scholarly journals Reduction of radiation biases by incorporating the missing cloud variability by means of downscaling techniques: a study using the 3-D MoCaRT model

2012 ◽  
Vol 5 (9) ◽  
pp. 2261-2276 ◽  
Author(s):  
S. Gimeno García ◽  
T. Trautmann ◽  
V. Venema
Keyword(s):  
Radiative Transfer ◽  
Spatial Resolution ◽  
Heterogeneous Media ◽  
Monte Carlo Model ◽  
Computational Cost ◽  
Three Dimensional ◽  
Accurate Solution ◽  
Stochastic Methods ◽  
Climate Modelling ◽  
One Dimensional

Abstract. Handling complexity to the smallest detail in atmospheric radiative transfer models is unfeasible in practice. On the one hand, the properties of the interacting medium, i.e., the atmosphere and the surface, are only available at a limited spatial resolution. On the other hand, the computational cost of accurate radiation models accounting for three-dimensional heterogeneous media are prohibitive for some applications, especially for climate modelling and operational remote-sensing algorithms. Hence, it is still common practice to use simplified models for atmospheric radiation applications. Three-dimensional radiation models can deal with complex scenarios providing an accurate solution to the radiative transfer. In contrast, one-dimensional models are computationally more efficient, but introduce biases to the radiation results. With the help of stochastic models that consider the multi-fractal nature of clouds, it is possible to scale cloud properties given at a coarse spatial resolution down to a higher resolution. Performing the radiative transfer within the cloud fields at higher spatial resolution noticeably helps to improve the radiation results. We present a new Monte Carlo model, MoCaRT, that computes the radiative transfer in three-dimensional inhomogeneous atmospheres. The MoCaRT model is validated by comparison with the consensus results of the Intercomparison of Three-Dimensional Radiation Codes (I3RC) project. In the framework of this paper, we aim at characterising cloud heterogeneity effects on radiances and broadband fluxes, namely: the errors due to unresolved variability (the so-called plane parallel homogeneous, PPH, bias) and the errors due to the neglect of transversal photon displacements (independent pixel approximation, IPA, bias). First, we study the effect of the missing cloud variability on reflectivities. We will show that the generation of subscale variability by means of stochastic methods greatly reduce or nearly eliminate the reflectivity biases. Secondly, three-dimensional broadband fluxes in the presence of realistic inhomogeneous cloud fields sampled at high spatial resolutions are calculated and compared to their one-dimensional counterparts at coarser resolutions. We found that one-dimensional calculations at coarsely resolved cloudy atmospheres systematically overestimate broadband reflected and absorbed fluxes and underestimate transmitted ones.

scholarly journals Reduction of radiation biases by incorporating the missing cloud variability via downscaling techniques: a study using the 3-D MoCaRT model

2012 ◽  
Vol 5 (1) ◽  
pp. 1543-1573
Author(s):  
S. Gimeno García ◽  
T. Trautmann ◽  
V. Venema
Keyword(s):  
Radiative Transfer ◽  
Spatial Resolution ◽  
Heterogeneous Media ◽  
Climate Modeling ◽  
Computational Cost ◽  
Three Dimensional ◽  
Accurate Solution ◽  
Stochastic Methods ◽  
One Dimensional ◽  
The One

Abstract. To handle complexity to the smallest detail in atmospheric radiative transfer models is in practice unfeasible. On the one hand, the properties of the interacting medium, i.e. the atmosphere and the surface, are only available at a limited spatial resolution. On the other hand, the computational cost of accurate radiation models accounting for three-dimensional heterogeneous media are prohibitive for some applications, esp. for climate modeling and operational remote sensing algorithms. Hence, it is still common practice to use simplified models for atmospheric radiation applications. Three-dimensional radiation models can deal with much more complexity than the one-dimensional ones providing a more accurate solution of the radiative transfer. In turn, one-dimensional models introduce biases to the radiation results. With the help of stochastic models that consider the multi-fractal nature of clouds, it is possible to scale cloud properties given at a coarse spatial resolution down to a finer resolution. Performing the radiative transfer within the spatially fine-resolved cloud fields noticeably helps to improve the radiation results. In the framework of this paper, we aim at characterizing cloud heterogeneity effects on radiances and broadband flux densities, namely: the errors due to unresolved variability (the so-called plane parallel homogeneous, PPH, bias) and the errors due to the neglect of transversal photon displacements (independent pixel approximation, IPA, bias). First, we study the effect of the missing cloud variability on reflectivities. We will show that the generation of subscale variability by means of stochastic methods greatly reduce or nearly eliminate the reflectivity biases. Secondly, three-dimensional broadband flux densities in the presence of realistic inhomogeneous cloud fields sampled at fine spatial resolutions are calculated and compared to their one-dimensional counterparts at coarser resolutions.

