Melt ponds are key elements in the energy balance of Arctic sea ice. Observing their temporal evolution is crucial for understanding melt processes and predicting sea ice evolution. Remote sensing is the only technique that enables large-scale observations of Arctic sea ice. However, monitoring melt pond deepening in this way is challenging because most of the optical signal reflected by a pond is defined by the scattering characteristics of the underlying ice. Without knowing the influence of meltwater on the reflected signal, the water depth cannot be determined. To solve the problem, we simulated the way meltwater changes the reflected spectra of bare ice. We developed a model based on the slope of the log-scaled remote sensing reflectance at 710 nm as a function of depth that is widely independent from the bottom albedo and accounts for the influence of varying solar zenith angles. We validated the model using 49 in situ melt pond spectra and corresponding depths from shallow ponds on dark and bright ice. Retrieved pond depths are accurate (root mean square error, RMSE=2.81 cm; nRMSE=16 %) and highly correlated with in situ measurements (r=0.89; p=4.34x10-17). The model further explains a large portion of the variation in pond depth (R.sup.2 =0.74). Our results indicate that our model enables the accurate retrieval of pond depth on Arctic sea ice from optical data under clear sky conditions without having to consider pond bottom albedo. This technique is potentially transferrable to hyperspectral remote sensors on unmanned aerial vehicles, aircraft and satellites.