Using the Newtonian relaxation technique in numerical sensitivity studies

In model-based sensitivity studies, the growth of model error over long-term integrations may lead to serious deviations between the simulated and actual states. To reduce these errors, we have developed a new modeling approach with application of the Newtonian relaxation technique, or nudging. In this approach, an identical artificial Newtonian relaxation term that reflects the difference between the model reference state and its analysis (available in many sensitivity studies) is added to the prognostic equations of the two simulated states, the reference state and the perturbed state (for which observations are nonexistent). We have conducted idealized sensitivity experiments with a shallow-water model to evaluate the benefits and viability of this approach and to test its sensitivity to changes in the nudging period and error in the analysis data. The experimental results confirm that this approach lead to more credible atmospheric responses to modified external forcing if the data error is within a reasonable range. The results also indicate that a 12-hour period is more favorable for nudging than a 24-hour period.