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