Abstract
The albedo of a water surface and the energy available for evaporation are strongly correlated and studying such processes is of paramount importance for water security at farm and regional levels. In this paper, water albedo (αw) and net all-wave radiation (Rn) were analyzed after being measured above the surface of an artificially cleaned and low-turbidity water used for tobacco irrigation. It was observed that αw decreased as the sun elevation (θ) increased, especially for clear and near clear skies. The results showed that αw can be reasonably predicted with a power law model either in terms of θ or Sg (incoming solar radiation) across different cloud cover conditions. From this study, a mean daily albedo of 0.05 is recommended. Three approaches were considered for estimation of daily Rn. In the first, a linear regression model strongly fitted Rn data in terms of Sg solely. The second option based on the definition of Rn was [0.95Sg - Lnet(56)], where Lnet(56) is net longwave (LW) radiation as used in the FAO56 model for reference evapotranspiration estimation, and the third was [0.95Sg - Lnet(MLR)], where MLR stands for multiple linear regression. The disadvantages of approaches (1) and (3), based on regressions, is that they are constrained to the type of water stored in the farm and the climatic conditions of the region. The performance of approach (2), where Lnet(56) is a widely used model, was comparable to the others can potentially be improved with a site-specific calibration. All three approaches for estimating daily Rn proposed in this study can possibily be extended to clear water that did not go through any filtration process.
Keywords albedo; net radiation; water turbidity; tobacco
Resumo
O albedo de uma superfície de água e a energia disponível para evaporação estão fortemente correlacionados e estudar tais processos é de suma importância para a segurança hídrica nível local e regional. Neste artigo, o albedo da água (αw) e a radiação líquida (Rn) foram analisados após serem medidos acima da superfície de água artificialmente limpa e de baixa turbidez usada para irrigação de cultivo de fumo. Observou-se que αw diminuiu com o aumento da elevação do sol (θ), especialmente para céu limpo e quase limpo. Os resultados mostraram que αw pode ser razoavelmente previsto com um modelo potencial em termos de θ ou Sg (radiação solar incidente) em diferentes condições de cobertura de nuvens. A partir deste estudo, um albedo médio diário de 0,05 é recomendado. Três abordagens foram consideradas para estimativa diária de Rn. Na primeira, um modelo de regressão linear ajustou-se fortemente aos dados de Rn em função de Sg, apenas. A segunda opção com base na definição de Rn foi [0,95Sg - Lnet(56)], onde Lnet(56) é a radiação líquida de onda longa do modelo FAO56 para estimativa da evapotranspiração de referência, e a terceira abordagem foi [0,95Sg - Lnet(MLR)], onde MLR significa regressão linear múltipla. As desvantagens das abordagens (1) e (3), baseadas em regressões, é que elas são restritas ao tipo de água armazenada na fazenda e às condições climáticas da região. O desempenho da abordagem (2), onde Lnet(56) é um modelo amplamente utilizado, foi comparável às outras e pode ser potencialmente melhorada com calibração local. Todas as três abordagens para estimar o Rn diário propostas neste estudo podem ser estendidas para águas claras que não passaram por nenhum processo de filtragem.
Palavras-chave albedo; radiação líquida; turbidez da água; fumo
1. Introduction
The radiation balance at a surface depends essentially on the time of day, the atmospheric conditions, and the nature of the surface (soil, water, vegetation, etc.). Time of day and cloud cover impact the magnitude of incoming radiation fluxes while the type of surface, described by its albedo (α) and emissivity (ɛ), affect the magnitude of outgoing fluxes while determining the amount of energy that can be absorbed by the surface and stored in the underlying medium.
The albedo of a water surface (αw) varies over the course of a day and during the year because it is a function of solar elevation and thus the angle of the direct solar beam to the water surface (Finch and Hall, 2005). Adding to this, other factors strongly influence αw such as the degree of cloudiness that affects the proportion of direct and diffuse radiation, water quality, and state of the surface, like height and orientation of waves, which in turn are related to the speed and direction of wind over water (Henderson-Sellers and Hughes, 1982; Katsaros et al., 1985; Jin et al., 2004; Liu et al., 2015). Studies on αw have typically been restricted to oceans (Payne, 1972; Cogley, 1979; Katsaros et al., 1985; Feng et al., 2016). Over a freshwater lake in Canada, Nunez et al. (1972) reported αw varying from 0.07 to 0.11 on a daily basis. Typical values for αw encompassing variable cloud cover conditions (from clear to overcast skies) are in the range of 0.10-0.50 at low sun and 0.03 to 0.10 at high sun (Shuttleworth, 2012). A mean value of αw for deep water is in the range of 0.04-0.08 (Jensen and Allen, 2016). Henderson-Sellers (1986) discussed several approaches for estimating αw. Vitale et al. (2019) successfully fitted seasonal data to sinusoidal functions to estimate αw in terms of month of the year over an intertidal wetland.
