  Recent technological advances in optical atomic clocks are opening new
perspectives for the direct determination of geopotential differences between
any two points at a centimeter-level accuracy in geoid height. However, so far
detailed quantitative estimates of the possible improvement in geoid
determination when adding such clock measurements to existing data are lacking.
We present a first step in that direction with the aim and hope of triggering
further work and efforts in this emerging field of chronometric geodesy and
geophysics. We specifically focus on evaluating the contribution of this new
kind of direct measurements in determining the geopotential at high spatial
resolution (~ 10 km). We studied two test areas, both located in France and
corresponding to a middle (Massif Central) and high (Alps) mountainous terrain.
These regions are interesting because the gravitational field strength varies
greatly from place to place at high spatial resolution due to the complex
topography. Our method consists in first generating a synthetic high resolution
geopotential map, then drawing synthetic measurement data (gravimetry and clock
data) from it, and finally reconstructing the geopotential map from that data
using least squares collocation. The quality of the reconstructed map is then
assessed by comparing it to the original one used to generate the data. We show
that adding only a few clock data points (less than 1 % of the gravimetry data)
reduces the bias significantly and improves the standard deviation by a factor
3. The effect of the data coverage and data quality on the results is
investigated, and the trade-off between the measurement noise level and the
number of data points is discussed.
