# Bayesian Analysis of Uncertainty in the GlobCover 2009 Land Cover Product at Climate Model Grid Scale

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Data

#### 2.1. GlobCover 2009

#### 2.2. Confusion Matrix

## 3. Simulating the Distribution of True Land Cover Classes

**α**is the $p\times 1$ parameter vector for a Dirichlet distribution, results in the posterior distribution for the region-wide error probabilities as

For $g=1,2,\dots ,N$ (1) Simulate ${\mathit{\lambda}}_{\mathbf{t}}\sim Di({\mathbf{c}}_{t}+\mathit{\alpha})$ for $t=1,2,\dots ,p$ For $s=1,2,\dots ,S$ (2) Calculate ${\pi}_{t}^{s}$ for $t=1,2,\dots ,p$ (3) Simulate ${\mathit{\lambda}}_{t}^{s}\sim Di\left(d{\mathit{\lambda}}_{t}\right)$ for $t=1,2,\dots ,p$ (4) Calculate ${\mathit{\kappa}}_{{t}^{\prime}}^{s}={({\kappa}_{1{t}^{\prime}}^{s},{\kappa}_{2{t}^{\prime}}^{s},\dots ,{\kappa}_{p{t}^{\prime}})}^{T}$ for ${t}^{\prime}=1,2,\dots ,p$ from Equation (2) (5) Simulate ${\mathit{\gamma}}^{s}\sim \frac{1}{{n}^{s}}{\sum}_{{t}^{\prime}=1}^{p}M({n}_{{t}^{\prime}}^{s},{\mathit{\kappa}}_{{t}^{\prime}}^{s})$ end end.

