Tuesday, October 26, 2010

Η Εγκάρσια Μερκατορική Προβολή (Transverse Mercator Projection) και το ΕΓΣΑ87



Για να καταλάβουμε τι είναι και πώς προκύπτουν οι ορθογώνιες συντεταγμένες πρέπει να πούμε δυο λόγια για την Εγκάρσια Μερκατορική Προβολή (Ε.Μ.Π.). Στην Ε.Μ.Π., η γήινη επιφάνεια προβάλλεται πάνω σε έναν κύλινδρο, ο άξονας του οποίου είναι κάθετος ως προς την ευθεία που ενώνει τους δύο πόλους. Ο μεσημβρινός που ορίζεται από την επαφή του κυλίνδρου με τη γήινη επιφάνεια είναι ο Κεντρικός Μεσημβρινός της προβολής και ταυτίζεται με τον κατακόρυφο άξονα του προβολικού συστήματος. Ο οριζόντιος άξονας όλων των Ε.Μ.Π. είναι ο Ισημερινός.
Το πλεονέκτημα της προβολής αυτής είναι ότι ελαχιστοποιούνται οι παραμορφώσεις στη ζώνη του κεντρικού μεσημβρινού. Αρχή των αξόνων θεωρείται το σημείο τομής του Ισημερινού με τον Κεντρικό Μεσημβρινό. Αυτό έχει σαν αποτέλεσμα οι τιμές στον άξονα των Y (απόσταση από τον Ισημερινό) να εμφανίζονται αρκετά μεγάλες στην Ελλάδα (της τάξης των 4.000.000 μέτρων). Εξάλλου στον άξονα των Χ -προκειμένου να αποφεύγονται οι αρνητικές τιμές στα δυτικά του κεντρικού μεσημβρινού- αντί για μηδέν στην τομή των αξόνων δίνεται η τιμή 500.000 μέτρα: έτσι στα δυτικά του Κεντρικού Μεσημβρινού οι τιμές είναι μικρότερες των 500.000 μέτρων και στα ανατολικά του μεγαλύτερες.
Οι μεσημβρινοί που βρίσκονται ανατολικά και δυτικά του Κεντρικού Μεσημβρινού δεν είναι ευθείες γραμμές αλλά καμπύλες με τα κοίλα στραμμένα προς τον κατακόρυφο άξονα. Επειδή καθώς απομακρυνόμαστε από τον Κεντρικό Μεσημβρινό αυξάνουν οι παραμορφώσεις των διαστάσεων των αντικειμένων (τις παραμορφώσεις αυτές προσπαθεί να εξισορροπήσει ο συντελεστής κλίμακας k), οι Ε.Μ.Π. εφαρμόζονται σε ζώνες μικρού εύρους (κάθε ζώνη χαρακτηρίζεται από τον Κεντρικό Μεσημβρινό και από το εύρος της). Η πιό γνωστή Εγκάρσια Μερκατορική Προβολή είναι η Διεθνής Εγκάρσια Μερκατορική Προβολή (Universal Tranverse Mercator ή UTM), όπου όλες οι ζώνες έχουν εύρος 6°. Αν και η χρήση της Διεθνούς Εγκάρσιας Μερκατορικής Προβολής (UTM) διαδόθηκε ευρέως, στη χώρα μας παρουσιάζονται αρκετά προβλήματα από την εφαρμογή της, με κυριότερο το ότι η χώρα "μοιράζεται" σε δύο ζώνες (τη Ζώνη 34, με Κεντρικό Μεσημβρινό τον 21ο και τη Ζώνη 35, με Κεντρικό Μεσημβρινό τον 27ο) με ζώνη επαφής την καίρια για υπολογισμούς περιοχή της Αττικής. Το πρόβλημα αυτό, όπως και άλλα θέματα που δεν ενδιαφέρουν άμεσα τις ερασιτεχνικές εφαρμογές, ήρθε να λύσει η δημιουργία