Flat Model for Representing Contiguous UTM Coordinates over Iraq Territory


The process of converting coordinates is, still, considered an important and difficult issue due to the way of conversion from geographic ellipsoidal system to the projected flat system. The most common method uses contiguous UTM system as one of the most accurate systems in the conversion process, but the users of the system face problems related to contiguity, especially at the large areas that lie within more than one zone. The aim of the present research is to solve the problem related to the multiple zones coverage found in the Iraqi territory using a mathematical model based on the use of Taylor series. The most accurate conversion equation used in this paper was based on the 4th order polynomial of two variables. The calculation of equations’ coefficients was performed using least square criterion for the coordinate’s values, i.e., either latitude, longitude) or East (E), North (N) coordinates. The two basic determinations, for the forward and backward, were applied. In the first stages, the conversion of the coordinates from Longitude/ Latitude to East/ North was determined. Then, the second conversion stage was determined, i.e., the coordinates conversion from East, North to Longitude, Latitude). For each phase, a spatial accuracy assessment was conducted. The results showed that the adopted mathematical model was successful to accomplish the conversion process. A very small error average of about 3 cm at east and less than 5 cm at north was reached using the 4th order polynomial equations.