An algorithm is developed to derive hydrostatically balanced geopotent
ials at significant levels from radiosonde reports of significant-leve
l temperatures and mandatory-level geopotentials and temperatures. It
minimizes the square of the nonhydrostatic differences in a layer wher
e at least one significant-level datum is reported and can be viewed a
s being a 1D analysis step that returns an estimate of the departures
from hydrostatic balance within the layer. The piecewise-polynomial in
terpolation of the minimization procedure is used to produce an expand
ed geopotential profile in any layer where significant-level data are
reported, and the integrated minimization error can be used as a quali
ty-control measure. The algorithm's performance has been evaluated usi
ng the global radiosonde dataset for a given synoptic time, and it is
found that it produces equivalent layer-mean temperature errors that a
re generally smaller than radiosonde observational errors.