A Method to Estimate Clear-Sky Albedo of Paddy Rice Fields

Abstract

As a major crop type in the global agroecosystem, paddy rice fields contribute to global greenhouse gas emissions. Surface albedo plays a vital role in estimating carbon emissions. However, it is difficult to find a broadband albedo estimation over paddy rice fields. The objective of this study was to derive an applicable method to improve albedo estimation over a paddy rice field. Field multiangle reflectance and surface albedo were collected throughout the growing season. A physically based model (AMBRALS) was utilized to reconstruct the directional reflectance into the spectral albedo. Multiple spectral albedos (at the wavelengths of 470, 550, 660, 850, 1243, 1640 and 2151 nm) were calculated, and new narrowband to broadband conversion coefficients were derived between the observed spectral albedo and broadband albedo. The conversion schemes showed high consistency with the field albedo observations in the shortwave (285–3000 nm), infrared (700–3000 nm), and visible (400–700 nm) bands. This method can help improve albedo estimation in partially submerged environments.

1. Introduction

Land surface albedo, the fraction of incident solar radiation reflected by the Earth’s surface, is a primary factor controlling the surface energy balance [1]. As one of the essential crop types in the global agricultural ecosystem, paddy rice is differentiated from other dryland crops by seasonal, partially submerged water [2]. It is crucial to accurately estimate the paddy rice albedo for the reliable retrieval of terrestrial greenhouse gas emissions [3,4]. However, due to complicated interactions between the bottom soil–middle water–upper plant features of paddy rice fields [5,6,7,8] and the scarcity of continuous albedo observations over paddy rice fields [9], realistic albedo estimation is challenging.

Remote sensing provides the ability to obtain global albedo observations. Generally, there are two ways to obtain remote sensing albedos: the physical retrieval method based on radiative transfer models and the empirical fitting method from remote sensing reflectance. The most extensively used physically based method is the kernel-driven model, which uses radiative transfer theory and has been successfully applied to Moderate Resolution Imaging Spectroradiometer (MODIS) and Landsat data [10]. The kernel-driven model applies several kernel functions to fit various surface properties, such as the Li-Sparse and Li-Dense [11] and Roujean model [12] for surface scattering and the Ross model [13] for volume scattering. The Isotropic-RossThick-LiSparse Reciprocal (RTLSR) kernels are often selected for retrieving the seasonal vegetation albedo due to the stability and good performance of this configuration [14,15,16,17].

The empirical conversion from narrowband (spectral) to broadband albedo is a more straightforward way to describe reflected solar radiation [18]. Many conversion formulas have been developed to adapt various nonflooded surface types and different kinds of satellite sensors [19,20,21,22,23,24,25,26]. Unique surfaces such as snow or glaciers are separately treated [27,28,29,30,31]. The most commonly used conversion schemes were introduced by Liang [18] and have been proven successful on many nonflood land surfaces.

Currently, there are no albedo estimation schemes for paddy rice fields. The existing albedo products from remote sensing have poor accuracy over partially flooded areas [32,33,34,35]. In addition, as an essential input parameter in land surface models (LSMs) [36,37], the albedo of paddy rice regions is now empirically considered as predefined values or simple derivations without matching growing status and seasonal variations [38,39,40,41]. It is necessary to develop an applicable albedo estimation method over paddy rice fields to improve estimations of greenhouse gas emissions.

Therefore, this study aimed to develop a broadband albedo estimation method over paddy rice fields. The method covers multiple broadband bands, including 400–700 nm (visible spectrum, VIS), 700–3000 nm (infrared spectrum, IR), and 285–3000 nm (full shortwave spectrum, SW). The seasonal albedo observations and synchronous reflectance measurements recorded in 2015 were used as the data basis. The kernel-driven directional reflectance model [42,43] was applied as a bridge between the field multiangle reflectance and multiband albedo to produce the spectral albedo. Nine viewing angles were analyzed to fit the best spectral albedo. After that, the narrowband-to-broadband albedo conversion schemes were derived through multiple variable regressions. Finally, the newly derived albedo results were compared with existing conversion schemes and field observations.