scholarly journals Three-dimensional effects in polarization signatures as observed from precipitating clouds by low frequency ground-based microwave radiometers

2006 ◽  
Vol 6 (3) ◽  
pp. 5427-5456
Author(s):  
A. Battaglia ◽  
C. Simmer ◽  
H. Czekala
Keyword(s):  
Radiative Transfer ◽  
Monte Carlo Model ◽  
Three Dimensional ◽  
Low Frequency ◽  
Radiative Transfer Model ◽  
Observation Angle ◽  
Transfer Model ◽  
One Dimensional ◽  
Dimensional Effects ◽  
The Impact

Abstract. Consistent negative polarization differences (i.e. differences between the vertical and the horizontal brightness temperature) are observed when looking at precipitating systems by ground-based radiometers at slant angles. These signatures can be partially explained by one-dimensional radiative transfer computations that include oriented non-spherical raindrops. However some cases are characterized by polarization values that exceed differences expected from one-dimensional radiative transfer. A three-dimensional fully polarized Monte Carlo model has been used to evaluate the impact of the horizontal finiteness of rain shafts with different rain rates at 10, 19, and 30 GHz. The results show that because of the reduced slant optical thickness in finite clouds, the polarization signal can strongly differ from its one-dimensional counterpart. At the higher frequencies and when the radiometer is positioned underneath the cloud, significantly higher negative values for the polarization are found which are also consistent with some observations. When the observation point is located outside of the precipitating cloud, typical polarization patterns (with troughs and peaks) as a function of the observation angle are predicted. An approximate 1-D slant path radiative transfer model is considered as well and results are compared with the full 3-D simulations to investigate whether or not three-dimensional effects can be explained by geometry effects alone. The study has strong relevance for low-frequency passive microwave polarimetric studies.

Computational Cost and Accuracy in Calculating Three-Dimensional Radiative Transfer: Results for New Implementations of Monte Carlo and SHDOM

2009 ◽  
Vol 66 (10) ◽  
pp. 3131-3146 ◽  
Author(s):  
Robert Pincus ◽  
K. Franklin Evans
Keyword(s):  
Monte Carlo ◽  
Radiative Transfer ◽  
Variance Reduction ◽  
Parallel Implementation ◽  
Monte Carlo Model ◽  
Computational Cost ◽  
Three Dimensional ◽  
Computation Time ◽  
Flux Divergence ◽  
Pixel Intensity

Abstract This paper examines the tradeoffs between computational cost and accuracy for two new state-of-the-art codes for computing three-dimensional radiative transfer: a community Monte Carlo model and a parallel implementation of the Spherical Harmonics Discrete Ordinate Method (SHDOM). Both codes are described and algorithmic choices are elaborated. Two prototype problems are considered: a domain filled with stratocumulus clouds and another containing scattered shallow cumulus, absorbing aerosols, and molecular scatterers. Calculations are performed for a range of resolutions and the relationships between accuracy and computational cost, measured by memory use and time to solution, are compared. Monte Carlo accuracy depends primarily on the number of trajectories used in the integration. Monte Carlo estimates of intensity are computationally expensive and may be subject to large sampling noise from highly peaked phase functions. This noise can be decreased using a range of variance reduction techniques, but these techniques can compromise the excellent agreement between the true error and estimates obtained from unbiased calculations. SHDOM accuracy is controlled by both spatial and angular resolution; different output fields are sensitive to different aspects of this resolution, so the optimum accuracy parameters depend on which quantities are desired as well as on the characteristics of the problem being solved. The accuracy of SHDOM must be assessed through convergence tests and all results from unconverged solutions may be biased. SHDOM is more efficient (i.e., has lower error for a given computational cost) than Monte Carlo when computing pixel-by-pixel upwelling fluxes in the cumulus scene, whereas Monte Carlo is more efficient in computing flux divergence and downwelling flux in the stratocumulus scene, especially at higher accuracies. The two models are comparable for downwelling flux and flux divergence in cumulus and upwelling flux in stratocumulus. SHDOM is substantially more efficient when computing pixel-by-pixel intensity in multiple directions; the models are comparable when computing domain-average intensities. In some cases memory use, rather than computation time, may limit the resolution of SHDOM calculations.

scholarly journals Three-dimensional effects in polarization signatures as observed from precipitating clouds by low frequency ground-based microwave radiometers

2006 ◽  
Vol 6 (12) ◽  
pp. 4383-4394 ◽  
Author(s):  
A. Battaglia ◽  
C. Simmer ◽  
H. Czekala
Keyword(s):  
Radiative Transfer ◽  
Monte Carlo Model ◽  
Three Dimensional ◽  
Low Frequency ◽  
Radiative Transfer Model ◽  
Observation Angle ◽  
Transfer Model ◽  
One Dimensional ◽  
Dimensional Effects ◽  
The Impact

