# Morphological Precision Assessment of Reconstructed Surface Models for a Coral Atoll Lagoon

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Site and Datasets

^{2}. The coral reefs of the Nansha Islands can be classified as atolls, table reefs, patch reefs, etc., which are mainly atolls that are dominated by large atolls. Most of the Nansha Islands have a marine tropical rain-forest climate, with prevailing northeast and southwest monsoons. During the southwest monsoon season, the coral reefs are often affected by typhoons from the western Pacific, with dramatic morphological changes. In addition, the Nansha Islands have abundant fishery resources and oil and gas resources, and the islands’ coral reef ecosystems have been greatly affected as their exploitation increased in recent years.

#### 2.2. Interpolation Methods for the Morphology Surface Model Reconstruction

#### 2.3. Morphological Precision Assessment of the Surface Models

#### 2.3.1. Assessment Approach of the Morphological Precision

- (1)
- The original dataset was homogeneously diluted into a model training dataset (approximately 70%), which was used to reconstruct the surface models, and a model testing dataset (approximately 30%), which was used to validate the precision of the surface models and to extract the morphological errors.
- (2)
- A TIN surface model was reconstructed from the original dataset and converted into a grid surface model with a resolution of 1 m by using “TIN to Raster” tool in ArcGIS 10.2, to represent the true synthetic morphology.
- (3)
- Several grid surface models were reconstructed from the training dataset by IDW, LPI, RBF, and OK interpolation with a resolution of 1 m, to represent the estimated simulation morphology.
- (4)
- The morphological errors were calculated between the simulation morphology and synthetic morphology. The statistical morphological error was extracted from the testing dataset to conduct the precision assessment and error analysis.
- (5)
- The statistical morphological errors of the geomorphic subunits at different decomposition scales were extracted from the boundary and testing datasets to evaluate the precision of the surface models and the performance of the interpolation methods.

#### 2.3.2. Morphological Precision Index System

_{c-ss}is the number of changes in the local slope shape of all of the checked points.

- (i)
- Based on the synthetic surface model and the simulated surface models, which were recorded as “S”, the average value of the surface models was calculated by using the focal statistics tool in ArcGIS 10.2 with a 3 × 3 neighborhood analysis window, which was recorded as “S
_{m}”. - (ii)
- The raster calculator tool in ArcGIS 10.2 was used to subtract “S” from “S
_{m}”, and the calculated results were recorded as “S_{m}-S”. - (iii)
- “S
_{m}-S” was reclassified into three local slope-shape types by using the raster calculator tool in ArcGIS10.2 based on the principle that the pixel value was greater than 0 for a concave slope, less than 0 for a convex slope, and equal to 0 for a flat slope; the result was recorded as “S_{sm}”. - (iv)
- The local slope shapes of the morphology’s synthetic surface model and simulated surface models were extracted by using the testing dataset. In addition, the changed number or the proportion of the local slope shape of the simulated surface models relative to the synthetic surface model was counted to evaluate the precision (CRLSS) of the different simulated surface models.

_{c-sa}is the number of changes in the local slope shape of all of the checked points.

- (i)
- Based on the synthetic surface model and the simulated surface models, the slope aspect of the surface models was calculated by using the aspect tool in ArcGIS 10.2, which were recorded as “S
_{a}”. The slope aspect in ArcGIS software is measured in a clockwise direction, ranging from 0 (positive north) to 360 (still positive north), that is, a complete circle. - (ii)
- “S
_{a}” was reclassified into eight directions by using the raster calculator tool in ArcGIS10.2 based on the principle that the pixel value was greater than or equal to 0 and less than 22.5 for North, greater than or equal to 22.5 and less than 67.5 for Northeast, greater than or equal to 67.5 and less than 112.5 for East, greater than or equal to 112.5 and less than 157.5 for Southeast, greater than or equal to 157.5 and less than 202.5 for South, greater than or equal to 202.5 and less than 247.5 for Southeast, greater than or equal to 247.5 and less than 292.5 for West, greater than or equal to 292.5 and less than 337.5 for Northwest, greater than or equal to 337.5 and less than 360 for North; the result was recorded as “S_{ar}”. - (iii)
- The local slope aspects of the synthetic surface model and the simulated surface models were extracted by the testing dataset. In addition, the changed numbers or proportions of the local slope aspect between them were counted to evaluate the precision (CRLSA) of the different simulated surface models.

