THE PAUSE IN GLOBAL WARMING: A NUMERICAL APPROACH

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1 THE PAUSE IN GLOBAL WARMING: A NUMERICAL APPROACH JAMAL MUNSHI ABSTRACT: A Monte Carlo simulation of monthly mean surface temperatures is used to construct a time series of 156 moving decadal temperature trends in a 165-year sample period from 1850 to We define the current pause in global warming as five consecutive moving decades without a statistically significant decadal temperature trend and find that although such pauses are prevalent in the dataset, the prevalence is mostly a feature of the non-warming first half of the period The current pause of is the sole such occurrence in the warming latter half of the sample period We conclude that the pause in warming is unlikely to be a manifestation of random natural variability in the context of an overall warming trend INTRODUCTION The theory of anthropogenic global warming (AGW) is that mankind's use of fossil fuels since 1750 in the post industrial era has caused a dangerous perturbation in the planet's climate system by injecting an external and unnatural flow of carbon dioxide (CO2) into nature's delicately balanced CO2 cycle (IPCC, 2014). Empirical evidence of the perturbation is two-fold. First, the observed unrelenting and accelerating rise in atmospheric CO2 from less than 200 parts per million by volume (ppmv) before 1750 to over 400 ppmv in 2015 is explained in terms of human emissions. Secondly, the observed concurrent rise in surface temperature is ascribed solely to the enhanced greenhouse effect of the atmosphere due to changes in composition imposed on it by human activity (NASA Earth Observatory, 2010) (IPCC, 2014). Although both of these relationships are controversial (Munshi, Responsiveness of Atmospheric CH4 to Human Emissions, 2015) (Munshi, Uncertain flow accounting and the IPCC carbon budget, 2015), the greater controversy in recent years has been the so called "pause" in global warming, a period of no decadal trend in recent years (Karl, 2015) (Nieves, 2015) (Munshi, A Robust Test for OLS Trends in Daily Temperature Data, 2015) (Scientific American, 2015) (IPCC, 2014). Climate science has responded to the recent pause by arguing that the pause is illusory or that the pause can be explained with innovative heat balances. In this short note we take a new approach. First we define the pause as five consecutive moving decades from 2001 to 2014 in which no decadal trend can be detected. We then use the Hadcrut4 dataset of global surface temperatures from 1850 to 2014 to estimate the probability of such a pause by way of the stochastic variability of nature during a period of long term warming. We set up a Monte Carlo simulation of moving decadal temperature trends and find that of the 13 observed pauses in the sample only one occurred in the latter half of the period from 1933 to The pause period of five consecutive moving decades without a decadal temperature trend in is found to be anomalous in the context of the global warming hypothesis. 1 Date: September 2015 Key words and phrases: global warming, climate change, global warming pause, warming hiatus, Monte Carlo simulation, stochastic process, moving decadal analysis, uncertainty, anthropogenic emissions, carbon dioxide, temperature trends, detrended analysis, agw, cagw, human emissions, fossil fuels, pause in global warming, warming hiatus, time series, Hadcrut4, bootstrap, numerical methods, decadal temperature trends, natural variability, climate variables Author affiliation: Sonoma State University, Rohnert Park, CA, 94928, munshi@sonoma.edu

2 THE PAUSE IN GLOBAL WARMING: A NUMERICAL APPROACH, JAMAL MUNSHI, DATA AND METHODS The UK Met Office Hadley Centre for Climate Change (Hadley Centre, 2015) maintains a temperature dataset of global monthly mean anomalies that includes both land and sea surface temperatures (Hadley Centre, 2015). The current version of the data is Hadcrut A feature of this dataset is that the uncertainty due to measurement error, sampling error, and coverage error are codified into a single standard deviation value for each monthly mean anomaly reported (Hadley Centre, 2013)(Morice, 2013). The data are processed and analyzed using a Monte Carlo simulation numerical procedure (Thomopoulos, 2012) (Shumway, 2011)(Munshi, Simulation in Finance, 2014) (Munshi, Uncertainty in radiocarbon dating, 2015) (Munshi, Uncertain flow accounting, 2015). The Microsoft spreadsheet used to set up the numerical analysis may be downloaded from the data archive for this note(munshi, Temp trend paper data archive, 2015). Screenshots from this spreadsheet are used below to describe the methodology applied. Figure 1: Random temperature samples for each month The first three rows in Figure 1 are the data as received from Hadcrut4. Row 1 contains the year and month. The mean monthly temperature anomaly and its standard deviation appear in Rows 2 and 3. Row 5 to Row 1004 represent a random sample of 1000 monthly temperature anomalies drawn from the Normal distribution represented by the mean and standard deviations in Rows 2 and 3. The RAND() and NORMSINV() Excel functions are used to generate these samples as shown in Figure 1. These samples are draw for each of 1,980 months in the 165-year sample period spanning Figure 2 shows that annual means for all 1000 monthly means in the Monte Carlo sample are computed by taking a simple average of the monthly means. Rows 4 to 1003 of Figure 2 contain 1000 annual means for each year. They are computed from the monthly means in Figure 1. The computed mean and standard deviation of these annual values are shown in Rows 2 and 3. For example, the annual mean and standard deviation of the temperature anomaly for 1850 are computed from rows B4 to B1003 as mean = and standard deviation = We are now ready to set up our moving decadal temperature trend computation shown in Figure 3.

