A technique for mapping downward longwave radiation using satellite and ground-based data in the tropics

Renewable Energy 103 (2017) 171e179

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A technique for mapping downward longwave radiation using satellite and ground-based data in the tropics I. Masiri a, *, S. Janjai a, M. Nunez b, P. Anusasananan a a b

Department of Physics, Faculty of Science, Silpakorn University, Nakhon Pathom, 73000, Thailand School of Land and Food, University of Tasmania, Hobart, 7001, Tasmania, Australia

a r t i c l e i n f o

a b s t r a c t

Article history: Received 31 May 2016 Received in revised form 7 October 2016 Accepted 10 November 2016 Available online 10 November 2016

This paper presents a technique for mapping monthly average hourly downward longwave (LWY) irradiance using ground- and satellite-based data. A model relating LWY irradiance to a satellite derivedbrightness temperature of the earth-atmospheric system, relative humidity and ambient air temperature was formulated. This model was validated against LWY irradiance obtained from measurements at 4 sites in the tropics and discrepancy in terms of root mean square errors and mean bias errors was found to be 1.89% and
0.69%, respectively. After the validation, the model was used to calculate monthly average hourly LWY irradiance over Thailand and the results were displayed as LWY maps. These maps reveal the influence of various factors on LWY irradiance. © 2016 Elsevier Ltd. All rights reserved.

Keywords: Downward longwave radiation Satellite data Tropics

1. Introduction An information on the amount of downward longwave (LWY) irradiance at the earth surface is of importance for many fields including renewable energy and meteorology. In renewable energy, LWY irradiance is important for designing radiative cooling equipment. In meteorology, LWY irradiance has an influence on the net radiation which affects the stability of the atmosphere. LWY irradiance is emitted by water vapour, carbon dioxide, ozone and cloud water droplets. Under clear sky conditions, LWY irradiance can be estimated from several radiative transfer computer codes such as LOWTRAN [1] and MODTRAN [2]. However, an accurate estimate of LWY irradiance using a radiative transfer code usually requires accurate profile of atmospheric parameters such as temperature and relative humidity, which are not often available. This makes LWY estimate by this approach impractical. The estimation of LWY irradiance under cloudy sky conditions using modeling approach is more complicated and needs even more atmospheric data which are usually unavailable on a routine observation. Although LWY irradiance can be measured by a pyrgeometer, routine measurement of LWY irradiance using this instrument is costly due to high instrument and maintenance costs.

* Corresponding author. E-mail address: [email protected] (I. Masiri). http://dx.doi.org/10.1016/j.renene.2016.11.018 0960-1481/© 2016 Elsevier Ltd. All rights reserved.

Consequently, the measurement of LWY irradiance around the world is sparse, certainly providing insufficient LWY irradiance data. Since the beginning of the last century, atmospheric researchers have attempted to develop simple models relating LWY irradiance to wide-spread measured meteorological parameters such as € m [3] is the first temperature and relative humidity. Ångstro researcher who proposed a model relating LWY irradiance to a blackbody irradiance estimated from screen-level air temperature (Ta) multiplied by a “bulk” or effective air column emissivity (εe). The bulk emissivity is meant to take into account the transparency of the atmosphere, implying for example that when εe ¼ 1, the near surface air layer is acting like black body. Conversely, if εe < 1, contributions from the colder upper layers of the atmosphere are important. Numerous authors have attempted to provide expressions for the bulk term εe in terms of other screen-level meteorological variables. It consists in essentially relating ratios of measured LWY =sTa4 to relevant variables containing screen-level vapour pressure [3,4], vapour pressure and air temperature [5e7], precipitable water vapour [8], precipitable water vapour and air temperature [9], or air temperature [10,11]. Clouds are efficient emitters of longwave radiation [12] and as a result, a number of models incorporate cloud cover data obtained from surface observations. The exact form of the relationship varies widely depending on the local environment. In the dry sub-Arctic environment of Barrow, Alaska, cloud cover (C) was found to be

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I. Masiri et al. / Renewable Energy 103 (2017) 171e179

(A)

(B)

A

B C

(C)

(D)

D

Fig. 1. Pictorial view of the pyrgeometers and positions of the sites (A, B, C and D indicate the northern, northeastern, central and southern regions of Thailand, respectively).