Detailed information on the radiation balance at a water surface can be obtained by a four-component net radiometer mounted above the surface. With such instrument, the albedo and the net all-wave radiation (Rn) can be derived from measurements of the shortwave and longwave components. But net radiometers are expensive and delicate instruments that require careful handling to attain accurate measurements (Myeni et al., 2020). Therefore, it is desirable to estimate Rn over water.
Henderson-Sellers (1986) reviewed several methods for calculating Rn within the context of open water evaporation modelling. Recently, Myeni et al. (2021) has investigated the performance of a model that uses land-based meteorological data to calculate Rn over open water surfaces. The importance of simple and reliable models for estimating Rn over water has been emphasized (Mengistu and Savage, 2017; Myeni et al., 2021). Incoming and net shortwave radiation fluxes have been shown to be good estimators of Rn under both clear and cloudy conditions and for a wide range of surfaces, including water (Alados et al., 2003). El-Bakry (1994) reported regression coefficients for estimation of Rn using incoming SW radiation at the Aswan High Dam Lake in Egypt and Li and Barnes (1980) developed similar relationships for Lake Albert in South Australia. Jensen et al. (1990) made a compilation of linear regression coefficients for estimating Rn for various cropped surfaces.
Storage of water in natural lakes, impoundments and farm reservoirs is of great importance to ensure water security. Around the world, huge amounts of water are lost every year from these water storages mainly in tropical regions and the study of the radiation balance at such surfaces help to develop programs for water conservation and management at local and regional levels. The purpose of this paper was to analyze the albedo of low-turbidity water stored in an agricultural reservoir for irrigation purposes. Measurements of all components of the radiation balance over two seasons provided enough data for modelling Rn over the water surface.
2. Material and Methods
A detailed description of the experimental site and the instrumentation used is presented in the first paper of this series, hereafter referred to as Part I. In summary, measurements of all components of the radiation balance were made over low-turbidity water used for irrigation of tobacco plants grown under shading in the east of Bahia. Experimental data were collected during the second parts of 2015 and 2016 using instruments mounted on-board a handmade floating platform as described by Borges et al. (2016) and Borges (2017), positioned in the center of an artificial reservoir.
A four-component net radiometer (model CNR4, Kipp & Zonen) measured continuously the incident and the outgoing shortwave (SW) and longwave (LW) radiation fluxes. Data were collected with dataloggers (model CR1000, Campbell Scientific) and stored in intervals of 5 min, 30 min, 60 min, and 1440 min, for further analysis. From the SW components, the water albedo αw was calculated according to Eq. (1), being albedo the ratio between reflected and incoming SW radiation.
where αw is the water surface albedo (dimensionless), Sr is the reflected SW radiation by the surface and Sg is the incoming SW radiation.
In the datalogger, the measured net all-wave radiation Rn was calculated from the four components according to Eq. (2).
where Snet is the net SW radiation, Lnet is the net LW radiation, Latm is the incoming LW radiation from the atmosphere, and Lout is the outgoing LW radiation from the surface. All terms in Eq. (2) are given in W/m2.
Here is used the same criteria and selected days mentioned in Part I regarding the effects of cloud cover on the radiation balance components through the mean daytime atmospheric transmissivity τatm for SW radiation.
2.1. Modelling of net radiation fluxes
In this Part II, approaches for modelling net SW radiation (Snet), net LW radiation (Lnet), and Rn are tested and evaluated based on daily observation of incoming SW radiation from the net radiometer and air temperature and relative humidity measured at the weather tower deployed in a row between the irrigation reservoirs during both 2015 and 2016 campaigns. Models to estimate the components of the radiation balance from atmospheric variables tend to use data commonly obtained with standard weather stations and from historical daily weather data sets. In the tobacco farm, for example, such models can be used to evaluate water loss by evaporation from the open water surfaces, an important information for implementation of a water management program.
The net SW radiation flux was estimated from Sg according to Eq. (3).
where Snet(e) is the estimated daily net SW radiation (W/m2) based on a constant value for water surface albedo (αwc) and Sg is the daily incoming SW radiation from the net radiometer (W/m2).
Two approaches were considered to estimate Lnet: (i) the same used in the FAO Penman-Monteith equation (Allen et al., 1998) to calculate reference evapotranspiration (Eq. (4)) and (ii) a multiple linear regression model having as input variables air temperature, relative humidity, and an indicator of daytime relative cloudiness.
where Lnet(56) is the estimated daily net LW radiation (W/m2) according to FAO 56 paper (Allen et al., 1998), σ is the Stefan-Boltzmann constant (5.67x10-8 W/m2.K4), Tx is the daily maximum air temperature (K), Tn is the daily minimum air temperature (K), ea is the daily mean actual vapor pressure (kPa), Sg and Sgo are as previously defined. The ratio Sg/Sgo represents relative cloudiness and in Eq. (4) is limited to 0.25 < Sg/Sgo ≤ 1.0 (ASCE, 2005).
