Numerical Method for Conditional Simulation of Levy Random Fields

Stochastic simulations of subsurface heterogeneity require accurate statistical models for spatial fluctuations. Incremental values in subsurface properties were shown previously to be approximated accurately by Levy distributions in the center and in the start of the tails of the distribution. New simulation methods utilizing these observations have been developed. Multivariate Levy distributions are used to model the multipoint joint probability density. Explicit bounds on the simulated variables prevent nonphysical extreme values and introduce a cutoff in the tails of the distribution of increments. Long-range spatial dependence is introduced through off-diagonal terms in the Levy association matrix, which is decomposed to yield a maximum likelihood type estimate at unobserved locations. This procedure reduces to a known interpolation formula developed for Gaussian fractal fields in the situation of two control points. The conditional density is not univariate Levy and is not available in closed form, but can be constructed numerically. Sequential simulation algorithms utilizing the numerically constructed conditional density successfully reproduce the desired statistical properties in simulations.     

Three-phase numerical model of water migration in partially frozen geological media: model formulation,validation, and applications

Water in the subsurface of the Earth’s cold regions—and possibly the subsurface of Mars—resides in the liquid, vapor, and ice phases. However, relatively few simulations addressing full three-phase, nonisothermal water dynamics in below-freezing porous media have been undertaken. This paper presents a nonisothermal, three-phase approach to modeling water migration in partially frozen porous media. Conservation equations for water (as ice, liquid, and vapor) and a single gas species (in the gas phase and dissolved in water) are coupled to a heat transport equation and solved by a finite-volume method with fully implicit time stepping. Particular attention is given to the method of spatial differencing when the pore space is partially filled with ice. The numerical model is able to reproduce freezing-induced water redistribution observed in laboratory experiments. Simulations of Earth permafrost dynamics and of the formation and evolution of a planetary-scale cryosphere on Mars demonstrate the new capabilities.     

Time–space continuity of daily maps of fractional snow cover and albedo from MODIS

Using reflectance values from the seven MODIS “land” bands with 250 or 500 m resolution, along with a corresponding cloud product, we estimate the fraction of each 500 m pixel that snow covers, along with the albedo of that snow. The daily products have data gaps and errors because of cloud cover and sensor viewing geometry. Rather than make users interpolate and filter these patchy daily maps without completely understanding the retrieval algorithm and instrument properties, we use the daily time series to improve the estimate of the measured snow properties for a particular day. We use a combination of noise filtering, snow/cloud discrimination, and interpolation and smoothing to produce our best estimate of the daily snow cover and albedo. We consider two modes: one is the “predictive” mode, whereby we estimate the snow-covered area and albedo on that day using only the data up to that day; the other is the “retrospective” mode, whereby we reconstruct the history of the snow properties for a previous period.     

Regional variability in dust‐on‐snow processes and impacts in the Upper Colorado River Basin

Dust deposition onto mountain snow cover in the Upper Colorado River Basin frequently occurs in the spring when wind speeds and dust emission peaks on the nearby Colorado Plateau. Dust loading has increased since the intensive settlement in the western USA in the mid 1880s. The effects of dust‐on‐snow have been well studied at Senator Beck Basin Study Area (SBBSA) in the San Juan Mountains, CO, the first high‐altitude area of contact for predominantly southwesterly winds transporting dust from the southern Colorado Plateau. To capture variability in dust transport from the broader Colorado Plateau and dust deposition across a larger area of the Colorado River water sources, an additional study plot was established in 2009 on Grand Mesa, 150 km to the north of SBBSA in west central, CO. Here, we compare the 4‐year (2010–2013) dust source, deposition, and radiative forcing records at Grand Mesa Study Plot (GMSP) and Swamp Angel Study Plot (SASP), SBBSA's subalpine study plot. The study plots have similar site elevations/environments and differ mainly in the amount of dust deposited and ensuing impacts. At SASP, end of year dust concentrations ranged from 0.83 mg g^?1 to 4.80 mg g^?1, and daily mean spring dust radiative forcing ranged from 50–65 W m^?2, advancing melt by 24–49 days. At GMSP, which received 1.0 mg g^?1 less dust per season on average, spring radiative forcings of 32–50 W m^?2 advanced melt by 15–30 days. Remote sensing imagery showed that observed dust events were frequently associated with dust emission from the southern Colorado Plateau. Dust from these sources generally passed south of GMSP, and back trajectory footprints modelled for observed dust events were commonly more westerly and northerly for GMSP relative to SASP. These factors suggest that although the southern Colorado Plateau contains important dust sources, dust contributions from other dust sources contribute to dust loading in this region, and likely account for the majority of dust loading at GMSP. Copyright © 2015 John Wiley & Sons, Ltd.     

