Most weather stations at farms, schools and other research institutes in the developing world do not have radiation sensors and this is usually attributed to high costs of these sensors. Net radiation as one component of radiation is important in crop farming as it influences germination, different growth stages, water demand, size and quality of yield among other things. This article seeks to demonstrate how a series of mathematical equations with temperature as a key physical quantity can be used to estimate net radiation using the basic minimum of resources affordable against readings from a standard net radiometer. To achieve this, daily data of maximum and minimum temperatures for 20 days was used from an automated weather station at Great Zimbabwe University in Zimbabwe. A standard CNR 1 net radiometer was installed at the station to give direct net radiation readings for comparison with the computed readings. A correlation between the calculated net radiation and the measured one gave 90.8% correspondents. Diurnal net radiation was following the maximum temperature trends. The average cost of a net radiometer sensor was US$ 3.700 which can be too high for an ordinary farmer or other small research institutes.

1. IOSR Journal of Applied Physics (IOSR-JAP)
e-ISSN: 2278-4861.Volume 5, Issue 5 (Jan. 2014), PP 01-06
www.iosrjournals.org
www.iosrjournals.org 1 | Page
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
Abstract: Most weather stations at farms, schools and other research institutes in the developing world do not
have radiation sensors and this is usually attributed to high costs of these sensors. Net radiation as one
component of radiation is important in crop farming as it influences germination, different growth stages, water
demand, size and quality of yield among other things. This article seeks to demonstrate how a series of
mathematical equations with temperature as a key physical quantity can be used to estimate net radiation using
the basic minimum of resources affordable against readings from a standard net radiometer. To achieve this,
daily data of maximum and minimum temperatures for 20 days was used from an automated weather station at
Great Zimbabwe University in Zimbabwe. A standard CNR 1 net radiometer was installed at the station to give
direct net radiation readings for comparison with the computed readings. A correlation between the calculated
net radiation and the measured one gave 90.8% correspondents. Diurnal net radiation was following the
maximum temperature trends. The average cost of a net radiometer sensor was US$ 3.700 which can be too
high for an ordinary farmer or other small research institutes.
Key words: net radiation, developing, cost, crop, temperature, Zimbabwe
I. Introduction
Weather stations in developing countries have been characterised by lack of maintenance of the
available equipment, they are ill equipped and generally less dense in an area. The reasons for the
aforementioned being primarily lack of funds to purchase the necessary equipment. The available stations
contribute to the knowledge of the climate of an area but the accuracy of the measured variables is
compromised. Measurement of radiation is important at stations as it provides useful data to experts in solar
energy industry, in crop farming, water management, and other sectors of the economy (Meyer, 1999). Air
temperature in the studies of meteorology is understood to be a direct response variable to the incoming solar
radiation. It is on this basis that temperature is used to estimate a radiation component as illustrated in the FAO
irrigation paper 56 (FAO,1998). The sun is the source of solar radiation and the radiation travels as
electromagnetic waves through the space to the atmosphere where it goes through various processes. Part of the
radiation is scattered and absorbed by the aerosol and water vapour in the atmosphere and some is incident on
the earth surface undisturbed and absorbed and reflected by the ground (Meyer, 1999). Net radiation then
constitutes the difference between the total downward radiation (longwave and shortwave) and total upward
radiation (longwave and shortwave). Net radiation is important particularly in crop farming as it is responsible
for germination of seeds, driving photosynthesis, determining the growing degree days of a crop, dictates soil
moisture content and soil temperatures (Simba et. al, 2013). It is therefore imperative to measure this component
of radiation as it informs the farmer on many aspects that will determine the quality and quantity of yield they
will realise. The research was carried out in Masvingo province, which is in the lowveld region of Zimbabwe
where average summer maximum temperatures are 28o
C, usually a season when crop farming is done
(Murwendo and Munthali, 2008). The main applications of net radiometers are in agrometeorology, for the
study of evapotranspiration and crop damage prevention; and in climatology, meteorology and hydrology for
measurement of the radiation balance (Ejieji, 2011). Net radiometers are used in monitoring over glaciers and
ice fields and this is of particular interest to global warming studies and in renewable energy the heat exchange
in thermal solar systems can be monitored. There are various types of net radiometers in the market and these
include: CNR 1 four component net radiometer, which is used in this study as the standard, Radiation Energy
Balance Systems (REBS) net radiometer and NR-Lite net radiometers. The article seeks to demonstrate how net
radiation can be calculated from temperature variables as an improvising strategy in an area where there are no
radiation sensors. The study will explore the accuracy, reliability and possible limitations of the method.

2. Computing net radiation from temperature variables: Improvising for under-resourced weather
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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 km² 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
A lot of weather stations at farms, schools and other research institutes in the developing world do not
have radiation sensors and this is usually attributed to high costs of these sensors. Net radiation as one
component of radiation is important in crop farming as it influences germination, different growth stages, water
demand, size and quality of yield among other things. It is against this background that alternative and
affordable ways of measuring this component of radiation can be employed to provide data.
Objective
This article seeks to demonstrate how a series of mathematical equations with temperature as a key
physical quantity can be used to estimate net radiation using the basic minimum of resources affordable.
Radiation and sensors
Part of the extraterrestrial radiation (Ra) is scattered, reflected or absorbed in the process of entering
the atmosphere. The amount of radiation that reaches the earth’s surface is called solar radiation (Rs). It depends
on Ra and the transmission through the atmosphere, which is largely dependent on cloud cover. Rs can be
measured in weather stations with pyranometers, radiometers or solarimeters. In some stations values of solar
radiation are part of the climatological data available. If it is not measured it can be calculated through the use of
an equation which relates solar radiation to extraterrestrial radiation and relative sunshine duration:
Rs = [0.25 + 0.5
N
n
] Ra..............................................................1
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
n
= Relative sunshine duration; Ra =
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
n
ratio can also be obtained from data on
cloud cover, if data on sunshine hours are not available.

