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# Advanced Functions of Temporal GIS ENVR 468

UNC

GPA 3.75

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This 18 page Class Notes was uploaded by Itzel Hilll on Sunday October 25, 2015. The Class Notes belongs to ENVR 468 at University of North Carolina - Chapel Hill taught by Marc Serre in Fall. Since its upload, it has received 41 views. For similar materials see /class/228866/envr-468-university-of-north-carolina-chapel-hill in Environment at University of North Carolina - Chapel Hill.

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Date Created: 10/25/15

SpaceTime mapping with Soft data Soft Data Xp Xs z is a STRF Soft data forXav is available at the soft data points psoft p1 pm The vector of random variables xso x1xns represents the 81quot RF at the soft data point ie xsoftXpla 3 Soft data of probabilistic type are eXpressed using the pdffSQgso as follow S 39 Zsoft 1 Pxso ltZsoft IZZO du f3 1quot FSWso Usually the pdf of soft data points are independent of one another so that f 5055019 f51 f5ns In general the pdf each individual soft datum fsoa fsogns can have various shapes f l istta LfsUM EXAMPLE At point p1 the soft pdf is Gaussian with mean m12 and valiance 0123 and at point p2 the soft pdf is uniform from a24 to 326 What is the soft pdf for SO 11 92 The answer is as follow 1 106 77402 1 26 1702 ex 7 7 fSZ1 T 61 P 2 all 6 exp 6 05 if 4 S g S 6 fsZ2 2 2 and 0 otherw1se fSUtso fSZ1fSZz Coding soft data in BMEGUI BlVTEGUl supports the following three data types 39339 Hard data 39339 Soft data with uniform distribution 39339 Soft data with Gaussian distribution When using the default settings BMEGUI assumes that the data file only contains hard data and in that case it uses only the fields described so far ie the X field the Y field the T field the optional ID field and the Data field containing the hard data values However when using a combination of hard and soft data then BMEGUI requires that the Data field be replaced by the following three fields The Data type field the Valuel field and the Value2 field The Data type field is used to specify the type of data The Valuel and Value2 fields are used to describe the data as follow 39339 Hard data 0 Data Type 0 o Valuel Field The true value e g a measurement without error 0 Value2 Field Same as Value 1 39339 Soft uniform data 0 Data Type 1 o Valuel Field Lower bound of the interval for the true value 0 Value2 Field Upper bound of the interval for the true value 39339 Soft Gaussian data 0 Data Type 2 o Valuel Field Mean also called expectation of the true value 0 Value2 Field Standard deviation of the true value around its mean Example CSV Format of hard and soft data X Y T Type Va11 Va12 74 35 40 55 0 0 0 4012 0 4012 Data type 1 Soft uniform data 74 35 4o 55 10 0 5528 a 5528 Lower Bound 10592 Upper Bound 12592 74 35 40 55 2 1 0 7637 0 9637 74 35 40 5540093440 9344 74 35 40 55 500980 98 74 35 40 5560096489096489 74 35 40 Data type 2 Soft Gaussian data 5570080230 Mean 07396 1 r Stande Deviation 01 w um H quotquot T u 74 35 40 5592065510 1 74 35 40 551000 5620 562 4 4 RWGUTHHH m 2h m M Theprocedurels 1 Check the Use Datatypequot shesk box then drop down boxes for Data Typequot Value1F1eldquotand ValueZ Data mud 16 Wamm Dwectam D UsevSWasuDeveDDmenlka Data F e D U5215Va5UDeveDDmenlDataF etetaH M Date Type Va ue He d Va uez He d mmwz Svace um me um Data um Egg use 2 Selectthe appropriate data sommns for DataTypequot Valuel erldquot and Va1ue2 eldquot 2 Chck Nextquot to move to me sesond melogbox Coding soft data in BMEIib In BMEIib the soft pdffsqso fs1 fsns is coded in a discretized form using 4 variables softpclftype n1 limi and probdens The reader can type help probasyntax for a detailed explanation of how these variables work The rst variable softpdftype is an integer taking values 1 2 3 and 4 It speci es the type of soft pdf as follows 1 for histogram 2 for linear 3 for histogram on a regular grid and 4 for linear on a regular grid Along each of the MS dimension the univariate pdffsogi is defined using intervals of values for If The interval limits are speci ed using the matrix limi and the value of fs 0 in these intervals is speci ed by the matrix probdens 0 n nle vector of the number of interval limits nlz39 is the number of interval limits used to define the soft pdffs at point Pi limi nle matrix of interval limits where l is equal to either maxnl or 3 depending on the softpclftype If softpclftype 1 or 2 then limi is a ns by maxnl matrix and limiil nlz39 are the interval limits for soft data 139 If softpdftype 3 or 4 then limi is a ns by 3 matrix The interval limits