#### 2.4. Performance Evaluation of the Interpolation Methods

_{AB})

_{A}and I

_{B}are (−1, +1), I

_{A}is the standardized value of factor A, I

_{B}is the standardized value of factor B, and I

_{AB}is the superposition value of the factors A and B.

## 3. Results

#### 3.1. Morphological Precision Comparison of the Lagoon Surface Models

#### 3.2. Morphological Precision Comparison of the Lagoon Geomorphic Subunit Surface Models

#### 3.3. Adaptive Analysis of the Interpolation Methods for Lagoon Geomorphic Subunits

## 4. Discussion

#### 4.1. Robustness and Geomorphic Type Adaptability of Interpolation Methods

#### 4.2. Effect of the Geomorphic Decomposition Scale

#### 4.3. Potential and Shortcomings of the Morphological Precision Index System

## 5. Conclusions

- (1)
- OK had the best performance in terms of RMSE but poor performance of CRLSS. IDW had the best performance in terms of CRLSS but poor performance of RMSE and CRLSA. RBF had the best performance in terms of CRLSA, but the worst performance of CRLSS. The performance of these interpolation methods was not sufficiently robust in the morphological reconstruction of lagoons. Because of their unique morphological characteristics, the surface models of the lagoon’s geomorphic subunits had various quality orders in the three of the morphological precision indices, indicating large differences in morphological precision among the lagoon’s geomorphic subunits. The morphological characteristics of the lagoon’s geomorphic subunits determined their anti-deformation ability in the three morphological precision indices when reconstructing morphological surface models.
- (2)
- The adaptive analysis results showed that IDW was the optimal method for lagoon slopes, LPI was the best method for lagoon bottoms and shallow patch reefs, and RBF was better than the other methods for deep patch reefs. Previous studies generally showed that kriging was superior to other interpolation methods in many fields, but kriging was not the optimal interpolation method for any of the lagoon’s geomorphic subunits when being measured by the morphological precision index system.
- (3)
- In addition to morphological features, the sampling point density and distribution, and different interpolation parameters, the geomorphic decomposition scale was an important factor affecting the reconstruction precision, which greatly affects the determination of the optimal interpolation method for geomorphic subunits and the morphological precision of the reconstructed surface models.
- (4)
- The proposed morphological precision index system can assess the morphological precision of reconstructed surface models more comprehensively from three aspects: the dispersion degree of the point, the direction accuracy of the line, and the shape accuracy of the area. This system can reflect the differences in reconstruction ability of interpolation methods in local morphologies. SAVEE can evaluate the performance of the reconstruction methods comprehensively by considering the differences in multiple precision indices. These methods extend the theory and method of morphological precision assessment and can be applied to other research fields. In future research, the morphological precision assessment theory and the new reconstruction approaches will be important directions for the theoretical research on geomorphological reconstruction.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Jaleel, A. The status of the coral reefs and the management approaches: The case of the Maldives. Ocean Coast. Manag.
