# Land Surface Albedos Computed from BRF Measurements with a Study of Conversion Formulae

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## Abstract

**:**

## 1. Introduction

## 2. Measurement and processing

**Figure 1.**The locations of the measurements. From the bottom up, H = Hanko, hexagon = Masala, diamond = Hyytiälä, S = Suonenjoki, circle = Rovaniemi, star = Pyhätunturi, downward pointing triangle = Sodankylä, upward pointing triangle = Vuotso, square = Kilpisjärvi. Helsinki is 20 km east of Masala.

- We measured grey gravel from SjÖkulla test field [21] in a laboratory and in the field with five illumination angles. The gravel was artificially made, homogeneous, and rough, with an average grain size of 1 cm.
- We took dry sand from several locations in Finland and measured it at several illumination angles.
- 27.8.2004, Hanko beach, laboratory
- 13.9.2005, Hietalahti beach, Helsinki, sunlight
- 13.9.2005, Football field, Helsinki, sunlight
- 17.7.2006, Hietalahti beach, Helsinki, sunlight
- 8.8.2006, Sodankylä, sunlight
- 31.5.2009, beach volley field, Hyytiälä, sunlight

- We measured new snow in Sodankylä on two successive nights on 4–5 of March 2008 using a lamp immediately after a snow fall at five angles of illumination. The snow grains still had clear flake shapes, but they had already begun breaking up into needles.
- We measured dry old snow on 1 April 2008 in Sodankylä using a lamp at four different illumination angles. The snow was several days or weeks old, the grains were rounded, and its temperature was well below zero.
- We measured very wet melting snow in March 2009 in a laboratory in Masala using a lamp at three different illumination angles.
- We combined the data on Moss from measurements in Masala and Suonenjoki, both in sunlight and using a lamp, with a total of eight angles of illumination. The samples mostly consisted of Hylocomium splendens species.
- 23.8.2004, Masala, laboratory
- 24.8.2004, Masala, sunlight
- 7.6.2005, Suonenjoki, laboratory
- 7.6.2005, Suonenjoki, laboratory
- 7.6.2005, Suonenjoki, laboratory
- 2.9.2004, Masala, laboratory, Pleurozium schreberi

- We measured lichen in Suonenjoki, Sodankylä, and Masala. There were seven samples with nine angles of illumination.
- 11.7.2001, Masala, laboratory
- 18.8. 2004, Masala, laboratory
- 7.6.2005, Suonenjoki, laboratory
- 9.6.2005, Suonenjoki, laboratory
**Figure 2.**Definition of the angles used in surface reflectance work: ϵ and ι are the zenith angles of the emergent (Observer) and incident (solar) radiation respectively, φ and ${\varphi}_{0}$ are the corresponding azimuths. The phase or back scattering angle α is the angle between the Observer and the Sun. The principal plane is fixed by the solar direction and the surface normal to it, while the cross plane is a vertical plane perpendicular to the principal plane. - 3.8.2006, Sodankylä, sunlight
- 3.8.2006, Sodankylä, sunlight
- 6.8.2006, Sodankylä, sunlight

- The Lingonberry data set contained two measurements from Suonenjoki and Sodankylä.
- 8.6.2005, Suonenjoki, laboratory
- 9.6.2005, Suonenjoki, laboratory
- 5.8.2006, Sodankylä, sunlight
- 6.8.2006, Sodankylä, sunlight

- We measured an incomplete set of wet and dry peat at Suonenjoki in August 2003.

**Figure 3.**The illumination spectra used for various broadband-albedo computations. The solid line is the incident sunlight to the surface that is used for surface broadband albedo. We measured it on 18 May 2009 in SjÖkulla in clear sky conditions with a solar zenith angle of about 60${}^{\circ}$. We used the dashed line to compute the PAR (photosynthetically active radiation) albedo. The dotted line represents the solar radiation above the atmosphere, and was used for the top of atmosphere (TOA) albedo (with two technical modifications to the atmospheric water vapour absorption bands around 1,400 nm and 1,800 nm to deal with instrument noise in the sunlight measurements). All spectra are normalised to the same value.

