On the Performance of Some Predictive Models for Global Solar ...

The African Review of Physics (2012) 7:0015

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On the Performance of Some Predictive Models for Global Solar Radiation Estimate in Tropical Stations: Port Harcourt and Lokoja

Olusola Tosin Kolebaje and Lateef Olajuwon Mustapha University of Ibadan, Ibadan, Nigeria

Using the sunshine duration and maximum and minimum temperatures as the input to five radiation models (Angstrom Prescott model, Second order Angstrom Prescott model, Third order Angstrom Prescott model, Hargreaves model and Garcia model), the monthly average daily global solar radiation in Port Harcourt (40 47’N 70 00’E) and Lokoja (70 48’N 60 44’E) are estimated. Model validation was performed by using the Mean Bias Error (MBE), Root Mean Square Error (RMSE), Mean Percentage Error (MPE), and the Pearson’s Correlation Coefficient as performance indicators. The proposed equations showed a good agreement with the measured radiation data obtained using pyranometer. The Angstrom Prescott model with a correlation coefficient of 0.953 gave the best MBE of -0.5391, best RMSE of 0.9872 and best MPE of -2.8888% in Port Harcourt. The third order Angstrom Prescott model with an RMSE of 1.4831 or the Angstrom Prescott model with RMSE 1.4730 is proposed for use in Lokoja. Garcia model with correlation coefficient 0.983 is proposed for use in Port Harcourt during the wet season as it gave the best MBE of -0.7022, best RMSE of 0.8656 and the best MPE of -4.2596%, while the third order Angstrom Prescott gave the best MBE of -0.3281 and best MPE of 1.6664%. The Angstrom Prescott model with the lowest MBE of 0.2965 and lowest MPE of 1.9753% is proposed for Lokoja during the wet season, while the second order Angstrom Prescott model with correlation coefficient of 0.872 is proposed for Lokoja during the dry season as it gave the lowest MBE of -0.1473, lowest RMSE of 0.9607 and lowest MPE of -0.6126%. Conclusively, it was observed that the temperature based models performed better during the wet season compared to the dry season in both Port Harcourt and Lokoja stations. This is evident as the wet season is more influenced by temperature as compared to the sunshine hour characterized dry season. Also, the third order Angstrom Prescott model does not improve significantly prediction ability over the second order Angstrom Prescott.

1.

Introduction

The energy transferred from the sun in the form of radiant to the earth’s surface is normally referred as the solar radiation. In any solar energy conversion system, the knowledge of global solar radiation is germane for the optimal design and prediction of the system performance [1]. The best way of knowing the amount of global solar radiation at a site is through recorded data. Daily solar radiation data are often required in agro-metrological calculations particularly in computing a water budget for irrigation or to run a crop growth simulation model but these are measured only at a few stations [2]. In fact, at global scale, the ratio of weather stations collecting solar radiation data relative to those collecting temperature data is estimated to be a ratio of 1:500 as cited by Thornton and Running [3]. When radiation records are not available, these can be estimated by means of an empirical relation using

the measured duration of sunshine, cloudiness or temperature [4]. Solar radiation data on the earth’s surface is required for engineers, agriculturists and hydrologists in many applications. Solar energy is a free, clean and inexhaustible source of energy. Its effective harnessing and utilization are of importance to the world especially at this time of rising fuel costs and environmental effects such as depletion of the ozone layer and greenhouse effect [5]. Since the values of global solar radiation are measured only at a few locations, then for places where no measured values are available, modelling becomes an essential and economical tool for the estimation of solar radiation. Though less accurate, modelling is a better tool for the estimation of solar radiation at places where measurements are not available. Using various metrological variables such as relative sunshine hours, cloudiness and


temperature, various models have been developed in [6-8, 4, 9-13]. The objective of this study is to develop equations (linear and polynomial) for estimating global solar radiation in Port-Harcourt and Lokoja, which are two tropical areas across different four climatic zones in Nigeria and to examine their performance in estimating the radiation at these locations. The model used are the Angstrom Prescott model, second order Angstrom Prescott and the third order Angstrom Prescott model, which are sunshine hour based, whereas the Hargreaves model and Garcia model are based on maximum and minimum temperatures. The performance (including seasonal) of the models developed for the two sites was investigated using relevant statistical tools. 2.

