Rohilla, Laxmi Na ain; Singh, Dinesh Kuma
A icle
Di ec no mal i adiance p edic ions using b oadband
models o Indian s a ions
Ene gy Repo s
P o ided in Coope a ion wi h:
Else ie
Sugges ed Ci a ion: Rohilla, Laxmi Na ain; Singh, Dinesh Kuma (2020) : Di ec no mal i adiance
p edic ions using b oadband models o Indian s a ions, Ene gy Repo s, ISSN 2352-4847, Else ie ,
Ams e dam, Vol. 6, Iss. 2, pp. 572-576,
h ps://doi.o g/10.1016/j.egy .2019.11.121
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ScienceDi ec
Ene gy Repo s 6 (2020) 572–576
www.else ie .com/loca e/egy
The 6 h In e na ional Con e ence on Powe and Ene gy Sys ems Enginee ing (CPESE 2019),
20–23 Sep embe 2019, Okinawa, Japan
Di ec no mal i adiance p edic ions using b oadband models o
Indian s a ions
Laxmi Na ain Rohilla∗, Dinesh Kuma Singh
Ne aji Subhas Uni e si y o Technology, Sec o -3, Dwa ka, New Delhi 110078, India
Recei ed 10 Oc obe 2019; accep ed 23 No embe 2019
A ailable online 14 Decembe 2019
Abs ac
In his pape h ee pa ame ic models CPCR2, MLWT2 and REST ha e been used o compu e di ec no mal i adiance
(DNI) o i e Indian s a ions, namely New Delhi, Pune, Jaipu , Kolka a and Mumbai. Compu ed alues o DNI ha e been
compa ed wi h measu ed alues in e ms o pe cen age oo mean squa e e o (RMSE) and pe cen age mean bias e o (MBE).
I is obse ed ha he a e age pe cen age RMSE o he yea is he minimum o MLWT2 model o Jaipu ollowed by New
Delhi and Pune and he alues a e 1.67%, 2.33% and 2.49%, espec i ely. Bu o coas al s a ions Kolka a and Mumbai he
co esponding minimum alues occu o CPCR2 model and REST model espec i ely, and he alues a e 2.62% and 2.76%,
espec i ely. I shows ha MLWT2 model pe o ms be e o mos o he Indian s a ions excep he coas al s a ions.
c
2019 Published by Else ie L d. This is an open access a icle unde he CC BY-NC-ND license
(h p://c ea i ecommons.o g/licenses/by-nc-nd/4.0/).
Pee - e iew unde esponsibili y o he scien i ic commi ee o he 6 h In e na ional Con e ence on Powe and Ene gy Sys ems Enginee ing (CPESE
2019).
Keywo ds: Di ec no mal i adiance; Roo mean squa e e o ; Mean bias e o
1. In oduc ion
Se e al au ho s including [1] has explained in hei wo k ha he sola ene gy sys ems a e mo e ene gy e icien
unde cloudless condi ions. Unde such condi ions, mos o he sola adia ion is in he o m o di ec adia ion.
Many de ices, like sola concen a o s, use only he di ec componen o he sola adia ion.
Ne wo k o di ec i adiance measu ing s a ions is a he sca ce h oughou he wo ld and he same is ue o
India as well. One way o knowing di ec adia ion a no mal incidence, also called di ec no mal i adiance (DNI), is
o measu e global and di use adia ion on ho izon al and hen con e hese alues in o DNI, by using zeni h angle.
Ano he way is o use a py heliome e and measu e DNI di ec ly. In India, DNI is measu ed by using py heliome e
only a ou synop ic hou s: 9:30, 11:30, 13:30 and 15:30, and his oo a ew s a ions only. The e is oo much
pauci y o DNI da a in India and his necessi a es he de elopmen o heo e ical models o p edic DNI unde
di e en a mosphe ic condi ions. In he p esen wo k as explained in he ea lie wo k by Na ain [1], i has been
∗Co esponding au ho .
E-mail add ess: [email p o ec ed] (L.N. Rohilla).
h ps://doi.o g/10.1016/j.egy .2019.11.121
2352-4847/ c
2019 Published by Else ie L d. This is an open access a icle unde he CC BY-NC-ND license (h p://c ea i ecommons.o g/
licenses/by-nc-nd/4.0/).
Pee - e iew unde esponsibili y o he scien i ic commi ee o he 6 h In e na ional Con e ence on Powe and Ene gy Sys ems Enginee ing
(CPESE 2019).