## 3. Results

#### 3.1. Albedos

**Figure 4.**Left: The spectrally-resolved hemispherical albedo at three angles of incidence: maximum, minimum and 60${}^{\circ}$(interpolated). Right: recovered broadband surface albedo (solid line, +), TOA albedo (dotted line, x) and PAR albedo (dashed line, diamond) as a function of the solar zenith angle. The black thin lines represent the broadband albedo obtained by combining all measured samples. The coloured thick lines and symbols correspond to the different samples, as listed by collection date, and represent the broadband albedo obtained by applying all illumination angles together (lines) and single illumination angles separately (symbols). The thin lines extrapolate to almost the full range of illumination angles but give less reliable values than the thick lines. The targets are grey gravel and sand in the upper and lower panels, respectively.

**Figure 5.**Left: The spectrally-resolved hemispherical albedo at three angles of incidence: maximum, minimum and 60${}^{\circ}$(interpolated). Right: recovered broadband surface albedo (solid line, +), TOA albedo (dotted line, x) and PAR albedo (dashed line, diamond) as a function of the solar zenith angle, as in Figure 4. The targets are from top down: new snow, old dry snow, wet snow.

#### 3.2. Evaluation of Narrow-to-Broadband Surface Albedo Conversion Equations

**(Table 4 in Appendix 1)**. We applied the conversion formula to the measured albedo values integrated over the given wavelength bands. We then compared the obtained broadband albedo estimate to the broadband

**Figure 6.**Left: The spectrally-resolved hemispherical albedo at three angles of incidence: maximum, minimum and 60${}^{\circ}$(interpolated). Right: recovered broadband surface albedo (solid line, +), TOA albedo (dotted line, x) and PAR albedo (dashed line, diamond) as a function of the solar zenith angle, as in Figure 4. The targets are from top down: moss, lichen, and lingonberry.

**Figure 7.**Left: Differences between the single peat sample from Suonenjoki when wet (dotted curve) and dry (solid line). Right: albedo of a SjÖkulla white gravel sample measured in different weather, cleanness, and ageing conditions. The angle of incidence was 60${}^{\circ}$± 5${}^{\circ}$.

**Table 1.**The broadband albedo values of various targets at the sun zenith value of 60${}^{\circ}$ obtained by direct integration of the measured spectra.

Target | Albedo |

Grey gravel | 0.09 |

Lingonberry | 0.20 |

Moss | 0.24 |

Sand | 0.30 |

Lichen | 0.31 |

Dry old snow | 0.65 |

Wet lab snow | 0.66 |

New snow | 0.79 |

**Figure 8.**The relative difference between two broadband albedo estimates and the sun zenith angle for various targets. We derived the two albedo values as follows: (1) by using various broadband conversion formulae from Liang [25] and (2) by directly integrating of the measured BRF spectrum.

**Figure 9.**The relative difference between two broadband albedo estimates and the sun zenith angle for various targets. We derived the two albedo values as follows: (1) by using various broadband conversion formulae from van Leeuwen and Roujean [26] and (2) by directly integrating the measured BRF spectrum.

**Figure 10.**The relative difference between two broadband albedo estimates and the sun zenith angle for snow. We derived the two albedo values were derived as follows: (1) by using various dedicated snow broadband conversion formulae from Greuell and Oerlemans, Knap and Oerlemans and Xiong et al. [22,23,24] and (2) by directly integrating the measured BRF spectrum.

**Figure 11.**The albedo calculated using broadband conversion methods versus the integrated measured BRF spectrum for various targets and the sun zenith angle values. Top: The conversion methods developed by Liang [25] are colour-coded as shown. Bottom: The conversion methods by vanLeeuwen and Roujean [26] are colour-coded as shown.