2. Materials and Methods

2.1. Study Area and Paddy Rice Growing Features

The experimental area was located in a paddy rice field (400 × 200 m) in Beijing, China (40.076°N, 116.204°E) (Figure 1). Beijing has a temperate continental climate with a hot, humid summer and a cold, dry winter. The annual precipitation in Beijing was approximately 566 mm, and the annual mean temperature was 12.7 °C. This paddy rice field was partially submerged by water from early June (day of year (DOY) 154) to late October (DOY 289) in 2015.

A Nikon-D50 digital camera (Nikon in Tokyo, Japan) was used to estimate vegetation cover fraction (FVC). Photos were shot at a height of 1.5 m from the nadir (direction point directly to the ground). According to the recommended sampling protocol over paddy rice fields [44,45], four elementary sampling units (ESUs, 20 × 20 m²) were selected. The diamond-shaped sampling box was performed at the ESU level. Three photos were taken at each point.

As Figure 2 illustrates, the FVC grew faster than the plant height from 3 June to 26 July. In the tillering stage, the FVC rapidly increased from 0.4 to 0.6 and then slowly increased to 0.8, while the plants’ height rose from 0.3 to 0.6 m during this time. After that, the FVC remained stable at approximately 0.8 and slightly decreased in late September. The height of rice plants continued to grow until mid-August and then started to decline.

2.2. Data Preparation

2.2.1. Directional Reflectance

We sampled multiangle reflectance and albedo over the paddy rice field throughout the growing season. The reflectance observation instrument was specially designed for paddy rice. The directional reflectance was measured with an Avafield-3 spectrometer (Avantes in Apeldoorn, The Netherlands), which measured the reflectance between 300 and 2500 nm. A 2.5 m optic fiber with a 25° field of view (FOV) was attached to the spectrometer. The multiangle reflectance data were collected in 10-day intervals under clear sky conditions. A total of 9 view angles including the forward and backward directions were used in sampling, which were −60°, −45°, −30°, −15°, 0°, 15°, 30°, 45°, and 60°. The backward view angles were marked with a negative symbol. More detailed multiangle reflectance measurements can be found in a previous study [9]. The time we measured the reflectance matched the ten-minute broadband albedo.

2.2.2. Albedo Observations

Regarding the surface broadband albedo, three pairs of pyranometers (Kipp & Zonen in Delft, The Netherlands) with different spectral ranges (400–2800, 700–2800, and 285–2800 nm) were set in the center of the paddy rice field throughout the growing season (Figure 1). The observation height of the pyranometer was 2.2 m from the bottom soil. The pyranometers recorded the data in 10-min steps.

The seasonal albedo and the sample diurnal albedo are illustrated in Figure 3. The asymmetry was significant on the diurnal albedo, with higher values in the morning than in the afternoon. The lower albedo values from 5 to 7 October were affected by cloudy days.

The diurnal mean albedo was averaged from the ten-minute data (7:00–16:00). The seasonality of the rice field albedo was evident in all three spectral ranges. Among them, the values of the infrared albedo (700–3000 nm) were higher than the values of the visible albedo (400–700 nm) and shortwave albedo (285–3000 nm). When the soil surface was totally submerged by water and younger plants (before 23 June), the albedos of all three bands were almost the same. Then, the albedo values started to show discrepancies with the growth in rice plants. During the tillering stage (23 June–9 July), with increasing number of rice leaves, the albedo of the photosynthetic band (400–700 nm) decreased, while the other two albedo bands rapidly increased. After, the shortwave and infrared albedo remained high and stable, while the photosynthetic albedo remained low. After 26 August, the rice grew to the ripening stage and the gradually yellowing leaves indicated a decrease in photosynthetic ability, which resulted in a slow increase in the albedo at 400–700 nm.

2.3. Proposed Method

The proposed method in this study derives broadband albedo by combining field albedo observations and model simulations. As Figure 4 illustrates, first, the model parameters of the spectral albedo were built from the directional reflectance. In this study, the spectral bands were 470, 550, 660, 850, 1243, 1640, and 2151 nm, consistent with previous studies [29]. The best viewing angles to generate the spectral albedo were given in this step. Second, the observed (ten-minute) broadband albedo and the generated spectral albedo were regressed to derive the conversion schemes from narrowband albedo to broadband albedo. Finally, our albedo estimations and the results from the existing conversion schemes for MODIS [18] were compared with the daily albedo observations.

