Influence of Surface Reflection (Albedo) in Simulating the Sun Drying of Paddy Rice

The sun drying of agricultural products is a complicated process involving heat transfer, mass transfer, and variable weather conditions. Surface reflection (albedo), a crop’s radiative property, plays an essential role in energy balance, and understanding its contribution can improve the thermal analysis. In this study, field experiments were conducted in the Philippines to explore the influence of surface albedo on the sun drying of paddy rice. First, we implemented energy and mass balance equations in a transient model with the surroundings using a graphical programming language in Matlab/Simulink®. Second, we identified the influence of albedo on the sun drying model by using a sensitivity analysis. Third, we investigated the relationship of paddy rice albedo and the solar zenith angle. Lastly, we integrated the albedo function into the sun drying model. The simulation outputs were validated with field experiments. A better estimation of the measured exit temperature and instantaneous mass were obtained when a variable albedo was applied. This study makes clear that introducing a variable albedo has a positive impact on model improvement. This information is important for application in solar drying technologies, so that the drying process can be better assessed.


Introduction
The sun drying of paddy rice is a common practice in the Philippines and many other countries in the tropics and subtropics. Immediately after harvesting/threshing, paddy rice is spread over mats positioned alongside roads or on other paved ground when weather conditions are favorable. To ensure and optimum milling process, it is recommended to dry the paddy rice to a moisture content (MC) of around 14% wet basis [1,2]. During the dry season, the grain temperature can reach up to 55 • C due to the direct exposure of the paddy rice to high solar radiation. Under these conditions, the paddy rice can reach a very low MC (<10% wet basis) [3,4], which may result in fissured grains after milling, thus decreasing its market value. However, during the rainy season, the lower radiation and extended rainy periods may lead to a prolonged drying process. This delay in drying increases the risk of paddy rice deterioration. This deterioration of paddy rice can be observed in the milled rice.
The sun drying of paddy rice is a complex process, which involves the removal of water through direct exposure of the crop to solar radiation. Heat is transferred from the surroundings and from the sun to the exposed crop surface. Raising the crop temperature helps to diffuse water vapor from the interior of the kernel to the surface. Hence, mathematical models have been developed to understand and predict the sun drying process of different agricultural products. Jain and Tiwari [5] proposed the calculation of the convective heat transfer coefficient (h c ), followed by the generation of a mathematical model for the estimation of the crop temperature (T crop ) and moisture evaporated (m ev ). To simplify the model's solution, a steady state condition is commonly used, and indeed several authors follow Figure 1. Thermal network of a one-dimensional model for the sun drying of paddy rice with layer thickness z and temperatures of ambient air, Tam, air exiting from the surface, Tae, paddy rice, Tpa, polyvinyl chloride (PVC) tarpaulin, Tta, asphalt, Tas, and soil, Tso.

External Node
According to the thermal network shown in Figure 1, energy balance at the external node can be expressed as: where mt (kg) is the instantaneous mass of the paddy, αpa (-) is the albedo of paddy rice, Gup (W m −2 ) is the total solar radiation, A (m −2 ) is the area of the crop exposed to the sun, hrc,pa-ae (W m −2 K −1 ) is the combined radiative and convective heat transfer coefficient from the paddy rice surface to the air, Tae (°C) is the temperature of the air exiting the paddy rice surface-henceforth called exit temperature-Tpa (°C) is the temperature of the paddy rice, and Qev (kJ m −2 s −1 ) is the rate of heat utilized to evaporate moisture. Qev is calculated as [38]: where hc,pa-ae (W m −2 K −1 ) is the convective heat transfer coefficient from the paddy rice surface to the air, rham (-) is the ambient relative humidity, and PTpa and PTae (N m −2 ) are the saturated vapor pressure at the respective temperatures. The values of PT were extracted from the temperature range from 25 to 55 °C [39], which corresponds to the operating condition of the sun drying experiments. A 1D lookup table block built in Simulink was used to retrieve the saturated vapor pressure at the respective temperatures [40]. The energy balance of moist air above the paddy rice is calculated as: where Tam (°C) is the ambient temperature and hw (W m −2 K 1 ) is the convective heat transfer coefficient for wind. hw is computed according to Duffie and Beckmann [41]: where Vw (m s −1 ) is the wind velocity. The radiative heat transfer coefficient hr,pa-ae is written as: T i-1 Figure 1. Thermal network of a one-dimensional model for the sun drying of paddy rice with layer thickness z and temperatures of ambient air, T am , air exiting from the surface, T ae , paddy rice, T pa , polyvinyl chloride (PVC) tarpaulin, T ta , asphalt, T as , and soil, T so .

