A Serially Complete U.S. Dataset of Temperature and Precipitation for Decision Support Systems

Transcription

1 Journal of Envronmental Informatcs 8() (006) 06JEI / ISEIS A Serally Complete U.S. Dataset of Temperature and Precptaton for Decson Support Systems Z. Chen, S. Goddard *, K. G. Hubbard, W. S. Sorensen, and J. You Department of Computer Scence and Engneerng, Unversty of ebraska-lncoln Lncoln, E 68588, USA Hgh Plans Regonal Clmate Center 77 Hardn Hall, Unversty of ebraska-lncoln Lncoln, E , USA ABSTRACT. The effect of mssng data can result n errors that exhbt temporal and spatal patterns n clmatologcal and meteorologcal research applcatons. Many clmate related tools perform best wth a serally complete dataset (SCD). To support the atonal Agrcultural Decson Support System (ADSS), a SCD wth no mssng data values for daly temperature and precptaton for the Unted States was developed usng a self-calbratng data qualty control (QC) lbrary. The lbrary performs two prmary functons: dentfes outlers and provdes estmates to replace mssng data values and outlers. Ths study presents the development of the SCD and the QC lbrary n detal. An n-depth evaluaton n terms of root mean square error (RMSE) and mean absolute error (MAE) for the SCD for the perod of s provded. The study shows an mpressvely low average RMSE n the range of.7 to 3.58 F for temperature and 0.07 to 0.3 nch for precptaton for the whole country for 30 years. The goal of ths study s to enhance drought rsk assessment and envronmental rsk analyss. Keywords: clmate data, qualty control, self-calbrate, serally complete dataset. Introducton There s a great demand n the clmate communty and federal agences for serally complete clmate datasets (SCD) for water management, envronmental systems, and natural resource modelng (Esched et al., 000). The effect of mssng data, or data gaps, n the calculaton of applcatons such as monthly mean temperature can result n errors that exhbt temporal and spatal patterns (Stooksbury et al., 999). In the area of nformaton vsualzaton, mssng data usually causes vsualzaton falure or provdes msleadng nterpretatons of data (Eaton et al., 003). Another area n whch the mssng data has sgnfcant mpact s agrcultural decson support systems. Consder, for example, the atonal Agrcultural Decson Support System (ADSS). The goal of such a project s to develop a support system of geospatal analyses for enhancng the drought rsk assessment and exposure analyss (Goddard et al., 003). A relatonal clmate database s a major component of the data layer n ADSS, whch retreves the clmate data from the atonal Clmate Data Center (CDC) and regonal clmate centers va the Appled Clmate Informaton System (ACIS). In practce, t was found that the data contans many gaps n the hstorcal record. For most statons, the mssng data gaps ranged from a couple days to months, and even to years. The ADSS system requres vald data and performs best wth a SCD because the system ncludes clmate related tools, such as the Standardzed Precptaton Index (SPI) (McKee et al., 993), the Palmer Drought Severty Index (PDSI) (Palmer, * Correspondng author: goddard@cse.unl.edu 965), and the Self-Calbratng PDSI (SC-PDSI) (Wells et al., 004). When there s mssng data (e.g. a couple weeks gap), the SPI can not be calculated for any nterval that ncludes the data gap. The SC-PDSI can be calculated, but t skps the data gap (assumng nothng happens for that nterval of tme), whch may result n an naccurate SC-PDSI and may lead to ncorrect clmate related decsons. To support the ADSS system wth a vald and serally complete dataset, a SCD wth no mssng data values of daly temperature and precptaton (PRCP) for the perod of 975 to 004 for the Unted States was bult. The SCD was bult by usng two prmary functons of a self-calbratng data qualty control (QC) lbrary: dentfcaton of outlers and provson of estmates to replace mssng data values and outlers. The estmaton method s a regresson-based spatal estmaton routne from the QC lbrary. To prevent error n natural resource montorng, Esched and hs colleagues made an early attempt to buld a serally complete dataset for the western Unted States (Esched et al., 000). However, ther methods have some lmtatons. For example, to be ncluded n the seralzaton procedure, a staton could not have more than 48 mssng months of data for the entre perod of record. In ther approaches, a month would be marked as mssng f t contaned more than 4 consecutve days of mssng temperatures or precptatons. The approach presented n ths study provdes the estmated values for all the statons that exst n the perod and does not have such a lmtaton. The semautomated qualty control procedures have been appled to check the valdty of clmate data from the coopera- 86