του Ελληνικού Γεωδαιτικού Συστήματος Αναφοράς, που προτάθηκε από τον καθηγητή Γιώργο Βέη το 1987. Η ύπαρξη ενός εθνικού Γεωδαιτικού Συστήματος Αναφοράς αποτελεί μεγάλο βήμα στην κατοχύρωση της τεχνογνωσίας μιας χώρας στο διεθνή χώρο. Πέραν των τεχνικών πλεονεκτημάτων του ΕΓΣΑ 87, όπως λέγεται συντομογραφικά το ελληνικό σύστημα, είναι σημαντικό ότι η Ελλάδα διαθέτει πλέον ένα σύγχρονο σύστημα αναφοράς, όπως όλες οι προηγμένες επιστημονικά χώρες, και αποτελεί χρέος μας να το χρησιμοποιούμε. Άλλωστε, ακόμα και τα απλά προγράμματα διαχείρισης δεδομένων GPS το έχουν πέλον καταχωρημένο και είναι βέβαιο ότι στα επόμενα χρόνια το ΕΓΣΑ 87 θα επικρατήσει καθολικά.
To ΕΓΣΑ 87 συνιστά ένα ενιαίο σύστημα αναφοράς για όλη την ελληνική επικράτεια. Σε αυτό το σύστημα δεν παρουσιάζονται ούτε το πρόβλημα του διαμοιρασμού της χώρας σε δύο ζώνες (περίπτωση προβολής UTM), ούτε των ανεξάρτητων συντεταγμένων ανά τμήματα (περίπτωση προβολής HATT). Έτσι λύνονται τα προβλήματα που παρουσιάζονταν στη σύνθεση χάρτη σε περιοχές που βρίσκονται στην επαφή των δύο ζωνών UTM (ζώνη 34 και 35, όπως η Αττική για παράδειγμα) ή των τετραγώνων του HATT. Το ΕΓΣΑ87 χρησιμοποιεί μια Εγκάρσια Μερκατορική Προβολή που καλύπτει ολόκληρη τη χώρα με μια ζώνη εύρους 9ο, με Κεντρικό Μεσημβρινό τον 24 ο και συντελεστή κλίμακας 0.9996. Η επιλογή αυτή ελαχιστοποιεί τις παραμορφώσεις - στο 99% της χώρας οι παραμορφώσεις κλίμακας είναι μικρότερες από 670 μέρη στο εκατομμύριο -, διευκολύνει τις αναγωγές από το ένα σύστημα στο άλλο και επιπρόσθετα παρέχει και το σημαντικό πλεονέκτημα της συμμορφίας, δηλ. της διατήρησης των σχημάτων στο χάρτη. Η προβολή του ΕΓΣΑ συντομογραφικά αναφέρεται ως TM87.
Το ΕΓΣΑ 87 χρησιμοποιείται ήδη από το 1990 από όλους τους κρατικούς φορείς παραγωγής χαρτών, καθώς και για τη σύνταξη του Εθνικού Κτηματολόγιου, ενώ τα περισσότερα ψηφιακά δεδομένα και συμβατικοί χάρτες που διατίθενται από δημόσιους και ιδιωτικούς φορείς βασίζονται στο ίδιο σύστημα. Από τους μη κρατικούς φορείς παραγωγής χαρτών, μόνο η ΑΝΑΒΑΣΗ έχει μεταφέρει όλα τα δεδομένα της και δουλεύει στο ΕΓΣΑ. Ακόμη, θα πρέπει να τονιστεί, ότι το ΕΓΣΑ 87 συμπεριλαμβάνεται (άμεσα ή έμμεσα) σε όλες τις τεχνολογικές εφαρμογές που σχετίζονται με την αυτοματοποιημένη χαρτογραφία, όπως είναι τα λογισμικά GIS και Τηλεπισκόπησης και το λογισμικό που συνοδεύει τις συσκευές του συστήματος παγκόσμιου εντοπισμού (GPS).

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