  We model SNRs at a variety of heights above the disk. Our detailed numerical
simulations include non-equilibrium ionization and recombination and follow the
remnants' evolution until their hot bubbles have cooled. We analytically
calculate the bubbles' buoyant acceleration. From the results, we estimate the
time and space average O VI, N V, and C IV column densities and emission
intensities, 1/4 keV soft X-ray surface brightness, area coverage, and volume
occupation of the population of isolated SNRs above the Galaxy's HI layer.
Irrespective of assumed supernova explosion energy, ambient nonthermal
pressure, or frictional drag coefficient, the predicted O VI column density
matches the observed distribution between 130 pc and 2000 pc. The SNRs' O VI
intensity is a significant fraction of the average observed intensity. Within
the range of uncertainty in the SN rate, such SNRs can explain all of the
observed 1/4 keV surface brightness attributed to the extraplanar gas beyond
the H I layer in the southern hemisphere (~400 x 10^-6 counts/s/arcmin^2).
Thus, extraplanar SNRs could be the most important source of hot gas between
the Local Bubble and z ~ 2000 pc in the relatively quiescent southern
hemisphere. These results stand whether the remnants are assumed to be buoyant
or not. The population of old extraplanar SNRs should cover most of the high
latitude sky, but bright young extraplanar SNRs should cover less than 1% of
the sky. Perhaps the l=247, b=-64 crescent in the 1/4 keV X-ray maps could be a
young remnant.
