controlling for regional differences in socioeconomic deprivation, along with the other demographic variables from the second model mentioned above. In this third model, the effect of temperature remained more or less unchanged, \( \widehat{\beta} \) = −0.026, 95 % CI [−0.085, 0.034]. Deprivation level itself had only a small relationship with assault incidence, \( \widehat{\beta} \) = 0.003, 95 % CI [−0.001, 0.007].

4 Discussion

Our analysis of the relationship between irregular daily variation in temperature and recorded assault incidence suggested a modest positive effect of temperature, with around 1.5 % more assaults for every 1 °C increase in temperature. This implies around 3.3 % extra assaults for each 1σ temperature increase. This estimate is reasonably similar to the 2.3 % per 1σ estimate found in a meta-analysis by Hsiang et al. (2013). Interestingly, the relationship between irregular variation in temperature and assault was very similar in size to that found between temperature and suicide in a recent New Zealand study (1.8 % per °C in Williams et al. 2015). The estimated effect of temperature on assaults resulting in hospitalisation (i.e., the most serious assaults) was very similar to the effect on recorded assaults. An analysis of the relationship between ENSO and recorded assaults also suggested a similar effect size of a 2 % increase in assaults per 1σ SOI increase, demonstrating the plausibility of a link between global meteorological conditions and assault incidence in New Zealand.

Bivariate analyses of seasonal and geographical variation in temperature similarly suggested that assaults were higher during warmer times of the year, and in warmer geographical regions, echoing the findings of previous studies (e.g., Anderson et al. 2000; Hipp et al. 2003). However, the apparent positive effects of these two forms of temperature variation were not robust to controls for daylength (for seasonal variation), or age and ethnicity (for geographical variation). These components of temperature variation are admittedly subject to potential confounding by variables other than those controlled: Other demographic and socioeconomic variables may confound the analysis of geographical variation, while seasonal patterns of human activity not directly caused by temperature may confound the analysis of the effects of seasonal variation in temperature. As such, the estimates reported for the effects of these components of variation may be either upwardly or downwardly biased. The analyses of seasonal and (especially) geographical variation in temperature were also subject to much greater sampling error than the analysis of irregular daily variation: The analysis of geographical variation in temperature and assault was based on a sample size of just 66 districts. As such, sampling error might be to blame for the lack of evidence for a positive effect of temperature in the controlled multivariable models.

This said, despite their limitations, analyses of seasonal and geographical variation do have an advantage over analyses of irregular daily variation in temperature. These analyses allow for some examination of the effects of sustained and predictable differences in temperature as opposed to random day-to-day variations. As such, they may have some value when attempting to draw inferences about the likely effects of sustained climate change. The fact that we did not find strong evidence that seasonal and geographical differences in temperature had a positive effect on assault incidence implies uncertainty about whether climate change will have an effect on assault rates that is adequately approximated by the apparent effects of irregular, day-to-day variation in temperature.

Another source of information bearing on the potential effect of sustained climate change is the analysis of relationship between long-term trends in temperature and violence. Such an analysis requires a longer time series than that examined in this study, although little obvious relationship was apparent between the trends in temperature and assault incidence over the study period (see Fig. 3).

4.1 The relationship between temperature and assault: Form and mechanism

The analyses used in our study assumed linear relationships between temperature and (the logarithm of) assault counts. Some previous studies have found evidence of a reduction in assaults with very high temperatures, with an inflection point of around 90 °F (32.2 °C; Bell and Fusco 1989; Cohn and Rotton 2005; Gamble and Hess 2012). We did not find evidence of such a non-monotonic relationship, although temperatures in New Zealand do not generally reach levels high enough to test this proposition (the highest daily mean temperature observed in the study data was 27.7 °C). Non-monotonicity in the relationship between temperature and interpersonal violence is a prediction of one theory that might explain the relationship between these two variables: the negative affect escape model (Bell and Baron 1976). As mentioned in the introduction, other explanations that have been advanced in the literature include an effect of temperature on opportunity for violence (Cohn and Rotton 2000), an effect of thermal discomfort on aggression (Anderson et al. 1995), and the hypothesis that higher temperatures increase alcohol consumption. We did not report any tests of these theories in the present study: these theories make only qualitative (and not quantitative) predictions about how temperature will affect violence, and as such, they cannot be used directly to generate quantitative predictions about future changes in interpersonal violence that may occur due to climate change. As such, their practical value when attempting to draw inferences about the effects of climate change may be somewhat limited.

