Trends in hemispheric warm and cold anomaliesScott M. Robeson1, Cort J. Willmott2, and Phil D. Jones3,4

1Department of Geography and Department of Statistics, Indiana University, Bloomington, Indiana, USA, 2Department ofGeography, University of Delaware, Newark, Delaware, USA, 3Climatic Research Unit, School of Environmental Sciences,University of East Anglia, Norwich, UK, 4Center of Excellence for Climate Change Research/Department of Meteorology,King Abdulaziz University, Jeddah, Saudi Arabia

Abstract Using a spatial percentile approach, we explore the magnitude of temperature anomaliesacross the Northern and Southern Hemispheres. Linear trends in spatial percentile series are estimated for1881–2013, the most recent 30 year period (1984–2013), and 1998–2013. All spatial percentiles in bothhemispheres show increases from 1881 to 2013, but warming occurred unevenly via modification of coldanomalies, producing a reduction in spatial dispersion. In the most recent 30 year period, trends alsowere consistently positive, with warm anomalies having much larger warming rates than those of coldanomalies in both hemispheres. This recent trend has largely reversed the decrease in spatial dispersion thatoccurred during the twentieth century. While the period associated with the recent slowdown of globalwarming, 1998–2013, is too brief to estimate trends reliably, cooling was evident in NH warm and coldanomalies during January and February while other months in the NH continued to warm.

1. Introduction

Near-surface temperature time series contain essential information for analyzing changes in the centraltendency of Earth’s thermal climate. Analyses of the near-surface instrumental record have shown that Earth’smean temperature has increased at a rate of approximately 0.06°C decade�1 from 1880 to 2012, increasing toover 0.15°C decade�1 from 1979 to 2012 [Hartmann et al., 2013]. The rate of global scale warming slowed to0.05°C decade�1 from 1998 to 2012 [Morice et al., 2012; Fyfe et al., 2013]. While changes in global meantemperature are a primary indicator of climate change, analyzing temperature observations at the globalscale integrates away important spatial detail.

The spatial arrangement and magnitude of temperature anomalies can shift dramatically from month tomonth, resulting in noisy time series at individual grid points when analyzed independently [Franzke, 2012;Robeson, 2004; Santer et al., 2011]. Meaningful trends calculated at fixed locations, therefore, can be difficultto detect, which is one of the reasons that large-scale spatial averages are frequently used. Here we use arelatively new and straightforward approach [Willmott et al., 2007; Nickl et al., 2010] to estimate the empiricalspatial distribution of temperature anomalies across each hemispheric surface. While shifts in spatialdistributions have been considered elsewhere [Donat and Alexander, 2012; Hansen et al., 2012; Huntingfordet al., 2013], trends in spatial frequency distributions of global or hemispheric temperature anomalies havenot been estimated empirically. This approach allows us to distinguish trends in warm and cold anomaliesand also to estimate spatial dispersion of temperature anomalies at the hemispheric scale.

2. Data and Methods

All results are derived from analyses of gridded HadCRUT4 data, which is a blend of the CRUTEM4 land-basedair temperature data [Jones et al., 2012] and the HadSST3 sea surface temperature data [Kennedy et al., 2011],both of which are gridded at 5° × 5° resolution. HadCRUT4 is a monthly temperature data set based onobservations to produce anomalies that are relative to a 1961 to 1990 base period. No spatial interpolation isapplied to estimate missing grid point values so data are provided only at those grid boxes that have validtemperature observations for a given month. The lack of infilled data provides an advantage in the currentanalysis as most methods of spatial interpolation smooth the spatial field and diminish the estimation ofthe magnitude and spatial dispersion of grid point anomalies [Ensor and Robeson, 2008]. As a result, theHadCRUT4 data set provides temperature estimates such that adjacent grid boxes use different observations,whereas an interpolated data set—and those produced through reanalysis—artificially increases spatial

ROBESON ET AL. ©2014. American Geophysical Union. All Rights Reserved. 9065

PUBLICATIONSGeophysical Research Letters

RESEARCH LETTER10.1002/2014GL062323

Key Points:• Cold anomaly trends from 1881 to2013 exceed those of warm anomalies

• Spatial dispersion of temperaturedecreased from 1881 to 2013

• Trends from 1984 to 2013 reversed thatpattern and increased spatial dispersion

Supporting Information:• Readme• Figures S1 and S2

Correspondence to:S. M. Robeson,srobeson@indiana.edu

Citation:Robeson, S. M., C. J. Willmott, andP. D. Jones (2014), Trends in hemisphericwarm and cold anomalies, Geophys. Res.Lett., 41, 9065–9071, doi:10.1002/2014GL062323.

