Both gage height and discharge rate are important factors in surface water hydrology. For most of the time they are closely coupled. When one of them is missing, we can always estimate the other using some relation algorithms. To date, there a few commonly used relation algorithms. For example: https://en.wikipedia.org/wiki/Rating_curve
Here are more materials: http://water.usgs.gov/edu/streamflow3.html
Based on these relations, a simple test was run to illustrate and estimate the discharge based on gage height.
Figure 1. Gage height-discharge relation curve. The blue crosses are observed gage height-discharge data. The red crosses are calculated after “parameter estimation” using curve fitting method.