the only good predictor of εe [13]. A popular approach is to partition LWY irradiance into a cloudless and cloudy portion, and uses a clear sky algorithm to describe the cloudless portion [14e18]. Iziomon et al. [18], describe the cloud term in terms of a quadratic in C that multiplies the cloudless sky εe, while in the Andean Altiplano, South America, the correction term is linear in C [19]. In most practical cases, cloud observations are relatively infrequent, so alternative methods involving satellite-derived cloud data are used. Present satellite algorithms provide cloud cover and atmosphere profile information which are then used to estimate LWY irradiance via radiative transfer models. Global datasets on LWY irradiance may be obtained on-line from the International Satellite Cloud Climatology Program (ISCCP) [20], the CERES Program [21,22] or the Gewex program (GEWEX-SRB) [23]. These are provided at a coarse spatial resolution of around 1  1 or more and at a coarse temporal resolution (3 hourly or coarser) as the data is mostly based on sun-synchronous polar-orbiting satellites. This coarse resolution is not sufficient for investigating the LWY irradiance over a specific location. As LWY irradiance is strongly influenced by cloud and cloud has a random nature in terms of structure and optical properties, cloud episodes would introduce considerable fluctuation in the LWY irradiance. However, cloud regional structure emerges after daily or longer term averaging. In this study, we choose to map monthly average hourly LWY irradiance. The resulting maps provide a climatology of LWY irradiance which is useful for various renewable energy applications such as the study of potential of nocturnal cooling. Our approach is two-fold. Firstly, we use the existing surface network of LWY irradiance, screen-level temperature and relative humidity to construct the model. Given the scarcity of surface-based cloud information, satellite-derived cloud brightness temperature is also used in the model development. Secondly, by using the temperature and relative humidity from high density network and satellite-derived brightness temperature, LWY irradiance over the entire area of the country is generated from the model. Merging of these two data should provide detailed distribution of LWY irradiance and its changes in the various regions of the country.

2. Methodology To develop the technique, for calculating LWY irradiance, several tasks were carried out as follows. 2.1. Measurement of LWY irradiance Pyrgeometer measurements (Kipp&Zonen, model CGR4) were conducted at four stations in Thailand covering different climatic zones. The instruments were deployed at Chiang Mai (18.78  N, 98.98  E) in the mountainous northern region, Ubon Ratchathani (15.25  N, 104.87  E) in the dry northeast region, Nakhon Pathom (13.82  N, 100.04  E) in the central region, and Songkhla (7.2  N, 100.60  E) in the southern maritime region (Fig. 1). For each site, the raw signals and the instrument internal temperature were recorded by a computer every 1 min over 24 h. The voltage signals were converted into LWY irradiance using a procedure provided by the manufacturer. The irradiance data were averaged to obtain monthly average of hourly longwave radiation. All pyrgeometers were calibrated by comparing them with a travelling reference pyrgeometer, which was sent to be calibrated at the manufacturer before and after the study period. The pyrgeometers at these sites were maintained by well-trained officers. The input optics of the pyrgeometers were regularly cleaned. The data period of LWY irradiance used in this work is shown in Table 1. These data were divided into two groups: the first group for modeling process and Table 1 Period of data collection used for modeling and validation processes. Sites

Periods For modeling process

For validation process

Chiang Mai Ubon Ratchathani Nakhon Pathom Songkhla

January 2012 e December 2014 August 2013 e December 2014

January e December 2015 January e December 2015

January 2012 e December 2014

January e December 2015

January 2013 e December 2014

January e December 2015

I. Masiri et al. / Renewable Energy 103 (2017) 171e179

the second group for validation process.

2.2. Processing of satellite data The study uses outgoing longwave irradiance from the earth/ atmosphere system detected by the MTSAT-1R satellite in the 10.3 to 11.3 mm band. Hourly data from this band is related to a “bulk” atmospheric temperature. The data can be displayed as images in a satellite projection showing the curvature of the earth. For ease of data utilization, the original images were rectified to a grid linearly proportional to latitude/longitude at the earth’s surface, with a spatial resolution of 5 km  5 km. In the next step, a map of Thailand was overlaid over the image and the map was adjusted to fit the boundary of the country using the coastline as reference. An example of the rectified image is shown in Fig. 2. Rectified image are composed of a matrix of 450  590 pixels, each containing grey levels that vary between 0 and 1023 (10-bit data) depending on the level of the signals received by the satellite sensor. The grey-level values of all pixels were converted into brightness temperature (TB) using a conversion table provided by a satellite data agency (www.data.jma.go.jp/mscweb/en/operation/ index.html). In this work, a six-year period (2010e2015) of satellite data was used. The TB data were partitioned into two groups. The first group was used for the modeling process and the second group was employed for the model validation. The period for each