2 Z. Chen et al. / Journal of Envronmental Informatcs 8() (006) tve clmatologcal statons at CDC snce 98 (Guttman et al., 990). Consstency checks between the daly maxmum temperature (TMAX) and the daly mnmum temperature (TMI) are appled based on the pre-defned general rules (Guttman et al., 990). General testng methods, such as the threshold method and the step-change method, were desgned for revewng data from a sngle staton to detect the potental outlers. Advanced procedures, such as spatal tests, have also proven useful (Esched et al., 995; Hubbard, 00). They compare data of a target staton aganst smultaneous data of surroundng statons. The spatal tests can be performed based on statstcal methods, e.g. lnear regresson and multple regresson. The self-calbratng data QC lbrary used n ths study ncludes both sngle staton methods and multple staton technques. Unlke other rule-based systems, such as the CDC system, whch uses predefned rules, the self-calbratng data QC lbrary approach s based on statstcal data of statons stored n a relatonal database. Usng the approach, a QC parameter database s frst generated from the statstcal result of a 30- year hstory of data for all statons processed. Based on that database, each of the QC routnes can be run separately. Furthermore, the users can apply dynamc parameters to control dfferent levels of assurance as desred for the data. Such an approach has been found to be accurate and flexble n several prevous studes (Hubbard and You, 005; Hubbard et al., 005). It s mportant to be noted that the lbrary conssts of a newly desgned spatal regresson test (SRT) method that assgns the weghts accordng to the standard error of estmate between the target staton and each of the surroundng statons. A prevous study shows that the SRT method outperforms the IDW method n estmaton (You et al., 005; Legates and Wllmott, 990; Stallngs et al., 99). A comparson between the approaches n the self-calbratng data QC lbrary and the QC procedures appled by CDC was prevously conducted through a seeded errors dataset by You et al. (005). The result determned that the SRT method and other approaches n the QC lbrary outperform the procedures appled by CDC. The man objectves of ths study were: (a) to create a SCD for daly temperature and precptaton for the Unted States for the perod of 975 to 004; (b) to evaluate the selfcalbratng data qualty control lbrary through the development of the SCD; (c) to ntroduce the QC lbrary as a framework for clmatologcal and meteorologcal research applcatons to enhance drought rsk assessment and envronmental rsk analyss. Although the focus of ths study s to create the 30-year SCD from hstorcal data, the approach can also be appled n real-tme data qualty control and real-tme SCD generaton. Examples of prevous clmatologcal and meteorologcal research usng the approach are reported by Hubbard and You (005), Hubbard et al. (005).. Buldng a Serally Complete Dataset.. Data Source The data source of the SCD s based on all of the statons (063 PRCP [precptaton], 386 TMAX [maxmum temperature], and 384 TMI [mnmum temperature] statons) avalable from the ACIS of the atonal Oceanc and Atmospherc Admnstraton s (OAA) Regonal Clmate Centers, whch ncludes the statons of the atonal Weather Servce (WS) Cooperatve Observer Program (COOP), the Hgh Plans Automated Weather Data etwork (AWD), the Internatonal Cvl Avaton Organzaton (ICAO) network and statons from the WS encoded n standard hydrologc exchange format (SHEF). The staton locatons are shown n Fgure. Snce some of the statons only exst before 975 and do not have data for the perod of 975 to 004, the estmaton method ntroduced n ths study cannot generate hgh correlaton coeffcents between some of these statons and ther surroundng statons. Thus, the fnal SCD result ncludes 8536 TMAX, 8548 TMI, and 377 PRCP statons n the contnental U.S. Fgure. All statons n the U.S... The Self-Calbratng Data QC Lbrary The QC lbrary contans several tests: threshold test, step change test, persstence test, and spatal regresson test. The frst three tests are sngle staton methods. They are tuned to the prevalng clmate at a staton and are used as QC procedures. The thresholds and lmts for these three tests are dentfed by staton clmatology at the monthly level. Compared to prevous efforts, whch manly used one set of lmts for a varable (e.g. TMAX), regardless of the tme of year, the methods presented n ths study are more accurate (Shafer et al., 000; Hubbard, 00). The spatal regresson test (SRT) s both desgned as a QC procedure and an estmaton method. All the tests are based on a QC parameter database. The QC parameter database s bult usng a 30-year hstory of data from all statons to be processed. Self-calbraton means that the QC parameters are calculated wth the hstorcal data from the statons and those parameters are appled n the data qualty control procedures for those statons. Please note, n ths study, the unt for temperature s Fahrenhet ( F) and the unt for precptaton s nch (n.). Mssng 87

3 Z. Chen et al. / Journal of Envronmental Informatcs 8() (006) data s marked wth Outlers are defned as mssng data values or the values that fal a QC test and need to be checked manually... Threshold Test The threshold test checks whether a gven varable (e.g. TMI) falls n a specfc range for the tme perod n queston (e.g. a month n the desgn). The thresholds for a varable x are: x f σ x x + f σ () x x where x s the mean daly value (e.g. mean of TMI) and σ x s the standard devaton of the daly values (e.g. the daly mnmum values) for the month n queston. Both σ x and x are calculated from a 30-year hstory of data for the gven staton and stored n the QC parameter database. The varable x may represent mnmum temperature, maxmum temperature, or precptaton. f s an optonal parameter to control dfferent levels of accuracy when applyng the QC tests. Users can dynamcally choose dfferent values of f accordng to the requrements of any specfc applcaton. That dynamc procedure allows an nformed choce regardng how many data ponts wll be flagged n the natural data stream. For example, σ x for the COOP staton of TMI n January s 3.4, and x s 7.9. After choosng f as 3.0 (a confdence level of 99.73%) and applyng Equaton (), any TMI n January for the staton that s lower than -3.3 ( x f σ x ) or hgher than 48. ( x + f σ x ) wll be flagged as an outler.... Step Change (SC) Test The step change test checks whether the change n conescutve values of the varable falls wthn the clmatologcally expected range for the month n queston. Here the step (also called rate-of-change) s defned as the dfferentce between values on day and, e.g. x = y y -. The step change test checks the step as follows: x f σ x x + f σ () s s where x has the same meanng as x defned above; x s the mean daly value and σ s s the standard devaton of rate-ofchange. Both σ s and x are calculated from a 30-year hstory of data for the gven staton and stored n the QC parameter database...3. Persstence Test The persstence test checks the varablty of the measurements. When a sensor fals t may report a constant value, thus the standard devaton σ wll become smaller. If the sensor s out of order for an entre reportng perod, σ wll be zero. On the other hand, the nstrument may work ntermttently and produce reasonable values nterspersed wth zero values, thereby greatly ncreasng the varablty for the perod. Hence, when the varablty s too hgh or too low the data should be flagged for further checkng. The test frst calculates 360 (30 ) monthly standard devaton values σ jk for each month j and year k of the 30-year record, and then calculates the monthly mean standard devaton values σ j by averagng σ jk over the 30 years. It then calculates the σ σ values, defned as the standard devaton of σ jk over the 30 years, usng the monthly mean standard devaton σ j. All of these results are stored n the QC parameter database. The persstence test compares the standard devaton for the tme perod beng tested to the lmts expected as follows: σ f σ σ σ + f σ (3) j σ j σ The data of the perod under consderaton passes the persstence test f the above relaton holds for the specfed value of f. A prevous analyss was performed on the data (97 to 000) to determne the relatonshp between the percentage of data passng those sngle staton tests (threshold test, step change test and persstence test) and varous values of f. It was found that n practce for statons n all condtons, 3.0 and 6.0 are acceptable values for f for temperature and precptaton, respectvely (Hubbard et al., 005)...4. Spatal Regresson Test (SRT) The spatal regresson test (Hubbard et al., 005) checks whether the value of a varable (e.g. TMI) falls wthn the confdence nterval formed from estmates based on best ft surroundng statons durng a tme perod of length T. (T = 365 adopted for ths study.) The surroundng statons are selected by specfyng a radus around the staton and fndng those statons wth the closest statstcal agreement to the target staton. Prevous research has shown that 80 klometers for a radus s acceptable for most statons n practce (Hubbard and You, 005). Therefore, n ths SCD study, 80 klometers was taken for all statons. Addtonal requrements for staton selecton are that the varable to be tested s one of the varables measured at the canddate staton and the data for that varable spans the tme perod to be tested. A staton that otherwse qualfes could be elmnated from consderaton f more than half of the data s mssng for the tme perod x. Some defntons for the SRT method are lsted below. x : the t y : the t th t day s value of the target staton. th th t day s value of the surroundng staton. x : the mean daly value of the target staton for the tme perod. th y : the mean daly value of the surroundng statons for the tme perod. T S = ( x x) ( y y ) xy t t t= T S = ( x x) xx t= T S = ( y y ) yy t t= t 88

