TRENDS IN DAILY PRECIPITATION AND TEMPERATURE EXTREMES ACROSS WESTERN GERMANY IN THE SECOND HALF OF THE 20TH CENTURY

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1 INTERNATIONAL JOURNAL OF CLIMATOLOGY Int. J. Climatol. 25: (2005) Published online in Wiley InterScience ( DOI: /joc.1182 TRENDS IN DAILY PRECIPITATION AND TEMPERATURE EXTREMES ACROSS WESTERN GERMANY IN THE SECOND HALF OF THE 20TH CENTURY YESHEWATESFA HUNDECHA* and ANDRÁS BÁRDOSSY Institute of Hydraulic Engineering, University of Stuttgart, Stuttgart, Germany Received 25 August 2003 Revised 12 January 2005 Accepted 24 January 2005 ABSTRACT The evolution of daily extreme precipitation and temperature from 1958 to 2001 was investigated within the German side of the Rhine basin. Trends of a set of extreme precipitation and temperature indices defined on daily time series of precipitation and temperature were calculated at 611 precipitation and 232 temperature stations located within the study area and their corresponding significances were tested using the non-parametric Kendall- tau test. The results obtained indicated that both the daily minimum and maximum extreme temperatures have increased over the investigation period, with the degree of change showing seasonal variability. On an annual basis, the change in the daily minimum extreme temperature was found to be greater than that of the daily maximum extreme temperature. The daily extreme heavy precipitation has shown increasing trends both in magnitude and frequency of occurrence in all seasons except summer, where it showed the opposite trend. The station values of the daily precipitation were also interpolated on a regular grid of 5 km 5 km so that the changes in the indices could be investigated on areal precipitation by aggregating the interpolated precipitation to any desired scale. This enables assessment of the hydrological consequences of the changes in the extreme precipitation. Although the spatial pattern remained more or less similar with that of the point-scale trends for all indices, the average trend magnitude showed an increase with the scale of the area on which precipitation was aggregated. Copyright 2005 Royal Meteorological Society. KEY WORDS: climate trends; extreme daily precipitation; extreme daily temperature; Rhine; western Germany 1. INTRODUCTION Many studies conducted in different parts of the world have revealed that the mean temperature has increased over the last century. At the global scale, an increase of 0.6 C in the mean temperature has been reported (Nicholls et al., 1996). It has also been observed that the daily minimum temperature has increased more than the daily maximum temperature (Easterling et al., 1997). It is also reported that surface precipitation has correspondingly increased in the mid to high latitudes over the same period. An increase of 10 50% has been observed over northern and western Europe (Watson et al., 1998). Although it is hard to attribute the observed increase in precipitation to the rise in temperature, many climate model studies conducted to simulate the effects of increased greenhouse gases suggest an increase in the mean precipitation and frequency of heavy precipitation (Bony et al., 1995; Meehl et al., 2000). Although the changes in the mean values of the climate variables have a bearing on the long-term climatic conditions, the changes in the extremes of the variables can have far-reaching economic and social consequences. Many of the previous studies on the analysis of observed changes in climate variables were focused mainly on the mean values rather than on the extremes. This is mainly due to the quality and quantity * Correspondence to: Yeshewatesfa Hundecha, Institute of Hydraulic Engineering, University of Stuttgart, Stuttgart, Germany; hundecha@iws.uni-stuttgart.de Copyright 2005 Royal Meteorological Society

