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Introduction to RClimDex v1.9 Xuebin Zhang, Yang Feng and Rodney Chan Climate Research Division Environment Canada Downsview, Ontario Canada December 12, 2018 Maintained by Rodney Chan Please contact rodney.chan@canada.ca for any question or comment. 1 Contents 1 Introduction 6 2 Installation of R 2.1 Brief introduction to R . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Installing R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Running R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 7 7 7 3 Installation of RClimDex 8 4 RClimDex 4.1 Getting started on RClimDex . . . . . . . . . . . . . . . . . 4.2 Quality control . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 Description of RClimDex quality control procedures 4.2.2 Loading datasets for quality control . . . . . . . . . 4.2.3 Quality control main menu and parameters . . . . . 4.2.4 Quality control results and plots . . . . . . . . . . . 4.3 Indices calculation . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 Loading data files for indices calculation . . . . . . . 4.3.2 Indices calculation main menu and parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 8 9 9 10 10 12 13 13 14 Appendix A List of ETCCDI core Climate Indices 17 Appendix B Data format 19 Appendix C Indices definition 20 Appendix D Threshold estimation and base period temperature indices calculation 25 D.1 Empirical quantile estimation . . . . . . . . . . . . . . . . . . . . 25 D.2 Bootstrap procedure for the estimation of exceedance rate for the base period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2 Acknowledgements to version 1 The initial version of RClimDex was developed by Xuebin Zhang and Yang Feng at the Climate Research Branch of Meteorological Service of Canada. Its initial development was funded by the Canadian International Development Agency through the Canada China Climate Change Cooperation (C5) Project. Lisa Alexander, Francis Zwiers, Byron Gleason, David Stephenson, Albert Klan Tank, Mark New, Lucie Vincent, and Tom Peterson made important contributions to the development and testing of the package. Jose Luis Santos at CIIFEN helped to translate this document into Spanish. Earlier versions of RClimDex have been used during CCl/CLIVAR ETCCDI workshops in Cape Town, South Africa, May 31-June 4, 2004, and in Maceio, Brazil, August 9-14, 2004. The lectures and attendees of the workshops provided very valuable suggestions for the improvement of RClimDex. Acknowledgements to version 2 The version 2 of RClimDex was developed by Xuebin Zhang, Yang Feng and Rodney Chan at the Climate Research Division of Environment Canada. The new version of RClimDex is made possible by Pacific Climate Impacts Consortium and their climdex.pcic package. All indices calculation now depends on the fast and well tested implemention of ClimDex from the climdex.pcic package. 3 Release notes Major changes in version 2: 1. Indices calculation replaced by climdex.pcic from RClimDex 2. Batch processing support 3. UX overhaul Changelog 2.0: Release version. Updated manual. Removed outlier checking for precipition upper limit in quality control. 1.9-1: Fix bug where indices calculation crashed when only one variable is present. (the others are all NAs) 1.9: If base period contains years at the start or end with all missing values, the base period will be shorten accordingly. Longitude and Latitude are replaced by Northern Hemisphere and Southern Hemisphere to better reflect the parameter. Fix bug where selecting a different output directory than the input data file will sometimes result in an error. (’/’ syntax issue) Fix bug where outliers are set against tmax or tmin even if they are purposely not provided. (all missing values) NA mask rules are implemented in climdex.pcic instead of RClimDex. Updated manual to reflect UX change for station selection. 1.8-2: Edits to FD0,SU25,TR20,ID0 to FD,SU,TR,ID to be more consistent. 1.8-1: Made some minor edits to vignettes in terms of spelling, grammer and structure. 1.8: Change the version numbering from 0.1-8 -> 1.8. Remove support for LS trend and plots for indices calculation. Updated dependency from climdex.pcic version 1.1-1 to 1.1-6 Updated function calls from RClimDex to climdex.pcic for version 1.1-6 from version 0.7-2 Fix bug where repeated indices calculation with multiple files will skip the first file. Fix bug where ”indcal” will appear in the names of output files from the first dataset when processing multiple files. 