Received 23 OCT 2014Accepted 20 NOV 2014Accepted article online 25 NOV 2014Published online 17 DEC 2014

covariance via the filtering and smoothing operations inherent in these approaches. While HadCRUT4 doesnot explicitly use the spatial covariance of the temperature field, the spatial percentile approach used here(and described below) produces temperature anomaly estimates that tend to be produced by cohesivespatial structures (Figure 1). The specific HadCRUT4 data used here (version HadCRUT4.2.0.0) are the mediansof the 100 ensembles for each grid box. The use of the medians of the ensembles provides temperatureanomaly estimates at each grid point that are resistant to slowly varying observational error [Morice et al.,2012]. The use of monthly mean temperature helps to offset any differential observational bias that mayoccur in minimum or maximum temperature data [Hubbard et al., 2004].

Our use of spatial percentiles builds on the concept of a geographic box plot [Willmott et al., 2007], which uses anarea-weighted percentile approach. In the framework of latitude-longitude data structures used within globaltemperature data sets, ordinary percentiles produce biased representations of the spatial distribution, as theydo not consider the area of each grid box. When calculating spatial percentiles, we sort eachmonth’s temperatureanomalies and then use the cumulative area of the grid boxes—rather than cumulative frequency—to determinethe hemispheric value associated with a given percentile. No interpolation between observed values is neededto calculate a spatial percentile, as each grid box represents a discrete area of the hemispheric surface. As aresult, for gridded temperature anomaly data, the Pth spatial percentile is the anomaly such that P%of the studyarea has a value less than or equal to that temperature anomaly. Conversely, [100� P%] of the study area hasvalues greater than that temperature anomaly. Just as an interquartile range is a robust measure of dispersionwithin a sample, the differences between the 95th spatial percentile (P95) and the 5th spatial percentile (P5)represent hemispheric scale spatial dispersion. To evaluate whether our results are an artifact of choosing theseparticular percentiles, we also show results for all spatial percentiles between the 5th and the 95th.

We separated the HadCRUT4 gridded data by hemisphere, as spatial patterns of temperature anomalies inthe two hemispheres are largely independent. Using HadCRUT4 data for all months from 1881 to 2013, wequantified the 1st to the 99th spatial percentiles, thereby estimating the empirical spatial distribution oftemperature anomalies across each hemispheric surface. A linear trend for each spatial percentile then isestimated using ordinary least squares regression.

To evaluate the effects of changing spatial coverage in the HadCRUT4 data set, we performed frozen gridanalyses [Jones et al., 1986] by determining which grid points had at least 80% and 90% data availability overthe 1881–2013 period and then repeated the entire analysis using only those grid points. Overall, the resultsshown below (in section 3) using all data are very similar to those for both 80% and 90% frozen grids, indicatingthat changes in spatial data coverage are not the cause of the observed trends in warm and cold anomalies.

Figure 1. Maps of temperature anomalies for January 2007, which is the warmest month in the Northern Hemisphereinstrumental record with a hemispheric mean temperature anomaly of 1.298°C: (a) observed spatial distribution of temperatureanomalies and (b) those grid cells that contribute to the 95th (shades of red) and 5th (shades of blue) spatial percentiles. Grid cellswithmissing data are indicated with an “x”. Warm and cold anomalies estimated using spatial percentiles (which use area of gridcells rather than their frequency) are not necessarily spatially contiguous, but they tend to have cohesive spatial structures.

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The spatial percentile approach is not sensitive to the absolute position of temperature anomalies butconveys the spatial dispersion across the domain of interest. Therefore, a pattern that merely shifts positionfrom month to month would produce no change in spatial percentiles while producing temporal variability(noise) at fixed locations. For presentation purposes, we show linear trends in the 5th to the 95th spatialpercentiles by 5 percentile increments. The tails of the spatial distribution, in this case represented by the 5thand 95th spatial percentiles, are useful indicators of cold and warm anomalies, respectively. Cold or warmanomalies of that size are extensive—larger than the area of Canada (3.9% of the area of the NH) and slightlysmaller than the area of Antarctica (5.5% of the area of the SH). The time series of the middle of the spatialdistribution—or hemispheric medians—also are used as reliable indicators of central tendency and as basesto evaluate changes in the tails of the spatial distribution.

3. Results

To examine time series for individual months, the 5th, 50th, and 95th spatial percentiles (P5, P50, and P95) forJanuary and July for the NH and SH, alongwith their trends from 1881 to 2013, are shown in Figure 2. The spatialpercentile approach provides a simple, powerful, and novel approach to estimating the magnitude andvariability of cold and warm temperature anomalies, both of which are central features of the climate system.