3. Computing net radiation from temperature variables: Improvising for under-resourced weather
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IV. Construction of a CNR1 four component net radiometer
Figure 2: The CNR1 Four-Component Net Radiation Sensor (source:
http://s.campbellsci.com/documents/us/manuals/nr01)
(1) SWin solar radiation sensor or pyranometer,
(2) LWin Far Infrared radiation sensor or pyrgeometer
(3) radiation shield
(4) leveling assembly for x- and y axis, block plus bolts for x-axis adjustment
(5) leveling assembly for x- and y axis, horizontal rod
(6) connection body containing the Pt100 temperature sensor, heater, and hole for user-supplied temperature
sensor (add cable gland M8)
(7) LWout Far Infrared radiation sensor or pyrgeometer
(8) leveling assembly for x- and y-axis, bolts for y-axis adjustment
(9) SWout solar radiation sensor or pyranometer
A level is located under the radiation screens.
A CNR 1 net radiometer combines two thermopile pyranometers for solar radiation measurement
incoming/reflected/albedo/balance) with two thermopile pyrgeometers for far infrared measurement
(balance/ground surface temperature/sky temperature). There are four separate signal outputs and the integrated
temperature sensor can be used to calculate the downward far infrared radiation. Via a data logger the
temperature signal can be used to control the built-in heating element to minimise dew and frost deposition.
(http://geneq.com/en/departments/environment/product/net-radiometer-cnr
Market prices of Net radiometers
Table 1: Showing market prices of some net radiometers and their accessories
Type of a net radiometer Market price Supplier
Radiation Energy Balance (REBS) $ 2.000 Delta-T Devices (UK)
CNR1 four component $ 5.000 Delta-T Devices(UK)
Albedometer CM 7B $5.663 Sky power international (Germany)
Net radiometer NR-LITE $2.483 Enercorp instruments Ltd (Canada)
Radiation balance transmitter $3.363 Enercorp instruments Ltd (Canada)
V. 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
n
, z, Ra, Rs, Rns Rso.
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.

4. Computing net radiation from temperature variables: Improvising for under-resourced weather
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VI. Net radiation (Rn) estimation
The net radiation is the difference between the incoming net shortwave radiation (Rns) 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
expression: aso R
z
R 




100000
2
75.0
..............................................................................(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:
)35.035.1()14.034.0()
2
)()(
(
4
min,
4
max,



so
s
a
KK
nl
R
R
e
TT
R

..............(4)
Where:
Rnl is the net outgoing longwave radiation ,MJ/m2
per day; σ is the Stefan Boltzmann constant (4.903
x 10-9
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);
Rs is the measured or calculated solar radiation (MJ/m2
per day) = [0.25+0.5
N
n
] Ra......(5)
Rso is calculated clear sky radiation (MJ/m2
per day) = [0.75+
100000
2z
] x Ra................(6)
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.

5. Computing net radiation from temperature variables: Improvising for under-resourced weather
www.iosrjournals.org 5 | Page
The following are constants used in the computation of net radiation, n=11.5 hours, N=13 hours,
N
n
=0.884615, Ra=41.9MJ/m2
/day, Rs=29.00768MJ/m2
/day, Rns=22.33592 MJ/m2
/day, Rso= 32.24261
MJ/m2
/day
Table 2: Showing calculation of net radiation, Rn from temperature readings.
Day Tmax/
o
C
Tmin/
o
C
σ
(T max,K)4
σ
(Tmin,K)4
ea
(kPa)
Rnl
MJ/m2
/day
Computed Rn
MJ/m2
/day
Measured Rn
MJ/m2
/day
1 306.8 291.0 43.40285 35.12924 2.1107 4.617238 17.71868 17.70668
2 299.8 291.2 39.57522 35.22592 1.7047 5.061216 17.2747 17.2627
3 303.0 290.9 41.29213 35.08098 1.7629 5.065843 17.27008 17.25808
4 300.2 291.4 39.78685 35.32279 1.7022 5.086392 17.24953 17.23453
5 304.0 291.0 41.83995 35.12924 1.7659 5.100174 17.23575 17.22375
6 299.0 289.6 39.15449 34.45808 1.5214 5.301007 17.03491 16.63491
7 292.5 289.6 35.85917 34.45808 1.2666 5.521277 16.81464 16.80264
8 299.0 289.6 39.15449 34.45808 1.5686 5.216729 17.11919 17.10719
9 304.0 291.0 41.83995 35.12924 1.9449 4.795388 17.54053 17.55253
10 302.0 292.5 40.74971 35.85917 1.9956 4.689553 17.64637 17.63437
11 297.2 293.7 38.22012 36.45126 1.7787 4.92628 17.40964 17.39764
12 298.6 291.0 38.94539 35.12924 1.7258 4.97603 17.35989 17.34789
13 300.0 290.9 39.68093 35.08098 1.7364 5.0041 17.33182 17.31982
14 303.0 291.5 41.29213 35.3713 1.9777 4.722221 17.6137 17.5837
15 300.0 292.7 39.68093 35.95735 1.8904 4.802088 17.53383 17.50383
16 299.0 291.4 39.15449 35.32279 1.7153 5.021163 17.31476 17.30276
17 300.4 292.7 39.89298 35.95735 1.8876 4.820221 17.5157 17.5027
18 300.5 293.6 39.94613 36.40164 1.9956 4.673569 17.66235 17.64935
19 297.4 291.8 38.3231 35.51714 1.6258 5.132212 17.20371 17.19071
20 294.7 291.4 36.95025 35.32279 1.5073 5.229435 17.10648 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.

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