Estimation of Point Rainfall Frequencies


 Brian Peters
 1 years ago
 Views:
Transcription
1 Me Éireann Irish Meeorologial Servie Tehnial Noe 6 Esimaion of Poin Rainfall requenies D.L. izgerald Me Éireann, Glasnevin Hill, Dublin 9, Ireland UDC: Oober, 2007 ISSN X
2 ESTIMATION O POINT RAINALL REQUENCIES WorkPakage.2, lood Sudies Updae A sudy underaken by Me Éireann for he Offie of Publi Works OPW
3 Table Of Conens Exeuive Summary. Page iii Inroduion.. DD Model Rainfall Daa Mapping Reliabiliy and Auray 6 5. Effes of Climae Change Comparisons wih TN Referenes Appendix A Developmen and Implemenaion of he Deph Duraionrequeny relaionships Appendix B Esimaion of he parameers of he loglogisi disribuion for lefensored samples Appendix C Cheks and Confidene Inervals for he gridded rainfall esimaes Appendix D Langbein s ormula Average Reurrene Inervals Appendix E Duraions less han 5 mins Appendix Glossary of erms used Esimaion of Poin Rainfall requenies. Me Éireann, Oober 2007 ii
4 Exeuive Summary A deph duraion frequeny model is developed whih allows for he esimaion of poin rainfall frequenies for a range of duraions for any loaion in Ireland. The model onsiss of an index median rainfall and a loglogisi growh urve whih provides a muliplier of he index rainfall. Rainfall saion daa were analysed and an index rainfall exraed, inerpolaed and mapped on a 2km grid. The model was fied o series of annual maxima and he growh urve parameers were deermined; hese were also inerpolaed and mapped on a 2km grid. Compuer appliaions were wrien o apply he model and produe gridded oupus of he reurn period rainfalls whih an easily be mapped; an appliaion for deriving rariy esimaes was also developed. An aoun is also given of he reliabiliy and probable auray of he model and he probable effes of Climae Change on exreme rainfalls. Esimaion of Poin Rainfall requenies. Me Éireann, Oober 2007 iii
5 Esimaion of Poin Rainfall requenies. Me Éireann, Oober 2007 iv
6 Design Rainfall Esimaes for he Irish lood Sudies Updae Proje Inroduion The work was underaken by Me Éireann using funding provided by he Offie of Publi Works OPW and is a module of he lood Sudies Updae SU Proje. The requiremen was o a produe a gridded se of parameer values summarising he rainfall DephDuraionrequeny DD relaionship, and hereby enable he produion of onsisen esimaes of poin rainfall frequenies over duraions ranging from 5 minues o 25 days. The esimaes were o supersede hose provided in Logue 975 in whih he mehods of SR lood Sudies Repor,975 were adaped o Irish ondiions. All he design rainfall oupus are for sliding duraions e.g. an 8 day esimae is for 92 onseuive hours and may sar a any hour of day; his onrass wih he raw daa whih are mosly for fixed duraions e.g. daily values read a 0900UTC. The body of his doumen desribes he model, he daa, he onversion of daily daa from fixed o sliding duraions, he mehods of spaial inerpolaion, and onains an assessmen of reliabiliy levels and onfidene inervals for he gridded esimaes. More ehnial desripions of some of hese opis are given in he appendies. Possible effes of limae hange and omparisons wih he esimaes from Logue 975 are also inluded. The model developed enables he esimaion of rainfall frequenies a any loaion. As series of annual maxima were employed hroughou, he rainfall frequenies are expressed in erms of reurn periods; his and oher ehnial erms will be explained. Some guidane going beyond he requiremens e.g. esimaion of 5minue and 0minue reurn period rainfalls is given and he maer of onvering reurn periods o average reurrene inervals is reaed. An underlying assumpion is ha he daa used in his sudy will reasonably represen he upoming rainfall regime. Given he onsensus view ha we are in a period of global warming his is no a safe assumpion even in he medium erm. General indiaors of he effes of global warming on he preipiaion regime are available bu are heavily dependen on he pariular parameerisaions used in he general irulaion model. The indiaions of he laes assessmen of he Irish limae modelling group, C4I Communiy Climae Change Consorium for Ireland, are given. However, appropriae adjusmens are no inluded in he esimaes of he reurn period rainfalls as i appears ha for quie a number of years ino he fuure he indiaions of he effes of global warming on preipiaion regime will hange from assessmen o assessmen. The laes advie on he probable effes of limae hange on exreme rainfalls should be sough. Esimaion of Poin Rainfall requenies. Me Éireann, Oober 2007