2 1190 Y. HUNDECHA AND A. BÁRDOSSY of historical data required for the analysis of extremes, which is not usually met in many parts of the world. A higher temporal resolution of the data than is required for analysis of the mean is needed and the data series should be complete, as missing data may potentially lead to exclusion of important extreme events, making the result prone to uncertainty. A limited number of studies done on extremes have shown that the minimum temperature is getting less extreme in different parts of the world. The number of frost days has decreased in Europe (Heino et al., 1999), North America (Easterling et al., 2000), and Australia (Plummer et al., 1999). Although conclusive evidence of an increase in the extreme precipitation at a global scale is not available, it has been observed that intense precipitation has increased over the USA (Karl et al. 1995; Karl and Knight, 1998), Australia (Suppiah and Hennessy, 1998; Hennessy et al., 1999; Plummer et al., 1999), and Japan (Iwashima and Yamamoto, 1993). Unlike temperature, precipitation shows a strong spatial variability. Historical records for both temperature and precipitation are normally available at point measurement locations. Although analysis of changes in the frequency of extreme precipitation at a given observation station tells something about the evolution of extremes in the vicinity of the station, the hydrological consequence of the changes can only be quantified if the changes are determined at a mesoscale or higher spatial scale. The areal extent of extreme precipitation is important for the assessment of hydrological consequences, such as flooding. Owing to the variability of precipitation, upscaling of the point observation to a scale relevant to hydrological impact assessment is not atrivialtask. This study is aimed at investigating the evolution of daily temperature and precipitation extremes in the second half of the last century across western Germany through statistical analysis of station data. It is also aimed at investigating the trends of extreme daily precipitation at different spatial scales through upscaling of the station observations. 2. STUDY AREA AND DATABASE The study was done on the German part of the Rhine basin. In the past few years, this basin has seen a number of extreme flooding events that have had severe consequences. Figure 1 shows a 30-year movingaverage discharge at gauge Worms, located on the upper part of the River Rhine. Although the flooding in the basin can to some extent be attributed to anthropogenic activities in the basin, the extreme precipitation events observed repeatedly within the basin are also responsible. Therefore, it is worthwhile investigating the evolution of the extreme climate variables within the basin. Daily precipitation data from more than 2000 stations and daily minimum and maximum temperatures from 462 stations for the time period from 1958 to 2001 were obtained from the German Weather Service. The data were collected according to the WMO standard and were regularly checked for their homogeneity. Based on completeness of the data set and proximity of the stations to the basin, data from 611 precipitation stations and 232 temperature stations were used for the analysis of extremes. Figure 2 shows the distribution of the precipitation and temperature stations within and around the study area. 3. METHODOLOGY Extremes of a climate or weather variable are basically events that are observed rarely and statistically they correspond to the far ends of the frequency distribution of the variable. Changes in extremes are, therefore, caused by changes in the frequency distribution of the variable. A change in the mean of the distribution of the variable, for example, results in a shift in the entire distribution of the variable to one side, and hence causes a change in the extreme in that direction. An increase inthemeantemperatureleadstoanincreaseinthe frequency of extremely hot temperatures and to a decrease in the frequency of extremely cold temperatures. The frequency of extremes and the mean are non-linearly related, and a small change in the mean may cause a large change in the frequency of extremes (Mearns et al., 1984; Easterling et al., 2000). Changes in extremes

3 TRENDS IN EXTREMES Q (m 3 /s) Year Figure 1. A 30-year moving-average discharge at Worms in the River Rhine Figure 2. Distribution of observation stations in the Rhine basin. This figure is available in colour online at com/ijoc