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group corresponds to that of LWY irradiance used in this work (Table 1). The mapping uses entire period of data (2010e2015). 2.3. Collection of ancillary data Air temperature and relative humidity data were collected from 80 meteorological stations across Thailand (Table 2) and used in the analysis as these two parameters have been found to help in the estimation of LWY irradiance. Air temperature and relative humidity are obtained 3-hourly and they were interpolated into hourly data. Then they need to be again spatially interpolated to cover the entire country. There are many methods for the spatial interpolation available in literature [24,25] and some authors (e.g. [26,27]) applied these methods for mapping climatological data. In this work, the local thin spline method [28] was used. This is because the method has given good final results for the case of global solar radiation and illuminance mappings of Thailand [27,29]. The calculation was carried out by employing the IDL (Interactive Data Language) software package [30]. To implement this calculation, the coordinate of the stations and the values of quantities to be interpolated (temperature and relative humidity) and the required interpolated resolution were input to the software. Then, the software gave the interpolated values. In this work, the spatial resolution of the interpolated values corresponding to that of the satellite pixel (5 km  5 km) was used. 2.4. Modeling LWY irradiance is described in terms of a bulk emissivity (εe) and air temperature (Ta) as:

LWY ¼ εe sTa4

(1)

or


εe ¼ LWY sTa4

(2)

Several authors [3,7] included water vapour pressure in the expression of εe. As water vapour pressure has a close relation with relative humidity which is commonly measured at meteorological stations, for the simplicity of the calculation, the relative humidity was chosen as one of the independent variables of εe. This choice gives good results which will be shown in the model validation at the end of this section. There are, however some important considerations when dealing with cloud cover. Partition the sky into a cloudy and cloudless portion is a common approach [14e18]. In such approach, cloud cover data from ground-based or satellitebased observations were needed and most reported works [14e18] used cloud cover data from ground-based observation. As satellite-based cloud cover has not yet been widely employed, we have chosen to use TB as a surrogate for cloud cover. At night and for partly cloudy skies, it is expected that TB will decrease with increased cloudiness due to cooler cloud tops. For overcast conditions, decreasing TB will relate to increasing cloud opacity and a cloud emissivity. For simplicity all the relevant terms comprising εe are expressed as a polynomial, i.e.:

εe ¼ ða0 þ a1 Ta þ a2 TB þ a3 RHÞ

Fig. 2. An example of the rectified image from the infrared channel of MTSAT-1R satellite.

(3)

where a0 to a3 are constants obtained in a linear regression of εe vs Ta, TB and RH. The value of εe is calculated from Eq. (2). Monthly averages of the above ancillary variables from the four stations were used in the regression. Table 3 shows the resultant regression coefficients and their

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Table 2 Names and locations of meteorological stations used in this study. No.

Station

Latitude

Longitude

No.

Station

Latitude

Longitude

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Mae Hong Son Chiang Rai Chiang Rai (Agri.) Chiang Mai Lampang Lampoon Phare Nan Uttaradit Nongkai Loey Udon Thani Sakon Nakhon Nakhon Panom Sukhothai Tak Maesod Phitsanuklok Phetchaboon Kampangphet

19.18 19.58 19.52 18.47 18.17 18.34 18.10 18.47 17.37 17.52 17.27 17.23 17.09 17.25 17.06 16.53 16.40 16.47 16.26 16.29

97.50 99.53 99.47 98.59 99.31 99.02 100.1 100.47 100.06 102.44 101.44 102.48 104.08 104.47 99.48 99.07 98.33 100.16 101.09 99.32

21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

Khon Khan Mukdahan Phichit Mahasarakham Kalasin Nakhon Sawan Chainat Chaiyaphoom Roi Et Ubon Ratchathani Srisaket Ayutthaya Pathum Thani Chachongsao Ratchaburi Suphanburi Lop Buri Bua Chum Samutprakan Samutprakan (Air.)