Climatic Zones under Study

Nigeria is situated between latitudes 40 and 140 North of the equator and between longitudes 30 and 150 east of the meridian (Iloeje N.P., 1965). Its greatest length from north to south is around 550 miles and from east to west over 700 miles. The area of Nigeria is 356,669 square miles. It is bounded in the north by the Niger republic and the Chad republic, on the east by the republic of Cameroon, on the south by the gulf of Guinea and on the west by the republic of Benin and Niger republic. Nigeria has a tropical climate with variable rainy and dry seasons depending on the location. It is hot and wet most of the year in the south but is drier farther inland. A savannah climate, with marked wet and dry seasons, prevails in the north and west, while a steppe climate with little precipitation is found in the far north. In general, the length of the rainy season decreases from south to north. In the south, the rainy season lasts from March to November, whereas in the far north it lasts only from mid-May to September. A marked interruption occurs during August in the south, resulting in a short dry season often referred to as the August break. Precipitation is heavier in the south, especially in the southeast, which receives more than 120 inches (3,000 mm) of rain a year, compared with about 70 inches (1,800 mm) in the southwest. Rainfall decreases progressively away from the coast; the far north receives no more than 20 inches (500 mm) a year.

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Temperature and humidity remain relatively constant throughout the year in the south, while the seasons vary considerably in the north. The humidity generally is high in the north, but it falls during the harmattan (the hot, dry northeast trade wind), which blows for more than three months in the north but rarely for more than two weeks along the coast (see Table 1 for climatic data). According to Olaniran [14], Nigeria can be divided into four zones which are: I. The Coastal Zone of Port Harcourt station is dominated by tropical maritime (mT) air for most of the year. This is found along the coast, up to some 100 to 150 kilometres inland. Temperatures are up to 270C to 300C most of the year and both the daily and annual ranges are as little as 100C and 50C, respectively. Relative humidity is around 80% and over 300cm of annual rainfall has the double maxima rainfall. This zone has a long wet season from 7 – 10 months [15]. II. The Guinea-Savannah Zone, where Lokoja has been selected, has longer temperature ranges, lower annual rainfall and shorter wet season of about 6 – 8 months in contrast to the Coastal region. It is the most widespread vegetation belt and has an annual rainfall of 100cm to 200cm and a well marked dry season of 4 – 6 months prone to bush fires and lateritic soil of medium to low fertility. The relative humidity is around 60% and the rainfall has double maxima [15]. III. The Midland Zone, which is predominantly highland and where the tropical continental (cT) air mass dominates but where the topography effectively extends the length of the humid period due to localized convection [15]. IV. The Sahelian Zone, where the cT air mass predominates and the mT air mass invade for between 3 and 5 months at most. This is found in the north-eastern extremity of the country. This type has highly accentuated continental climate with very wide annual and diurnal temperature ranges of about 150C and 200C, respectively. The total annual precipitation is generally less than 75 cm. The dry season is excessively dry and long (up to 8 to 10 months) and desert-like conditions prevail [15].


147

Table 1: Weather characteristics of climatic zones under study. LOCATION

LATITUDE (radians)

LONGTITUDE

(0C)

MEAN ANNUAL RAINFALL (cm)

MEAN WIND SPEED (Km/hr)

MEAN AIR TEMPERATURE

PORT HARCOURT

4047’N (0.0835 rad)

7000’E

230C

331.21

9.44

LOKOJA

7048’N (0.1362 rad)

6044’E

290C

287.98

7.59

3. 3.1.

regression between the relative incoming solar radiation and the square root of ∆:

Methodology Model description

The Angstrom correlation [6] has served as a basic approach to estimate global radiation for a long time. Prescott [7] put the correlation in a better form known as the Angstrom-Prescott model as;

(1)

Where:

is the global solar radiation in MJm-2day-1; is the extraterrestrial radiation in MJm-2day-1; is the sunshine duration in hours; is the daylight hour in hours.