This said, the observation that temperature had a positive relationship with assault incidence even at relatively cold temperatures is inconsistent with the idea that the relationship between temperature and assault occurs because warmer temperatures produce discomfort. Similarly, our analyses of the effect of humidity have some bearing on the plausibility of the theory that assaults rise in hotter temperatures due to thermal discomfort. In the recorded assault data, irregular variation in humidity had a negative main effect on assault incidence, and no significant interaction with temperature. These findings are not consistent with the thermal discomfort theory, since higher humidity levels increase thermal discomfort in warm weather. Previous studies have similarly found small or even negative relationships between humidity and assault incidence (Gamble and Hess 2012; Rotton and Cohn 2000, 2004). On the other hand, our findings when analysing assaults resulting in hospitalisation were a little more consistent with the thermal discomfort theory: No statistically significant main effect of humidity was found, but there was a significant and positive interaction between temperature and humidity.

4.2 How will rising temperatures affect rates of interpersonal violence?

Projections for regional warming in New Zealand were reported by the Ministry for the Environment (2008). Across twelve general circulation models and six emissions scenarios the mean estimate of warming by 2090 was 2.1 °C. Perhaps the best estimate of the effect of temperature available in our study can be obtained from the analysis of the effects of irregular daily variation in temperature on recorded assaults, irregular variation being the component of variation least vulnerable to confounding. The resulting coefficient for temperature of 0.015 and its 95 % confidence interval of [0.012, 0.017] implies that a 2.1 °C increase in temperature might result in between 2.6 and 3.7 % more assaults than would otherwise occur. However, across all the models reported in this article—including those analysing the effects of seasonal and geographical variation in temperature—the best estimate of the effect of a 2.1 °C increase in temperature ranged widely. The projections vary from a 5.9 % decrease in assaults (based on the geographical variation model for hospitalisations with age and ethnicity controlled), to a 26.9 % increase (based on the same model without demographic controls). This range of predictions suggests the presence of substantial uncertainty about the effect of temperature on future assaults.

Furthermore, even if climate change does have an increasing effect on assault rates, this does not necessarily imply that the actual future assault rate in New Zealand will be higher than today’s. Any effect of rising temperatures may be superimposed on other changes in the assault rate, including phenomena such as the long-term decline in human violence in recent centuries and millennia (Pinker 2011).

On the other hand, climate change may affect interpersonal violence via mechanisms that may not have observable effects in the data studied here, meaning that there is a risk that the models estimated in this study could underestimate the true effect of climate change on assault incidence. Anderson and DeLisi (2011) suggest, for example, that food scarcity and environmental disasters may increase violent crime rates. Agnew (2011) argues that climate change will increase crime via a number of pathways, including impacts on social strain, support and control structures, and social conflict arising due to competition over scarce resources, migrations, and poverty. As well as potential effects on interpersonal violence, climate change may also impact the probability of conflict between groups and states by compromising economic security, culture, and identity, altering migration flows, and harming the ability of states to provide important infrastructure and public services (Adger et al. 2014). Indeed, there is some empirical evidence that temperature increases heighten the probability of intergroup conflict (e.g., Hsiang et al. 2013), although this hypothesis is still contested in the literature (Adger et al. 2014; Salehyan 2008). Given that global warming of the magnitude likely over the following century has not been observed since long before humans started to collect assault statistics, producing accurate predictions about how the incidence of violence will change in a warming world remains a challenging task. Despite the positive relationship between temperature and the incidence of interpersonal violence, great uncertainty remains about how the incidence of violence will change in a warming world.