16.26 16.32 16.20 16.15 16.19 15.48 15.09 15.48 16.03 15.15 15.02 14.32 14.16 13.34 13.29 14.28 14.48 15.16 13.31 13.41

102.50 104.43 100.22 103.04 103.35 100.10 100.11 102.02 103.41 104.52 104.15 100.43 100.37 101.27 99.47 100.08 100.37 101.12 100.45 100.44

41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Prachinburi Nakhon Ratchasima Chokchai Surin Buriram Nangrong Sakaew Kanchanaburi Thong Pha Phum Nakhon Pathom Bangkok Don Muang Chonburi Pattaya Satthahip Phetchaburi Rayong Chantaburi Prachoup Khiri Khan Hua Hin

14.03 14.58 14.43 14.53 16.19 14.37 13.42 14.01 14.45 14.01 13.40 13.55 13.22 12.55 12.41 13.09 12.38 12.37 11.50 12.35

101.22 102.05 102.10 103.30 103.35 102.43 102.35 99.32 98.38 99.58 100.36 100.36 100.59 100.52 100.59 100.40 101.21 102.07 99.50 99.58

61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80

Trat Chumporn Ranong Surat Thani Kho Samui Prasang Nakhon Si Thammarat Nakhon Si Thammarat (Agri.) Patthalung Phang Nga Phuket Kao Lanta Krabi Trang Songkhla Had Yai Sa Toon Pattani Yala Narathiwat

11.46 10.29 9.59 9.08 9.28 8.34 8.25 8.20 7.35 8.51 7.53 7.32 8.06 7.31 7.12 6.55 6.39 6.47 6.31 6.25

102.53 99.11 98.37 99.09 100.03 99.15 99.58 100.05 100.10 98.16 98.24 99.03 98.58 99.37 100.36 100.26 100.05 101.09 101.17 101.49

500 480 460 LWÈmodel (W/m2)

respective t-statistic and p-value (probability). The t-statistic is defined as the ratio of the estimated coefficient divided by its standard error. A high t-statistic indicates high correlation between the variable associated with the coefficient under consideration to the dependent variable (εe). P-value represents the probability that the correction occurs by chance. In general, the absolute value of tstatistic being greater than 2 implies that the variable associated to that coefficient is significantly correlates to the independent variable at the 95% level of confidence [31,32]. From Table 3, the absolute values of t-statistic for all coefficients are higher than 2, meaning that a0, Ta, TB and RH correlate significantly with εe. Eq. (1) with the fitted regression coefficients was then used to estimate LWY irradiance for the four stations during the independent year 2015. Results shown in Fig. 3 are satisfactory, with a coefficient of determination (R2) of 0.89 and a root mean square error (RMSE) of 8.09 Wm-2.

440 420 400 380 360 340 320

---- 1:1 line

300 Table 3 Values of the empirical coefficients and their related statistical parameters. Coefficients a0 a1 a2 a3

¼ ¼ ¼ ¼


0.60797 0.00532 (K
1)
0.00103 (K
1) 0.00260 (%
1)

t-statistic

p-value


4.27 13.08
13.18 22.37

<0.0005 <0.0005 <0.0005 <0.0005

300 320 340 360 380 400 420 440 460 480 500 LWÈ meas (W/m2) Fig. 3. Plot of monthly averages hourly LWY irradiance from the measurements ðLWYmeas Þ vs monthly average hourly LWY irradiance calculated from the model ðLWYmodel Þ for Chiang Mai, Ubon Ratchathani, Nakhon Pathom and Songkhla. Results gave an R2 ¼ 0.89 and RMSE ¼ 8.09 Wm-2.

I. Masiri et al. / Renewable Energy 103 (2017) 171e179

175

Table 4 Model performance for clear sky condition. LW0 is longwave irradiance (Wm
2); Ta is screen-level air temperature in K, ea is water vapour pressure in hPa and A, B are regression constants obtained from fitting the models to LW0, Ta and ea at the four stations for 2015. Model

Relationship

RMSE

MBE (W/m2)

% ðATa2 ÞsTa4

(W/m2)

%

Swinbank [10]

LW0 ¼

5.94

22.7

0.33

1.27

Idso & Jackson [33]

LW0 ¼ ½1
A expð
BðTc
Ta Þ2 ÞsTa4    LW0 ¼ A Teaa sTa4

19.83

75.88

19.26

73.68

3.82

14.62


1.16


4.44

LW0 ¼ ½1
ð1 þ WÞexpð
ðA þ BWÞ0:5 ÞsTa4 "    #

3.84

14.70


1.45


5.54

3.90

14.94


1.42


5.45

3.81

14.59


1.04


3.98

Brutsaert [5] Prata [8] Crawford and Duchon [14]

