IOSR Journal of Applied Physics (IOSR-JAP) e-ISSN: 2278-4861. Volume 5, Issue 5 (Jan. 2014), PP 01-06 www.iosrjournals.org

Computing net radiation from temperature variables: Improvising for under-resourced weather stations in developing countries. Farai Malvern, SIMBA Department Of Physics, Geography and Environmental Science, Great Zimbabwe

University

I.

Introduction

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Computing net radiation from temperature variables: Improvising for under-resourced weather II.

Study area

Masvingo province is divided into seven districts which are; Gutu, Masvingo, Bikita, Zaka, Chivi, Mwenezi and Chiredzi. The province occupies the drier Lowveld area in the south of Zimbabwe. Most of the area in the province is devoted to cattle ranching, subsistence crop farming, with mining and irrigated sugar growing also significant. Rainfall is highly variable and uncertain, making the province prone to droughts. (Makadho, 1996). Masvingo province is in the south-eastern part of Zimbabwe. It borders Mozambique on its eastern border and the provinces of Matabeleland South to the south, Midlands to the north and west and Manicaland to the north east. The province has an area of 56,566 kmÂ˛ and a population of approximately 1.3 million in 2002,(CSO, 2002).

Figure 1 v v : Map of Masvingo province (Simba et.al 2013).

III.

Problem statement

n ] Ra..............................................................1 N

Where: Rs = Solar or shortwave radiation (MJ/m2 per day); n = Actual sunshine hours (hour); N = Maximum possible duration of sunshine; hours or daylight hours (hour);

n = Relative sunshine duration; Ra = N

Extraterrestrial radiation (MJ/m2 per day) The maximum duration of sunshine (N) can be calculated using equations. However, to simplify the calculation procedures, values of N for different latitudes can be read from Tables in FAO irrigation paper 56 for the Southern Hemisphere. The actual duration of sunshine (n) is recorded with a sunshine recorder and is part of the climatological data provided by weather stations. The

n ratio can also be obtained from data on N

cloud cover, if data on sunshine hours are not available.

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Computing net radiation from temperature variables: Improvising for under-resourced weather IV.

Construction of a CNR1 four component net radiometer

V.

Market price \$ 2.000 \$ 5.000 \$5.663 \$2.483 \$3.363

Supplier Delta-T Devices (UK) Delta-T Devices(UK) Sky power international (Germany) Enercorp instruments Ltd (Canada) Enercorp instruments Ltd (Canada)

Methodology

The method used in this study is based on 20 day maximum and minimum temperature data for the month of January 2012 for a station at Great Zimbabwe University in Masvingo province in Zimbabwe. The automated weather station used was the RainWise MKIII Weather Transmitter type with a The CC-3000 MK-III Computer Interface datalogger. The weather station had temperature sensors, relative humidity sensor and wind sensors. The necessary constants required to get the calculated net radiation were n, N,

n , z, Ra, Rs, Rns Rso. N

The actual vapour pressure readings, ea, were estimated for corresponding mean air temperature and relative humidity readings available, using tables in FAO irrigation paper 56. The calculated net radiation was compared against the readings of a CNR1 four component net radiometer which is a standard instrument. The CNR 1 was running concurrently with temperature sensors at the station. Temperatures were recorded at intervals of 30 min and averaged for the whole day using an automated temperature sensor and the data was stored in a datalogger. The calculated and measured temperatures were then plotted on a regression curve to determine the level of correspondents.

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Computing net radiation from temperature variables: Improvising for under-resourced weather VI.

