[HOME PAGE]

[RELATED POST ON CONFIRMATION BIAS]

1. A notable feature of the “Common but Differentiated Responsibilities” principle of the Kyoto Protocol/UNFCCC is that the rich industrialized countries (Annex-1) are required to compensate poor developing countries (non-Annex) for “adaptation cost” of climate change impacts such as rising seas and extreme weather. Initially, all such events in the nonAnnex countries were fundable under the Framework Convention but later it was argued that this funding policy is arbitrary because natural variability is known to cause extreme weather events anyway even in the absence of fossil fuel emissions and that therefore not all extreme weather events can be attributed to fossil fuel emissions and not all extreme weather events are relevant in the context of climate adaptation assistance from the Annex I countries to the nonAnnex countries (Allen, 2003). This principle was formalized in the Warsaw International Mechanism (WIM) for Loss and Damage Associated with Climate Change Impacts (UNFCCC, 2013).
2. The Warsaw International Mechanism (WIM) has redefined climate change adaptation funding as a form of compensation for “loss and damage” suffered by nonAnnex countries because of sea level rise or extreme weather events caused by fossil fuel emissions which are thought to be mostly a product of the industrialized countries. Accordingly, the WIM requires that loss and damage suffered by the nonAnnex countries for which compensation is sought from climate adaptation funds must be attributable to fossil fuel emissions.
3. A probabilistic methodology was devised to address the need for attribution in the WIM and It has gained widespread acceptance in both technical and policy circles as a tool for the allocation of limited climate adaptation funds among competing needs of the VNAL countries (Stott, 2013) (Otto, 2015) (Otto, 2012) (James, 2014) (Trenberth, 2015) (Peterson, 2012) (Huggel, 2013). The probabilistic event attribution methodology (PEA) uses a large number of climate model experiments with multiple models and a multiplicity of initial conditions. A large sample size is used because extreme weather events are rare and their probability small by definition. The probability of an observed extreme weather event with anthropogenic emissions and the probability without anthropogenic emissions are derived from climate model experiments as P1 and P0. If the probability with emissions (P1) exceeds the probability without emissions (P0), the results are interpreted to indicate that emissions played a role in the occurrence of the event in question. Otherwise the event is assumed to be a product of natural variation alone. The probability that fossil fuel emissions played a role in the extreme weather event is represented as P = (P1-P0)/P0. A contentious issue in PEA analysis is that of uncertainty in the values of P0 and P1 and in the model results themselves. Policy analysts fear that large uncertainties of climate models (Oreskes, 1994) (Frame, 2011) (Curry, 2011) and shortcomings of the PEA methodology (Zwiers, 2013) (Hulme, 2011) provide sufficient reason to question the reliability of PEA to serve its intended function as a criterion for access to climate adaptation funds (Hulme, 2011). Mike Hulme argues that much greater statistical confidence in the PEA test is needed to justify denial of adaptation funding for loss and damage from weather extremes that do not pass the PEA test. Yet another concern with respect to the PEA methodology, and one that is the subject of this post, is the apparent tendency in climate science to extend the interpretation of PEA results beyond their intended function of climate adaptation fund allocation and into the realm of empirical evidence.
4. It has long been claimed that basic principles of climate science imply that fossil fuel driven AGW will increase the frequency and severity of extreme weather events such as tropical cyclones, tornadoes, heat waves, extreme cold, droughts, floods, landslides, and even forest fires (IPCCAR4, 2007) (IPCCSREX, 2012) (IPCCAR5, 2014) (Easterling-Meehl, 2000) (Easterling-Evans, 2000) (Karl, 2003) (Min, 2011) (Allen, 2002) (Rosenzweig, 2001) (Mirza, 2003) (Coumou, 2012) (VanAalst, 2006) (Burton, 1997) (Flannigan, 2000) (Stocks, 1998) (Gillett N. , 2004). It is argued that the harm from these extreme weather effects of AGW provides scientific, ecological, social, political, and economic justification for urgent and costly reductions in fossil fuel emissions as a way of attenuating AGW because the social and economic cost of adaptation later is greater than the cost of mitigation now (Stern, 2006) (Metz, 2007) (IPCC, 2014). It is this catastrophic nature of AGW that provides the rationale for the policy proposal  that requires Annex I countries to reduce emissions by changing their energy infrastructure from fossil fuels to renewables (UNFCCC, 2014) (UNFCCC, 2016). And yet, this line of reasoning is weakened by a frustrating inability of climate science to produce empirical evidence that relates extreme weather disasters to emissions (IPCCSREX, 2012) (IPCCAR4, 2007) (Sheffield, 2008) (Bouwer, 2011) (Munshi, 2015) (IPCCAR5, 2014) (NCEI, 2015) (Woollings, 2014). Of particular note in this regard is that claims made by the IPCC in 2007 with regard to the effect of AGW on the frequency and intensity of tropical cyclones, droughts, and floods have been all but retracted in their very next Assessment Report in 2014 (IPCCAR5, 2014). Thus, climate scientists, though convinced of the causal connection between AGW and extreme weather events, are nevertheless unable to provide acceptable empirical evidence to support what to them is obvious and “unequivocal” (Curry, 2011) (Zwiers, 2013) (Munshi, 2016) (Frame, 2011) (Hulme, 2014).