4 1192 Y. HUNDECHA AND A. BÁRDOSSY are also caused by a change in the variance of the distribution of the variable. An increase in the variance of the variable leads to an increase in the frequency of both sides of the extreme. A change in the extremes in a rather complicated way may be caused by changes in both the mean and the variance of the distribution of the variable simultaneously and a change in the shape of the distribution. Therefore, changes in extremes can be assessed if one is able to detect changes in the parameters of the frequency distribution of the variable of interest. Trends in the annual and annual seasonal extremes of daily precipitation and temperature can be analysed by fitting appropriate theoretical distribution functions to the observed daily data over each season of a year and analysing for the changes in the parameters of the distribution functions over the years of investigation. This, however, requires making an assumption about the distribution function, and it has a serious practical limitation when analysing data from many stations. The assumption made about the distribution function may not be met by many stations, and the results of the analysis may lead to a wrong interpretation of the changes in the extremes. The problem posed by the limited knowledge about the distribution of the daily precipitation and temperature in analysing the changes in their extremes can be handled by implementing a non-parametric, distribution-free approach. Extreme indices that can be estimated from the empirical distribution of the daily precipitation and temperature are defined and their changes are analysed directly. The indices can be defined based on some predefined arbitrary threshold magnitudes. However, the problem with such a definition is that the indices are applicable only to a specific climate region, as the threshold values may not be considered extremes in other climate regions. Therefore, many of the indices used in this study were defined using thresholds defined based on statistical quantities such as the 90th or 10th percentiles. The only exception is a threshold value of 0 C fixed to define frost days; which is, of course, applicable to all climates. The base period for the calculation of normals was set between 1961 and The extreme indices used in this study and their definitions are listed in Table I. Annual and seasonal values of the indices were calculated on a yearly basis for each station for the time period from 1958 to 2001 and a trend test was performed on the time series thus generated. The distributionfree rank-based Kendall tau trend test (Kendall, 1975) was used with permutation (Good, 1993) to assess the presence of a trend in the time series and calculate the corresponding significance level. The test statistic was calculated as the standard Kendall tau test statistic (Hirsch et al., 1982). Generally, the Kendall tau test statistic follows a standard normal distribution and the significance level of the calculated test statistic can, therefore, be estimated based on the cumulative distribution function of the standard normal variate. A distribution-free approach to the significance test, a permutation test (Good, 1993), was used to check the significance level Table I. Indices of daily extreme precipitation and temperature Designation Description Precipitation-related indices Prec90p 90th percentile of rain-day amounts (mm/day) 5D-total Greatest 5-day total rainfall SDII Simple daily intensity (rain per rain day) CDD Max no. of consecutive dry days P>90p Percentage of total rainfall from events greater than long-term 90th percentile N>90p No. of events greater than long-term 90th percentile of rain days Temperature-related indices Tmax90p Tmax 90th percentile Tmin10p Tmin 10th percentile Fd Number of frost days Tmin < 0 C HWDI a Heat wave duration a This index is defined as the number of consecutive days in a given season of a year for which the daily maximum temperature on each day exceeds the long-term 90th percentile of that calendar day s maximum temperature calculated over a 5 day window centred on that calendar day.

5 TRENDS IN EXTREMES 1193 of the test statistic in this study. The magnitudes of the trends were then calculated by fitting a least-squares linear regression line into the annual seasonal time series of the indices (Wilks, 1995). In order to assess the hydrological implications of the changes in extreme precipitation, the analysis should be made at a spatial scale relevant to hydrological modelling. This scale may range from grid cells of a few hundred metres or kilometres to a catchment scale, depending on the type of model implemented. Since the models use the precipitation series directly, it is more meaningful first to upscale the point observations to the relevant scale and then investigate the changes in the measures of extreme of the upscaled precipitation, instead of upscaling the point measures of extreme and then assessing their changes. For upscaling precipitation, a 5 km 5 km grid was generated across the study area and the mean daily amount of precipitation over each grid cell was estimated as the weighted sum of the nearby station values using a geostatistical method. External drift kriging (Ahmed and de Marsily, 1987) was implemented. This is a non-stationary kriging approach that is suitable for incorporating secondary information in estimating the amount of precipitation at an unsampled location. As precipitation tends to show a dependency on topographic elevation due to orographic effects, a digital elevation model was used as a source of secondary information to interpolate the amount of precipitation. According to the method, the expected value of precipitation z(u,t) at a given point u and time t is assumed to be a linear function of some drift variable H(u), which in this case is some function of topographic elevation: E[z(u,t) H(u)] = a(u,t) b(u,t)h (u) (1) where a(u,t) and b(u,t) are unknown coefficients. It is not necessary to calculate them explicitly. Instead, they are implicitly estimated from the kriging system of equations that are established under the condition that an unbiased estimation of precipitation is done with a minimum estimation variance. The estimated value of precipitation is z (u,t) = n(u) i=1 λ i (u,t)z(u i,t) (2) where n(u) is the number of stations from which the precipitation at location u is interpolated and λ i (u,t) is the weight assigned to the ith station used for interpolation, which is estimated using the following system of kriging equations: n(u) j=1 j=1 λ j (u,t)γ t (u i u j ) µ 1 (u,t) µ 2 (u,t)h (u i ) = γ t (u i u), n(u) λ j (u,t) = 1 n(u) λ j (u,t)h (u j ) = H(u) j=1 i = 1,...,n where µ 1 (u,t) andµ 1 (u,t) are Lagrange parameters that account for constraints on the weights. γ t () is the variogram function, which was estimated on the daily basis by fitting a theoretical variogram as a combination of a spherical variogram and a pure nugget effect into the experimental variogram calculated from the daily precipitation record of the stations within and around the study area. The secondary variable H(u) should be numeric and be available at all sampled locations, as well as at all locations where estimation is to be done. As precipitation shows a gradual increase with elevation and the rate of increase becomes slower as the elevation increases, the square root of topographic elevation was used as the drift variable, which was verified using cross-validation. The important quality of this interpolation approach is that the correlation between the secondary variable and the primary variable is assessed locally based on the correlation of the variables at the observation points in the neighbourhood of the estimation location. Therefore, a change in correlation between the variables (3)