**2013**, 82, 104–118. [Google Scholar] [CrossRef] - Moberg, F.; Folke, C. Ecological goods and services of coral reef ecosystems. Ecol. Econ.
**1999**, 29, 215–233. [Google Scholar] [CrossRef] - Parzen, M.; Lipsitz, S.R. A meta-analysis of reef island response to environmental change on the Great Barrier Reef. Earth Surf. Process. Landf.
**2015**, 40, 1006–1016. [Google Scholar] - Zhao, H.; Wang, L.; Yuan, J. Sustainable Development of the Coral Reefs in the South China Sea Islands. Trop. Geogr.
**2016**, 36, 55–65. (In Chinese) [Google Scholar] - Coles, S.L.; Looker, E.; Burt, J.A. Twenty-year changes in coral near Muscat, Oman estimated from manta board tow observations. Mar. Environ. Res.
**2015**, 103, 66–73. [Google Scholar] [CrossRef] [PubMed] - Hughes, T.P.; Huang, H.; Young, M.A.L. The Wicked Problem of China’s Disappearing Coral Reefs. Conserv. Biol.
**2013**, 27, 261–269. [Google Scholar] [CrossRef] [PubMed] - Lapointe, B.E.; Thacker, K.; Hanson, C.; Getten, L. Sewage pollution in Negril, Jamaica: Effects on nutrition and ecology of coral reef macroalgae. Chin. J. Oceanol. Limnol.
**2011**, 29, 775–789. [Google Scholar] [CrossRef] - Mcwilliams, J.P.; Côté, I.M.; Gill, J.A.; Sutherland, W.J.; Watkinson, A.R. Accelerating impacts of temperature-induced coral bleaching in the caribbean. Ecology
**2005**, 86, 2055–2060. [Google Scholar] [CrossRef] - Kayanne, H.; Aoki, K.; Suzuki, T.; Hongo, C.; Yamano, H.; Ide, Y.; Iwatsuka, Y.; Takahashi, K.; Katayama, H.; Sekimoto, T.; et al. Eco-geomorphic processes that maintain a small coral reef island: Ballast Island in the Ryukyu Islands, Japan. Geomorphology
**2016**, 271, 84–93. [Google Scholar] [CrossRef] - Perry, C.T.; Smithers, S.G.; Kench, P.S.; Pears, B. Impacts of Cyclone Yasi on nearshore, terrigenous sediment-dominated reefs of the central Great Barrier Reef, Australia. Geomorphology
**2014**, 222, 92–105. [Google Scholar] [CrossRef] - Liu, G.; Strong, A.E.; Skirving, W. Remote sensing of sea surface temperatures during 2002 Barrier Reef coral bleaching. Eos Trans. Am. Geophys. Union
**2003**, 84, 137–141. [Google Scholar] [CrossRef] - Palandro, D.A.; Andréfouët, S.; Hu, C.; Hallock, P.; Müller-Karger, F.E.; Dustan, P.; Callahan, M.K.; Kranenburg, C.; Beaver, C.R. Quantification of two decades of shallow-water coral reef habitat decline in the Florida Keys National Marine Sanctuary using Landsat data (1984–2002). Remote Sens. Environ.
**2008**, 112, 3388–3399. [Google Scholar] [CrossRef] - Rogers, C.; Miller, J. Permanent ‘phase shifts’ or reversible declines in coral cover? Lack of recovery of two coral reefs in St. John, US Virgin Islands. Mar. Ecol. Prog.
**2006**, 306, 103–114. [Google Scholar] [CrossRef] - Hoegh-Guldberg, O. Climate change, coral bleaching and the future of the world’s coral reefs. Mar. Freshw. Res.
**1999**, 50, 839–866. [Google Scholar] [CrossRef] - Duvat, V.K.E.; Pillet, V. Shoreline changes in reef islands of the Central Pacific: Takapoto Atoll, Northern Tuamotu, French Polynesia. Geomorphology
**2017**, 282, 96–118. [Google Scholar] [CrossRef] - Mann, T.; Westphal, H. Multi-decadal shoreline changes on Takú Atoll, Papua New Guinea: Observational evidence of early reef island recovery after the impact of storm waves. Geomorphology
**2016**, 257, 75–84. [Google Scholar] [CrossRef] - Duce, S.; Vila-Concejo, A.; Hamylton, S.M.; Webster, J.M.; Bruce, E.; Beaman, R.J. A morphometric assessment and classification of coral reef spur and groove morphology. Geomorphology
**2016**, 265, 68–83. [Google Scholar] [CrossRef] - Xu, S.Y.; Sun, Y.Y. Computer aided geomorphologic simulation. Acta Geogr. Sin.