4 Z. Chen et al. / Journal of Envronmental Informatcs 8() (006) For a gven staton x, the frst step of the SRT method s to generate estmates from each surroundng staton. For the th surroundng statons y,, let a be the ntercept and b be the slope of the lnear regresson lne. An estmate s formed by Equaton (4): ext = a + b y (4) t where a = y b x and b = S xy / S xx. th For the surroundng staton, the test calculates T estmates for the tme perod of length T. The standard error of estmate s (also known as root mean square error) of the T estmates s defned as: T [ ( xt ext) ] t= s = T / It also calculates r to determne f the regresson mo- del fts the data, r = ( Sxy Sxy) /( Sxx Syy). Another mportant ssue s how to account for possble systematc tme shftng of observatons. Ths problem occurs when an observer consstently wrtes the observaton down on the day before or after the actual date of observaton. In ths study, t shfts the smultaneous data of a surroundng staton by -, 0, and day and calculates all the ntermedate parameters. The shftng that results n the lowest standard error of estmate s s recorded. All of these ntermedate parameters (a, b, s and r ) are stored n the QC parameter database. Once all the ntermedate parameters are calculated, the SRT method obtans a weghted estmate x by utlzng the standard error of estmate s for all the lnear regressons n the weghtng process, as descrbed by Equaton (5). The surroundng statons are ranked accordng to the magntude of s and the statons wth the lowest s beng used n the weghtng process. e x =± [ ] ( ) s xt ( sgn ) = s / = where sgn s defned as ext/ ext, the sgn of e. Care must xt be taken to preserve the correct sgn on the sum of the top part of Equaton (5) and x. The SRT method assgns more weght to the statons that have a lower s relaton to the target staton. The weghted standard error of estmate (s ) s calculated as follows: = s = ( ) s (5) (6) Confdence ntervals can be calculated on the bass of s and f. The value x of the staton can be tested to determne whether or not t falls wthn the confdence ntervals. x f s x x + f s (7) If the relatonshp n Equaton (7) holds, then the data passes the spatal regresson test. Unlke dstance weghtng technques, ths method does not assume that the best staton to compare aganst s the closest staton; nstead t looks to the relatonshps among the actual data of statons to determne whch statons should be used to make the estmates and what weghts those statons should receve. It was found that the spatal regresson method can dentfy and correct most of the systematc errors, snce the regresson functon can mplctly adjust for measurements between the dfferences caused by topographcal effect such as the temperature falls n relaton to the elevaton. Tests have shown that the ncluson of more than fve surroundng statons does not sgnfcantly mprove the estmates (You et al., 005), and the more surroundng statons, the more computaton tme. Hence, equal to fve was chosen...5. QC Parameter Database The QC parameter database s an essental part of the self-calbratng data QC lbrary. The database provdes the standard QC statstcal parameters for the statons n queston. Those parameters are the bass on whch QC tests are run and estmats are computed. The parameters defne the operatonal procedures for the qualty control of clmate varables snce t s unlkely to have a general rule for all statons. Storng the parameters n a database allows modfcatons and adjustments to the operatonal QC process through those parameters wthout changng the basc QC routnes. In the current QC parameter database, there are seven tables: threshold, step, persstence, spatal_reg, dst_weght, nearby, and reg_stats tables. For three of the seven tables, threshold, step, and persstence table, ther parameters are at the monthly level and are the same n dfferent years. For example, there are twelve monthly σ x (the standard devaton of the daly values for the threshold test) per staton per varable for all years. The other four tables are desgned for spatal tests and estmatons. The spatal_reg and dst_weght table store constant parameters n terms of tme and can be calculated once for all the years. The reg_stats and the nearby table store regresson parameters and ther contents can be generated n dfferent tme unts. The result wll vary over tme. In ths study, a year was chosen as the tme unt for the two tables. There are several reasons why the calculaton of the regresson parameters s performed year by year. Frst, some statons may be closed and some new statons may be added, therefore the surroundng statons relatve to the target staton may be dfferent from year to year. More mportantly, the 89

