VARIABILITY AND EXTREMES IN STATISTICALLY DOWNSCALED CLIMATE CHANGE PROJECTIONS AT GREENWOOD NOVA SCOTIA

Transcription

1 VARIABILITY AND EXTREMES IN STATISTICALLY DOWNSCALED CLIMATE CHANGE PROJECTIONS AT GREENWOOD NOVA SCOTIA MICHAEL PANCURA* GARY S. LINES Meteorological Service of Canada, Atlantic Region Science Report Series October 2005 CLIMATE CHANGE DIVISION Meteorological Service of Canada- Atlantic Region Environment Canada 45 Alderney Drive Dartmouth N.S. B2Y 2N6 *Corresponding author-

2 ISBN Catalogue No. En57-36/ E 2

3 ABSTRACT Values of daily maximum temperature (Tmax), daily minimum temperature (Tmin), and total daily precipitation (Pcpn), previously downscaled using the Statistical Downscaling Model (SDSM) and the Canadian General Circulation Model (CGCM1) running the GHG+A1 simulation, were analyzed for variability and extremes. In addition, 52 extreme weather indices were defined using Stardex software, and comparisons in variability were made between values of these indices observed in the base climate period ( ) and values projected for three future periods, namely the 2020 s ( ), the 2050 s ( ), and the 2080 s ( ). Finally, one extreme event, the maximum annual 5-day precipitation total, was examined using the extreme value analysis (EV1) method of Gumbel, to determine any change in return period between the base climate values and the projected values. Analyses were performed at all sites, however because of the hugh volume of data produced, only the results from one arbitrarily selected site in Atlantic Canada, namely Greenwood, Nova Scotia, were reported in detail. In the case of temperature, projected changes in variability indicated that by the 2080 s, the probability of the occurrence of heat waves (i.e. one or more days with Tmax > 32C) would more than triple, while the occurrence of very cold days (i.e. days with Tmin < -15C) would be about 2.5 times less likely. Furthermore, extreme value analysis revealed that the 115mm, 100 year return period extreme event (maximum annual 5-day total precipitation) in the base climate ( ), was projected to recur as often as once every 10 years during the 2050 s ( ), which represents a reduction in the return period by a factor of 10. Published research results from various parts of the world, including western Canada, concluded that even a slight warming in surface temperature correlated with an increased likelihood of severe weather events in these areas. The findings of this paper for increased surface temperature projections at Greenwood suggest that the correlation for increased frequency of extreme weather may apply to parts of Nova Scotia as well. Users of these results are reminded that the projections in this paper were downscaled using SDSM and CGCM1 GHG+A1. Downscaled results from other GCM s running the same emission scenarios would likely produce a range of different, but equally plausible, results. ACKNOWLEDGEMENTS The authors are indebted to Clare Goodess, (Stardex project coordinator) for providing the Stardex source code; to Malcolm Haylock (Stardex project web master) for his assistance in interpreting and modifying the Stardex Fortran code; to Serge Desjardins (Environment Canada Research meteorologist) for providing a Unix platform to run Stardex; to Bridget Thomas (Environment Canada Climate Research meteorologist) for her aid in interpreting probabilities; to Bob Morris (Environment Canada meteorologist) for providing the Gumbel Excel algorithm; to Sarah Evans (Environment Canada intern) for proof reading the earlier versions; and to Trevor Murdock (CICS project Web manager) and Bridget Thomas for peer reviewing the final manuscript 3

4 TABLE OF CONTENTS ABSTRACT ACKNOWLEDGEMENTS TABLE OF CONTENTS LIST OF FIGURES LIST OF TABLES INTRODUCTION,, Purpose,, Defining Climate Variability and Extremes.,, Geographic Background..,, Climate Change Global Scale SDSM Downscaling Extreme Weather Events Societal Impact Extreme Weather Indices (Stardex) Extreme Value Analysis (Gumbel) DATA METHODOLOGY Climate change Analysis of Variability in Basic Weather Parameters (Tmax, Tmin, and Pcpn) Analysis of Variability in Weather Extremes Using Stardex Extreme Value Analysis (Gumbel RESULTS Climate Change Analysis in Variability in Basic Downscaled Parameters (Tmax, Tmin, and Pcpn) Daily Maximum Temperature (Tmax) Daily Minimum Temperature (Tmin) Analysis of Variability and Extremes in Total daily Precipitation (Pcpn) Annual Precipitation Anomalies Changes in Precipitation Frequency (Number of Days without Precipitation Changes in Precipitation Intensity Analysis of Variability in Stardex Extremes The 10 Stardex Core Indices Hottest Days (Tmax90p) Coldest Days (Tmin10p) Frost Days (125Fd) Wettest Days (Prec90p) Maximum Annual 5-day Precipitation Total (644R5d Extreme Value Analysis (Gumbel) SUMMARY CONCLUSIONS NEXT STEPS REFERENCES