4 0.1-7: Vignettes is added to package. Manual has been updated with more details. Startup message has been added for clearer instruction. Check for precipitation exceeding upper limit. Output indices plot as pdf instead of jpg. Change quality control rules to allow some datasets to be flagged but not disrupted from processing. Log messages are updated to be more natural. Fix bug in multiple dataset where parameters are changed due to data quality, the changed will revert back after that file instead of remaining for the rest of the files. Fix bug in leap days being NA instead of being repeated of 28th February. 0.1-6: Datasets are padded with NA to ensure the datasets filled up a whole year. 0.1-5: Change NA mask rules to 15 NA threshold for annual and 3 NA threshold for monthly. Fix bug where any NA in values resulted in invalid dates. Fix bug where NA mask was not apply to TMAXmean and TMINmean. Updated RX5day, RX1day. There were issues in old RClimdex NA mask. Updated missing marker to accept character values. Updated thresholds such that some indices calculation are skiped when there are too many NA. 0.1-4: Initial pacakage version - UX overhaul, batch processing support, indices calculation replaced by climdex.pcic from RClimDex. Updated GSL. There were issues in counting one less day in old RClimdex. (missing +1) Updated TNn. There were issues with January, even one NA will trigger NA for that month. (missing na.rm=T) 5 1 Introduction ClimDex is a Microsoft Excel based program that provides an easy-to-use software package for the calculation of indices of climate extremes for monitoring and detecting climate change. It was developed by Byron Gleason at the National Climate Data Centre (NCDC) of NOAA, and has been used in CCl/CLIVAR workshops on climate indices from 2001. The original objective was to port ClimDex into an environment that does not depend on a particular operating system. It was very natural to use R as our platform, since R is a free and yet very robust and powerful software for statistical analysis and graphics. It runs under both Windows and Unix environments. In 2003 it was discovered that the method used for computing percentile-based temperature indices in ClimDex and other programs resulted in inhomogeneity in the indices series. A fix to the problem requires a bootstrap procedure that makes it almost impossible to implement in an Excel environment. This has made it more urgent to develop the R based package. RClimDex is designed to provide a user friendly interface to compute indices of climate extremes. It computes all 27 core indices recommended by the CCl/CLIVAR Expert Team for Climate Change Detection Monitoring and Indices (ETCCDI) as well as some other temperature and precipitation indices with user defined thresholds. The 27 core indices include almost all the indices calculated by ClimDex (Version 1.3). This version of RClimDex has been developed under R 2.15.2. It also depends on the R library of climdex.pcic (Version 1.1-6) and PCICt (Version 0.5-4) for computing the 27 core indices as well as the R library of Tcl/Tk (Version 2.15.2) for the graphical user interface. This RClimDex package should run with R 2.15.2 or a later version. The depended R libraries are available from the official CRAN website and needs to be downloaded and installed before the installation of the RClimDex package. A main objective of constructing climate extremes indices is to use for climate change monitoring and detection studies. This requires that the indices be homogenized. Data homogenization has been planned but is not implemented in this release. Current RClimDex only includes a simple data quality control procedure that was provided in ClimDex. As in ClimDex, we require that data are quality controlled before the indices can be computed. This manual provides step-by-step instructions on the following. 1. The installation of R and setting up the user environment 2. Quality control of daily climate data 3. Calculation of the 27 core indices 6 2 2.1 Installation of R Brief introduction to R R is a language and environment for statistical computing and graphics. It is a GNU implementation of the S language developed by John Chambers and colleagues at Bell Laboratories (formerly AT&T, now Lucent Technologies). Splus provides a commercial implementation of the S language. 