## A Monte Carlo study of the seagrass-induced depth bias in bathymetric lidar |

Optics Express, Vol. 19, Issue 8, pp. 7230-7243 (2011)

http://dx.doi.org/10.1364/OE.19.007230

Acrobat PDF (1396 KB)

### Abstract

A bathymetric lidar survey is the most cost efficient method of producing bathymetric maps in near shore areas where the ocean bottom is both highly variable and of greatest importance for shipping and recreation. So far, not much attention has been paid to the influence of bottom materials on the lidar signals. This study addresses this issue using a Monte Carlo modeling technique. The Monte Carlo simulation includes a plane parallel water body and a flat bottom with or without seagrass. The seagrass canopy structure is adopted from Zimmerman (2003). Both the surface of the seagrass leaves and the bottom are assumed to be Lambertian. Convolution with the lidar pulse function followed by the median operator is used to reduce the variance of the resultant lidar waveform. Two seagrass orientation arrangements are modeled: seagrass in still water with random leaf orientation and seagrass with a uniform orientation as would be expected when under the influence of a water current. For each case, two maximum canopy heights, 0.5 m and 1 m, three shoot densities, 100, 500, and 1000, and three bending angles, 5, 25, and 45 degrees, are considered. The seagrass is found to induce a depth bias that is proportional to an effective leaf area index (eLAI) and the contrast in reflectance between the seagrass and the bottom material.

© 2011 OSA

## 1. Introduction

3. G. C. Guenther, R. W. L. Thomas, and P. E. LaRocque, “Design considerations for achieving high accuracy with the shoals bathymetric lidar system,” Proc. SPIE **2964**, 54–71 (1996). [CrossRef]

5. C.-K. Wang and W. D. Philpot, “Using airborne bathymetric lidar to detect bottom type variation in shallow waters,” Remote Sens. Environ. **106**(1), 123–135 (2007). [CrossRef]

6. L. R. Bissonnette, G. Roy, L. Poutier, S. G. Cober, and G. A. Isaac, “Multiple-scattering lidar retrieval method: tests on Monte Carlo simulations and comparisons with in situ measurements,” Appl. Opt. **41**(30), 6307–6324 (2002). [CrossRef] [PubMed]

11. E. P. Zege, I. L. Katsev, and I. N. Polonsky, “Analytical solution to LIDAR return signals from clouds with regard to multiple scattering,” Appl. Phys. B **60**(4), 345–353 (1995). [CrossRef]

12. P. Bruscaglioni, A. Ismaelli, and G. Zaccanti, “Monte-Carlo calculations of LIDAR returns: procedures and results,” Appl. Phys. B **60**(4), 325–329 (1995). [CrossRef]

16. D. M. Winker and L. R. Poole, “Monte-Carlo calculations of cloud returns for ground-based and space based LIDARS,” Appl. Phys. B **60**(4), 341–344 (1995). [CrossRef]

## 2. Airborne bathymetric lidar system

## 3. The Monte Carlo simulation

### 3.1. Air/water interface processes

### 3.2. In water processes

*θ*. When integrated over all possible scattering directions the integral sums to unity:

**Λ**and the relationship

**Λ**is generated, and the azimuth angle of the scattered photon is 2π

**Λ**.

12. P. Bruscaglioni, A. Ismaelli, and G. Zaccanti, “Monte-Carlo calculations of LIDAR returns: procedures and results,” Appl. Phys. B **60**(4), 325–329 (1995). [CrossRef]

13. H. R. Gordon, “Interpretation of airborne oceanic lidar: effects of multiple scattering,” Appl. Opt. **21**(16), 2996–3001 (1982). [CrossRef] [PubMed]

15. L. R. Poole, “Radiative transfer model for airborne laser fluorosensors: inclusion of water Raman scattering,” Appl. Opt. **21**(17), 3063–3065 (1982). [CrossRef] [PubMed]

*d*is the geometric distance in the sea water between the photon and the receiver,

_{T}*N*is the number of seagrass leaves between the photon and the receiver. Figure 1(a) shows the geometric relationship of these quantities.