LW0 ¼ A þ B sin m þ 26p

ea Ta

1=7

sTa4

   a sTa4 LW0 ¼ 1
A exp
Be Ta

Iziomon et al. [18]

Table 5 Models used for comparison. LW0 irradiance is the downward longwave radiation under cloudless conditions and C is the fractional cloud cover. Author(s)

Location

Form

Jacobs [34] Maykut and Church [13]

Baffin Island, Canada Alaska, USA

LWY ¼ LW0 ð1 þ 0:26CÞ

Sugita and Brutsaert [35]

Kansas, USA

LWY ¼ LW0 ð1 þ 0:0496C 2:45 Þ

Konzelmann et al. [36]

Greenland

LWY ¼ LW0 ð1
C 4 Þ þ 0:952C 4 sTa4

Crawford and Duchon [14]

Oklahoma, USA

LWY ¼ LW0 ð1
CÞ þ C sTa4

Iziomon et al. [18]

Germany

LWY ¼ LW0 ð1 þ 0:0035C 2 Þ

3. Model comparisons Our model relationship uses brightness temperature as a convenient way to represent the effect of cloud on LWY irradiance during both day and night. It differs from other models which use cloud cover obtained from surface observation. In this section we compare our model relationships with others in the published literature. The analysis is done in two steps. Firstly, clear sky models are compared with measured data to determine best performance for our environment. The optimum clear sky relationship is then used in the various cloud models and compared with measurements and with our estimates using Eq. (3). For the comparison in the first step, the coefficients of clear sky models in this study were adjusted using irradiance under clear sky (LW0), screen-level temperature (Ta) and water vapour pressure (ea) using the data (Table 1) from the four stations. The model with adjusted coefficients was used to calculate LW0 in 2015 at the four stations. The discrepancies between measured and calculated LW0 were presented in terms of root mean square error (RMSE) and mean bias error (MBE) as shown in Table 4. From Table 4, the best performance was obtained with the model of Iziomon et al. [18], followed by Crawford and Duchon [14] and Prata [8] models. It is interesting to note that all three models

LWY ¼ LW0 ð1 þ 0:22C 2:75 Þ

include vapour pressure in an exponential or power format. The clear sky relationship of Iziomon et al. model was then used to construct the all-sky relationships shown in Table 5. An added model has been included, that of Jacobs [34] which did not provided a clear sky relationship for his all-sky irradiance. All express LWY irradiance as the product of a cloudless sky irradiance LW0 and a second term which is a linear or non-linear function of fractional cloud cover C. To arrive at a monthly value of fractional cloud cover (C), visual observation of clouds taken at the four stations were used to derive cloud cover data. The values of cloud cover were then applied to obtain hourly all-sky conditions between the hours of 09:00 and 15:00 for all four stations during the independent year 2015. The cloud coefficients are adjusted in the second comparison using data period for modeling process (Table 1) and then tested with the independent data for 2015. Table 6 presents the results. The model developed in this study and that of Sugita and Brutsaert [35] outperformed the others when using the “Original” comparison. Adjusting all model coefficients with local data has a very significant effect on the MBE but much less on the RMSE. In terms of all-sky performance, our model and that of Jacobs [34] were best, followed by Iziomon et al. [18].

Table 6 Comparison of seven LWY models with measured 2015 hourly data at four stations during daytime hours (09:00e15:00). Data are grouped into “Original, with the models being applied using their original coefficients and “Adjusted” where the coefficients are statistically adjusted during years 2012e2014. Model

Original

Adjusted

RMSE

This model Jacobs [34] Maykut and Church [13] Sugita and Brutsaert [35] Konzelmann et al. [36] Crawford and Duchon [14] Iziomon et al. [18]

MBE 2

RMSE 2

MBE 2

%

W/m

%

W/m

%

W/m

%

W/m2

1.89 12.71 4.79 2.92 29.85 7.15 4.26

8.09 54.39 20.53 12.51 127.75 30.61 18.23


0.69 12.33 3.19
1.92
24.05 6.54
3.49


2.98 52.77 13.68
8.22
102.94 27.97
14.96

1.89 2.14 2.38 2.30 29.78 2.94 2.19

8.09 9.18 10.21 9.86 127.48 12.59 9.37


0.69
0.24
0.60
0.53
24.00 0.09
0.41


2.98
1.01
2.58
2.27
102.74 0.39
1.77

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I. Masiri et al. / Renewable Energy 103 (2017) 171e179

(a)

(c)

(b)

(d)

Fig. 4. Monthly average of LWY irradiance for January at (a) 5:00, (b) 9:00, (c) 13:00 and (d) 20:00 local time.