External Node
According to the thermal network shown in Figure 1, energy balance at the external node can be expressed as: where m t (kg) is the instantaneous mass of the paddy, α pa (-) is the albedo of paddy rice, G up (W m −2 ) is the total solar radiation, A (m −2 ) is the area of the crop exposed to the sun, h rc,pa-ae (W m −2 K −1 ) is the combined radiative and convective heat transfer coefficient from the paddy rice surface to the air, T ae ( • C) is the temperature of the air exiting the paddy rice surface-henceforth called exit temperature-T pa ( • C) is the temperature of the paddy rice, and Q ev (kJ m −2 s −1 ) is the rate of heat utilized to evaporate moisture. Q ev is calculated as [38]: where h c,pa-ae (W m −2 K −1 ) is the convective heat transfer coefficient from the paddy rice surface to the air, rh am (-) is the ambient relative humidity, and P Tpa and P Tae (N m −2 ) are the saturated vapor pressure at the respective temperatures. The values of P T were extracted from the temperature range from 25 to 55 • C [39], which corresponds to the operating condition of the sun drying experiments. A 1D lookup table block built in Simulink was used to retrieve the saturated vapor pressure at the respective temperatures [40]. The energy balance of moist air above the paddy rice is calculated as: where T am ( • C) is the ambient temperature and h w (W m −2 K 1 ) is the convective heat transfer coefficient for wind. h w is computed according to Duffie and Beckmann [41]: where V w (m s −1 ) is the wind velocity. The radiative heat transfer coefficient h r,pa-ae is written as: where the emissivity ε of a solid body is equal to the absorbance (1-α) measured at the same wavelengths according to Kirchhoff's law [32,42] and σ is the Boltzmann constant (5.6696 × 10 −8 W m −2 K −4 ). The calculation of the mass of paddy rice m t during drying is done by subtracting the evaporated water from the initial mass m 0 . The evaporated mass of water m ev is obtained as: where t (h) is the time of the sampling interval and L (kJ kg −1 ) is the latent heat of vaporization, which is calculated as [43]:

Intermediate Nodes
The energy balance of the intermediate nodes is driven by heat conduction. Figure 1 shows the thermal network across the bottom layers, and the rate of thermal energy flow into the bottom layers is given as: where T i corresponds to the material temperature of the respective node and C i is the lumped thermal capacity of the material around the node, which can be calculated by knowing the specific heat capacity c pi (kJ m −3 K −1 ), and the thickness z i (m) of the material (9).
The thermal conductance K i is given as: where λ i (kJ m −2 K −1 ) is the thermal conductivity of the material i (soil, asphalt, and PVC tarpaulin). The temperatures T top and T bottom of the layers are known boundary conditions between the layers and are given in (11) and (12), respectively: Equations (1)- (12) were solved numerically using a variable order solver based on the numerical differentiation formulas in the ordinary differential equations (ODE15s solver Matlab/Simulink ® Version 9.6 [56]). Figure 2 illustrates the flow chart procedure of the simulation.  Equations (1)- (12) were solved numerically using a variable order solver based on the numerical differentiation formulas in the ordinary differential equations (ODE15s solver Matlab/Simulink ® Version 9.6 [56]). Figure 2 illustrates the flow chart procedure of the simulation.

Measurement of Albedo
To analyze the actual values for the albedo of paddy rice, experiments were performed at the International Rice Research Institute (IRRI), located in Los Baños, Laguna province, Republic of the Philippines (14°9′55′′ N, 121°15′3′′ E, 21 m a.s.l.). The albedo of paddy rice was measured according to the protocol developed by Sailor et al. [37]. In total, three sets of experiments were conducted, namely on 29 and 30 November 2012, 1 December 2012, and on 14, 15, and 25 April 2013, mostly under clear sky conditions. According to Sailor et al. [37], the measurements should be performed around noon. The measurements carried out in this study were between 10:30 and 15:00. Figure 3 shows the setting of the sensors for the measurement of albedo.