5 LIST OF FIGURES Fig 1. Map Showing Sites in Atlantic Canada...7 Fig 2 Schematic showing the effect on extreme temperatures when (a) the mean temperature increases, (b) the variance increases, and (c) when both the mean and variance increase for a normal distribution of temperature Fig 3 Scatter plot at Global scale of various GCM models for Greenwood NS (after CICS, 2003)...10 Fig 4 Variability, Means and Probability of Extremes..12 Fig 5 Daily Tmax Probability Greenwood NS Fig 6 Projected Number of Hot Days per Greenwood NS Fig 7 Daily Tmin Probability Greenwood NS Fig 8 Projected Number of Cold Days per Greenwood NS Fig 9 Annual Precipitation Greenwood NS, vs Fig 10 Percentage of Northeast USA in Extreme Drought (after NRCC) Fig 11 Change in Number of Days with no Greenwood NS..20 Fig 12 Projected Changes in Daily Precipitation Greenwood NS...20 Fig 13 Tmax90p Probability Greenwood NS. 21 Fig 14 Tmin10p Probability Greenwood NS..22 Fig 15 Change in Frost Free Greenwood NS Fig 16 Annual Threshold Values of Prec90p (wettest Greenwood NS Fig 17 Maximum Annual 5-day Pcpn Fig R5d Return Greenwood NS, Fig R5d Return Greenwood NS 2050 s

6 LIST OF TABLES Table 1 Annual Average Projected Change in Downscaled Variables Table 2 Tmax Statistics...15 Table 3 Exceedance Probabilities & Return Periods of Selected Tmax Values...16 Table 4 Tmin Statistics.17 Table 5 Exceedance Probabilities & Return Periods of Selected Tmin Values..18 Table 6 Summary of STARDEX Core Indices- Mean Annual Values Table 7 Tmax90p Threshold Statistics..22 Table 8 Tmin10p Statistics (Statistical Significance (p<0.05) shown in bold).22 Table 9 125Fd Statistics..23 Table 10 Prec90p Statistics Table R5d Statistics Table 12 Return period (yrs) vs. Reduced Variate

7 VARIABILITY AND EXTREMES IN STATISTICALLY DOWNSCALED CLIMATE CHANGE PROJECTIONS AT GREENWOOD NOVA SCOTIA 1.0 INTRODUCTION Climate Change Division, Meteorological Service of Canada, Atlantic Region Environment Canada, 45 Alderney Drive, Dartmouth, Nova Scotia, B2Y 2N6 1.1 Purpose The purpose of this paper was to examine climate variability and extremes at 14 sites in Atlantic Canada using previous statistically downscaled data, and to provide detailed findings at one site, namely Greenwood NS (Fig 1). As used in this paper, variability in a normally distributed parameter occurs when changes in the mean, the variance, or both cause the probability distribution to shift, resulting in changes in the frequency of occurrence of extreme events in either the upper or lower tail of the distributions (Fig 2). To detect variability in non-normal distributions a slightly different comparison technique is required, which will be discussed in detail in section 3.2. Fig 1. Sites in Atlantic Canada Values of daily maximum temperature (Tmax), daily minimum temperature (Tmin) and total daily precipitation (Pcpn), which had previously been downscaled by Lines and Pancura (2003) for 30 year periods centred on the 2020 s ( ), 2050 s ( ), and 2080 s ( ), were reexamined for variability and extremes. The downscaling had been performed using the Statistical Downscaling Model (SDSM, 2001) developed by Wilby et al (2002), and the General Circulation Model (CGCM1) running the GHG+A1 emissions scenario (Flato et al,2000, Boer et al,2000). 1.2 Defining Climate Variability and Extremes Changes in climate variability and extremes have received increased attention in recent years. However, understanding what these terms mean, and how changes are brought about, are made difficult by the various interactions that may occur between changes in the mean and variance of specific distributions (Meehl et al, 2000). The concepts are illustrated in Fig 2 below. 7

8 Fig 2 Schematic showing the effect on extreme temperatures when (a) the mean temperature increases, (b) the variance increases, and (c) when both the mean and variance increase for a normal distribution of temperature (After IPCC,2001). The following excerpt from the report by the IPCC (2001) helps to further summarize and clarify the concepts illustrated in Fig 2. Such interactions vary from variable to variable depending on their statistical distribution. For example, the distribution of temperatures often resembles a normal distribution where non-stationarity of the distribution implies changes in the mean or variance. In such a distribution, an increase in the mean leads to new record high temperatures (Figure 2a), but a change in the mean does not imply any change in variability. For example, in Figure 2a, the range between the hottest and coldest temperatures does not change. An increase in variability without a change in the mean implies an increase in the probability of both hot and cold extremes as well as the absolute value of the extremes (Figure 2b). Increases in both the mean and the variability are also possible (Figure 2c), which affects (in this example) the probability of hot and cold extremes, with more frequent hot events with more extreme high temperatures and fewer cold events. Other combinations of changes in both mean and variability would lead to different results. 8