4. Monthly average hourly distributions of LW↓ irradiance over Thailand All input parameters were retrieved on a monthly average hourly basis. The averaging process of all model variables was carried out over a six-year period (2010e2015). They included brightness temperature obtained from satellite data, and relative humidity and air temperature interpolated from 80 meteorological stations. In the final step, Eq. (1) was used to calculate monthly average hourly LWY irradiance covering the entire country. Fig. 4 displays geographical distribution monthly average LWY

irradiance images for January at 5:00, 9:00, 13:00 and 20:00 local time. They feature considerable regional and diurnal variabilities. Overall, there is a strong north/south gradient, a result of latitudinal variability, encompassing approximately 6 N to 20 N and affecting air temperature and relative humidity gradients. Typically, it may translate in a 20e25 Wm-2 gradient in LWY irradiance between the humid and warm south and the cool mountain north. Another feature is the tongue of relatively high LWY that protrudes north of Bangkok at 05:00, 09:00 and 20:00, a result of northward transport of warm, moist air from the Gulf of Thailand. In the mainland part of the country, the gradient of LWY is in the NE/SW direction. The

I. Masiri et al. / Renewable Energy 103 (2017) 171e179

(a)

(c)

177

(b)

(d)

Fig. 5. Noontime patterns of LWY irradiance in four months of the year, (a) January, (b) March, (c) June and (d) September.

contours of the LWY field are aligned NW/SE. The N/S gradient is seasonally dependent, as may be seen in Fig. 5 which shows noontime patterns in four months of the year, January, March, June and September. It is very prominent in January, less prominent in March, and is not evident in June and September during the wet season. It is likely that heavy cloud cover in the entire country disrupts any latitudinal variation in either relative humidity or air temperature. Maximum LWY occurs at around latitude 15 N in these last two months. More detailed temporal features are shown in Fig. 6 which plots LWY irradiance in graphs showing month (y axis) vs hour (x

axis). A northern (lat:18.8 N; long:100.2 E), middle (lat:13.8 N; long:100.0 E) and southern (lat:7.2 N; long:100.4 E) location are considered. Several variations are observed. All three locations feature highest LWY irradiance during daylight hours and in the wet season characterized by high humidity and cloud cover. However, the period of high LWY irradiance is between May and November for the northern location between April to December in the middle location, and between March to December in the southern location. Lowest LWY irradiance occurs between midnight to 9:00 and in January to March.

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I. Masiri et al. / Renewable Energy 103 (2017) 171e179

(a)

(b)

(c)

Fig. 6. Temporal feature of LWY irradiance for (a) northern (lat:18.8 N; long:100.2 E), (b) middle (lat:13.8 N; long:100.0 E) and (c) southern (lat:7.2 N; long:100.4 E) locations.

5. Discussion and conclusion This study has developed a technique to estimate monthly averages of hourly LWY irradiance at the surface for both day and night. A regression model is developed using screen-level temperature and relative humidity from 80 surface stations and

brightness temperature from the infrared channel of MTSAT-1R satellite. A novel feature is the use of brightness temperature as this term is sensitive to increasing cloudiness as well as cloud thickness, two terms that are important in estimating LWY irradiance. Data from four stations measuring LWY irradiance in Thailand during the period shown in Table 1 are used to build up the