2.2 Installing R RClimDex requires the base package of R (Version 2.15.2 or later). The installation of R involves a very simple procedure. First, connect to the R project website at www.r-project.org, then follow the links to download the most recent version of R for your computer operating system from any mirror site of CRAN. For Microsoft Windows XP and later, download the base R Windows installer. Run that installer and R will be automatically installed on your computer, with a shortcut to R on your desktop. The Tcl/Tk library is included in the default installation of R. For Linux, download the proper precompiled binaries and follow the instruction to install R. For other UNIX systems, you may need to download the source code and compile it yourself. For Mac OSX 10.9 (Mavericks) and above, download the latest version of the R signed package. Validate the signature using pkgutil for example –checksignature R-3.2.1.pkg in the Terminal. Run the R signed package to install. Select custom install during installtion to enable Tcl/Tk library. Connect to XQuartz website at xquartz.macosforge.org to use X11 which is required for the graphical user interface of RClimDex. Download the latest XQuartz image and install. There is now an R app in Lauchpad. For Mac OSX 10.5 (Leopard) to 10.8 (Mountain Lion), download the last supported legacy version of the R signed package of the corresponding Mac OSX version. Validate the signature by checking the MD5 checksum with the website. For example to check the MD5 checksum type in md5 R-3.2.1.pkg in the Terminal application. Run the R signed package to install and during installation select custom install to enable Tcl/Tk library. R is now installed and in the Application folder. For Mac OSX 10.8 (Mountain Lion), connect to XQuartz website at xquartz.macosforge.org to use X11 which is required for the graphical user interface of RClimDex. Download the latest XQuartz image and install. 2.3 Running R For Windows, double click the R icon on your desktop, or launch it through Windows Start Menu. This usually gets you into the R user interface. R 64bit will also be installed if your system supports 64bit. It is recommended to use R 64bit if your system is 64bit. You may quit the program by clicking on the 7 top menu under File then Exit. Under Linux, just run the command R to give you the R console. You may quit by typing in the command q(). Under OSX, click on the R app in Lauchpad, or double click the R icon in your Application folder. This usually gets you into the R user interface. You may quit the program by clicking on the top menu under R then Quit R. 3 Installation of RClimDex RClimDex is now an R package. Most recent version of RClimDex is avaliable from the ETCCDI website at http://etccdi.pacificclimate.org/software.shtml, where registration is required. Please install RClimDex as a local package in R. RClimDex now depends on the climdex.pcic. With an internet connection, launch R in the same directory as the RClimDex package. Then run the following commands: install.packages("climdex.pcic") install.packages("RClimDex_1.9-1.tar.gz", repos=NULL, type="source") Select a CRAN mirror to install or update the R package of climdex.pcic then run the other command to install RClimDex. RClimDex has been developed under R 2.15.2. This version of RClimDex depends on the R library of climdex.pcic (Version 1.1-6) and PCICt (Version 0.5-4) for computing the 27 core indices as well as the R library of Tcl/Tk (Version 2.15.2) for the graphical user interface. The depended R libraries will be downloaded and installed automatically during the installation of the RClimDex package. For Windows, you may change the current R working directory by clicking on the top menu under File then Change dir..., afterwards select the directory where you store the RClimDex package before installing. Under OSX, please click on the top menu under Misc then Change Working Directory... to change the current R working directory. Please select the directory where RClimDex package is stored before installing. 4 4.1 RClimDex Getting started on RClimDex RClimDex can be loaded like any other R packages. All dependent libraries will also be loaded. Please type in the following into the R console: library("RClimDex") 8 In order to launch RClimDex user interface and to begin using RClimdex, simply type in the following into the R console. rclimdex.start() You may type in the command into the R console again to relaunch the user interface. RClimDex is not programmed to support concurrent sessions within the same R console, therefore please launch one user interface at a time. Alternatively you may launch another seperate R console in another window for an additional session of RClimDex. Please note that RClimDex only supports one current session per R console. Figure 1: RClimDex main menu. 4.2 4.2.1 Quality control Description of RClimDex quality control procedures We highly recommend to executing the quality control step of RClimDex before proceeding to indices calculation. Simply press the Run Quality Control button to begin as shown in Figure 1. Data quality control consists of the following procedures. 