# A New Global fAPAR and LAI Dataset Derived from Optimal Albedo Estimates: Comparison with MODIS Products

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## Abstract

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## 1. Introduction

#### 1.1. Leaf Area Index (LAI)

^{2}·m

^{−2}) [11] and ranges from 0 (bare ground) to over 10 (dense forest). LAI determines the interception of solar energy (and thus the fAPAR) for photosynthesis, as well as the available area for gas and water exchange between plant and atmosphere. LAI in a remote sensing sense, in contrast, is (typically) defined as one-sided leaf area per unit ground area (m

^{2}·m

^{−2}) i.e., 0.5 of the total [1,12], primarily from the point of view of light interception. Projected leaf area is often the more general requirement for radiation interception, which is dependent on leaf angle distribution [13,14]. Here, LAI is defined in the latter sense as half the total canopy area per unit ground area (m

^{2}·m

^{−2}).

#### Caveats: LAI

^{2}). Indirect methods are thus widely used to infer LAI, typically via upward-looking hemispherical photographs (hemiphotos) or bespoke instruments that compare light levels above and below the canopy (e.g., LI-COR LAI 2200c Plant Canopy Analyser [16]; the Delta-T SunScan Canopy Analysis System [17] and so on). In these cases, LAI is inferred based on assumptions of the canopy absorption properties (e.g., all canopy elements are black) and architecture (e.g., assuming the canopy is horizontally homogeneous, and/or leaf angle distribution is uniform or spherical) [18,19].

^{−2}m within shoots, to 10

^{2}m at the stand level). Clumping acts to reduce $\tilde{LAI}$compared to the true value, $\langle LAI\rangle $, as the degree of clumping increases. In contrast, very regular canopies (crops for example) will tend to have $\tilde{LAI}$ > $\langle LAI\rangle $ [19,21].

#### 1.2. fAPAR: Fraction of Absorbed Photosynthetically Active Radiation

#### Caveats: fAPAR

## 2. Experimental Section

#### 2.1. GlobAlbedo-Derived LAI and fAPAR

#### 2.1.1. Two-Stream Model

#### 2.1.2. Two-Stream Model Inversion

^{T}represents the transpose operator; ${\mathit{X}}_{post}$ and ${\mathit{C}}_{{\mathit{X}}_{post}}$ are the mean and uncertainty covariance matrix of $P\left(\mathit{X}\right)$; ${\mathit{C}}_{{\mathit{X}}_{post}}^{-1}$ is the inverse of ${\mathit{C}}_{{\mathit{X}}_{post}}$. The resulting ${\mathit{X}}_{post}$ minimizes the cost function $J\left(\mathit{X}\right)$. In practice, $J\left(\mathit{X}\right)$ is minimized using a gradient descent method using the adjoint of $J\left(\mathit{X}\right)$. Uncertainty ranges ${\mathit{C}}_{{\mathit{X}}_{post}}$ for ${\mathit{X}}_{post}$ are approximated through inversion of the Hessian matrix of $J\left(\mathit{X}\right)$. The Jacobian matrix of first derivatives of fluxes with respect to parameters is used to propagate parameter uncertainty to flux uncertainty. All derivative code is derived via automatic differentiation of the code that implements $J\left(\mathit{X}\right)$ [33,34].

#### 2.1.3. Spatial Resolution

#### 2.1.4. Data Format

#### 2.1.5. Time Period and Data Size

#### 2.1.6. FLUXNET Sites Used for Site-Level Comparisons

- Grasslands
- Deciduous broadleaf
- Evergreen needleleaf
- Mixed forest
- Crop/natural

#### 2.2. MODIS LAI and fAPAR

## 3. Results and Discussion

#### 3.1. Global LAI and fAPAR Derived from GlobAlbedo

_{fAPAR}, lies mainly between 0.1 and 0.4; uncertainty in LAI, σ

_{LAI}, is generally highest in areas of high LAI, with some exceptions in Western Europe, China and SE Asia. In these regions, persistent cloud likely causes the higher retrieval uncertainty. This ability of the two-stream inversion package, JRC-TIP, to provide parameter retrieval uncertainty as a consistent part of the retrieval process is a key reason for using such an approach. Data assimilation applications for example, require explicit consideration of uncertainty in driving observations [41,42,43]. The GlobAlbedo product includes uncertainty estimates on a per pixel basis. This is a key difference from other global EO-derived estimates of fAPAR and LAI, for which parameter retrieval uncertainty is either absent, or quantised and hard to interpret as a “real” uncertainty [44].