I. Masiri et al. / Renewable Energy 103 (2017) 171e179

regression coefficients, while station data from 2015 are used for model validation. When tested with the independent data, the model gave satisfactory results, with an R2 of 0.89 and an RMSE of 8.09 Wm-2. Present published models that estimate all-sky LWY are constrained to daytime observations as they use cloud cover data from ground-based measurements. Comparisons were done for both cloudy and cloudless conditions. In the cloudless case the models were assessed against 2015 data with the relationship of Iziomon et al. [18] performing best with an RMSE and MBE of 3.81% and
1.04%, respectively. In the cloudy case the relation of Iziomon et al. [18] was used to describe cloudless irradiance. The models were then assessed against 2015 data with their original coefficients and with the cloudy regression coefficients fitted using data period for modeling processes (Table 1). Of these, our model and the locally-tuned Jacobs [34] model performed best (RMSE: 2.14% (Jacobs) vs. 1.89% (this study); MBE:
0.24% (Jacobs) vs.
0.69% (this study)). There was a substantial improvement in three out of the six models examined when local tuned coefficients were used. Using our model, we have obtained a detailed diurnal variability of LWY irradiance on a monthly average basis. We believe that this type of processing is most appropriate as most applications require diurnal information after filtering for random short-term cloud effects. Using this technique, we have been able to show considerable diurnal variability in the country, superimposed on a regional N/S gradient which is highest during the dry winter months but decreases as the wet season approaches. The use of brightness temperature as a surrogate for cloud cover could be easily applied to other environments where detailed diurnal information on LWY is required. We have used an empirical regression relationship to describe the bulk sky emissivity εe, In future work, it might be possible to develop a relation similar to Eq. (3) using cloud cover obtained from the information on the emissivity of cloud as a function of its brightness temperature and related parameters. A useful goal is to use brightness temperature within a more physically realistic expression such as that presented by Crawford and Duchon [14] which requires few empirical coefficients and has performed consistently well in our study as well as others. Hourly-specific longwave radiation could also be examined with emphasis on temporal and spatial averaging and their effects on errors in the calculation. Future studies of this nature are warranted given the importance of longwave radiation in a range of applications. Acknowledgement The authors would like to thank the Thailand Research Fund (TRF) for the partially financial support to this work under its International Research Network (IRN) (IRN57W0001). References [1] F.X. Kneizys, E.P. Shettle, L.W. Abreu, et al., Users’ Guide to LOWTRAN7, Report No. AFGL-TR-88e0177, Air Force Geophysics Laboratory, Hanscom AFB, MA, 1988. [2] H.E. Snell, G.P. Anderson, J. Wang, J.-L. Moncet, J.H. Chetwynd, S.J. English, Validation of FASE (FASCODE for the Environment) and MODTRAN3: updates and comparisons with clear-sky measurements, in: Proceedings of Conf. On Passive Infrared Remote Sensing of Clouds and the Atmosphere III, vol. 2578, SPIE, Paris, France, 1995, 25e27 September. € m, A study of the radiation of the atmosphere, Smithson. Inst. Misc. [3] A. Ångstro Collect. 65 (1918) 159e161. [4] D. Brunt, Notes on radiation in the atmosphere, Q. J. R. Meteorol. Soc. 58 (1932) 389e418.

