Theoretical Framework for the Assessment of Uncertainties in Snow Depth Measurements

Abstract:

In recent years, marked improvements in our knowledge of the statistical properties of the spatial distribution of snow properties have been achieved thanks to improvements in measuring technologies (e.g., LIDAR, TLS, and GPR). Despite of this, objective and quantitative frameworks for the evaluation of uncertainties in snow measurements have been lacking. Here, we present a theoretical framework for quantitative evaluations of the uncertainty of point measurements of snow depth when used to represent the average depth over a profile section or an area. We define the error as the expected value of the squared difference between the real mean of the profile/field and the sample mean from a limited number of measurements. The model is tested for one and two dimensional survey designs that range from a single measurement to an increasing number of regularly-spaced measurements. Using high-resolution (~ 1m) LIDAR snow depths at three locations in Colorado, we show that the sample errors follow the theoretical behavior. Furthermore, we show how the determination of the spatial location of the measurements can be reduced to an optimization problem for the case of a predefined number of measurements, or to the designation of an acceptable uncertainty level to determine the total number of regularly-spaced measurements required to achieve such error. On this basis, a series of figures are presented that can be used to aid in the determination of the survey design under the conditions described, and under the assumption of prior knowledge of the spatial covariance/correlation properties. With this methodology, better objective survey designs can be accomplished, tailored to the specific applications for which the measurements are going to be used. Although we discuss the proposed methodology in the context of snow depth, the theoretical framework can be extended to other spatially distributed snow variables (e.g., SWE and/or snow depth) or hydrologic variables (e.g., soil moisture) whose statistical properties can be compared to those of snow depth. Applications of the methodology will be discussed, such as the selection of the location of snow/meteorological stations in mountain environments or survey design to be able to capture watershed scale means.