**2000**, 55, 266–273. (In Chinese) [Google Scholar] - Chen, C.; Liu, F.; Li, Y.; Yan, C.; Liu, G. A robust interpolation method for constructing digital elevation models from remote sensing data. Geomorphology
**2016**, 268, 275–287. [Google Scholar] [CrossRef] - Hu, H.; Shu, H. An improved coarse-grained parallel algorithm for computational acceleration of ordinary Kriging interpolation. Comput. Geosci.
**2015**, 78, 44–52. [Google Scholar] [CrossRef] - Chen, C.; Li, Y. A robust method of thin plate spline and its application to DEM construction. Comput. Geosci.
**2012**, 48, 9–16. [Google Scholar] [CrossRef] - Erdoğan, S. Modelling the spatial distribution of DEM error with geographically weighted regression: An experimental study. Comput. Geosci.
**2010**, 36, 34–43. [Google Scholar] [CrossRef] - Chen, C.; Yue, T. A method of DEM construction and related error analysis. Comput. Geosci.
**2010**, 36, 717–725. [Google Scholar] [CrossRef] - Bater, C.W.; Coops, N.C. Evaluating error associated with lidar-derived DEM interpolation. Comput. Geosci.
**2009**, 35, 289–300. [Google Scholar] [CrossRef] - Lu, G.Y.; Wong, D.W. An adaptive inverse-distance weighting spatial interpolation technique. Comput. Geosci.
**2008**, 34, 1044–1055. [Google Scholar] [CrossRef] - Yu, Z.W. Surface interpolation from irregularly distributed points using surface splines, with Fortran program. Comput. Geosci.
**2001**, 27, 877–882. [Google Scholar] [CrossRef] - Bartier, P.M.; Keller, C.P. Multivariate interpolation to incorporate thematic surface data using inverse distance weighting (IDW). Comput. Geosci.
**1996**, 22, 795–799. [Google Scholar] [CrossRef] - Ding, Q.; Wang, Y.; Zhuang, D. Comparison of the common spatial interpolation methods used to analyze potentially toxic elements surrounding mining regions. J. Environ. Manag.
**2018**, 212, 23–31. [Google Scholar] [CrossRef] [PubMed] - Geach, M.R.; Stokes, M.; Telfer, M.W.; Mather, A.E.; Fyfe, R.M.; Lewin, S. The application of geospatial interpolation methods in the reconstruction of Quaternary landform records. Geomorphology
**2014**, 216, 234–246. [Google Scholar] [CrossRef] - Arun, P.V. A comparative analysis of different DEM interpolation methods. Egypt. J. Remote Sens. Space Sci.
**2013**, 16, 133–139. [Google Scholar] - Chaplot, V.; Darboux, F.; Bourennane, H.; Leguédois, S.; Silvera, N.; Phachomphon, K. Accuracy of interpolation techniques for the derivation of digital elevation models in relation to landform types and data density. Geomorphology
**2006**, 77, 126–141. [Google Scholar] [CrossRef] - Zimmerman, D.; Pavlik, C.; Ruggles, A.; Armstrong, M.P. An Experimental Comparison of Ordinary and Universal Kriging and Inverse Distance Weighting. Math. Geol.
**1999**, 31, 375–390. [Google Scholar] [CrossRef] - Laslett, G.M.; Mcbratney, A.B. Further comparison of spatial methods for predicting soil pH. Soil Sci. Soc. Am. J.
**1990**, 54, 1553–1558. [Google Scholar] [CrossRef] - Zhou, M.; Liu, Y.; Manchun, L.I.; Sun, C.; Wei, Z. Geomorphologic information extraction for multi-objective coral islands from remotely sensed imagery: A case study for Yongle Atoll, South China Sea. Geogr. Res.
**2015**, 34, 677–690. (In Chinese) [Google Scholar] - Wise, S. Cross-validation as a means of investigating DEM interpolation error. Comput. Geosci.