5. It is likely this frustration with the absence of trends in the historical data on extreme weather that motivated climate scientists to turn to PEA analysis as an alternative to empirical evidence of the extreme weather effects of AGW (WMO, 2016) (Stott, 2013) (Trenberth, 2015) (Otto, 2015). Thus, the PEA procedure has been extrapolated and generalized well beyond the context of its narrow definition in terms of the WIM. Such extrapolation allows climate science to present positive PEA results as evidence that extreme precipitation, floods, droughts, heat waves, and cold spells are attributable to fossil fuel emissions (WMO, 2016) (Sneed, 2017). In keeping with its elevated status, the PEA methodology has been re-christened as Event Attribution Science or just Event Attribution. Here we show with the high profile example of the autumn floods of 2000 in England and Wales that this interpretation of PEA results (Stott, 2013) commits the fallacy of circular reasoning and that therefore positive PEA results by themselves do not constitute empirical evidence that AGW causes extreme weather events.
6. Critical commentaries on the PEA methodology have been published by Hulme, Boardman, Kelman and others (Hulme, 2011) (Hulme, 2014) (Boardman, 2008) (Boardman, 2003) (Kelman, 2001). Mike Hulme’s work exposes the weaknesses and the limits of the PEA methodology, John Boardman shows that the PEA methodology had erroneously ascribed non-meteorological aspects of the floods to climate change, and Kelman exposes certain inconsistencies in the details of the flood data and what had been assumed in the Event Attribution climate model analysis. This work describes Event Attribution Science in a case study format using the high profile example of the Event Attribution analysis of the floods in England and Wales in the year 2000 by (Pall, 2011). A critical evaluation of these interpretations is made in light of the relevant precipitation data (Met Office, 2017) and non-meteorological factors that affect flood impact severity (Boardman, 2003) (Boardman, 2008). The use of the Event Attribution Science to present evidence of the effect of fossil fuel emissions on the severity of extreme weather events is evaluated in this context.
7. In mid-September of the year 2000 an unrelenting sequence of rainstorms began to strike in various parts of England and Wales. By mid-October flooding became widespread and devastating. The rainstorms and floods continued in multiple sequential flooding events until mid-December (Kelman, 2001) (Marsh, 2001) (Marsh, 2002). The series of rainstorms taken together is considered to be a rare and extreme meteorological event in terms of the amount of precipitation, the duration, and the high runoff rates in all the rivers in the region and considered to be a consequence of climate change (Reynard, 2001) (Pall, 2011).
8. A study of the autumn 2000 floods by Terry Marsh found that 640 mm of rain fell in the four months of rain ending December 15, 2000 and 1033 mm of rain fell in the eight months ending in April 2001. By both measures, the year 2000 ranks first in the 235-year data record going back to 1766 (Marsh, 2001). An estimate of the total volume of water delivered to the ground by the rainstorms is also reported in the Marsh study in terms of the combined flows of the Rivers Thames, Severn, Welsh Dee, and Wharfe. By this measure the year 2000 ranked second after 1947 for 10-day and 30-day outflows and first, just ahead of 1947, for 60-day and 90-day outflows (Marsh, 2001). Marsh also points out that the 2000 floods did not occur in isolation. They fall in the middle of cluster of flood years in the area prior to 2000 that includes 1989, 1993, 1994, and 1998 and since 2000 in 2007, 2013-2014, and 2015-2016 (Marsh, 2001) (Marsh, 2002) (Marsh, 2007) (Huntingford, 2014) (Schaller, 2016) (Marsh, 2016).
9. These storm and precipitation events came to be thought of as extreme and unnatural and research interest turned to the effect of human influences in the form of anthropogenic global warming and climate change on the apparent unnatural increase in the frequency and intensity of floods in the UK (Reynard, 1996) (Reynard, 1998) (Reynard, 2001) (Macklin, 2003) (Wilby, 2008). It was in this context that the newly minted Event Attribution methodology was applied to the autumn floods of 2000 using an array of climate models and a large sample of climate model runs.