The multiple linear regression technique (MLR) allows the investigation of an association among three or more variables (Akritas, 2016) and is generally written as an equation relating the response variable Y to the predictor variables X1,…, Xk and an intrinsic error variable (ɛ) as given in Eq. (5).
where β0 is the intercept and βi (i = 1, 2,…, k) are the multiple regression coefficients of the dependent variable Y on the independent variable Xi (i = 1, 2,…, k).
In the present study, atmospheric parameters readily available from standard weather stations and commonly associated to the exchange of LW radiation between the surface and the atmosphere were considered as candidates for independent variables in the MLR model. The model was parameterized with data from 2015 using a stepwise procedure in R (R Core Team, 2017) and validated with the data collected in 2016. The objective of such a procedure is arriving at an optimal prediction equation by using statistical criteria to eliminate unnecessary predictors leading to the final form of the regression model that includes only those predictor variables that can explain the observed variability in the dependent variable.
Finally, three approaches were considered for modelling net all-wave radiation Rn. The first, consisted in using incoming SW radiation Sg to predict Rn by means of a simple linear regression. This method has been widely used over different types of surfaces including water (Sene et al., 1991; El-Bakry, 1994). As the first approach, in this paper Rn was modelled using Snet(e) as the predictor variable, according to Eq. (6). The second (Eq. (7)) and third (Eq. (8)) approaches followed the definition of Rn as the sum of net SW and net LW radiation fluxes. Initially, Rn was given as the sum of Eqs. (3) and (4) and then as the sum of Eqs. (3) and (5).
where Rn(1,2,3) is the estimated daily net all-wave radiation (W/m2), a0 and a1 are regression coefficients, and Lnet(MLR) is the estimated daily net LW radiation with the multiple linear regression model.
3. Results and Discussion
3.1. Albedo of the water surface
In this paper, daily water surface albedo (αw) was calculated as the ratio of 24-h mean values of Sr to Sg in W/m2. In 2015, the daily αw varied from 0.034 to 0.072 with an average of 0.050 and in 2016 it varied from 0.031 to 0.067 with an average value of 0.044. Considering both years, the daily mean αw was 0.047. Albedo generally increased to above 0.06 on cloudy days and decreased to near 0.03 on relatively clear days. These results are consistent with Finch and Hall (2005) and Jensen and Allen (2016) who highlighted the low average value of water albedo (0.06) compared to other surfaces, like vegetation. In agricultural crops, for example, mean albedo in the range of 0.20 to 0.25 area recommended. Henderson-Sellers (1986) and Shutlleworth (2012) suggest a mean albedo of 0.08 for water including effects of cloud cover.
Figure 1 shows the daily course of αw for the four days selected in Part I with contrasting atmospheric transmissivity (τatm) as follows: τatm = 0.72 (DOY 247/2015), τatm = 0.55 (DOY 310/2016), τatm = 0.36 (DOY 286/2016), and τatm = 0.18 (DOY 303/2015). In Fig. 1A, αw is given as a function of sun elevation angle (θ) in the range of 0 to 90° using 5-min data, while in Fig. 1B, hourly values were plotted as a function of local time. Clearly, αw tended to decrease as θ increased, a pattern extensively reported in other studies (Katsaros et al., 1985; Jin et al., 2004; Liu et al., 2015). Most of the albedo data plotted in Fig. 1A are below 0.30. However, high αw values (> 0.50) occurred with low θ at sunrise and sunset regardless of cloud cover conditions. It is difficult to interpret albedo values occurring early in the morning and late afternoon. It is known that, physically, sun glint is a phenomenon that causes the very high values of αw at these times under clear sky conditions. It is also possible that albedo was impacted, to some degree, by sensor oscillation in the raft in windy days and sides of the water reservoir at low θ.
Daily course of the low-turbidity water albedo αw for the four selected days with contrasting cloud cover. DOY 247/2015 (CSS, τatm = 0.72), DOY 310/2016 (MSS, τatm = 0.55), DOY 286/2016 (MCS, τatm = 0.36), and DOY 303/2015 (CCS, τatm = 0.18). CSS = completely sunny (clear) sky, MSS = mostly sunny sky, MCS = mostly cloudy sky, and CCS = completely cloudy (overcast) sky.
In Fig. 1B, U-shape curves are seen on clear and near clear days (DOY 247 and 310), with maximums occurring early in the morning and late afternoon when sun angles were low, and minimums occurring around noon when sun angles were the highest. Under high atmospheric transmissivity, a well-defined relationship between water albedo and time was observed (Nunez et al., 1972; Henderson-Sellers, 1986; Liu et al., 2015). On the other hand, Fig. 1B also shows that as the degree of cloudiness increased, the U-shape pattern changed so that the timing of maximum and minimum αw values became more difficult to predict and αw amplitude decreased.