**2011**, 37, 978–991. [Google Scholar] [CrossRef] - Wang, C.; Liu, X.J.; Tang, G.A.; Tao, Y. Morphologic Fidelity of Grid Digital Elevation Model. Geomat. Inf. Sci. Wuhan Univ.
**2009**, 34, 146–149. (In Chinese) [Google Scholar] - Heritage, G.L.; Milan, D.J.; Large, A.R.G.; Fuller, I.C. Influence of survey strategy and interpolation model on DEM quality. Geomorphology
**2009**, 112, 334–344. [Google Scholar] [CrossRef] - Aguilar, F.J. Effects of Terrain Morphology, Sampling Density, and Interpolation Methods on Grid DEM Accuracy. Photogramm. Eng. Remote Sens.
**2005**, 71, 805–816. [Google Scholar] [CrossRef] - Desmet, P.J.J.; Govers, G. Two-dimensional modelling of the within-field variation in rill and gully geometry and location related to topography. Catena
**1997**, 29, 283–306. [Google Scholar] [CrossRef] - Tang, G. Progress of DEM and digital terrain analysis in China. Acta Geogr. Sin.
**2014**, 69, 1305–1325. (In Chinese) [Google Scholar] - Loh, D.K.; Ytc, H.; Choo, Y.K.; Holtfrerich, D.R. Integration of a rule-based expert system with GIS through a relational database management system for forest resource management. Comput. Electron. Agric.
**1994**, 11, 215–228. [Google Scholar] [CrossRef] - Chen, S.Y.; Cheng, Z.Y.; Loh, D.K. Islands valuation of spatial appraisal based on SAVEE method—With the Nansha Islands as an example. Mar. Environ. Sci.
**2012**, 31, 107–110. (In Chinese) [Google Scholar] - Loh, D.K.; Stipdonk, S.E.P.V.; Holtfrerich, D.R.; Hsieh, Y.T.C. Spatially constrained reasoning for the determination of wildlife foraging areas. Comput. Electron. Agric.
**1996**, 15, 323–334. [Google Scholar] [CrossRef] - Wilson, J.; Gallant, J. Digital Terrain Analysis in Terrain Analysis: Principles and Applications; Wiley: New York, NY, USA, 2000; Volume 479, pp. 1–27. [Google Scholar]
- Laslett, G. Kriging and Splines: An Empirical Comparison of their Predictive Performance in Some Applications. J. Am. Stat. Assoc.
**1994**, 89, 391–400. [Google Scholar] [CrossRef] - Creutin, J.D.; Obled, C. Objective analyses and mapping techniques for rainfall fields: An objective comparison. Water Resour. Res.
**1982**, 18, 413–431. [Google Scholar] [CrossRef] - Zhang, T.; Xu, X.; Xu, S. Method of establishing an underwater digital elevation terrain based on kriging interpolation. Measurement
**2015**, 63, 287–298. [Google Scholar] [CrossRef] - Rezaee, H.; Asghari, O.; Yamamoto, J.K. On the reduction of the ordinary kriging smoothing effect. J. Min. Environ.
**2011**, 2, 25–40. [Google Scholar] - Yamamoto, J.K. Correcting the Smoothing Effect of Ordinary Kriging Estimates. Math. Geol.
**2005**, 37, 69–94. [Google Scholar] [CrossRef] - Erdoğan, S. A comparision of interpolation methods for producing digital elevation models at the field scale. Earth Surf. Process. Landf.
**2009**, 34, 366–376. [Google Scholar] [CrossRef] - Watson, D.F. A refinement of inverse distance weighted interpolation. Geo-Processing
**1985**, 2, 315–327. [Google Scholar] - Sun, Z.; Zhao, H. Features of dynamic geomorphology of coral reefs in nansha islands. Trop. Oceanol.
**1996**. (In Chinese) [Google Scholar] - Yilmaz, H.M. The effect of interpolation methods in surface definition: An experimental study. Earth Surf. Process. Landf.
**2007**, 32, 1346–1361. [Google Scholar] [CrossRef] - Desmet, P.J.J. Effects of Interpolation Errors on the Analysis of DEMs. Earth Surf. Process. Landf.
**2015**, 22, 563–580. [Google Scholar] [CrossRef]