Measurement of Albedo
To analyze the actual values for the albedo of paddy rice, experiments were performed at the International Rice Research Institute (IRRI), located in Los Baños, Laguna province, Republic of the Philippines (14 • 9 55 N, 121 • 15 3 E, 21 m a.s.l.). The albedo of paddy rice was measured according to the protocol developed by Sailor et al. [37]. In total, three sets of experiments were conducted, namely on 29 and 30 November 2012, 1 December 2012, and on 14, 15, and 25 April 2013, mostly under clear sky conditions. According to Sailor et al. [37], the measurements should be performed around noon. The measurements carried out in this study were between 10:30 and 15:00. Figure 3 shows the setting of the sensors for the measurement of albedo.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 6 of 17 Albedo was determined by measuring total solar radiation (direct and diffuse solar radiation) with an upward-facing pyranometer, while measuring reflected solar radiation was done with a downward-facing pyranometer (CMP11 and CMP6, Kipp and Zonen, Delftechpark, Delft, the Netherlands) from a vertical distance of 0.18 m above the paddy surface. The properties of the two pyranometers are presented in Table 2. Separate outputs for each sensor were automatically recorded using a data logger (34970A, Agilent Technologies Inc., Loveland, CO, United States of America). Data were logged at 1-min intervals. The advantages of using the circular shield ( Figure 3) are the reduction of the area subjected to the measurement from the minimum 4 m (standard [35]) to 1 m, the performance of the experiment without the restriction of a larger testing space, and the avoidance of the solar reflection of the surrounding surfaces on the downward pyranometer. Therefore, this setup allowed the reflected radiation to be measured over the course of the day by excluding the areas shaded by the pyranometer, its support, and the circular shield. Albedo was calculated as: where αpa (-) is the albedo of paddy rice, αcs (-) is the albedo of the circular shield, Ddown (W m −2 ) is the radiation measured by the inverted pyranometer, Gup (W m −2 ) is the radiation measured by the upright pyranometer, γdiff (-) is the diffuse fraction, and the view factors F between the sensor and the six surfaces are: (a) unshaded paddy sample F(sensor-a), , (e) crescent shade of the circular shield F(sensor-e), (f) and shaded part of the circular shield F(sensor-f), these surfaces are shown in Figure 4. Albedo was determined by measuring total solar radiation (direct and diffuse solar radiation) with an upward-facing pyranometer, while measuring reflected solar radiation was done with a downward-facing pyranometer (CMP11 and CMP6, Kipp and Zonen, Delftechpark, Delft, the Netherlands) from a vertical distance of 0.18 m above the paddy surface. The properties of the two pyranometers are presented in Table 2. Separate outputs for each sensor were automatically recorded using a data logger (34970A, Agilent Technologies Inc., Loveland, CO, USA). Data were logged at 1-min intervals. The advantages of using the circular shield ( Figure 3) are the reduction of the area subjected to the measurement from the minimum 4 m (standard [35]) to 1 m, the performance of the experiment without the restriction of a larger testing space, and the avoidance of the solar reflection of the surrounding surfaces on the downward pyranometer. Therefore, this setup allowed the reflected radiation to be measured over the course of the day by excluding the areas shaded by the pyranometer, its support, and the circular shield. Albedo was calculated as: where α pa (-) is the albedo of paddy rice, α cs (-) is the albedo of the circular shield, D down (W m −2 ) is the radiation measured by the inverted pyranometer, G up (W m −2 ) is the radiation measured by The clearness index was used for the calculation of γdiff, according to Berrizbeitia et al. [57] and is valid for latitudes between 8.5° and 28° N.   (14) where kt is the ratio of total solar radiation Gup and extraterrestrial radiation Gext. Gext is calculated as: • cos (15) where N is the Julian day of the year and θ is the solar zenith angle, which is represented in (16): where δ is the declination angle, ϕ is the latitude, and ω is the hour angle. For modeling the daytime-dependent course of albedo, an approach of Zheng et al. [58] was chosen: where a, b, and c denote statistically estimated coefficients.
Finally, the albedo was integrated as a variable into the model for the sun drying of paddy rice.

