The default method for color representation on displays involves sRGB as device-independent encoding color space. For improving color reproduction accuracy, we develop a device-specific display characterization model for the Apple iPad Air 2. In separate articles, we will evaluate the same method for other devices and for other display technologies. This model is combined with an easy-to-implement new method to account for the influence of illuminance from ambient light. The combination is called the mobile display characterization and illumination model (MDCIM) for the iPad Air 2, representing modern liquid crystal displays. Seven observers performed psychophysical tests at ambient illuminance levels from 600 to 3000 lx. They visually compared colors of calculated images with those of physical samples. The MDCIM model achieves similar color reproduction accuracy as when using the default method involving sRGB encoding at 1000 lx, while considerably improving color accuracy at other illuminance levels. At 600 lx, 98% of the observers prefer images directly generated with the MDCIM model over those created using the default method. The average color reproduction accuracy improves by two categories on a five-point scale. At 3000 lx, the percentage of colors that is represented at least reasonably well, according to the subjective assessment of visual observers, increased from 0% to 60%.