10. The results showed that the 2000 floods were more likely in “the world as it is” (with fossil fuel emissions) than in “the world that might have been” without fossil fuel emissions. Based on this PEA result the autumn floods of 2000 in England and Wales were attributed to climate change and indirectly to fossil fuel emissions (Pall, 2011).
11. However, the attribution of the floods to emissions remains controversial. First, floods are not purely meteorological events because important non-meteorological factors play a role in the intensity and devastation of flooding at any given level of rainfall (Kelman, 2001) (Boardman, 2003) (Boardman, 2008) (Boardman, Don’t blame the climate, 2008). Also, the known large natural variability in precipitation in England and Wales provides a simpler explanation of extreme flooding events than the effect of anthropogenic carbon dioxide emissions found in climate models (Kay, 2009) (Shackley, 1998) (Young, 1996) (Beder, 1999) (Curry, 2011) (Frame, 2011) (Hulme, 2014) (Deser, 2012).
12. This case study examines patterns in the 251-year record of precipitation in England and Wales from 1766 to 2016 in the context of the conclusions drawn from PEA analysis about the autumn floods of 2000 in England and Wales and considers whether a simpler and more natural explanation exists for this precipitation event. Historical monthly mean precipitation data for England and Wales are provided by the Met Office of the Government of the UK (MetOffice, 2017). Precipitation data are recorded in millimeters of water equivalent at standard conditions in a continuous annual time series for a 251-year period from 1766 to 2016 for each of the twelve calendar months.
13. The data along with their OLS linear trends are depicted graphically, month by month, in Charts1-6 below the text in the chart section of this post. We note in these figures that the calendar months differ significantly in terms of mean monthly precipitation, the variance of precipitation, and the overall trend in the study period. These differences (highlighted in Charts 7-8) show that mean monthly precipitation characteristics differ markedly among the calendar months. On average, autumn is the wettest and spring the driest. Summer and winter lie in between with winter wetter than summer. Year to year variability in precipitation is also different among the calendar months. Charts 9-14 show large differences among the calendar months in standard deviations measured in a moving 30-year window. The generational (30-year) time scale is generally used in the study of climate phenomena (Ackerman, 2006) (WMO, 2016). The red line in these charts marks the no-trend boundary between rising and declining trends.
14. To maintain the integrity of these observed differences, monthly mean precipitation data are not combined. Instead each month is studied in isolation as a phenomenon of nature unique to that month. A benefit of this methodology is that it facilitates the interpretation of historical trend analysis in terms of the season of the floods under study.
15. Outlier analysis is carried out by examining the ten largest values from each time series one at a time starting with the largest and moving sequentially to the smallest. At each step a hypothesis test is used to determine whether the value removed belongs to the distribution of all values that are less than the value removed. The null hypothesis is H0: testValue ≤ mean(all values less than the test value). If the null hypothesis is rejected the test value is marked as an outlier and described as an extreme year (Dixon, 1950) (Aggarwal, 2015). The procedure is carried out separately for each calendar month.
16. A generational (30-year) moving window is used to compute a time series of 221 variability measures for each calendar month. Variability is expressed as the standard deviation and studied for trends. A statistically significant rising trend in this series is expected if climate change is causing the precipitation series to become more volatile. Statistical significance is determined using classical hypothesis testing at a maximum false positive error rate of α=0.001 consistent with “Revised Standards for Statistical Evidence” published by the National Academy of Sciences to address an unacceptably large proportion of irreproducible results in published research (Johnson, 2013) (Siegfried, 2010).
17. The proposition that anthropogenic CO2 emissions since the Industrial Revolution have increased the amount of precipitation in England and Wales implies that the study period 1766-2016 should show a statistically significant rising trend in precipitation amounts. The simple OLS trend lines for mean monthly precipitation amounts are shown in Charts 1-6. Only three out of the twelve calendar months show a statistically significant trend. The winter months of December and January show the required rising trend in precipitation while the summer month of July shows a declining trend. No evidence of a trend in mean monthly precipitation amount is found in the other nine calendar months.
18. To explain the autumn 2000 floods in England and Wales in terms of trends, a positive trend is necessary for the four months from September to and December. A positive result for December alone does not provide sufficient evidence that rising trends in the amount of precipitation were responsible for the floods of 2000. It is also noted that the summer floods of 2007 appear anomalous in this line of reasoning as the only evidence of a trend in the summer months is a declining trend for July. The event attribution finding that the autumn floods of 2000 were caused by climate change is consistent with historical record.