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[5] W. Brutsaert, On a derivable formula for long-wave radiation from clear skies, Water Resour. Res. 11 (1975) 742e744. [6] S.B. Idso, A set of equations for full spectrum and 8e14 mm and 10.5e12.5 mm thermal radiation from cloudless skies, Water Resour. Res. 17 (1981) 295e304. [7] A. Golaka, R.H.B. Exell, Nocturnal downward atmospheric radiation in a tropical wet and dry climate with data from the North of Thailand, Int. J. Ambient Energy 28 (2) (2007) 73e82. [8] A.P. Prata, A new long-wave formula for estimating downward clear-sky radiation at the surface, Q. J. R. Meteorol. Soc. 122 (1996) 1127e1151. [9] A.C. Dilley, D.M. O’Brien, Estimating downward clear sky long-wave irradiance at the surface from screen temperature and precipitable water, Q. J. R. Meteorol. Soc. 124 (1998) 1391e1401. [10] W.C. Swinbank, Long-wave radiation from clear skies, Q. J. R. Meteorol. Soc. 89 (1963) 339e348. [11] R.H.B. Exell, M.I. Kalwar, Atmospheric radiation and sky temperatures in Thailand, J. Sci. Soc. Thail. 2 (1976) 160e167. [12] D. Lamb, J. Verlinde, Physics and Chemistry of Clouds, Cambridge University Press, Cambridge, 2011. [13] G.A. Maykut, P.E. Church, Radiation climate of Barrow, Alaska, 1962-66, J. Appl. Meteorol. 12 (1973) 620e628. [14] T.M. Crawford, C.E. Duchon, An improved parameterization for estimating effective atmospheric emissivity for use in calculating daytime downwelling long-wave radiation, J. Appl. Meteorol. 38 (1999) 474e480. [15] H.F. Duarte, N.L. Dias, S.R. Maggiotto, Assessing daytime downward longwave radiation estimates for clear and cloudy skies in Southern Brazil, Agric. For. Meteorol. 139 (3) (2006) 171e181. [16] M. Choi, J.M. Jacobs, W.P. Kustas, Assessment of clear and cloudy sky parameterizations for daily downwelling longwave radiation over different land surfaces in Florida, USA, Geophys. Res. Lett. 35 (20) (2008). [17] F. Carmona, R. Rivas, V. Caselles, Estimation of daytime downward longwave radiation under clear and cloudy skies conditions over a sub-humid region, Theor. Appl. Climatol. 115 (1e2) (2014) 281e295. [18] M.G. Iziomon, H. Mayer, A. Matzarakis, Downward atmospheric longwave irradiance under clear and cloudy skies: measurement and parameterization, J. Atmos. Solar-Terrestrial Phys. 65 (10) (2003) 1107e1116. [19] J.P. Lhomme, J.J. Vacher, A. Rocheteau, Estimating downward long-wave radiation on the Andean Altiplano, Agric. For. Meteorol. 145 (2007) 139e148. [20] Y. Zhang, W.B. Rossow, A.A. Lacis, V. Oinas, M.I. Mishchenko, Calculation of radiative fluxes from the surface to top of atmosphere based on ISCCP and other global data sets: refinements of the radiative transfer model and the input data, J. Geophys. Res. Atmos. 109 (D19) (2004). [21] B.A. Wielicki, B.R. Barkstrom, E.F. Harrison, R.B. Lee III, G.L. Smith, J.E. Cooper, Clouds and the Earth’s radiant energy system (CERES): an earth observing system, Bull. Am. Meteorol. Soc. 72 (1996) 853e868. [22] G.L. Smith, B.A. Wielicki, B.R. Barkstrom, R.B. Lee, K.J. Priestley, T.P. Charlock, P. Minnis, D.P. Kratz, N.G. Loeb, Clouds and earth radiant energy system (CERES): an overview, Adv. Space Res. 33 (2004) 1125e1131. [23] P.W. Stackhouse Jr., S.K. Gupta, S.J. Cox, T. Zhang, J.C. Mikovitz, L.M. Hinkelman, The NASA/GEWEX Surface Radiation Budget Release 3.0: 24.5-year Dataset GEWEX News, 21(1), 2011, pp. 10e12. [24] N. Panigrahi, Computing in Geographic Information Systems, CRC Press, Boca Raton, 2014. [25] S. Naoum, I.K. Tsanis, Ranking spatial interpolation techniques using a GISbased DSS, Glob. Nest 6 (1) (2004) 1e20. [26] D.A. Jones, W. Wang, R. Fawcett, High-quality spatial climate data-sets for Australia, Aust. Meteorol. Oceanogr. J. 58 (4) (2009) 233e248. [27] S. Janjai, J. Laksanaboonsong, M. Nunez, A. Thongsathitya, Development of a method for generating operational solar radiation maps from satellite data for a tropical environment, Sol. Energy 78 (6) (2005) 739e751. [28] R. Franke, Smooth interpolation of scattered data by local thin plate splines, Comput. Math. Appl. 8 (4) (1982) 273e281. [29] S. Janjai, K. Tohsing, M. Nunez, J. Laksanaboonsong, A technique for mapping global illuminance from satellite data, Sol. Energy 82 (6) (2008) 543e555. [30] K.P. Bowman, An Introduction to Programming with IDL: Interactive Data Language, Academic Press, California, 2006. [31] R.E. Walpole, R.H. Myers, S.L. Myers, Probability & Statistics for Engineers & Scientists, Prentice Hall, New York, 2002. [32] H.D. Young, Statistical Treatment of Experimental Data, McGraw-Hill, New York, 1962. [33] S.B. Idso, R.D. Jackson, Thermal radiation from the atmosphere, J. Geophys. Res. 74 (1969) 5397e5403. [34] J.D. Jacobs, Radiation climate of Broughton Island, in energy budget studies in relation to fast-ice breakup processes in Davis Strait, Inst. Arct. Alp. Res. 26 (1978) 105e120. [35] M. Sugita, W. Brutsaert, Cloud effect in the estimation of instantaneous downward longwave radiation, Water Resour. Res. 29 (1993) 599e605. [36] T. Konzelmann, R.S.W. van d Wal, W. Greuell, Bintanja, R. Henneken, E.A.C., A. Abe-Ouchi, Parameterization of global and longwave incoming radiation for the Greenland ice sheet, Global Planet. Change 9 (1994) 143e164.