**Figure 12.**The albedo calculated using broadband conversion methods versus the integrated measured BRF spectrum for various targets and the sun zenith angle values. The dedicated snow conversion methods developed by Greuell and Oerlemans, Knap and Oerlemans and Xiong et al. [22,23,24] are colour-coded as shown and the target is snow for all points.

**Table 2.**We obtained the mean and standard deviation values of the difference in estimated albedo values as follows (1) by using various broadband conversion formulae; and (2) by directly integrating the measured BRF spectrum. All targets and sun zenith angles are included.

All | Land | Snow | ||||

Mean | Standard dev. | Mean | Standard dev. | Mean | Standard dev. | Method |

0.018 | 0.014 | 0.014 | 0.014 | 0.023 | 0.015 | POLDER, [25] |

0.022 | 0.018 | 0.015 | 0.01 | 0.034 | 0.022 | SEVIRI 234, [26] |

0.026 | 0.014 | 0.021 | 0.015 | 0.035 | 0.007 | AVHRR, [25] |

0.027 | 0.021 | 0.021 | 0.018 | 0.038 | 0.022 | AVHRR 4, [26] |

0.028 | 0.02 | 0.022 | 0.011 | 0.039 | 0.026 | AVHRR 123, [26] |

0.031 | 0.023 | 0.015 | 0.007 | 0.058 | 0.011 | MODIS, [25] |

0.031 | 0.024 | 0.024 | 0.016 | 0.043 | 0.03 | SEVIRI 123, [26] |

0.032 | 0.022 | 0.024 | 0.016 | 0.045 | 0.026 | SEVIRI 4, [26] |

0.034 | 0.02 | 0.028 | 0.014 | 0.043 | 0.025 | AVHRR 12, [26] |

0.034 | 0.025 | 0.035 | 0.03 | 0.033 | 0.017 | ASTER, [25] |

0.038 | 0.028 | 0.02 | 0.011 | 0.069 | 0.019 | Landsat, [25] |

0.04 | 0.021 | 0.034 | 0.013 | 0.051 | 0.028 | SEVIRI 12, [26] |

0.04 | 0.027 | 0.021 | 0.011 | 0.07 | 0.016 | SPOT VGT, [25] |

0.047 | 0.046 | 0.015 | 0.012 | 0.099 | 0.029 | MISR, [25] |

0.055 | 0.022 | 0.059 | 0.022 | 0.048 | 0.02 | SEVIRI 1234, [26] |

0.067 | 0.034 | 0.056 | 0.017 | 0.085 | 0.048 | GOES, [25] |

0.039 | 0.02 | AVHRR, [22] | ||||

0.043 | 0.027 | Landsat, [22] | ||||

0.044 | 0.015 | AVHRR, [24] snow model | ||||

0.049 | 0.017 | MISR, [22] | ||||

0.05 | 0.015 | Landsat, [23] | ||||

0.051 | 0.03 | MODIS 12, [22] | ||||

0.052 | 0.016 | MODIS 124, [22] | ||||

0.053 | 0.024 | AVHRR, [24] SHEBA | ||||

0.078 | 0.045 | AVHRR, [24] snow/ice |

**Table 3.**The ratio of the mean difference of albedo estimates derived by (1) using broadband conversion; and, (2) direct integration of the BRF spectrum. In the nominator, the broadband conversion has been derived using optimised parameter values and, in the denominator, by using original parameter values.

Optimal/Original | Method |

0.03 | MODIS, [25] |

0.05 | Landsat, [25] |

0.07 | SPOT VGT, [25] |

0.08 | ASTER, [25] |

0.11 | SEVIRI 1234, [26] |

0.19 | AVHRR, [25] |

0.31 | AVHRR 123, [26] |

0.31 | MISR, [25] |

0.31 | POLDER, [25] |

0.35 | SEVIRI 123, [26] |

0.41 | SEVIRI 234, [26] |

0.63 | SEVIRI 12, [26] |

0.64 | AVHRR 12, [26] |

0.64 | GOES, [25] |

0.88 | SEVIRI 4, [26] |

0.95 | AVHRR 4, [26] |

## 4. Discussion

## 5. Conclusions

## Author Contribution

## Acknowledgements

## A. Appendix

**Table 4.**The studied broadband conversion methods of various satellite instruments and respective channels and resolutions.