6 1194 Y. HUNDECHA AND A. BÁRDOSSY across the study area is implicitly accommodated. If they happen to be uncorrelated, then the secondary variable is ignored in the estimation of the kriging weights. Measures of extremes were calculated on grids of 5, 10, 25, and 50 km to investigate the effect of upscaling on the changes in extremes. The precipitation values on the higher grid sizes were calculated by aggregating the precipitation interpolated on the 5 km grid. 4. RESULTS 4.1. Temperature indices All the temperature indices investigated showed seasonal variability. In general, it was found that the daily maximum temperature is getting more extreme, as shown in Figure 3, whereas the minimum is getting less extreme. Table II summarizes the numbers of stations with positive/negative trends together with the corresponding numbers of significant trends for the extreme temperature indices investigated in this study. Except in autumn, both the 90th percentile daily maximum and the 10th percentile daily minimum temperatures showed increasing trends for the majority of the stations, with many of the increases being significant. One should, however, note that there are only a few stations showing an increasing trend in the 10th percentile daily minimum in winter. The highest average increase in the 90th percentile daily maximum temperature was observed in winter, which is 2.7 C over the investigation period. The summer 90th percentile daily maximum increased by a lesser amount (1.4 C). Similarly, the 10th percentile daily minimum also showed a greater increase in winter than in summer (2.1 C and 1.1 C respectively). Figures 4 and 5 show the winter and summer average trends in the 90th percentile daily maximum and 10th percentile daily minimum temperatures respectively. In autumn, both indices showed a decreasing trend at many of the stations investigated. However, there were only a few significant decreases. On average, the 90th percentile daily maximum temperature dropped by 1.2 C and the 10th percentile minimum showed a slight decrease of about 0.1 C. The annual trend, however, showed a greater increase in the 10th percentile daily minimum (1 C) than the 90th percentile daily maximum temperature (0.6 C). The observation that the extreme daily minimum temperature is getting less extreme was confirmed by the fact that the number of frost days is also decreasing in all seasons. Especially in winter and spring, many stations showed a significant decrease, with a drop in the average number of frost days by 8 days and 6 days respectively. Similarly, the increasing trend of the extreme daily maximum temperature is supported by the increasing trend of heat wave duration for all seasons for the majority of the stations. Many of the increases in winter were noted to be significant. The changes in the extreme daily temperature indices averaged over all the stations over the investigation period for all seasons are shown in Table III. No specific spatial pattern was noticed in the significant trends in temperature-related extremes. Stations showing significant trends are evenly distributed within the study area Precipitation indices Trends in the extreme daily precipitation indices also showed seasonal variability. The number of stations that showed positive/negative trends in the extreme daily precipitation indices and the corresponding numbers Table II. Number of temperature stations with positive/negative trends and the corresponding number of significant (p <5%) trends for temperature indices Index Winter Spring Summer Autumn Annual Tmax90p Tmin10p Fd HWDI