5 Z. Chen et al. / Journal of Envronmental Informatcs 8() (006) Orgnal data Hstory data Step QC tests Flagged? o Step QC parameter database Yes Step 3 QC estmaton SRT Step 4 Data of surroundng statons SCD output Fgure. The buldng process for the SCD. correlaton coeffcent may be dfferent between two statons n dfferent years, dfferent seasons. It has been shown that the qualty of the estmates s strongly affected by seasonalty (Esched et al., 000). However, t s very costly to calculate all the correlaton coeffcents seasonally or monthly between a target staton and each of ts surroundng statons. In ths study, a Sun server (Sun-Fre-880) was used, and the average tme to retreve data from the ACIS system and perform the calculatons to generate the yearly regresson parameters s about 5 mnutes per staton. Even calculated yearly, t took 0 days on the Sun server to generate the parameter database for the whole country and another 5 days to buld the SCD. It wll take several tmes more to do that seasonally and ten tmes more to do that monthly. Snce the research objectve s to buld the SCD for the whole country wth more than 0,000 statons, a trade-off was made between accuracy and computaton tme by generatng the nearby and reg_stats tables wth an entry for each varable per staton per year. For applcatons wth only a small number of statons or a short tme perod nvolved, t mght be feasble to compute the regresson parameters monthly..3. Methodology.3.. Buldng a Serally Complete Dataset The buldng of the SCD dataset s a mult-step process as depcted n Fgure. Step, the QC parameter database for all the statons processed was bult. Step, once the QC para meter database s avalable, the QC tests are appled on the orgnal data usng the database. Any outler wll be flagged, ncludng mssng data or data dentfed by the QC tests that need to be checked manually. Step 3, the QC estmaton me- thod SRT was chosen to generate estmates based on the QC parameter database. Step 4, the orgnal values that are not flagged as outlers or the estmates wll be selected and ntegrated nto the fnal SCD output dependng on the result from Step. () Buldng the QC Parameter Database. The QC parameter database s the essental part of the SCD buldng process, as shown n Fgure. The QC parameters are stored n a relatonal database wth an entry for each varable (e.g. TM- AX) per staton. For example, one entry n the threshold table wll gve all parameters necessary to run the threshold test on a staton for one varable. A lack of entres n any QC parameter table ndcates that no parameters have been calculated. In that case, a decson was made to ether adopt a default parameter or use certan methods to nterpolate a replacement from the nformaton n the database. The reg_stats table s at the core of the estmaton method; hence t s explaned n detal. The content of the reg_stats table s shown n Table. The column target_staton s for the staton n queston. For example, s a staton n the COOP network; KAIA s a staton n the ICAO network and a54669 s a staton n AWD network. Column sur_staton stores the nformaton to dentfy the surroundng statons. var encodes the varable processed. In the ACIS system, means TMAX, means TMI, and 4 means PRCP. dstance stores the physcal dstance n klometers between two statons. The correlaton coeffcents are represented by a, b, s and r. a and b are the parameters n Equaton (4). The s s the standard error of estmate between two statons. (Although these are determned on an annual bass n ths study, they can be calculated and appled n other tme perods dependng on the 90

6 Z. Chen et al. / Journal of Envronmental Informatcs 8() (006) Table. The Content of Reg_stats Table target_staton sur_staton var dstance a b r s lag year a KAIA a KAIA a applcaton.) The smaller s, the hgher the correlaton coeffcent s. The r s a standard metrc for nterpretng model ft. The r s always between 0 and. The 0 means the regresson model does not ft the data at all; whle means the regresson model fts the data perfectly. To account for possble systematc tme shftng of observatons, lag s used to record the shftng that results n the lowest s. Fnally, year dentfes the year of the entry. A typcal staton has approxmately 8 surroundng statons for temperature and more for precptaton. Hence the reg_stats table has approxmately 600 ( varables) entres per staton for 30 years for TMAX, TMI and PRCP. Each entry needs to be calculated wth the data of the target staton and that of ts surroundng statons for the same tme perod. Ths s partly why the SCD process s so computatonally ntensve. Another computatonally ntensve part s dong the estmaton. () Runnng QC Tests to Identfy Outlers. Once the QC parameter database s ready, the next step s to apply QC tests on observed data to dentfy outlers. Three sngle staton based QC tests were chosen: threshold test, step change test, and persstence test. If any test dentfes a daly value as an outler, t needs to be replaced wth an estmate generated wth the method descrbed below. The SRT test can be used to dentfy more outlers. However, the SRT estmaton method wll be appled n the next step to provde the estmated values. Hence t would be duplcated n ths step. There are two types of dynamc mechansms here. Frst, users can choose what knd of tests and how many tests to apply to the data. Second, for each test, users can choose dfferent values of the optonal parameter f. Both of these choces are solely dependent on the level of accuracy requred by the applcaton. In the SCD applcaton, for f, 3.0 and 6.0 for temperature and precptaton are chosen, respectvely. (3) Generatng Daly Estmates Usng SRT Method. As llustrated n Fgure, the creaton of a serally complete dataset ncludes the replacement of daly outlers. To fnd a replacement for the daly value, the SRT method s used to calculate an estmate based on the QC parameter database by usng the smultaneous daly values at surroundng statons. Snce the correlaton coeffcents between statons n the database are calculated and stored yearly, the estmaton for daly values s also done year by year. For a gven staton n any year, the surroundng statons are frst sorted by the yearly standard error of estmate s (defned n Secton.3.) n ascendng order and the frst fve surroundng statons are chosen that have the lowest s. That step turns out to be crtcal and has sgnfcantly mproved the accuracy over sortng statons by dstance. Ths pre-selecton of surroundng statons, based on the correlaton coeffcents, s a necessary and mportant step. Once the surroundng statons are chosen, The SRT method s appled to do the estmaton usng the parameters n the database. If some of the frst fve statons do not qualfy, the other surroundng statons that follow wll be chosen as a backup. There are several reasons why a staton may not qualfy. For example, the correlaton coeffcent may not be calculated n a partcular year because of mssng data. (4) Generatng Serally Complete Daly Values. Once the estmaton s done, the serally complete estmated daly values for the target statons from 975 to 004 are generated. The next step s to replace the outler daly values wth the estmates. A sample of the SCD output for TMAX at the staton s depcted n Table. In Table, the column Date records the date of the daly value. Orgnal stores the orgnal observed value and Estmated s for the estmated daly value. Fnal stores the fnal daly SCD output. Dff keeps the dfference between the orgnal daly value and the estmated; t wll be empty f ether the orgnal or the estmated value s mssng. The T_Flag, S_Flag, and P_Flag are the flags of the three QC tests (threshold test, step change test, and persstence test, respectvely). means the daly value does not pass the test whle 0 means pass. - means mssng daly value (marked -99 n the orgnal value). If any of the three flags s not 0, the column Flag wll be set and the estmated daly value wll replace the orgnal observed value n the fnal SCD output. Because of the systematc tme shftng of observatons 9