Instrument/Resolution/ | Conversion formula, ${\alpha}_{bb}=$ | Wavelength range of channels used in the conversion formula [μm] | ||||||

Method | Channel 1 | Channel 2 | Channel 3 | Channel 4 | Channel 5 | Channel 6 | * | |

ASTER, 15 m [25] | $0.484{\alpha}_{1}+0.335{\alpha}_{3}-0.324{\alpha}_{5}+0.551{\alpha}_{6}+0.305{\alpha}_{8}$ | 0.52…0.6 | 0.63…0.69 | 0.78…0.86 | 1.6…1.7 | 2.15…2.18 | 2.18…2.22 | ^{a} |

$-0.367{\alpha}_{9}-0.0015$ | ||||||||

AVHRR, 1.1 km [25] | $-0.3376{\alpha}_{1}^{2}-0.2707{\alpha}_{2}^{2}+0.7074{\alpha}_{1}{\alpha}_{2}+0.2915{\alpha}_{1}$ | 0.57…0.71 | 0.72…1.01 | |||||

$+0.5256{\alpha}_{2}+0.0035$ | ||||||||

GOES, 4 km [25] | $0.0759+0.7712{\alpha}_{1}$ | 0.52…0.72 | ||||||

Landsat, 30 km [25] | $0.356{\alpha}_{1}+0.130{\alpha}_{3}+0.373{\alpha}_{4}+0.085{\alpha}_{5}+0.072{\alpha}_{7}$ | 0.45…0.51 | 0.52…0.60 | 0.63…0.69 | 0.75…0.90 | 1.55…1.75 | 2.09…2.35 | |

$-0.0018$ | ||||||||

MISR, 275 m [25] | $0.126{\alpha}_{2}+0.343{\alpha}_{3}+0.451{\alpha}_{4}+0.0037$ | 0.42…0.45 | 0.54…0.55 | 0.66…0.67 | 0.85…0.87 | |||

MODIS, 500 m [25] | $0.160{\alpha}_{1}+0.291{\alpha}_{2}+0.243{\alpha}_{3}+0.116{\alpha}_{4}+0.112{\alpha}_{5}$ | 0.62…0.67 | 0.84…0.87 | 0.46…0.48 | 0.54…0.56 | 1.23…1.25 | 1.63…1.65 | ^{b} |

$+0.081{\alpha}_{7}-0.0015$ | ||||||||

POLDER, 6 km [25] | $0.112{\alpha}_{1}+0.388{\alpha}_{2}-0.266{\alpha}_{3}+0.668{\alpha}_{4}+0.0019$ | 0.43…0.46 | 0.66…0.68 | 0.74…0.79 | 0.84…0.88 | |||

SPOT, 1 km [25] | $-0.0022+0.3512{\alpha}_{1}+0.1629{\alpha}_{2}+0.3415{\alpha}_{3}+0.1651{\alpha}_{4}$ | 0.43…0.47 | 0.61…0.68 | 0.78…0.89 | 1.58…1.75 | |||

EPS/AVHRR, 1 km[26] | 0.586…0.679 | 0.733…0.979 | 1.585…1.631 | 0.437…0.970 | ||||

123 | $0.3880+0.5234{\alpha}_{1}+0.3102{\alpha}_{2}+0.1097{\alpha}_{3}$ | |||||||

12 | $3.0238+0.4967{\alpha}_{1}+0.3148{\alpha}_{2}$ | |||||||

4 | $3.6848+0.8008{\alpha}_{4}$ | |||||||

SEVIRI, 5 km [26] | 0.601…0.678 | 0.780…0.839 | 1.572…1.698 | 0.476…0.910 | ||||

124 | $0.5095+0.5972{\alpha}_{1}+0.3071{\alpha}_{2}-0.0872{\alpha}_{4}$ | |||||||