The model parameters and are constants to be estimated by regression technique. Fagbenle [9], Udo [12], Ogelman et al. [16], Akinoglu and Ecevit [17] and Ogolo [18] proposed a quadratic and cubic form of the AngstromPrescott model known as the second order Angstrom-Prescott model and Third-order Angstrom Prescott model, respectively.

(2)

(3)

Where, , , , , , , and are empirical coefficients. The three models discussed above are sunshine hour based models. Hargreaves and Samani [8] developed an empirical equation that took the form of a linear

∆T .

(4)

Where, ∆ is the difference between maximum and minimum temperatures and and are empirical coefficients. The Garcia model is the only attempt made to estimate incoming solar radiation in Peru. The model is an adaptation of the Angstrom-Prescott model

∆!

(5)

The Hargreaves model and the Garcia model are both temperature based models as they employ minimum and maximum temperatures as the required metrological data. The site specific inputs for the calculation of extraterrestrial solar radiation are latitude and sunset hour angle. The extraterrestrial daily solar radiation (in MJm-2d-1) is determined by the sets of equations given below [19].

"#$% &

' ( ) *+ sin / sin 0 cos / cos 0 sin + 3 (6) ) 1 0.033 cos 0 0.409 sin

&7

$

&7

(7)

: 1.39

(8)

$

+ cos ;< #: tan / tan 0%

(9)


148

Where: ' ( ) + / 0 ?

The daylight hours N (hours) is also calculated using the equation given below [19].

is the extraterrestrial radiation (MJm-2d-1); is the solar constant = 0.082 MJm-2d-1; is the inverse relative distance Earth-Sun; is the sunset hour angle (radians); is the latitude (radians); is the solar declination (radians); is the Number of the day in the year between 1(1 January) and 365 or 366 (31 December).

" &

+

(10)

The extraterrestrial radiation and daylight hours for stations used in this research were calculated and are shown in Tables 2 and 3 below.

Table 2: Extraterrestrial radiation (MJm-2day-1) of the location of study.

MONTH

PORT HARCOURT

LOKOJA

JANUARY

34.3038

32.9941

FEBRUARY

36.1046

35.1779

MARCH

37.4756

37.1339

APRIL

37.3842

37.6885

MAY

36.1702

36.9692

JUNE

35.2518

36.2670

JULY

35.5581

36.4651

AUGUST

36.6687

37.1612

SEPTEMBER

37.1950

37.0792

OCTOBER

36.2720

35.5243

NOVEMBER

34.5368

33.3170

DECEMBER

33.5572

32.1384

Table 3: Daylight hours (hours) of the location of study.

MONTH

PORT HARCOURT

LOKOJA

JANUARY

11.7523

11.5974

FEBRUARY

11.8446

11.7486

MARCH

11.9697

11.9534

APRIL

12.1035

12.1726

MAY

12.2139

12.3534

JUNE

12.2675

12.4413

JULY

12.2412

12.3981

AUGUST

12.1452

12.2409

SEPTEMBER

12.0159

12.0291

OCTOBER

11.8824

11.8105

NOVEMBER

11.7732

11.6317

DECEMBER

11.7226

11.5487


3.2.

149

Acquisition of data

The data used in this study was collected from the Nigerian Metrological Agency (NIMET), Oshodi, Lagos. The data was extracted from the monthly meteorological observation at NIMET Oshodi sent from various locations across the country. 4.

Campbell in 1853 and later modified in 1879 by Sir George Gabriel Stokes. The device is designed to record the hours of bright sunshine that will burn a hole through the card. It is of great importance to install the device in an area where the sun will not be blocked by buildings, trees or other obstructions. 5.