7 . The DephDuraionrequeny DD Model A DD model onsiss of:. An index rainfall value e.g. he median or mean 2. A growh urve whih provides a muliplier of he index rainfall The model developed here applies o a single loaion and is mahemaial form enables he esimaion of reurn period rainfalls over a range of duraions D and reurn periods T. Appendix A gives he jusifiaion for using he loglogisi disribuion as he growh urve and he median of he series of annual maxima as he index rainfall. The growh urve is of form: R T, D = T, T = R 2, D, T > where is he umulaive disribuion funion. RT,D is he rainfall of duraion D wih reurn period T, where T is he average number of years beween years wih one or more rainfalls exeeding he value RT,D. I is imporan o noe ha T is no he average reurrene inerval ARI beween rainfalls exeeding RT,D. Analysis of annual maxima leads naurally o he expression of ime inervals in erms of reurn periods. Analysis of parial duraion series PDS, also ermed peakoverhreshold POT analysis, leads o average reurrene inervals. How o onver a given ARI ino a value of T so ha rainfall for a given ARI may be esimaed from annual series is disussed in he nex seion. R2,D is he populaion median a duraion D i.e. half he annual falls exeed R2,D sine T = 2 orresponds o = 0.5 and is he index rainfall ; i as as a saling faor in he DD model. A plausible form for he variaion of he median wih duraion is see Appendix A R s 2, D = R2, D 2 where D = is a suiably hosen uni duraion whih is 24 hours d for boh he d o 25d rainfalls D >= and for duraions less han 24hours D <. Thus he d median rainfall, R 2,, plays a pivoal role in he DD model. The full DD model ombines and 2 and is: R T, D s = R2, D T, T> 3 The exponen s in 2 deermines he muliplier of R2, yielding R2,D as duraion, D, varies. The exponen in is he shape parameer of he loglogisi growh urve see Appendix A and deermines he muliplier of R2,D whih yields RT, D, he rainfall a reurn period T and duraion D. Esimaion of Poin Rainfall requenies. Me Éireann, Oober
8 The final forms of he models onsised of 3 wih 24 hours as he uni duraion and wih he exponens of form:. o 25 days: D = a +b lnd, D ranging o 25 4 s D = e + f lnd 5 Here ln is he naural logarihm. Noe ha wih D =, = a = 24, he shape parameer a he day 24hour duraion. Boh exponens are aken o be funions of D and no of T..2 24hours o 5 minues: D = 24 + h ln D, D < 6 s = s 7 Here D = 0.75 a 8 hours, D = 0.5 a 2 hours, D = 0.25 a 6 hours and so on. The shape parameer is, again, a funion of duraion bu he duraion exponen s is no. Only wo parameers, h and s need be deermined as 24 is available from he work on o 25 days.. The reasons for hese hoies are disussed in Appendix A..3 Implemening he DD model The wo DD models were fied o he saion daa by a mehod desribed in Appendix A. Geosaisial mehods Kianidis, 997 were used o inerpolae he saion values of he parameers o he 2km grid. Two esimaes are required:. RT,D he reurn period rainfall a duraion D, given reurn period T and duraion D and 2. T, he reurn period given duraion D and rainfall amoun RT,D Esimaing RT,D and/or T a grid poins is hen sraighforward. The mehod of inerpolaion beween grid poins is desribed a he end of Appendix A where he maer of he mos appropriae parameer values o aah o he represenaive poin of a ahmen is briefly disussed. Programs were wrien o esimae RT,D over he 2km grid and also o alulae eiher RT,D or T a any loaion..4 Conversion aors for Parial Duraion Series PDS By definiion annual maximum series AMS onsis of he highes fall for eah year; he seond highes fall is ignored wheher or no i exeeds he highes fall in oher years. Parial duraion series PDS onsis of all falls exeeding a erain hreshold ogeher wih heir imes of ourrene. The reurn period T is bes hough of as he inverse of a probabiliy e.g. he rainfall orresponding o T = 50 has a probabiliy of 0.02 of being exeeded nex year. Risk an also be expressed in erms of reurn period rainfalls. The rainfall orresponding o T = 238 years has a probabiliy of 0.9 of no being exeeded during he nex 25 years Esimaion of Poin Rainfall requenies. Me Éireann, Oober
9 Zuhini & Adamson, 989 i.e. he risk r is 0.. Assuming ha he annual maxima are saisially independen and all are drawn from he same disribuion n T = / r 8 where he design horizon is n years and he risk is r. The analysis of PDS gives he average period beween rainfall evens ha exeed a pariular value and is ofen ermed he average reurrene inerval ARI for a given duraion D. or high values of T, values of ARI and T are nearly equal bu for T less han 20 years he differene an be signifian. Langbein 949 provides a formula see Appendix D for he relaionship beween T and ARI whih yields: T =.6 for ARI =/2 T =.58 for ARI = T = 2.54 for ARI = 2 The approximaion T = ARI improves as ARI inreases. Thus he PDS rainfall for ARI = 2 is he reurn period rainfall for T =2.54 years. As annual series were used in his sudy we an only esimae growh urves for reurn period rainfalls bu he Langbein formula enables heir onversion ino PDS rainfalls wih a known ARI. Esimaion of Poin Rainfall requenies. Me Éireann, Oober
