2.2.3. MISR

The multi-angle imaging spectroradiometer (MISR) [17] sensor onboard NASA's Earth Observing System (EOS) Terra satellite provides high accuracy surface albedo products from near simultaneous multi-angular views. The MISR level 2 land/surface albedo products provide land DHR and BHR over four narrow bands: blue (446 ± 21 nm), green (558 ± 15 nm), red (672 ± 11 nm) and near infrared (866 ± 20 nm), at a resolution of 1.1 km. Liang's model [18] is used here to retrieve the total shortwave broadband albedo by linearly combining the spectral albedos as follows:

$$a^{MISR} = 0.126 \cdot a\_2 + 0.343 \cdot a\_3 + 0.415 \cdot a\_4 + 0.0037 \tag{1}$$

where *α*2, *α*3 and *α*4 represent MISR spectral albedos for band 2, 3 and 4, *αMISR* is the total broadband shortwave albedo. In this study, MISR pixels near each of the tower sites were extracted between 2012 and 2016. It should be noted that, the BHR products from MISR are different to MODIS and CGLS, because they represent the actual blue-sky albedo rather than an idealised white-sky.

#### *2.3. Surface Albedo from Tower Measurements*

DHR and BHR [19] are calculated from the ratios of the measured upwelling and downwelling solar radiant fluxes, but they are based on different assumptions about how the atmospheric scattering processes can affect the intensity of downwelling diffuse radiation. If the atmospheric scattering effects are removed, then the illumination can be assumed to originate from a single infinitesimally small point source. In this case, the measured ratio between the upwelling and downwelling radiations becomes the DHR. If the atmospheric scattering effects are included, then the illumination is assumed to be uniform from all angles and this is known as the "white sky". This results in the BHR being calculated from the measured ratio between the upwelling and downwelling radiation. Both DHR and BHR represent extreme cases that rarely exist in the physical "real world". In all previous works of satellite-derived albedo validation using in situ measurements, a compromised value between DHR and BHR has been used for an indirect comparison [20,21]. This compromised value is intended to

represent the in situ albedo, which is called the blue-sky (or clear sky) albedo and can be computed as follows:

$$BlueSkyAlbedo = \pounds \cdot \text{BHR} + (1 - \beta) \cdot \text{DHR} \tag{2}$$

where β denotes the proportion of diffuse component in downwelling solar radiation. Normally, β is measured at ground-tower sites by a separate pyranometer, which is independent from the pyranometers that measure the total downwelling and upwelling radiations. This independent pyranometer is mounted with a sun tracker that shields the sensor from direct sunlight. If the ground-based pyranometer that measures diffuse radiation is not available, a satellite aerosol product (e.g., MOD04/MYD04 of MODIS or the aerosol optical depth (AOD) retrieved as part of the GlobAlbedo (http://www.globalbedo.org/) product [22]) can be used to estimate β, but this is with high temporal and spatial uncertainties.

**Table 1.** List of tower sites with key characteristics: acronyms, geographical coordinates, network, footprint (see Equation (12)) and land cover type, defined by International Geosphere-Biosphere Programme (IGBP). Station names in bold are those whose results are shown below.


Sites marked with \* are claimed to be spatially representative, which is sometimes referred to as homogeneous by [11]. \*\* US-BRW is spatially representative during snow covered periods, but heterogeneous during the snow melt season. N.B. The three sites marked with # do not have diffuse radiation measurements, so the method introduced in Section 2.3.1 is used to estimate diffuse radiation [23].

Blue-sky albedo can be estimated by combining the DHR and BHR data from satellite measurements and the β value from tower measurements. In this way, the estimated albedo value at local solar noon can be used directly for comparison with the ground-based albedo. However, there are two major critical issues in this inter-comparison: (1) β is measured at local solar noon and, often, under cloud-free conditions. The blue-sky albedo in this case is dominated by the DHR because the β value is close to zero under cloud-free conditions. (2) DHR and BHR cannot be assessed separately from the blue-sky albedo using this method. To overcome these issues, a new strategy is proposed in which albedo is derived into the DHR and BHR components separately, solely from in situ tower data. A conceptual flowchart of this processing chain is illustrated in Figure 2, and details are introduced in Sections 2.3.1 and 2.3.2.

**Figure 2.** Flowchart illustrating the algorithm for retrieving directional hemispherical reflectance (DHR) and bi-hemispherical reflectance (BHR) from tower measurements. *βB* and *βD* represent the threshold of the diffuse ratio for filtering BHR and DHR, respectively. σ represents the standard deviation of the calculated BHR and DHR values. *SWin*, *SWout* and *SWdi f* represent the downwelling total, upwelling total and downwelling diffuse shortwave radiation, respectively.

