This paper describes how NOVI responds to daily precipitation for vegetation under water-limited growth conditions (e.g., in arid or semi-arid environments). An analytical model was developed to address timing to peak NOVI response and total duration of NOVI response to a rainfall event with the passage of time. The model also describes how effectively the vegetation uses precipitated water. A case study in the Sandhills area of Nebraska, with NOVI calculated from Landsat-MSS images, showed that the model can accurately portray NOVI time series, and then can be used to derive some useful information about relations of NOVI and precipitation. For the vegetation in the test area, we found that the peak vegetative response to a precipitation event shifts from about 14 days after the rainfall event at the beginning of a growing season to 25 days at the late stage of the season, and then shifts back to 12 days at the end of the season. The duration of response, similar to the peak response in behavior, is 22, 61, and 25 days, respectively.