9 Consequently, even when changes in extremes can be documented, unless a specific analysis has been completed, it is often uncertain whether the changes are caused by a change in the mean, variance, or both. In addition, uncertainties in the rate of change of the mean confound interpretation of changes in variance since all variance statistics are dependent on a reference level, i.e., the mean. For variables that are not well approximated by normal distributions, like precipitation, the situation is even more complex, especially for dry climates. For precipitation, for example, changes in the mean total precipitation can be accompanied by other changes like the frequency of precipitation or the shape of the distribution including its variability. All these changes can affect the various aspects of precipitation extremes including the intensity of precipitation (amount per unit time) It should be noted that methods to measure the effects of changes in the variability and extremes in two variables simultaneously (temperature and precipitation) were beyond the scope of this paper. 1.3 Geographic Background Atlantic Canada consists of four provinces ( Nova Scotia, New Brunswick, Prince Edward Island and Newfoundland & Labrador) and is situated along the northeast coast of North America covering nearly 20 degrees of latitude and 20 degrees of longitude (Fig 1). The climate of the region is varied, including Atlantic, Boreal, and Sub-Arctic climates and is strongly influenced by both the warm Gulf Stream and the cold Labrador Current. Utilizing GCM output over this region limits the researcher to a small number of grid-boxes to cover all sites of interest. Six were used in this study, spanning 300 x 400km each according to the horizontal resolution of the CGCM1. Some of these boxes are defined as ocean boxes (e.g. box 33x10y, which is closest to Cartwright), and where the climate variables respond as if the surface boundary is North Atlantic Ocean water. 1.4 Climate Change Global Scale On a global scale, mean annual surface temperature has increased over the past century by 0.6 C (IPCC, 2001). Within the climate change scientific community, there is general consensus that this increase, especially during the past 50 years, can be attributed partly to Greenhouse Gas (GHG) emissions due to human activity. Global Climate Models (GCMs), which are capable of providing credible projections of climate changes into the next 100 years use a coarse global grid scale (IPCC, 2001). Temperature and precipitation trends however, differ on a regional scale due to the different feedbacks appearing at the synoptic to local scale. This results in differing impacts at different regional scales. To date, impacts researchers have only had GCM scale output to help determine the impacts of climate change to species and ecosystems on a year time scale. In order to best assess the expected climate change impacts on a species, ecosystem or natural resource in a region, climate variables and climate change scenarios must be developed on a regional or even site-specific scale (Wilby et al, 2002). To provide these values, projections of climate variables must be downscaled from the GCM results, utilizing either dynamical or statistical methods (IPCC, 2001). Downscaling is thus a process that correlates the projections of a GCM model at the global scale of the model with site specific effects of local climate forcing. In general, downscaling can be accomplished by using either a Regional Climate Model (RCM), or a statistical technique. Since RCM model output is not readily available for Atlantic Canada, a statistical technique was chosen for this study. Statistical models are not only readily available, but have the added advantage of being extremely parsimonious. Thus most downscaling experiments can be run in minutes on a Personal Computer (PC) with a moderate processor speed ( MHz), allowing for multiple computations to be run in real time, if required. Impacts researchers frequently find that the horizontal resolution of most GCM s is too coarse for most applications. For example, in the Canadian General Circulation Model (CGCM1) described by Flato et al (2000), Boer et al (2000), global grid box size is approximately 300x400km, or 120,000 square km, which is about the area of New Brunswick (Fig 1). In some cases, ecosystems under climatic stress have habitats of 100 km 2 or less, and thus global scale output is not suitable when studying climate change at individual species scales. 9

10 The ideal solution would be to increase horizontal resolution by using Regional Climate Models (RCM s). However, RCM results, which require considerably more resources and computational time than GCM s, are not widely available for Atlantic Canada. Their output has also not been as widely applied and tested as GCM results. Statistical models on the other hand, are more parsimonious, and when used in conjunction with readily available GCM output, can be trained to produce downscaled scenarios in a matter of minutes. A further limitation of this preliminary study is that only one GCM model was used. Fig 3 shows an alternative method of displaying global scale projected output. Data from 25 different GCM models was made available by the Canadian Institute for Climate Studies (CICS, 2003), at the University of Victoria web site (UVIC, 2003), valid for the approximate coordinates of Greenwood NS. Fig 3 Scatter plot at Global scale of various GCM models For Greenwood NS (after CICS, 2003) 1.5 SDSM Downscaling This study utilized the downscaled results obtained by using the Statistical Downscaling Model (SDSM) developed by Wilby et al (2002). A detailed discussion of downscaling using SDSM is described in the above paper and by Lines and Barrow (2003), and what follows is only a brief overview of the procedure. SDSM may be described as a hybrid of multiple regression and stochastic downscaling techniques. Downscaled results are statistically significant at 95% or more. Observed data sets of daily maximum temperature (Tmax), daily minimum temperature (Tmin), and total daily precipitation (Pcpn), the predictands, were regressed against statistically selected predictors using National Centre for Environmental Prediction (NCEP, 2005) data sets from The resulting regression equations were then calibrated against data. The accuracy of the resulting equations can be verified when the current climate ( ) is downscaled and compared to observed values for the same period. These validated models were then used to construct suites of downscaled climate variable projections at selected sites in Atlantic Canada. Predictor values from the first generation of the Canadian Coupled General Circulation Model (CGCM1) (Boer et al., 2000; Flato et al., 2000) running the Greenhouse Gas plus Aerosol simulation (GHG+A1) were obtained from the Canadian Climate 10