19. Charts 9-14 are graphical displays of the standard deviation of mean monthly precipitation in a generational moving window. The results provide evidence that mean monthly precipitation in the autumn months of October and November, the winter months of January and February, and the spring month of March have become more volatile over the study period. The summer month of July shows a decreasing trend in volatility and the other six months show no evidence of a trend in volatility.
20. The evidence of rising volatility in the months of October and November might have been consistent with the attribution of the floods of 2000 to climate change had the volatility been associated with greater precipitation. Without evidence of a rising trend in precipitation in these months it is unclear whether the greater variance relates to extreme dry years or extreme wet years. To explain floods in terms of climate change evidence of more extreme wet years is necessary.
21. A search for extreme wet years is made by using outlier analysis. For the purpose of this analysis, a wet year is deemed to be extreme if it is an outlier in the context of all years in the time series with less precipitation. The analysis begins with the identification of the ten highest precipitation years for each calendar month. They are shown in Charts 15-20. Each of the ten wettest years is tested against all years with less rainfall to determine if it is an outlier in the sense that it does not belong in the distribution of the comparison series. These hypothesis tests are carried out at a maximum false positive error rate of α=0.001. Since twelve tests are made the overall study-wide false positive error rate is approximately 0.012 or 1.2% (Holm, 1979). Statistically significant results are identified with filled markers. These outliers are deemed to be extreme precipitation years.
22. February, September, November, and December contain no extreme years. The other eight months contain at least one extreme wet year. April contains four, May contains three, and March and August contain two each. January, July, and October contain only one extreme year. For the autumn floods of 2000, the relevant months are September, when the rains started, and October, November, and December when they continued and intensified. Only one extreme event is found for these months and it occurred in October 1903 with 218 mm of precipitation. October of 2000 is indeed the second wettest October on record with 188 mm of precipitation but it is not an outlier as 188 mm is well within expected variability of the distribution of October precipitations at α=0.001.
23. These results, together with the absence of a rising trend in precipitation amount or volatility show no empirical support for the claim made with Event Attribution analysis that the autumn 2000 floods were caused by extreme precipitation events attributable to anthropogenic CO2 emissions. In terms of the cluster of flood years in the UK in the period 1989 to 2015, the only extreme year that occurs in the same season as the floods is the extreme for January in the year 2014 because it coincides with the winter 2013-2014 floods. The years 2000 and 2012 are also found in the list of extremes in Figure 10 but not in the season of the floods in those years.
24. The presentation of empirical evidence for a given theory proceeds as follows. First, a testable implication of the theory is deduced. Then, data are collected, either experimental data or field data. The data must be independent of the theory and their collection must be unbiased. In the case of classical hypothesis testing, the testable implication is then tested against the data with the null hypothesis that the theory is false. If the null hypothesis is rejected, the data constitute empirical evidence in support of the theory (Popper, 2005) (Pearl, 2009) (Kothari, 2004).
25. In the case of Event Attribution analysis with climate models, the results serve the intended purpose of providing a non-subjective method for the allocation of climate adaptation funds in accordance with WIM guidelines. However, their further interpretation as evidence of the extreme weather effects of fossil fuel emissions involves circular reasoning because climate model results are not data independent of the theory but a mathematical expression of the theory itself; and the selection of specific events to test for event attribution contains a data collection bias (Munshi, 2016) (Koutsoyiannis, 2008) (VonStorch, 1999). A related post compares the confirmation bias in event attribution analysis with superstition. SUPERSTITION AND CONFIRMATION BIAS. Yet another contentious issue in event attribution with climate models is the known chaotic behavior of climate at decadal time scales in terms of what is described as Internal Climate Variability described in a related post on non-linear dynamics and chaos at brief time scales: IS CLIMATE CHAOTIC?

[HOME PAGE]

CITATIONS

Ackerman, S. (2006). Meteorology: Understanding the Atmosphere (Jones and Bartlett Titles in Physical Science). Cengage Learning.
Adger, N. (2003). Adaptation to climate change in the developing world. Progress in development studies , 3.3 (2003): 179-195.
Aggarwal, C. (2015). Outlier analysis. Springer International PublishingAllen, M. (2002). Constraints on future changes in climate and the hydrologic cycle. Nature , 419.6903 (2002): 224-232.
Allen, M. (2003). Liability for climate change. Nature , 421.6926 (2003): 891-892.
Allen, M. (2009). Warming caused by cumulative carbon emissions towards the trillionth tonne. Nature , 458.7242 (2009): 1163-1166.
Beder, S. (1999). Climatic Confusion and Corporate Collusion: Hijacking the Greenhouse Debate. The Ecologist , (1999): 119-122.