10 2. Rainfall daa for he lood Sudies Updae 2. Irish Saions Noe: In his seion Irish daa is aken o mean daa from rainfall saions in he Republi of Ireland 2.. Daily UTC daa: The requiremen was o form series of annual maxima for a leas six duraions ranging from one o weny five days. On assessing he amoun of qualiy onrol needed o rea eah duraion i was deided ha he produion of omplee daily series was he beer opion. The Me Éireann arhive for periods wihin was used as his had already undergone exensive qualiy onrol. However, dry monhs and daily falls in exess of 75.0mm were reexamined and some fauly daa orreed before forming he iniial able of daily rainfall. Highqualiy saions were piked ou by examining he number of aumulaed oals or missing days in eah monh of reord. or hese saions aumulaions were broken up ino daily values and missing days esimaed o give a omplee se of daily values. or mos saions esimaions were made by using up o six neighbouring saions wih similar wihin abou 0% average annual rainfall AAR; hese were ranked in order of preferene and he firs o have a omplee reord for a period requiring esimaion used as his had he pereived advanage of using a oal aually reorded in he general area raher han a weighed mean. If he AAR of he saion requiring esimaion differed onsiderably from is neares neighbours hen hree neighbours wih omplee daily reords were hosen and he global monhly raios of arge saion over neighbour deermined. or missing monhs he oal was aken as a weighed mean of he hree esimaed oals and hen redued o daily values by referene o he daily falls a he neares neighbour. Monhs wih a oal bu no daily values were reaed by forming he weighed mean of he hree neighbours and giving i equal weigh o he arge saion oal; he agreemen beween he wo was usually good. Again daily values were found from he esimaed monhly oal by referene o he neares neighbour. The remaining missing or aumulaed days were reaed by muliplying he daily values a he neares available neighbour by he monhly raio. Annual maxima exraed from he original and reaed daa showed ha he differenes were usually small as he qualiy of he hosen saions was high. Using hese mehods daily values for 474 saions were exraed; heir average period of reord was 4.2 years, wih a range of 20 o 64 years. Annual maxima for, 2, 3, 4, 6, 8, 0, 2, 6, 20 and 25 days ogeher wih he saring dae were pu ino a able of 24,98 rows. The loaion of hese saions plus 03 saions from Norhern Ireland are shown in igure. Esimaion of Poin Rainfall requenies. Me Éireann, Oober
11 2..2 Shorduraion falls Daa for nine sliding duraions beween 5 minues and 24 hours are available from 39 saions for periods ranging from 5 o 55 years bu 37 of he saions have 30 or more years of reord. The loaions of he 39 saions used are shown in igure 2. Mosly he daa were exraed from Dines reorder hars bu sine he midnineies hese have been replaed by ipping buke reorders TBR a some saions. In he periods of overlap he differenes beween he Dines and TBRs were found o be generally small and no adjusmen for he ransiion was made. The maxima of all falls aaining or exeeding a leas one of a se of hresholds were exraed. The hresholds are: Duraion 5m 30m h 2h 3h 4h 6h 2h 24h Threshold mm The dae assigned is ha of he day on whih mos, or all, of he oal for he rainfall even was reorded. Qualiy onrol onsised of:. Cheking he daes of ourrene and values of he UTC oals of 30mm or more agains hose of he 24h values. 3. Examining he rows of he able for onsiseny. Doubful or missing values deeed were esimaed by referene o he neares saions. or he 6 synopi saions a more exensive qualiy onrol was possible as all lok hour o 24 lokhour oals reahing or exeeding he hresholds and heir daes of ourrene were heked agains he orresponding absolue maximum values. To exra annual series we mus deal wih he problem of years wih no value exeeding he hreshold. In he ase of synopi saions good esimaes an be made from he lokhour values, if desired. The sraegy applied o all saions was o rus in he qualiy of he daa and assume ha he missing values were below he appropriae hresholds and hene unimporan for fiing a probabiliy disribuion loglogisi o exremes. The sample ould be regarded as ensored and mehods ha ake aoun of his developed o deermine he parameers Appendix B. In he even, only he ordered se of values greaer han or equal o he sample median was needed o fi he disribuion; forunaely, a all saions hese series were omplee. 2.2 Daa from Norhern Ireland Through he good offies of he UK Me Offie and he Cenre for Eology & Hydrology Wallingford he daily and hourly series of annual maxima from Norhern Ireland used in he lood Esimaion Handbook 999 were made available. Of he daily saions 03 wih a leas 20 years of reord a duraions of, 2, 4 and 8 days were used in his sudy. The hourly daa onsised of 8 saions wih lenghs of reord beween and 9 years and wih daa a duraions of, 2, 4, 6, 2, 8 and 24 hours. Esimaion of Poin Rainfall requenies. Me Éireann, Oober