7 TRENDS IN EXTREMES 1195 Figure 3. Seasonal changes in the 90th percentile daily maximum temperature ( C) between 1958 and 2001 Table III. Average changes in the daily extreme temperature indices between 1958 and 2001 Index Winter Spring Summer Autumn Annual Tmax90p ( C) Tmin10p ( C) FD (days) HWDI (days) of significant trends are summarized in Table IV. The percentage changes averaged over all the stations are also shown in Table V. Indices related to intense precipitation generally showed an increasing trend in winter and a decreasing trend in summer. In spring and autumn, the indices showed an increasing trend, but not as strongly as in winter. The 90th percentile rain-day amount, for example, increased significantly at the majority of the stations in winter, with a 20.7% rise in the value averaged over all the stations. It also increased at most of the stations in spring and autumn, although not as strongly or as significantly as in winter. The drop

8 1196 Y. HUNDECHA AND A. BÁRDOSSY Air temperature [ C] Air temperature [ C] Observed series Trend line Observed series Trend line Year Year Winter trend Summer trend Figure 4. Winter and summer trends in the average 90th percentile daily maximum temperature Year Air temperature [ C] Observed series Trend line Air temperature [ C] Observed series Trend line Year Winter trend Summer trend Figure 5. Winter and summer trends in the average 10th percentile daily minimum temperature in the average 90th percentile rain day amount in summer was found to be 6.4%, which is considerably less than that of the rise in winter. Figure 6 shows the average winter and summer trends in the 90th percentile rain-day amount. A similar trend pattern was obtained for the average intensity of precipitation on rain days, indicating that the precipitation is getting heavier for winter and the transition seasons, whereas it is getting less severe in summer (Tables IV and V). The hydrological consequence of accumulated precipitation falling on a number of consecutive days may be more severe than just an intense precipitation falling on a single day. The trend of the greatest 5-day total rainfall was investigated and it showed a trend pattern similar to the previous two extreme indices, increasing strongly in winter both in terms of the average magnitude and the number of stations showing significant increases. On the other hand, the summer trend was found to be the opposite for the majority of stations, with the average decrease being only 30% of the increase in winter. The transition seasons have seen an

9 TRENDS IN EXTREMES Precipitation [mm/day] Precipitation [mm/day] Observed series Trend line Observed series Trend line Year Year Winter trend Summer trend Figure 6. Winter and summer trends in the average 90th percentile rain day Table IV. Number of precipitation stations with positive/negative trends and the corresponding number of significant (p <5%) trends for precipitation indices Index Winter Spring Summer Autumn Annual Prec90P SDII D-total P>90p N>90p CDD Table V. Average percentage changes of the daily extreme precipitation indices between 1958 and 2001 Index Winter Spring Summer Autumn Annual Prec90p CDD D-total SDII P>90p N>90p increase in the index, but not as significantly and strongly as in winter. Figure 7 shows the spatial pattern of the seasonal trends of this index. In addition to the extreme indices discussed before, the changes in the frequency of extreme daily precipitation were studied by analysing the percentage of the annual seasonal total rainfall and the number of rainfall events from events greater than the long-term 90th percentile rainfall. The percentage of total rainfall from events exceeding the long-term 90th percentile rain amount increased at most stations in winter and

10 1198 Y. HUNDECHA AND A. BÁRDOSSY Figure 7. Seasonal percentage changes in the 5-day total rainfall between 1958 and 2001 spring, with many of them being significant in winter. In summer, this measure decreased at most stations, but was only significant for some of them. Although this measure showed an increasing trend at many stations in autumn, there were also a considerably large number of stations for which a decreasing trend was evident. The magnitude of the increases, however, surpasses that of the decreases, and the net increase, therefore, is fairly high (11.9%). The number of events greater than the long-term 90th percentile rain amount also increased at the majority of stations in winter and the transition seasons and decreased in summer. There were many significant changes in all seasons. Many of the significant increases in the extreme heavy precipitation indices were noted to be at stations located in areas of higher elevation. This has provoked speculation that the form of precipitation might have changed through time due to the rise in temperature, leading to a lower probability of underestimation of the precipitation measuring devices that otherwise would be higher if it were in snow form. Investigation of the trend in the number of rain days above 0 C (no snow days) showed that it did not show a significant increase at the majority of stations. However, the ratio of snow to liquid rainfall in winter showed a significant drop over the years at many stations. The significance is further intensified when considering the ratio for precipitation events exceeding the 90th percentile rain-day amount. This may, to some extent, be a reason for

