2- مبنای مسطحاتی Datum What is Datum? Spheroid Ellipsoid Geoid

Spheroid The earth is not a perfect sphere. True sphere

Mastering ArcGIS Ellipsoid Chapter 3 Ellipsoid Actual shape is closer to an ellipsoid then mapping a point onto an ellipsoid better represents its position on the earth’s surface 3

زمین بدون اقیانوس و دریاها

Geoid Mastering ArcGIS Chapter 3 زمین یک بیضوی ایده آل نیز نیست. ژئوئید یک سطح فرضی است که بر پایه اندازه گیری های ثقل سنجی تعیین موقعیت شده است. سطح ژئوئید بسیار نامنظم، ناهموار و پیچیده است بنابراین نمی توان از این سطح به عنوان یک مبنای ریاضی استفاده کرد. در قسمت هایی از سطح زمین که ژئوئید منطبق بر بیضوی زمین است می توان از بیضوی سطح زمین برای تولید نقشه استفاده نمود. 5

Mastering ArcGIS Chapter 3 Datum Best fit for North America To minimize the discrepancy between the geoid and ellipsoid, a datum is defined A datum shifts the ellipsoid relative to the geoid to achieve a best fit between the two A local datum optimizes the shift for the best fit at a particular location. It may also use a surveyed network of points to make further adjustments A geocentric or world-centered datum optimizes the fit for the entire earth Worse fit for South America Copyright © 2009 by Maribeth H. Price 6

Mastering ArcGIS summary Chapter 3 Datum: The best possible fit between the earth geoid and the mapping ellipsoid Common Datums North American 1983 (uses GRS80 spheroid) North American 1927 (Clarke1866 spheroid) World Geodetic System 1984 or WGS84 Global Reference System 1980 or GRS80 Sphere Spheroid Geoid Datum 7

Datum examples Local datums World datums Mastering ArcGIS Chapter 3 Datum examples Local datums Optimized for a country or continent or local area May include fitted survey points for additional corrections World datums Optimized for the entire globe Local datums World datums Copyright © 2009 by Maribeth H. Price 8

Projections and datums Mastering ArcGIS Chapter 3 Projections and datums Every map projection is based on a GCS Every GCS has a datum Therefore: Every projection has a datum Projections based on different datums will be offset from one another Amount of offset depends on region Offset typically ranges from 0 – 300 meters UTM Zone 13 NAD 1983 ≠ UTM Zone 13 NAD 1927! Copyright © 2009 by Maribeth H. Price 9

Typical datum offset Roads in NAD83 Photo in NAD27 Mastering ArcGIS Chapter 3 Typical datum offset Roads in NAD83 Photo in NAD27 Copyright © 2009 by Maribeth H. Price 10

False easting and northing Mastering ArcGIS 3- جابجایی مرکز مختصات False easting and northing Chapter 3 Note the negative coordinate values (-x,y) (x,y) Reference latitude (0,0) (-x,-y) (x,-y) Central meridian 11

False easting and northing Mastering ArcGIS Chapter 3 False easting and northing False easting = 500,000 (x,y) (x,y) Reference latitude (x,y) (x,y) False northing = 500,000 (0,0) Central meridian Copyright © 2009 by Maribeth H. Price 12

Universal Transverse Mercator UTM

Universal Transverse Mercator Mastering ArcGIS Chapter 3 Universal Transverse Mercator Zone 16 South Dakota Based on Transverse Mercator (cylindrical) projection World divided into 60 zones 6 degrees wide Distortion is minimal within each zone Maps of different areas use best zone Best for maps covering small area in one zone Copyright © 2009 by Maribeth H. Price 14

Where is the zone 1 ? UTM Zone number=Round(longitude/6)+31 Zone 1 : 180° W - 174° W Central meridian : 177°W UTM Zone number=Round(longitude/6)+31

UTM Easting(X) Northing(Y)

How is UTM domain ?

The number 712000mE is read as, “712,000 meters East.” 711 is short-hand for 711,000, and is 1000 meters West of 712000mE.

The number 4765000mN is read, “4,765,000 meters north” of the equator. The next UTM number above is 4766, and is 1000 meters north.

Setting the display units Mastering ArcGIS Chapter 3 Setting the display units Copyright © 2009 by Maribeth H. Price 20