Two-dimensional analysis of atmospheric characteristics commonly utilizes predefined isobaric surfaces (i.e., 500-hPa), effectively ignoring information between levels or relying on assumptions and approximations to define general meteorological processes. A common technique for atmospheric analysis involves the quasi-geostrophic (QG) system, whereby vorticity and temperature fields are used to diagnose variations in geopotential height and vertical velocity at select levels. This technique utilizes a small amount of information, yet can be time consuming and error prone since forecasters must view each level and variable individually to make largely qualitative assessments. With the advent of higher graphical processing power on PCs and increasing accuracy of numerical weather prediction (NWP) models, three-dimensional visualization imposes no limits on the vertical placement or types of variables displayed on maps, reducing the time required to analyze gridded atmospheric data and removing some assumptions inherent in QG analysis. For example, in three-dimensional analysis, the assumption that the 500 mb level is the level of non-divergence need not be made because divergence may be viewed concurrently with vorticity. Despite the potential benefits, the adoption of three-dimensional analysis has been slow in the operational meteorology community. This is partly due to logistical issues related to the huge data requirement of three-dimensional visualization and a continued lack of processing power. However, another reason is that there are few links between the two-dimensional patterns of the QG diagnostic fields on the significant levels, which are heavily relied upon by the operational forecasting community, to the three-dimensional shape of those fields in the atmospheric volume. To address this issue, a careful study of the three-dimensional structure of each of the QG fields is required. This project begins that process by determining whether three-dimensional visualization could aid in model verification by calculating each component of the QG omega and geopotential tendency equations. The analysis fields from a selection of events with strong synoptic forcings were chosen from the 12-km operational North American Mesoscale (NAM) model. Using a finite differencing methodology that is dependent on the wavelength of the synoptic waves being analyzed, vertical velocities and geopotential height perturbations were calculated at each grid point of the analysis field by employing the QG omega equation and the QG geopotential tendency equation. The open-source visualization software, Paraview, was used to visualize the three-dimensional omega and geopotential tendency fields through a combination of contours and volume rendering. It was found that although the data display considerable low-amplitude patterns, the method can identify and quantify large perturbations in the height and vertical velocity fields within the data volume. This can enhance the diagnostics of NWP-generated atmospheric data for operational forecasting purposes, and can also be used to aid in verification of medium to large-scale simulated weather features.