1. Replace all user-defined missing values, with default as -99.9, into NA (internal R missing value). 2. Replace all unreasonable values into NA. If any of the following cases occurs, it usuaully means there is a significant issue in the dataset and require user to review. Please review the log subdirectory after quality control is completed. (a) Daily precipitation value less than zero millimeter. (b) Daily maximum temperature less than daily minimum temperature. 9 (c) Daily temperature values greater than 70 degree Celsius or less than -70 degree Celsius. (d) Leap days. (i.e. 29th February) (e) All values corresponding to an impossible date. (i.e. 32nd March 2013, 12th June 20AA, etc.) (f) Any non-numeric values. 3. Identifies outliers of daily temperature values outside of user-defined region, with default as values further than 3 times standard deviation from the mean value for that calendar day. Users can define other multiples of standard deviation away from mean. Note that the outliers are most often valid values. 4.2.2 Loading datasets for quality control In the File Open Window, you may select the dataset to execute the quality control of RClimDex. You may need to change directory to where the dataset is stored. RClimDex expects file extension of either .csv or .txt however you may display files of all types by selecting ALL files in the Files of type dropdown menu (See Figure 2). Please note that the dataset must be formatted as described in Appendix B. Windows and Linux users may press and hold shift key or crtl key (OSX users may use cmd key) to select multiple datasets. When multiple datasets are selected, RClimDex would perform quality control based on the same parameters selected on the quality control menu to all datasets in sequence. The output filenames of multiple datasets correspond with their filenames respectively and cannot be changed. 4.2.3 Quality control main menu and parameters The following is a brief descripition to each parameter as shown in Figure 3. 1. Output file location: The local directory where RClimDex will store the output files from quality control. 2. Station name or code: Output filename prefix. (Only available when processing only one dataset) 3. Number of standard deviation for temperature: The threshold for outliers from daily record. Any daily temperature values away from mean in terms of standard deviation for that particular calendar day above threshold will be flagged as outlier in the log file. 4. Missing marker: Character string as the indicator for missing values in input dataset. The output file location is where all outputs from RClimDex will be stored. After a successful quality control execution, you will find a csv file ending with a suffix of .indcal.csv, which is the post quality controlled dataset. Please select this dataset instead of your original dataset for the indices calculation. In addition, there is a log file in txt format with details about the quality control a log 10 Figure 2: File selection for quality control. Figure 3: Quality control menu of RClimDex. 11 subdirectory that contains plots and statistics about the quality control. Lastly, there are the indices subdirectory which would be where the indices calculation outputs be stored. If you are only executing quality control on one dataset, you may rename the output filename. The other parameters relates to the actual quality control. They are the outlier settings in terms of standard devation away from mean value, an upper limit for precipitation values in millimeters and the missing marker. Please note that the default missing marker of -99.9 will always be used in addition to your userdefined missing marker. Press the Perform Quality Control button to begin quality control and press the Quit button to exit to main menu. Also note that quality control will not automatically quit after completion. If you desire to perform indices calculation on the post quality controlled dataset, simply press the Quit button to go back to the main menu then press the Run Indices Calculation button on the main menu. Under the buttons, there are log messages in which RClimDex communicates with the user. It will provide details for current status, including but not limited to which file is loaded, what process is being executed, was the quality control successfully performed and number of files remaining to processs. 