We use the IRS on Spitzer to observe the southern part of the reflection nebula NGC 2023, including the Southern Ridge, which is a photodissociation region par excellence excited by HD 37903. Five pure-rotational H2 emission lines are detected and mapped over and around the Southern Ridge in order to compare with predicted level column densities from theoretical PDR models. We find very good agreement between PDR model predictions and emission line intensities and ratios measured with Spitzer, leading us to conclude that grain photoelectric heating sufficiently warms the gas to produce the observed H2 line emission via collisional excitation. On the Southern Ridge, we infer a hydrogen nucleus density n_H approx 2x10^5 cm^-3 and radiation field strength χ\ approx 10^4 relative to the local Galactic interstellar radiation field. This high value for χ\ independently predicts a distance toward HD 37903 of 300 pc, and is consistent with the most recent HIPPARCOS results. Over the map we find that both n_H and χ\ vary by a factor of sim 3. Such 2-D variations provide clues about the underlying 3-D structure of the Southern Ridge field, which appears to be the tip of a molecular cloud. We also map variations in excitation temperature and the ortho-to-para ratio, the latter attaining values of sim 1.5---2.0 on the Southern Ridge, and find that PDR modeling can readily reproduce observed ortho-to-para ratios that are