1

2

3

4

5

6

7 ?

8

9

10

11

12

13

14 5 ppb/y = ? current CH4 budget = 500 Tg/y atmos CH4 ~ 5000 Tg so 5/1800 = 14 Tg so the growth rate is 3% imbalance in budget

15 ?

16 ?

17 1987 Montreal Protocol did what?1990 London Amendments did what? Why did CFC-12 keep on rising? 50% reduction in CFC use beginning 1993, complete by 1998 phaseout in CFC production by 2000 (2010 in developing countries) when did phaseout occur? which gas responds more quickly? CFC-11, lifetime ~50 y CFC-12, lifetime ~120 y

18 ? Was the stratospheric loss partly masked by the tropospheric increase

19 Many statistical methods exist for estimating trends in environmental time series (see Chandler and Scott, 2011 for a review). The assessment of long-term changes in historical climate data requires trend models that are transparent and robust, and that can provide credible uncertainty estimates. Linear Trends Historical climate trends are frequently described and quantified by estimating the linear component of the change over time (e.g., AR4). Such linear trend modelling has broad acceptance and understanding based on its frequent and widespread use in the published research assessed in this report, and its strengths and weaknesses are well known (von Storch and Zwiers, 1999; Wilks, 2006). Challenges exist in assessing the uncertainty in the trend and its dependence on the assumptions about the sampling distribution (Gaussian or otherwise), uncertainty in the data, dependency models for the residuals about the trend line, and treating their serial correlation (Von Storch, 1999; Santer et al., 2008). The quantification and visualization of temporal changes are assessed in this chapter using a linear trend model that allows for first-order autocorrelation in the residuals (Santer et al., 2008; Supplementary Material 2.SM.3). Trend slopes in such a model are the same as ordinary least squares trends; uncertainties are computed using an approximate method. The 90% confidence interval quoted is solely that arising from sampling uncertainty in estimating the trend. Structural uncertainties, to the extent sampled, are apparent from the range of estimates from different data sets. Parametric and other remaining uncertainties (Box 2.1), for which estimates are provided with some data sets, are not included in the trend estimates shown here, so that the same method can be applied to all data sets considered.

20 Nonlinear Trends There is no a priori physical reason why the long-term trend in climate variables should be linear in time. Climatic time series often have trends for which a straight line is not a good approximation (e.g., Seidel and Lanzante, 2004). The residuals from a linear fit in time often do not follow a simple autoregressive or moving average process, and linear trend estimates can easily change when recalculated for shorter or longer time periods or when new data are added. When linear trends for two parts of a longer time series are calculated separately, the trends calculated for two shorter periods may be very different (even in sign) from the trend in the full period, if the time series exhibits significant nonlinear behavior in time (Box 2.2, Table 1).

21 Many methods have been developed for estimating the long-term change in a time series without assuming that the change is linear in time (e.g., Wu et al., 2007; Craigmile and Guttorp, 2011). Box 2.2, Figure 1 shows the linear least squares and a nonlinear trend fit to the GMST values from the HadCRUT4 data set (Section 2.4.3). The nonlinear trend is obtained by fitting a smoothing spline trend (Wood, 2006; Scinocca et al., 2010) while allowing for first-order autocorrelation in the residuals (Supplementary Material 2.SM.3). The results indicate that there are significant departures from linearity in the trend estimated this way.

22 Figure | (a) Global mean surface temperature (GMST) anomalies relative to a 1961–1990 climatology based on HadCRUT4 annual data. The straight black lines are least squares trends for 1901–2012, 1901–1950 and 1951–2012. (b) Same data as in (a), with smoothing spline (solid curve) and the 90% confidence interval on the smooth curve (dashed lines). Note that the (strongly overlapping) 90% confidence intervals for the least square lines in (a) are omitted for clarity. See Figure 2.20 for the other two GMST data products.

23 Box 2.2, Table 1 shows estimates of the change in the GMST from the two methods. The methods give similar estimates with 90% confidence intervals that overlap one another. Smoothing methods that do not assume the trend is linear can provide useful information on the structure of change that is not as well treated with linear fits. The linear trend fit is used in this chapter because it can be applied consistently to all the data sets, is relatively simple, transparent and easily comprehended, and is frequently used in the published research assessed here.

