The influence of topography on the radiation balance in complex terrain has so far been investigated either with very simple or very sophisticated approaches that are limited, respectively, by an uncontrolled spatial representation of radiative fluxes or heavy computational efforts. To bridge this gap in complexity, this paper proposes the radiosity approach, well known in computer graphics, to study anisotropic reflections of radiation in complex terrain. To this end the radiosity equation is rederived in the context of three-dimensional radiative transfer. The discretized equation is solved by means of an adapted version of progressive refinement iteration. To systematically study terrain effects, the geometrical disorder provided by the topography is considered in its simplest approximation by Gaussian random fields. These model topographies capture the most important length scales of complex terrain, namely a typical elevation and a typical valley width via the variance and the correlation length of the field, respectively. The mean reflected radiation is computed as a function of these length scales and sun elevation, thereby explicitly addressing finite system sizes and grid resolutions. A comparison with an isotropic parameterization of terrain reflections reveals that mean values are similar whereas spatial distributions vary remarkably. It is also shown that the mean reflected radiation in real topography is reasonably well characterized by the Gaussian approximation. As a final application of the method, the effective albedo of a topography is shown to vary with sun elevation and domain-averaged albedo, leading to albedo differences up to 0.025.
New parameterisations were developed to calculate the emission and resuspension flux of pollen grains. These new parameterisations were included in the comprehensive mesoscale model system KAMM/DRAIS. Two types of simulations were performed. In the first case, horizontally homogeneous meteorology was assumed. In this case, pollen concentration rapidly decreased with the distance from the source. In the second case, where the fully threedimensional model was applied, atmospheric lifetime of the pollen grains increased remarkably. This was mainly caused by the vertical wind speeds induced by topographic effects. Consequently, the pollen grains could travel much larger distances until they were deposited and finally removed from the atmosphere. This is an important finding with respect to the problem of cross pollination. Due to the lack of measurements, a number of parameters had to be assumed. However, the parameterisation proposed may well serve as a starting point of a daily pollen forecast with numerical models.
Much effort has been invested in developing snow models over several decades, resulting in a wide variety of empirical and physically based snow models. For the most part, these models are built on similar principles. The greatest differences are found in how each model parameterizes individual processes (e.g., surface albedo and snow compaction). Parameterization choices naturally span a wide range of complexities. In this study, we evaluate the performance of different snow model parameterizations for hydrological applications using an existing multimodel energy-balance framework and data from two wellinstrumented alpine sites with seasonal snow cover. We also include two temperature-index snow models and an intensive, physically based multilayer snow model in our analyses. Our results show that snow mass observations provide useful information for evaluating the ability of a model to predict snowpack runoff, whereas snow depth data alone are not. For snow mass and runoff, the energy-balance models appear transferable between our two study sites, a behavior which is not observed for snow surface temperature predictions due to site-specificity of turbulent heat transfer formulations. Errors in the input and validation data, rather than model formulation, seem to be the greatest factor affecting model performance. The three model types provide similar ability to reproduce daily observed snowpack runoff when appropriate model structures are chosen. Model complexity was not a determinant for predicting daily snowpack mass and runoff reliably. Our study shows the usefulness of the multimodel framework for identifying appropriate models under given constraints such as data availability, properties of interest and computational cost.
Abstract. Fractional snow-covered area (SCA) is a key parameter in large-scale hydrological, meteorological and regional climate models. Since SCA affects albedos and surface energy balance fluxes, it is especially of interest over mountainous terrain where generally a reduced SCA is observed in large grid cells. Temporal and spatial snow distributions are, however, difficult to measure over complex topography. We therefore present a parameterization of SCA based on a new subgrid parameterization for the standard deviation of snow depth over complex topography. Highly resolved snow depth data at the peak of winter were used from two distinct climatic regions, in eastern Switzerland and in the Spanish Pyrenees. Topographic scaling parameters are derived assuming Gaussian slope characteristics. We use computationally cheap terrain parameters, namely, the correlation length of subgrid topographic features and the mean squared slope. A scale dependent analysis was performed by randomly aggregating the alpine catchments in domain sizes ranging from 50 m to 3 km. For the larger domain sizes, snow depth was predominantly normally distributed. Trends between terrain parameters and standard deviation of snow depth were similar for both climatic regions, allowing one to parameterize the standard deviation of snow depth based on terrain parameters. To make the parameterization widely applicable, we introduced the mean snow depth as a climate indicator. Assuming a normal snow distribution and spatially homogeneous melt, snow-cover depletion (SCD) curves were derived for a broad range of coefficients of variations. The most accurate closed form fit resembled an existing fractional SCA parameterization. By including the subgrid parameterization for the standard deviation of snow depth, we extended the fractional SCA parameterization for topographic influences.For all domain sizes we obtained errors lower than 10 % between measured and parameterized SCA.
A new interception model was integrated in a snowmelt model and for the first time the spatial variability of forest snow was effectively represented due to the inclusion of new forest structure metrics. The model was tested at 1273 field points surrounding Davos, Switzerland, that feature an extremely wide range of canopy and forest structure. The behavior of the new model was compared against a widely applied interception model. Due to the inclusion of novel forest structure parameters (mean distance to canopy and total gap area) in the new model, simulated interception mimicked the horizontal layout of canopy structure, while the standard interception model yielded fairly homogeneous interception estimations even under highly heterogeneous canopy conditions. The large variance of estimated interception between points using the new model translated into significant effects on under-canopy snow water equivalent and snow depth. Precipitation conditions were also analyzed, and further differences between the models were related to storm intensity. In climates characterized by large storm events, the new interception model provides significantly higher interception estimations (i.e., lower under-canopy snow) than the standard model, whereas in climates characterized by small storms events, the new model yields lower interception estimations (i.e., higher under-canopy snow) in areas with moderately sized to large canopy gaps. Key Points:Framework to integrate a new interception model into snowmelt models Model resolves spatial distribution of under-canopy snow in heterogeneous forests Model performs well under a broad range of canopy openness
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