## 4. Results

#### 4.1. Statistics for Example Classes

#### 4.2. Global Posterior Distributions

#### 4.3. Beta Diversity

## 5. Discussion

#### 5.1. Underlying Causes of Uncertainty

#### 5.2. Assumptions and Limitations

#### 5.3. The Role of the Prior

#### 5.4. Application to Modelling

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Friedl, M.A.; McIver, D.K.; Hodges, J.C.; Zhang, X.; Muchoney, D.; Strahler, A.H.; Woodcock, C.E.; Gopal, S.; Schneider, A.; Cooper, A.; et al. Global land cover mapping from MODIS: Algorithms and early results. Remote Sens. Environ.
**2002**, 83, 287–302. [Google Scholar] [CrossRef] - Friedl, M.A.; Sulla-Menashe, D.; Tan, B.; Schneider, A.; Ramankutty, N.; Sibley, A.; Huang, X. MODIS collection 5 global land cover: Algorithm refinements and characterization of new datasets. Remote Sens. Environ.
**2010**, 114, 168–182. [Google Scholar] [CrossRef] - Bartholomé, E.; Belward, A. GLC2000: A new approach to global land cover mapping from Earth observation data. Int. J. Remote Sens.
**2005**, 26, 1959–1977. [Google Scholar] [CrossRef] - Bontemps, S.; Defourny, P.; Van Bogaert, E.; Arino, O.; Kalogirou, V.; Ramos Perez, J. GlobCover 2009: Products Description and Validation Report. 2011. Available online: http://ionia1.esrin.esa.int/docs/GLOBCOVER2009_Validation_Report_2 (accessed on 1 November 2016).
- Arino, O.; Bicheron, P.; Achard, F.; Latham, F.; Witt, R.; Weber, J.L. The most detailed portrait of Earth. ESA Bull.
**2008**, 136, 25–31. [Google Scholar] - Oleson, K.W.; Bonan, G.B. The effects of remotely sensed plant functional type and leaf area index on simulations of boreal forest surface fluxes by the NCAR land surface model. J. Hydrometeorol.
**2000**, 1, 431–446. [Google Scholar] [CrossRef] - Steyaert, L.; Hall, F.; Loveland, T. Land cover mapping, fire regeneration, and scaling studies in the Canadian boreal forest with 1 km AVHRR and Landsat TM data. J. Geophys. Res.
**1997**, 102, 29581–29598. [Google Scholar] [CrossRef] - Desai, A.R.; Moore, D.J.P.; Ahue, W.K.M.; Wilkes, P.T.V.; De Wekker, S.F.J.; Brooks, B.G.; Campos, T.L.; Stephens, B.B.; Monson, R.K.; Burns, S.P.; et al. Seasonal pattern of regional carbon balance in the central Rocky Mountains from surface and airborne measurements. J. Geophys. Res. Biogeosci.
**2011**, 116. [Google Scholar] [CrossRef] - Woodward, F.; Lomas, M.; Quaife, T. Global responses of terrestrial productivity to contemporary climatic oscillations. Philos. Trans. R. Soc. B Biol. Sci.
**2008**, 363, 2779–2785. [Google Scholar] [CrossRef] [PubMed] - Poulter, B.; Frank, D.C.; Hodson, E.L.; Zimmermann, N.E. Impacts of land cover and climate data selection on understanding terrestrial carbon dynamics and the CO
_{2}airborne fraction. Biogeosciences**2011**, 8, 2027–2036. [Google Scholar] [CrossRef] - Schimel, D.S.; House, J.; Hibbard, K.; Bousquet, P.; Ciais, P.; Peylin, P.; Braswell, B.H.; Apps, M.J.; Baker, D.; Bondeau, A.; et al. Recent patterns and mechanisms of carbon exchange by terrestrial ecosystems. Nature
**2001**, 414, 169–172. [Google Scholar] [CrossRef] [PubMed] - DeFries, R.S.; Field, C.B.; Fung, I.; Justice, C.O.; Los, S.; Matson, P.A.; Matthews, E.; Mooney, H.A.; Potter, C.S.; Prentice, K.; et al. Mapping the land surface for global atmosphere-biosphere models: Toward continuous distributions of vegetation’s functional properties. J. Geophys. Res.
**1995**, 100, 20867–20882. [Google Scholar] [CrossRef] - Hansen, M.; DeFries, R.; Townshend, J.; Carroll, M.; Dimiceli, C.; Sohlberg, R. Global percent tree cover at a spatial resolution of 500 meters: First results of the MODIS vegetation continuous fields algorithm. Earth Interact.
**2003**, 7, 1–15. [Google Scholar] [CrossRef] - Schuh, A.; Denning, A.; Corbin, K.; Baker, I.; Uliasz, M.; Parazoo, N.; Andrews, A.; Worthy, D. A regional high-resolution carbon flux inversion of North America for 2004. Biogeosciences
**2010**, 7, 1625–1644. [Google Scholar] [CrossRef] - Werner, C.; Butterbach-Bahl, K.; Haas, E.; Hickler, T.; Kiese, R. A global inventory of N
_{2}O emissions from tropical rainforest soils using a detailed biogeochemical model. Glob. Biogeochem. Cycles**2007**, 21. [Google Scholar] [CrossRef] - Foody, G.M. Status of land cover classification accuracy assessment. Remote Sens. Environ.
**2002**, 80, 185–201. [Google Scholar] [CrossRef] - Maselli, F.; Conese, C.; Petkov, L. Use of probability entropy for the estimation and graphical representation of the accuracy of maximum likelihood classifications. ISPRS J. Photogramm. Remote Sens.
**1994**, 49, 13–20. [Google Scholar] [CrossRef] - Tchuenté, A.T.K.; Roujean, J.L.; De Jong, S.M. Comparison and relative quality assessment of the GLC2000, GLOBCOVER, MODIS and ECOCLIMAP land cover data sets at the African continental scale. Int. J. Appl. Earth Obs. Geoinform.
**2011**, 13, 207–219. [Google Scholar] [CrossRef] - Quaife, T.; Quegan, S.; Disney, M.; Lewis, P.; Lomas, M.; Woodward, F. Impact of land cover uncertainties on estimates of biospheric carbon fluxes. Glob. Biogeochem. Cycles
**2008**, 22. [Google Scholar] [CrossRef] - Woodward, F.; Lomas, M. Vegetation dynamics—Simulating responses to climatic change. Biol. Rev.
**2004**, 79, 643–670. [Google Scholar] [CrossRef] [PubMed] - Poulter, B.; Ciais, P.; Hodson, E.; Lischke, H.; Maignan, F.; Plummer, S.; Zimmermann, N.E. Plant functional type mapping for earth system models. Geosci. Model Dev.
**2011**, 4, 993–1010. [Google Scholar] [CrossRef] - Green, E.; Strawderman, W. Determining the accuracy of thematic maps. Statistician
**1994**, 43, 77–85. [Google Scholar] [CrossRef] - Denham, R.; Mengersen, K.; Witte, C. Bayesian analysis of thematic map accuracy data. Remote Sens. Environ.
**2009**, 113, 371–379. [Google Scholar] [CrossRef] - Cripps, E.; O’Hagan, A.; Quaife, T. Quantifying uncertainty in remotely sensed land cover maps. Stoch. Environ. Res. Risk Assess.
**2013**, 27, 1239–1251. [Google Scholar] [CrossRef] - Conese, C.; Maselli, F. Use of error matrices to improve area estimates with maximum likelihood classification procedures. Remote Sens. Environ.
**1992**, 40, 113–124. [Google Scholar] [CrossRef] - Best, M.; Pryor, M.; Clark, D.; Rooney, G.; Essery, R.; Ménard, C.; Edwards, J.; Hendry, M.; Porson, A.; Gedney, N.; et al. The Joint UK Land Environment Simulator (JULES), model description—Part 1: Energy and water fluxes. Geosci. Model Dev.
**2011**, 4, 677–699. [Google Scholar] [CrossRef]