In situ Mixing of Organic Matter Decreases Hydraulic Conductivity of Denitrification Walls in Sand Aquifers

In a previous study, a denitrification wall was constructed in a sand aquifer using sawdust as the carbon substrate. Ground water bypassed around this sawdust wall due to reduced hydraulic conductivity. We investigated potential reasons for this by testing two new walls and conducting laboratory studies. The first wall was constructed by mixing aquifer material in situ without substrate addition to investigate the effects of the construction technique (mixed wall). A second, biochip wall, was constructed using coarse wood chips to determine the effect of size of the particles in the amendment on hydraulic conductivity. The aquifer hydraulic conductivity was 35.4 m/d, while in the mixed wall it was 2.8 m/d and in the biochip wall 3.4 m/d. This indicated that the mixing of the aquifer sands below the water table allowed the particles to re-sort themselves into a matrix with a significantly lower hydraulic conductivity than the process that originally formed the aquifer. The addition of a coarser substrate in the biochip wall significantly increased total porosity and decreased bulk density, but hydraulic conductivity remained low compared to the aquifer. Laboratory cores of aquifer sand mixed under dry and wet conditions mimicked the reduction in hydraulic conductivity observed in the field within the mixed wall. The addition of sawdust to the laboratory cores resulted in a significantly higher hydraulic conductivity when mixed dry compared to cores mixed wet. This reduction in the hydraulic conductivity of the sand/sawdust cores mixed under saturated conditions repeated what occurred in the field in the original sawdust wall. This indicated that laboratory investigations can be a useful tool to highlight potential reductions in field hydraulic conductivities that may occur when differing materials are mixed under field conditions.     

From drought to flood: A water balance analysis of the Tuolumne River basin during extreme conditions (2015–2017)

The degree to which the hydrologic water balance in a snow-dominated headwater catchment is affected by annual climate variations is difficult to quantify, primarily due to uncertainties in measuring precipitation inputs and evapotranspiration (ET) losses. Over a recent three-year period, the snowpack in California's Sierra Nevada fluctuated from the lightest in recorded history (2015) to historically heaviest (2017), with a relatively average year in between (2016). This large dynamic range in climatic conditions presents a unique opportunity to investigate correlations between annual water availability and runoff in a snow-dominated catchment. Here, we estimate ET using a water balance approach where the water inputs to the system are spatially constrained using a combination of remote sensing, physically based modelling, and in-situ observations. For all 3 years of this study, the NASA Airborne Snow Observatory (ASO) combined periodic high-resolution snow depths from airborne Lidar with snow density estimates from an energy and mass balance model to produce spatial estimates of snow water equivalent over the Tuolumne headwater catchment at 50-m resolution. Using observed reservoir inflow at the basin outlet and the well-quantified snowmelt model results that benefit from periodic ASO snow depth updates, we estimate annual ET, runoff efficiency (RE), and the associated uncertainty across these three dissimilar water years. Throughout the study period, estimated annual ET magnitudes remained steady (222 mm in 2015, 151 mm in 2016, and 299 mm in 2017) relative to the large differences in basin input precipitation (547 mm in 2015, 1,060 mm in 2016, and 2,211 mm in 2017). These values compare well with independent satellite-derived ET estimates and previously published studies in this basin. Results reveal that ET in the Tuolumne does not scale linearly with the amount of available water to the basin, and that RE primarily depends on total annual snowfall proportion of precipitation.