We used a physical model (Algorithm for Model Bidirectional Reflectance Anisotropies of the Land Surface (AMBRALS)) [46] to aggregate directional reflectance to the spectral albedo. The inversion mode of the AMBRALS model was adopted, the white-sky albedo and black-sky albedo were generated, and the diffuse ratio of the sky was calculated from the MODIS aerosol product to derive the blue-sky albedo [47,48].

The AMBRALS model provides a linear expression [12] to describe the surface anisotropy:

$$R\left(\theta ,\vartheta ,\varphi ,\Lambda \right)={{\displaystyle \sum }}_k{f}_k\left(\Lambda \right)K_k\left(\theta ,\vartheta ,\varphi \right)$$

(1)

where $R\left(\theta ,\vartheta ,\varphi ,\Lambda \right)$ is bidirectional reflectance in waveband $\Lambda$, $f_k\left(\Lambda \right)$ is the kernel model parameter, $K_k\left(\theta ,\vartheta ,\varphi \right)$ is the model kernel, $\theta$ is solar zenith angle (SZA), $\vartheta$ is view zenith angle (VZA), and $\varphi$ is view-sun relative azimuth angle. Define a least square error function to minimize the $\partial e^2/\partial f_k$:

$$e^2\left(\Lambda \right)=\frac{1}{d}{{\displaystyle \sum }}_l\left\{\frac{{\left(\rho \left({\theta }_l,{\vartheta }_l,{\varphi }_l,\Lambda \right)-R\left({\theta }_l,{\vartheta }_l,{\varphi }_l,\Lambda \right)\right)}^2}{{\omega }_l\left(\Lambda \right)}\right\}$$

(2)

which derives the solutions for the model parameter $f_k$. The directional-hemispherical and bihemispherical integrals of the kernel model kernels can be defined as follows:

$$h_k\left(\theta \right)={{\displaystyle \int }}_0^{2\pi }{{\displaystyle \int }}_0^{\frac{\pi }{2}}{K}_k\left(\theta ,\vartheta ,\varphi \right)sin\left(\vartheta \right)cos\left(\vartheta \right)d\vartheta d\varphi$$

(3)

$$H_k=2{{\displaystyle \int }}_0^{\pi /2}{h}_k\left(\theta \right)sin\left(\theta \right)cos\left(\theta \right)d\theta$$

(4)

Then, the black-sky albedo and white-sky albedo are:

$${\alpha }_{bs}\left(\theta ,\Lambda \right)={{\displaystyle \sum }}_k{f}_k\left(\Lambda \right)h_k\left(\theta \right)$$

(5)

$${\alpha }_{ws}\left(\Lambda \right)={{\displaystyle \sum }}_k{f}_k\left(\Lambda \right)H_k$$

(6)

Black-sky albedo is defined as the albedo in the absence of a diffuse component and is a function of the solar zenith angle. White-sky albedo is defined as the albedo in the absence of a direct component when the diffuse component is isotropic, which is a constant [49].

Black-sky albedo and white-sky albedo mark the extreme cases of completely direct and completely diffuse illumination, respectively. Actual albedo is a value interpolated between these two depending on the aerosol optical depth. If the diffuse skylight is assumed to be an isotropic fraction $S\left(\theta ,\tau \left(\Lambda \right)\right)$ of total illumination, then the actual spectral albedo is:

$$\alpha \left(\theta ,\Lambda \right)=\left\{1-S\left(\theta ,\tau \left(\Lambda \right)\right)\right\}{\alpha }_{bs}\left(\theta ,\Lambda \right)+S\left(\theta ,\tau \left(\Lambda \right)\right){\alpha }_{ws}\left(\Lambda \right)$$

(7)

Then, the broadband albedo can be converted by the empirical conversion weights $c_i$, which reflect the distribution of downwelling radiative flux:

$$A\left(\theta \right)={{\displaystyle \sum }}_i{c}_i\alpha \left(\theta ,{\Lambda }_i\right)$$

(8)

