# Parallel Computation of EM Backscattering from Large Three-Dimensional Sea Surface with CUDA

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Electromagnetic Backscattering from an Electrically Large Sea Surface

#### 2.1. Slope-Deterministic Kirchhoff Approximation Model (SDKAM)

#### 2.2. Slope-Deterministic Two-Scale Model (SDTSM)

#### 2.3. Slope-Deterministic Composite Scattering Model (SDCSM)

## 3. NVIDIA Tesla K80 GPU Features and GPU-Based SDCSM Implemented

#### 3.1. NVIDIA Tesla K80 GPU Haredare Resource

#### 3.2. SDCSM Parallel Computing with CUDA

- Initialize the size of electrically large sea surface ${L}_{x}\times {L}_{y}$, the spatial step of the sea surface $\Delta x\times \Delta y$, the wind speed ${u}_{10}$, the wind direction ${\varphi}_{w}$, the incident and scattering angles ${\theta}_{i}$ and ${\theta}_{s}$, the incident and scattering azimuth angles ${\varphi}_{i}$ and ${\varphi}_{s}$, the frequency $f$, the grid and block sizes corresponding to the CUDA program.
- Transfer the electrically large sea surface data from the CPU to the GPU.
- Compute the NRCS of individual triangular meshing on the electrically large sea surface independently in parallel on the GPU by all threads within a block.
- Copy the results from the GPU back to the CPU.