Drying Experiments
To parametrize the model, sun drying experiments were performed on the premises of IRRI. Three batches of experiments were performed during the rainy season (October 2011 and November 2012) and dry season (May 2012 and April 2013). The paddy rice was spread out on a black PVC tarpaulin with a bulk height (zpa) of 40 mm. The grains were mixed manually by using a wooden rake at 1-h intervals during daylight.
To investigate the drying performance, omega sensors (OM-EL-USB-2, Omega, Stamford, CT, United States of America) were used to monitor temperature and relative humidity over the paddy rice surface, and a separate omega sensor was used to measure ambient conditions. The precision of the temperature and relative humidity measurements of the omega logger was ±2 and ±5%, respectively. These sensors were placed at different positions, as shown in Figure 5. Total solar radiation was measured by a pyranometer (CMP11, Kipp & Zonen, Delftechpark, Delft, Netherlands). Pyranometers were connected to a data logger (34970A, Agilent Technologies, Inc., The clearness index k t was used for the calculation of γ diff, according to Berrizbeitia et al. [57] and is valid for latitudes between 8.5 • and 28 • N.
where k t is the ratio of total solar radiation G up and extraterrestrial radiation G ext . G ext is calculated as: where N is the Julian day of the year and θ is the solar zenith angle, which is represented in (16): where δ is the declination angle, φ is the latitude, and ω is the hour angle. For modeling the daytime-dependent course of albedo, an approach of Zheng et al. [58] was chosen: where a, b, and c denote statistically estimated coefficients. Finally, the albedo was integrated as a variable into the model for the sun drying of paddy rice.

Drying Experiments
To parametrize the model, sun drying experiments were performed on the premises of IRRI. Three batches of experiments were performed during the rainy season (October 2011 and November 2012) and dry season (May 2012 and April 2013). The paddy rice was spread out on a black PVC tarpaulin with a bulk height (z pa ) of 40 mm. The grains were mixed manually by using a wooden rake at 1-h intervals during daylight.
To investigate the drying performance, omega sensors (OM-EL-USB-2, Omega, Stamford, CT, United States of America) were used to monitor temperature and relative humidity over the paddy rice surface, and a separate omega sensor was used to measure ambient conditions. The precision of the temperature and relative humidity measurements of the omega logger was ±2 and ±5%, respectively. These sensors were placed at different positions, as shown in Figure 5. Total solar radiation was measured by a pyranometer (CMP11, Kipp & Zonen, Delftechpark, Delft, Netherlands). Pyranometers were connected to a data logger (34970A, Agilent Technologies, Inc., Loveland, CO, United States of America). Data were logged at 5-min intervals and merged with the data from the temperature/humidity loggers after each drying experiment.
where mini (g) is the initial mass of the sample. From the initial mass of paddy rice m0 (kg) used per experimental batch (about 500 kg), the instantaneous mass mt was calculated for one-hour intervals: where MC0 is the initial moisture content and MCt is the instantaneous moisture content at time t.

Sensitivity Analysis
The parameters with a significant influence in the model were explored with the sensitivity analysis (SA) tool of the Matlab/Simulink ® software. The SA was used to test how the variation of the input parameters affects the output behavior of the model [60,61]. Random samples of the individual parameters were generated by using a uniform distribution of its values collected from the literature. Experiments to determine the parameters′ influence on the thermal model were performed using 100 random samples of the exit temperature Tae and the instantaneous mass mt. Then, a Monte Carlo evaluation was carried out on Tae and mt. Finally, the standardized regression coefficient ( ) was calculated between all the parameters under the partial derivatives by using (20).
where is the regression coefficient, is the standard deviation of the corresponding sample, and is the standard deviation of the partial derivatives. A tornado plot shows the results of the SA where m ini (g) is the initial mass of the sample. From the initial mass of paddy rice m 0 (kg) used per experimental batch (about 500 kg), the instantaneous mass m t was calculated for one-hour intervals: where MC 0 is the initial moisture content and MC t is the instantaneous moisture content at time t.