### 3.3. Ocean bottom processes

**Λ**is generated and

**Λ**is generated and the azimuth angle of the reflected photon is 2π

**Λ**. As with the proportional energy collection of photons in the water, the weight contributed to the detected signal by a photon reflected from the bottom iswhere

### 3.4. The seagrass bed processes

*γ*describes the tilt of a seagrass leaf away from the zenith, i.e., 0° corresponds to standing vertically and 90°corresponds to laying horizontally on the bottom. Since the seagrass leaf is assumed to consist of rectangular strips with homogeneous mass density, regardless of the different age stage of each leaf, Eq. (16) is essentially the pdf of the length of seagrass leaf in the bed.

**Λ**and

_{1}**Λ**, are generated independently. Ifthe random number pair is accepted, and the leaf length is

_{2}23. R. C. Zimmerman, “A biooptical model of irradiance distribution and photosynthesis in seagrass canopies,” Limnol. Oceanogr. **48**(1_part_2), 568–585 (2003). [CrossRef]

25. Y. M. Govaerts, S. Jacquemoud, M. M. Verstraete, and S. L. Ustin, “Three-dimensional radiation transfer modeling in a dicotyledon leaf,” Appl. Opt. **35**(33), 6585–6598 (1996). [CrossRef] [PubMed]

26. T. W. Brakke, J. A. Smith, and J. M. Harnden, “Bidirectional scattering of light from tree leaves,” Remote Sens. Environ. **29**(2), 175–183 (1989). [CrossRef]

**Λ**is generated and compared with the ratio

**Λ**is less than

### 3.5. Variance reduction and simulation verification

27. R. Zanella, P. Boccacci, L. Zanni, and M. Bertero, “Efficient gradient projection methods for edge-preserving removal of Poisson noise,” Inverse Probl. **25**(4), 045010 (2009), doi:. [CrossRef]

## 4. Results and discussion

^{2}), and two leaf orientations with three different bending angles (5, 25, and 45 degrees). Two seagrass types, eelgrass and turtlegrass [23

23. R. C. Zimmerman, “A biooptical model of irradiance distribution and photosynthesis in seagrass canopies,” Limnol. Oceanogr. **48**(1_part_2), 568–585 (2003). [CrossRef]

23. R. C. Zimmerman, “A biooptical model of irradiance distribution and photosynthesis in seagrass canopies,” Limnol. Oceanogr. **48**(1_part_2), 568–585 (2003). [CrossRef]

28. E. J. Hochberg, M. J. Atkinson, and S. Andrefouet, “Spectral reflectance of coral reef bottom-types worldwide and implications for coral reef remote sensing,” Remote Sens. Environ. **85**(2), 159–173 (2003). [CrossRef]

*c*= 0.25 m

^{−1}, ω

_{0}= 0.6, and the ocean bottom is set at the depth of 9 m.

3. G. C. Guenther, R. W. L. Thomas, and P. E. LaRocque, “Design considerations for achieving high accuracy with the shoals bathymetric lidar system,” Proc. SPIE **2964**, 54–71 (1996). [CrossRef]

^{2}, canopy height of 1 m, leaf azimuth angle of 0 degree) is larger than the minimum eLAI of that with 45 degrees (shoot density of 100 shoots/m

^{2}, canopy height of 0.5 m, leaf azimuth angle of 180 degrees).

^{2}. In general, other seagrass parameters being the same, the depth bias increases with shoot density and bending angle (Table 3). However, one single seagrass parameter is insufficient to represent the depth bias. A better correlation relationship is found between depth bias and eLAI, where the depth bias increases negatively (meaning the bottom determined by lidar is shallower than the bottom without seagrass) with increasing eLAI. Two trends of depth bias for sand (open symbol) and mud (solid symbol) bottoms can be seen in Fig. 4. It is postulated that the reflectance contrast between sand bottom and turtlegrass is not as significant as that between mud bottom and turtlegrass (e.g., Table 2), so the depth bias induced by similar eLAI values (i.e., similar seagrass structural and optical properties) is less for a sand bottom. Thus, the summarized results of the depth bias for different seagrass parameters listed in Table 3 are grouped by bottom type.

