Multi-core-CPU and GPU-accelerated radiative transfer models based on the discrete ordinate method

Physically-based approaches for estimating Leaf Area Index (LAI) using remote sensing data rely on radiative transfer (RT) models. Currently, many RT models are freely available, but determining the appropriate RT model for LAI retrieval is still problematic. This study aims to evaluate the necessity of RT model selection for LAI retrieval and to propose a retrieval methodology using different RT models for different vegetation types. Both actual experimental observations and RT model simulations were used to conduct the evaluation. Each of them includes needleleaf forests and croplands, which have contrasting structural attributes. The scattering from arbitrarily inclined leaves (SAIL) model and the four-scale model, which are 1D and 3D RT models, respectively, were used to simulate the synthetic test datasets. The experimental test dataset was established through two field campaigns conducted in the Heihe River Basin. The results show that the realistic representation of canopy structure in RT models is very important for LAI retrieval. If an unsuitable RT model is used, then the root mean squared error (RMSE) will increase from 0.43 to 0.60 in croplands and from 0.52 to 0.63 in forests. In addition, an RT model’s potential to retrieve LAI is limited by the availability of a priori information on RT model parameters. 3D RT models require more a priori information, which makes them have poorer generalization capability than 1D models. Therefore, physically-based retrieval algorithms should embed more than one RT model to account for the availability of a priori information and variations in structural attributes among different vegetation types.

Radiative transfer models have been widely used to interpret the radar backscatter from forested areas. Most of these models are based on an iterative solution of the radiative transfer equation, usually solved up to first or second order, thus taking into account single and double scattering. Although this method leads to results agreeing well with copolarized backscatter measurements, it produces less accurate estimates for horizontal-vertical (HV) polarization. This paper presents a radiative transfer backscatter model that accounts for multiple scattering by using the discrete ordinate and eigenvalue method applied to a layered medium. Using parameters derived from an architectural tree model, calculations at C- and L-band are compared with HV data acquired for a maritime pine forest in the southwest of France during the Spaceborne Imaging Radar-C missions. Good agreement is found at C-band for all values of forest biomass, and reasonable agreement at L-band for high biomass, when the soil backscatter plays a minor role. For low biomass, the L-band modeling is inadequate because of difficulties in estimating the soil backscatter. Comparison with calculations from a first-order radiative transfer model shows that multiple scattering is significant, especially at C-band.

Ray effects through two- and three-dimensional isotropically scattering, participating media are investigated using four ordinates methods: discrete ordinates, using a classical quadrature scheme and a refined azimuthal discretization around the azimuthal angle endpoints; and finite volume, with and without refined azimuthal discretization around the azimuthal angle endpoints. The discrete ordinates method with refined azimuthal angular discretization consists of a coupling of Gaussian quadrature for polar discretization and control azimuthal angle discretization splitting into a quadruple range. For both the discrete ordinates method with refined azimuthal angular discretization and the finite volume method with refined azimuthal angular discretization, the azimuthal direction is discretized such that azimuthal grid points are close to the azimuthal angle endpoints. Radiative heat transfer through isotropically scattering, participating and optically thin media within enclosures considering uniform and strip diffuse boundary conditions is considered. Excellent agreement between the discrete ordinates method/ finite volume method with refined azimuthal angular discretization and the benchmark literature results is achieved for high-order azimuthal discretization, whereas finer high-order azimuthal discretization is required for the finite volume method. Ray effects are eliminated for combinations of higher-order azimuthal discretization and refined azimuthal discretization around the azimuthal angle endpoints. It has also been found that, in order to eliminate ray effects, the discrete ordinates and finite volume methods’ quadrature sets’ order must be increased as the medium’s aspect ratio decreases or when the size of the diffuse strip of incident radiation on one of the medium’s surfaces is decreased.