Abstract. Consistent negative polarization differences (i.e. differences between the vertical and the horizontal brightness temperature) are observed when looking at precipitating systems by ground-based radiometers at slant angles. These signatures can be partially explained by one-dimensional radiative transfer computations that include oriented non-spherical raindrops. However some cases are characterized by polarization values that exceed differences expected from one-dimensional radiative transfer. A three-dimensional fully polarized Monte Carlo model has been used to evaluate the impact of the horizontal finiteness of rain shafts with different rain rates at 10, 19, and 30 GHz. The results show that because of the reduced slant optical thickness in finite clouds, the polarization signal can strongly differ from its one-dimensional counterpart. At the higher frequencies and when the radiometer is positioned underneath the cloud, significantly higher negative values for the polarization are found which are also consistent with some observations. When the observation point is located outside of the precipitating cloud, typical polarization patterns (with troughs and peaks) as a function of the observation angle are predicted. An approximate 1-D slant path radiative transfer model is considered as well and results are compared with the full 3-D simulations to investigate whether or not three-dimensional effects can be explained by geometry effects alone. The study has strong relevance for low-frequency passive microwave polarimetric studies.

Evaluation of shortwave radiation fluxes in the multi-layer SPARTACUS-Urban scheme using DART

2021 ◽  
Author(s):  
Megan Stretton ◽  
William Morrison ◽  
Robin Hogan ◽  
Sue Grimmond
Keyword(s):  
Radiative Transfer ◽  
Urban Form ◽  
Climate Models ◽  
Weather Prediction ◽  
Computational Cost ◽  
Three Dimensional ◽  
Shortwave Radiation ◽  
Radiative Transfer Model ◽  
Transfer Model ◽  
Urban Structure

<p>The heterogenous structure of cities impacts radiative exchanges (e.g. albedo and heat storage). Numerical weather prediction (NWP) models often characterise the urban structure with an infinite street canyon – but this does not capture the three-dimensional urban form. SPARTACUS-Urban (SU) - a fast, multi-layer radiative transfer model designed for NWP - is evaluated using the explicit Discrete Anisotropic Radiative Transfer (DART) model for shortwave fluxes across several model domains – from a regular array of cubes to real cities .</p><p>SU agrees with DART (errors < 5.5% for all variables) when the SU assumptions of building distribution are fulfilled (e.g. randomly distribution). For real-world areas with pitched roofs, SU underestimates the albedo (< 10%) and shortwave transmission to the surface (< 15%), and overestimates wall-plus-roof absorption (9-27%), with errors increasing with solar zenith angle. SU should be beneficial to weather and climate models, as it allows more realistic urban form (cf. most schemes) without large increases in computational cost.</p>

scholarly journals High resolution and Monte Carlo additions to the SASKTRAN radiative transfer model

2015 ◽  
Vol 8 (3) ◽  
pp. 3357-3397 ◽  
Author(s):  
D. J. Zawada ◽  
S. R. Dueck ◽  
L. A. Rieger ◽  
A. E. Bourassa ◽  
N. D. Lloyd ◽  
...  
Keyword(s):  
Monte Carlo ◽  
High Resolution ◽  
Radiative Transfer ◽  
Spatial Resolution ◽  
High Spatial Resolution ◽  
Reference Model ◽  
Monte Carlo Model ◽  
Radiative Transfer Model ◽  
Transfer Model ◽  
Systematic Bias

Abstract. The OSIRIS instrument on board the Odin spacecraft has been measuring limb scattered radiance since 2001. The vertical radiance profiles measured as the instrument nods are inverted, with the aid of the SASKTRAN radiative transfer model, to obtain vertical profiles of trace atmospheric constituents. Here we describe two newly developed modes of the SASKTRAN radiative transfer model: a high spatial resolution mode, and a Monte Carlo mode. The high spatial resolution mode is a successive orders model capable of modelling the multiply scattered radiance when the atmosphere is not spherically symmetric; the Monte Carlo mode is intended for use as a highly accurate reference model. It is shown that the two models agree in a wide variety of solar conditions to within 0.2%. As an example case for both models, Odin-OSIRIS scans were simulated with the Monte Carlo model and retrieved using the high resolution model. A systematic bias of up to 4% in retrieved ozone number density between scans where the instrument is scanning up or scanning down was identified. It was found that calculating the multiply scattered diffuse field at five discrete solar zenith angles is sufficient to eliminate the bias for typical Odin-OSIRIS geometries.