The four days in Fig. 1 comprise a representative range of conditions for τatm (from 0.18 to 0.72) in the region, so it was expected that the average αw for these particular days was similar to the mean value (0,047) for both seasons. The daily albedo computed using mean daily values of Sg and Sr (see Table 3 in Part I) were 0.045 for DOY 247, 0.038 (DOY 310), 0.054 (DOY 286), and 0.061 (DOY 303), with an overall average of 0.049.
Table 1 shows adjustments of a power-law model for estimation of αw in terms of θ and incoming SW radiation (Sg), which by itself is a function of θ. Five-min average data were used to calibrate the model. Generally, the coefficient of determination (r2) decreased as cloud cover increased. For the case of all-cloud cover condition in Table 1, the model predicts αw varying from 0.25 to 0.03 in the θ interval from 5° to 90°, whose values are within the range of measured albedo over the low-turbidity water during both the 2015 and 2016 seasons.
Coefficients for the power-law fitting for estimating the low-turbidity water surface albedo (αw) in a tropical climate from incident SW radiation flux (Sg) in W/m2 and sun elevation angle (θ) in degree.
In order to investigate the influence of τatm on αw, the two extreme cases of cloud cover (CCS and CSS) were considered based on the 5-min data sets of both years. Before processing the raw data, a quality control procedure was applied as follows: (i) all data were deleted from the series when the calculated τatm was not a number, τatm ≤ 0 or τatm ≥ 1; (ii) all data were deleted when calculated θ was not a number or θ ≤ 0; (iii) all data were deleted when αw was not a number or when αw ≤ 0 or αw > 1; and (iv) all data were deleted when Rn < 0.
As previously discussed in Fig. 1 and according to Katsaros et al. (1985) and Jin et al. (2004), Fig. 2A illustrates that under high sun elevation above the horizon and with flat water surface, the albedo for water tends to be higher in the presence of clouds (overcast and near overcast skies), as the diffuse, multi-direction SW radiation in the atmosphere increases the mean angle of incidence of radiation from the vertical and the effect of solar elevation is considerably dampened. In the absence of clouds (clear sky and near clear skies) the incidence angle from vertical is small and the albedo is lowest under high sun elevation. The opposite occurs when the sun is low above the horizon (θ < 30º). In this condition, the albedo tends to be larger in the absence of clouds and decreases sharply with sun angle, as the angle of incidence of the radiation beam from vertical becomes smaller.
Plot of low-turbidity water albedo against sun elevation angle for the two extreme conditions of cloud cover (A) and against atmospheric transmissivity for SW radiation for four intervals of sun elevation angle (B).
Figure 2A also shows that, for a given sun elevation angle, the variability in αw under dense cloud cover was substantially higher. This higher variability can be a combined effect of the state of the surface (lack of flatness due to wind blowing) and diffuse radiation reaching the surface in larger proportions compared to the direct beam. It is interesting to observe that from around 25° to 35° of sun elevation, the two extreme cloud cover data sets tended to intersect and the relationship between αw and θ seems to be less dependent on the degree of cloudiness. A second plot (Fig. 2B) was developed to explore how water albedo relates to the full range of τatm for a set of arbitrarily chosen θ intervals. In Fig. 2B, the albedo of the low turbidity water was very sensitive to changes in τatm under low sun elevation angle (θ ≤ 10°). In this range, αw increased rapidly as τatm increased, most likely due to larger sunglint from the greater amount of direct sun beam at higher τatm. In the θ range from 25° to 35°, αw was essentially constant across the τatm values, pattern also reported by Oke (1995). At higher θ values (> 50°), the water albedo shows a slightly decreasing pattern with atmospheric transmissivity, with lowest values of αw toward clear sky in accordance with Fig. 2A.
3.2. Models for estimating net radiation fluxes
Modelling net radiation fluxes from commonly measured weather data makes the determination of radiation balance more viable and independent of high-cost and delicate instrumentation. It also increases the ability to apply the methodology using historical data sets. The proposed approach to predict net SW radiation for the low-turbidity water (Eq. (3)) is simplified and made more general by requiring only a knowledge of αwc, as a constant value for water albedo. On a daily basis, the αwc adopted here is 0.05, which is the average water surface albedo for both years calculated from 24-h Sr and Sg fluxes. This value was also obtained from measured Snet data (totaling 189 points of daily data from both years) that were plotted against Snet(e) and αw was successively changed until the best fitting (Y = 1.0007·X, coefficient of determination r2 = 0.99996, and standard error of estimate SEE = 1.53 W/m2) was obtained, which occurred when αwc was set equal to 0.047 or about 0.05.
