NWC REU 2021
May 24 - July 30



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An Examination of the Accuracy of Objective Analysis Schemes

Alexander Ingalls and Bradley G. Illston


What is already known:

  • Objective Analysis schemes have been developed since the late 1940’s for use in weather map forecasting and diagnosis
  • The Barnes objective analysis scheme has been improved and revised several times with peripheral discussions of its accuracy
  • Several values for parameters of the Barnes scheme have been found to provide superior results in reclaiming short and long Fourier wavelengths of some atmospheric variable

What this study adds:

  • A quantifiable metric to compare objective analysis values to observation values
  • An overview of the Barnes scheme’s accuracy in terms of three meteorological variables over twelve days using data from the Oklahoma Mesonet
  • A plausible relationship of increased errors associated with data points along the boundary of some finite area


The properties of errors associated with objective analysis models are examined in terms of atmospheric variables to obtain a better understanding of the accuracy of such methods. Several schemes have been developed since the late 1940s which are used for weather forecasting and diagnosis. This information is ultimately conveyed to the public; therefore, an examination of their accuracy is prudent. A removal and replacement technique is utilized to compare interpolated values to their corresponding observational values. The observation data are collected from a network of mesoscale weather stations from which three variables, air temperature, relative humidity, and wind speed, are analyzed. In order to determine some metric of accuracy, errors are considered to be interpolated values that exceed the observation instrument’s calibration range. These errors are then investigated further through a statistical analysis. The resulting analysis shows three levels of errors. The first and most fundamental level shows a comparison of the magnitude of errors. For a particular day and time, the results showed a root mean squared error for air temperature to be 1.37 C. The second shows the relative amount of error per variable per observation station and geographically where these errors occur most often. The results show that the majority of errors were air temperature (55.62%) and relative humidity errors (40.13%), while wind speed errors account for just 4.25% of errors. The third is an accumulative view of how many errors stations had over 12 candidate days (one per month) over a year with an average root mean squared error of 13 errors for any given Mesonet station. Further analysis of the results suggests that there may be a relationship between so called ‘edge-cases’ and frequency of errors, where an observation near the boundary of some finite area may not have sufficient input data to perform the interpolation effectively. It was found that 60% of the top ten stations with errors were indeed boundary cases. The results could also suggest that seasonal variability influences the scheme’s accuracy, particularly during winter months, however a more robust investigation is likely required.

Full Paper [PDF]