EVENT ATTRIBUTION AND THE PRECIPITATION RECORD FOR ENGLAND AND WALES, JAMAL MUNSHI, 2017 17
Boardman, J. (2008). Don’t blame global warming for floods . Retrieved 2017, from The Guardian: https://www.theguardian.com/society/2000/nov/08/guardiansocietysupplement9
Boardman, J. (2008). Don’t blame the climate. Retrieved 2017, from The Guardian: https://www.theguardian.com/society/2000/nov/08/guardiansocietysupplement9
Boardman, J. (2003). Muddy floods on the South Downs, southern England: Problem and responses. Retrieved 2017, from Researchgate: https://www.researchgate.net/publication/222674579_Muddy_floods_on_the_South_Downs_southern_England_Problem_and_responses
Botzen, W. (2008). Cumulative CO2 emissions: shifting international responsibilities for climate debt. Climate Policy , 8.6, 569-576.
Bouwer, L. (2011). Have disaster losses increased due to anthropogenic climate change? Bulletin of the American Meteorological Society , 92.1 (2011): 39-46.
Bowley, A. (1928). The standard deviation of the correlation coefficient. Journal of the American Statistical Association , 31-34.
Box, G. (1994). Time series analysis: forecasting and control. Englewood Cliffs, NJ: Prentice Hall.
Burton, I. (1997). Vulnerability and adaptive response in the context of climate and climate change. Climatic Change , 36.1 (1997): 185-196.
Callendar, G. (1938). The Artificial Production of Carbon Dioxide and Its Influence on Climate. Quarterly Journal of the Royal Meteorological Society , 64: 223-40.
Chatfield, C. (1989). The Analysis of Time Series: An Introduction. NY: Chapman and Hall/CRC.
Coumou, D. (2012). A decade of weather extremes.”. Nature climate change , 2.7 (2012): 491-496.
Curry, J. (2011). Climate science and the uncertainty monster. Bulletin of the American Meteorological Society , 92.12 (2011): 1667-1682.
Deser, C. (2012). Communication of the role of natural variability in future North American climate. Nature Climate Change , 2.11 (2012): 775-779.
Dettinger, M. (2011). Climate change, atmospheric rivers, and floods in California–a multimodel analysis of storm frequency and magnitude changes. JAWRA Journal of the American Water Resources Association , 47.3 (2011): 514-523.
Dixon, W. (1950). Analysis of extreme values. The Annals of Mathematical Statistics , 21.4 (1950): 488-506.
Draper&Smith. (1998). Applied Regression Analysis. Wiley.
Easterling, D. (2009). Is the climate warming or cooling? Geophysical Research Letters , 36.8 (2009).
Easterling-Evans. (2000). Observed variability and trends in extreme climate events: a brief review. Bulletin of the American Meteorological Society , 81.3 (2000): 417-425.
Easterling-Meehl. (2000). Climate extremes: observations, modeling, and impacts. Science , 289.5487 (2000): 2068-2074.
Finkelstein, I. (2011). The Large Stone Structure” in Jerusalem: Reality versus Yearning. Zeitschrift des Deutschen Palästina-Vereins , (2011): 1-10.
Flannigan, M. (2000). Climate change and forest fires. Science of the total environment , 262.3 (2000): 221-229.
EVENT ATTRIBUTION AND THE PRECIPITATION RECORD FOR ENGLAND AND WALES, JAMAL MUNSHI, 2017 18
Flynn, M. (2013). Ecological diagnosis from biotic data by Hurst exponent and the R/S analysis adaptation to short time series. Biomatematica , 23 (2013): 1-14.
Frame, D. J. (2011). The problems of markets: science, norms and the commodification of carbon. The Geographical Journal , 177.2 (2011): 138-148.
Gillett, N. (2013). Constraining the ratio of global warming to cumulative CO2 emissions using CMIP5 simulations. Journal of Climate , 26.18 (2013): 6844-6858.
Gillett, N. (2004). Detecting the effect of climate change on Canadian forest fires. Geophysical Research Letters , 31.18 (2004).
Hansen, J. (2016). Ice melt, sea level rise and superstorms:. Atmos. Chem. Phys. , 16, 3761–3812, 2016.
Hansen, J. (1981). Impact of Increasing Atmospheric Carbon Dioxide. Science , 213: 957-66.
Holm, S. (1979). A simple sequentially rejective multiple test procedure. Scandinavian Journal of Statistics , 6:2:65-70.
Holman, I. (2003). The contribution of soil structural degradation to catchment flooding: a preliminary investigation of the 2000 floods in England and Wales. Hydrology and Earth System Sciences Discussions , 7.5 (2003): 755-766.
Huggel, C. (2013). Loss and damage attribution. Nature Climate Change , 3.8 (2013): 694-696.
