Ice borehole thermometry: Sensor placement using greedy optimal sampling

Abstract. Borehole thermometry is an important tool for reconstructing past climate conditions, assessing changes in land energy storage, and understanding subsurface thermal regimes such as permafrost and glacial dynamics. Optimizing the temperature sensor placement within boreholes allows us to maximize the informativeness of temperature measurements, particularly in polar regions where operational constraints necessitate cost-effective solutions. Traditional sensor placement methods such as linear or exponential spacing, often overlook site-specific subsurface heat distribution characteristics, potentially limiting the accuracy of the measured temperature profile. In this paper, we propose a greedy optimal sampling technique for strategically placing temperature sensors in ice boreholes. Utilizing heat transfer model simulations, this method selects sensor locations that minimize interpolation errors in reconstructed temperature profiles. We apply our approach to two distinct borehole sites: EPICA Dronning Maud Land site in East Antarctica and the Greenland Ice Core Project site, each with unique surface conditions. Our results demonstrate that the greedy optimal sensor placement significantly outperforms conventional linear and exponential spacing methods, reducing sampling errors by up to a factor of ten and thus achieving similar informativeness with fewer sensors. This strategy offers a cost-effective means to maximize the information obtained from borehole temperature measurements, thereby potentially enhancing the precision of climate reconstructions.