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The global increase in mean temperature¹ and its effects on organisms^{4, 12, 14, 15} are well documented. However, knowledge of mean temperature alone has important limitations when applied to problems of ecology^{16, 17}. Temperature has nonlinear effects on rates of biochemical processes, organism physiology, life history and population growth^{18, 19}, and ecological interactions²⁰. Because of these ubiquitous nonlinear effects of temperature, changes in temperature variation can have profound physiological and ecological impacts that match or even exceed the effects of mean temperatures^{8, 9, 21}. Understanding and predicting the biological consequences of climate change will require knowledge not only of changes in mean temperatures, but also of changes in temperature variation²².

So far, temporal temperature variation has primarily been described in terms of changing extremes^{1, 23}. Analyses of monthly and yearly averages of daily temperature extremes reveal that daily and annual minimum and maximum temperatures have increased across the globe since 1950¹. Larger increases in minimum temperatures have driven reductions in the differences between daily and seasonal extremes (diurnal temperature range and extreme temperature range), suggesting a global decrease in daily and annual temperature variation¹. However, the time window over which data are averaged can strongly affect not only the likelihood of detecting trends in temperature variability, but also the direction of those trends²². Further, the monthly and yearly temperature means analysed for these studies may be of limited relevance to most organisms, which have generation times of days to weeks^{10, 16}. Despite the potentially strong effects on organisms of daily temperature cycling^{9, 24}, efforts to characterize high-frequency climate variability have been hindered by data of insufficient temporal resolution and limited analytical techniques for estimating cycling patterns from high-frequency data²².

To assess changes in temperature variability at temporal scales relevant to organisms, we used a spectral technique to derive variability estimates directly from high-frequency weather station data. Spectral techniques have recently been applied to estimate changes in climate^{13, 25} and the biological impacts of those changes²⁶, but these and other standard approaches require regularly sampled data, which is usually generated by averaging temperatures across convenient time windows (for example, monthly means). Given the strong nonlinear effects of temperature on organisms, such averaging may hide much of the biologically-relevant signal.

The Lomb–Scargle periodogram can robustly identify the strengths of biologically-relevant periodicities (that is, one year or less) in time series with uneven sampling²⁷ (Methods and Supplementary Figs 1–3). We used the Lomb–Scargle periodogram, corrected for red noise²⁷, to estimate the ranges of diurnal and annual temperature cycling (DTC and ATC, respectively, twice the sinusoidal amplitudes; Methods and Supplementary Fig. 2), and deviations from diurnal and annual cycling (residual variation, Supplementary Figs 1 and 10) for individual weather station records from across the globe. The straightforward approach outlined here allows one to accurately capture most temperature variability (>90%, Supplementary Fig. 1, mean residual 0.04 °C, maximum 0.5 °C, Supplementary Fig. 10) with only two numbers: DTC and ATC. Modelling of instantaneous temperatures, which is often critical for projections of the ecological impacts of climate change²⁸, requires minimal additional parameters: mean temperature, the phases of DTC and ATC, and the distribution of residuals from the fit.

We first estimated global spatial variation in mean temperature and in temperature cycling by analysing over 1 billion temperature measurements from 7,906 weather stations that sampled over the period of 1 January 1926 to 31 December 2009 (Fig. 1 and Methods and Supplementary Fig. 6). Spatial variation in mean temperature of these stations matched expectations: mean temperature was essentially flat in the tropics and decreased roughly monotonically with increasing distance from the equator (Fig. 1a, e).

Each point represents a weather station (7,906 total) for which we determined (for the entire temperature record, longest record: 1926–2010): mean temperature (a,e), the range of diurnal temperature cycling (DTC; b,f), the range of annual temperature cycling (ATC; c,g), and the natural log of the ratio of DTC to ATC (ln(D/A); d,h). Right-hand figures show latitudinal variation in these variables, with latitude on the y axis, value on the x axis, and cubic spline fits (λ = 0.6) indicated by black lines. For each figure pair, the colour of the point indicates its value, with the scale shown on the right-hand plot. Grey dashed lines indicate tropical boundaries.

We obtained hourly temperature records from 21,369 global weather stations (Supplementary Information). We included only station records for which diurnal and annual cycling fits were both significant relative to an AR1 null expectation using χ² and Monte Carlo tests²⁷ (Supplementary Fig. 2; α = 0.01). Based on simulations (Supplementary Fig. 3), we included only stations that sampled at least every six hours on average, in all seasons, and that had no gaps in sampling more than 10% of the total record length. We excluded five Antarctic stations with small sections of aberrant temperature records (Supplementary Table 1). Finally, we excluded station records for which Lomb–Scargle (see below) and Redfit 3.8 (ref. 27) methods differed in raw estimates. After these exclusions, 7,906 station records remained and were used for analyses of the geographical distribution of temperature variation (Fig. 1). For anomaly analyses (Fig. 2), we included only stations (1,458) that sampled throughout the WMO standard normal period¹. We used the Lomb–Scargle periodogram to estimate the amplitudes of DTC and ATC (Methods and Supplementary Figs 2 and 3), and a modified Redfit 3.8 (ref. 27) to perform AR1 correction. To correct for the uneven spatial distribution of stations (Fig. 1 and Supplementary Fig. 6), we computed means of temperature metrics for all stations within 5° latitude by 5° longitude grid cells (483 total cells: 116 tropical, 244 temperate, and 123 polar). We weighted cell means and standard error means for biogeographic regions by area.

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