Sensitivity Analysis
The parameters with a significant influence in the model were explored with the sensitivity analysis (SA) tool of the Matlab/Simulink ® software. The SA was used to test how the variation of the input parameters affects the output behavior of the model [60,61]. Random samples of the individual parameters were generated by using a uniform distribution of its values collected from the literature. Experiments to determine the parameters influence on the thermal model were performed using 100 random samples of the exit temperature T ae and the instantaneous mass m t . Then, a Monte Carlo evaluation was carried out on T ae and m t . Finally, the standardized regression coefficient (R) was calculated between all the parameters under the partial derivatives by using (20).
where b x is the regression coefficient, σ x is the standard deviation of the corresponding sample, and σ y is the standard deviation of the partial derivatives. A tornado plot shows the results of the SA analysis [61].

Albedo Model
Matlab Version 9.6 software [62] was used for fitting the experimental values of paddy rice albedo by applying the non-linear least squares method to the two proposed models. The model with the highest coefficient of determination (R 2 ) and the lowest root mean square error (RMSE) was selected.
Code developed in Matlab Version 9.6 software was used to assess model performance at constant and variable albedos. R 2 , RMSE, and mean absolute percentage error (MAPE) were used to indicate the accuracy of the prediction. Fluctuations in albedo were encountered when clouds passed through the experimental area. A higher albedo of paddy rice was observed in the rainy season than in the dry season, with values of 0.29 and 0.25, respectively, at noon. Nevertheless, the obtained values were higher than the mean value calculated from literature data ( Table 1).

Measurements of Albedo
Appl. Sci. 2020, 10, x FOR PEER REVIEW 9 of 17 the highest coefficient of determination (R 2 ) and the lowest root mean square error (RMSE) was selected.
Code developed in Matlab Version 9.6 software was used to assess model performance at constant and variable albedos. R 2 , RMSE, and mean absolute percentage error (MAPE) were used to indicate the accuracy of the prediction. Fluctuations in albedo were encountered when clouds passed through the experimental area. A higher albedo of paddy rice was observed in the rainy season than in the dry season, with values of 0.29 and 0.25, respectively, at noon. Nevertheless, the obtained values were higher than the mean value calculated from literature data ( Table 1).

Measurements of Albedo
With an R 2 of 0.7880 and RSME of 0.0299. Based on Equation (17), the albedo can be modeled for the course of the day as a function of the solar zenith angle: α = 0.2704 + 1.816·10 −5 ·e 0.1761·θ (21) With an R 2 of 0.7880 and RSME of 0.0299. Figure 7 shows the tornado plot in which parameters are ranked by influence. An example of these results is shown for one batch during the rainy season (4 June 2012). According to the sensitivity analysis, the albedo has the most significant influence, and the other parameters have little effect. This means that at a higher albedo, lower air temperatures are expected. In the case of the instantaneous mass of paddy rice during drying, albedo is also the main parameter of influence, and the other parameters have less impact. Higher albedo values result in lower energy. Therefore, using a constant albedo value in the model may result in the over/underestimation of paddy rice temperature, and consequently, drying rate. Similar results were found for all the experiments and they showed a significant influence of albedo, with a correlation R ranging from −0.81 to −0.67 for the estimation of the exit temperature and from 0.92 to 0.98 for the instantaneous mass during drying.     cp ta -volumetric heat capacity, λ pvc -thermal conductivity; Asphalt: cp as -volumetric heat capacity, λ as -thermal conductivity; Soil: cp so -volumetric heat capacity, λ so -thermal conductivity, h c heat transfer coefficient from the paddy rice to the air). Figure 8 shows an example of the weather conditions during the sun drying of paddy rice during the rainy season (19 October 2011) and dry season (22 May 2012). Weather data collected for the other experiments were similar to the corresponding season. The sun drying conditions in the dry season were characterized by an ambient relative humidity of about 40%; the ambient temperature ranged from 30 to 38 • C, and solar irradiation ranged from 4 to 5 kWh m −2 d −1 . Compared with conditions in the rainy season, higher values of relative humidity of about 60%, lower temperatures of about 30 • C, and lower solar radiation values of about 3 kWh m −2 d −1 were expected, primarily due to cloudiness. In both seasons, relative humidity reached values of over 80%, with temperatures of around 25 • C during the night. Furthermore, a higher variability of solar radiation is typically experienced during the rainy season. from 30 to 38 °C, and solar irradiation ranged from 4 to 5 kWh m −2 d −1 . Compared with conditions in the rainy season, higher values of relative humidity of about 60%, lower temperatures of about 30 °C , and lower solar radiation values of about 3 kWh m −2 d −1 were expected, primarily due to cloudiness. In both seasons, relative humidity reached values of over 80%, with temperatures of around 25 °C during the night. Furthermore, a higher variability of solar radiation is typically experienced during the rainy season.   Figure 9 shows the simulated and the experimental temperatures over the paddy rice during the dry and rainy seasons. Due to lower cloudiness, a higher temperature was expected during the dry season compared to the rainy season. Nevertheless, the simulated exit temperature in the rainy season showed higher variation at night compared with the experimental temperature over the paddy rice. This variation was not observed during the dry season. During the course of the day, the simulated temperature over the paddy rice for the rainy season showed higher values compared to the dry season. It could be as much as 5 • C higher than the experimental value. Therefore, we can assume that the dynamic sun drying model provides an accurate estimation of the crop temperature.