7 Z. Chen et al. / Journal of Envronmental Informatcs 8() (006) (- and day), the result does not nclude the estmates for the frst day (975--) and the last day (004--3)..3.. Evaluaton Measures Several measures are sutable for expermentally comparng the accuracy of estmaton methods. Mean-absoluteerror (MAE) and root-mean-square-error (RMSE) are used n ths research to evaluate the errors between the observed and estmated data. The lower MAE and RMSE are, the more accurate the method s MAE = RMSE = = F A = ( F A ) Equatons (8) and (9) compute MAE and RMSE, where F s the estmated value, as shown n the Estmated column n Table ; A s the observed value, as shown n the Orgnal column n Table ; s number of data. In the calculaton of MAE and RMSE for a staton, only those orgnal observed daly values that pass all three QC tests, that s to say, the Dff n Table s not empty, are consdered. To evaluate the result for statons, the yearly MAE and yearly RMSE (975 to 004) for all the statons processed are frst calculated. Hence for any staton, there wll be 30 yearly MAE/RMSE. The yearly MAE and yearly RMSE are averaged over 30 years to calculate the average_mae and average_rmse of a staton. A sample evaluaton result for the staton of TMAX s shown n Table 3. (8) (9) 3. Results and Dscusson The evaluaton of the overall accuracy n the US s conducted at several levels for each varable. At the staton level, the average_mae and average_rmse of a staton are calculated as depcted n Table 3. The results of all the statons processed over the whole country are then analyzed. To gan dfferent levels of vew of the accuracy of the SRT estmaton method, the county layer, the clmate dvson layer, and the state layer are added to the evaluaton based on the results at the staton level. At the county level, the average_mae and average_rmse for all the statons are summarzed to calculate the county-wde average MAE and RMSE. At the clmate dvson level, the average MAE and RMSE for all the statons are summarzed to calculate the clmate-dvson-wde average MAE and RMSE. At the state level, the average MAE and RMSE for all the statons are summarzed to calculate the statewde average MAE and RMSE. 3.. TMAX As noted below, the result shows that the best accuracy s n the southeastern plans regons, followed by the coastal areas (the eastern coast s better than the western coast). The poorest accuracy areas are the western mountanous regons. There are several possble reasons for the relatvely poor estmates n the western mountanous regons. The topographcal dversty of the surroundng statons leads to a degradaton of spatal coherence among statons, whch results n hgher MAE and RMSE. Another possble reason s the staton densty. Recall from Fgure that the staton densty n the East s much hgher than that n the West. The areas wth the most sparsely dstrbuted statons are the western mountanous regons. Analyss ndcates that, the hgher the densty of the statons s, the better temperature estmates can be acheved usng the SRT method. Ths result s consstent wth re- Table. A Sample SCD Output for Staton of TMAX Date Orgnal Estmated Fnal Flag Dff T_Flag S_Flag P_Flag

8 Z. Chen et al. / Journal of Envronmental Informatcs 8() (006) search reported n (You et al., 005). Table 3. A Sample Evaluaton Output for Staton of TMAX Year MAE RMSE Average Hghest Lowest TMAX at County Level The dstrbuton of accuracy at the county level s llustrated n Fgures 3a and 3b. The dfference between the West and the East s very sgnfcant. In Fgure 3a, for most countes n the East, the average MAE s between 0.9 and.38, hghlghted wth dstrbuted whte blocks, where the average MAE s less than.6. For most countes n the West, the average MAE s between.99 and 4.8, hghlghted wth some dstrbuted dark-black blocks n the mountanous regons, where the average MAE s above.98. The dstrbuton of the average RMSE n Fgure 3b s almost the same as the average MAE n Fgure 3a TMAX at Clmate Dvson Level The accuracy at the clmate dvson level s llustrated n Fgures 3c and 3d. The result s smlar to that at the county level. In Fgure 3c, for most clmate dvsons n the East, the average MAE s between.36 and.44, hghlghted wth dstrbuted whte blocks, where the average MAE s less than.74. For most clmate dvsons n the West, the average MAE s between.07 and 4.90, hghlghted wth some dstrbuted dark-black blocks n the mountanous regons, where the average MAE s above.98. The dstrbuton of the average RMSE n Fgure 3d s almost the same as the average MAE n Fgure 3c TMAX at State Level The result s smlar to that of other levels. It can be seen from Fgure 3e that for most states, the statewde average MAE s very good, between.33 and.5. The states wth the best estmates are n the Southeast. The states wth the poorest estmates are Colorado, Wyomng, Montana, and evada, where the MAE s between.53 and 3.5. Fgure 3f depcts the accuracy dstrbuton of RMSE at the state level. It s smlar to the MAE n Fgure 3e. For most states, the statewde average RMSE s between.7 and The states wth the lowest RMSE are n the Southeast and the states wth the hghest RMSE are also n the mountanous regons. The statewde average RMSE over the 48 states are also averaged, the resultng RMSE for the whole country s.74. In comparson to the prevous effort by Esched et al. (000), the RMSE of that study s between. and 3.96 for the twelve months and 034 statons. The medan RMSE of that study s between.44 and 3.3. For most states, the RMSE of ths study ranges from.7 to 3.58, wth the natonwde average of.74. However, a drect comparson s dffcult for several reasons. Frst, the calculaton method of RMSE s not the same. Actually, t s unclear how the RMSE was calculated n that study. Second, the results of that study only cover the Western US. Thrd, and more mportantly, most of the statons selected n that study are COOP statons. Many of the COOP statons have a long hstory and have more than 50 years of data (some COOP statons have even 00 years of data), as documented n the metadata for each staton. As analyzed n Subsecton 3.4, the more data a staton has, the more accurate the estmaton method wll be. If appled only to COOP statons n ths study, the estmaton accuracy usng the SRT method can be mproved. An experment for seven states shows that the accuracy can be mproved by % to 4%. Generally, we beleve the approach of ths study yelds more accurate results. The average RMSE of ths study seems a lttle bt hgher than that calculated wth the SRT method from a prevous study (You et al., 005). There are three reasons for t. Frst, the RMSE of the prevous study s for the dataset of 00, but the RMSE reported here n ths study s the average of 30 years, from 975 to 004. The RMSE of ths study for year 00 only s about 0% lower than the 30-year average. Second, the prevous study only appled to COOP statons. Thrd, to make a trade-off between computaton tme and accuracy as explaned n Secton..5, T s 365 n ths study, but the prevous study used T = 60. ot wthstandng these factors, the results of these two studes are smlar. 3.. TMI As dscussed below, the result s smlar to that of TMAX. The best accuracy s n the southeastern plans regons, followed by the coastal areas (the eastern coast s better than the western coast). The poorest accuracy areas are the western mountanous regons. otce that the accuracy of TMAX s sgnfcantly better than that of TMI over the whole country TMI at County Level The dstrbuton of accuracy at the county level s llustrated n Fgures 4a and 4b. The result s smlar to that of TMAX. The dfference between the West and the East s very sgnfcant. In Fgure 4a, for most countes n the East, the average MAE s between 0.95 and.75, hghlghted wth dstrbuted whte blocks, where the average MAE s less than.9. For most countes n the West, the average MAE s between.3 and 5.3, hghlghted wth some dstrbuted 93

