A multiscale methodology for the determination of the macroscopic optical properties of snow is presented. It consists of solving the coupled volume‐averaged radiative transfer equations for two ...semi‐transparent phases – ice and air – by Monte Carlo ray tracing in an infinite slab via direct pore‐level simulations on the exact 3D microstructure obtained by computed tomography. The overall reflectance and transmittance are computed for slabs of five characteristic snow types subjected to collimated and diffuse incident radiative flux for wavelengths 0.3–3 μm. The effect of simplifying the snow microstructure and/or the radiative transfer model is elucidated by comparing our results to (i) a homogenized radiation model and considering a particulate medium made of optical equivalent grain size spheres (DISORT), or (ii) a multiphase radiation model considering a packed bed of identical overlapping semi‐transparent spheres. The calculations are experimentally validated by transmittance measurements. Significant differences in the macroscopic optical properties are observed when simplifying the snow morphology and the heat transfer model (i.e., homogenized versus multiphase). The proposed approach allows – in addition to determine macroscopic optical properties based on the exact morphology and obtained by advanced heat transfer model – for detailed understanding of radiative heat transfer in snow layers at the pore‐scale level.
Key Points
Snow's optical properties heavily rely on exact microstructure
Direct pore‐level radiation modeling leads to accurate snow's optical properties
In‐dept investigaiton of absorption in snow on the pore‐level scale is achieved
•Radar reflectivity is sensitive to the cutoff point of the snowflake size distribution (SSD).•The choice of SSD cutoff size is crucial for snowfall lacking large snowflakes.•Rather overestimate than ...underestimate maximum snowflake size for snowfall retrievals.•Uncertainty in maximum snowflake size contributes to non-uniqueness of snowfall retrievals.•Defining a characteristic snowflake size mitigates effect of uncertainties in SSD parameters.
The cutoff point of the snowflake (or snow and ice particle) size distribution (SSD) used for modeling the snowfall radar reflectivity and for snowfall retrievals in radar remote sensing is characterized by high uncertainties because only very limited information is available about the maximum snowflake size for different snow types and snowfall conditions. To complement previous works that examined the influence of other snowfall microphysical characteristics on the analysis of snowfall radar reflectivity, this study investigates the impact of SSD cutoff size on modeled snowfall radar reflectivity factors at X, Ku, Ka, and W band and evaluates implications for radar snowfall retrievals. While a detailed assessment can only be realized for snowfall retrieval algorithms individually, this study focuses on identifying typical snowfall characteristics where accounting for uncertainties in SSD cutoff size can be especially important. These include snowflake populations limited to a maximum snowflake size of a few mm or characterized by a small SSD (exponential) slope parameter or a large SSD (gamma distribution) shape parameter. In general, using SSD cutoff sizes that overestimate the maximum snowflake size has a smaller impact on modeled radar reflectivity and simulated snowfall retrievals than underestimating the maximum snowflake size by the same amount. Summarizing SSDs by their median volume diameter, i.e., combining SSD slope parameter, shape parameter, and cutoff size into a single characteristic snowflake size, mitigates the impact that uncertainties in these parameters can have on the analysis of snowfall radar reflectivity and may therefore offer a robust approach for relating radar snowfall retrievals to snowfall microphysics.
Quantifying snow grain size is crucial to analyze radiative transfer and mechanical interactions in the snow cover. We present a nondestructive method for fast measurements of snow optically ...equivalent diameter (OED). The method consists of diffuse near-infrared reflectance measurements by a compact integrating sphere setup to derive OED. This principle is realized in the handheld InfraSnow instrument. The correlation between snow OED and reflectance is calculated by applying Monte Carlo ray tracing to a 3-D implementation of the measurement geometry. Including the geometrical boundary conditions is essential to obtain a good agreement between modeled and measured InfraSnow reflectance values. In addition to InfraSnow reflectance, snow density is required as second input parameter to the OED analysis. Our InfraSnow OED measurements agree with reference OED measurements by micro computed tomography (micro-CT) within 25% for seven of the ten tested snow blocks. Furthermore, the relative differences between both measurement methods are close to the estimated uncertainties of the InfraSnow methodology. If density is measured by micro-CT and then used as InfraSnow model input to derive OED, an average agreement with the reference micro-CT OED values within 13% is found. If density is measured by a permittivity sensor, the average agreement is within 20%.