4.2.4 Quality control results and plots Figure 4: A sample plot from quality control. Red circle indicates values were flagged by quality control. Please note that while unreasonable values are removed, other problematic data like outliers are simply flagged in a log file and are not changed. They simply alert the user to pay more attention and make correction only if needed. Besides the main results of post quality controlled dataset, there are a few more outputs from quality control of RClimDex. All of these outputs are in the log subdirectory. Please review these log files for a better understanding of the changes quality control made to the dataset. (a) filename.indcal.csv; The post quality control data file. (b) log.datestamp.timestamp.txt; Detail log from RClimDex. (c) log/filename prcpPLOT.pdf; Plot of daily precipitation values and histogram of precipitation values. (d) log/filename tmaxPLOT.pdf; Plot of daily maximum temperature values. 12 (e) log/filename tminPLOT.pdf; Plot of daily minimum temperature values. (f) log/filename dtrPLOT.pdf; Plot of daily diurnal temperature range values. (g) log/filename prcpQC.csv; Table of all daily precipitation values that were flagged and removed. (h) log/filename tmaxQC.csv; Table of all daily maximum temperature values that were flagged and removed. (i) log/filename tminQC.csv; Table of all daily minimum temperature values that were flagged and removed. (j) log/filename tepstdQC.csv; Table of all outlier temperature values that were only flagged. (k) log/filename nastatistic.csv; Summary table of the annual and monthly sums of values flagged and removed. For the outlier tables, there are twelve columns. Three columns each for date, daily maximum temperature, daily minimum temperature and diurnal temperature range. For all temperature columns, there are the lower bound of accepted values, the temperature value of that day and the upper bound of accepted values. The boundaries for outliers are user-defined by the number of standard deviation away from mean. A record is added to the outlier table if any outlier temperature values are flagged for that day. All plots in quality control provide a quick visual understanding of where values are flagged. As seen in Figure 4, the red circles in the plots are where values are flagged. For daily precipitation values, a histogram is provided as well. 4.3 4.3.1 Indices calculation Loading data files for indices calculation In the File Open Window, you may select the dataset from which indices are calculated. You may need to change directory to where the quality controlled dataset is stored. RClimDex expects file extension of .indcal.csv, which a post RClimDex quality controlled dataset. You may also display files of all types by selecting ALL files in the Files of type dropdown menu and select files that are in the format as described in Appendix B. Please note that we highly recommend users to first go through quality control of RClimDex prior to indices calculation. User may want to check and review the values flagged by the RClimDex quality control prior to indices calculation. You may make changes to the post quality controlled dataset (.indcal.csv file) by a spreadsheet editor such as Excel or Numbers in Windows and OSX or any text editor in Linux. Windows and Linux users may press and hold shift key or crtl key (OSX users may use cmd key) to select multiple files. When multiple data files are selected, RClimDex would perform indices calculation based on the same parameters 13 and indices selected on the indices calculation menu to all selected datasets in sequence. The output filenames of multiple files corresponds with their original filenames respectively and can not be changed. 4.3.2 Indices calculation main menu and parameters The following is a brief descripition to each parameter as shown in Figure 6. 1. Output file location: The local directory where RClimDex will store the output files from indices calculation. 2. Station name or code: Output filename prefix. (Only available when processing only one dataset) 3. Missing marker: Character string as the indicator for missing values in input dataset. 4. Base period: The base period usually is a long enough period preferably more than 10 years in which climatology do not change much for a given station. (a) First year: Starting year of base period. (Always begin on 1st of January) (b) Last year: Ending year of base period. (Always end on 31st of December) 5. Station location: It will affect indices such as CSDI and GSL based on the hemisphere the station is located. Please select datasets from the same hemisphere when processing multiple dateset. Station location only have options to select between Northern Hemisphere or Southern Hemisphere. 6. Threshold of daily maximum temperature: (a) Upper: User defined threshold for summer days, similar to SU. (b) Lower: User defined threshold for ice days, similar to ID. 7. Threshold of daily minimum temperature: (a) Upper: User defined threshold for tropical nights, similar to TR. (b) Lower: User defined threshold for frost days, similar to FD. 8. Threshold of precipitation (mm): User defined total counts of daily precipitation above the user defined threshold, similar to R10 and R20. 