3 THE PAUSE IN GLOBAL WARMING: A NUMERICAL APPROACH, JAMAL MUNSHI, Figure 2: Computation of annual means Figure 3: Moving decadal temperature trends For each row of 1000 rows of simulated annual mean temperature anomaly values, a trend is computed using OLS least squares with the Microsoft Excel LINEST() function. In Figure 3, rows 4 to 1003 contain the 1000 trend values for each year. Rows 2 and 3 contain their mean and standard deviation computed using the AVERAGE() and STDEV() functions. These two rows contain the essential information for our analysis. The year-values shown in Row 1 of Figure 3 represent the last year of the moving decade. For example our first moving decade is (Row 1) and it shows a mean decadal temperature trend of degc per year. The standard deviation of the decadal trend is The second moving decade goes from 1851 to 1860 and it shows a mean decadal trend of degc per year with a standard deviation of ; and so on. It is noted that the moving decade method contains a bias because the middle years are weighted more than the end years. Each moving decadal trend is put to a hypothesis test for statistical significance (Figure 4). In each case the null hypothesis that the trend is zero is tested against the alternate that that the trend is not zero. H 0: µ=0, H A: µ 0

4 THE PAUSE IN GLOBAL WARMING: A NUMERICAL APPROACH, JAMAL MUNSHI, A maximum false positive error rate of α=0.001 is used for each comparison. The value is lower than conventional values of α in accordance with "Revised standards for statistical evidence" published by the National Academy of Sciences (Johnson, 2013). If we fail to reject H 0, we conclude that no trend is detected in the decade. If we reject H 0 we conclude that the decade contains a warming trend if the sign of the mean (Row 3) is positive and a cooling trend if it is negative. Because of the large number of comparisons, the multiple comparison adjustment shows that there is a 15.6% probability of finding a spurious trend in random numbers if 156 comparisons are made(holm, 1979). Figure 4: Hypothesis test for moving decadal temperature trends The interpretation of the current pause period of five consecutive moving decades with no decadal temperature trends is a contentious and controversial issue (Karl, 2015) (Nieves, 2015) (Trenberth, 2013) (Meehl, Model-based evidence of deep-ocean heat uptake during surface temperature hiatus periods, 2011) (Cheng, 2014) (Easterling, 2009) (Schmidt, 2014) (Kosaka, 2013) (Lovejoy, 2014) (Crowley, 2014). Climate science has yet to come to a consensus on whether the pause actually exists or whether it is just an artifact of the data in terms of measurement, aggregation, adjustment, interpretation, and analysis; and if it exists whether it can be explained in a warming context in terms of solar activity, volcanic activity, aerosols, ocean uptake, ENSO phenomena, natural stochastic variability of surface temperature, or some combination of these factors. The natural variability of climate has been highlighted by a number of researchers (Hunt, 2011) (Swanson, 2009) (Hasselmann, 1976) (Santer, 2011) (Huber, 2014) (Lovejoy, 2014), and it forms the starting point of our empirical investigation into the behavior of moving decadal trends in temperature. Since the controversial pause period involves five consecutive moving decades with no decadal trend in temperature, we set up a test to determine whether such occurrences coexist with warming trends over a longer time scale. If such coexistence is found in the data it will be taken to mean that the current pause is not inconsistent with an overall warming trend because the pause can be explained by random natural variability. On the other hand if such coexistence is not found, then the pause can serve as evidence against an overall warming trend until a generally accepted consensus is found that explains the existence of the pause. It should be mentioned that the analysis of decadal trends in the study of climate change is commonly used with some precedence in the literature (Ricke, 2014) (NASA Earth Observatory, 2010) (Brown, 2015) (Meehl, 2013). However, the use of moving decades is an innovation that requires critical evaluation. It is motivated by the known influence of the choice of start and end years on the computed decadal OLS trend (Liebermann, 2010) and it represents an effort to randomize that influence.