Measurements of the directional and spatial distribution of the radiation intensity have been made for an irradiated India ink suspension, and the results have been used to determine radiation fluxes associated with the forward and backward directions. The inherent radiative properties of the ink have also been measured and used with appropriate theories (the discrete ordinate and three-flux methods) to predict the radiation field within the suspension. For the prescribed laboratory conditions, the radiation is concentrated within a cone of half angle θ ≈ 0.85 rad throughout the suspension, and for this region good agreement is obtained between the intensity measurements and predictions based on the discrete ordinate method. Good agreement is also obtained between radiation fluxes measured for the forward direction and predictions based on both the discrete ordinate and three-flux methods. Agreement between the predicted and measured intensities for θ ≳ 0.85 rad, as well as agreement between predicted and measured radiation fluxes for the backward direction, is less satisfactory. Differences are attributed to uncertainties in the radiation intensity and phase function measurements.

Many algorithms for image processing and pattern recognition have recently been implemented on GPU (graphic processing unit) for faster computational times. However, the implementation using GPU encounters two problems. First, the programmer should master the fundamentals of the graphics shading languages that require the prior knowledge on computer graphics. Second, in a job which needs much cooperation between CPU and GPU, which is usual in image processings and pattern recognitions contrary to the graphics area, CPU should generate raw feature data for GPU processing as much as possible to effectively utilize GPU performance. This paper proposes more quick and efficient implementation of neural networks on both GPU and multi-core CPU. We use CUDA (compute unified device architecture) that can be easily programmed due to its simple C language-like style instead of GPU to solve the first problem. Moreover, OpenMP (Open Multi-Processing) is used to concurrently process multiple data with single instruction on multi-core CPU, which results ineffectively utilizing the memories of GPU. In the experiments, we implemented neural networks-based text detection system using the proposed architecture, and the computational times showed about 15 times faster than implementation using CPU and about 4 times faster than implementation on only GPU without OpenMP.

<strong class="journal-contentHeaderColor">Abstract.</strong> With semiconductor technology gradually approaching its physical and thermal limits, Graphics processing unit (GPU) is becoming an attractive solution in many scientific applications due to their high performance. This paper presents an application of GPU accelerators in air quality model. We endeavor to demonstrate an approach that runs a PPM solver of horizontal advection (HADVPPM) for air quality model CAMx on GPU clusters. Specifically, we first convert the HADVPPM to a new Compute Unified Device Architecture C (CUDA C) code to make it computable on the GPU (GPU-HADVPPM). Then, a series of optimization measures are taken, including reducing the CPU-GPU communication frequency, increasing the size of data computation on GPU, optimizing the GPU memory access, and using thread and block indices in order to improve the overall computing performance of CAMx model coupled with GPU-HADVPPM (named as CAMx-CUDA model). Finally, a heterogeneous, hybrid programming paradigm is presented and utilized with the GPU-HADVPPM on GPU clusters with Massage Passing Interface (MPI) and CUDA. Offline experiment results show that running GPU-HADVPPM on one NVIDIA Tesla K40m and NVIDIA Tesla V100 GPU can achieve up to 845.4x and 1113.6x acceleration. By implementing a series of optimization schemes, the CAMx-CUDA model resulted in a 29.0x and 128.4x improvement in computational efficiency using a GPU accelerator card on a K40m and V100 cluster, respectively. In terms of the single-module computational efficiency of GPU-HADVPPM, it can achieve 1.3x and 19.4x speedup on NVIDIA Tesla K40m GPU and NVIDA Tesla V100 GPU respectively. The multi-GPU acceleration algorithm enables 4.5x speedup with 8 CPU cores and 8 GPU accelerators on V100 cluster.

