Refraction coefficient determination and modelling for the territory of the Kingdom of Saudi Arabia

Transcription

1 Presened a he FIG ongress 08, May 6-, 08 in Isanbul, Turkey Refracion coefficien deerminaion and modelling for he erriory of he Kingdom of Saudi Arabia Ohman AL-KHERAYEF, KSA Vasil VALHINOV, BG Rossen GREBENITHARSKY, KSA Sanislava VALHEVA, BG Bandar AL-MUSLMANI, KSA Uhman AL-RUBAIA, KSA General ommission for Survey P. O. Box: 8798, Riyadh: 65, Saudi Arabia Tel , Fax o.alkherayef@gcs.gov.sa

2 onens: oinroducion oaim oproblem background and mehodology of compuaions ofield ess carried ou in he KSA Naional Verical Nework and available daa Sofware developmen Refracion coefficien compuaion and accuracy esimaion oonclusions and recommendaions

3 Inroducion Precise levelling is essenial for esablishing a Naional Verical Reference Sysem (NVRS); Refracion affecs precise levelling by increasing he loop misclosures; refracion effec on measured heigh difference per seup could reach up o - mm; Levelling insrumen s sofware auomaically correc for refracion using sandard amospheric-pressure models; The real influence of refracion on he line of sigh depends on he opography roughness along he levelling line and he air emperaure (Angus-Leppan, 984) If emperaure observaions obained during levelling are available, he refracion effec could be modelled -> improve he accuracy of he levelling neworks 3

4 Aim The aim: o presen resuls from he Refracion oefficien Deerminaion for Precise Levelling Observaion (RD_PLO) projec closely linked o he esablishmen of a new Naional Verical Reference Frame for he KSA The focus: ) compuaion and modelling of refracion for precise geodeic levelling using he available emperaure riples colleced during he precise levelling; ) accouning for opography roughness along he line of sigh by employing he so-called equivalen heigh. 4

5 Problem background and mehodology Kukkamaki s formula for refracion correcion o rod reading: ( ) 0 0 i i i Z Z Z Z d cg R assuming: wih classical formula refracion coef.: 3 ln ln where, 3 wih modified refracion coefficien: ( ) 3 ln ln bu 5 wih heoreical refracion coefficien: -/3

6 Problem background and mehodology Kukkamaki s formula for refracion correcion o rod reading: ( ) 0 0 i i i Z Z Z Z d cg R New refracion coefficien formula: assuming: bu he available i a i do no saisfy he condiion Uiliing: b a b a b a 3 3 assuming ln 3 4 ln T T T 3 T 6

7 Problem background and mehodology ompuing he equivalen heigh: S S l dl he S h S 0 i 0 li h i l i l i Refracion effec on he heigh difference is: ref ( R R ) back for Accouning for opography roughness: equiv ref h e _ back h e _ for ref uses boh modified classical and new formulae for refracion coefficien! 7

8 Field ess: NVN & available daa GS is responsible for he esablishmen of Naional Verical Nework (NVN) for he KSA Since 00, GS has carried ou four phases of precise geodeic levelling: boh in forward and backward direcion A mos phases simulaneous measuremens of emperaure a 3 differen reference levels above he ground 8

9 Field ess: NVN & available daa Amoun of daa o be processed: levelling: > ; emperaure: >

10 Field ess: sofware developmen Funcions of he differen REFRATION submodules 0

11 Field ess: compuaions & accuracy Scenarios for refracion coefficien compuaions For each scenario wo formulas were applied (he modified classical formula and he new one) ) one average -value for he erriory of he KSA ) wo ypes of -values per seup considering: case of normal amosphere, where (values<0) 54% of he compued -values case of inverse amosphere, where (-values>0) 46% of he compued -values 3) average -value per secion 4) -values referring o he middle poin of he secion (subjeced o saisical esing) 5) average secion -values from single/double runs (subjeced o correlaion analysis) 6) -values per levelling line secions as a moving average from secion -values; All -values in 5) and 6) are consisen; wih STD of abou 0.0; The -values for forward and backword direcions are coheren which shows he exisence of a real signal In filered values

12 Field ess: compuaions & accuracy 3D GIS models of refracion coefficien

13 Field ess: compuaions & accuracy Resuls validaion improvemen (60% - 70%) in levelling line misclosures obained wihin he heigh dependen 3D refracion model improvemen due o equivalen heigh reaching up o 70% per observed versus 43% per onracor s values of refracion correcions 3

14 Field ess: compuaions & accuracy Resuls validaion loop misclosures decreased wih 3-4 cm (70% improvemen); he effec of he equivalen heigh was no considered loop misclosures improvemen of 30% when he equivalen heigh was included 4

15 onclusions and recommendaions: Four possible scenarios based on he geodeic applicaion (he desired accuracy of levelling) and he availabiliy of emperaure measuremens; All scenarios need o be esed and validaed wih respec o heir conribuion o accuracy improvemen on he enire precise levelling nework in erms of adjused heighs. 5

16 onclusions and recommendaions: 6

17 onclusions and recommendaions: For fuure applicaions of Kukkamaki s formula, reference levels for he emperaure sensors shown in he Figure on he righ should are recomended; The emperaure measuremens are needed only o deermine he ype of he amosphere (normal or inverse), i.e. he sign of while he acual come from a R model; The new formula for compuing could be used as well, providing ha he relevan emperaure measuremens are obained a reference levels of 0.5 m,.5 m and 3.5 m 7

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