## 4. Initial Parallel Implemented and Further Optimization

#### 4.1. Initial Parallel Implemented

#### 4.2. Further Optimization with Coalesced Global Memory Access

#### 4.3. Further Optimization with Constant Memory

#### 4.4. Further Optimization with Fast Math Compiler Option

#### 4.5. Further Optimization with Asynchronous Data Transfer (ADT)

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Alper, W.R.; Bruening, C. On the relative importance of motion-related contribution to the SAR imaging mechanism of ocean surface waves. IEEE Trans. Geosci. Remote Sens.
**1986**, 24, 873–885. [Google Scholar] [CrossRef] - Li, J.; Zhang, M.; Fan, W.; Nie, D. Facet-based investigation on microwave backscattering from sea surface with breaking waves: Sea spikes and SAR imaging. IEEE Trans. Geosci. Remote Sens.
**2017**, 55, 2313–2325. [Google Scholar] [CrossRef] - Li, X.; Xu, X. Scattering and Doppler spectral analysis for two-dimensional linear and nonlinear sea surface. IEEE Trans. Geosci. Remote Sens.
**2011**, 49, 603–611. [Google Scholar] [CrossRef] - Joung, S.J.; Shelton, J. 3 Dimensional ocean wave model using directional wave spectra for limited capacity computers. In Proceedings of the OCEANS 91 Proceedings, Honolulu, HA, USA, 1–3 October 1991. [Google Scholar]
- Linghu, L.; Wu, J.; Huang, B.; Wu, Z.; Shi, M. GPU-accelerated massively parallel computation of electromagnetic scattering of a time-evolving oceanic surface model I: Time-evolving oceanic surface generation. IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens.
**2018**, 11, 1–11. [Google Scholar] [CrossRef] - Ulaby, F.T.; Moore, R.K.; Fung, A.K. Microwave Remote Sensing: Active and Passive; Artech House: Norwood, MA, USA, 1986. [Google Scholar]
- Beckmann, P.; Spizzichino, A. The Scattering of Electromagnetic Waves from Rough Surface; Artech House: Norwood, MA, USA, 1963. [Google Scholar]
- Rice, S.O. Reflection of electromagnetic waves from slightly rough surface. Commun. Pure Appl. Math.
**1951**, 4, 351–378. [Google Scholar] [CrossRef] - Bourlier, C.; Berginc, G. Microwave analytical backscattering models from randomly rough anisotropic sea surface-comparison with experimental data in C and Ku bands. PIER
**2002**, 37, 31–78. [Google Scholar] [CrossRef] - Bourlier, C. Azimuthal harmonic coefficients of the microwave backscattering from a non-Gaussian ocean surface with the first-order SSA method. IEEE Trans. Geosci. Remote Sens.
**2004**, 42, 2600–2611. [Google Scholar] [CrossRef] - Bass, F.G.; Fuks, I.M. Wave Scattering from Statistically Rough Surface; Pergamon Press Oxford: New York, NY, USA, 1979; pp. 418–442. [Google Scholar]
- Wu, Z.; Zhang, J.; Guo, L.; Zhou, P. An improved two-scale mode with volume scattering for the dynamic ocean surface. PIER
**2009**, 89, 39–46. [Google Scholar] [CrossRef] - Fung, A.K.; Lee, K. A semi-empirical sea-spectrum model for scattering coefficient estimation. IEEE J. Ocea. Eng.
**1982**, 7, 166–176. [Google Scholar] [CrossRef] - Chen, H.; Zhang, M.; Zhao, Y.; Luo, W. An efficient slope-deterministic facet model for SAR imagery simulation of marine scene. IEEE Trans. Antennas Propag.
**2010**, 58, 3751–3756. [Google Scholar] [CrossRef] - Chen, H.; Zhang, M.; Nie, D. Robust semi-deterministic facet model for fast estimation on EM scattering from ocean-like surface. PIER
**2009**, 18, 347–363. [Google Scholar] [CrossRef] - Lee, C.A.; Gasster, S.D.; Plaza, A.; Chang, C.-I.; Huang, B. Recent developments in high performance computing for remote sensing: A review. IEEE J. Sel. Top. Appl. Earth Observ.
**2011**, 4, 508–527. [Google Scholar] [CrossRef] - Wilt, N. The CUDA Handbook: A Comprehensive Guide to GPU Programming, 1st ed; Addision-Wesley: Crawfordsville, IN, USA, 2013. [Google Scholar]
- Sanders, J.; Kandrot, E. CUDA by Example: An Introduction to General-Purpose GPU Programming, 1st ed; Addision-Wesley: Ann Arbor, MI, USA, 2010. [Google Scholar]
- Su, X.; Wu, J.; Huang, B.; Wu, Z. GPU-accelerated computation of electromagnetic scattering of a double-layer vegetation model. IEEE J. Sel. Topics Appl. Earth Observ. Remote Sens.
**2013**, 6, 1799–1806. [Google Scholar] [CrossRef] - Wu, J.; Deng, L.; Jeon, G. Image autoregressive interpolation model using GPU-parallel optimization. IEEE Trans. Ind. Inf.
**2017**, 14, 426–436. [Google Scholar] [CrossRef] - Jiang, W.; Zhang, M.; Wei, P.; Yuan, X. CUDA-based SSA method in application to calculating EM scattering from large two-dimensional rough surface. IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens.
**2014**, 7, 1372–1382. [Google Scholar] [CrossRef] - Jiang, W.; Zhang, M.; Wei, P.; Nie, D. Spectral decomposition modeling method and its application to EM scattering calculation of large rough surface with SSA method. IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens.
**2015**, 8, 1848–1854. [Google Scholar] [CrossRef] - Guo, X.; Wu, J.; Wu, Z.; Huang, B. Parallel computation of aerial target reflection of background infrared radiation: Performance comparison of OpenMP, OpenACC, and CUDA implementations. IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens.
**2016**, 9, 1653–1662. [Google Scholar] [CrossRef] - Mielikainen, J.; Huang, B.; Huang, H.A.; Goldberg, M.D. Improved GPU/CUDA based parallel weather and research forecast (WRF) single moment 5-class (WSM5) cloud microphysics. IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens.
**2012**, 5, 1256–1265. [Google Scholar] [CrossRef] - Plant, W.J. Studies of backscattered sea return with a CW, dual-frequency, X-band radar. IEEE Trans. Antennas Propag.
**1977**, 25, 28–36. [Google Scholar] [CrossRef] - Fuks, I.M. Theory of radio wave scattering at a rough sea surface. Soviet Radiophys.
**1966**, 9, 513–519. [Google Scholar] [CrossRef] - Brown, G.S. Backscattering from a Gaussian-distributed, perfectly conducting rough surface. IEEE Trans. Antennas Propag.
**1985**, 10, 445–451. [Google Scholar] [CrossRef] - Efouhaily, T.; Chapron, B.; Katsaros, K.; Vandemark, D. A unified directional spectrum for long and short wind-driven waves. J. Geophys. Res.
**1997**, 102, 15781–15796. [Google Scholar] [CrossRef][Green Version] - Voronovich, A.G.; Avorotni, V.U. Theoretical model for scattering of radar signals in Ku- and C-bands from a rough sea surface with breaking waves. Wave Random Complex Media
**2001**, 11, 247–269. [Google Scholar] [CrossRef]

**Figure 1.**Illustration of electromagnetic (EM) scattering from an electrically large oceanic surface.

**Figure 3.**Normalized radar cross section (NRCS) of EM backscattering echoes from an electrically large sea surface versus the incident angles based on the Slope-Deterministic Kirchhoff Approximation Model (SDKAM), Slope-Deterministic Two-Scale Model (SDTSM), and slope-deterministic composite scattering model (SDCSM) when cutoff number is equal to k/3.