11 Impacts Scenarios (CCIS, 2003). A major limitation of regression techniques is the assumption of time-invariance in the predictandpredictor relationships. Studies have shown that this has already been violated in the current climate (Wilby, 1997). Furthermore GCM models may be biased in certain predictor, e.g. the CGCM1 has been reported to be strongly biased in temperature and specific humidity (Gachon, 2005). Because of potential bias within GCM models, it is strongly recommended (IPCC, 2001), that impacts researchers examine downscaled results from two or more models. 1.6 Extreme Weather Events There are many references in the literature that link increases in the frequency or intensity of extreme weather events with increasing surface temperature. Some of the findings noted by Francis and Hengeveld (1998) in their paper on Extreme Weather and Climate Change are summarized below. Increased hail activity and hailstone size in France with increased average overnight low temperature [after Dessens (1995)]. The Goddard Institute for Space Research reports a 6% increase in lightning activity for every 1 C rise in the Earth s average surface temperature. Since lightning is a frequent cause of forest fires, a warmer climate would likely increase the fire hazard, particularly during summer dry spells [after Hengeveld (1998)]. A tendency for tornado frequency to increase in the spring and early summer in the Prairie Provinces in step with increases in average monthly temperature [after Etkin (2000)]. A 4 C rise in Toronto s average temperature would likely increase the risk of summer days with Tmax >30 C from 1 in 10 to almost 1 in 2 [after Hengeveld(1998)].. A 0.5 C rise in average temperature would increase the number of extremely hot days (Tmax >35 C) in the state of Victoria (Australia) by 25%; with a rise of 1.5 C, the number of hot days would increase by % [after Hengeveld (1998)]. An Australian study for the Central USA suggests that heavy rainfalls will become more frequent, while light rainfalls will occur less often in a warmer climate [after Gordon et al (1992)]. A Canadian study suggests a warmer climate will increase the number of severe storms north of 30 N latitude, while the number of less intense storms will remain either constant or decrease [after Lambert (1995)]. The above examples make it clear that slight increases in Earth s average surface temperature do increase the likelihood of occurrence of extreme weather events in various parts of the world. This paper will concentrate on determining whether changes in variance and mean in the distributions of downscaled parameters do in fact suggest increases in the probability of occurrence of extreme weather events for a projected warmer climate in Atlantic Canada Societal Impact Society is impacted more by changes in extremes than by changes in means. Up until recently most GCM models running climate change experiments have dwelt on potential changes in climatic averages. Some authors, notably Katz et al (1992), have argued that variability is more important than averages when assessing the impacts of climate change, since the primary impact of climate change on society results from extreme events. This concept was expanded by Schnar et al (2004), who proposed that the European summer heat wave of 2003 could be explained by a regime with an increased variability in temperature in addition to increases in mean temperature. 11

12 Variability vs Average Distribution A MeanT=10.0C;Std=10.6 A B EE@35C p=0.0785;t=13yrs Probability Distribution B Mean T=20C;Std=10.6 Distribution C Mean T=10C;Std=30 C p=0.2023;t=5yrs p=0.0092;t=109yrs Temperature Fig 4. Variability, Means and Probability of Extremes The problem was alluded to previously in Section 1.2, and is further illustrated here with a specific example. Fig 4 depicts three versions of a Gaussian distribution of maximum daily temperature. Distributions A and B have identical variance but different means; distributions A and C have identical means but different variance. The vertical solid line at some distance to the right represents an extreme event (EE). An examination of these distributions will show that the exceedance probability (p) and return period (T) of the extreme event EE in distribution A is p=0.01 (T=100 yrs). This probability increases to p=0.08 (T=13yrs) if the mean increases as in distribution B, or to p=0.20 (T=5yrs) if the variance increases as in distribution C. Thus a quantitative increase in the probability of occurrence (frequency) of an extreme event can be obtained from an analysis of the shift in the distribution due to a change in the mean, a change in the variance, or a change in both. 1.8 Extreme Weather Indices (Stardex) Extreme weather indices, as defined by the Stardex (Statistical and Regional dynamical Downscaling of Extremes for European regions) software package, were made available by the European Commission-Fifth Framework Programme (Stardex, 2002). The full FORTRAN source code (open), mathematical definitions of the indices, descriptions of all indices particularly the 10 core indices and the method used to determine trend and statistical significance are all obtainable on the Stardex web site (Stardex,2002). Stardex input requires a space (or coma) delimited file for each site containing data in the following sequence; year, month, day, Tmax, Tmin, Tmean, and Pcpn. The current version, Version 3.3.0, will calculate up to 57 indices for quantifying expected changes in extremes. Of the 57 indices, 24 describe temperature, and 33 precipitation. The software requires as input daily values of Tmax, Tmin, Tmean, and Pcpn for 10,950 consecutive days for 30 years (no leap years). The software calculates all indices seasonally as well as annually (except for degree days, growing season length, and frost season length). Although the Stardex electronic file sizes are relatively small (52k/station/period), the Excel output file sizes cover 20 legal pages/station/period. Only the 10 so-called core indices were analyzed in detail (see Appendix). Of the 10 core indices, six describe rainfall, and four are temperature. The six rainfall indices are selected to provide a mix of measures of intensity, frequency, and proportion of total. All thresholds are percentile-based and so can be used for a wide variety of climates. Some of the indices consider properties of only the rain-day (day with precipitation) distribution, while others use the entire 12