^{2}, canopy height of 1 m, bending angle of 45 degrees, and leaf azimuth angle of 0 degree; shown as green open circle in Fig. 5(a) and green solid rectangle in Fig. 5(b)) would be considered to be significantly biased. On the other hand, many of the cases for mud bottom have the depth bias smaller than −1 ns, and some are biased as much as −2.22 ns.

**48**(1_part_2), 568–585 (2003). [CrossRef]

## 5. Conclusions

**48**(1_part_2), 568–585 (2003). [CrossRef]

*Thalassia testudinum*Banks ex König) populations near Lee Stocking Island, Bahamas, and three eelgrasses (

*Zostera marina*L.) populations from California and Washington, USA. Both seagrasses are modeled as elongated rectangular strips with a thickness of 250 μm and width of 5 cm [23

**48**(1_part_2), 568–585 (2003). [CrossRef]

## Acknowledgments

## References and links

1. | G. C. Guenther, “Airborne lidar bathymetry,” in |

2. | G. C. Guenther, A. G. Cunningham, P. E. LaRocque, and D. J. Reid, “Meeting the accuracy challenge in airborne lidar bathymetry,” EARSeL eProceedings (2001), Vol. 1, pp. 1–27. |

3. | G. C. Guenther, R. W. L. Thomas, and P. E. LaRocque, “Design considerations for achieving high accuracy with the shoals bathymetric lidar system,” Proc. SPIE |

4. | M. Lee, “Benthic mapping of coastal waters using data fusion of hyperspectral imagery and airborne laser bathymetry,” PhD dissertation (University of Florida, 2003). |

5. | C.-K. Wang and W. D. Philpot, “Using airborne bathymetric lidar to detect bottom type variation in shallow waters,” Remote Sens. Environ. |

6. | L. R. Bissonnette, G. Roy, L. Poutier, S. G. Cober, and G. A. Isaac, “Multiple-scattering lidar retrieval method: tests on Monte Carlo simulations and comparisons with in situ measurements,” Appl. Opt. |

7. | R. M. Measures, |

8. | L. R. Bissonnette, “Multiple scattering of narrow light beams in aerosols,” Appl. Phys. B |

9. | C. Flesia and P. Schwendimann, “Analytical multiple-scattering extension of the Mie theory: the LIDAR equation,” Appl. Phys. B |

10. | A. V. Starkov, M. Noormohammadian, and U. G. Oppel, “A stochastic model and a variance-reduction Monte-Carlo method for the calculation of light transport,” Appl. Phys. B |

11. | E. P. Zege, I. L. Katsev, and I. N. Polonsky, “Analytical solution to LIDAR return signals from clouds with regard to multiple scattering,” Appl. Phys. B |

12. | P. Bruscaglioni, A. Ismaelli, and G. Zaccanti, “Monte-Carlo calculations of LIDAR returns: procedures and results,” Appl. Phys. B |

13. | H. R. Gordon, “Interpretation of airborne oceanic lidar: effects of multiple scattering,” Appl. Opt. |

14. | G. W. Kattawar and G. N. Plass, “Time of flight lidar measurements as an ocean probe,” Appl. Opt. |

15. | L. R. Poole, “Radiative transfer model for airborne laser fluorosensors: inclusion of water Raman scattering,” Appl. Opt. |

16. | D. M. Winker and L. R. Poole, “Monte-Carlo calculations of cloud returns for ground-based and space based LIDARS,” Appl. Phys. B |

17. | J. Heslin, W. J. Lillycrop, and R. Pope, “CHARTS: an evolution in airborne lidar hydrography,” presented at U.S. Hydro Conference, Biloxi, Missippi, 24–27 March 2003. |

18. | G. Cunningham, Marine Survey Division, Optech Inc., 100 Wildcat Road, Toronto, Ontario M3J 2Z9, Canada (personal communication, 2004). |