9. Indices selections: Please refer to Appendix A for more information and full definition can be found in Appendix C. The output files location is where all outputs from RClimDex will be stored. There is a log file in txt format about the indices calculation. There are also the indices subdirectory which would be where the indices calculation outputs be stored. You may only rename the output filename if you are not processing multiple dataset. The current version of RClimDex does not support different indices calculation selection for each individual dataset when processing multiple dataset. In other words, only the indices selected are calculated for multiple 14 Figure 5: File selection for indices calculation. Figure 6: Indices calculation menu of RClimDex. 15 dataset. Please note that the default missing marker of -99.9 will always be used in addition to your user-defined missing marker. The base period always begin from the 1st of January and ends on the 31st of December of the user defined period. RClimDex determines the hemisphere from the station location with radio button for Northern or Southern Hemisphere. Keep in mind to have all datasets from the same hemisphere when processing multiple datasets because RClimDex assumes same parameters when processing multiple datasets which includes the hemisphere. The threshold values for temperature are for user-defined frost days, summer days, ice days and tropical nights, where precipitation threshold is for user defined number of days with daily precipitation values above threshold. Each index can be individually selected to be or not to be calculated for the datasets. More information about the indices can be found in Appendix A and full definition can be found in Appendix C. Press the Perform Indices Calculation button to begin and press the Quit button to exit to main menu. Also note that indices calcualtion will not automatically quit after completion. RClimDex communicates with the user in the log message box below the buttons. This is where details about the current status, such as which dataset is loaded, what process is being performed, number of datasets remaining, etc. are displayed. 16 A List of ETCCDI core Climate Indices ID Indicator name Definitions Units FD Frost days Annual count when TN(daily minimum) < 0°C days SU Summer days Annual count when TX(daily maximum) > 25°C days ID Ice days Annual count when TX(daily maximum) < 0°C days TR Tropical nights Annual count when TN(daily minimum) > 20°C days GSL Growing length Annual (1st Jan to 31st Dec in NH, 1st July to 30th June in SH) count between first span of at least 6 days with TG > 5°C and first span after 1st July (1st January in SH) of 6 days with TG < 5°C days TXx Max Tmax Monthly maximum value of daily maximum temp °C TNx Max Tmin Monthly maximum value of daily minimum temp °C TXn Min Tmax Monthly minimum value of daily maximum temp °C TNn Min Tmin Monthly minimum value of daily minimum temp °C TN10p Cool nights Percentage of days when TN < 10th percentile % TX10p Cool days Percentage of days when TX < 10th percentile % TN90p Warm nights Percentage of days when TN > 90th percentile % TX90p Warm days Percentage of days when TX > 90th percentile % season 17 ID Indicator name Definitions Units WSDI Warm spell duration indicator Annual count of days with at least 6 consecutive days when TX>90th percentile days CSDI Cold spell duration indicator Annual count of days with at least 6 consecutive days when TN<10th percentile days DTR Diurnal temperature range Monthly mean difference between TX and TN °C RX1day Max 1-day precipitation amount Monthly maximum 1-day precipitation mm RX5day Max 5-day precipitation amount Monthly maximum consecutive 5-day precipitation mm SDII Simple daily intensity index Annual total precipitation divided by the number of wet days (defined as PRCP >= 1.0mm) in the year mm/day R10 Number of heavy precipitation days Annual count of days when PRCP >= 10mm days R20 Number of very heavy precipitation days Annual count of days when PRCP >= 20mm days Rnn Number of days above nn mm Annual count of days when PRCP >= nn mm, nn is user defined threshold days CDD Consecutive days dry Maximum number of consecutive days with RR < 1mm days CWD Consecutive days wet Maximum number of consecutive days with RR >= 1mm days R95p Very wet days Annual total PRCP when RR > 95th percentile mm R99p Extremely wet days Annual total PRCP when RR > 99th percentile mm PRCPTOT Annual total wetday precipitation Annual total PRCP in wet days (RR >= 1mm) mm 18 B Data format All indices calculation are outputted as comma-separated values (CSV) files for tables and portable document format (PDF) files for all plots. RClimDex likewise accepts CSV files as input data. RClimDex also accepts space-delimited ASCII text file as input data. Space-delimited format has each element separated by one or more spaces. The input dataset must satisfy the following requirements. 