While all three spatial percentiles in both hemispheres have positive trends over 1881–2013, it is clear that trendsare somewhat larger in the tails of the NH distribution and that temperature anomalies in the SH generally havemuch smaller magnitude and temporal variability. The 5th and 95th spatial percentiles in January demonstratethe large interannual variability during cold season months in the NH, as stronger land-ocean contrasts andassociated circulation variations produce large spatial gradients in temperature anomalies during NH cold seasonmonths [Wallace et al., 1995]. The large interannual variation in warm and cold anomalies in the NH ismodulated in the hemispheric median (black line in Figure 2). Although long-term and 30 year trends in thehemispheric median and mean are very similar, the influence of large temperature anomalies in the tails of thespatial distribution can produce hemispheric means that differ from the median for any given month.

Figure 2. Time series and linear trends of 95th (red), 50th (black), and 5th (blue) spatial percentiles of HadCRUT4 temperatureanomalies from 1881 to 2013: (a) NH January, (b) SH January, (c) NH July, and (d) SH July. Each spatial percentile gives thetemperature anomaly for a given area of the hemispheric surface (e.g., 5% of the hemisphere is colder than the 5th spatialpercentile and 5% of the hemisphere is warmer than the 95th spatial percentile). Slopes of linear trends (“b”) are given in°C decade�1. Warm and cold anomalies in NH cold season months, such as January, have much greater interannualvariability than NH warm season months or any time of year in the SH.

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Cold anomaly trends in Figure 2 are consistently larger than the trends for warm anomalies, representing adecrease in the spatial dispersion of temperature in both hemispheres. Quantitative trend estimates in allspatial percentiles from 1881 to 2013 substantiate this reduction in spatial dispersion for all times of the yearacross both hemispheres (Figure 3). Rates of change in cold anomalies during the cold season in the NH areparticularly large and exceed 0.1°C decade�1 in most months. In both the NH and SH, cold anomalies havesubstantially larger trends than those in the hemispheric medians (or other central parts of the spatialdistribution), signifying that both hemispheres warmed unevenly from 1881 to 2013 through enhancedmodification of cold anomalies. The pattern in the NH, where both cold and warm anomalies have warmedfaster than the central parts of the spatial distribution, is clearly different from the SH where warming incold anomalies dominated. To address the question of which grid points are driving the results, two sets ofmaps that show the frequencywithwhich a grid point contributes to the 5th and 95th spatial percentiles for theNH and SH are provided in the supporting information (Figures S1 and S2). The extreme cold and warmanomalies occur primarily—but not exclusively—over land in the NH, while the SH response is driven by moreof a mixture of land and ocean grid points. Even in the NH, however, it remains important to blend land andocean grids as many extreme anomalies are composed of a combination of land and ocean data. The maskingof land or ocean grid points would truncate the spatial arrangement of anomalies, making them disjunct.

While quasi-linear, the time series of the 5th and 95th spatial percentiles (Figure 2) show that decadal scaletrends in warm and cold anomalies, especially in the NH, have not been monotonically linear or positive.There has been considerable variability in the magnitude and sign of decadal scale trends in both warm andcold anomalies, particularly during the cold season in the NH. Nonlinear approaches can provide meaningfulestimates of recent temperature change [Ji et al., 2014], but we focus on contemporary rates of change inwarm and cold anomalies for the most recent 30 year period (1984–2013) and the 16 year period from 1998to 2013, the period when the rate of global warming slowed considerably. With respect to the most recent30 year period, there was substantial hemispheric scale warming (Figure 4). Rates of change in the mediantemperature anomaly in the NH were consistently higher than the SH median, with trends around 0.2°Cdecade�1 for all months (Figure 4a). Median anomalies in the SH warmed at a rate of about 0.1°C decade�1

across all months (Figure 4b). For most months, cold and warm anomalies in the NH warmed at rates that

Figure 3. Linear trends (°C decade�1) in the 5th to the 95th spatial percentiles (by increments of 5 percentiles) of eachmonth’s temperature anomalies for 1881–2013: (a) Northern Hemisphere and (b) Southern Hemisphere. Nearly allmonths have trends in the 5th spatial percentile that exceed those in the 95th spatial percentile, indicating a decrease inspatial dispersion over this time period.