#### 3.2. Site-Specific and Regional GlobAlbedo-Derived fAPAR and LAI

#### 3.2.1. Flux Site Comparisons by Cover Type

^{2}and RMSE of the linear fit in each case.

#### Grasslands

^{2}values, which range from 0.76 to 0.95. GA-derived values lie below the corresponding MO values for all sites bar US-Ar2 i.e., there is a positive slope between GA and MO values. The intercept between the two estimates of fAPAR is ≤ 0.12 in all cases.

^{2}values between the two LAI datasets lie between 0.77 and 0.87 with the exception of CN-Du3, which has a larger slope of ~2 and intercept of 1.3. This suggests there is a particular difference at this site, in terms of canopy structure between the datasets. Other than this there is a consistent positive slope i.e., as for fAPAR, MODIS LAI values are generally higher than the corresponding GA-derived values. The variation in uncertainty is apparent in both fAPAR and LAI, particularly at the RU-Upo and US-AR2 sites.

#### Deciduous Broadleaf Forest

^{2}values for fAPAR range from 0.86 to 0.92, with positive slope between 1.34 and 1.43 and intercept between 0.07 and 0.11.

^{2}values lie between 0.84 and 0.90, with slope of around 2–2.3 in all cases, and with intercepts between −0.3 and −0.2.

#### Evergreen Needleleaf Forest

^{2}values range from 0.52 to 0.77, i.e., markedly lower than for the cover types above, with positive slope ranging from 1.4 up to 2.23 for the FI-Ves site, and intercept between −0.16 and 0.1.

^{2}values of 0.6–0.84, but with very large slopees in all cases, from 3.1 to >8 in the case of the FI-Ves site, and intercept values of −1.74–0.04. These values would suggest that there is a significant difference in the way the respective parameter retrievals operate over evergreen needleleaf forests. The MODIS algorithm requires tree cover to exceed 70% to be classified as forest, which may be marginal in some of these areas; it is also possible that including understory in the MODIS RT retrieval scheme introduces further differences. Notably, uncertainty is large in the MODIS LAI retrievals, particularly in the DE-SfN and FI-Ves sites. The latter is a very northerly site, with a short growing season, persistent snow cover and observations that will contain low sun angles through large parts of even mid-summer. These factors will all introduce greater uncertainty to RT parameter retrievals.

#### Mixed Forest

^{2}values lie between 0.77 and 0.88 with slope lying between 1.1 and 1.74, and with intercept −0.1–0.08.

^{2}values lie between 0.75 and 0.83, with slope between 1.5 and 3.5 and intercept between −0.72 and 0.2

#### Crop/Natural

^{2}values of 0.81–0.95, with much lower slope (0.97–1.42) than for the forest sites above and intercepts in the range −0.2–0.1.

^{2}values > 0.9, but lower for EE-Aar and ML-Kem (r

^{2}values 0.68 and 0.71 respectively). Slope in these sites lies between 1.06 and 1.32 (again, the ML-Kem site is the higher one) and intercepts are −0.41–0.15.

#### Miscellaneous

^{2}~ 0.6), but very different peak values between GA and MO values. Both these sites experience significant and extended snow cover during the winter, which will affect retrieval values and timing during spring particularly. In addition, both sites have significant understory which may have a different phenology to the overstory forest canopy. Mixed phenology of this sort is always likely to introduce uncertainty in retrieved timing information. This is also likely to affect the MODIS and GlobAlbedo-derived parameter retrievals slightly differently due to the different assumptions underlying the retrieval methods.

^{2}~ 0.1). This is likely to be due to both cloud, and the inherently different seasonality in these tropical regions, dominated by evergreen broadleaf trees and rainfall seasonality. The uncertainty in the MODIS values is testament to this variability.

^{2}values close to 0. This would indicate that the derived values should be interpreted with care in terms of timing and magnitude (relative or otherwise) at sites of this sort.

#### Summary of Site Comparisons

#### 3.2.2. Regional Comparisons

- h09v05: Central USA
- h18v03: Western Europe
- h18v07: Central West Africa
- h29v12: South Australia

#### Central USA: Tile h09v05

^{2}= 0.3, and for LAI r

^{2}= 0.08 i.e., there is very little spatial correspondence between the GA and MO values, particularly for LAI. There is clearly a strong seasonal variation in LAI, with much higher values (and range) observed over DOY 185 than for DOY 361 over both years. Areas of low vegetation cover such as this (and/or particularly heterogeneous areas) are likely to prove more problematic for RT parameter retrieval at these scales than mid-range LAI, heterogeneous regions. Correct identification of the underlying land cover class (or biome) is simply more difficult/uncertain, resulting in potentially higher uncertainty in retrieved RT model parameters. This is particularly the case for scrub/grasslands and low LAI savannas.

