Uncertainty analysis for evaluating the accuracy of snow depth measurements

Abstract. A methodology for quantifying the accuracy of snow depth measurement are demonstrated in this study by using the equation of error propagation for the same type sensors and by compariong autimatic measurement with manual observation. Snow depth was measured at the Centre for Atmospheric Research Experiments (CARE) site of the Environment Canada (EC) during the 2013–2014 winter experiment. The snow depth measurement system at the CARE site was comprised of three bases. Three ultrasonic and one laser snow depth sensors and twelve snow stakes were placed on each base. Data from snow depth sensors are quality-controlled by range check and step test to eliminate erroneous data such as outliers and discontinuities.

In comparison with manual observations, bias errors were calculated to show the spatial distribution of snow depth by considering snow depth measured from four snow stakes located on the easternmost side of the site as reference. The bias error of snow stakes on the west side of the site was largest. The uncertainty of all pairs of stakes and the average uncertainty for each base were 1.81 and 1.52 cm, respectively. The bias error and normalized bias removed root mean square error (NBRRMSE) for each snow depth sensor were calculated to quantify the systematic error and random error in comparison of snow depth sensors with manual observations that share the same snow depth target. The snow depth sensors on base 12A (11A) measured snow depth larger (less) than manual observation up to 10.8 cm (5.21 cm), and the NBRRMSEs ranged from 5.10 to 16.5%. Finally, the instrumental uncertainties of each snow depth sensor were calculated by comparing three sensors of the same type installed at the different bases. The instrumental uncertainties ranged from 0.62 to 3.08 cm.