The directional reflectance can be modeled as several kernels that represent the scattering types: isotropic scattering, volumetric scattering from horizontally homogeneous leaf canopies, and geometric-optical surface scattering from scenes containing three-dimensional objects:

$$R\left(\theta ,\vartheta ,\varphi ,\lambda \right)=f_{iso}\left(\lambda \right)+f_{vol}\left(\lambda \right)k_{vol}\left(\theta ,\vartheta ,\varphi \right)+f_{geo}\left(\lambda \right)k_{geo}\left(\theta ,\vartheta ,\varphi \right)$$

(9)

where $k_{vol}$ is the volume scattering as a function of solar zenith angle ${\theta }_s$, view zenith angle ${\theta }_v$, and relative azimuth angle $\varphi$; $k_{geo}$ is the surface scattering from the canopy; $f_{vol}$ and $f_{geo}$ are the weights of the kernels; and $f_{iso}$ is a constant corresponding to isotropic scattering. More detailed information about the kernel mathematics can be found in the algorithm documents of the MODIS product (MOD43B).

RossThick and LiSparse-R kernels were adopted in this study. A simple mathematical expression was found in the AMBRALS model to express the integrations of directional reflectance, which provides a numerical way to calculate the spectral albedo:

$$h_k\left(\theta \right)=g_{0k}+g_{1k}{\theta }^2+g_{2k}{\theta }^3$$

(10)

$${\alpha }_{bs}\left(\theta ,\Lambda \right)=f_{iso}\left(\Lambda \right)\left(g_{0iso}+g_{1iso}{\theta }^2+g_{2iso}{\theta }^3\right)+f_{vol}\left(\Lambda \right)\left(g_{0vol}+g_{1vol}{\theta }^2+g_{2vol}{\theta }^3\right)+f_{geo}\left(\Lambda \right)\left(g_{0geo}+g_{1geo}{\theta }^2+g_{2geo}{\theta }^3\right)$$

(11)

The white-sky albedo (${\alpha }_{ws}\left(\Lambda \right)$) is given as a constant in the outputs of the AMBRALS model with the kernel coefficients.

3. Results

3.1. Generation of Spectral Albedo from Directional Reflectance

The clear-sky spectral albedo was derived from the relationships between field multiangle reflectance and kernel-driven simulations. Figure 5 shows the relationships between the directional reflectance and spectral albedo including all spectral bands. As Figure 5 illustrates, the fitting relationships were more discrete when the directional reflectance was higher than 0.5. A linear relationship was found between the directional reflectance and spectral albedo:

$${\alpha }_{\lambda }\left(\vartheta \right)=k_1{\rho }_{\lambda }\left(\vartheta \right)+k_2$$

(12)

where ${\alpha }_{\lambda }$ is the spectral albedo, $k_1$ and $k_2$ are the model coefficients, and ${\rho }_{\lambda }$ indicates the reflectance from the specified viewing zenith angle ($\vartheta$).

The fitting coefficients for spectral albedo are shown in

Table 1. Statistics of the relationships between reflectance and spectral albedo.

Data Info	Coefficient		Statistics
VZA	k1	k2	R2	RMSE
60°	1.063	−0.003	0.961	0.036
45°	0.972	−0.006	0.965	0.031
30°	0.879	−0.004	0.964	0.029
15°	0.758	−0.001	0.945	0.031
0°	0.711	0.003	0.923	0.035
−15°	0.795	0.004	0.928	0.038
−30°	0.908	0.006	0.944	0.038
−45°	1.025	0.009	0.944	0.043
−60°	1.128	0.011	0.947	0.045
Mean values	-	-	0.947	0.037

. The average R² was 0.947, and the average RMSE was 0.037. According to Table 1, the oblique reflectance contributed more information to estimating the spectral albedo. Forward observations (positive VZA) produced higher accuracy than nadir and backward observations, whose R² values were greater than 0.96 and RMSEs were lower than 0.037. The best fitting came from the forward 30°, which suggested that the forward 30° might be a more reliable viewing angle for estimating the spectral albedo over paddy rice fields.