1. The input dataset must have the file extension .csv or .txt 2. Columns must be YEAR MONTH DAY PRCP TMAX TMIN in that order 3. The records must be in calendar date order. Missing dates are allowed. This is an example of an input dataset as a space-delimited ASCII file. 1950 1950 1950 1950 1950 2 2 2 2 2 3 4 5 6 9 -99.9 0 0 11.4 0 -3.1 -1.3 -0.5 -1 -1.8 -6.8 -3.6 -7.9 -9.1 -8.4 This is an example of an input dataset as a CSV file. 1950,2,3,-99.9,-3.1,-6.8 1950,2,4,0,-1.3,-3.6 1950,2,5,0,-0.5,-7.9 1950,2,6,11.4,-1,-9.1 1950,2,9,0,-1.8,-8.4 19 C Indices definition Definitions for indicators are listed in Appendix A. For practical reasons, in this version of the software, not all indices are calculated on a monthly basis. Monthly indices are calculated if no more than 3 days are missing in a month, while annual values are calculated if no more than 15 days are missing in a year. No annual values will be calculated if any one month’s data are missing. For threshold indices, a threshold is calculated if at least 75% of data are present. For spell duration indicators (marked with a *), a spell can continue into the next year and is counted against the year in which the spell ends. A cold spell (CSDI) for example in the Northern Hemisphere beginning on 31st December 2000 and ending on 6th January 2001 is counted towards the total number of cold spells in 2001. 1. FD Let T nij be the daily minimum temperature on day i in period j. Count the number of days where: T nij < 0°C 2. SU Let T xij be the daily maximum temperature on day i in period j. Count the number of days where: T xij > 25°C 3. ID Let T xij be the daily maximum temperature on day i in period j. Count the number of days where: T xij < 0°C 4. TR Let T nij be the daily minimum temperature on day i in period j. Count the number of days where: T nij > 20°C 5. GSL Let Tij be the daily mean temperature on day i in period j. Count the number of days between the first occurence of at least 6 consecutive days with: Tij > 5°C 20 and the first occurence after 1st July (1st January in SH) of at least 6 consecutive days with: Tij < 5°C 6. TXx Let T xij be the daily maximum temperature in month i, period j. The maximum daily maximum temperature each month is then: T Xij = max(T xij ) 7. TNx Let T nij be the daily minimum temperature in month i, period j. The maximum daily minimum temperature each month is then: T Nij = max(T nij ) 8. TXn Let T xij be the daily maximum temperature in month i, period j. The minimum daily maximum temperature each month is then: T Xij = min(T xij ) 9. TNn Let T nij be the daily minimum temperature in month i, period j. The minimum daily minimum temperature each month is then: T Nij = min(T nij ) 10. Tn10p Let T nij be the daily minimum temperature on day i, period j and let T nin 10 be the calendar day 10th percentile centered on a 5-day window (calculated using method in Appendix D). The percentage of time is determined where: T nij < T nin 10 11. Tx10p Let T xij be the daily maximum temperature on day i, period j and let T xin 10 be the calendar day 10th percentile centered on a 5-day window (calculated using method in Appendix D). The percentage of time is determined where: T xij < T xin 10 21 12. Tn90p Let T nij be the daily minimum temperature on day i, period j and let T nin 90 be the calendar day 90th percentile centered on a 5-day window (calculated using method in Appendix D). The percentage of time is determined where: T nij > T nin 90 13. Tx90p Let T xij be the daily maximum temperature on day i, period j and let T xin 90 be the calendar day 90th percentile centered on a 5-day window (calculated using method in Appendix D). The percentage of time is determined where: T xij > T xin 90 14. WSDI* Let T xij be the daily maximum temperature on day i, period j and let T xin 90 be the calendar day 90th percentile centered on a 5-day window (calculated using method in Appendix D). Then the number of days per period is summed where, in interval, of at least 6 consecutive days: T xij > T xin 90 15. CSDI* Let T nij be the daily minimum temperature on day i, period j and let T nin 10 be the calendar day 10th percentile centered on a 5-day window (calculated using method in Appendix D). Then the number of days per period is summed where, in