This study explores the potential of using Doppler (power) spectra from vertically pointing C-band radar birdbath scans to investigate precipitating clouds above the radar. First, the new birdbath ...scan strategy for the network of dual-polarization C-band radars operated by the German Meteorological Service (Deutscher Wetterdienst, DWD) is outlined, and a novel spectral postprocessing and analysis method is presented. The postprocessing algorithm isolates the weather signal from non-meteorological contributions in the radar output based on polarimetric attributes, identifies the statistically significant precipitation modes contained in each Doppler spectrum, and calculates characteristics of every precipitation mode as well as multimodal properties that describe the relation among different modes when more than a single mode is identified. To achieve a high degree of automation and flexibility, the postprocessing chain combines classical signal processing with clustering algorithms. Uncertainties in the calculated modal and multimodal properties are estimated from the small variations associated with smoothing the measured radar signal.
Significant progress has been made in approximating snowflakes with increasingly realistic shape models and then simulating their microwave scattering properties for snowfall remote sensing. This ...study aims to complement prior findings by analyzing the natural variability within snowstorms. The approach consists of (i) deriving the variability of snowflake diameters, aspect ratios, and orientation angles from automated snowflake observations during individual snowstorms, (ii) calculating the corresponding variability of snowflake backscatter cross sections at 24, 35, 94, and 183 GHz, and (iii) evaluating the impact of the analyzed snowflake variability on modeled snowfall equivalent radar reflectivity factors (Ze). For seven snowstorms, the observed natural variability in snowflake diameter, aspect ratio, and orientation leads to distributions of snowflake backscatter cross sections that span up to 6 orders of magnitude. The impact on modeled radar reflectivity is smaller with distributions of Ze values spanning less than 1 order of magnitude and with median absolute deviations and standard deviations of up to 25%, depending on the analyzed frequency and the applied snowflake parameterization. An assessment of different characterizations of snowflake aspect ratio and orientation indicates that a simplistic description of aspect ratios and orientation angles through constant values which do not correspond with the observed snowflake distributions for the analyzed snowstorm can lead to relative differences in modeled Ze of |ΔZe|≥60%. These differences in Ze are generally smaller than uncertainties in Ze associated with the parameterization of snowflake mass but still translate into significant uncertainties for the retrieval of snowfall rates from radar reflectivity measurements.
Key Points
Snowstorms are characterized by high variability of snowflake microstructures and backscatter cross sections
Snowflake variability has a significant impact on modeled snowfall radar reflectivity
The characterization of snowflake aspect ratio and orientation is important for accurately modeling snowfall radar reflectivity
The snowflake microstructure determines the microwave scattering properties of individual snowflakes and has a strong impact on snowfall radar signatures. In this study, individual snowflakes are ...represented by collections of randomly distributed ice spheres where the size and number of the constituent ice spheres are specified by the snowflake mass and surface-area-to-volume ratio (SAV) and the bounding volume of each ice sphere collection is given by the snowflake maximum dimension. Radar backscatter cross sections for the ice sphere collections are calculated at X-, Ku-, Ka-, and W-band frequencies and then used to model triple-frequency radar signatures for exponential snowflake size distributions (SSDs). Additionally, snowflake complexity values obtained from high-resolution multi-view snowflake images are used as an indicator of snowflake SAV to derive snowfall triple-frequency radar signatures. The modeled snowfall triple-frequency radar signatures cover a wide range of triple-frequency signatures that were previously determined from radar reflectivity measurements and illustrate characteristic differences related to snow type, quantified through snowflake SAV, and snowflake size. The results show high sensitivity to snowflake SAV and SSD maximum size but are generally less affected by uncertainties in the parameterization of snowflake mass, indicating the importance of snowflake SAV for the interpretation of snowfall triple-frequency radar signatures.