19. | C. D. Mobley, |

20. | G. I. Marchuk, G. A. Mikhailov, M. A. Nazaraliev, R. A. Darbinjan, B. A. Kargin, and B. S. Elepov, |

21. | T. J. Petzold, “Volume scattering functions for selected ocean waters,” SIO Ref. 72–78 (Scripps Institution of Oceanography, 1972). |

22. | R. Barbini, F. Colao, E. Cupini, N. Ferrari, G. Ferro, and A. Palucci, “Marine code for modelling range resolved oceanographic lidar fluorosensor measurements,” EARSeL eProceedings (2001), Vol. 1, pp. 77–87. |

23. | R. C. Zimmerman, “A biooptical model of irradiance distribution and photosynthesis in seagrass canopies,” Limnol. Oceanogr. |

24. | R. Y. Rubinstein, |

25. | Y. M. Govaerts, S. Jacquemoud, M. M. Verstraete, and S. L. Ustin, “Three-dimensional radiation transfer modeling in a dicotyledon leaf,” Appl. Opt. |

26. | T. W. Brakke, J. A. Smith, and J. M. Harnden, “Bidirectional scattering of light from tree leaves,” Remote Sens. Environ. |

27. | R. Zanella, P. Boccacci, L. Zanni, and M. Bertero, “Efficient gradient projection methods for edge-preserving removal of Poisson noise,” Inverse Probl. |

28. | E. J. Hochberg, M. J. Atkinson, and S. Andrefouet, “Spectral reflectance of coral reef bottom-types worldwide and implications for coral reef remote sensing,” Remote Sens. Environ. |

**OCIS Codes**

(280.3640) Remote sensing and sensors : Lidar

(280.1355) Remote sensing and sensors : Bathymetry

**ToC Category:**

Remote Sensing

**History**

Original Manuscript: January 25, 2011

Revised Manuscript: March 11, 2011

Manuscript Accepted: March 12, 2011

Published: March 31, 2011

**Virtual Issues**

Vol. 6, Iss. 5 *Virtual Journal for Biomedical Optics*

**Citation**

Chi-Kuei Wang, William Philpot, Minsu Kim, and Hou-Meng Lei, "A Monte Carlo study of the seagrass-induced depth bias in bathymetric lidar," Opt. Express **19**, 7230-7243 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-8-7230