24 Table | Estimates of the mean change in global mean surface temperature (GMST) between 1901 and 2012, 1901 and 1950, and 1951 and 2012, obtained from the linear (least squares) and nonlinear (smoothing spline) trend models. Half-widths of the 90% confidence intervals are also provided for the estimated changes from the two trend methods. Trends in °C per decade Method – – –2012 Least squares ± ± ± 0.027 Smoothing spline ± ± ± 0.018

25

26

27

28

29

30

31

32 Box 2.4 | Extremes Indices As SREX highlighted, there is no unique definition of what constitutes a climate extreme in the scientific literature given variations in regions and sectors affected (Stephenson et al., 2008). Much of the available research is based on the use of so-called ‘extremes indices’ (Zhang et al., 2011). These indices can either be based on the probability of occurrence of given quantities or on absolute or percentage threshold exceedances (relative to a fixed climatological period) but also include more complex definitions related to duration, intensity and persistence of extreme events. For example, the term ‘heat wave’ can mean very different things depending on the index formulation for the application for which it is required (Perkins and Alexander, 2012). Box 2.4, Table 1 lists a number of specific indices that appear widely in the literature and have been chosen to provide some consistency across multiple chapters in AR5 (along with the location of associated figures and text). These indices have been generally chosen for their robust statistical properties and their applicability across a wide range of climates. Another important criterion is that data for these indices are broadly available over both space and time. The existing near-global land-based data sets cover at least the post-1950 period but for regions such as Europe, North America, parts of Asia and Australia much longer analyses are available. The same indices used in observational studies (this chapter) are also used to diagnose climate model output (Chapters 9, 10, 11 and 12). The types of indices discussed here do not include indices such as NIÑO3 representing positive and negative phases of ENSO (Box 2.5), nor do they include extremes such as 1 in 100 year events. Typically extreme indices assessed here reflect more ‘moderate’ extremes, for example, events occurring as often as 5% or 10% of the time (Box 2.4, Table 1). Predefined extreme indices are usually easier to obtain than the underlying daily climate data, which are not always freely exchanged by meteorological services. However, some of these indices do represent rarer events, for example, annual maxima or minima. Analyses of these and rarer extremes (e.g., with longer return period thresholds) are making their way into a growing body of literature which, for example, are using Extreme Value Theory (Coles, 2001) to study climate extremes (Zwiers and Kharin, 1998; Brown et al., 2008; Sillmann et al., 2011; Zhang et al., 2011; Kharin et al., 2013). Extreme indices are more generally defined for daily temperature and precipitation characteristics (Zhang et al., 2011) although research is developing on the analysis of sub-daily events but mostly only on regional scales (Sen Roy, 2009; Shiu et al., 2009; Jones et al., 2010; Jakob et al., 2011; Lenderink et al., 2011; Shaw et al., 2011). Temperature and precipitation indices are sometimes combined to investigate ‘extremeness’ (e.g., hydroclimatic intensity, HY-INT; Giorgi et al., 2011) and/or the areal extent of extremes (e.g., the Climate Extremes Index (CEI) and its variants (Gleason et al., 2008; Gallant and Karoly, 2010; Ren et al., 2011). Indices rarely include other weather and climate variables, such as wind speed, humidity or physical impacts (e.g., streamflow) and phenomena. Some examples are available in the literature for wind-based (Della-Marta et al., 2009) and pressure-based (Beniston, 2009) indices, for health-relevant indices combining temperature and relative humidity characteristics (Diffenbaugh et al., 2007; Fischer and Schär, 2010) and for a range of dryness or drought indices (e.g., Palmer Drought Severity Index (PDSI) Palmer, 1965; Standardised Precipitation Index (SPI), Standardised Precipitation Evapotranspiration Index (SPEI) Vicente-Serrano et al., 2010) and wetness indices (e.g., Standardized Soil Wetness Index (SSWI); Vidal et al., 2010) In addition to the complication of defining an index, the results depend also on the way in which indices are calculated (to create global averages, for example). This is due to the fact that different algorithms may be employed to create grid box averages from station data, or that extremes indices may be calculated from gridded daily data or at station locations and then gridded. All of these factors add uncertainty to the calculation of an extreme. For example, the spatial patterns of trends in the hottest day of the year differ slightly between data sets, although when globally averaged, trends are similar over the second half of the 20th century (Box 2.4, Figure 1). Further discussion of the parametric and structural uncertainties in data sets is given in Box 2.1. Box 2.4, Figure 1 | Trends in the warmest day of the year using different data sets for the period 1951–2010. The data sets are (a) HadEX2 (Donat et al., 2013c) updated to include the latest version of the European Climate Assessment data set (Klok and Tank, 2009), (b) HadGHCND (Caesar et al., 2006) using data updated to 2010 (Donat et al., 2013a) and (c) Globally averaged annual warmest day anomalies for each data set. Trends were calculated only for grid boxes that had at least 40 years of data during this period and where data ended no earlier than Grey areas indicate incomplete or missing data. Black plus signs (+) indicate grid boxes where trends are significant (i.e., a trend of zero lies outside the 90% confidence interval). Anomalies are calculated using grid boxes only where both data sets have data and where 90% of data are available.

33

34

35