12 Esimaion of Poin Rainfall requenies. Me Éireann, Oober
13 2.3 Conversion from fixed o sliding duraions The daa available were he day, 2day..25day annual maxima derived from daily oals read a 0900UTC. However, he aim was o esimae he 24hour, 48 hour 600hour reurn period rainfalls where 24hour is he annual maximum for any 24hour period wihin he year. How o do his from he UTC daa involves onversion faors from fixed o sliding duraions. The maer was examined in wo ways:. A he 4 longererm synopi saions he loglogisi disribuion was fied o he, 2, 3, 4, 6, 8, 0, 2, 6, 20 and 25day annual maxima of he UTC rainfall oals and also o heir 24, 48, 72, 96, 44, 92, 240, 288, 384, 480 and 600 lokhour oals. Reurn period rainfalls of 2, 5, 0, 20, 50, 00, 250, 500 and 000 years were alulaed for eah and he raios examined. No allowane was made for he ransiion from lokhour values o absolue values as inspeion showed ha, even for 24 hours, he faor was very lose o one. Use of he year JanuaryDeember revealed signifian endofyear effes espeially a he longer duraions. As a hek he AprilMarh period was used and i was found ha he values of he reurn period rainfalls were lile hanged and so AprilMarh was used as he rainfall year. 2. or he eleven UTC duraions, 2, 3, 4, 6, 8, 0, 2, 6, 20 and 25 days hresholds of 23, 30, 35, 40, 48, 55, 60, 65, 70, 75 and 80mm were se and he nday exeedanes ompared wih he orresponding lokhour values; orresponding was aken as saring wihin a erain inerval ha had he saring dae of he UTC aumulaions as a fairly enral value. Various inervals were ried and he general effe of narrowing he inerval n xi was o slighly derease he raios. Sample average raios = were n i= yi derived from he individual evens, his in preferene o he raio of he sample avg xi averages = whih gave slighly lower values. As poined ou in avg y i Dwyer & Reed 995 he raio of he sample averages is equivalen o a weighed sum of he individual raios, wih greaer weigh given o he larger evens. The resuls of fiing he loglogisi disribuion, presened below in Table A, sugges ha for he median rainfall he onversion faors should be : d 2d 3d 4d 6d 8d 0d 2d 6d 20d 25d RP = The work on evens gives : Evens Noe ha he faors based on means of aual evens are generally lower. This may be aribued in fair measure o he fa ha for evens he imes of ommenemen of he UTC and hourly aumulaions are fairly lose while, espeially for he 24 and 48hour duraions, he ime of sar of he UTC and hourly annual maxima may, on oasion, be separaed by monhs i.e. here is an exra soure of Esimaion of Poin Rainfall requenies. Me Éireann, Oober
14 variaion. If you exra he mean of. as a haraerisi muliplier for he day evens i is from a posiively skewed disribuion wih a median of.05 bu wih 32 of a oal 2285 ases in exess of.25 and a range from.0 o 2.0. In Table A he range of he RP2 median faor is from.086 o.257 wih a mean of.53, a median.48 and a sandard deviaion of abou Sine i is he index rainfall, he values for he 2year reurn period rainfall are mos imporan bu i is of ineres o see how he faors vary wih inreasing reurn period. Table A gives he means over foureen synopi saions of he raios of he lokhour esimaes of reurn period rainfalls o he orresponding fixedduraion values for eah of he eleven duraions. In general he raios derease wih reurn period bu are nearly onsan for he oneday rainfalls and for duraions of 6 days or more, while he 2 day falls inrease wih reurn period. As expeed he derease of he raio wih duraion is onsisen over all reurn periods. Table A ixed v Sliding Duraions Mean of Adjusmen aors Days RP 2 RP5 RP0 RP20 RP50 RP00 RP250 RP500 RP000 Evens Sine he onversion from day UTC o 24 hour median values is ruial o he shorduraion model, he medians of annual maximum series a he 39 saions for whih absolue 24hour maxima were available were ompared wih he medians of he UTC annual maximum series over he same years. The quarile summary of he 39 raios is: Minimum Q Median Mean Q3 Maximum Only 3 of he 39 values exeeded.20 and only exeeded.25. The inerquarile range yields an esimae of abou 0.05 for he sandard deviaion. Linear regression gives.28 as he raio. The ompeing mean value is.5, he onversion faor for he loglogisi esimae of he median raio and his was adoped as i ompares wih.6 used in EH 999 and.4 used in he New Zealand HIRDS sysem. Esimaion of Poin Rainfall requenies. Me Éireann, Oober