3.2. Conversion Formulas from Narrowband to Broadband

We derived conversion schemes for MODIS, the most commonly used sensor when estimating the surface albedo. Multiple linear regression was adopted at full shortwave (285–3000 nm), infrared (700–3000 nm), and visible (400–700 nm) bands. The derived broadband albedo was a function of spectral albedo generated from the reflectance of forward 30°. The linear conversion forms weighted with the given coefficients are listed in

Table 2. Broadband albedo conversion coefficients and standard error (SE) (* p < 0.05).

Spectral Albedo	Shortwave		Infrared *		Visible *
-	Coeff	SE	Coeff	SE	Coeff	SE
${\alpha }_{470}$	−1.524	0.023	-	-	−1.357	0.402
${\alpha }_{550}$	0.197	0.693	-	-	1.1718	0.137
${\alpha }_{660}$	0.128	0.282	-	-	−0.0528	0.019
${\alpha }_{850}$	1.1263	0.048	0.556	0.257	-	-
${\alpha }_{1243}$	0.0713	0.266	0.407	0.079	-	-
${\alpha }_{1640}$	0.0894	0.064	0.205	0.138	-	-
${\alpha }_{2151}$	−0.023	0.091	−0.055	0.121	-	-
Intercept	0.063	0.069	0.075	0.028	0.0525	0.012

:

3.3. Intercomparison of Broadband Albedo

We compared the fitted broadband albedo derived from new conversion schemes with field measurements and Liang’s results (Figure 6). The daily field albedo was the baseline in our comparison. For the VIS band, except for phase 3, the values showed good consistency in the other growth stages. Albedos were almost the same in phase 1 when the paddy rice field was covered mainly by water. Liang’s albedo conversion presented a slight overestimation (≈0.01) in phase 2, and showed an underestimation when the rice plants were fully matured in phase 3. For the IR band, due to the radiation absorption of the water surface, both Liang’s conversions and our results were close to the pyranometer’s results (≈0.1) before the rice tillering stage (phase 1). Thereafter, the rapid growth and extension of vegetation leaves significantly increased the field albedo between 2 and 12 July. In phase 2, from the mean values, our results underestimated the field observations by 0.052 while Liang’s conversion overestimated the field observations by approximately 0.018. In phase 3, both Liang’s and our albedos were close to the field albedo.

The variations in the albedo in the shortwave band were similar to those in the infrared band in phases 1 and 2 (Figure 6c). For the SW band, our results slightly underestimated the field observations by 0.015 and Liang’s conversion overestimated the field observations by approximately 0.01. In phase 3, Liang’s conversion schemes showed underestimation and our fitted results were consistent.

For the whole growing season, the regressions between fitted and field broadband albedo are illustrated in Figure 7. For the shortwave albedo, the results of this study showed higher accuracy than those from Liang’s conversions. The underestimations in phases 1 and 3 led to the relatively lower accuracy of Liang’s conversion schemes. Liang’s conversion results were close to our results in the infrared and visible bands.

4. Discussion

4.1. SZA Dependence on Broadband Albedo Conversion

In this study, the SZAs were grouped into four ranges: 20°–30°, 30°–40°, 40°–50°, and 50°–65°. In Figure 8, SZA presents lower RMSE values in the ranges of 30°–40° and 40°–50° at most VZAs. The larger SZAs (>50°) did not show significant degradation in accuracy (

Table 3. The R² values of SZA dependence.

VZA and SZA	R2
-	20°–30°	30°–40°	40°–50°	50°–65°
60°	0.987	0.994	0.993	0.984
45°	0.985	0.994	0.996	0.986
30°	0.980	0.991	0.995	0.993
15°	0.963	0.982	0.987	0.992
0°	0.951	0.985	0.978	0.990
−15°	0.967	0.982	0.982	0.987
−30°	0.979	0.987	0.989	0.989
−45°	0.988	0.988	0.984	0.987
−60°	0.994	0.993	0.981	0.985

), which is different than the results in a previous study [50]. The higher fitting accuracy of SZA dependence throughout the growing season indicates the robustness of our albedo conversion method.

The weak dependences on wavelengths and the higher fitting accuracy on SZA indicated that the albedo derivation in this study could include more spectral bands and adapt more measurement time points.

4.2. Spectral Dependence on Broadband Albedo Conversion

As

Table 4. Broadband albedo conversion coefficients and standard error (SE).