The net radiation is the difference between the incoming net shortwave radiation (R ns) and the outgoing net longwave radiation (Rnl): Rn = Rns - Rnl ..............................................................................................2 Where: Rn = Net radiation (MJ/m2 per day); Rns = Net incoming shortwave radiation (MJ/m2 per day); Rnl = Net outgoing longwave radiation (MJ/m2 per day) ; Rn is normally calculated from the measured shortwave radiation (Rs) (FAO, 1998). To explain the calculation of Rn, it is important to first explain some concepts and define certain parameters in the process of deriving the inputs of Equation 5 for the calculation of Rs. The calculation of clear sky radiation (Rso), when n=N, is required to compute net longwave radiation. Rso is given by the following simplified

 

 

2z

expression: Rso  0.75   Ra  100000 

..............................................................................(3) Where Rso is the clear sky solar radiation (MJ/m2 per day); z is station elevation above sea level (m) Net outgoing longwave radiation (Rnl) The rate of longwave radiation emission is proportional to the absolute temperature (Kelvin) of the surface raised to the fourth power. Rnl is calculated using the following expression:

Rnl  (

 (Tmax, K ) 4   (Tmin,K ) 4 2

)  (0.34  0.14 ea )  (1.35

Rs  0.35) Rso ..............(4)

Where: Rnl is the net outgoing longwave radiation ,MJ/m2 per day; σ is the Stefan Boltzmann constant (4.903 x 10 MJ/K4 per m2 per day); Tmax,K is Maximum absolute temperature during the 24 hr period(K); Tmin,K is Minimum absolute temperature during the 24 hr period (K); ea is the actual vapour pressure (kpa); Rs/Rso is the relative shortwave radiation (limited ≤1); -9

Rs is the measured or calculated solar radiation (MJ/m2 per day) = [0.25+0.5 Rso is calculated clear sky radiation (MJ/m2 per day) = [0.75+

n ] Ra......(5) N

2z ] x Ra................(6) 100000

Ra is the extraterrestrial radiation derived from the Tables in FAO Irrigation Paper 56 for the southern hemisphere for the month of January. Net incoming shortwave radiation (Rns) The net solar or shortwave radiation, resulting from the balance between incoming and reflected solar radiation, is given by: Rns = (1 - 0.23) Rs.......................................................................................................(7) Where: Rns is the net solar or shortwave radiation (MJ/m2 per day); Rs is the incoming solar or shortwave radiation (MJ/m2 per day) Clear sky radiation (Rso) The calculation of clear sky radiation (Rso), when n = N, is required to compute net longwave radiation. Rso is given by equation 6. Where: Rso = Clear sky solar radiation (MJ/m2 per day) z = Station elevation above sea level (m) estimated using a GPS device.

VII.

Results And Discussions

The results and discussion are a summary of the findings from the study. The section highlights results from computing the net radiation, comparing it to the measured radiation to costs implications. The section also shows the accuracy of the calculating method and correction factors that can be incorporated for future works.

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Computing net radiation from temperature variables: Improvising for under-resourced weather The following are constants used in the computation of net radiation, n=11.5 hours, N=13 hours,

n =0.884615, Ra=41.9MJ/m2/day, Rs=29.00768MJ/m2/day, Rns=22.33592 MJ/m2/day, Rso= 32.24261 N MJ/m2/day Table 2: Showing calculation of net radiation, Rn from temperature readings. Day 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Tmax/ o C 306.8 299.8 303.0 300.2 304.0 299.0 292.5 299.0 304.0 302.0 297.2 298.6 300.0 303.0 300.0 299.0 300.4 300.5 297.4 294.7

Tmin/ o C 291.0 291.2 290.9 291.4 291.0 289.6 289.6 289.6 291.0 292.5 293.7 291.0 290.9 291.5 292.7 291.4 292.7 293.6 291.8 291.4

σ (T max,K)4 43.40285 39.57522 41.29213 39.78685 41.83995 39.15449 35.85917 39.15449 41.83995 40.74971 38.22012 38.94539 39.68093 41.29213 39.68093 39.15449 39.89298 39.94613 38.3231 36.95025

σ (Tmin,K)4 35.12924 35.22592 35.08098 35.32279 35.12924 34.45808 34.45808 34.45808 35.12924 35.85917 36.45126 35.12924 35.08098 35.3713 35.95735 35.32279 35.95735 36.40164 35.51714 35.32279

ea (kPa) 2.1107 1.7047 1.7629 1.7022 1.7659 1.5214 1.2666 1.5686 1.9449 1.9956 1.7787 1.7258 1.7364 1.9777 1.8904 1.7153 1.8876 1.9956 1.6258 1.5073