#### 2.3.1. Directional Hemispherical Reflectance (DHR)

In Figure 2, the *SWin*, *SWout* and *SWdi f* represent the downwelling total, upwelling total, and downwelling diffuse shortwave radiation measured from the tower sites, respectively. The downwelling diffuse radiation was measured at all of the selected SUFRAD and BSRN tower sites, but was unavailable at three FLUXNET tower sites (i.e., the Calperum, Guyaflux and Niwot Ridge sites). To deal with this challenge, we calculated β from the potential top of atmosphere radiance *SWin*(*po<sup>t</sup>*) using Equation (3). The parameter *SWin*(*po<sup>t</sup>*) is provided in the FLUXNET dataset, or, if not, can be estimated based on the geographic location of the tower and the sun-tower geometry [23]. Experimental results demonstrated that diffuse ratios estimated from Equation (3) had a good agreemen<sup>t</sup> with real measurements when β was very low or very high.

$$\mathcal{B} = \left( \mathcal{S} \mathcal{W}\_{\text{in}(\text{pot})} - \mathcal{S} \mathcal{W}\_{\text{in}} \right) / \mathcal{S} \mathcal{W}\_{\text{in}(\text{pot})} \tag{3}$$

According to Equation (2), the DHR can be well approximated by the blue-sky albedo when *β* tends towards zero. Such low values of *β* can be reached under completely cloudless conditions with a very low level of aerosol at local solar noon. From empirical heuristic studies we verified that a threshold of *βD* = 0.1 was suitable for screening out undesired tower measurements, because data that meet the condition of *β* ≤ *βD* within ±1 h local solar noon, for all sites, can be considered sufficient to perform the validation of DHR derived from satellite measurements. A threshold of *βD* lower than 0.1

can reduce the amount of remaining data dramatically, because *β* does not often reach such a low level within the specified ±1 h at local solar noon, due to broken cloud cover.

Once the ±1 h local solar noon data are screened by the condition *β* ≤ *β<sup>D</sup>*, the mean and standard deviation (σ) over a sliding time-window of 30 days can be calculated. In this example the time-window for averaging the tower data was set as 30 days for CGLS, so that the in situ DHR and BHR could be compared with these CGLS products. However, a narrower time-window can also be adopted if enough data can be collected for estimating DHRs using this strategy. This method can cause a bias in the derived DHR values because the effect of BHR in the blue-sky albedo is ignored. However, the effect of BHR in the blue-sky albedo will not exceed the predefined threshold of *β<sup>D</sup>*. Therefore, in order to estimate the uncertainty of the DHRs, the *σ* of the final in situ DHRs is dilated by *β<sup>D</sup>*, so as to represent the effect of BHR on DHR. Figure 3 shows an example of ground-based albedo (*SWout*/*SWin*) at different stages of in situ DHR creation from the data of FLUXNET Tumbarumba site in 2015. The main steps of producing in situ DHRs can be summarised as follows: (1) Calculating *SWout*/*SWin* for all the data points; (2) filtering data with negative upwelling or downwelling radiation values; (3) filtering data with solar zenith angle larger than 75◦, because the linear BRDF model does not work for these zenith angles; (4) retaining data that meet the condition *β* ≤ *βD*; (5) retaining data within ±1 h of local solar noon; (6) applying a weighting function over the time window of 30 days; and (7) including the estimation of uncertainty values.

**Figure 3.** An example of processed FLUXNET Tumbarumba tower data showing the steps in the production of in situ DHRs.

#### 2.3.2. Bi-Directional Hemispherical Reflectance (BHR)

In contrast, the in situ BHR can be approximated by the blue-sky albedo when β tends towards 1. This high diffusion ratio can only be reached under certain conditions, such as under thick unbroken stratus clouds, which are often formed before sunrise and after sundown. Under this assumption, a lower threshold of *βB* = 0.9 was used to filter undesirable measurements from the raw data. Once the data are filtered by this condition (β ≥ *βB*), the BHR was calculated from the *SWout*/*SWin* from the remaining data. Similarly, the mean and the standard deviation over a sliding time-window, which is 30 days in this example, were calculated. The effect of DHR on in situ BHR should be taken into account when assuming the BHR, and can be approximated by the blue-sky albedo. From trial-and-error, the *σ* of the final in situ BHR need to be increased by 1 − *βB* to represent its uncertainty. Figure 4 shows an example of ground-based albedos at different stages of in situ BHR creation from the data of FLUXNET Tumbarumba site in 2015. The processing and filtering steps were the same as specified above for DHR.

**Figure 4.** A sample of processed FLUXNET Tumbarumba tower data for producing in situ BHRs.