#### Western Europe: Tile h18v03

^{2}values of 0.8 and 0.77 for fAPAR and LAI respectively. The consistently lower values of both GlobAlbedo-derived LAI and fAPAR (and much lower range) discussed above, are also apparent in the 2D scatter plots.

#### Central and West Africa: Tile h18v07

^{2}~ 0.5. As explained above for the Caxiuanã and Guyaflux tower site comparisons, this may be due to strong spatial and temporal patterns of seasonal rainfall variation across the tile. The response of grasslands, and savanna more generally, is very dependent on (and even defined by) rainfall. This is likely to dominate vegetation timing patterns in these areas, making comparisons difficult. The implication is that care should be taken in interpreting the values from either dataset in this sort of area: timing and magnitude of fAPAR or LAI will be dependent on which sort of retrieval is used.

#### South Australia: Tile h29v12

^{2}> 0.9 for both. This indicates that although the LAI values are consistently low, a much stronger agreement between GlobAlbedo-derived and MODIS values exists for this kind of cover than for the others shown above. In these regions it is entirely appropriate to compare and even cross-calibrate GlobAlbedo-derived and MODIS values.

#### 3.3. Whole-Hemisphere Comparisons

^{2}values exceeding 0.8 for: 37% of NH tiles and 52% of SH tiles on 2005 DOY 001 (NH winter, SH summer). This fraction rises in 2005 for DOY 185 to 48% and 63% of the NH and SH tiles respectively. For 2011, the distribution of r

^{2}values is almost identical. The slope and intercept of the correlation between the two products obviously represent the translation from one to the other. If the two datasets are to be compared or used in conjunction with each other, then these values could be used for transforming from one to the other. From Figure 13 the gradient between the fAPAR products lies between 0.5 and 1.5 for ~70% of all tiles on DOY 001, and 80% of all tiles on DOY 185 for both 2005 and 2011. Lastly, the intercept of the linear regression of the fAPAR products lies within −0.1 and 0.1 for 90%–95% of all tiles in both 2005 and 2011, with a slightly greater spread of values for winter cases than summer.

^{2}exceeding 0.8 for 13% (NH) and 20% (SH) of tiles for 2005 DOY 001, and 15% (NH) and 34% (SH) of tiles for 2005 DOY 185. The values for 2011 are very similar. This indicates that the correlation is stronger in general for the SH tiles. The gradient of the correlation between the LAI products lies between 0.5 and 1.5 for 42% (NH) and 24% (SH) of cases in 2005 DOY 001. These percentages switch around for 2005 DOY 185, to 27% (NH) and 34% (SH). This suggests there is a greater variation in the gradient of the relationship between the LAI estimates in winter than in summer. For 2011, the gradient lies between 0.5 and 1.5 for 31%–38% of all cases.

## 4. Discussion

**mean slope 1.01, σ = 0.78****mean intercept 0.03, σ = 0.10**

**mean slope 1.70, σ = 1.73****mean intercept 0.15, σ = 0.58**

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**(

**Top**): global 25 km map of GlobAlbedo-derived fAPAR for DOY 185 2002; (

**Bottom**): uncertainty σ

_{fAPAR}of retrieved fAPAR for the same time period.

**Figure 2.**(

**Top**): global 25 km map of GlobAlbedo-derived LAI for DOY 185 2002; (

**Bottom**): uncertainty σ

_{LAI}of retrieved LAI for the same time period.

**Figure 3.**Top row: GlobAlbedo-derived and MODIS fAPAR values for 2002–2011; second row: scatter plot of fAPAR values; third row: GlobAlbedo-derived and MODIS LAI values for 2002–2011; fourth row: scatter plot of LAI values. Error bars for GlobAlbedo values represent the uncertainty of parameter retrieval, and for the MODIS data, the variance of the 3 × 3 pixel window centered on the comparison site.

**Figure 4.**Top row: GlobAlbedo-derived and MODIS fAPAR values for 2002–2011; second row: scatter plot of fAPAR values; third row: GlobAlbedo-derived and MODIS LAI values for 2002–2011; fourth row: scatter plot of LAI values. Error bars for GlobAlbedo values represent the uncertainty of parameter retrieval, and for the MODIS data, the variance of the 3 × 3 pixel window centered on the comparison site.