Estimation of Temperatures
Appl. Sci. 2020, 10, x FOR PEER REVIEW 11 of 17 Figure 9 shows the simulated and the experimental temperatures over the paddy rice during the dry and rainy seasons. Due to lower cloudiness, a higher temperature was expected during the dry season compared to the rainy season. Nevertheless, the simulated exit temperature in the rainy season showed higher variation at night compared with the experimental temperature over the paddy rice. This variation was not observed during the dry season. During the course of the day, the simulated temperature over the paddy rice for the rainy season showed higher values compared to the dry season. It could be as much as 5 °C higher than the experimental value. Therefore, we can assume that the dynamic sun drying model provides an accurate estimation of the crop temperature.   Figure 10 provides the simulated temperatures of the soil T so , asphalt T as , PVC tarpaulin T ta , paddy rice T pa , and air exiting the paddy rice surface T ae . It can be seen that the paddy rice temperature reached temperatures higher than 50 • C during the dry season. While temperatures reached almost 50 • C or lower during the rainy season.  Figure 10 provides the simulated temperatures of the soil Tso, asphalt Tas, PVC tarpaulin Tta, paddy rice Tpa, and air exiting the paddy rice surface Tae. It can be seen that the paddy rice temperature reached temperatures higher than 50 °C during the dry season. While temperatures reached almost 50 °C or lower during the rainy season.  ; temperature: air exiting the paddy rice surface T ae , paddy rice T pa , PVC tarpaulin T ta , asphalt T as , and soil T so . Figure 11 shows a comparison of the simulated and the experimental moisture content of paddy rice during sun drying. The drying curves for the rainy season and the dry season are shown exemplarily. It was observed that the moisture content decreased continuously with drying time. The absence of connection lines in Figure 11 indicates night periods. The MC of the paddy rice for all the experiments decreased from the range of 0.18 to 0.38 to about 0.16 within 3.5 to 76.7 h (Table 3). Although there were slight discrepancies between the simulated and the experimental moisture content, the results obtained by the sun drying model are in good agreement with the experimental data, as the MAPE values were below 2%.

