Representation of Horizontal Transport Processes in Snowmelt Modeling by Applying a Footprint Approach

The energy balance of an alpine snow cover significantly changes once the snow cover gets patchy. The local advection of warm air causes above-average snow ablation rates at the upwind edge of the snow patch. As lateral transport processes are typically not considered in models describing surface exchange, e. g., for hydrological or meteorological applications, small-scale variations in snow ablation rates are not resolved. The overall model error in the hydrological model Alpine3D is split into a contribution from the pure " leading edge effect" and a contribution from an increase in the mean air temperature due to a positive snow-albedo feedback mechanism. We found an overall model error for the entire ablation period of 4% for the almost flat alpine test site Gletschboden and 14% for the Wannengrat area, which is located in highly complex terrain including slopes of different aspects. Terrestrial laser scanning measurements at the Gletschboden test site were used to estimate the pure " leading edge effect" and reveal an increase in snow ablation rates of 25-30% at the upwind edge of a snow patch and a total of 4-6% on a catchment scale for two different ablation days with a snow cover fraction lower than 50%. The estimated increase of local snow ablation rates is then around 1-3% for an entire ablation period for the Gletschboden test site and approximately 4% for the Wannengrat test site. Our results show that the contribution of lateral heat advection is smaller than typical uncertainties in snow melt modeling due to uncertainties in boundary layer parameters but increases in regions with smaller snow patch sizes and long-lasting patchy snow covers in the ablation period. We introduce a new temperature footprint approach, which reproduces a 15% increase of snow ablation rates at the upwind edge of the snow patch, whereas observations indicate that this value is as large as 25%. This conceptual model approach could be used in hydrological models. In addition to improved snow ablation rates, the footprint model better represents snow mask maps and turbulent sensible heat fluxes from eddy-covariance measurements.

The Uncertainty of Seasonal Snow Energy- and Mass Balance Simulations as a Function of Typical Input Uncertainty

Mathias Thierry Pierre Bavay, Charles Fierz, Michael Lehning

The assessment of water resources and their change in time as well as many other applications from hydrology to meteorology require the successful modelling of the dynamics of the seasonal snow cover. Especially if extrapolation in time, e.g. for climate change scenario assessment, is aimed for, the use of energy balance models has been proven to be more trustworthy than simpler temperature index models. The disadvantage of the energy balance method is the requirement of a variety of input quantities, which are not always but become increasingly accessible. What is missing, however, is an in-depth assessment of the influence of typical errors in the individual input quantities on model performance. This contribution presents a sensitivity study, which compares the influence of typical errors and uncertainties in radiation, wind, temperature and humidity input, both measured and modeled, with errors caused by insufficient knowledge of solid precipitation rates. The analysis is carried out with the widely used SNOWPACK model and focuses on the build-up and melt of a mid-latitude seasonal snow cover. While mass input uncertainties still dominate the overall performance especially at high elevations (alpine zone), errors in wind and radiation can cause very significant effects as well. Wind is considered to be more critical in this context, because its spatial variation is both more pronounced and more difficult to estimate than the spatial variation in short- and longwave radiation. In absence of reliable radiation input, its value can successfully be calculated or parameterized if e.g. cloud information is available. Errors in air temperature input or a failure of a correct assessment of its spatial variability can be locally very important because of the feed-back mechanism via atmospheric stability. For the overall mass balance of a seasonal snow cover, humidity errors are less important. Notable exceptions are applications such as the correct assessment of surface hoar formation or prediction of melt rates during rain on snow events, for which good humidity input is required. A main conclusion is that input data through a combination of measurement stations and weather models are now widely available with sufficient quality to even allow a small-scale distributed application of energy balance models.

2013

Theoretical Framework for the Assessment of Uncertainties in Snow Depth Measurements

Michael Lehning, Ernesto Trujillo Gomez

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 the 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.

2014

Micrometeorological processes driving snow ablation in an Alpine catchment

Mathias Thierry Pierre Bavay, Thomas Grünewald, Michael Lehning

Mountain snow covers typically become patchy over the course of a melting season. The snow pattern during melt is mainly governed by the end of winter snow depth distribution and the local energy balance. The objective of this study is to investigate micro-meteorological processes driving snow ablation in an Alpine catchment. For this purpose we combine a meteorological boundary-layer model (Advanced Regional Prediction System) with a fully distributed energy balance model (Alpine3D). Turbulent fluxes above melting snow are further investigated by using data from eddy-correlation systems. We compare modeled snow ablation to measured ablation rates as obtained from a series of Terrestrial Laser Scanning campaigns covering a complete ablation season. The measured ablation rates indicate that the advection of sensible heat causes locally increased ablation rates at the upwind edges of the snow patches. The effect, however, appears to be active over rather short distances of about 4–6 m. Measurements suggest that mean wind velocities of about 5 m s−1 are required for advective heat transport to increase snow ablation over a long fetch distance of about 20 m. Neglecting this effect, the model is able to capture the mean ablation rates for early ablation periods but strongly overestimates snow ablation once the fraction of snow coverage is below a critical value of approximately 0.6. While radiation dominates snow ablation early in the season, the turbulent flux contribution becomes important late in the season. Simulation results indicate that the air temperatures appear to overestimate the local air temperature above snow patches once the snow coverage is low. Measured turbulent fluxes support these findings by suggesting a stable internal boundary layer close to the snow surface causing a strong decrease of the sensible heat flux towards the snow cover. Thus, the existence of a stable internal boundary layer above a patchy snow cover exerts a dominant control on the timing and magnitude of snow ablation for patchy snow covers.

2011