15 2.4 Noaion When i is neessary o disinguish beween he wo, he slidingduraion rainfalls obained by muliplying he fixedduraion falls by he appropriae onversion faor will be referred o as d, 2d, 3d 25d rainfalls; he fixed duraion falls will be labelled d09, 2d09,.25d09. Subdaily duraions are always sliding duraions. The Irish shorduraion daa onsis of absolue maxima exraed from rainfall evens for duraions up o and inluding 24 hours. In wha follows he laer value is referred o as abs24. The d value is a lose approximaion o abs24 and has he advanage of being muh more widely available. The d rainfall will be labelled slide24 when onsidering duraions of 24h o 5m i.e. i is being used as a subsiue for abs24. Esimaion of Poin Rainfall requenies. Me Éireann, Oober
16 3. Mapping 3. Mapping he Index Rainfall The pivoal value is he median oneday rainfall, RMEDd whih is losely approximaed by: RMED d =.5RMEDd 09 9 The number of values of RMEDd available was 577 of whih 03 were in Norhern Ireland. This did no seem adequae o produe values on a 2km grid. orunaely, here is a srong linear relaionship beween AAR average annual rainfall and RMEDd. In he ase of he averages AAR690 he relaion RMED d = AAR690 0 has a oeffiien of deerminaion R 2 = ha an be inreased o by he addiion of loaion oordinaes e.g. easing and norhing in meres for eah saion: RMEDd = AAR easing norhing To exploi he srong relaionships 0 or values of AAR690 on a grid were needed. The saions for whih AAR690 were available numbered 946 of whih 242 were in Norhern Ireland. Drawing on onsiderable experiene of esimaing AAR, 0 values were added in daasparse areas. The 047 daa poins were used o produe values of AAR690 on a 2km grid using geosaisial mehods Kianidis, 997 and he R pakage, geor. The gross dependene of AAR on elevaion and loaion was removed by linear regression and he residuals inerpolaed o he grid using ordinary kriging wih a moving neighbourhood i.e. weighed linear ombinaions of nearby values. The values of he regression equaion a eah grid poin were added o he gridded residuals o produe he final resul. Comparison wih previously mapped values of AAR690 showed very good agreemen. Kriging was again used o produe gridded values of RMEDd. The number of saions having values of boh RMEDd and AAR690 was 468. The residuals from he regression of RMEDd on AAR690 were inerpolaed o he 2km grid and he regression esimaes added o produe he final mapping, igure Comparison of reorded and inerpolaed values of he median rainfall There were 09 saions having a value of RMEDd bu no value of AAR690. Using gridded RMEDd as he daa values, he 09 kriging esimaes KMEDd of RMEDd were obained ogeher wih heir kriging sandard errors ksd. RMEDd The raio is approximaely normally disribued wih mean and KMEDd sandard error of The perenage differenes are less han 5% in 02 of he 09 ases, 66 are less han 7.5%, 50 less han 5% and 30 less han 2.5%. I indiaes ha KMEDd is an appropriae esimaor of RMEDd and jusifies he assumpion ha he mapped value is a good esimaor of he aual median rainfall a a sie. The kriging sandard error, ksd,of KMEDd refles he variabiliy of he esimaes whih are weighed means of he surrounding gridpoin values and so he sandard Esimaion of Poin Rainfall requenies. Me Éireann, Oober 2007
17 error will be higher where he median rainfall hanges more rapidly wih disane e.g. in and near mounainous areas. I is reasonably well approximaed by: 2 2 ksd = 0.00 KMEDd, R = This kriging sandard error inreases monoonially wih KMEDd and ranges from abou mm o 9mm as KMEDd varies from 3 o 94 mm. As he higher values of KMEDd our in he mounains where he densiy of he raingauge nework is lowes, he unerainy aahing o he inerpolaed values is highes here. The kriging sandard error an be used o esimae he error of inerpolaion and hene is of ineres as a measure of he reliabiliy of KMEDd. Esimaion of Poin Rainfall requenies. Me Éireann, Oober
18 3.2 Mapping he model parameers 3.2. d o 25d sliding duraions No useful relaionships were found beween he four model parameers and median rainfall, AAR or easing and norhing. Hene, all parameers were inerpolaed o he 2km grid using ordinary kriging wih a moving neighbourhood i.e. a weighed mean wih weigh dependen on disane h o 5m sliding duraions The model adoped mean ha no new mappings were required. The gridded d shape parameer = 24 and he grid of he median oneday rainfall were needed bu hese had been mapped as par of he work on he d o 25d model. The wo model parameers h and s for he shorduraions falls an hen be alulaed a any poin by means of he sheme oulined in Appendix A Enforing Consiseny on he model parameers or he 4parameer model D = a + b lnd and s D = e + f lnd 3 To mee he requiremen ha, for he same reurn period T, he esimae should inrease wih duraion we