**Figure 1.**The proportion of six land cover classes as recorded in the GlobCover2009 data: (

**a**) class 14; (

**b**) class 40; (

**c**) class 90; (

**d**) class 130; (

**e**) class 140 and (

**f**) class 150. Class definitions are given in Table 1.

**Figure 2.**The posterior estimate (mean) of the proportion of six land cover classes: (

**a**) class 14; (

**b**) class 40; (

**c**) class 90; (

**d**) class 130; (

**e**) class 140 and (

**f**) class 150. Class definitions are given in Table 1.

**Figure 3.**The modelled uncertainty, approximated by the posterior standard deviation, in six land cover classes: (

**a**) class 14; (

**b**) class 40; (

**c**) class 90; (

**d**) class 130; (

**e**) class 140 and (

**f**) class 150. Class definitions are given in Table 1.

**Figure 4.**Scatter plots of land cover proportion reported in the GlobCover product against the mean of the posterior. The classes are (

**a**) class 14; (

**b**) class 40; (

**c**) class 90; (

**d**) class 130; (

**e**) class 140 and (

**f**) class 150. The x–axis is the original data and the y–axis is the output from the statistical model.

**Figure 5.**The modelled posterior PDF in the total area covered by each land cover type. Vertical dashed lines show the corresponding totals from the Glob Cover product itself. Class definitions are given in Table 1.

**Figure 7.**2D marginal posterior distributions for southern Africa. Axis labels indicate the land cover class, and contour values are the likelihoods that each contour corresponds to. The axes themselves show total area covered by the class in ${m}^{2}$. The vertical and horizonatal lines show the areas predicted areas from the original data.

**Table 1.**Land cover classes represented in the GlobCover 2009 product. N refers to the total number of samples of that class in the reference data. P refers to the producer’s accuracy (%). U refers to the user’s accuracy (%).

ID | N | P | U | Description |
---|---|---|---|---|

11 | 78 | 24 | 73 | Post-flooding or irrigated croplands |

14 | 402 | 35 | 67 | Rainfed croplands |

20 | 20 | 100 | 12 | Mosaic Cropland (50%–70%)/Vegetation (grassland, shrubland, forest) (20%–50%) |

30 | 12 | 100 | 8 | Mosaic Vegetation (grassland, shrubland, forest) (50%–70%)/Cropland (20%–50%) |

40 | 344 | 72 | 88 | Closed to open (>15%) broadleaved evergreen and/or semi-deciduous forest (>5 m) |

50 | 89 | 60 | 40 | Closed (>40%) broadleaved deciduous forest (>5 m) |

60 | 22 | 32 | 14 | Open (15%–40%) broadleaved deciduous forest (>5 m) |

70 | 68 | 41 | 40 | Closed (>40%) needleleaved evergreen forest (>5 m) |

90 | 48 | 50 | 29 | Open (15%–40%) needleleaved deciduous or evergreen forest (>5 m) |

100 | 51 | 25 | 25 | Closed to open (>15%) mixed broadleaved and needleleaved forest (>5 m) |

110 | 5 | 100 | 6 | Mosaic Forest/Shrubland (50%–70%)/Grassland (20%–50%) |

120 | 3 | 100 | 4 | Mosaic Grassland (50%–70%)/Forest/Shrubland (20%–50%) |

130 | 229 | 29 | 44 | Closed to open (>15%) shrubland (<5 m) |

140 | 213 | 18 | 31 | Closed to open (>15%) grassland |

150 | 97 | 59 | 35 | Sparse (>15%) vegetation (woody vegetation, shrubs, grassland) |

160 | 6 | 50 | 14 | Closed (>40%) broadleaved forest regularly flooded—Fresh water |