**Figure 5.**Top row: GlobAlbedo-derived and MODIS fAPAR values for 2002–2011; second row: scatter plot of fAPAR values; third row: GlobAlbedo-derived and MODIS LAI values for 2002–2011; fourth row: scatter plot of LAI values. Error bars for GlobAlbedo values represent the uncertainty of parameter retrieval, and for the MODIS data, the variance of the 3 × 3 pixel window centered on the comparison site.

**Figure 6.**Top row: GlobAlbedo-derived and MODIS fAPAR values for 2002–2011; second row: scatter plot of fAPAR values; third row: GlobAlbedo-derived and MODIS LAI values for 2002–2011; fourth row: scatter plot of LAI values. Error bars for GlobAlbedo values represent the uncertainty of parameter retrieval, and for the MODIS data, the variance of the 3 × 3 pixel window centered on the comparison site.

**Figure 7.**Top row: GlobAlbedo-derived and MODIS fAPAR values for 2002–2011; second row: scatter plot of fAPAR values; third row: GlobAlbedo-derived and MODIS LAI values for 2002–2011; fourth row: scatter plot of LAI values. Error bars for GlobAlbedo values represent the uncertainty of parameter retrieval, and for the MODIS data, the variance of the 3 × 3 pixel window centered on the comparison site.

**Figure 8.**Top row: GlobAlbedo-derived and MODIS fAPAR values for 2002–2011; second row: scatter plot of fAPAR values; third row: GlobAlbedo-derived and MODIS LAI values for 2002–2011; fourth row: scatter plot of LAI values. Error bars for GlobAlbedo values represent the uncertainty of parameter retrieval, and for the MODIS data, the variance of the 3 × 3 pixel window centered on the comparison site.

**Figure 9.**Regional comparison of GlobAlbedo-derived (GA) and MODIS (MO) fAPAR and LAI. (

**Top row**): GA fAPAR (

**left panel**) and LAI (

**right panel**); (

**middle row**): MO fAPAR (

**left panel**) and LAI (

**right panel**); (

**bottom row**): heatmap scatter plot between the GA (x-axis) and MO (y-axis) values, DOY 185 for all years 2002–2011: fAPAR (

**left panel**) and LAI (

**right panel**).

**Figure 10.**Regional comparison of GlobAlbedo-derived (GA) and MODIS (MO) fAPAR and LAI. (

**Top row**): GA fAPAR (

**left panel**) and LAI (

**right panel**); (

**middle row**): MO fAPAR (

**left panel**) and LAI (

**right panel**); (

**bottom row**): heatmap scatter plot between the GA (x-axis) and MO (y-axis) values, DOY 185 for all years 2002–2011: fAPAR (

**left panel**) and LAI (

**right panel**).

**Figure 11.**Regional comparison of GlobAlbedo-derived (GA) and MODIS (MO) fAPAR and LAI. (

**Top row**): GA fAPAR (

**left panel**) and LAI (

**right panel**); (

**middle row**): MO fAPAR (

**left panel**) and LAI (

**right panel**); (

**bottom row**): heatmap scatter plot between the GA (x-axis) and MO (y-axis) values, DOY 185 for all years 2002–2011: fAPAR (

**left panel**) and LAI (

**right panel**).

**Figure 12.**Regional comparison of GlobAlbedo-derived (GA) and MODIS (MO) fAPAR and LAI. (

**Top row**): GA fAPAR (

**left panel**) and LAI (

**right panel**); (

**middle row**): MO fAPAR (

**left panel**) and LAI (

**right panel**); (

**bottom row**): heatmap scatter plot between the GA (x-axis) and MO (y-axis) values, DOY 001 for all years 2002–2011: fAPAR (

**left panel**) and LAI (

**right panel**).

**Figure 13.**Comparison of whole hemisphere GlobAlbedo-derived (GA) and MODIS (MO) fAPAR. Each panel shows a histogram of NH and SH histograms of correlation coefficient (r

^{2}), slope and intercept, for regression of GA v MO. (

**Top row**), 2005: (

**left panel**): day-of-year (DOY) 001; (

**right panel**): DOY 185. (

**Bottom row**), 2011: (

**left panel**): DOY 001; (

**right panel**): DOY 185.

**Figure 14.**Comparison of whole hemisphere GlobAlbedo-derived (GA) and MODIS (MO) LAI. Each panel shows a histogram of NH and SH correlation coefficient (r