<strong class="journal-contentHeaderColor">Abstract.</strong> With semiconductor technology gradually approaching its physical and thermal limits, Graphics processing unit (GPU) is becoming an attractive solution in many scientific applications due to their high performance. This paper presents an application of GPU accelerators in air quality model. We endeavor to demonstrate an approach that runs a PPM solver of horizontal advection (HADVPPM) for air quality model CAMx on GPU clusters. Specifically, we first convert the HADVPPM to a new Compute Unified Device Architecture C (CUDA C) code to make it computable on the GPU (GPU-HADVPPM). Then, a series of optimization measures are taken, including reducing the CPU-GPU communication frequency, increasing the size of data computation on GPU, optimizing the GPU memory access, and using thread and block indices in order to improve the overall computing performance of CAMx model coupled with GPU-HADVPPM (named as CAMx-CUDA model). Finally, a heterogeneous, hybrid programming paradigm is presented and utilized with the GPU-HADVPPM on GPU clusters with Massage Passing Interface (MPI) and CUDA. Offline experiment results show that running GPU-HADVPPM on one NVIDIA Tesla K40m and NVIDIA Tesla V100 GPU can achieve up to 845.4x and 1113.6x acceleration. By implementing a series of optimization schemes, the CAMx-CUDA model resulted in a 29.0x and 128.4x improvement in computational efficiency using a GPU accelerator card on a K40m and V100 cluster, respectively. In terms of the single-module computational efficiency of GPU-HADVPPM, it can achieve 1.3x and 19.4x speedup on NVIDIA Tesla K40m GPU and NVIDA Tesla V100 GPU respectively. The multi-GPU acceleration algorithm enables 4.5x speedup with 8 CPU cores and 8 GPU accelerators on V100 cluster.

Abstract. Lagrangian models are fundamental tools to study atmospheric transport processes and for practical applications such as dispersion modeling for anthropogenic and natural emission sources. However, conducting large-scale Lagrangian transport simulations with millions of air parcels or more can become rather numerically costly. In this study, we assessed the potential of exploiting graphics processing units (GPUs) to accelerate Lagrangian transport simulations. We ported the Massive-Parallel Trajectory Calculations (MPTRAC) model to GPUs using the open accelerator (OpenACC) programming model. The trajectory calculations conducted within the MPTRAC model were fully ported to GPUs, i.e., except for feeding in the meteorological input data and for extracting the particle output data, the code operates entirely on the GPU devices without frequent data transfers between CPU and GPU memory. Model verification, performance analyses, and scaling tests of the Message Passing Interface (MPI) – Open Multi-Processing (OpenMP) – OpenACC hybrid parallelization of MPTRAC were conducted on the Jülich Wizard for European Leadership Science (JUWELS) Booster supercomputer operated by the Jülich Supercomputing Centre, Germany. The JUWELS Booster comprises 3744 NVIDIA A100 Tensor Core GPUs, providing a peak performance of 71.0 PFlop s−1. As of June 2021, it is the most powerful supercomputer in Europe and listed among the most energy-efficient systems internationally. For large-scale simulations comprising 108 particles driven by the European Centre for Medium-Range Weather Forecasts' fifth-generation reanalysis (ERA5), the performance evaluation showed a maximum speed-up of a factor of 16 due to the utilization of GPUs compared to CPU-only runs on the JUWELS Booster. In the large-scale GPU run, about 67 % of the runtime is spent on the physics calculations, conducted on the GPUs. Another 15 % of the runtime is required for file I/O, mostly to read the large ERA5 data set from disk. Meteorological data preprocessing on the CPUs also requires about 15 % of the runtime. Although this study identified potential for further improvements of the GPU code, we consider the MPTRAC model ready for production runs on the JUWELS Booster in its present form. The GPU code provides a much faster time to solution than the CPU code, which is particularly relevant for near-real-time applications of a Lagrangian transport model.