mus have: e + 2f lnd + b lnt > 0 4 Near 000 years and near day his beomes e + 7b > 0 or a given duraion, o have a posiive rae of hange wih inreasing reurn period T requires: a + b lnd > 0 5 A abou 30 days his requires a b > d o 25d Irish model In nearly 7% of ases here ours he problem ha a high reurn periods ~000years ha he 2day esimae may be slighly less han he day esimae. The basi reason is ha he shape parameer is dereasing oo sharply. This an be simply orreed by enforing he ondiion : e + 7b > 0 6 or a given duraion he reurn period rainfall esimaes mus inrease wih T bu his presened no problem. An example of he oupu is shown in igure Consiseny of he model for he Norhern Ireland daa The parameer values for he Irish daa for d o 8d had similar quariles o he d o 25d daa see Table, Appendix A. Hene, i was deided o use he Norhern Ireland daa as if i were for periods up o 25d, a onvenien bu deidedly risky assumpion. The ondiion e+7b > 0 had o be imposed in nearly 7% of ases and his adjusmen also remedied he failure of 8% of he saions o mee he requiremen a +3.5 b >0. Esimaion of Poin Rainfall requenies. Me Éireann, Oober
19 Esimaion of Poin Rainfall requenies. Me Éireann, Oober
20 3.2.6 Model for 24 hours o 5 minues Reall ha he model is of form: s 24 + h ln D = R2, D T 7 R T, D A a given duraion he esimae inreases wih reurn period T if: + h ln D > A a given reurn period he esimae inreases wih duraion if: s + hln T > 0 9 These ondiions were kep in mind when assigning values o h and so no onsiseny problems arose wih he shorduraion model as 0.03 h 0, ln D 0 and s An example of he model oupu is shown in igure alls of duraions less han 5 minues Esimaes of rainfall dephs for duraions less han 5min are onsidered in Appendix E. The onlusion is ha i is probably bes o employ 5minue esimaes and apply he given formula for he mean fraion as a funion of he fraional duraion. In he ase of en and five minue duraions he fraions of he fifeen minue dephs are 0.85 and 0.6 respeively. Esimaion for inervals of less han 5 minues duraion should be regarded as highly speulaive. Esimaion of Poin Rainfall requenies. Me Éireann, Oober
21 4. Reliabiliy and Probable Auray of he Reurn Period Rainfalls These maers are disussed in more deail in Appendix C where he enaive onlusions are:. The 24hour o 600hour esimaes may be used wih fair onfidene for reurn periods up o abou 500 years 2. The esimaes for duraions of less han 24 hours may be used wih fair onfidene for reurn periods up o abou 250 years. The saisial analysis was done on he assumpion ha he daa are represenaive of he fuure rainfall regime. Given onerns abou probable hanges in preipiaion limae in he shor o medium erm due o global warming his is by no means assured. How, or even if, o adjus he esimaes is no a quesion o whih here is a good answer a presen bu some general, perhaps even useful, observaions are made in he nex seion. Aeping he urren onsensus on he high likelihood of hanges in he preipiaion limae, here seems o be lile sense in esimaing 500year reurn period rainfalls. However, equaion 8 shows ha he very praial maer of esimaing a 0% risk for a ime horizon of 50 years requires a reurn period rainfall for 475 years. Also in Appendix C a mehod is given for aahing a sandard error o any esimaed reurnperiod rainfall from knowledge of he values of he median rainfall and he shape parameer plus a very large assumpion abou he effeive sample size. This saisial measure of spread gives an idea of he probable auray of he value. I has o be regarded as merely a rough guide. Informaion on he rainfall exremes of he las 00 years or so may be had in Rohan 986 or Hand e al Esimaion of Poin Rainfall requenies. Me Éireann, Oober
22 5. Probable Effes of Climae Change on Exreme Rainfalls The mos reen IPCC repor on regional limae projeions Chrisensen e al., 2007 saes ha over Norhern Europe beween and he median hange in preipiaion was a 5% inrease for he monhs of DJ, 2% for MAM, 2% for JJA and 8% for SON. Relaive o he wees period in here was a 43% inrease in we evens in DJ. However hese were over a large area and he model resoluion a ~ 200km was raher oarse. The laes assessmen from C4I Communiy Climae Change Consorium for Ireland saes ha over Ireland by midenury here may well be:. An inrease of abou 5% in winer rainfall amouns 2. Drier summers wih 20% lower preipiaion in some areas, mos likely he eas and souheas. 3. A 20% inrease in he woday exreme rainfalls, espeially in norhern areas and smaller inreases in he one and five day exremes. 