L.N. Rohilla and D.K. Singh / Ene gy Repo s 6 (2020) 572–576 573
assumed ha he e is no cloud co e and p edic ions a e made unde di e en amoun o wa e apo , ozone con en
and humidi y e c.
Many au ho s ha e wo ked along hese lines. Sola adia ion models o p edic ing he a e age daily and hou ly
global adia ion, beam adia ion and di use adia ion ha e been e iewed by Powe [2]. Pa ame e iza ion Model
C has been discussed by Iqbal [3]. King and Buckius [4] ha e explained di ec sola ansmi ance o a clea
sky, ha accu a ely p edic s he a ia ion wi h undamen al quan i ies. Di ec i adiance model, has been explained
by Bi d and Huls om [5]. The pa ame e ized model o global adia ion unde pa ially cloudy skies has been
explained by Choudha y [6]. As explained by Ko i e al. [7] ha he di ec sola i adiance can also be accu a ely
calcula ed om global and di use ho izon al i adiance measu emen s a e co ec ing he di use i adiance alues.
In he s udy o Munee e al. [8], Me eo ological Radia ion Model (MRM) enables compu a ion o ho izon al
beam and di use sola adia ion using basic me eo ological pa ame e s — hou ly d y and we bulb empe a u e,
a mosphe ic p essu e and b igh sunshine du a ion. Eigh een clea sky b oadband models o es ima ing he DNI
in Alge ia ha e been in es iga ed by Benkaciali e al. [9]. Sola adia ion and illuminance was es ima ed om
he me eo ological pa ame e s by Munee e al. [10]. Powe [2] employed he mon hly-a e aged clima e u bidi y
da a o No h Ame ica and Eu ope o e alua e he ela ionships among mon hly-a e aged obse ed beam adia ion,
clea -sky beam i adiance, sunshine du a ion and, day-leng h. A hyb id model was designed by Yang e al. [11]
o es ima ing mon hly mean daily global adia ion by employing hou ly- eco ded b igh sunshine ime in Japan.
Gueyma d [12,13,14] has explained abou he p edic ion o di ec sola ansmi ance and i adiance by using
a ious b oadband models and concluded ha ou models, i.e. mul i-laye -weigh ed ansmi ance model, e sion
2 (MLWT2), Yang’s model, CPCR2 and e e ence e alua ion o sola ansmi ance (REST) a e showing good
ag eemen wi h measu ed alues.
In he p esen s udy, h ee models, CPCR2, MLWT2 and REST as p oposed by Gueyma d [12,13,14] ha e been
selec ed o compu e DNI a di e en hou s and di e en mon hs o he yea , o Indian opical condi ions.
2. Models desc ip ion
2.1. CPCR2 model
This is he wo bands model. The limi s o he model ha e been chosen as 0.29 µm and 2.7µm. These alues
app oxima ely co espond o he a e age sensi i i y limi s o wo widely used py anome e s, he Eppley PSP (0.285–
2.8µm) and he Kipp & Zonen CM6 (0.3–2.5µm). The cu o wa eleng h be ween he UV/ isible band, B1, and
he in a ed (IR) band, B2, has been se o 0.7µm. This model has been ound o be he bes model in ea lie
s udies made by Gueyma d [15] and Ba le e al. [16]. I is comple ely desc ibed by Gueyma d [17]. E en hough
his model depends on Angs om’s wa e exponen α, i has been ixed he e a 1.3.
2.2. MLWT2 model
This model is modi ied e sion o MLWT1, which was o iginally de eloped as bo h a adia ion and u bidi y
p edic ion me hod by Gueyma d [12,13,18]. MLWT2 model was based on he ela i ely new concep o mul ilaye
spec al weigh ing, which is gi en by Gueyma d [19] and Molineaux and Ineichen [20]. This me hod a oids he
limi a ions o he Bee –Bougue –Lambe law when applied o la ge spec al o b oad bands. I equi es in ica e
pa ame e iza ions because he ansmi ance o an a mosphe ic laye depends on he spec al cha ac e is ics o all he
laye s. This echnique gua an ees be e o e all accu acy. I also akes in o accoun he a iable e ec o ci cumsola
adia ion, which inc eases wi h u bidi y and ai mass. In he cu en wo k, all he basic unc ional o m is simila
o he o iginal MLWT2 model as explained by Gueyma d [12,13], excep ha he o al NO2abso p ion is no aken
in o accoun . The equa ion o MLWT2 model is: Ebn =EonTRgToTWTa. He e Ebn, is di ec no mal i adiance; Eon,
he ex a- e es ial i adiance (i.e. he sola cons an imes he sun–ea h dis ance co ec ion ac o ); TRg, is he
Rayleigh and uni o mly mixed gas ansmi ance; To, he ozone ansmi ance; TW, he wa e apo ansmi ance
and Ta, he ae osol ansmi ance.