Hulme, M. (2014). Attributing weather extremes to climate change. Progress in Physical Geography , 38.4 (2014): 499-511.
Hulme, M. (2011). Is weather event attribution necessary for adaptation funding? Science , 334.6057 (2011): 764-765.
Huntingford, C. (2014). Potential influences on the United Kingdom’s floods of winter 2013/14. Nature Climate Change , 4.9 (2014): 769-777.
Huq, S. (2004). Mainstreaming adaptation to climate change in least developed countries (LDCs). Climate Policy , 4.1 (2004): 25-43.
IPCC. (2014). Climate Change 2013 The Physical Science Basis. Geneva: IPCC/UNEP.
IPCC. ( 2014). Climate Change 2014–Impacts, Adaptation and Vulnerability: Regional Aspects. Cambridge, UK: Cambridge University Press.
IPCCAR4. (2007). AR4 WG1 Chapter 7: Couplings between changes in the climate system and biogeochemistry. Geneva: IPCC.
IPCCAR5. (2014). Climate Change 2014: Impacts, Adaptation, and Vulnerability. Retrieved 2017, from IPCC.CH: http://ipcc.ch/report/ar5/wg2/
IPCCAR5. (2014). Observations: Atmosphere and surface. Retrieved 2017, from climatechange2013.org: http://www.climatechange2013.org/images/report/WG1AR5_Chapter02_FINAL.pdf
IPCCSREX. (2012). SREX. Retrieved 2017, from IPCC: https://www.ipcc.ch/pdf/special-reports/srex/SREX_Full_Report.pdf
James, R. (2014). Characterizing loss and damage from climate change. Nature Climate Change , 4.11 (2014): 938-939.
Johnson, V. (2013). Revised standards for statistical evidence. Retrieved 2015, from Proceedings of the National Academy of Sciences: http://www.pnas.org/content/110/48/19313.full
Karl, T. (2003). Modern global climate change. Science , 302.5651 (2003): 1719-1723.
Kay, A. (2009). Comparison of uncertainty sources for climate change impacts: flood frequency in England. Climatic Change , 92.1 (2009): 41-63.
EVENT ATTRIBUTION AND THE PRECIPITATION RECORD FOR ENGLAND AND WALES, JAMAL MUNSHI, 2017 19
Keeling, C. (1973). Industrial production of carbon dioxide from fossil fuels and limestone. Tellus , 25: 174-198.
Kelly-Adger. (2000). Theory and practice in assessing vulnerability to climate change andFacilitating adaptation. Climatic change , 47.4 (2000): 325-352.
Kelman, I. (2001). The autumn 2000 floods in England and flood management. Weather , 56.10 (2001): 346-360.
Kothari, C. R. (2004). Research methodology: Methods and techniques. New Age International.
Koutsoyiannis, D. (2008). On the credibility of climate predictions. Hydrological Sciences Journal , 53.4 (2008): 671-684.
Lacis, A. (2010). Principal Control Knob Governing Earth’s Temperature. Science , 330.
Lavers, D. (2011). Winter floods in Britain are connected to atmospheric rivers. Geophysical Research Letters , 38.23 (2011).
Lins, H. (2011). Stationarity: Wanted dead or alive? JAWRA Journal of the American Water Resources Association , 47.3 (2011): 475-480.
Lloyd‐Hughes, B. (2002). A drought climatology for Europe. International journal of climatology , 22.13 (2002): 1571-1592.
Macklin, M. (2003). River sediments, great floods and centennial‐scale holocene climate change.” . Journal of Quaternary Science , 18.2 (2003): 101-105.
Marsh, T. (2001). The 2000/01 floods in the UK—a brief overview. Weather , 56.10 (2001): 343-345.
Marsh, T. (2007). The summer 2007 floods in England and Wales–a hydrological appraisal. Wallingford: NERC/Centre for Ecology & Hydrology.
Marsh, T. (2002). The UK floods of 2000–2001: a hydrometeorological appraisal. Water and Environment Journal , 16.3 (2002): 180-188.
Marsh, T. (2016). The winter floods of 2015/2016 in the UK-a review. Wallingford: NERC/Centre for Ecology & Hydrology.
Matthews, H. (2009). The proportionality of global warming to cumulative carbon emissions. Nature , 459.7248 (2009): 829-832.
McGray, H. (2007). Weathering the storm: Options for framing adaptation and development. Washington, DC 57 (2007): World Resources Institute.
McKee, T. (1993). The relationship of drought frequency and duration to time scales. Proceedings of the 8th Conference on Applied Climatology (p. Vol. 17. No. 22). Boston, MA: American Meteorological Society.
