EDIT

 * Update 2 for version 5.x-1.0

/**

 * Implementation of hook_api_update_N().

 *

 * Database updates consist of 3 parts:

 *    1 digit for Drupal core compatibility

 *    1 digit for your module's major release version (e.g. is this the 5.x-1.* (1) or 5.x-2.* (2) series of your module?)

 *    2 digits for sequential counting starting with 00

 * The 2nd digit should be 0 for initial porting of your module to a new Drupal core API.

 *

 * Update 1 for version 5.x-3.0

 */

function cdm_dataportal_update_5301() {

  $items = array();

  // add new default to

  $annotation_types_filter = variable_get('annotations_types_as_footnotes', FALSE);

  if($annotation_types_filter) {

    $annotation_types_filter['NULL_VALUE'] = 'NULL_VALUE';

  }

  $items[] = _modify_variable('annotations_types_as_footnotes', $annotation_types_filter);

  return $items;

}