574 L.N. Rohilla and D.K. Singh / Ene gy Repo s 6 (2020) 572–576
2.3. REST model
This model has been p oposed by Gueyma d [12,13,14] and i s o m is as ollows: Ebn =EonTRTgToTWTa.
He e Ebn , is di ec no mal i adiance; Eon , he ex a- e es ial i adiance (i.e. he sola cons an imes he sun–ea h
dis ance co ec ion ac o ); TR, is he Rayleigh ansmi ance; Tg, he uni o mly mixed gas ansmi ance; To, he
ozone ansmi ance; TW, he wa e apo ansmi ance and Ta, he ae osol ansmi ance.
3. Me eo ological da a
Fi e s a ions o di e en clima ic condi ions ha e been chosen. The s a ions chosen a e — New Delhi ep esen ing
composi e clima e; Kolka a, being highly indus ialized, ep esen s highly pollu ed, wa m and humid a mosphe e;
Jaipu , being a dese s a ion, ep esen s ho and d y clima e; Mumbai, being coas al ci y, ep esen wa m and
humid clima e; Pune ep esen s mode a e clima e. The sola adia ion da a, comp ising o mon hly mean hou ly
global and di use sola adia ion o hese Indian s a ions, ha e been collec ed om India Me eo ology Depa men
(IMD) Pune, India. Mon hly mean alues a e aged o e he yea o all he i e s a ions, a e shown in Table 1.
Table 1. Geog aphical and clima ic da a o i e Indian s a ions used in his s udy.
Jan Feb Ma Ap May Jun Jul Aug Sep Oc No Dec
Kolka a (2002) Ta20 22 26 29 30 30 29 29 28 27 23 21
[22.65◦N, 88.45◦ERH76 75 73 74 77 80 81 82 80 77 75 74
6 masl] O30.24 0.26 0.26 0.27 0.28 0.27 0.26 0.26 0.26 0.25 0.25 0.25
Igh 11.71 16.34 17.42 19.33 18.81 15.65 14.48 15.02 14.99 15.31 13.49 11.83
Jaipu (1999) Ta16 21 24 30 36 33 30 29 28 28 23 18
[26.93◦N, 75.86◦E RH48 45 26 22 37 41 70 70 52 28 38 43
431 masl] O30.26 0.27 0.28 0.29 0.29 0.29 0.28 0.27 0.26 0.25 0.25 0.26
Igh 15.22 17.26 23.48 26.56 26.20 24.94 18.77 19.94 19.36 17.33 16.02 13.89
Mumbai (2001) Ta21 23 24 26 29 28 27 26 26 25 25 23
[19.12◦N, 72.85◦E RH67 68 72 75 78 81 87 87 86 82 75 71
14 masl] O30.24 0.26 0.26 0.27 0.28 0.27 0.26 0.26 0.26 0.25 0.25 0.25
Igh 17.17 20.71 23.71 24.61 25.02 16.16 14.13 14.32 16.05 15.06 16.17 15.23
New Delhi (1999) Ta15 16 21 27 31 35 34 32 29 26 21 17
[28.63◦N, 77.20◦E RH53 53 54 40 38 56 65 72 54 44 44 54
216 masl] O30.26 0.27 0.28 0.29 0.29 0.30 0.28 0.27 0.27 0.26 0.25 0.26
Igh 10.23 15.05 20.98 23.45 22.71 21.25 18.04 18.88 16.36 14.35 14.49 11.67
Pune (2002) Ta15 16 17 20 22 22 21 20 22 22 19 14
[18.53◦N, 73.85◦E RH48 45 26 22 37 41 70 70 52 28 38 43
559 masl] O30.26 0.27 0.28 0.29 0.29 0.29 0.28 0.27 0.26 0.25 0.25 0.26
Igh 18.72 19.94 23.54 25.92 24.10 16.62 20.37 13.00 20.20 18.81 18.04 16.33
Ta: Mon hly mean daily empe a u e (◦C); RH: Mon hly mean daily ela i e humidi y (%); O3: Ozone amoun (cm).