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### References

- G. C. Guenther, “Airborne lidar bathymetry,” in Digital Elevation Model Technologies and Applications: The DEM Users Manual, D. F. Maune, ed. (ASPRS, 2001)
- G. C. Guenther, A. G. Cunningham, P. E. LaRocque, and D. J. Reid, “Meeting the accuracy challenge in airborne lidar bathymetry,” EARSeL eProceedings (2001), Vol. 1, pp. 1–27.
- G. C. Guenther, R. W. L. Thomas, and P. E. LaRocque, “Design considerations for achieving high accuracy with the shoals bathymetric lidar system,” Proc. SPIE 2964, 54–71 (1996). [CrossRef]
- M. Lee, “Benthic mapping of coastal waters using data fusion of hyperspectral imagery and airborne laser bathymetry,” PhD dissertation (University of Florida, 2003).
- C.-K. Wang and W. D. Philpot, “Using airborne bathymetric lidar to detect bottom type variation in shallow waters,” Remote Sens. Environ. 106(1), 123–135 (2007). [CrossRef]
- L. R. Bissonnette, G. Roy, L. Poutier, S. G. Cober, and G. A. Isaac, “Multiple-scattering lidar retrieval method: tests on Monte Carlo simulations and comparisons with in situ measurements,” Appl. Opt. 41(30), 6307–6324 (2002). [CrossRef] [PubMed]
- R. M. Measures, Laser Remote Sensing (Krieger, 1992)
- L. R. Bissonnette, “Multiple scattering of narrow light beams in aerosols,” Appl. Phys. B 60(4), 315–323 (1995). [CrossRef]
- C. Flesia and P. Schwendimann, “Analytical multiple-scattering extension of the Mie theory: the LIDAR equation,” Appl. Phys. B 60(4), 331–334 (1995). [CrossRef]
- A. V. Starkov, M. Noormohammadian, and U. G. Oppel, “A stochastic model and a variance-reduction Monte-Carlo method for the calculation of light transport,” Appl. Phys. B 60(4), 335–340 (1995). [CrossRef]
- E. P. Zege, I. L. Katsev, and I. N. Polonsky, “Analytical solution to LIDAR return signals from clouds with regard to multiple scattering,” Appl. Phys. B 60(4), 345–353 (1995). [CrossRef]
- P. Bruscaglioni, A. Ismaelli, and G. Zaccanti, “Monte-Carlo calculations of LIDAR returns: procedures and results,” Appl. Phys. B 60(4), 325–329 (1995). [CrossRef]
- H. R. Gordon, “Interpretation of airborne oceanic lidar: effects of multiple scattering,” Appl. Opt. 21(16), 2996–3001 (1982). [CrossRef] [PubMed]
- G. W. Kattawar and G. N. Plass, “Time of flight lidar measurements as an ocean probe,” Appl. Opt. 11(3), 662–666 (1972). [CrossRef] [PubMed]
- L. R. Poole, “Radiative transfer model for airborne laser fluorosensors: inclusion of water Raman scattering,” Appl. Opt. 21(17), 3063–3065 (1982). [CrossRef] [PubMed]
- D. M. Winker and L. R. Poole, “Monte-Carlo calculations of cloud returns for ground-based and space based LIDARS,” Appl. Phys. B 60(4), 341–344 (1995). [CrossRef]
- J. Heslin, W. J. Lillycrop, and R. Pope, “CHARTS: an evolution in airborne lidar hydrography,” presented at U.S. Hydro Conference, Biloxi, Missippi, 24–27 March 2003.
- G. Cunningham, Marine Survey Division, Optech Inc., 100 Wildcat Road, Toronto, Ontario M3J 2Z9, Canada (personal communication, 2004).
- C. D. Mobley, Light and Water: Radiative Transfer in Natural Waters (Academic, 1994).
- G. I. Marchuk, G. A. Mikhailov, M. A. Nazaraliev, R. A. Darbinjan, B. A. Kargin, and B. S. Elepov, The Monte Carlo Methods in Atmospheric Optics, (Springer-Verlag, 1980)
- T. J. Petzold, “Volume scattering functions for selected ocean waters,” SIO Ref. 72–78 (Scripps Institution of Oceanography, 1972).
- R. Barbini, F. Colao, E. Cupini, N. Ferrari, G. Ferro, and A. Palucci, “Marine code for modelling range resolved oceanographic lidar fluorosensor measurements,” EARSeL eProceedings (2001), Vol. 1, pp. 77–87.
- R. C. Zimmerman, “A biooptical model of irradiance distribution and photosynthesis in seagrass canopies,” Limnol. Oceanogr. 48(1_part_2), 568–585 (2003). [CrossRef]
- R. Y. Rubinstein, Simulation and the Monte Carlo Method (Wiley, 1981)
- Y. M. Govaerts, S. Jacquemoud, M. M. Verstraete, and S. L. Ustin, “Three-dimensional radiation transfer modeling in a dicotyledon leaf,” Appl. Opt. 35(33), 6585–6598 (1996). [CrossRef] [PubMed]
- T. W. Brakke, J. A. Smith, and J. M. Harnden, “Bidirectional scattering of light from tree leaves,” Remote Sens. Environ. 29(2), 175–183 (1989). [CrossRef]
- R. Zanella, P. Boccacci, L. Zanni, and M. Bertero, “Efficient gradient projection methods for edge-preserving removal of Poisson noise,” Inverse Probl. 25(4), 045010 (2009), doi:. [CrossRef]
- E. J. Hochberg, M. J. Atkinson, and S. Andrefouet, “Spectral reflectance of coral reef bottom-types worldwide and implications for coral reef remote sensing,” Remote Sens. Environ. 85(2), 159–173 (2003). [CrossRef]

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