The relativistic redshift between two earth-bound clocks can be interpreted in terms of gravity potential variation between the clock locations. A clock with a fractional frequency uncertainty of 10-18 is sensitive to a gravity potential variation of 0.1 m2/s2 or a height difference of 1 cm. Case studies for four regions affected by different mass change processes - Himalaya, Amazon, Greenland, and Fennoscandia - have been carried out. As the clocks rest on the deformable Earth's surface, clock observations do not only include potential variations due to mass changes but also associated variations due to the vertical deformation of the land. For the simulations, vertical displacements were derived from real GNSS (Global Navigation Satellite Systems) measurements, and mass variations were computed from GRACE (Gravity Recovery And Climate Experiment) solutions. In the Himalayan region, seasonal variations with a maximum range of -0.20.2 m2/s2 were obtained. There, early and long-lasting precipitation patterns in North-East India and the gradual spreading towards the West can be observed by a dedicated clock network. For the Amazon region, seasonal variations with a maximum range of -0.50.5 m2/s2 observed by clocks also reveals the Amazon's seasonal properties of annual rainfall variability at the North and South of the equator. The rainy season in the North of the equator is during the summer season from June to August, but from November to April in the South of the equator. The long-term trend of the ice mass loss in Greenland between 2004 and 2015 causes signals of potential variations of 1 m2/s2 that again can clearly be observed by clock measurements. Especially, the higher rates of mass variations in the west and south parts of Greenland can well be observed. The land uplift pattern of Fennoscandia due to the GIA (Glacial Isostatic Adjustment) can also be detected using optical clocks, however, the vertical deformations dominate the signal and not the mass changes. These examples illustrate that terrestrial clock networks can be used in the future as a modern tool for detecting various time-variable gravity signals for understanding the regional/local patterns of the variations and for providing complementary information to other geodetic techniques.