9 Z. Chen et al. / Journal of Envronmental Informatcs 8() (006) Fgure 3. (a) average MAE of TMAX for countes; (b) average RMSE of TMAX for countes; (c) average MAE of TMAX for clmate dvsons; (d) average RMSE of TMAX for clmate dvsons; (e) average MAE of TMAX for states; (f) average RMSE of TMAX for states. dark-black blocks n the mountanous regons, where the average MAE s above The dstrbuton of the average RMSE n Fgure 4b s almost the same as the average MAE n Fgure 4a TMI at Clmate Dvson Level s less than.5. For most clmate dvsons n the West, the average MAE s between.87 and 4.56, hghlghted wth some dstrbuted dark-black blocks n the mountanous regons, where the average MAE s above The dstrbuton of the average RMSE n Fgure 4d s almost the same as the average MAE n Fgure 4c. The dstrbuton of accuracy at the clmate dvson level s llustrated n Fgures 4c and 4d. The result s smlar to that at the county level. In Fgure 4c, for most clmate dvsons n the East, the average MAE s between.46 and.48, hghlghted wth dstrbuted whte blocks, where the average MAE TMI at State Level The result s smlar to that of TMAX at the state level. It can be seen from Fgure 4e that for most states the statewde average MAE s between.80 and 3.. The states wth the 94

10 Z. Chen et al. / Journal of Envronmental Informatcs 8() (006) Fgure 4. (a) average MAE of TMI for countes; (b) average RMSE of TMI for countes; (c) average MAE of TMI for clmate dvsons; (d) average RMSE of TMI for clmate dvsons; (e) average MAE of TMI for states; (f) average RMSE of TMI for states. best estmates are n the Southeast. The states wth the poorest estmates are n the West. Fgure 4f depcts the accuracy dstrbuton of RMSE at the state level. It s smlar to the MAE n Fgure 4e. For most states, the statewde average RMSE s between.43 and The states wth the lowest RMSE are n the Southeast. The states wth the hghest RMSE are also n the western mountanous regons. The statewde average RMSE over the 48 states are also averaged, the resultng RMSE for the whole country s 3.7. In comparson to the prevous effort by Esched et al. (000), the RMSE of that study s between. and 4.58 for the twelve months and 035 statons. The medan RMSE of 95 that study s between.68 and 3.6. For most states, the RMSE of ths study ranges from.43 to 4.09, wth the natonwde average of 3.7. However, lke TMAX, A drect comparson between the results of ths study wth that one s not meanngful PRCP How the result for precptaton dffers from the result for TMI or TMAX are specfed below. In most areas ncludng the mountanous regons, the accuracy s good but the poorest estmates are found n the southeastern coastal areas. There are several possble reasons for the poorest estmates of precptaton n the southeastern coastal areas. Those

11 Z. Chen et al. / Journal of Envronmental Informatcs 8() (006) Fgure 5. (a) average MAE of PRCP for countes; (b) average RMSE of PRCP for countes; (c) average MAE of PRCP for clmate dvsons; (d) average RMSE of PRCP for clmate dvsons; (e) average MAE of PRCP for states; (f) average RMSE of PRCP for states. areas are n tropc or near tropc clmate and are strongly affected by the Gulf of Mexco, the Atlantc Ocean and the Carbbean Sea. The clmates n those areas are typcal tropcal oceanc clmate. Hurrcanes and other small types of storms usually produce sgnfcant ranfall n some partcular areas seasonally and may not have smlar effects n surroundng areas. Furthermore, snce the approach calculates the correlaton coeffcents among statons yearly, t may not work very well n areas lke those havng strongly seasonal precptaton. Recall from Fgure that the staton densty n the East s much hgher than that n the West. The areas wth the most sparsely dstrbuted statons are the western mountanous regons. However, unlke the results of temperature, the hgher the densty of the statons does not lead to the better accu- racy PRCP at County Level The dstrbuton of accuracy at the county level s llustrated n Fgures 5a and 5b. The dfference between the West and the East s very sgnfcant, but unlke the results of TMAX or TMI, the accuracy n the West s much better than that of the East. In Fgure 5a, for most countes n the East, the average MAE s between 0.08 and 0.9, hghlghted wth some dark-black blocks n the southeastern coastal areas, where the average MAE s above 0.3. For most countes n the West, the average MAE s between 0.0 and 0.07, hghlghted wth several contnued whte areas, where the average MAE s less than The dstrbuton of the average RMSE 96