Estimation of Moisture Content during Drying
Appl. Sci. 2020, 10, x FOR PEER REVIEW 12 of 17 absence of connection lines in Figure 11 indicates night periods. The MC of the paddy rice for all the experiments decreased from the range of 0.18 to 0.38 to about 0.16 within 3.5 to 76.7 h (Table 3).
Although there were slight discrepancies between the simulated and the experimental moisture content, the results obtained by the sun drying model are in good agreement with the experimental data, as the MAPE values were below 2%.    To assess the model with constant or variable albedo values, RMSE, MAPE, and R 2 were used for T ae and m t . Figure 12 shows that for T ae , the RMSE and MAPE are lower in most cases for variable albedo in both seasons, with values for RMSE ranging from 3 to 7.5 and below 10% for MAPE, while R 2 shows a minor increment for variable albedo compared to the constant values. Interestingly for the instantaneous mass, RMSE and MAPE show a more significant improvement of the model outputs when a variable albedo is used. Furthermore, the R 2 shows slightly higher values of the model with variable albedo compared to the constant albedo (Table 3). Overall, these results indicate that there is a strong influence of variable albedo in the developed sun drying model. albedo in both seasons, with values for RMSE ranging from 3 to 7.5 and below 10% for MAPE, while R 2 shows a minor increment for variable albedo compared to the constant values. Interestingly for the instantaneous mass, RMSE and MAPE show a more significant improvement of the model outputs when a variable albedo is used. Furthermore, the R 2 shows slightly higher values of the model with variable albedo compared to the constant albedo (Table 3). Overall, these results indicate that there is a strong influence of variable albedo in the developed sun drying model.
(a) (b) Figure 12. The lowest root mean square error RMSE and the mean absolute percentage error MAPE for constant and variable albedo αpa for exit temperature Tae (a) and for predicted instantaneous mass mt (b) during the rainy season and dry season.

Discussion
In previous studies on simulating sun drying, constant albedo values have been used, and the energy exchange within the layers under the paddy rice has been neglected. Moreover, steady state rather than transient state conditions are commonly assumed for solving equations in thermal analysis. Thus, temporary heat and mass transfer analyses were explored and presented in this paper.
In reviewing the literature, Sailor et al.'s [37] approach resulted in a practical procedure to assess the measurement of albedo. We obtained an albedo value of around 0.25-0.28, corresponding to the period from 11:00 to 13:00 ( Figure 6). This albedo value is higher than the values reported by other studies such as Arninze et al. [21] and Bala [32], who proposed an albedo of 0.16 for brown rice. On the other hand, the presented range found in this study lies within the range provided by Arya [17], who proposed values for wheat and rice in a range from 0.18 to 0.25. The albedo of paddy rice was shown to correlate with solar zenith angle, showing an R 2 of 0.7880 and RSME of 0.0299. Hence, the solar zenith angle should be used for the parametrization of the albedo of paddy rice in modeling schemes in solar drying applications [10,58].
The results of the sun drying model show that when a variable, daytime-dependent albedo was applied, most of the RMSE and MAPE values were smaller for the estimation of the exit temperature and for the instantaneous mass than when using a constant albedo. Another important finding is that Figure 12. The lowest root mean square error RMSE and the mean absolute percentage error MAPE for constant and variable albedo α pa for exit temperature T ae (a) and for predicted instantaneous mass m t (b) during the rainy season and dry season.

Discussion
In previous studies on simulating sun drying, constant albedo values have been used, and the energy exchange within the layers under the paddy rice has been neglected. Moreover, steady state rather than transient state conditions are commonly assumed for solving equations in thermal analysis. Thus, temporary heat and mass transfer analyses were explored and presented in this paper.
In reviewing the literature, Sailor et al.'s [37] approach resulted in a practical procedure to assess the measurement of albedo. We obtained an albedo value of around 0.25-0.28, corresponding to the period from 11:00 to 13:00 ( Figure 6). This albedo value is higher than the values reported by other studies such as Arninze et al. [21] and Bala [32], who proposed an albedo of 0.16 for brown rice. On the other hand, the presented range found in this study lies within the range provided by Arya [17], who proposed values for wheat and rice in a range from 0.18 to 0.25. The albedo of paddy rice was shown to correlate with solar zenith angle, showing an R 2 of 0.7880 and RSME of 0.0299. Hence, the solar zenith angle should be used for the parametrization of the albedo of paddy rice in modeling schemes in solar drying applications [10,58].
The results of the sun drying model show that when a variable, daytime-dependent albedo was applied, most of the RMSE and MAPE values were smaller for the estimation of the exit temperature and for the instantaneous mass than when using a constant albedo. Another important finding is that RMSE and MAPE with variable albedos are much lower for the instantaneous mass than for the exit temperature, showing that the model provides a better estimation of instantaneous mass. This was already observed from the sensitivity analysis, where albedo showed higher standardized regression values for the instantaneous mass than for the exit temperature.

Conclusions
A clear understanding of the incident solar radiation is essential for the effective use of the solar energy.