Purpose: For microdosimetric calculation event-by-event Monte Carlo (MC) simulation is considered the most accurate, but it is very time-consuming. In this work we present an event-by-event MC simulation of low energy electron and proton for accelerated microdosimetric MC simulations on a graphic processing unit (GPU). Methods: The MC simulation of particle was implemented in C and executed on a multi-core CPU, and a commercially available general purpose GPU using the compute unified device architecture (CUDA). Additionally, a hybrid implementation scheme was realized by employing OpenMP and CUDA so that both GPU and multi-core CPU were utilized simultaneously. The two implementation schemes have been tested and compared with the sequential single threaded MC simulation on the CPU. A calculation time comparison was established on the speed-up for a set of benchmarking cases of electron and proton. Results: Dosimetric results were obtained with both the parallel and serial MC codes. A GPU over CPU speed-up of 67.2 and 19.2 times was achieved for 300 eV and 2 keV electron tracks respectively. For proton tracks, the GPU-based code was approximately 5 times faster than the CPU-single-thread code. By incorporating a multi-core CPU and running the MC code simultaneously on the GPU and CPU, an increase of 2%-7% and 20% in the speedup was noticed for electrons and protons tracks respectively. A good dosimetric agreement between the CPU- and GPU-based MC methods was observed for both electrons and proton. Conclusions: A GPU-based MC method for microdosimetric calculations of low energy electron and proton has been presented. The results indicate the capability of our GPU-based implementation for accelerated MC simulations of both electron and proton without loss of accuracy. Lastly, the potential of a hybrid approach by utilizing simultaneously a GPU and a multi-core CPU for further acceleration of MC microdosimetric calculations has been demonstrated.

Watershed analysis, as a fundamental component of digital terrain analysis, is based on the Digital Elevation Model (DEM), which is a grid (raster) model of the Earth surface and topography. Watershed analysis consists of computationally and data intensive computing algorithms that need to be implemented by leveraging parallel and high-performance computing methods and techniques. In this paper, the Multiple Flow Direction (MFD) algorithm for watershed analysis is implemented and evaluated on multi-core Central Processing Units (CPU) and many-core Graphics Processing Units (GPU), which provides significant improvements in performance and energy usage. The implementation is based on NVIDIA CUDA (Compute Unified Device Architecture) implementation for GPU, as well as on OpenACC (Open ACCelerators), a parallel programming model, and a standard for parallel computing. Both phases of the MFD algorithm (i) iterative DEM preprocessing and (ii) iterative MFD algorithm, are parallelized and run over multi-core CPU and GPU. The evaluation of the proposed solutions is performed with respect to the execution time, energy consumption, and programming effort for algorithm parallelization for different sizes of input data. An experimental evaluation has shown not only the advantage of using OpenACC programming over CUDA programming in implementing the watershed analysis on a GPU in terms of performance, energy consumption, and programming effort, but also significant benefits in implementing it on the multi-core CPU.

Lagrangian models are fundamental tools to study atmospheric transport processes and for practical applications such as dispersion modeling for anthropogenic and natural emission sources. However, conducting large-scale Lagrangian transport simulations with millions of air parcels or more can become numerically rather costly. In this study, we assessed the potential of exploiting graphics processing units (GPUs) to accelerate Lagrangian transport simulations. We ported the Massive-Parallel Trajectory Calculations (MPTRAC) model to GPUs using the open accelerator (OpenACC) programming model. The trajectory calculations conducted within the MPTRAC model were fully ported to GPUs, i.e., except for feeding in the meteorological input data and for extracting the particle output data, the code operates entirely on the GPU devices without frequent data transfers between CPU and GPU memory. Model verification, performance analyses, and scaling tests of the MPI/OpenMP/OpenACC hybrid parallelization of MPTRAC were conducted on the JUWELS Booster supercomputer operated by the Jülich Supercomputing Centre, Germany. The JUWELS Booster comprises 3744 NVIDIA A100 Tensor Core GPUs, providing a peak performance of 71.0 PFlop/s. As of June 2021, it is the most powerful supercomputer in Europe and listed among the most energy-efficient systems internationally. For large-scale simulations comprising 108 particles driven by the European Centre for Medium-Range Weather Forecasts' ERA5 reanalysis, the performance evaluation showed a maximum speedup of a factor of 16 due to the utilization of GPUs compared to CPU-only runs on the JUWELS Booster. In the large-scale GPU run, about 67 % of the runtime is spent on the physics calculations, conducted on the GPUs. Another 15 % of the runtime is required for file-I/O, mostly to read the large ERA5 data set from disk. Meteorological data preprocessing on the CPUs also requires about 15 % of the runtime. Although this study identified potential for further improvements of the GPU code, we consider the MPTRAC model ready for production runs on the JUWELS Booster in its present form. The GPU code provides a much faster time to solution than the CPU code, which is particularly relevant for near-real-time applications of a Lagrangian transport model.