Rnl MJ/m2/day 4.617238 5.061216 5.065843 5.086392 5.100174 5.301007 5.521277 5.216729 4.795388 4.689553 4.92628 4.97603 5.0041 4.722221 4.802088 5.021163 4.820221 4.673569 5.132212 5.229435

Computed Rn MJ/m2/day 17.71868 17.2747 17.27008 17.24953 17.23575 17.03491 16.81464 17.11919 17.54053 17.64637 17.40964 17.35989 17.33182 17.6137 17.53383 17.31476 17.5157 17.66235 17.20371 17.10648

Measured Rn MJ/m2/day 17.70668 17.2627 17.25808 17.23453 17.22375 16.63491 16.80264 17.10719 17.55253 17.63437 17.39764 17.34789 17.31982 17.5837 17.50383 17.30276 17.5027 17.64935 17.19071 17.09448

The table shows results of calculated net radiation from maximum and minimum temperatures from a weather station at Great Zimbabwe University. The maximum recorded net radiation was on day 1 which corresponds to the day when maximum daily temperature was registered. This indicates that net radiation is highly related to temperature patterns. The average net radiation calculated for the twenty day period was 17.3478 MJ/m2/day and measured was 17.3155 MJ/m2/day.

Figure 3: Correlation curve between computed and measured net radiation value The regression curve illustrates the correspondents of the calculated to the measured net radiation. There is a 90.8% correspondents which is a high agreement between the two variables. However this implies that there is an error of ±4.1% in estimating net radiation from temperature variables.

Figure 4: Diurnal variation of maximum temperatures and measured net radiation. www.iosrjournals.org

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Computing net radiation from temperature variables: Improvising for under-resourced weather The daily variation of the measured net radiation to the maximum temperatures indicate a strong relationship as both variables peak and deep on the same days.

VIII.

Conclusion

The average net radiation measured and calculated were close which implies that the temperature variables indeed can be used to estimate net radiation. The regression curve gave the error margin of ± 4.1% which is the correction factor to be used. The average market price for the sensors of US\$3700 is high and can be avoided as proved by the calculations. The weather station can have a simple Stevenson screen with maximum and minimum temperatures, a sunshine recorder and possibly wind sensors to estimate the net radiation and relative humidity.

References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]

(http://geneq.com/en/departments/environment/product/net-radiometer-cnr Campbell products. http://s.campbellsci.com/documents/us/manuals/nr01) Central Statistics Office (CSO) (2002).“Zimbabwe Population Profile”. http://www.zimstat.co.zw/dmdocuments/Census/Census.pdf Delta T devices. www.delta-t.co.uk Ejieji, C. J. (2011). Performance of Three Emprical Reference Evaporation Models under Three Sky Conditions using two solar radiation estimation methods at Ilorin, Nigeria. Agricultural Engineering International: CICR journal. Manuscript No. 1673. 13(3). Enercorp Instruments limited. http://www.enercorp.com/ FAO. 1998a. Crop evapotranspiration: Guidelines for computing crop water requirements. By: Richard Allen, Luis Pereira, Dirk Raes and Martin Smith. FAO Irrigation and Drainage Paper 56. Rome, Italy. Makadho, J. M. (1996) “potential Effects of Climate on Corn Production in Zimbabwe”, Climate Research, Vol.6, pp.146-151. Meyer. S . (1999). Standard reference evaporation for inland, south eastern Australia. CSIRO land and Water, Adelaide LaboratorynTechnical Report 35/98. Available online at: http://turing.une.edu.au/~hschiret/Docs/tr35-98.pdf Murwendo T. & Munthali A. (2008). The value of backyard trees to people’s lives in Masvingo City, Zimbabwe J. Geogr. Res. 2(1):24-37. Simba F.M, Mubvuma M, Murwendo T, Chikodzi D (2013). Prediction of yield and biomass productions: A remedy to climate change in semi-arid regions of Zimbabwe. International Journal of Advance Agriculture Research Vol 1. pp 14-21 Skypower international . http://skypowerinternational.com/

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