Once αw was defined, the net SW radiation flux was then modelled from Sg measured at the weather station as Snet(e) = 0.95·Sg, which means that on average, 95% of the daily SW radiation incident over the clear water surface in the irrigation reservoirs tended to be absorbed. Therefore, compared to other natural surfaces, clear water is on average one of the most effective absorbing mediums of SW solar radiation (Katsaros et al., 1985; Oke, 1995; Jensen and Allen, 2016).
As mentioned previously, two approaches were applied to model net LW radiation, the FAO56 equation without site-specific calibration (Eq. (4)) and a multiple linear regression model (Eq. (5)) using atmospheric data from a standard automatic weather station as the predictor variables. The inputs to the FAO56 Lnet model (Allen et al., 1998) are Tx (maximum air temperature, K), Tn (minimum air temperature, K), ea (actual vapor pressure, kPa), and the Sg/Sgo ratio (relative cloudiness index, dimensionless). Based on daily data from 2015 (135 data points), it was found that Lnet(56) underestimated measured values for water by about 30%, with a mean ratio between estimated and measured Lnet equal to 0.70 (max = 1.32, min = 0.18, standard deviation, sd = 0.18). Measured Lnet was plotted against Lnet(56) resulting in a linear regression fitting (Y = A + B·X) with the following parameters: A = 24.91 W/m2, B = 0.7734, r2 = 0.608, and SEE = 7.99 W/m2. One data point (30th October) was excluded from this analysis because the condition of Sg/Sgo > 0.25 was violated.
The same 2015 set of daily data was used to derive the coefficients for the multiple linear regression (MLR) model. Several weather variables commonly associated to the exchange of LW radiation between surface and atmosphere were considered, such as Tx (°C), Tn (°C), ea (kPa), Sg/Sgo (dimensionless), mean air temperature (Tm, °C) given as (Tx + Tn)/2, maximum relative humidity (RHx, %), minimum relative humidity (RHn, %), air temperature amplitude (δT, °C), and vapor pressure deficit (VPD, kPa). Fourth-degree powers of Tx and Tn were also considered, as in the FAO56 Lnet model following the Stefan-Boltzmann law. These variables were tested as a single input and in pairs in the form of products. After many runs, the best fitting relationshiop (r2 = 0.721, SEE = 6.87 W/m2) was obtained when measured daily Lnet was expressed as a function of Tx (°C), Tn (°C), RHx (%), RHn (%), and Sg/Sgo according to Eq. (9).
Different from the FAO56 Lnet model, in Eq. (9) the Sg/Sgo ratio is allowed to be lower than or equal to 0.30 since values in this range were used for derivation. Validation of Lnet(MLR) against daily data obtained in 2016 (independent data set with N = 54) showed a linear regression fitting through the origin (Y = B·X) with a high coefficient of determination (r2 = 0.986), slope near 1 (B = 0.981), and a small standard error of estimate (SEE = 6.76 W/m2).
Figure 3 depicts the course of measured and estimated net LW radiation for the year 2016 by both methods. This plot is a form of validation for the FAO56 Lnet approach that could not be done in the same way that was done for the multiple linear regression, since the original constants in that approach were not changed. It is interesting to observe that both sets of estimated data not only agree with each other, but also agree with the measured values for Lnet. Basically, both FAO56 and MLR approaches concomitantly produced an overestimation or underestimation of measured Lnet values. Like in 2015, the ratio between estimated and measured Lnet in 2016 was lower than 1 (0.61 on average, max = 0.91, min = 0.11, sd = 0.16) for the FAO56 Lnet model and 1.04 (max = 1.79, min = 0.80, sd = 0.16) for the MLR model. Therefore, the use of Eq. (9) to estimate the net outgoing LW radiation from the low turbidity water seems to be a better option as compared to the FAO56 Lnet model. The better performance for the Lnet(MLR) was expected, since the regression is tailored to the experimental data. Because of this, the Lnet(MLR) is not universal, which means that it cannot be applied to similar water surfaces under climatic conditions that might differ substantially from those encountered in the east of Bahia region.
Course of measured and estimated daily net longwave radiation over the low-turbidity water surface in 2016 from DOY 136 to DOY 189 (54-day interval).
The FAO56 equation (Eq. (4)) for estimating Lnet was developed for vegetated surfaces in the context of crop water requirement studies (Wright, 1982; Burman and Pochop, 1994; Allen et al., 1998). That equation assumes an emissivity of 0.98 for the soil-vegetation mixture and the calculation of net emissivity with the Brunt (1932) model. The mixture emissivity is similar to that recommended for water surfaces (ɛw = 0.97) (Davies et al., 1971; Konda et al., 1994; Jensen and Allen 2016). On the other hand, the FAO56 equation uses air temperature at screen height to estimate both incoming and outgoing LW radiation and the equation is recommended for computation of reference crop evapotranspiration (Jensen et al., 1990; Jensen and Allen, 2016). But Fig. 4B in Part I shows that, under the same environmental conditions, differences between water temperature Tw and air temperature Ta can be significant over the course of a day. Such differences might explain the inability of the FAO56 Lnet equation to predict Lnet over the low turbidity water surface in the experimental area of this study. In order to improve the estimates with this equation, one option would be a site-specific calibration by adjusting the coefficients for net emissivity and the cloud cover factor to account for local conditions (Kjaersgaard et al., 2007; Wu et al., 2017; Kofronova et al., 2019).