13 distribution. The four core temperature indices include the important fixed threshold 0 C, but otherwise are applicable to all climates. For temperature there are two magnitude-based indices and two frequency-based indices. Both hot and cold extremes are analyzed for frequency and magnitude. Stardex output includes the 30 annual values for each of the extreme weather indices of the tri-decade being analyzed, and the following statistics: maximum, minimum, mean, standard deviation, trend, and the statistical significance of the trend (a trend is considered statistically significant for p<0.05). Individual researchers might find this software useful for similar projects. Analysis of extreme indices therefore not only consists of the above statistics, but also comparisons of projected vs. base climate periods for each index, for inferences about changes in probability of occurrence. 1.9 Extreme Value Analysis (Gumbel) This paper also calculated the return period of one extreme event, namely, the maximum annual 5-day precipitation total, following the procedure outlined by Bruce (1966) using the method of moments developed by Gumbel (1941). The remainder of this paper will discuss data sources, methodology used, results obtained, summary, conclusions, next steps, acknowledgements and references. 2.0 DATA The analysis of variability and extremes used two sets of data; observational data sets and downscaled data sets. Both data sets were identical to those previously described by Lines et al (2002), and Lines et al (2005). The downscaled data sets developed in the above report were generated by using SDSM and CGCM1 running the Greenhouse Gas plus Aerosol (GHG +A1) experiment. The version of SDSM used in this study (Version 2.2.0) produced 20 ensembles (default value) of downscaled daily data. So, each future period projected by SDSM contains exactly 10,950 values per parameter (no leap years). Since this version of SDSM employs a monthly model for the multiple regressions, there is a projected value for each day ; however these values are statistically derived and should not be used to infer information on a per calendar day basis. In the case of temperature, ensemble means were used. In the case of precipitation the ensemble means could not be used because many days in the downscaled scenarios are without precipitation, and the averaging process could have led to a scenario with precipitation on every day. The authors thus ranked the 20 ensembles into worst case and best case scenarios, defined by the magnitude of the variance of each distribution. For this study, the worst case precipitation scenario was arbitrarily chosen to be used as input into the Gumbel and Stardex analyses. 3.0 METHODOLOGY 3.1 Climate change The method used to downscale projected climate change parameters has been fully described in a previous paper by Lines et al (2005), and will not be further discussed here. However, for convenience, the annual downscaled results for the basic parameters Tmax, Tmin, and Pcpn are summarized in the results section of this paper. 3.2 Analysis of Variability in Basic Weather Parameters (Tmax, Tmin, and Pcpn) Variability in the distributions of Tmax and Tmin were analyzed using probability distributions and histograms. Since temperature is considered to be normally distributed (IPCC, 2001), Gaussian curves were fitted to the daily series of Tmax and Tmin, for both the historical and projected data sets. Differences in the means (averages) and the variance (standard deviation) between historical and 13

14 projected distributions were analyzed for variability, i.e. for changes in probability of occurrence of particular extreme events. Histogram analysis was used to highlight the probable increase in the annual number of hot days (Tmax >30 C), very hot days (Tmax >35 C), and extremely hot days (Tmax >40 C). In addition, the probable decrease in the annual number of cold days (Tmin <-10 C), very cold days (Tmin <-15 C), and bitterly cold days (Tmin <-20 C) was determined. As was pointed out earlier (IPCC, 2001) precipitation is not well approximated by normal distributions. Thus variability and extremes in precipitation series was investigated using annual precipitation anomalies, and histogram analysis to determine changes in frequency and intensity. Precipitation intensity categories (mm/day) followed Houghton (1997), and were placed into 8 categories or bins; <0.2, , , , , , , , >25.6. The resulting analyses showed the percentage change in frequency within each category each tri-decade. A day with precipitation was defined when daily total precipitation > 0.2mm Analysis of Variability in Weather Extremes Using Stardex This study used Stardex version which produced 250 analyses of 52 indices. The software calculated all indices seasonally as well as annually (except degree days, growing season length, and frost season length). Required input is a comma delimited file containing values for the year, month, day, Tmax, Tmin, Tmean, and Pcpn, one row/day for each of 10,957 consecutive days in the base climate period (including leap years), and 10,950 days for projected periods. Output contains the 30 annual extremes, the mean (μ), standard deviation (σ), linear trend, and a Kendall-tau significance test (p<0.05) of the trend. Although the output electronic file sizes are relatively small (52k/station/period), when printed in Excel output data requires 20 legal pages/station/period. Thus for this report only the results for 10 core indices are included, and only the following five indices were analyzed in detail Tmax90p which targets the threshold value of the 90 th percentile of maximum daily temperature (hottest days); Tmin10p which targets the 10 th percentile of the minimum daily temperature (coldest days); 125Fd, which targets the number of frost (or frost free days); Prec90p, which targets the 90 th percentile of precipitation day amounts (wettest days); and 644R5d which targets the maximum 5-day precipitation total (wettest 5- day storm). To run Stardex using projected data, a few programming changes were made. Since projected data do not include leap years (resulting in 7 less days in a 30-year period), the coding for leap years was disabled. Thus two flavours of Stardex were employed in this study: one for the base climate period , and one for the three projected periods , , and A more elegant re-write of the user defined inputs within Stardex is planned for a later date. 3.4 Extreme Value Analysis (Gumbel) The return periods of an extreme value 644R5d, the maximum annual 5-day precipitation totals, were also analyzed, using the method of moments developed by Gumbel (1941) and adapted to precipitation extremes by Bruce (1966). A template developed by Morris at Environment Canada (2001), containing an Excel macro, was used to determine the return period of any size 120-hour storm. The algorithm produced the line of best fit to the observed data, including the 95% confidence limits on a reduced variate axis. The accompanying equation (along the abscissa) readily allows conversion from reduced variate to return period (in years). The template was used to estimate the return periods of any size maximum annual 120-hr rainfall for the base climate period ( ), which was then compared to the projected output for the 2050 s. 14