Met Office. (2017). The wet autumn of 2000. Retrieved 2017, from metoffice: http://www.metoffice.gov.uk/climate/uk/interesting/autumn2000.html
MetOffice. (2017). Rainfall Data. Retrieved 2017, from MetOffice: http://www.metoffice.gov.uk/services/industry/data/commercial/rainfall
MetOffice. (2017). Weather stations. Retrieved 2017, from MetOffice: http://www.metoffice.gov.uk/learning/science/first-steps/observations/weather-stations
MetOffice. (2017). When does spring start? Retrieved 2017, from MetOffice: http://www.metoffice.gov.uk/learning/learn-about-the-weather/how-weather-works/when-does-spring-start
EVENT ATTRIBUTION AND THE PRECIPITATION RECORD FOR ENGLAND AND WALES, JAMAL MUNSHI, 2017 20
Metz, B. (2007). Climate Change Mitigation. Contribution of Working Group III to the fourth assessment report of the Intergovernmental Panel on Climate Change. Cambridge, UK: IPCC.
Min, S.-K. (2011). Human contribution to more-intense precipitation extremes. Nature , 470.7334 (2011): 378-381.
Mirza, M. (2003). Climate change and extreme weather events: can developing countries adapt? Climate policy , 3.3 (2003): 233-248.
Mudelsee, M. (2014). Climate Time Series Analysis: Classical Statistical and Bootstrap Methods. Springer.
Munshi, J. (2015). A General Linear Model for Trends in Tropical Cyclone Activity. Retrieved 2017, from ssrn.com: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2630932
Munshi, J. (2017). PEA Paper Archive. Retrieved 2017, from Google Drive: https://drive.google.com/open?id=0ByzA6UNa41ZfUkt4T1VZRjJYUmM
Munshi, J. (2016). Some Methodological Issues in Climate Science. Retrieved 2017, from ssrn.com: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2873672
NCEI. (2015). Historical records and trends for tornadoes. Retrieved 2017, from noaa.gov: https://www.ncdc.noaa.gov/climate-information/extreme-events/us-tornado-climatology/trends
Obasi, G. (1994). WMO’s role in the international decade for natural disaster reduction. Bulletin of the American Meteorological Society , 75.9 (1994): 1655-1661.
Obergassel, W. (2016). Phoenix from the Ashes—An Analysis of the Paris Agreement to the United Nations Framework Convention on Climate Change. Wuppertal : Wuppertal Institute for Climate, Environment and Energy.
Oreskes, N. (1994). Verification, validation, and confirmation of numerical models in the earth sciences. Science , 263.5147 (1994): 641-646.
Otto, F. (2012). Reconciling two approaches to attribution of the 2010 Russian heat wave. Geophysical Research Letters , 39.4 (2012).
Otto, F. (2015). The science of attributing extreme weather events and its potential contribution to assessing loss and damage associated with climate change impacts. Retrieved 2017, from UNFCCC: https://unfccc.int/files/adaptation/workstreams/loss_and_damage/application/pdf/attributingextremeevents.pdf
Pall, P. (2011). Anthropogenic greenhouse gas contribution to flood risk in England and Wales in autumn 2000. Nature , 470.7334 (2011): 382-385.
Pearl, J. (2009). Causality. Cambridge, England: Cambridge University Press.
Peterson, T. (2012). Explaining extreme events of 2011 from a climate perspective. Bulletin of the American Meteorological Society , 93.7 (2012): 1041-1067.
Popper, K. (2005). The logic of scientific discovery. Routledge.
Ralph, F. (2006). Flooding on California’s Russian River: Role of atmospheric rivers. Geophysical Research Letters , 33.13 (2006).
Rasool, S. (1971). Atmospheric carbon dioxide and aerosols: Effects of large increases on global climate. Science , 173, 138-141, doi:10.1126/science.173.3992.138.
Revelle, R. (1956). Carbon dioxide exchange between atmosphere and ocean and the question of an increase in atmospheric CO2 during the past decades. UC La Jolla, CA: Scripps Institution of Oceanography.
EVENT ATTRIBUTION AND THE PRECIPITATION RECORD FOR ENGLAND AND WALES, JAMAL MUNSHI, 2017 21
Reynard, N. (1998). Impact of climate change on the flood characteristics of the Thames and Severn rivers. 2nd International RIBAMOD Conference. Wallingford: Institute of Hydrology.
Reynard, N. (1996). The effects of climate change due to global warming on river flows in Great Britain. Journal of hydrology , 183.3-4 (1996): 397-424.