Net all-wave radiation Rn was modelled following three approaches (Eqs. (6) to (8)). In the first one, Snet(e) = 0.95·Sg was taken as the predictor variable and Eq. (10) is the result of the linear regression analysis that produced a model with a high correlation (r2 = 0.951 and SEE = 9.66 W/m2), since Rn is closely correlated with net SW radiation, which in turn is closely correlated with Sg. Derivation of Eq. (10) used data from 2015 (N = 135) and was restricted to Snet(e) values from about 79 W/m2 to 306 W/m2. Validation with the 2016 data set (N = 54) showed a linear model passing through the origin (Y = B·X) with B = 1.034, r2 = 0.998, and SEE = 7.56 W/m2.
Figure 4 compares measured daily Rn with calculated values obtained with the approaches Rn(2) (Eq. (7)) and Rn(3) (Eq. (8)). A better agreement between measured and estimated Rn was obtained with the Rn(3) approach (Fig. 4B), where the y-intercept is closer to 0, the slope is closer to 1 and SEE is 7.37 W/m2, about 33% lower than the SEE in Fig. 4A. The ratio of estimated Rn(2) to measured Rn [Rn(2)/Rn] averaged 1.13 while for the ratio Rn(3)/Rn the average was 1.01, suggesting that Rn calculated with the FAO56 Lnet model overestimated measured Rn in 13%, on average.
Measured all-wave net radiation against calculated net-all wave radiation with Lnet(56) (A) and with Lnet(MLR) (B), where 56 stands for FAO 56 Penman-Monteith equation and MLR stands for multiple linear regression model.
The use of a well-fitted simple linear regression to estimate Rn over water surface in terms of incoming SW radiation or net SW radiation is a valid option where data on solar radiation are available and the water clearness remains fairly constant over time, which is the case for the experimental area of this study. In the tobacco farm, every year from April to August, the tanks are refilled with clean water coming from the filtration system to supply crop demand during the next irrigation season (September to March). If a nearby land-based weather station also provides data on other parameters such as air temperature (maximum and minimum) and relative humidity (maximum and minimum) that can be used with the Eq. (9), then the Rn(3) approach becomes a viable option for estimation of Rn over the water surface in the irrigation tanks, as part of a program to maximize the water management in the farm. On the other hand, improvements in Rn(2) can be achieved with the application of a site-specific calibration for the FAO56 Lnet model.
4. Final Considerations
This is the Part II of the paper series on the radiation balance measured with a four-component net radiometer above an open low-turbidity water used for irrigation of tobacco plants in the east of Bahia, Brazil. The focus here was to analyze the surface albedo and model the net shortwave (SW) radiation (Snet), the net longwave (LW) radiation (Lnet), and the net all-wave radiation (Rn) on a daily basis.
It was observed that water albedo (αw) tended to decrease as the sun elevation (θ) increased, especially for clear skies and near clear skies. Under such conditions, a well defined U-shape curve was found with minimum hourly αw occurring around noon. This pattern was not so evident under cloudy and near cloudy skies. The results showed that αw can be reasonably predicted with a power law model either in terms of θ or Sg (incoming SW radiation) across different cloud cover conditions. Under cloudy sky, αw was higher for θ above 25°-30° compared to clear sky. Below that, αw was higher for clear sky conditions. For the low-turbidity water, a mean daily albedo of 0.05 is recommended from this study, so net SW radiation was modelled as 0.95Sg. Net LW radiation was successfuly modelled with the multiple linear regression (MLR) technique, where Lnet(MLR) was expressed as a function of five input variables commonly measured in standard weather stations. Similar performance was not obtained with Lnet(56), which is the FAO56 model for net LW radiation used in crop evapotranspiration.
Three approaches were considered for estimation of daily Rn. In the first approach, a linear regression model strongly fitted Rn data in terms of Sg solely. The second option based on the definition of Rn was [0.95Sg - Lnet(56)] and the third was [0.95Sg - Lnet(MLR)]. The disadvantages of approaches (1) and (3), based on regressions, is that they are constrained to the type of water used for irrigating the tobacco crop and the climatic conditions of the region, as well. The performance of approach (2), an universal model, was comparable to the others and can potentially be improved with a site-specific calibration. All three approaches for estimating daily Rn proposed in this study can possibily be extended to clear water that did not go through any filtration process.
