The Precipitation-Moisture Relation and the Madden-Julian Oscillation

A linearized precipitation anomaly field is derived based on an empirical equation that relates it to column integrated water vapor. The linearized equation shows that precipitation variance is directly proportional to the climatological mean precipitation, scaled by a parameter that describes rainfall's sensitivity to changes in relative humidity. A comparison between TRMM precipitation, ERA-Interim, and the derived precipitation shows that the derived precipitation compares more favorably with TRMM than ERA-Interim. This difference has to do with ERA-Interim's precipitation field exhibiting less sensitivity to humidity than TRMM data. Implications to the MJO-mean state bias issue in climate models is discussed. 

 Furthermore, a ``precipitation tendency" equation is constructed that elucidates the moist processes responsible for the evolution of precipitation in the MJO. It is found that precipitation is most sensitive to water vapor near the equator, becoming less sensitive with distance away from the equator. By applying the weak-temperature gradient approximation, it is found that moistening from vertical moisture advection in association with regions of shallow ascent is the largest contributor to propagation near the equator, decaying quickly with distance away from the equator. Horizontal moisture advection is a strong contributor to the precipitation tendency and is less narrowly confined to the equator.