**Figure 1.**Study site: (

**a**) Location of the Nansha Islands. (

**b**) Satellite image of the study site. (

**c**) Geomorphology of the lagoon at the study site.

**Figure 3.**Schematic diagram of local slope shapes: (

**a**) flat slope, (

**b**) concave slope, and (

**c**) convex slope.

**Figure 4.**Schematic diagram of local slopes with different aspects: (

**a**) flat slope with different aspects, (

**b**) concave slope with different aspects, and (

**c**) convex slope with different aspects.

**Figure 5.**Superposition process of the influencing factors in the spatial appraisal and valuation of environment and ecosystems (SAVEE) evaluation.

**Figure 6.**Elevation field models of the lagoon. The first elevation field model was generated from the synthetic surface model from (

**a**) TIN, and the others were generated from the simulated surface models that were reconstructed by (

**b**) inverse distance weighting (IDW), (

**c**) local polynomial interpolation (LPI), (

**d**) radial basis function interpolation (RBF), and (

**e**) ordinary kriging (OK). The Pattern areas were selected from (

**f**) the lagoon’s geomorphic subunits for further comparison: (

**i**) lagoon slope, (

**ii**) lagoon bottom, (

**iii**) deep patch reef, and (

**iv**) shallow patch reef. These patterns (

**i-a**–

**iv-e**) reflect the differences in the simulated and synthetic surfaces in the elevation field model.

**Figure 7.**Slope shape field models of the lagoon. The first slope shape field model was generated from the synthetic surface model from (

**a**) TIN, and the others were generated from the simulated surface models that were reconstructed by (

**b**) IDW, (

**c**) LPI, (

**d**) RBF, and (

**e**) OK. The pattern areas were selected from (

**f**) the lagoon’s geomorphic subunits for further comparison: (

**i**) lagoon slope, (

**ii**) lagoon bottom, (

**iii**) deep patch reef, and (

**iv**) shallow patch reef. The patterns (

**i-a**–

**iv-e**) reflect the differences in the simulated and synthetic surfaces in the slope shape field model.

**Figure 8.**Slope aspect field models of the lagoon. The first slope aspect field model was generated from the synthetic surface model from (

**a**) TIN, and the others were generated from the simulated surface models that were reconstructed by (

**b**) IDW, (

**c**) LPI, (

**d**) RBF, and (

**e**) OK. The pattern areas were selected from (

**f**) the lagoon’s geomorphic subunits for further comparison: (

**i**) lagoon slope, (

**ii**) lagoon bottom, (

**iii**) deep patch reef, and (

**iv**) shallow patch reef. The patterns (

**i-a**–

**iv-e**) reflect the differences in the simulated and synthetic surfaces in the slope aspect field model.

**Figure 9.**Root mean square error (RMSE) of the surface models with 1-m resolution were reconstructed by (

**a**) IDW, (

**b**) LPI, (

**c**) RBF, and (

**d**) OK: Z

_{e}represents the estimated value and Z

_{o}represents the observed value.

**Figure 10.**Change rate of the local slope shape (CRLSS) of the surface models with 1-m resolution were reconstructed by (

**a**) IDW, (

**b**) LPI, (

**c**) RBF, and (

**d**) OK. The six colors in the figure represent the changes among three different local slope shapes, and the size of the shaded area represents the ratio of the changes of different local slope shapes.

**Figure 11.**Change rate of the local slope aspect (CRLSA) of the surface models with 1-m resolution were reconstructed by (

**a**) IDW, (

**b**) LPI, (

**c**) RBF, and (

**d**) OK. The eight letters in the figure represent eight different local slope aspects of the synthetic surface model, and the eight different colors represent the eight different local slope aspects of the reconstructed surface model. The size of the color block represents the ratio of each original local slope aspect in the synthetic surface model’s change to the other eight local slope aspects in the reconstructed surface model.

**Figure 12.**RMSE of the surface models of different geomorphic subunits: (

**a**) lagoon slope, (

**b**) lagoon bottom, (

**c**) deep patch reef, and (

**d**) shallow patch reef. Z

_{e}represents the estimated value and Z

_{o}represents the observed value.

**Figure 13.**CRLSS of the surface models of different geomorphic subunits: (

**a**) lagoon slope, (

**b**) lagoon bottom, (

**c**) deep patch reef, and (

**d**) shallow patch reef. The six colors in the figure represent the changes among the three different local slope shapes, and the size of the shaded area represents the ratio of the changes of different local slope shapes.

**Figure 14.**CRLSA of the surface models of different geomorphic subunits: (

**a**) lagoon slope, (

**b**) lagoon bottom, (

**c**) deep patch reef, and (

**d**) shallow patch reef. The eight letters in the figure represent eight different local slope aspects of the synthetic surface model, and the eight different colors represent the eight different local slope aspects of the reconstructed surface model. The size of the color block represents the ratio of changes in each original local slope aspect in the synthetic surface model to the other eight local slope aspects in the reconstructed surface model.