Acknowledgments
The authors manifest their appreciation to the Fundação de Amparo à Pesquisa do Estado da Bahia / State of Bahia Foundation for Scientific Research (FAPESB) for the financial support through a research grant (TO APP0075/2011) and doctorate scholarship (TO BOL0545/2013) to Tatyana Keyty de Souza Borges without which this research would not have been possible. Support from the Idaho Agricultural Experiment Station (IDA01620) and Nebraska Agricultural Experiment Station is acknowledged.
References
- AKRITAS, M. Probability and Statistics with R for Engineers and Scientists New York: Pearson, 513 p., 2016.
-
ALADOS, I.; FOYO-MORENO, I.; OLMO, F.J.; ALADOS-ARBOLEDAS, L. Relationship between net radiation and solar radiation for semi-arid shrub-land. Agricultural and Forest Meteorology, v. 116, n. 3-4, p. 221-227, 2003. doi
» https://doi.org/10.1016/S0168-1923(03)00038-8 - ALLEN, R.G.; PEREIRA, L.S.; RAES, D.; SMITH, M. Crop Evapotranspiration: Guidelines for Computing Crop Water Requirements. Irrigation and Drainage Paper 56 Rome: FAO, 1998.
- ASCE. The ASCE Standardized Reference Evapotranspiration Equation Reston: ASCE, 205 p., 2005.
- BORGES, T.K.S. Evaporação em Superfície de água Livre com Baixa Turbidez Tese de Doutorado em Engenharia Agrícol, Universidade Federal do Recôncavo da Bahia, Cruz das Almas, 120 p., 2017.
- BORGES, T.K.S.; OLIVEIRA, A.S.; SILVA, N.D.; SANTANA, C.E. Plataforma flutuante de baixo custo para pesquisas em micrometeorologia e qualidade da água em reservatórios. Revista Geama, v. 4, n. 1, p. 38-45, 2016.
- BURMAN, R.; POCHOP, L.O. Evaporation, Evapotranspiration and Climatic Data Amsterdam: Elsevier, 278 p., 1994.
-
BRUNT, D. Notes on radiation in the atmosphere. Quarterly Journal of Royal of Meteorological Society, v. 58, n. 247, p. 389-420, 1932. doi
» https://doi.org/10.1002/qj.49705824704 -
COGLEY, J.G. The albedo of water as a function of latitude. Monthly Weather Review, v. 107, n. 6, p. 775-781, 1979. doi
» https://doi.org/10.1175/1520-0493(1979)107<0775:TAOWAA>2.0.CO;2 -
DAVIES, J.A.; ROBISON, P.J.; NUNEZ, M. Field determinations of surface emissivity and temperature for Lake Ontario. Journal of Applied Meteorology, v. 10, n. 4, p. 811-819, 1971. doi
» https://doi.org/10.1175/1520-0450(1971)010<0811:FDOSEA>2.0.CO;2 -
EL-BAKRY, M.M. Net radiation over the Aswan High Dam Lake. Theoretical and Applied Climatology, v. 49, n. 3, p. 129-133, 1994. doi
» https://doi.org/10.1007/BF00865529 -
FENG, Y.; LIU, Q.; QU, Y.; LIANG, S. Estimation of the ocean water albedo from remote sensing and meteorological reanalysis data. IEEE Transactions on Geosciences and Remote Sensing, v. 54, n. 2, p. 850-868, 2016. doi
» https://doi.org/10.1109/TGRS.2015.2468054 - FINCH, J.W.; HALL, R.L. Evaporation from lakes. In: ANDERSON, M. G.; McDONNEL, J. J. (Org.). Encyclopedia of Hydrological Sciences Chichester: Wiley, p. 635-646, 2005.
-
HENDERSON-SELLERS, B. Calculating the surface energy balance for lake and reservoir modeling: A review. Reviews of Geophysics, v. 24, n. 3, p. 625-649, 1986. doi
» https://doi.org/10.1029/RG024i003p00625 -
HENDERSON-SELLERS, A.; HUGHES, N.A. Albedo and its importance in climate theory. Progress in Physical Geography: Earth and Environment, v. 6, n. 1, p. 1-44, 1982. doi
» https://doi.org/10.1177/030913338200600101 - JENSEN, M.E.; ALLEN, R.G. Evapotranspiration and Irrigation Water Requirements. Manuals and Reports on Engineering Practice 70 New York: ASCE, 360 p., 1990.
- JENSEN, M.E.; ALLEN, R.G. Evaporation, Evapotranspiration and Irrigation Water Requirements. Manuals and Report on Engineering Practice 70 Reston: ASCE, 769 p., 2016.