123 | $0.4724+0.5370{\alpha}_{1}+0.2805{\alpha}_{2}+0.1297{\alpha}_{3}$ | |||||||

12 | $3.8259+0.5119{\alpha}_{1}+0.2782{\alpha}_{2}$ | |||||||

234 | $0.0831+0.0541{\alpha}_{2}+0.1106{\alpha}_{3}+0.7659{\alpha}_{4}$ | |||||||

4 | $3.8317+0.7926{\alpha}_{4}$ | |||||||

AVHRR, 1.1 km [22] | $0.718{\alpha}_{1}-0.137{\alpha}_{1}^{2}+0.317{\alpha}_{2}^{2}$ | 0.574…0.704 | 0.720…1.000 | |||||

Landsat, 30 m [22] | $0.422{\alpha}_{2}+0.337{\alpha}_{4}+0.113{\alpha}_{4}^{2}$ | 0.519…0.611 | 0.772…0.898 | |||||

MISR , 275 m [22] | $0.383{\alpha}_{2}^{2}+0.743{\alpha}_{3}-0.624{\alpha}_{3}^{2}+0.402{\alpha}_{4}^{2}$ | 0.548…0.565 | 0.663…0.679 | 0.852…0.879 | ||||

MODIS, [22] | 0.620…0.677 | 0.838…0.875 | 0.544…0.564 | |||||

500 m, 124 | $0.734{\alpha}_{1}-0.717{\alpha}_{1}^{2}+0.428{\alpha}_{2}^{2}+0.458{\alpha}_{4}^{2}$ | |||||||

250 m, 12 | $0.714{\alpha}_{1}-0.110{\alpha}_{1}^{2}+0.286{\alpha}_{2}^{2}$ | |||||||

Landsat, 30 m [23] | $0.726{\alpha}_{2}-0.322{\alpha}_{2}^{2}-0.051{\alpha}_{4}+0.581{\alpha}_{4}^{2}$ | 0.52…0.60 | 0.75…0.90 | |||||

AVHRR, 1.1 km [24] | ||||||||

SHEBA data | $0.007+0.542{\alpha}_{1}+0.340{\alpha}_{2}$ | 0.58…0.68 | 0.725…1.1 | |||||

Snow model | $0.007+0.434{\alpha}_{1}+0.464{\alpha}_{2}$ | |||||||

Snow/ ice | $0.28(1+8.26\gamma ){\alpha}_{1}+0.63(1-3.96\gamma ){\alpha}_{2}+0.22$, | |||||||

where $\gamma =({\alpha}_{1}-{\alpha}_{2})/({\alpha}_{1}+{\alpha}_{2})$ |

^{a}Channels 7—9: 2.23… 2.28, 2.29… 2.36, 2.36… 2.43

^{b}Channel 7: 2.11…2.15

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**MDPI and ACS Style**

Peltoniemi, J.I.; Manninen, T.; Suomalainen, J.; Hakala, T.; Puttonen, E.; Riihelä, A.
Land Surface Albedos Computed from BRF Measurements with a Study of Conversion Formulae. *Remote Sens.* **2010**, *2*, 1918-1940.
https://doi.org/10.3390/rs2081918

**AMA Style**

Peltoniemi JI, Manninen T, Suomalainen J, Hakala T, Puttonen E, Riihelä A.
Land Surface Albedos Computed from BRF Measurements with a Study of Conversion Formulae. *Remote Sensing*. 2010; 2(8):1918-1940.
https://doi.org/10.3390/rs2081918

**Chicago/Turabian Style**

Peltoniemi, Jouni I., Terhikki Manninen, Juha Suomalainen, Teemu Hakala, Eetu Puttonen, and Aku Riihelä.
2010. "Land Surface Albedos Computed from BRF Measurements with a Study of Conversion Formulae" *Remote Sensing* 2, no. 8: 1918-1940.
https://doi.org/10.3390/rs2081918