12 Z. Chen et al. / Journal of Envronmental Informatcs 8() (006) n Fgure 5b s almost the same as the average MAE n Fgure 5a PRCP at Clmate Dvson Level The dstrbuton of accuracy at the clmate dvson level s llustrated n Fgures 5c and 5d. The result s smlar to that at the county level. In Fgure 5c, for most clmate dvsons n the East, the average MAE s between 0.08 and 0.7, hghlghted wth some dark-black blocks n the southeastern coastal areas, where the average MAE s above 0.3. For most clmate dvsons n the West, the average MAE s between 0.0 and 0.07, hghlghted wth several contnued whte areas, where the average MAE s less than The dstrbuton of the average RMSE n Fgure 5d s almost the same as the average MAE n Fgure 5c PRCP at State Level The result s dfferent from TMI or TMAX. It can be seen from Fgure 5e that for most states, the statewde average MAE s between 0.03 and 0.. In contrast wth temperatures, the states wth the best estmates are n the West and Mdwest. The states wth the poorest estmates are n the Southeast, especally the southeastern coastal areas lke Florda, Alabama and Lousana. The average MAE of those states s between 0. and 0.4, about twce hgher than the average values n other states. Areas n the ortheast have the average accuracy wth the MAE between 0.06 and Fgure 5f depcts accuracy dstrbuton of RMSE at the state level. It s almost the same as the MAE n Fgure 5e. For most states, the statewde average RMSE s between 0.07 and 0.3. The states wth the lowest RMSE are n the West and Mdwest. The states wth the hghest RMSE are n the southeastern coastal areas. In comparson to the prevous effort by Esched et al. (000), the RMSE of that study s between 0.6 and 0.9 for the twelve months and 69 statons n the Western US. The medan RMSE of that study s between 0.7 and For most states, the RMSE of ths study ranges from 0.07 to 0.3. However, t s dffcult to do a drect comparson for reasons smlar to TMAX. Moreover, the results of that study do not nclude the southeastern coastal areas where t s relatvely dffcult to do accurate estmatons. Generally, we beleve the approach of ths study yelds more accurate results Statons Wth and Wthout 30 Years of Observed Data Approxmately 40% of the statons have orgnal observed data from 975 to 004. The remanng 60% of the statons, especally those of the AWD network (typcally star -ted n the 980s), have less than 30 years of observed data. Even for those 40% of the statons, mssng data gaps ranged from a couple days to months, and even to years. The accuracy of the SRT method between the statons wth 30 years (975 to 004) of orgnal observed data and all the statons n ebraska are compared. Although ths evaluaton s conduc- ted n ebraska, smlar results are expected for the rest of the US. For the tables and fgures n ths subsecton, S30 represents the statons wth 30 years of orgnal observed data and Sall represents all the statons n the state. The results dscussed below show that for both temperature and precptaton, the accuracy of S30 s always sgnfcantly better than that of Sall. That s, the more data a staton has, the more accurate the estmaton method wll be. In both stuatons, snce there are more surroundng statons, the accuracy of the SRT method for temperatures s mprovng after 990. Ths confrms the concluson from prevous research (You et al., 005), that the SRT method was found to perform relatvely poor when the weather statons are sparsely dstrbuted. However, t s nterestng to note that, for precptaton, more surroundng statons do not mprove the accuracy Daly Maxmum Temperature As shown n Table 4, Fgures 6a and 6b, the accuracy n terms of MAE or RMSE of S30 s always better than those of Sall for TMAX. The average MAE and RMSE of S30 of the 30 years are both.% lower than those of Sall. Smlar relatons exst for the lowest/hghest yearly average MAE/ RMSE n the 30 years between S30 and Sall. Fgure 6a also depcts that both S30 and Sall have smlar trends from 975 to 004. Both of the two lnes start from 975 wth approxmate average values and reach the peak n 979. The accuracy s gettng better n the 980s. After 99, the accuracy s qute mpressve (MAE of S30 s around.5 F). The lnes of RMSE n Fgure 6b confrm the smlar trends n Fgure 6a. Table 4. Comparson between Statons wth and wthout Observed 30-year Data umber of Statons Ave-MAE -all Lowest Ave- MAE-year Hghest Ave- MAE-year Ave-RMSE -all Lowest Ave- RMSE-year Hghest Ave- RMSE-year TMI TMAX PRCP S30 Sall S30 Sall S30 Sall Daly Mnmum Temperature As shown n Table 4, Fgures 6c and 6d, although the dfference between S30 and Sall s more sgnfcant than that of TMAX, there are very smlar results for TMI. The two 97

13 Z. Chen et al. / Journal of Envronmental Informatcs 8() (006).4. E TMAX MAE s30 sall E TMAX RMSE s30 sall Ave-MAE ( o F).0.8 Ave-RMSE ( o F) Years a Years b.5 E TMI MAE 3.6 E TMI RMSE Ave-MAE ( o F) s30 sall Ave-RMSE ( o F) s30 sall Years Years c d E PRCP MAE 0.6 E PRCP RMSE Ave-MAE (In.) e s30 sall Years Years Fgure 6. Comparson of statons wth and wthout 30-year data: (a) MAE of TMAX; (b) RMSE of TMAX; (c) MAE of TMI; (d) RMSE of TMI; (e) MAE of PRCP; (f) RMSE of PRCP. Ave-RMSE (In.) s30 sall f lnes (MAE and RMSE) of S30 are totally under those of Sall. Thus the accuracy n terms of the MAE or RMSE of S30 s always sgnfcantly better than that of Sall. The average MAE of S30 for the 30 years s 3.4% lower than that of Sall. The same relatons exst for the lowest and hghest average MAE n the 30 years between S30 and Sall. Fgure 6c also depcts that both S30 and Sall have smlar trends from 975 to 004. The two lnes start from 975, wth a lttle bt hgher MAE n the 970s, become better but fluctuate n the 980s. In the 990s, they provde the best accuracy and have approxmately average accuracy after 000. The average RMSE of S30 of the 30 years s 3.0% lower than that of Sall. Lke MAE, the lowest and hghest average RMSE of S30 are about 0% lower than those of Sall. The trends for RMSE n Fgure 6d are smlar to that of MAE Daly Precptaton As shown n Table 4 and Fgures 6e and 6f, lke the relatons n temperature, the accuracy n terms of MAE or RMSE of S30 s always better than that of Sall for PRCP. The average MAE and RMSE of S30 of the 30 years are 4.6% and 5.8% lower than those of Sall, respectvely. The same relatons exst for the lowest/hghest average MAE/RMSE n the 30 years between S30 and Sall. Fgure 6e depcts that both S30 and Sall have smlar trends from 975 to 004. However, 98

