Objective Optimum Interpolation Equation

Introduction : This calculator calculates an analysis field by comparing the first guess Xg and the observation Xo to their errors, where X is equal to M for wind speed, P for pressure, or Z for Geopotential height. This calculation gives a more accurate result for the analysis field. In this calculator, you have 4 input values:
  1. Observed (Xo)
  2. First Guess (Xg)
  3. Error Observed (eo)
  4. Error First Guess (eg)

The algorithm for the Objective Optimum Interpolation is:

Mathematical equation for objective optimum interpolation

Table 14-1. Typical errors of weather observations (from ECMWF Meteor. Bulletin M3.2, 1994)
Sensor type Eo
Wind errors in the lower troposphere (m/s)
Surface stations and ship obs 3 to 4

Drifting buoy

5 to 6
Rawinsonde, pilot bal., wind prof. 2 to 3
Aircraft and satellite 3
Pressure errors (kPa)
Surface weather stations 0.1
Ship and drifting buoy 0.2
S. Hemisphere manual analysis 0.4
Geopotential height errors (m)
Surface weather stations 7
Ship and drifting buoy 14
S. Hemisphere manual analysis 32
Rawinsonde 13 to 26

Objective Optimum Interpolation Equation


Input Values:

Observed (Xo)
First Guess (Xg)
Error Observed (eo)
Error First Guess (eg)

Results:

Analysis Value (Xa)