5 THE PAUSE IN GLOBAL WARMING: A NUMERICAL APPROACH, JAMAL MUNSHI, DATA ANALYSIS AND RESULTS A Monte Carlo simulation procedure yielded 156 values of moving decadal trends and their standard deviations. These results, along with hypothesis tests for the statistical significance of the decadal trends are listed in Table 1. The values of the decadal trends range from degc/year to degc/yr with a mean of degc/yr. The information in Table 1 is summarized in Figure 5 where the mean values of all 156 moving decadal trends are depicted graphically. Figure 5: Summary of the 156 moving decadal trends in the sample period Of the 156 moving decadal trends in the overall study period , 40% showed a warming trend and 14% showed a cooling trend. The largest segment is the "No Trend" category with 45% of the decades without a statistically significant trend in either direction. These statistics are somewhat different in the two halves of the sample period with the latter half showing a stronger warming trend with half the moving decades containing a decadal warming trend. Another relevant difference between the two halves is that more than half of the moving decades in the early half show no statistically significant trend while this proportion is reduced to 36% in the latter half. The last three columns in Table 4 contain a search for five consecutive moving decadal trends in the same direction. When this pattern is found the last decade in the series is tagged with a value of "1" and when it is not found the value is set to "0". A simple sum of each column of flags is displayed in the first row of each of these columns. The summation shows that there were 25 occurrences of five consecutive

6 THE PAUSE IN GLOBAL WARMING: A NUMERICAL APPROACH, JAMAL MUNSHI, moving decades of decadal warming and 13 occurrences of five consecutive moving decades with no decadal trend. There were no occurrences of five consecutive moving decades with a cooling decadal trend. The known so called "global cooling" period from 1940 to 1970 contains 10 moving decades with a cooling decadal trend but they are interspersed with periods of no detectable decadal trend. The 165-year sample period shows an overall warming trend of degc/year and yet it contains 13 pauses defined as occurrences of five consecutive moving decades that do not contain decadal temperature trends. These data appear to indicate that pauses can co-exist with global warming because they can be explained by random natural variability or the stochastic nature of climate variables. If that were the case our findings would be consistent with that of researchers who have sought an explanation of the current pause in terms of natural variability. However, a very different picture emerges when we divide the period into two halves of 78 moving decades each. The differences between the two halves depicted in Figure 5 become even more stark when we look for five consecutive moving decades with each containing the same decadal trend. The results are summarized in Table 6. Figure 6: Comparison of the two halves of the sample period Figures 5 and 6 together show that the latter half of the sample period contains more moving decades that show a warming trend and fewer moving decades that show no trend or a cooling trend. In particular, Figure 6 shows that the great prevalence of pause-like conditions 2 in the sample period is mostly a feature of the first half of the period with 12 such occurrences. In the second half of the sample period , the current pause is the sole such phenomenon. Likewise, we see in Figure 6 that the warming trend in the period is mostly a feature of the second half because no temperature trend is detected in the first half We conclude that pause-like conditions are common in periods with no long term 3 temperature trend but uncommon and perhaps even singular and anomalous in periods with a long term warming trend. All data and computational details used in this work are available for download in the online data archive for this paper (Munshi, Temp trend paper data archive, 2015). 2 no decadal trend detected in five consecutive moving decades 3 80 years or more

7 THE PAUSE IN GLOBAL WARMING: A NUMERICAL APPROACH, JAMAL MUNSHI, Table 1:LIST OF ALL 156 MOVING DECADAL TEMPERATURE TRENDS FROM TO TREND STDEV TSTAT P-VALUE DECISION TYPE WARMING COOLING NO TREND FAIL NONE REJECT COOL REJECT COOL REJECT COOL FAIL NONE FAIL NONE FAIL NONE FAIL NONE FAIL NONE FAIL NONE FAIL NONE REJECT WARM FAIL NONE FAIL NONE FAIL NONE FAIL NONE FAIL NONE FAIL NONE FAIL NONE REJECT WARM REJECT WARM REJECT WARM REJECT WARM REJECT WARM FAIL NONE FAIL NONE REJECT COOL REJECT COOL REJECT COOL REJECT COOL FAIL NONE FAIL NONE FAIL NONE FAIL NONE FAIL NONE FAIL NONE FAIL NONE FAIL NONE FAIL NONE FAIL NONE REJECT WARM REJECT WARM REJECT WARM REJECT WARM FAIL NONE REJECT COOL REJECT COOL REJECT COOL FAIL NONE REJECT COOL REJECT COOL REJECT COOL 0 0 0