interval, of at least 6 consecutive days: T xij > T xin 90 16. DTR Let T xij and T nij be the daily maximum and minimum temperature respectively on day i, period j. If I represents the number of days in j, then: I X DT R = (T xij − T nij ) i=1 I 17. RX1day Let RRij be the daily precipitation amount on day i in period j. Then maximum 1-day values for period j are: 22 RX1dayj = max(RRij ) 18. RX5day Let RRkj be the daily precipitation amount for the 5-day interval ending on day k in period j. Then maximum 5-day values for period j are: RX5dayj = max(RRkj ) 19. SDII Let RRwj daily precipitation amount on wet days, w(RR ≥ 1mm), in period j. If W represents the number of wet days in j, then: W X SDIIj = RRwj w=1 W 20. R10 Let RRij be the daily precipitation amount on day i in period j. Count the number of days where: RRij ≥ 10mm 21. R20 Let RRij be the daily precipitation amount on day i in period j. Count the number of days where: RRij ≥ 20mm 22. Rnn Let RRij be the daily precipitation amount on day i in period j. If nn represents any reasonable daily precipitation value in millimeters then, count the number of days where: RRij ≥ nn 23. CDD* Let RRij be the daily precipitation amount on day i in period j. Count the largest number of consecutive days where: RRij < 1mm 23 24. CWD* Let RRij be the daily precipitation amount on day i in period j. Count the largest number of consecutive days where: RRij ≥ 1mm 25. R95p Let RRwj daily precipitation amount on wet days, w(RR ≥ 1mm), in period j and let RRwn 95 be the 95th percentile on wet days in the base period. If W represents the number of wet days in the period, then: R95pj = W X RRwj , where RRwj > RRwn 95 w=1 26. R99p Let RRwj daily precipitation amount on wet days, w(RR ≥ 1mm), in period j and let RRwn 99 be the 99th percentile on wet days in the base period. If W represents the number of wet days in the period, then: R99pj = W X RRwj , where RRwj > RRwn 99 w=1 27. PRCPTOT Let be the RRij daily precipitation amount on day i in period j. If I represents the number of wet-days in j, then: P RCP T OTj = I X i=1 24 RRij D D.1 Threshold estimation and base period temperature indices calculation Empirical quantile estimation The quantile of a distribution is defined as Q(p) = F −1 (p) = inf{x : F (x) ≥ p}, 0 < p < 1 where F (x) is the distribution function. Let {X(a) , ..., X(n) } denote the order statistics of {X1 , ..., Xn } (i.e. sorted values of {X}), and let Q̂i (p) denote the ith sample quantile definition. The sample quantiles can be generally written as Q̂i (p) = (1 − γ)X(j) + γX(j+1) Hyndman and Fan (1996) suggest a formula to obtain medium un-biased estimate of the quantile by letting j =int(p × n + (1 + p)/3) and letting γ = p × n + (1 + p)/3 − j, where int(u) is the largest integer not greater than u. The empirical quantile is set to the smallest or largest value in the sample when j < 1 or j > n respectively. That is, quantile estimates corresponding to p < 1/(n+1) are set to the smallest value in the sample, and those corresponding to p > n/(n + 1) are set to the largest value in the sample. D.2 Bootstrap procedure for the estimation of exceedance rate for the base period It is not possible to make an exact estimate of the thresholds due to sampling uncertainty. To provide temporally consistent estimate of exceedance rate throughout the base period and out-of-base period, we adapt the following procedure (Zhang et al. 2004) to estimate exceedance rate for the base period. (a) The base period is divided into one out-of-base year, the year for which exceedance is to be estimated, and a base-period consisting the remaining years from which the thresholds would be estimated. (b) A n-year block of data is constructed by using the n − 1 year base-period data set and adding an additional year of data from the base-period (i.e. one of the years in the base-period is repeated). This constructed n-year block is used to estimate thresholds. (c) The out-of-base year is then compared with these thresholds and the exceedance rate for the out-of-base year is obtained. (d) Steps (b) and (c) are repeated for additional n − 2 times, by repeating each of the remaining n − 2 in-base years in turn to construct the n-year block. (e) The final index for the out-of-base year is obtained by averaging the n − 1 estimates obtained from steps (b), (c) and (d). 25 References [1] Hyndman, R.J., and Y. Fan, 1996: Sample quantiles in statistical packages. The American Statistician, 50, 361-367. [2] Zhang, X., G. Hegerl, F.W. Zwiers, and J. Kenyon, 2005: Avoiding inhomogeneity in percentile-based indices of temperature extremes. J. Climate, 18, 1647-1648. 26
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