Retrieval schemes often use two important components: 1) a radiative transfer model (RTM) inside the retrieval procedure or to construct the learning dataset for the training of the statistical retrieval algorithms and 2) a numerical weather prediction (NWP) model to provide a first guess or, again, to construct a learning dataset. This is particularly true in operational centers. As a consequence, any physical retrieval or similar method is limited by inaccuracies in the RTM and NWP models on which it is based. In this paper, a method for partially compensating for these errors as part of the sensor calibration is presented and evaluated. In general, RTM/NWP errors are minimized as best as possible prior to the training of the retrieval method, and then tolerated. The proposed method reduces these unknown and generally nonlinear residual errors by training a separate preprocessing neural network (NN) to produce calibrated radiances from real satellite data that approximate those radiances produced by the “flawed” NWP and RTM models. The final “compensated/flawed” retrieval assures better internal consistency of the retrieval procedure and then produces more accurate results. To the authors’ knowledge, this type of NN model has not been used yet for this purpose. The calibration approach is illustrated here on one particular application: the retrieval of atmospheric water vapor from the Advanced Microwave Scanning Radiometer for Earth Observing System (AMSR-E) and the Humidity Sounder for Brazil (HSB) measurements for nonprecipitating scenes, over land and ocean. Before being inverted, the real observations are “projected” into the space of the RTM simulation space from which the retrieval is designed. Validation of results is performed with radiosonde measurements and NWP analysis departures. This study shows that the NN calibration of the AMSR-E/HSB observations improves water vapor inversion, over ocean and land, for both clear and cloudy situations. The NN calibration is efficient and very general, being applicable to a large variety of problems. The nonlinearity of the NN allows for the calibration procedure to be state dependent and adaptable to specific cases (e.g., the same correction will not be applied to medium-range measurement and to extreme conditions). Its multivariate nature allows for a full exploitation of the complex correlation structure among the instrument channels, making the calibration of each single channel more robust. The procedure would make it possible to project the satellite observations in a reference observational space defined by radiosonde measurements, RTM simulations, or other instrument observational space.

When calculating the infrared spectral energy distributions (SEDs) of galaxies in radiation-transfer models, the calculation of dust grain temperatures is generally the most time-consuming part of the calculation. Because of its highly parallel nature, this calculation is perfectly suited for massively parallel general-purpose graphics-processing units (GPUs). This paper presents an implementation of the calculation of dust grain equilibrium temperatures on GPUs in the Monte-Carlo radiation transfer code sunrise , using the CUDA API. The GPU can perform this calculation 69 times faster than the eight CPU cores, showing great potential for accelerating calculations of galaxy SEDs.

A new approach of direction discretization and oversampling for 3D anisotropic radiative transfer modeling

This paper describes an efficient implementation of Bayesian hierarchical model for space time variability of latent heat flux. Model parameters are estimated using Gibbs sampler. Many computations in the Gibbs sampling scheme are time intensive. Some time intensive computations in the model are matrix operations such as matrix multiplication, matrix inverse, matrix LU decomposition. We have used graphical processing unit (GPU) to run time intensive matrix operations. Some time intensive operations are transformed to matrix operations to take advantage of GPU. To run the model in GPU model is implemented in Compute Unified Device Architecture (CUDA). Two GPUs are used to run the model one is NVIDIA Graphics card Tesla C2075 with 448 cores and other is NVIDIA Graphics card GT 520 with 48 cores. To study the gain in speedup on the GPU we have implemented the model using single threaded C to run on CPU. A comparative study of implementation on CPU and the two GPUs is carried out for 100 iterations of the Gibbs sampler. We found 30-130 fold speedup on Tesla GPU as compared to single threaded CPU code.KeywordsBayesian hierarchical modelLatent heat fluxGraphical Processing Unit