11 TRENDS IN EXTREMES 1199 the significant increase in the extreme daily precipitation in winter. Further analysis was also undertaken to investigate whether the frequency of circulation patterns associated with wet days has shown an increasing trend over the investigation period. Objective circulation patterns werederived by classifying sea-levelpressure distribution taken from the National Centers for Environmental Prediction National Center for Atmospheric Research reanalysis data set (Kistler et al., 2001) using a fuzzy-rule-based classification technique (Bárdossy et al., 1995). However, no significant increase was evident over the investigation period. Dry conditions can also depict an extreme precipitation condition, and so the evolution of the maximum consecutive number of dry days was also studied. Winter and autumn are characterized by a decrease in this index at most of the stations, but many significant decreases were noticed only in autumn. Summer and spring, on the other hand, showed an increase, with many significant increases in summer Effect of scale in extreme precipitation indices Extreme precipitation indices were studied for precipitation interpolated at 5, 10, 25, and 50 km grids. The spatial configuration of the trends calculated at all scales was noted to be similar to that of the point scale (see Figure 8). The average seasonal trend of each index, however, became more pronounced as the scale Figure 8. Seasonal percentage changes in the 5-day total rainfall between 1958 and 2001 based on interpolated precipitation on 10 km grid. This figure is available in colour online at

12 1200 Y. HUNDECHA AND A. BÁRDOSSY Table VI. Percentages of total area showing positive/negative trends and the corresponding significant (p <5%) trends of precipitation indices on 5 km grids Index Winter Spring Summer Autumn Annual Prec90P CDD D-total SDII P>90p N>90p Table VII. Percentages of total area showing positive/negative trends and the corresponding significant (p <5%) trends of precipitation indices on 25 km grids Index Winter Spring Summer Autumn Annual Prec90P CDD D-total SDII P>90p N>90p

13 TRENDS IN EXTREMES 1201 Figure 9. Areas of significant trends in the winter 5-day total rainfall corresponding to areal precipitation at different scales: (a) 5 km grid; (b) 10 km grid; (c) 25 km grid increased. Tiny areas showing the opposite trend at lower scales were engulfed as the scale increased, and the resulting aggregation clearly led to a situation where more areas show the trend observed at the majority of the stations. A similar situation was observed with the significances of the trends. Pockets of significant changes were noted to disappear as the areal scale increased, and significant changes were more concentrated in areas where most stations showed significant trends. Tables VI and VII, for 5 km and 25 km grid sizes respectively, summarize the percentages of the total area showing positive/negative trend signs and percentages of the total area corresponding to significant changes for interpolated precipitation series. Figure 9 also shows areas of significant changes in the 5-day total amount of precipitation in winter corresponding to areal precipitation series at different scales. 5. SUMMARY AND CONCLUSIONS This study has tried to investigate whether the weather in the Rhine basin is getting more extreme. Many of the results obtained suggest that the trends in the extreme daily weather variables are consistent with the observations made in the majority of the countries located in the Northern Hemisphere. It has been found that both the extreme daily maximum and minimum temperatures have increased. Although the degree of increase of the two extremes was noted to vary from season to season (on an annual basis), the extreme minimum has shown a greater increase than the extreme maximum, which is consistent with the global-scale observation. The extreme heavy precipitation has also become more extreme, both in terms of magnitude and frequency, in winter and the transition seasons. The summer trend is, on the other hand, towards a less extreme situation. Annually, the trend has been found to be towards more extreme rain days and increased contribution of extreme events to the total amount of precipitation. The strongest trend towards a severe extreme condition was noticed for the winter season. This may explain the frequent wintertime flooding in the Rhine basin in recent years. Comparison of the trends of extreme precipitation indices of point precipitation and areal precipitation at different scales also showed that the configuration of the trend distribution remains similar. The magnitudes of the average trend, however, were noted to increase with increasing scale of the area on which precipitation is aggregated.