Instrumentation

At the Nigerian meteorological agency, global solar radiation is measured through the use of the Gunn Bellani radiometer (GB), which is a simple, cheap and easy to maintain instrument commonly used in solar radiation estimation and evaporation studies. The instrument provides a time-integrated assessment of radiation falling on a black body by measuring the volume of liquid distilled by the radiation. It is available in two forms: water filled for daily radiation of up to 6.28MJm-2 and alcohol filled for daily radiation of up to 37.68MJm-2. It requires neither powering nor any special skill to operate and has been found suitable for field estimation of daily total radiation. The liquid is contained in a thin walled copper sphere blackened externally. Sealed into this, with its upper end above liquid level, is the distillation tube. The latter collects liquid distilled from the bulb in its lower section, which is graduated in 0.1 ml divisions. The bulb holds about 42 ml of the working fluid. Initially, the liquid is transferred to the copper sphere by inverting the instrument, and the level remaining in the graduated receiver is noted. When exposed to solar radiation, the fluid in the blackened copper sphere vaporizes and condenses in the graduated receiver. Periodically, or at the end of each day, radiation level is recorded. Folayan [20] calibrated GB readings with pyranometer readings and came up with a conversion factor, which may be mathematically expressed as: 1@AB 1.357#E0.176%G?@;

Treatment of Data

Models were developed for the locations under study by using 15 years (1976-1988, 1991-1992) for Port Harcourt and 15 years (1976-1988, 1992, 1995) for Lokoja station. The average monthly values of the sunshine hours, global radiation, and maximum and minimum temperature data for Port Harcourt and Lokoja stations were calculated. Regression equation for each of the models were developed from the dataset of monthly mean of ⁄ , ⁄ , ∆ . and ∆ ⁄ and which are stated below: PORT HARCOURT Angstrom-Prescott

0.239 0.717

(12)

Second-order Angstrom-Prescott

0.177 1.239 : 0.986

(13)

Third-order Angstrom-Prescott

0.197 0.981 0.053 : 1.317

(14) Hargreaves model

(11)

The maximum and minimum thermometers are used to measure the highest and lowest temperature reached by air in a day at the Nigerian meteorological agency. These are kept at a height of 1.5 meters above the ground in a white wooden louvered shelter called Stevenson screen. Maximum and minimum thermometers are liquid in glass thermometers used for determining daily maximum and minimum temperatures. At the meteorological agency, sunshine hour data is obtained using the Campbell-stokes sunshine recorder. It was invented by John Francis

Garcia model

:0.104 0.190∆T .

(15)

(16)

0.188 0.362

∆!

LOKOJA Angstrom-Prescott

0.258 0.612

(17)


150


Dry Season

0.320 0.357 : 0.252

(18)

Angstrom-Prescott


0.318 0.513

(27)


0.306 0.464 0.000 : 0.189

(19)

(28)


Hargreaves model

0.429 0.169 1.031

0.229 0.106∆T .

(20)

0.400 0.137 0.000 1.139

(29)

Garcia model

0.422 0.169

Hargreaves model

∆!

(21)

Models were developed for the wet season (AprilOctober) and dry season (November-May) for Port Harcourt and Lokoja based on dataset of monthly mean of ⁄ , ⁄, ∆ . and ∆⁄ for the months in each season.

0.250 0.643

(31)

0.377 0.137

∆!

0.174 1.303 : 1.296

(23)

0.231 0.548 1.884 : 4.215

0.091 1.401 : 0.928

:0.371 0.290∆T .

(34)

(25)

:0.257 0.272∆T .

(35)

Garcia model

Garcia model

Hargreaves model

Hargreaves model

(33)

0.091 1.401 0.928 0.000

(24)

(32)



0.286 0.537


(22)


Garcia model

Angstrom-Prescott

Angstrom-Prescott

(30)

Wet Season

Wet Season

0.281 0.067∆T .

LOKOJA

PORT HARCOURT

0.026 0.640

∆!

(26)

0.169 0.526

∆!

(36)


151