^{2}), slope and intercept, for regression of GA v MO. (

**Top row**), 2005: (

**left panel**): day-of-year (DOY) 001; (

**right panel**): DOY 185. (

**Bottom row**), 2011: (

**left panel**): DOY 001; (

**right panel**): DOY 185.

FLUXNET Code, Full Name | Location: Lat, Lon |
---|---|

Grassland | |

AU-Stp: Australia, Stuart Plains | −17.15, 133.35 |

CN-Du3: China, Doulun Degraded Meadow | 42.06, 116.28 |

RU-Upo: Russia, Ust Pojeg | 61.93, 50.23 |

US-AR2: ARM USDA UNL OSU Woodward Switchgrass 2 | 36.64, −99.60 |

Deciduous broadleaf forest | |

US-Oho: Ohio Oak Openings | 41.55, −83.84 |

US-UMB: Univ. of Michigan Biological Station | 45.56, −84.71 |

US-WCr: Willow Creek | 45.81, −90.08 |

US-Wi3: Wisconsin Mature Hardwood | 46.63, −91.10 |

Evergreen needleleaf forest | |

DE-SfN: Schechenfilz Nord, Germany | 47.81, 11.33 |

FI-Ves: Vesijako, Finland | 61.37, 25.11 |

PL-Tcz: Tuczno, Poland | 53.19, 16.10 |

US-NR2: Niwot Ridge, Colorado, US | 40.04, −105.55 |

Mixed forest | |

AT-StM: Stubai Meadow, Austria | 47.13, 11.31 |

CH-Dsc: Dischma, Switzerland | 46.79, 9.86 |

EE-Hi2: Hiiesoo, Estonia | 59.35, 27.10 |

US-Ha2: Harvard Forest Hemlock, US | 42.54, −72.18 |

Crop/Natural | |

CA-MA2: Manitoba Agricultural Site 2, Canada | 50.17, −97.88 |

EE-Aar: Aardlapalu, Estonia | 58.31, 26.74 |

ML-Kem: Kelma, Mali | 15.22, −1.57 |

US-Wi6: Wisconsin Pine Barrens, US | 46.62, −91.30 |

Miscellaneous | |

DE-Hai: Hainich, Germany (mixed forest) | 51.08, 10.45 |

DE-Tha: Tharandt, Germany (evergreen needleleaf) | 50.96, 13.57 |

BR-Cax: Caxiuanã Forest, Brazil (evergreen broadleaf) | −1.72, −51.46 |

GF-Guy: Guyaflux, French Guiana (evergreen broadleaf) | 5.28, −52.92 |

Biome | Slope (Lower, Upper) | Intercept (Lower, Upper) | ||
---|---|---|---|---|

fAPAR | LAI | fAPAR | LAI | |

Grassland | 0.9, 1.1 | 1.2, 2.1 | −0.1, 0.07 | −0.3, 1.3 |

Deciduous broadleaf forest | 1.3, 1.4 | 2, 2.3 | −0.1 | −0.5, −0.3 |

Evergreen needleleaf forest | 1.4, 2.3 | 3.1, 8.3 | −0.2, 0.1 | −1.7, 0 |

Mixed forest | 1.1, 1.7 | 1.5, 3.5 | −0.1, 0.1 | −0.7, 0.2 |

Crop/natural | 1, 1.4 | 1.1, 1.6 | −0.2, 0.1 | −0.4, 0.2 |

Miscellaneous | 0.2, 1.4 | 0.1, 2.5 | −0.1, 0.5 | −0.1, 3.5 |

© 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**

Disney, M.; Muller, J.-P.; Kharbouche, S.; Kaminski, T.; Voßbeck, M.; Lewis, P.; Pinty, B.
A New Global fAPAR and LAI Dataset Derived from Optimal Albedo Estimates: Comparison with MODIS Products. *Remote Sens.* **2016**, *8*, 275.
https://doi.org/10.3390/rs8040275

**AMA Style**

Disney M, Muller J-P, Kharbouche S, Kaminski T, Voßbeck M, Lewis P, Pinty B.
A New Global fAPAR and LAI Dataset Derived from Optimal Albedo Estimates: Comparison with MODIS Products. *Remote Sensing*. 2016; 8(4):275.
https://doi.org/10.3390/rs8040275

**Chicago/Turabian Style**

Disney, Mathias, Jan-Peter Muller, Said Kharbouche, Thomas Kaminski, Michael Voßbeck, Philip Lewis, and Bernard Pinty.
2016. "A New Global fAPAR and LAI Dataset Derived from Optimal Albedo Estimates: Comparison with MODIS Products" *Remote Sensing* 8, no. 4: 275.
https://doi.org/10.3390/rs8040275