4. More frequen rainfall exremes in auumn. All his would sugges an inrease in exreme rainfalls for duraions of 24 hours or more, espeially in auumnwiner. Drier summers sugges an inrease in he frequeny of droughs. The breakdown of droughs is someimes he oasion of heavy shorduraion rainfalls. The general suggesion of mos of he senarios is ha safey faors of maybe as muh as 20% on rainfall deph migh be inorporaed as an aemp a a no regres poliy in he fae of unerainy. A purely saisial exerise in izgerald 2005 omes up wih safey faors for  day rainfalls a Phoenix ParkDublin of abou % for a 20year reurn period rainfall, 9% for he 00year value and 33% for 000year rainfall, his based on 22 years of daily daa. Given he wide variaion in prediions from assessmen o assessmen or beween saisial exerises i would be wise always o seek he laes advie on he probable effes of limae hange on exremes of preipiaion before onsidering an adjusmen o he model esimaes of reurn period rainfall. Esimaion of Poin Rainfall requenies. Me Éireann, Oober
CO2 Cost Pass Through and Windfall Profits in the Power Sector
CO Cos Pass Through and Windfall Profis in he Power Seor Jos Sijm, Karsen Neuhoff and Yihsu Chen May 006 CWPE 0639 and EPRG 067 These working papers presen preliminary researh findings, and you are advised
More informationMining the Most Interesting Rules
Appears in Pro. of he Fifh ACM SIGKDD In l Conf. on Knowledge Disovery and Daa Mining, 145154, 1999. Mining he Mos Ineresing Rules Robero J. Bayardo Jr. IBM Almaden Researh Cener hp://www.almaden.ibm.om/s/people/bayardo/
More informationA Working Solution to the Question of Nominal GDP Targeting
A Working Soluion o he Quesion of Nominal GDP Targeing Michael T. Belongia Oho Smih Professor of Economics Universiy of Mississippi Box 1848 Universiy, MS 38677 mvp@earhlink.ne and Peer N. Ireland Deparmen
More informationToday s managers are very interested in predicting the future purchasing patterns of their customers, which
Vol. 24, No. 2, Spring 25, pp. 275 284 issn 7322399 eissn 1526548X 5 242 275 informs doi 1.1287/mksc.14.98 25 INFORMS Couning Your Cusomers he Easy Way: An Alernaive o he Pareo/NBD Model Peer S. Fader
More informationThe U.S. Treasury Yield Curve: 1961 to the Present
Finance and Economics Discussion Series Divisions of Research & Saisics and Moneary Affairs Federal Reserve Board, Washingon, D.C. The U.S. Treasury Yield Curve: 1961 o he Presen Refe S. Gurkaynak, Brian
More informationAnchoring Bias in Consensus Forecasts and its Effect on Market Prices
Finance and Economics Discussion Series Divisions of Research & Saisics and Moneary Affairs Federal Reserve Board, Washingon, D.C. Anchoring Bias in Consensus Forecass and is Effec on Marke Prices Sean
More informationDoes Britain or the United States Have the Right Gasoline Tax?
Does Briain or he Unied Saes Have he Righ Gasoline Tax? Ian W.H. Parry and Kenneh A. Small March 2002 (rev. Sep. 2004) Discussion Paper 02 12 rev. Resources for he uure 1616 P Sree, NW Washingon, D.C.
More informationCentral Bank Communication: Different Strategies, Same Effectiveness?
Cenral Bank Communicaion: Differen Sraegies, Same Effeciveness? Michael Ehrmann and Marcel Frazscher * European Cenral Bank Michael.Ehrmann@ecb.in, Marcel.Frazscher@ecb.in November 2004 Absrac The paper
More informationFollow the Leader If You Can, Hedge If You Must
Journal of Machine Learning Research 15 (2014) 12811316 Submied 1/13; Revised 1/14; Published 4/14 Follow he Leader If You Can, Hedge If You Mus Seven de Rooij seven.de.rooij@gmail.com VU Universiy and
More informationAre Under and Overreaction the Same Matter? A Price Inertia based Account
Are Under and Overreacion he Same Maer? A Price Ineria based Accoun Shengle Lin and Sephen Rasseni Economic Science Insiue, Chapman Universiy, Orange, CA 92866, USA Laes Version: Nov, 2008 Absrac. Theories
More informationHow to calculate effect sizes from published research: A simplified methodology
WORKLEARNING RESEARCH How o alulae effe sizes from published researh: A simplified mehodology Will Thalheimer Samanha Cook A Publiaion Copyrigh 2002 by Will Thalheimer All righs are reserved wih one exepion.
More informationWhen Should Public Debt Be Reduced?
I M F S T A F F D I S C U S S I ON N O T E When Should Public Deb Be Reduced? Jonahan D. Osry, Aish R. Ghosh, and Raphael Espinoza June 2015 SDN/15/10 When Should Public Deb Be Reduced? Prepared by Jonahan
More informationThe concept of potential output plays a
Wha Do We Know (And No Know) Abou Poenial Oupu? Susano Basu and John G. Fernald Poenial oupu is an imporan concep in economics. Policymakers ofen use a onesecor neoclassical model o hink abou longrun
More informationAsymmetry of the exchange rate passthrough: An exercise on the Polish data 1
Asymmery of he exchange rae passhrough: An exercise on he Polish daa Jan Przysupa Ewa Wróbel 3 Absrac We propose a complex invesigaion of he exchange rae passhrough in a small open economy in ransiion.