-
JIN, Z.; CHARLOCK, T.P.; SMITH JR, W.L.; RUTLEDGE, K. A parameterization of ocean surface albedo. Geophysical Research Letters, v. 31, n. 22, p. 1-4, 2004. doi
» https://doi.org/10.1029/2004GL021180 -
KATSAROS, K.B.; McMURDIE, L.A.; LIND, R.L.; DEVAULT, J.E. Albedo of a water surface, spectral variation, effects of atmospheric transmittance, sun angle and wind speed. Journal of Geophysical Research, v. 90, n. C4, p. 7313-7321, 1985. doi
» https://doi.org/10.1029/JC090iC04p07313 -
KONDA, M.; IMASATO, N.; NISHI, K.; TODA, T. Measurement of the sea surface emissivity. Journal of Oceanography, v. 50, p. 17-30, 1994. doi
» https://doi.org/10.1007/BF02233853 -
KJAERSGAARD, J.H.; CUENCA, R.H.; PLAUBORG F.L.; HANSEN, S. Long-term comparisons of net radiation calculation schemes. Boundary-Layer Meteorology, v. 123, n. 3, p. 417-431, 2007. doi
» https://doi.org/10.1007/s10546-006-9151-8 -
KOFRONOVA, J.; MIROSLAV, T.; SIPEK, V. The influence of observed and modelled net longwave radiation on the rate of estimated potential evapotranspiration. Journal of Hydrology and Hydromechanics, v. 67, n. 3, p. 280-288, 2019. doi
» https://doi.org/10.2478/johh-2019-0011 -
LI, C.W.; BARNES, I.W. The relationship between net and global radiation over water. Theoretical and Applied Climatology, v. 28, n. 1-2, p. 91-100, 1980. doi
» https://doi.org/10.1007/BF02243837 -
LIU, H.; FENG, J.; SUN, J.; WANG, L.; XU, A. An eddy covariance measurements of water vapor and CO2 fluxes above the Erhai Lake. Science China Earth Sciences, v. 58, n.3, p. 317-328, 2015. doi
» https://doi.org/10.1007/s11430-014-4828-1 -
MYENI, L.; MOELETSI, M.E.; CLULOW, A.D. Assessment of three models for estimating daily net radiation in southern Africa. Agricultural Water Management, v. 229, 105951, 2020. doi
» https://doi.org/10.1016/j.agwat.2019.105951 -
MYENI, L.; SAVAGE, M.J.; CLULOW, A.D. Modelling daily net radiation of open water surfaces using land-based meteorological data. Water SA, v. 47, n. 4, p. 498-504, 2021. doi
» https://doi.org/10.17159/wsa/2021.v47.i4.3882 -
NUNEZ, M.; DAVIES, J.A.; ROBINSON, P.J. Surface albedo at a tower site in Lake Ontario. Boundary-Layer Meteorology, v. 3, n. 1, p. 77-86, 1972. doi
» https://doi.org/10.1007/BF00769108 - OKE, T.R. Boundary Layer Climates London: Routledge, 464 p., 1995.
-
PAYNE, R.E. Albedo of the sea-surface. Journal of the Atmospheric Science, v. 29, p. 959-970, 1972. doi
» https://doi.org/10.1175/1520-0469(1972)029<0959:AOTSS>2.0.CO;2 -
R CORE TEAM. R: A Language and Environment for Statistical Computing R Foundation for Statistical Computing, Vienna, Austria. URL https://www.R-project.org/, 2017.
» https://www.R-project.org/ -
SENE, K.J.; GASH, J.H.C.; McNEIL, D.D. Evaporation from a tropical lake: comparison of theory with direct measurements. Journal of Hydrology, v. 127, n. 1-4, p. 193-217, 1991. doi
» https://doi.org/10.1016/0022-1694(91)90115-X - SHUTTLEWORTH, W.J. Terrestrial Hydrometeorology Chichester: Wiley-Blackwell, 448 p., 2012.
-
VITALE, A.J.; GENCHI, S.A.; PICCOLO, M.C. Assessing the surface radiation balance and associated components in an intertidal wetland. Journal of Coastal Research, v. 35, n. 1, p. 158-164, 2019. doi
» https://doi.org/10.2112/JCOASTRES-D-17-00086.1 -
WRIGHT, J.L. New evapotranspiration crop coefficients. Journal of Irrigation and Drainage Engineering, v. 108, n. 1, p. 57-74, 1982. doi
» https://doi.org/10.1061/JRCEA4.0001372 -
WU, B.; LIU, S.; ZHU, W.; YAN, N.; XING, Q.; TAN, S. An improved approach for estimating daily net radiation over the Heihe River Basin. Sensors, v. 17, p. 1-18, 2017. doi
» https://doi.org/10.3390/s17010086
Publication Dates
-
Publication in this collection
11 Mar 2024 -
Date of issue
2024
History
-
Received
18 Jan 2023 -
Accepted
19 July 2023