15 4.0 RESULTS 4.1 Climate Change The projected climate change values obtained earlier by Lines et al (2005) are reproduced in Table 1 below. All changes are with respect to the base climate period Table 1 Annual Average Projected Change in Downscaled Variables (after Lines et al-2005) Tmax Tmin Pcpn SDSM CGCM1 SDSM CGCM1 SDSM CGCM1 Tri-decade C C C C C C C C C C C C % % % % % % NS Greenwood Kentville Shearwater Nappan PEI Charlottetown NB Moncton Chatham Charlo Fredericton Saint John NL Gander St Johns Cartwright Goose Bay Table 1 compares SDSM downscaled values at specific sites to grid box values projected by CGCM1 in each of the three tri-decades indicated, i.e. 20 = , 50 = , and 80 = For example, at Greenwood during the 2080 s, SDSM projects temperature to increase by 5.3 C and precipitation by 10%, whereas CGCM1 projects 4.1 C and 5% respectively. These differences are due to the role played by local scale climatic forcing. All SDSM downscaled values are statistically significant (p<0.05). 4.2 Analysis in Variability in Basic Downscaled Parameters (Tmax, Tmin, and Pcpn) Daily Maximum Temperature (Tmax) Since temperature is considered to be normally distributed (IPCC, 2001), the distributions of Tmax and Tmin were examined for changes in means and variance, and how changes in these two statistics affected the probability of occurrence of record hot or cold weather. The relevant statistics for Tmax from observed and downscaled data are summarized in Table 2 below. TABLE 2 Tmax Statistics s 2050 s 2080 s Average (μ) Std Deviation (σ) Maximum Minimum Table 2 shows an increase of 5.4 C in the mean value of Tmax by the 2080 s, with ~10% increase in variability (standard deviation). Since temperature is considered to be normally distributed 15

16 (IPCC,2001), Gaussian distributions were fitted to the historical and projected daily values of Tmax as shown in Fig 5 below. The combined change in both mean and variance in Tmax is shown in Fig 5. This shift towards warmer temperatures is such that an extreme event represented by the red line (Tmax = 32 C) will be three times more likely in a 2080 s climate (p=0.1), than it was during the base climate period (p=0.03). This shorter return period due to global warming is generally referred to as the reduction factor. Probability Distribution Greenwood NS Probability p=0.1; T=10 p=0.06; T=17 p=0.04; T=24 p=0.03; T= Temperature (C) Fig 5 Daily Tmax Probability Greenwood NS Table 3 shows the exceedance probabilities and return periods of select values of Tmax >30 C. Table 3 Exceedance Probabilities & Return Periods of Selected Tmax Values Exceedance probability p Return period T (yrs) Tmax( C) s 2050 s 2080 s s 2050 s 2080 s > > > > > > For example, Table 3 shows that the projected probability of occurrence of Tmax >40 C is five times more likely in the 2080 s (0.02) as it was in the historical period (0.004). The histograms in Fig 6 show the increase, with respect to the base climate, of days with Tmax >30 C (hot days), Tmax >35 C (very hot days), and Tmax >40 C (extremely hot days). Since the Glossary of Meteorology (1959) defines a heat wave as one or more days with Tmax 32 C, Table 3 indicates that the probability of increased heat waves is projected to be 1.4 times more likely by the 2020 s, ~2 times more likely by the 2050 s, and 3.2 times more likely by the 2080 s then they were during

17 Projected Number of Hot Days/Year 50.0 Number of Days Hist >30 >35 >40 >45 Hot category Fig 6. Projected Number of Hot Days per Greenwood NS Daily Minimum Temperature (Tmin) The relevant statistics for Tmin from observed and projected data are summarized in Table 4 below. Table 4 Tmin Statistics s 2050 s 2080 s Average (μ) Std Deviation (σ) Maximum Minimum Since minimum temperature is considered to be normally distributed (IPCC,2001), Gaussian distributions were fitted to the historical and projected daily values of Tmin as shown in Fig 7 below. Probability Distribution Greenwood NS p=0.04;t=24 p=0.02;t=48 p=0.016;t=61 p=0.0155;t= Table 4 shows the average daily minimum temperature warming 3.9 C by the 2080 s, with only minor changes in variance (standard deviation) Temperature (C) Fig 7 Daily Tmin Probability Greenwood NS 17