Verification of a Finite Element Method for Solving One-Dimensional Equations of Blood Flow Incorporating a Viscoelastic Wall Model

2009 ◽  
Author(s):  
Rashmi Raghu ◽  
Charles A. Taylor
Keyword(s):  
Blood Flow ◽  
Surgical Planning ◽  
Computational Cost ◽  
Three Dimensional ◽  
Momentum Equation ◽  
Cross Sectional ◽  
One Dimensional ◽  
The One ◽  
Modeling Flow ◽  
Three Dimensional Simulations

The one-dimensional (1-D) equations of blood flow consist of the conservation of mass equation, balance of momentum equation and a wall constitutive equation with arterial flow rate, cross-sectional area and pressure as the variables. 1-D models of blood flow enable the solution of large networks of blood vessels including wall deformability. Their level of detail is appropriate for applications such as modeling flow and pressure waves in surgical planning and their computational cost is low compared to three-dimensional simulations.

Three Dimensional Radiative Transfer in ICON-LEM

2020 ◽  
Author(s):  
Fabian Jakub ◽  
Bernhard Mayer
Keyword(s):  
Radiative Transfer ◽  
Detrimental Effect ◽  
Energy Transport ◽  
Three Dimensional ◽  
Cloud Formation ◽  
One Dimensional ◽  
3D Effects ◽  
Computational Simplicity ◽  
Boundary Layer Dynamics ◽  
Side Illumination

<pre class="moz-quote-pre">Recent studies have shown that the effects of three dimensional radiative transfer may impact cloud formation and precipitation. While one-dimensional solvers are favoured due to their computational simplicity, they do however neglect any horizontal energy transport. In particular, the 1D approximation neglects 3D effects such as cloud side illumination and the displacement of the cloud's shadow at the surface which are relevant whenever the sun is not in the zenith. This has a detrimental effect on the results of high resolution simulations. 3D radiative transfer has the potential to considerably change the boundary layer dynamics, the evolution of clouds, their lifetime and precipitation onset. To this date, studies that investigate the influence of 3D effects on realistic NWP settings are rare, primarily because there haven't been 3D radiative transfer solvers around that were fast enough to be run interactively in a forecast simulation. For that purpose we adapted the TenStream solver (parallel 3D radiative transfer solver for LES) to unstructured meshes and coupled it to ICON-LEM. We will present the new solver in the context of ICON-LEM simulations, the methodologies used and its characteristics.</pre>

LOD-MS for Gross-Pitaevskii Equation in Bose-Einstein Condensates

2013 ◽  
Vol 14 (1) ◽  
pp. 219-241 ◽  
Author(s):  
Linghua Kong ◽  
Jialin Hong ◽  
Jingjing Zhang
Keyword(s):  
Energy Conservation ◽  
Computational Cost ◽  
Three Dimensional ◽  
Schrodinger Equations ◽  
Pitaevskii Equation ◽  
Schrödinger Equations ◽  
One Dimensional ◽  
Exactly Solvable ◽  
Bose Einstein ◽  
Energy Conservation Law

AbstractThe local one-dimensional multisymplectic scheme (LOD-MS) is developed for the three-dimensional (3D) Gross-Pitaevskii (GP) equation in Bose-Einstein condensates. The idea is originated from the advantages of multisymplectic integrators and from the cheap computational cost of the local one-dimensional (LOD) method. The 3D GP equation is split into three linear LOD Schrödinger equations and an exactly solvable nonlinear Hamiltonian ODE. The three linear LOD Schrödinger equations are multisymplectic which can be approximated by multisymplectic integrator (MI). The conservative properties of the proposed scheme are investigated. It is mass-preserving. Surprisingly, the scheme preserves the discrete local energy conservation laws and global energy conservation law if the wave function is variable separable. This is impossible for conventional MIs in nonlinear Hamiltonian context. The numerical results show that the LOD-MS can simulate the original problems very well. They are consistent with the numerical analysis.

scholarly journals Analysis of the Discrete Theory of Radiative Transfer in the Coupled “Ocean–Atmosphere” System: Current Status, Problems and Development Prospects

2020 ◽  
Vol 8 (3) ◽  
pp. 202 ◽  
Author(s):  
Viktor P. Afanas’ev ◽  
Alexander Yu. Basov ◽  
Vladimir P. Budak ◽  
Dmitry S. Efremenko ◽  
Alexander A. Kokhanovsky
Keyword(s):  
Radiative Transfer ◽  
Three Dimensional ◽  
Operator Method ◽  
Current Status ◽  
One Dimensional ◽  
Current State ◽  
The Matrix ◽  
The One ◽  
Discrete Theory ◽  
Development Prospects

In this paper, we analyze the current state of the discrete theory of radiative transfer. One-dimensional, three-dimensional and stochastic radiative transfer models are considered. It is shown that the discrete theory provides a unique solution to the one-dimensional radiative transfer equation. All approximate solution techniques based on the discrete ordinate formalism can be derived based on the synthetic iterations, the small-angle approximation, and the matrix operator method. The possible directions for the perspective development of radiative transfer are outlined.

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