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exceeded the hemispheric median from 1984 to 2013. Warm NH anomalies, in particular, warmed at veryhigh rates, with several months having trends exceeding 0.5°C decade�1. In nearly all months in bothhemispheres, warm anomaly trends exceeded those of cold anomalies, indicating an increase in spatialdispersion in the recent temperature record. Difference time series between the 95th and 5th percentileconfirm that the decrease in spatial dispersion that occurred during the 20th century has largely beenreversed in the last 30 years (this is evident for January and July in Figure 2). Overall, there was considerablewarming across the entire spatial distribution of both hemispheres from 1984 to 2013, but a nontrivialamount of the change in the NH occurred through enhanced warming of warm anomalies.

We also extended the analysis of warm and cold anomalies to 1998–2013 in which there has been a documented“pause” in global warming [Fyfe et al., 2013; Easterling and Wehner, 2009; Kaufmann et al., 2011]. The tails of thespatial distribution of anomalies in the NH show a distinctive pattern of cooling in January and February andwarming from March to November (Figure 5), consistent with the results of Cohen et al. [2012] and Seneviratneet al. [2014]. In the SH, the months from January to July show a distinct pattern of warming in cold anomaliesand cooling in warm anomalies. While the cold season in the NH shows substantial cooling in both cold andwarm anomalies, especially during February, cold and warm anomalies from March to November showmoderate warming. Overall, however, this brief period makes meaningful trend detection difficult, particularlygiven that pauses in warming of this duration have occurred throughout the historical record [Lovejoy, 2014].

4. Discussion and Summary

Our results show that trends in extreme warm and cold anomalies produced an overall reduction in spatialdispersion in both hemispheres during 1881–2013. This long-term trend largely reversed itself in the mostrecent 30 year period, where warm anomaly trends have exceeded cold anomaly trends by a wide margin.Trends in all NH spatial percentiles were particularly large from 1984 to 2013 and exceeded 0.1°C decade�1,with trends in warm anomalies exceeding 0.4°C decade�1 in most months. The period associated with the“pause” in global warming (1998–2013) has intriguing patterns of strong cooling in both cold and warmanomalies during NH winter and continued warming at other times of year. The SH, on the other hand,showed a pattern of warming in cold anomalies and cooling in warm anomalies (and almost no change in

Figure 4. Linear trends (°C decade�1) in the 5th to the 95th spatial percentiles (by increments of 5 percentiles) of eachmonth’s temperature anomalies for 1984–2013: (a) Northern Hemisphere and (b) Southern Hemisphere. In this mostrecent 30 year period, trends in the 95th spatial percentile exceed those in the 5th spatial percentile, indicating an increasein spatial dispersion. Note the different y axis scale from Figure 3.

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central tendency) during January through July, with modest warming in other months. But this period isconsidered too short to reliably determine meaningful trends. Overall, however, it is clear that warm and coldanomalies in the NH are the most dynamic feature of Earth’s near-surface thermal climate and can have largeswings over decadal timescales. Many of the most extreme warm and cold anomalies tend to occur incontinental locations between 40 and 70°N, such that changes in warm and cold anomalies in high-latitudenorthern continents are clearly important indicators of interannual global temperature variability.

Recent research has linked cold extremes in the northern midlatitudes to declining Arctic sea ice extent [Hondaet al., 2009; Tang et al., 2013]. While anomaly trends in themost recent 30 year period indicate strongwarming inall spatial percentiles in the NH, spatial dispersion increased markedly over this period, which is consistent withan increase in amplified planetary waves in the midlatitudes [Screen and Simmonds, 2014]. Conversely, trendsfrom 1998–2013 show cooling in both cold and warm anomalies during the cold season, with particularly largenegative trends in February. These recent temperature anomaly trends have large uncertainty but are consistentwith the hypothesized link of Arctic temperature change to extremeweather patterns in themidlatitudes duringthe cold season [Kaufmann et al., 2011; Serreze et al., 2011; Francis and Vavrus, 2012]. Strong observationalevidence for causal mechanisms such as enhanced persistence of atmospheric circulation, however, is stilllacking during this period [Barnes et al., 2014;Davini et al., 2012] and there is evidence that cold season variabilityis actually decreasing [Screen, 2014]. While the results for 1998–2013 are intriguing, continued monitoring oftemperature anomalies over appropriately long time periods—across the full range of spatial percentiles—isneeded to document meaningful changes in Earth’s thermal climate.

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AcknowledgmentsThis research was supported in part bythe U.S. NSF (grant 1208853) and by asabbatical leave to S.R. from IndianaUniversity. P.J. has been supported bythe U.S. DoE (grant DE-SC0005689).The data used here are available fromthe Met Office Hadley Centre and theClimatic Research Unit at the Universityof East Anglia in the UK. The insightfulcomments of two anonymous reviewersare greatly appreciated.

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