14 Z. Chen et al. / Journal of Envronmental Informatcs 8() (006) unlke TMI or TMAX, the lnes fluctuate. There s no best accuracy tme perod as there was for the temperatures. The trends for RMSE n Fgure 6f are lke MAE of Fgure 6e, but the dfference between S30 and Sall s more sgnfcant. 4. Concluson Ths study developed a serally complete daly temperature and precptaton dataset for the Unted States usng the self-calbratng data qualty control lbrary. Wth the SCD, many clmate related tools (e.g. SPI, SC-PDSI) are enabled and the ADSS can provde more accurate results, whch wll lead to the mprovement of drought rsk assessment and envronmental rsk analyss. The SCD estmaton result s accurate. Frst, the preselecton of surroundng statons and the calculaton of the estmates are based on the correlaton coeffcents among statons, whch mproved the accuracy over the selecton and calculaton based on dstance. Second, the approach can account for fallng temperature n relaton to elevaton. Thrd, the choce of yearly correlaton coeffcents among statons s a tradeoff between computaton tme and accuracy. The results show that the choce s reasonable and t mproves the qualty of the estmaton that s strongly affected by seasonalty. Fourth, the tme shftng feature of the SRT estmaton method reduces the affect of statons wth dfferent tmes of observaton. All of these features allow the estmaton to have mpressvely low systematc errors. Because the topographcal dversty of the surroundng statons n the mountanous regons leads to a degradaton of spatal coherence among statons, the estmates for statons n the plans regons are relatvely better than statons n the mountanous regons. Besdes that, the accuracy of the estmaton s affected by several other factors. Estmaton s affected by the densty of statons. Estmaton errors for temperature ncrease as the statons become sparser. Estmaton s also affected by the data completeness. The more data a staton has, the more accurate the estmaton method wll be. In areas where the complexty of terran domnates, such as the coastal areas and the mountanous regons, further nvestgaton of the new estmaton technques s needed. The current estmaton method may be mproved by combnng t wth temporal estmaton technques (wthn the hstorcal record for a staton) and a terran regresson. The approach of the self-calbratng data QC lbrary s flexble. The QC parameter database and the dynamc procedures of usng varous values of the optonal parameter f allow an nformed choce regardng how many data ponts wll be flagged n the natural data stream. Users can make choces dynamcally, dependng solely on the requrements of any partcular applcaton. The modfcatons and adjustments to the operatonal QC process can be acheved through those parameters n the database or the optonal parameter values (f) wthout changng the basc QC routnes. References Eaton, C., Plasant, C. and Drzd, T. (003). The challenge of mssng and uncertan data, n Proc. IEEE InfoVs Poster Compendum 003, IEEE Computer Socety Press, pp Esched, J.K., Baker, B.C., Karl, T.R. and Daz, H.F. (995). The qualty control of long-term clmatologcal data usng objectve data analyss. J. Appl. Meteorol., 34(), Esched, J. K., Pasters, P.A., Daz, H.F., Plantco, M.S. and Lott,.J. (000). Creatng a serally complete, natonal daly tme seres of temperature and precptaton for the western Unted States. J. Appl. Meteorol., 39(9), Goddard, S., Harms, S.K., Rechenbach, S.E., Tadesse, T. and Waltman, W.J. (003). Geospatal decson support for drought rsk management. Commun. ACM, 46(), Guttman,.B. and Quayle, R.G. (990). A revew of cooperatve temperature data valdaton. J. Atmos. Ocean. Technol., 7, Hubbard, K.G. (00). Multple staton qualty control procedures, n Automated Weather Statons for Applcatons n Agrculture and Water Resources Management, World Meteorologcal Organzaton, AGM-3 WMO/TD, Hubbard, K.G., Goddard, S., Sorensen, W.D., Wells,. and Osug, T.T. (005). Performance of qualty assurance procedures for an appled clmate nformaton system. J. Atmos. Ocean. Technol., (), 05-. Hubbard, K.G. and You, J. (005). Senstvty analyss of qualty assurance usng spatal regresson approach-a case study of the maxmum mnmum ar temperature. J. Atmos. Ocean. Technol., (0), Legates, D.R. and Wllmott, C.J. (990). Mean seasonal and spatal varablty n global surface ar temperature. Theor. Appl. Clmatol., 4, -. McKee, T.B., Doesken,.J. and Klest, J. (993). The relatonshp of drought frequency and duraton to tme scales, n Proc. of 8th Conference on Appled Clmatology, Amercan Meteorologcal Socety, Boston, Massachusetts, pp Palmer, W.C. (965). Meteorologcal Drought, Research Paper o.45, US Department of Commerce Weather Bureau, Washngton, DC, pp. 58. Peterson, T.C., Vose, R.S., Schmoyer, R. and Razuvaev, V. (997). Qualty control of monthly clmate data: The GHC experence. Int. J. Clmatol.. Shafer, M.A., Febrch, C.A., Arndt, D.S., Fredrckson, S.E. and Hughes, T.W. (000). Qualty assurance procedures n the Oklahoma Mesonet. J. Atmos. Ocean. Technol., 7, Stallngs, C., Huffman, R.L., Khorram, S. and Guo, Z. (99). Lnkng gleams and GIS, n Proc. Amercan Socety of Agrcultural Engneers. Stooksbury, D.E., Idso, C.D. and Hubbard, K.G. (999). The effects of data gaps on the calculated monthly mean maxmum and mnmum temperatures n the contnental Unted States, A spatal and temporal study. J. Clmatol.,, The Appled Clmate Informaton System. Wade, C.G. (987). A qualty control program for surface mesometeorologcal data. J. Atmos. Ocean. Technol., 4, Wells,., Goddard, S. and Hayes, M.J. (004). A self-calbratng palmer drought severty ndex. J. Clmate, 7(), You, J., Hubbard, K.G. and Goddard, S. (006). Comparson of spatal estmators-a case study of spatal regresson and nverse dstance weghtng. Int. J. Clm. (submtted). 99