Knowledge Base

How to convert the horizontal and vertical components to east and north

This article describes how to convert the u (horizontal) and v (vertical) components from the ice motion data set to East and North components on the Earth's surface. Instructions for both the Northern and Southern Hemispheres are described below:

Northern Hemisphere

In the Northern Hemisphere, the longitudes are:

         -180°/180°       

                |

    -90° ---------- 90°

                |

                0°

The directions in the product are:

  • u: toward the right on the grid
  • v: upward (toward the top) on the grid
  • East is counterclockwise
  • North is toward the center of the grid

To compute the East and North components, apply a rotation matrix, which results in:

  • E:   u * cos L  +  v * sin L
  • N:  -u * sin L  +  v * cos L
    • where L is the longitude
    • Note the negative sign in the first term of N

 This can be checked by verifying that:

  • at L=0o, a u-only vector (to the right) corresponds to east (positive E)
  • at L=0o, a v-only vector (toward the top) corresponds to north (positive N)
  • at L=90o, a u-only vector (to the right) corresponds to south (negative N)
  • at L=90o, a v-only vector (toward the top) corresponds to east (positive E)

Southern Hemisphere

In the Southern Hemisphere, the longitudes are:

                0°       

                |

    -90° ---------- 90°

                |

        -180°/180°

The directions in the data set are:

  • u: toward the right on the grid
  • v: upward (toward the top) on the grid
  • East is clockwise
  • North is outward from the center of the grid

To compute East and North components, apply a rotation matrix, which results in:

  • E:   u * cos L  -  v * sin L
  • N:   u * sin L  +  v * cos L
    • where L is the longitude
    • Note the negative sign in the second term of E

 This can be checked by verifying that:

  • at L=0o, a u-only vector (to the right) corresponds to east (positive E)
  • at L=0o, a v-only vector (toward the top) corresponds to north (positive N)
  • at L=90o, a u-only vector (to the right) corresponds to north (positive N)
  • at L=90o, a v-only vector (toward the top) corresponds to west (negative E)