8 THE PAUSE IN GLOBAL WARMING: A NUMERICAL APPROACH, JAMAL MUNSHI, FAIL NONE FAIL NONE FAIL NONE FAIL NONE REJECT WARM REJECT WARM REJECT WARM REJECT WARM REJECT WARM REJECT WARM REJECT WARM FAIL NONE FAIL NONE FAIL NONE REJECT WARM REJECT WARM REJECT WARM FAIL NONE FAIL NONE FAIL NONE REJECT WARM REJECT WARM FAIL NONE FAIL NONE FAIL NONE FAIL NONE REJECT WARM REJECT WARM REJECT WARM REJECT WARM REJECT WARM REJECT WARM REJECT WARM REJECT WARM REJECT WARM FAIL NONE FAIL NONE FAIL NONE FAIL NONE REJECT COOL REJECT COOL REJECT COOL FAIL NONE FAIL NONE FAIL NONE REJECT COOL REJECT COOL FAIL NONE FAIL NONE FAIL NONE FAIL NONE REJECT WARM REJECT WARM REJECT WARM FAIL NONE 0 0 0

9 THE PAUSE IN GLOBAL WARMING: A NUMERICAL APPROACH, JAMAL MUNSHI, REJECT COOL REJECT COOL REJECT COOL FAIL NONE FAIL NONE FAIL NONE FAIL NONE REJECT WARM FAIL NONE REJECT COOL REJECT COOL FAIL NONE FAIL NONE FAIL NONE REJECT WARM REJECT WARM REJECT WARM REJECT WARM REJECT WARM REJECT WARM FAIL NONE REJECT WARM REJECT WARM REJECT WARM REJECT WARM REJECT WARM REJECT WARM REJECT WARM REJECT WARM REJECT WARM FAIL NONE REJECT WARM REJECT WARM REJECT WARM REJECT WARM REJECT WARM REJECT WARM REJECT WARM REJECT WARM REJECT WARM REJECT WARM REJECT WARM REJECT WARM REJECT WARM FAIL NONE FAIL NONE FAIL NONE FAIL NONE FAIL NONE 0 0 1

10 THE PAUSE IN GLOBAL WARMING: A NUMERICAL APPROACH, JAMAL MUNSHI, SUMMARY AND CONCLUSIONS A Monte Carlo simulation of monthly mean surface temperature anomalies is used to construct a time series of 156 moving decadal temperature trends in a 165-year sample period from 1850 to We define a pause in warming as five consecutive moving decades without a statistically significant decadal temperature trend. The full temperature dataset shows an overall warming trend and contains 13 such pauses including the controversial current pause period which occurs in our dataset in However, when the dataset is split into two halves, it is found that the warming trend derives from the second half and that the occurrence of pauses derives from the first half. The first half contains no warming trend and 12 pauses while the second half shows a strong warming trend and contains only one pause at the end of the period. The data appear to indicate that pauses and warming trends are mutually exclusive and that therefore, the current contentious pause of is not likely to be the result of random natural variability in the context of a longer period of global warming. 5. REFERENCES Brown, P. (2015). Comparing the Model-Simulated Global Warming Signal to Observations Using Empirical Estimates of Unforced Noise. Retrieved 2015, from Duke Environment: Cheng, X. (2014). Varying planetary heat sink led to global warming slowdown. Science, 345: Crowley, T. J. (2014). Recent global temperature plateau in the context of a new proxy reconstruction. Earth's Future, 2: Easterling, D. R. (2009). Is the climate warming or cooling? Geophysical Research Letters, 36: L EPA. (2015). Climate Change Indicators in the United States. Retrieved 2015, from Climate Change: Hadley Centre. (2015). Hadcrut4. Retrieved 2015, from Met Office Hadley Centre for Climate Change: Hadley Centre. (2013). Hadcrut4 ensemble. Retrieved 2915, from Met Office Hadley Center:

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