	470 nm	550 nm	660 nm	850 nm	1243 nm	1640 nm	2151 nm
60°	1.117	0.981	1.064	0.938	0.913	0.912	0.971
45°	1.195	1.125	1.102	1.025	1.020	1.049	1.056
30°	1.050	1.177	1.073	1.117	1.135	1.224	1.162
15°	1.096	1.303	1.090	1.288	1.295	1.422	1.172
0°	1.099	1.235	1.081	1.335	1.358	1.450	1.159
−15°	0.989	1.089	1.005	1.198	1.208	1.285	1.076
−30°	0.853	0.931	0.877	1.051	1.065	1.073	0.994
−45°	0.814	0.792	0.722	0.933	0.938	0.923	0.892
−60°	0.720	0.709	0.654	0.853	0.849	0.816	0.799

illustrates, except for the forward 15° and nadir VZAs, similar fitting slopes were observed in the other VZAs between the directional reflectance and spectral albedo. The slope values showed consistent variations in each VZA among all the wavelengths, which hinted at the independence of wavelengths in estimating the spectral albedo. Regarding fitting errors for all the VZAs, relatively higher RMSEs were varied for longer wavelengths (1243, 1640, and 2151 nm), which is understandable because of the varied characteristics of the spectral absorption in shortwave wavelengths [51], especially over submerged water fields. These assessments support incorporating more spectral bands in albedo estimations with fewer errors.

The conversion schemes in this study use the same number of bands and similar spectral ranges as the methods in previous studies. The performance of our method was better in SW albedo than in IR and VIS albedo, which suggests the better fitting ability of the longer wavelength used in this study and the insufficient consideration of water background in previous studies.

A previous study [50] reported similar spectral dependence results in the visible and near-infrared spectral bands (443–865 nm). Our study further reported the weak dependence of the longer SWIR bands (>1243 nm). A study also discussed the spectral dependence in estimating albedo [52] and found that the error was only 1% in the estimation of the TOA broadband albedo. In summary, the model derived in this study is dependable from directional reflectance to spectral albedo and has more spectra tolerances for other remote sensors.

Although all field measurements used in this study were extracted under clear-sky conditions, there were still a few diffuse components in the reflected radiance that could not be separated. Therefore, the directional reflectance used in this study was apparent bidirectional reflectance [53], and the estimated albedo should be called apparent albedo (clear-sky abedo), which includes the direct and diffuse components.

4.3. Applicability of the Proposed Method

In this study, we designed a method to estimate clear-sky albedo over paddy rice fields, which provides a clear technical path and direct conversion coefficients between spectral and broadband albedo. The advantages of this method are twofold: (1) The constructing procedures are duplicable and the AMBRALS model is stable, optimal, and free. In addition, the method can be extended to other kinds of land cover. (2) The albedo conversion coefficients are available throughout the growing season of paddy rice. Meanwhile, the disadvantages are: (1) a certain amount of measured data is required, and (2) the output coefficients need validation before being applied over similar land surfaces.

This study provides conversion coefficients based on specific wavelengths that cover spectral bands of the MODIS platform. If more conversion schemes are needed, through our assessments, the derivations of conversion coefficients for new satellite sensors or transplantations from one surface type to another are feasible and easy to complete.

5. Conclusions

Albedo is an essential parameter for estimating the greenhouse gas emissions of paddy rice. Through radiative transfer model simulations and field measurements, this study proposed a new narrowband to broadband method to estimate the paddy rice field albedo in the visible (400–700 nm), infrared (700–3000 nm), and full shortwave (285–3000 nm) spectral bands. The new method showed good consistency with field measurements throughout the growing season and was weakly affected by wavelengths. The method could be flexibly used in field environments and with remote sensing platforms.

This study method has the potential to couple with the land surface model and to extend the conversion schemes to other wetland types. The conversion schemes in the current study will be more representative if more data from various wetland types (such as marshes and swamps) are included. Therefore, deriving more universal albedo conversion schemes for all wetland types is a future research objective.

This study provided a simple method for albedo calculation over paddy rice fields and helped improve carbon emission estimations over similar kinds of partially submerged vegetation.