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Analyzing the validity and success of a data assimilation algorithm when somestate variable observations are not available is an important problem inmeteorology and engineering. We present an improved data assimilation algorithmfor recovering the exact full reference solution (i.e. the velocity andtemperature) of the 3D Planetary Geostrophic model, at an exponential rate intime, by employing coarse spatial mesh observations of the temperature alone.This provides, in the case of this paradigm, a rigorous justification to anearlier conjecture of Charney which states that temperature history of theatmosphere, for certain simple atmospheric models, determines all other statevariables.

On the Charney Conjecture of Data Assimilation Employing Temperature Measurements Alone: The Paradigm of 3D Planetary Geostrophic Model