18 From the Tmin distribution curve (Fig 7), this change in mean value is such that a Tmin <-15 C is two and a half times less likely in a 2080 s climate (p=0.016, T=64) than it was during (p=0.04, T=24). Table 5 shows the exceedance probabilities and return periods for selected values of Tmin. Table 5 Exceedance Probabilities & Return Periods of Selected Tmin Values Exceedance probability p Return period T (yrs) Tmax( C) s 2050 s 2080 s s 2050 s 2080 s < < < < < Number of Cold Days Projected Number of Cold days/yr Hist <-20 <-15 <-10 Daily Minimum Temperature (C) Fig 8 shows the projected change in number of days with Tmin <-10 C (cold days), Tmin <-15 C (very cold days), and Tmin <-20 C (bitterly cold days. Cold days are projected to become less common, while very cold and bitterly cold days are projected to be become highly unlikely in future scenarios. Fig 8. Projected Number of Cold Days per Greenwood NS Analysis of Variability and Extremes in Total daily Precipitation (Pcpn) As was mentioned earlier in Section 1.2, precipitation is not well approximated by normal distributions (IPCC, 2001). In this section historical and projected precipitation data were analyzed for changes in annual anomalies, changes in frequency (days with precipitation), and precipitation intensity (amount per unit time) that would indicate changes in variability and extremes Annual Precipitation Anomalies Fig 9 shows annual precipitation anomalies for the base climate period ( ) (left portion of the graph) compared to the 2080 s projected period (right portion). Fig 9 illustrates that the base climate period has 10 positive anomalies and 15 negative anomalies; whereas the projected climate has 19 positive and 7 negative anomalies. This increase in positive annual anomalies is in accord with the projected 10% annual increase projected by the downscaled scenarios. Apart from the one correlation between the annual precipitation deficits in at Greenwood NS, which coincided with the severe drought conditions as reported throughout the northeast USA during the same period (NRCC, 2003) as shown in Fig 10, there is no simple way to infer flood or drought frequency from annual anomalies. Seasonal precipitation analyses were not performed in this report. 18

19 Analysis of Climate Greenwood NS Annual Pcpn Anomaly (mm) Anomaly -500 Year Fig9 Annual Precipitation Greenwood NS, vs Fig 10 Percentage of Northeast USA in Extreme Drought (after NRCC) Changes in Precipitation Frequency (Number of Days without Precipitation) Historical and projected periods were analyzed for changes in frequency, i.e. changes in the number of days with (without) precipitation. 19

20 Increase in # of days INCREASE IN PRECIPITATION FREE DAYS 2020's 2050's 2080's Projected Tri-decade Fig 11 shows that in all three projected periods, days without precipitation will increase; ergo the number of days with precipitation will decrease. Since total annual precipitation is projected to increase by ~10% (Table 1), and since the number of days with precipitation is projected to decrease (Fig 11), the amount of precipitation per wet day is projected to go up. The mean value of P3 (646SDII) Pcpn/Pcpn-day in Tables A2-A5 in the Appendix confirms this inference. Fig 11 Change in Number of Days with no Greenwood NS Changes in Precipitation Intensity Both the historical and projected records were categorized into bins representing the total amount of precipitation that falls per day. Bin ranges followed the categories suggested by Houghton (1997). Changes in Daily Rainfall Intensity Change in # days > 's 2050's 2080's Fig 12 showing the change in projected intensity versus the intensity from the base climate period, clearly illustrates that in future the number of days with precipitation < 2mm will decrease dramatically, while days with precipitation > 2mm will increase. This is in agreement with the earlier projection that more precipitation will fall on fewer days. Rainfall Category (Bin) Fig 12 Projected Changes in Daily Precipitation Greenwood NS 4.3 Analysis of Variability in Stardex Extremes Stardex software (Stardex, 2002) was used to identify and compute 52 extreme weather indices both seasonally and annually (see Appendix, Table A1). Only the 10 annual core indices at Greenwood NS were analyzed for variability (see Appendix, Tables A2-A5), and only five Stardex extremes (Tmax90p, Tmin10p, 125fd, Prec90p, and 644R5d) are discussed in detail in this report The 10 Stardex Core Indices The complete analysis of the 10 core indices is contained in Tables A2-A5 (see Appendix). A summary of Tables A2-A5 are reproduced in Table 6 below. 20

21 Table 6 Summary of STARDEX Core Indices- Mean Annual Value Units s 2050 s 2080 s T1 Tmax90p C T2 Tmin10p C T3 125Fd Days T4 144HWDI Days P1 Prec90p Mm/day P2 644R5d Mm P3 646SDII Mm/day P4 641CDD Days P5 691R90T % 40.3% 38.2% 37.7% 38.5% P6 692R90N days A description of each index is included in the Appendix, Table A1. A mathematical definition of these 10 cores indices in addition to all other Stardex indices is included on the Stardex web site (Stardex, 2002). The five indices highlighted in bold in Table 6 were examined in detail and are described more fully below. They represent the hottest days (Tmax90p), coldest days (Tmin10p), frost days (125Fd), wettest days (Prec90p) and maximum annual 5-day precipitation total (644R5d) Hottest Days (Tmax90p) 0.6 Probability Distribution Greenwood NS EV 0.5 Probability Temperature (C) Fig 13 Tmax90p Probability Greenwood NS The Stardex weather extreme Tmax90p represents the threshold value of the 90 th percentile of the daily maximum temperature, i.e. the lowest temperature within the 10 percent of the hottest days. The probability distributions for Tmax90p for each of the four 30 year periods at Greenwood are illustrated in Fig 13. For example, the 90 th percentile of the distribution in Fig 2 would be at 25.7C, which agrees with the mean of the Tmax90p distribution shown below. The relevant statistics for Tmax90p from Tables A2-A5 are summarized in Table 7 below. 21