170 | 8 | 75 | 55 | Closed (>40%) broadleaved semi-deciduous and/or evergreen forest regularly |

flooded—Saline water | ||||

180 | 30 | 23 | 39 | Closed to open (>15%) vegetation (grassland, shrubland, woody vegetation) on |

regularly flooded or waterlogged soil—Fresh, brackish, or saline water | ||||

190 | 45 | 20 | 69 | Artificial surfaces and associated areas (urban areas >50%) |

200 | 246 | 69 | 88 | Bare areas |

210 | 110 | 70 | 93 | Water bodies |

220 | 44 | 68 | 83 | Permanent snow and ice |

Class ID | 11 | 14 | 20 | 30 | 40 | 50 | 60 | 70 | 90 | 100 | 110 | 120 | 130 | 140 | 150 | 160 | 170 | 180 | 190 | 200 | 210 | 220 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

11 | 19 | 4 | 1 | 2 | ||||||||||||||||||

14 | 29 | 141 | 7 | 1 | 9 | 11 | 2 | 1 | 1 | 5 | 4 | |||||||||||

20 | 10 | 75 | 20 | 11 | 3 | 2 | 1 | 3 | 12 | 14 | 3 | 7 | 2 | |||||||||

30 | 6 | 58 | 12 | 12 | 1 | 1 | 1 | 17 | 21 | 3 | 1 | 1 | 2 | 5 | 1 | |||||||

40 | 2 | 16 | 249 | 3 | 1 | 1 | 8 | 1 | 1 | 1 | ||||||||||||

50 | 17 | 20 | 53 | 2 | 6 | 2 | 12 | 15 | 3 | 1 | 1 | 1 | ||||||||||

60 | 11 | 10 | 2 | 7 | 1 | 14 | 3 | 1 | 2 | |||||||||||||

70 | 3 | 2 | 2 | 2 | 28 | 6 | 4 | 9 | 5 | 1 | 3 | 1 | 3 | 1 | ||||||||

90 | 1 | 1 | 3 | 2 | 17 | 24 | 4 | 7 | 11 | 2 | 3 | 2 | 5 | 1 | ||||||||

100 | 1 | 1 | 9 | 8 | 1 | 13 | 6 | 8 | 2 | 2 | ||||||||||||

110 | 14 | 1 | 2 | 1 | 2 | 5 | 18 | 20 | 4 | 1 | 1 | 3 | 8 | |||||||||

120 | 1 | 8 | 2 | 1 | 6 | 2 | 3 | 17 | 16 | 5 | 2 | 5 | ||||||||||

130 | 1 | 24 | 12 | 7 | 2 | 3 | 1 | 66 | 19 | 2 | 1 | 5 | 2 | 1 | 3 | |||||||

140 | 1 | 24 | 3 | 1 | 1 | 4 | 20 | 38 | 12 | 2 | 6 | 11 | 1 | |||||||||

150 | 4 | 1 | 3 | 6 | 2 | 5 | 30 | 57 | 2 | 4 | 29 | 13 | 7 | |||||||||

160 | 16 | 1 | 3 | 1 | ||||||||||||||||||

170 | 1 | 1 | 1 | 6 | 2 | |||||||||||||||||

180 | 1 | 1 | 1 | 5 | 7 | 3 | ||||||||||||||||

190 | 1 | 1 | 1 | 9 | 1 | |||||||||||||||||

200 | 3 | 1 | 1 | 3 | 5 | 6 | 1 | 169 | 1 | 1 | ||||||||||||

210 | 2 | 2 | 2 | 77 | ||||||||||||||||||

220 | 1 | 1 | 4 | 30 |

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons by Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Quaife, T.; Cripps, E.
Bayesian Analysis of Uncertainty in the GlobCover 2009 Land Cover Product at Climate Model Grid Scale. *Remote Sens.* **2016**, *8*, 314.
https://doi.org/10.3390/rs8040314

**AMA Style**

Quaife T, Cripps E.
Bayesian Analysis of Uncertainty in the GlobCover 2009 Land Cover Product at Climate Model Grid Scale. *Remote Sensing*. 2016; 8(4):314.
https://doi.org/10.3390/rs8040314

**Chicago/Turabian Style**

Quaife, Tristan, and Edward Cripps.
2016. "Bayesian Analysis of Uncertainty in the GlobCover 2009 Land Cover Product at Climate Model Grid Scale" *Remote Sensing* 8, no. 4: 314.
https://doi.org/10.3390/rs8040314