Recent Lyman series and Balmer series airglow measurements provide a fresh opportunity to investigate the density distribution and variability of atomic hydrogen in the upper atmosphere. Dedicated nightside Balmer α Fabry-Perot spectrometer measurements at the Pine Bluff Observatory (PBO), University of Wisconsin-Madison, have been acquired since late 1999 taking advantage of several technological advances. Extreme ultraviolet spectral radiance measurements by the Espectr¿grafo Ultravioleta extremo para la Radiaci¿n Difusa (EURD) instrument on the Spanish MINISAT-1 satellite from October 1997 to December 2001 provide extensive sets of geocoronal Lyman ¿, Lyman γ and He 584 ¿ emission intensities. In this paper, coincident EURD Lyman ¿ and PBO Balmer α radiance measurements from the early March 2000 new moon period are presented. In addition to serving as examples of the data sets now available, the data volume poses an analysis challenge not faced in prior geocoronal studies. A data-model comparison search procedure employing resonance radiation transport results for extensive sets of parametric density distribution models is being developed for use in analyses of multiple large data sets; this is described, and example results for the PBO and EURD March 2000 data sets are presented. The tightness of the constraints obtained for the solar line-center Lyman ¿ irradiance and the atomic hydrogen column abundance is somewhat surprising, given the crudeness of the parameter binning in the search procedure and the fact that a small number of recognized corrections remain to be made to each data set.