22 Table 7 Tmax90p Threshold Statistics s 2050 s 2080 s Average(μ) Std Deviation(σ Maximum Minimum Trend p < Table 7 shows a large (6.9 C) (statistically significant increase in the mean threshold value, with a 33% increase in the variability (standard deviation) by the 2080 s. Statistically significant tri-decades (i.e. p<0.05) are shown in bold. As shown in Fig 13, the probability of occurrence of the threshold value of 28.7 C, which is highly unlikely in the base climate period, will be exceeded ~50% of the time in the 2020 s, ~85% of the time in the 2050 s, and virtually 100% of the time in the 2080 s Coldest Days (Tmin10p) In a similar manner the Stardex weather extreme Tmin10p represents the threshold value of the 10 th percentile of the daily minimum temperature, or the highest temperature of the 10 percent of the coldest days. The probability distributions for Tmin10p are illustrated in Fig 14 below. frequency Probability Distribution Greenwood Nova Scotia EV Temperature(C) Fig 14 Tmin10p Probability Greenwood NS The relevant statistics for Tmin10p from Tables A2-A5 are summarized in Table 8 below. Table 8 Tmin10p Statistics (Statistical Significance (p<0.05) shown in bold) s 2050 s 2080 s Average(μ) Std Deviation(σ) Maximum Minimum Trend p < Table 8 shows an increase of 5.3 C in the mean threshold value with an approximate 300% decrease in the variability (standard deviation) as early as the 2020 s. From Fig 14, the probability of occurrence 22

23 of the threshold value of -8 C, which is highly unlikely in the base climate period, will be exceeded ~60% of the time in the 2020 s, ~90% of the time in the 2050 s, and virtually 100% of the time in the 2080 s. The average increasing trend of ~ C/year becomes statistically significant as early as the 2020 s Frost Days (125Fd) The Stardex weather extreme 125Fd calculates the number of frost days, or days with Tmin <0 C. The relevant statistics for 125fd from Tables A2-A5 are summarized in Table 9 below. Table 9 125Fd Statistics s 2050 s 2080 s Average(μ) Std Deviation(σ) Maximum Minimum Trend p < It should be noted that the more interesting extreme is the number of frost free days, which equals ( Fd). Fig 15 below shows the projected change in number of frost free days with reference to the base climate period In a warmer climate, one would expect the number of frost free days to increase. Fig 15 shows the trend for all tri-decades. There is a slight decrease in frost free days during the 2020 s. However by the 2050 s and 2080 s the number of frost free days rises in accordance with the assumption of global warming. Fig 15 Change in Frost Free Greenwood NS Wettest Days (Prec90p) The Stardex weather extreme Prec90p is an intensity extreme and identifies the 90 th percentile threshold value of the wettest days encountered per tri-decade. Stardex returns one value for each year for both historical and projected tri-decades. The relevant statistics for Prec90p from Tables A2- A5 are summarized in Table 10 below. Table 10 Prec90p Statistics s 2050 s 2080 s Average(μ)

24 Std Deviation(σ) Maximum Minimum Trend p < Fig 16 and Table 10 show a moderate rise in precipitation on the wettest days into the 2050 s, followed by a slight decrease. Individual tri-decadal trends, however, are not statistically significant (p>>0.05). Fig 16 Annual Threshold Values of Prec90p (wettest Greenwood NS Maximum Annual 5-day Precipitation Total (644R5d) The Stardex weather extreme 644R5d is a measure of the maximum annual precipitation occurring in any consecutive 120 hour (5-day) period. Stardex returns one value for each year for both historical and projected tri-decades. The relevant statistics for 644R5d for Greenwood from Tables A2-A5 are summarized in Table 11 below. Table R5d Statistics s 2050 s 2080 s Average(μ) Std Deviation(σ) Maximum Minimum Trend p < Fig 17 and Table 11 show a 15% increase in mean values by the 2020 s, with values remaining steady thereafter. Individual tri-decadal trends, however, are not statistically significant (p>>0.05). 24

25 Fig 17 Maximum Annual 5-day Pcpn Table 11 also lists the maximum value for 644R5d, generated by SDSM and detected by Stardex in each tri-decade. 4.4 Extreme Value Analysis (Gumbel) The return periods of the Stardex weather extreme 644R5d (maximum annual 5-day precipitation total) were obtained using the method of moments developed by Gumbel (1941), following the technique described by Bruce (1966). A template developed by and for Environment Canada (Morris, 2001) containing an Excel macro was used for all calculations. The algorithm plotted the actual annual maxima, the line of best fit to the observed data, and the 95% confidence limits. In the calculations, the x-axis is the Reduced Variate (RV), where RV= ln (ln (T/T-1)), with T being the required return period in years, ln is the natural logarithm. Return period can be estimated from Table 12 below, which shows the equivalence between return period (years) and reduced Variate, or it can be calculated from the relationship Reduced Variate = RV = ln(ln(t/(t-1))). In many hydrologic applications, structures are often designed to withstand the extreme represented by the 100 year return period value (CEEA, 1996). The Gumbel distribution of the maximum annual 5-day precipitation total (644R5d) storm for the base climate period is shown in Fig 18 below. In the example, the heavy line is the line of best fit to the observed data, while the dashed lines represent the upper and lower 95% confidence limits. Illustrated in red is the 100 year return period of the maximum annual 5 day precipitation total (644R5d) CEEA design storm, whose value is approximately 115mm. 25