Cloud and precipitation processes are still a main source of
uncertainties in numerical weather prediction and climate change
projections. The Priority Programme “Polarimetric Radar Observations meet
...Atmospheric Modelling (PROM)”, funded by the German Research Foundation
(Deutsche Forschungsgemeinschaft, DFG), is guided by the hypothesis that
many uncertainties relate to the lack of observations suitable to challenge
the representation of cloud and precipitation processes in atmospheric
models. Such observations can, however, at present be provided by the
recently installed dual-polarization C-band weather radar network of the
German national meteorological service in synergy with cloud radars and
other instruments at German supersites and similar national networks
increasingly available worldwide. While polarimetric radars potentially
provide valuable in-cloud information on hydrometeor type, quantity,
and microphysical cloud and precipitation processes, and atmospheric models
employ increasingly complex microphysical modules, considerable knowledge
gaps still exist in the interpretation of the observations and in the
optimal microphysics model process formulations. PROM is a coordinated
interdisciplinary effort to increase the use of polarimetric radar
observations in data assimilation, which requires a thorough evaluation and
improvement of parameterizations of moist processes in atmospheric models.
As an overview article of the inter-journal special issue “Fusion of radar
polarimetry and numerical atmospheric modelling towards an improved
understanding of cloud and precipitation processes”, this article outlines
the knowledge achieved in PROM during the past 2 years and gives
perspectives for the next 4 years.
The snowflake microstructure determines the microwave scattering properties of individual snowflakes and has a strong impact on snowfall radar signatures. In this study, individual snowflakes are ...represented by collections of randomly distributed ice spheres where the size and number of the constituent ice spheres are specified by the snowflake mass and surface-area-to-volume ratio (SAV) and the bounding volume of each ice sphere collection is given by the snowflake maximum dimension. Radar backscatter cross sections for the ice sphere collections are calculated at X-, Ku-, Ka-, and W-band frequencies and then used to model triple-frequency radar signatures for exponential snowflake size distributions (SSDs). Additionally, snowflake complexity values obtained from high-resolution multi-view snowflake images are used as an indicator of snowflake SAV to derive snowfall triple-frequency radar signatures. The modeled snowfall triple-frequency radar signatures cover a wide range of triple-frequency signatures that were previously determined from radar reflectivity measurements and illustrate characteristic differences related to snow type, quantified through snowflake SAV, and snowflake size. The results show high sensitivity to snowflake SAV and SSD maximum size but are generally less affected by uncertainties in the parameterization of snowflake mass, indicating the importance of snowflake SAV for the interpretation of snowfall triple-frequency radar signatures.
Snow density is one of the key properties to characterize a snow cover. We present diffuse near-infrared transmittance measurements with an integrating sphere setup in the laboratory. We analyze 8 ...snow samples taken from melt forms, decomposed, rounded, faceted and machine made snow. Reference measurements of specific surface area (optically equivalent grain size) and density are done by micro-computed tomography and used as input for transmittance calculations. A diffuse flux extinction model cannot be applied to simulate transmittance as our setup cannot be approximated by an infinite snow block thickness. Calculations with a more intricate radiative transfer model (DISORT) agree with our measurements within the estimated grain size and density variability for all probed natural snow types. Only our machine made snow shows a morphology which cannot be modeled by DISORT. Thus, our results show for the first time a direct experimental correlation between transmittance and snow specific surface area and density without the need for an empirical fitting parameter. We feel this to be an important step towards a possible high-resolution, quantitative optical measurement method to determine snow density in combination with an independent specific surface area measurement.
Chromosome structure in mammals is thought to regulate transcription by modulating three-dimensional interactions between enhancers and promoters, notably through CTCF-mediated loops and ...topologically associating domains (TADs)
. However, how chromosome interactions are actually translated into transcriptional outputs remains unclear. Here, to address this question, we use an assay to position an enhancer at large numbers of densely spaced chromosomal locations relative to a fixed promoter, and measure promoter output and interactions within a genomic region with minimal regulatory and structural complexity. A quantitative analysis of hundreds of cell lines reveals that the transcriptional effect of an enhancer depends on its contact probabilities with the promoter through a nonlinear relationship. Mathematical modelling suggests that nonlinearity might arise from transient enhancer-promoter interactions being translated into slower promoter bursting dynamics in individual cells, therefore uncoupling the temporal dynamics of interactions from those of transcription. This uncovers a potential mechanism of how distal enhancers act from large genomic distances, and of how topologically associating domain boundaries block distal enhancers. Finally, we show that enhancer strength also determines absolute transcription levels as well as the sensitivity of a promoter to CTCF-mediated transcriptional insulation. Our measurements establish general principles for the context-dependent role of chromosome structure in long-range transcriptional regulation.
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