14 1202 Y. HUNDECHA AND A. BÁRDOSSY ACKNOWLEDGEMENTS We would like to thank Malcolm Haylock (Climate Research Unit of the University of East Angelia) for his work on the diagnostic software tool used in this work to calculate values of the extreme indices. The work presented in this paper is part of the STARDEX research project, supported by the European Commission (contract no.: EVK2-CT ). REFERENCES Ahmed S, de Marsily G Comparison of geostatistical methods for estimating transmissivity using data on transmissivity and specific capacity. Water Resources Research 23(9): Bárdossy A, Duckstein L, Bogardi I Fuzzy rule based classification of atmospheric circulation patterns. International Journal of Climatology 15: Bony S, Duvel JP, LeTreut H Observed dependence of the water vapour and clear-sky greenhouse effect on sea surface temperature. Climate Dynamics 11: Easterling DR, Horton B, Jones PD, Peterson TC, Karl TR, Parker DE, Salinger MJ, Razuvayev V, Plummer N, Jamason P, Folland CK Maximum and minimum temperature trends for the globe. Science 277: Easterling DR, Evans JL, Groisman PY, Karl TR, Kunkel KE, Ambenje P Observed variability and trends in extreme climate events: a brief review. Bulletin of the American Meteorological Society 81: Good P Permutation Tests: A Practical Guide to Resampling Methods for Testing Hypotheses. Springer-Verlag. Heino R, Brazdil R, Førland EJ, Tuomenvirta H, Alexandersson H, Beniston M, Pfister C, Rebetez M, Roesner S, Rosenhagen G, Wibig J Progress in the study of climatic extremes in northern and central Europe. Climatic Change 42: Hennessy KJ, Suppiah R, Page CM Australian rainfall changes, Australian Meteorological Magazine 48: Hirsch RM, Slack JR, Smith RA Techniques of trend analysis for monthly water quality data. Water Resources Research 18: Iwashima T, Yamamoto R A statistical analysis of the extreme events: long-term trend of heavy daily precipitation. Journal of the Meteorological Society of Japan 71: Karl TR, Knight RW Secular trends of precipitation amount frequency and intensity in the United States. Bulletin of the American Meteorological Society 79: Karl TR, Knight RW, Plummer N Trends in high-frequency climate variability in the twentieth century. Nature 377: Kendall MG Rank Correlation Methods. Griffin: London. Kistler R, Kalnay E, Collins W, Saha S, White G, Woollen J, Chelliah M, Ebisuzaki W, Kanamitsu M, Kousky V, van den Dool H, Jenne R, Fiorino M The NCEP NCAR 50-year reanalysis: monthly means CD ROM and documentation. Bulletin of the American Meteorological Society 82(2): Mearns LO, Katz RW, Schneider SH Extreme high temperature events: changes in their probabilities with changes in mean temperature. Journal of Climate and Applied Meteorology 23: Meehl GA, Zwiers F, Evans J, Knutson T, Mearns L, Whetton P Trends in Extreme weather and climate events: Issues related to modelling extremes in projections of future climate change, Bulletin of the American Meteorological Society 81(3): Nicholls N, Gruza GV, Jouzel J, Karl TR, Ogallo LA, Parker DE Observed climate variability and change. In Climate Change 1995: The Science of Climate Change, Houghton JT, Filho LGM, Callander BA, Harris N, Kattenberg A, Maskell K (eds). Cambridge University Press: Cambridge; Plummer N, Salinger MJ, Nicholls N, Suppiah R, Hennessy KJ, Leighton RM, Trewin BC, Page CM, Lough JM Changes in climate extremes over the Australian region and New Zealand during the twentieth century. Climatic Change 42(1): Suppiah R, Hennessy KJ Trends in total rainfall, heavy rainfall events and number of dry events in Australia, International Journal of Climatology 18: Watson RT, Zinyowera MC, Moss RH (eds) The Regional Impacts of Climate Change: An Assessment of Vulnerability. Cambridge University Press: Cambridge UK. Wilks DS Statistical Methods in the Atmospheric Sciences. Academic Press.