Reynard, N. (2001). The flood characteristics of large UK rivers: potential effects of changing climate and land use. Climatic change , 48.2 (2001): 343-359.
Rosenzweig, C. (2001). Climate change and extreme weather events; implications for food production, plant diseases, and pests. Global change and human health , 2.2 (2001): 90-104.
Schaller, N. (2016). Human influence on climate in the 2014 southern England winter floods and their impacts. Nature Climate Change , 6.6 (2016): 627-634.
Shackley, S. (1998). Uncertainty, complexity and concepts of good science in climate change modelling: Are GCMs the best tools? Climatic change , 38.2 (1998): 159-205.
Sheffield, J. (2008). Global trends and variability in soil moisture and drought characteristics, 1950–2000, from observation-driven simulations of the terrestrial hydrologic cycle. Journal of Climate , 21.3 (2008): 432-45.
Shumway, R. (2011). Time series analysis. Springer. . Springer.
Siegfried, T. (2010). Odds Are, It’s Wrong. Retrieved 2016, from Science News: https://www.sciencenews.org/article/odds-are-its-wrong
Sneed, A. (2017, January 2). Yes, Some Extreme Weather Can Be Blamed on Climate Change. Scientific American , pp. https://www.scientificamerican.com/article/yes-some-extreme-weather-can-be-blamed-on-climate-change/.
Solomon, S. (2009). Irreversible climate change due to carbon dioxide emissions. Proceedings of the national academy of sciences , pnas-0812721106.
Sornette, D. (1996). Rank‐ordering statistics of extreme events: Application to the distribution of large earthquakes. Journal of Geophysical Research: Solid Earth , 101.B6 (1996): 13883-13893.
Stern, N. (2006). What is the economics of climate change? HENLEY ON THAMES: WORLD ECONOMICS-HENLEY ON THAMES.
Stocks, B. (1998). Climate change and forest fire potential in Russian and Canadian boreal forests. Climatic change , 38.1 (1998): 1-13.
Stott, P. (2013). Attribution of weather and climate-related events . Climate Science for Serving Society. Springer Netherlands , 2013. 307-337.
Trenberth, K. (2015). Attribution of climate extreme events. Nature Climate Change , 5.8 (2015): 725-730.
UNFCCC. (2014). Kyoto Protocol. Retrieved 2017, from unfccc: http://unfccc.int/kyoto_protocol/background/items/2879.php
UNFCCC. (2014). Parties and Observers. Retrieved 2016, from UNFCCC: http://unfccc.int/parties_and_observers/items/2704.php
UNFCCC. (2016). The Paris Agreement. Retrieved 2017, from UNFCCC: http://unfccc.int/paris_agreement/items/9485.php
UNFCCC. (2014). UNFCCC and Kyoto Protocol. Retrieved 2016, from United Nations: http://unfccc.int/kyoto_protocol/items/2830.php
EVENT ATTRIBUTION AND THE PRECIPITATION RECORD FOR ENGLAND AND WALES, JAMAL MUNSHI, 2017 22
UNFCCC. (2013). Warsaw International Mechanism for Loss and Damage associated with Climate Change Impacts. Retrieved 2017, from UNFCCC: http://unfccc.int/adaptation/workstreams/loss_and_damage/items/8134.php
VanAalst, M. (2006). The impacts of climate change on the risk of natural disasters. Disasters , 30.1 (2006): 5-18.
VonStorch, H. (1999). Misuses of statistical analysis in climate research. In Analysis of Climate Variability (pp. . 11-26). Berlin Heidelberg: Springer .
Wilby, R. (2008). Climate change and fluvial flood risk in the UK: more of the same? Hydrological processes , 22.14 (2008): 2511-2523.
WMO. (2016). Explaining extreme weather events of 2015. Geneva: World Meterological Organization.
Woollings, T. (2014). Twentieth century North Atlantic jet variability. Quarterly Journal of the Royal Meteorological Society , 140.680 (2014): 783-791.
Young, P. (1996). Simplicity out of complexity in environmental modelling: Occam’s razor revisited. Journal of applied statistics , 23.2-3 (1996): 165-210.
Zwiers, F. (2013). Climate extremes: challenges in estimating and understanding recent changes in the frequency and intensity of extreme climate and weather events. Climate Science for Serving Society, Springer Netherlands , 2013. 339-389.

CHARTS 1-6: OLS LINEAR TRENDS ACROSS THE FULL SAMPLE

CHARTS 7-8: A COMPARISON OF THE 12 CALENDAR MONTHS

CHARTS 9-14: STANDARD DEVIATION IN A MOVING 30-YEAR WINDOW

CHARTS 15-20: EXTREME VALUES AND OUTLIERS