A Model for Pollutant Concentrations During Snow-Melt

Abstract

In recent years extensive measurements of pollutant concentrations within the environment have been made over Western Europe following reports of unusually high pollution levels within rivers and lakes, especially after the start of the spring melting period. A simple model is presented to describe theoretically the pollutant efflux within the first fractions of melt water released from a snow-pack at the start of the melting season. The dominant features included are the appearance of a wave-front as heading the unsaturated flow of melt water and the pollutant dispersion arising from the interaction of the flow with the porous structure of the snow-pack and molecular diffusion. Computed results are shown describing the evolution of pollutant concentration profiles in the first run-off stage from a snow-pack subjected to an applied uniform surface heating.

Major fraction of black carbon is flushed from the melting New Hampshire snowpack nearly as quickly as soluble impurities

“…In Winter 3, Cl − and NO 3 − inventories consistently decrease at a quicker rate than SWE (Figures c and e). This result is expected given the wide body of literature on the ionic pulse [ Johannessen et al ., ; Johannessen and Henriksen , ; Hibberd , ; Williams and Melack , ; Bales et al ., ; Harrington and Bales , , ; Satoh et al ., ; Feng et al ., ; Lee et al ., ; Williams et al ., ]. There are a few exceptions (i.e., points above the 1:−1 line), which is indicative of impurity inventory gain during melt.…”

“…We also include measurements of major ions Cl − and NO 3 − to validate our approach of evaluating changes in impurity burden. Previous studies using lysimeters have shown that ionic species pulse from the snowpack at the onset of melt [ Johannessen et al ., ; Johannessen and Henriksen , ; Hibberd , ; Williams and Melack , ; Bales et al ., ; Harrington and Bales , , ; Satoh et al ., ; Feng et al ., ; Lee et al ., ; Williams et al ., ]. Therefore, if daily integrated snowpit sampling allows us to detect a pulse of major ions, the same method should be applicable to the study of BC melt dynamics.…”

Isotopic evolution of snowmelt 2. Verification and parameterization of a one‐dimensional model using laboratory experiments

“…The best fit values of ψ are 0.4, 2.5 and 5.5 for experiments 1, 2, and 3. Using these values and the height of the snow column, the rate constant k r is calculated using in which [ Hibberd , 1984]. The calculated k r is 0.17 hr −1 for experiment 1, 0.17 hr −1 for experiment 2 and 0.14 hr −1 for experiment 3.…”

Isotopic evolution of snowmelt 1. A physically based one‐dimensional model

“…Solutions to this equation break down at a saturation wave front, which must be treated separately. If we define the wave front as the location where the fluid volume flux increases abruptly, then the wave front propagates at a velocity η* given for ripe snow by [ Hibberd , 1984] where S + and S − are the saturation values directly behind and preceding the wave front.…”