**Figure 4.**NRCS of electrically large oceanic surface compared with the experiment data when the frequency is equal to 13.9 GHz at different wind speed.

**Figure 8.**Schematic of the usage of shared memory in place of global memory for data transfers between global memory and the device.

**Figure 9.**Schematic of the usage of constant memory for avoiding repeated calculations during the kernel execution.

**Figure 11.**Description of the percentage of GPU runtime consumed by different GPU operations after using the fast math compiler option.

**Figure 13.**Runtime for the GPU-based SDCSM program with and without asynchronous data transfer (ADT) optimization.

**Table 1.**Runtime and speedup for the graphics processing units (GPU)-based SDCSM program compared with conventional serial C program.

Total Time | Read File | Execution Time | I/O | |
---|---|---|---|---|

Serial program (ms) | 47,593.6 | -- | -- | -- |

Parallel program (ms) | 86.31 | 8.663 | 39.99 | 37.657 |

speedup | 551.4× | -- | -- | -- |

**Table 2.**Runtime and speedup for the GPU-based SDCSM program with coalesced global memory access optimization.

CPU Runtime (ms) | GPU-Runtime (ms) | Speedup | |
---|---|---|---|

Serial program | 47,593.6 | -- | -- |

Initial Parallel program | 86.31 | 551.4x | |

Utilizing shared memory | 84.03 | 566.4x |

**Table 3.**Runtime and speedup for the GPU-based SDCSM program with constant memory access optimization.

CPU Runtime (ms) | GPU-Runtime (ms) | Speedup | |
---|---|---|---|

Serial program | 47,593.6 | -- | -- |

Non-optimized | 84.03 | 566.4× | |

Optimized | 82.56 | 576.5× |

**Table 4.**The results of mean absolute error (MAE) and MAE/mean with and without the –use_fast_math compiler option.

Variable | Variable Description | Non-Fast Math | Fast Math | ||
---|---|---|---|---|---|

MAE | MAE/Mean | MAE | MAE/Mean | ||

${\sigma}_{hh}^{SDCSM}$ | The NRCS for HH polarization | $1.014\times {10}^{-11}$ | $1.590\times {10}^{-6}$ | $1.226\times {10}^{-11}$ | $1.923\times {10}^{-6}$ |

${\sigma}_{vv}^{SDCSM}$ | The NRCS for VV polarization | $1.261\times {10}^{-10}$ | $1.352\times {10}^{-6}$ | $1.352\times {10}^{-10}$ | $1.451\times {10}^{-6}$ |

**Table 5.**Runtime and speedup for the GPU-based SDCSM program with asynchronous data transfer (ADT) optimization.

CPU Runtime (ms) | GPU-Runtime (ms) | Speedup | |
---|---|---|---|

Serial program | 47,593.6 | -- | -- |

Non-optimized | 60.68 | 784.3× | |

Optimized | 23.34 | 2039.1× |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Linghu, L.; Wu, J.; Wu, Z.; Wang, X. Parallel Computation of EM Backscattering from Large Three-Dimensional Sea Surface with CUDA. *Sensors* **2018**, *18*, 3656.
https://doi.org/10.3390/s18113656

**AMA Style**

Linghu L, Wu J, Wu Z, Wang X. Parallel Computation of EM Backscattering from Large Three-Dimensional Sea Surface with CUDA. *Sensors*. 2018; 18(11):3656.
https://doi.org/10.3390/s18113656

**Chicago/Turabian Style**

Linghu, Longxiang, Jiaji Wu, Zhensen Wu, and Xiaobing Wang. 2018. "Parallel Computation of EM Backscattering from Large Three-Dimensional Sea Surface with CUDA" *Sensors* 18, no. 11: 3656.
https://doi.org/10.3390/s18113656