More informationKONSTANTĪNS BEŅKOVSKIS IS THERE A BANK LENDING CHANNEL OF MONETARY POLICY IN LATVIA? EVIDENCE FROM BANK LEVEL DATA
ISBN 9984 676 20 X KONSTANTĪNS BEŅKOVSKIS IS THERE A BANK LENDING CHANNEL OF MONETARY POLICY IN LATVIA? EVIDENCE FROM BANK LEVEL DATA 2008 WORKING PAPER Lavias Banka, 2008 This source is o be indicaed
More informationParttime Work, Wages and Productivity: Evidence from Matched Panel Data
Parime Work, Wages and Produciviy: Evidence from Mached Panel Daa Alessandra Caaldi (Universià di Roma "La Sapienza" and SBSEM) Sephan Kampelmann (Universié de Lille, CLERSE, SBSEM) François Rycx (Universié
More informationExchange Rate PassThrough into Import Prices: A Macro or Micro Phenomenon? Abstract
Exchange Rae PassThrough ino Impor Prices: A Macro or Micro Phenomenon? Absrac Exchange rae regime opimaliy, as well as moneary policy effeciveness, depends on he ighness of he link beween exchange rae
More informationI M F S T A F F D I S C U S S I O N N O T E
I M F S T A F F D I S C U S S I O N N O T E February 29, 2012 SDN/12/01 Two Targes, Two Insrumens: Moneary and Exchange Rae Policies in Emerging Marke Economies Jonahan D. Osry, Aish R. Ghosh, and Marcos
More informationBoard of Governors of the Federal Reserve System. International Finance Discussion Papers. Number 1003. July 2010
Board of Governors of he Federal Reserve Sysem Inernaional Finance Discussion Papers Number 3 July 2 Is There a Fiscal Free Lunch in a Liquidiy Trap? Chrisopher J. Erceg and Jesper Lindé NOTE: Inernaional
More informationCostSensitive Learning by CostProportionate Example Weighting
CosSensiive Learning by CosProporionae Example Weighing Bianca Zadrozny, John Langford, Naoki Abe Mahemaical Sciences Deparmen IBM T. J. Wason Research Cener Yorkown Heighs, NY 0598 Absrac We propose
More informationEDUCATION POLICIES AND STRATEGIES
EDUCATION POLICIES AND STRATEGIES Naional Educaion Secor Developmen Plan: A resulbased planning handbook 13 Educaion Policies and Sraegies 13 Educaion Policies and Sraegies 13 Naional Educaion Secor Developmen
More informationBIS Working Papers No 365. Was This Time Different?: Fiscal Policy in Commodity Republics. Monetary and Economic Department
BIS Working Papers No 365 Was This Time Differen?: Fiscal Policy in Commodiy Republics by Luis Felipe Céspedes and Andrés Velasco, Discussion Commens by Choongsoo Kim and Guillermo Calvo Moneary and Economic
More informationBIS Working Papers. Globalisation, passthrough. policy response to exchange rates. No 450. Monetary and Economic Department
BIS Working Papers No 450 Globalisaion, passhrough and he opimal policy response o exchange raes by Michael B Devereux and James Yeman Moneary and Economic Deparmen June 014 JEL classificaion: E58, F6
More informationThe Macroeconomics of MediumTerm Aid ScalingUp Scenarios
WP//6 The Macroeconomics of MediumTerm Aid ScalingUp Scenarios Andrew Berg, Jan Goschalk, Rafael Porillo, and LuisFelipe Zanna 2 Inernaional Moneary Fund WP//6 IMF Working Paper Research Deparmen The
More informationANALYSIS AND COMPARISONS OF SOME SOLUTION CONCEPTS FOR STOCHASTIC PROGRAMMING PROBLEMS
ANALYSIS AND COMPARISONS OF SOME SOLUTION CONCEPTS FOR STOCHASTIC PROGRAMMING PROBLEMS R. Caballero, E. Cerdá, M. M. Muñoz and L. Rey () Deparmen of Applied Economics (Mahemaics), Universiy of Málaga,
More informationResearch Division Federal Reserve Bank of St. Louis Working Paper Series
Research Division Federal Reserve Bank of S. Louis Working Paper Series Wihsanding Grea Recession like China Yi Wen and Jing Wu Working Paper 204007A hp://research.slouisfed.org/wp/204/204007.pdf March
More informationOUTOFBAG ESTIMATION. Leo Breiman* Statistics Department University of California Berkeley, CA. 94708 leo@stat.berkeley.edu
1 OUTOFBAG ESTIMATION Leo Breiman* Saisics Deparmen Universiy of California Berkeley, CA. 94708 leo@sa.berkeley.edu Absrac In bagging, predicors are consruced using boosrap samples from he raining se
More informationDynamic Contracting: An Irrelevance Result
Dynamic Conracing: An Irrelevance Resul Péer Eső and Balázs Szenes Sepember 5, 2013 Absrac his paper considers a general, dynamic conracing problem wih adverse selecion and moral hazard, in which he agen
More informationBanco Central de Chile Documentos de Trabajo. Central Bank of Chile Working Papers EXCHANGE RATE PASSTHROUGH INTO IMPORT PRICES: THE CASE OF CHILE
Banco Cenral de Chile Documenos de Trabajo Cenral Bank of Chile Working Papers N 465 Abril 2008 EXCHANGE RATE PASSTHROUGH INTO IMPORT PRICES: THE CASE OF CHILE Robero Álvarez Paricio Jaramillo Jorge Selaive
More informationImproved Techniques for Grid Mapping with RaoBlackwellized Particle Filters
1 Improved Techniques for Grid Mapping wih RaoBlackwellized Paricle Filers Giorgio Grisei Cyrill Sachniss Wolfram Burgard Universiy of Freiburg, Dep. of Compuer Science, GeorgesKöhlerAllee 79, D79110
More information