are on a regular grid and limiil3 are the lower limit increment and upper limit of the interval limits for soft data 139 probdens nsXp matrix of pdf values where p is equal to either maxnll or maxnl depending on the softpclftype If softpclftype l or 3 then probdens is a ns by maxnll matrix The pdf value is constant in each interval and probdens i nlil are the value of the pdf in each interval If softpclftype 2 or 4 then probdens is a ns by maxnl matrix The pdf value varies linearly between interval limits and probdens i nli are the value of the pdf at each interval limit EXAMPLE with softpdftype 1 soft pdf of histogram type gtgt so pd ype1 gtgt n14 gtgt limi0 2 3 4 gtgt probdens1 3 27 gtgt h xobap10ts0 pd ypenllimipr0bdens EXAMPLE with softpdftype 2 soft pdf of linear type gtgt softpdftype2 gtgt n14 gtgt limi0 2 3 4 gtgt probdens0 4 1 07 gtgt h xobap10ts0 pd ypenllimipr0bdens probdens EXAMPLE with softpdftype 3 soft pdf of histogram type on regular grid gtgt softpdftype3 gtgt n15 gtgt limi0 1 4 gtgt probdens1 2 3 28 gtgt h 3r0bap10ts0 pd ypenllimipr0bdens prubdens 2 limi EXAMPLE with softpdftype 4 soft pdf of linear type on regular grid gtgt so pd ype4 gtgt n15 gtgt limi0 1 4 gtgt probdens0 3 1 2 06 gtgt h 3r0bap10ts0 pd ypenllimipr0bdens probdens Writing and reading soft data fromto files The writeProbam and readProbam functions allow the user to read and write soft probabilistic data fromto a file Syntax gt gtwritePr obacsisSTsoftp dftyp enllirniprob densfiletitledatafile gt gt csisST softp dftypenllirnipr ob densfiletitle readPr obadatafile EXAMPLE the following file named somesoftdatatxt contains the soft data at two points BME Probabilistic data 7 s1 s2 code for the variable equal to 1 Type of soft pdf equal to 1 corresponding to histogram number of limit values nl limits of intervals nl values probability density nl 1 values 1 09 1 1 4 01 03 07 11 01 02 1 1 2 01 03 Plotting soft data U39II OO fl 0 fl The probaplotm function allowing to plot soft data has the following syntax gtgt hprobaplotsoftpdftypenllimiprobdensSidx EXAMPLE gtgt CSisSTsoftpdftypenllimiprobdensfiletitlereadProba39somesoftdatatxt gtgt subplot211 hprobaplotsoftpdftypenllimiprobdens39391 gtgt subplot212 hprobaplotsoftpdftypenllimiprobdens 3939 1 5 1 05 g t 1 2 14 4 3 2 1 01 0 15 02 025 0 3 035 Generating soft data The probaGaussianm and probaUniformm generate soft data of with Gaussian and uniform distributions respectively For example the following code generate a two soft data points the first is Gaussian with mean 2 and variance 3 the second data point is Gaussian With mean 1 and variance 4 gtgt softpdftypenllimiprobdens 3robaGaussian21034 gtgt subplot211 hprobaplotsoftpdftypenllimiprobdens39391 gtgt subplot212 hprobaplotsoftpdftypenllimiprobdens 92 The SRF Xs is a function of space only in a 2D spatial domain This SRF has a mean trend equal to zero and a covariance Crc0eXp3rar with c01 ar5 Additionally we have hard data at two hard data points At s 14 Xs1 2 and at s52 Xs17 And we have soft data 1 9 and 23 We want to estimate the posterior pdf and it s moments at 11 specify the general knowledge orderNaN39 The mean trend is equal to zero covmodel eXponentialCquot covariance is exponential Crc0eXp3rar covparam1 5 parameters for the covariance model c01 ar5 specify the specificatory knowledge ch1 45 239 Hard data has two data points at 14 and 52 zh12391739 Value ofhard data at 04 is 12 and at 52 it is 17 cs1 92 3 Soft data has two data points at 1 9 and 23 softpdftype239 Soft pdf type2 correspoinding to linear nl439339 Number of limits for each soft data points limi0 2 3 61 2 4 NaN Limits for each soft data points probdens0 2 10 023390 2 0 NaN339 soft pdf value for each limit value specify calculation parameters nhmax10 maX number of hard data in estimation neighborhood nsmax10 max number of soft data in estimation neighborhood dmax100 dmaxmaX spatial search radius for estimation neighborhood optionsBMEoptions Use default options specify the coordinate of estimation point ckl l The estimation point is 11 calculate BlVlE posterior pdf using BMEprobanf zpdfinfo BllEprobanf ckchcszhsoftpdftypenllimiprobdenscovmodelcovparamnhmaXnsmaXdmaXor deroptions calculate moments of BME posterior pdf using BNlEprobaMoments momentsinfoBMEprobaMomentsckchcszhsoftpdftypenllimiprobdenscovmodelcovparamnhmaXnsmaX dmaXorderoptions eXpecvalkmoments l varkmoments 2 analmn oflhe mapping pmms w Hard dala puiuns Son pd39a 1 9 0 Soft dale pnlnts Eslimalion points 35 3 k 25 239 V Son mile 2 3 05 15 05 1 t m 5 04 0 5 0 D 0 1 3 4 5 1 1 5 2 25 3 3 5 A y courdinata x BME pusJanm pm a cunrdlnnta xy11

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