Interpolation Methods | Interpolation Parameters | ||||
---|---|---|---|---|---|

Neighborhood Type | Search Sectors | Search Neighbors | Kernel Function | Function Variable | |

IDW | Circular | 4 sectors | 10–15 | Power | Power = 2 |

LPI | Circular | 4 sectors | 10–15 | Gaussian | Order = 1 |

RBF | Circular | 4 sectors | 10–15 | Multiquadric | Smoothness = 0 |

OK | Circular | 4 sectors | 10–15 | Spherical | Nugget = 4 |

**Table 2.**Performances of the interpolation methods for the morphological surface model reconstructions.

Morphological Precision Indices | Quality Order of the Surface Models that Were Reconstructed by the Interpolation Methods |
---|---|

RMSE | OK > RBF > LPI > IDW |

CRLSS | IDW > LPI > OK > RBF |

CRLSA | RBF > OK > LPI > IDW |

**Table 3.**Mean morphological precision values of the surface models of different geomorphic subunits.

Geomorphology Subunits | Mean Value of the Morphological Precision | ||
---|---|---|---|

RMSE | CRLSS | CRLSA | |

Lagoon slope | 0.3200 | 55.25% | 40.11% |

Lagoon bottom | 0.3781 | 53.80% | 47.17% |

Deep patch reef | 0.7769 | 58.07% | 30.11% |

Shallow patch reef | 0.5553 | 55.78% | 37.38% |

**Table 4.**Comprehensive evaluation value of the interpolation methods that were applied to the geomorphic subunits.

Interpolation Methods | Comprehensive Values in the Geomorphic Subunits | |||
---|---|---|---|---|

Lagoon Slope (×10^{−}^{6}) | Lagoon Bottom (×10^{−}^{6}) | Deep Patch Reef (×10^{−}^{3}) | Shallow Patch Reef (×10^{−}^{5}) | |

IDW | 2.89 | 2.39 | 0.12 | 0.75 |

LPI | 1.55 | 3.11 | 1.10 | 2.46 |

RBF | 1.81 | 2.92 | 1.43 | 2.31 |

OK | 1.84 | 2.99 | 1.38 | 2.42 |

**Table 5.**Morphological precision of surface models and performance comprehensive evaluation values of interpolation methods when the patch reef was decomposed by the second-order and third-order geomorphic scales.

Geomorphology Units | Interpolation Methods | Morphological Precision | Comprehensive Evaluation Values | |||
---|---|---|---|---|---|---|

2nd-Order | 3rd-Order | RMSE | CRLSS | CRLSA | ||

Patch reef | IDW | 1.1473 | 54.25% | 37.80% | 0.91 × 10^{−4} | |

LPI | 0.6419 | 54.78% | 31.03% | 7.85 × 10^{−4} | ||

RBF | 0.5876 | 62.29% | 28.47% | 9.91 × 10^{−4} | ||

OK | 0.5939 | 59.29% | 28.39% | 9.65 × 10^{−4} | ||

Deep patch reef | IDW | 1.2237 | 54.50% | 36.77% | 0.12 × 10^{−3} | |

LPI | 0.6689 | 54.04% | 30.15% | 1.10 × 10^{−3} | ||

RBF | 0.6031 | 63.51% | 26.83% | 1.43 × 10^{−3} | ||

OK | 0.6117 | 60.21% | 26.67% | 1.38 × 10^{−3} | ||

Shallow patch reef | IDW | 0.7034 | 53.10% | 42.48% | 0.75 × 10^{−5} | |

LPI | 0.5011 | 58.15% | 35.02% | 2.46 × 10^{−5} | ||

RBF | 0.5113 | 56.78% | 35.86% | 2.31 × 10^{−5} | ||

OK | 0.5054 | 55.10% | 36.17% | 2.42 × 10^{−5} |

© 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**

Wang, Q.; Su, F.; Zhang, Y.; Jiang, H.; Cheng, F.
Morphological Precision Assessment of Reconstructed Surface Models for a Coral Atoll Lagoon. *Sustainability* **2018**, *10*, 2749.
https://doi.org/10.3390/su10082749

**AMA Style**

Wang Q, Su F, Zhang Y, Jiang H, Cheng F.
Morphological Precision Assessment of Reconstructed Surface Models for a Coral Atoll Lagoon. *Sustainability*. 2018; 10(8):2749.
https://doi.org/10.3390/su10082749

**Chicago/Turabian Style**

Wang, Qi, Fenzhen Su, Yu Zhang, Huiping Jiang, and Fei Cheng.
2018. "Morphological Precision Assessment of Reconstructed Surface Models for a Coral Atoll Lagoon" *Sustainability* 10, no. 8: 2749.
https://doi.org/10.3390/su10082749