Igh : Mon hly mean daily global adia ion (MJ/m2day); masl: me e abo e sea le el.
Global and Di use adia ion a e measu ed by using he moelec ic py anome e s. These py anome e s a e
calib a ed once a yea wi h e e ence o he Wo ld Radiome ic Re e ence (WRR). The es ima ed unce ain y in
he measu ed da a is abou ±5%. The alues o Angs om u bidi y ac o , β, o hese loca ions we e compu ed by
Louche e al. [21], by aking Angs om’s wa e exponen αas 1.3. Es ima ion o a mosphe ic u bidi y o Indian
loca ions ha e been s udied by Na ain and Ga g [22] and Ahe and Agashe [23].
The o he me eo ological da a includes mon hly mean hou ly alues o a mosphe ic p essu e, empe a u e and
ela i e humidi y. This da a is used o compu e he amoun o p ecipi able wa e in he a mosphe e, by using an
equa ion gi en by Leckne [24]. Da a o ozone con en s o he s udied s a ions ha e been aken om [3]. One-yea
da a o each o he i e Indian s a ions was used in his s udy and he yea o each s a ion is shown in Table 1.
4. Resul s and discussions
A compu e p og am was w i en o compu e hou ly alue o DNI by using h ee di e en models; CPCR2,
REST and MLWT2 model, o each o he 5 Indian s a ions men ioned ea lie . The model-compu ed alues ha e
L.N. Rohilla and D.K. Singh / Ene gy Repo s 6 (2020) 572–576 575
been compa ed wi h he measu ed alues in e ms o pe cen age oo mean squa e e o , RMSE (%) and pe cen age
mean bias e o , MBE (%), and he esul s a e shown in Table 2. The compu a ions we e no pe o med o he
monsoon mon hs, June o Sep embe , as du ing hese mon hs i is cloudy.
Table 2. RMSE (%) and MBE (%) o compu ed DNI wi h h ee models, in compa ison o measu ed DNI, o
New Delhi (1999), Pune (2002), Jaipu (1999), Kolka a (2002) and Mumbai (2001).
Loca ion Mon h RMSE (%) MBE (%)
REST MLWT2 CPCR2 REST MLWT2 CPCR2
New Delhi Jan 5.76 3.86 3.15 −4.51 −3.26 −2.74
Feb 3.07 1.06 2.06 −2.33 −0.51 −2.00
Ma 2.38 1.00 2.73 −1.86 −0.63 −2.72
Ap 1.46 0.74 2.66 −0.99 −0.50 −2.65
May 0.92 1.59 2.99 −0.28 −1.39 −2.96
Oc 3.63 5.74 4.40 −3.00 −5.55 −4.38
No 5.19 2.33 3.19 −4.52 −2.12 −3.16
Dec 6.63 2.37 2.45 −5.60 −2.09 −2.25
A e age 3.63 2.33 2.95 −2.89 −2.01 −2.86
Pune Jan 3.32 1.90 4.09 −2.82 −1.68 −4.08
Feb 2.53 1.51 3.97 −2.13 −1.22 −3.95
Ma 1.87 1.27 3.71 −1.34 −0.88 −3.68
Ap 1.65 1.52 3.75 −1.10 −1.12 −3.73
May 2.18 3.76 5.39 −1.99 −3.64 −5.39
Oc 3.19 4.32 5.57 −2.95 −4.21 −5.55
No 3.73 2.98 4.71 −3.35 −2.83 −4.71
Dec 3.99 2.67 4.55 −3.62 −2.53 −4.54
A e age 2.81 2.49 4.47 −2.41 −2.26 −4.45
Jaipu Jan 5.72 1.89 3.70 −4.80 −1.61 −3.70
Feb 3.57 1.19 3.38 −2.93 −0.85 −3.35
Ma 2.08 0.92 2.85 −1.33 −0.05 −2.81
Ap 1.47 0.78 2.83 −0.82 −0.04 −2.80
May 1.30 1.04 3.41 −0.89 −0.77 −3.40
Oc 3.45 3.05 4.44 −3.04 −2.89 −4.41
No 4.96 2.35 4.00 −4.20 −2.01 −3.97
Dec 6.65 2.17 3.83 −5.61 −1.88 −3.78
A e age 3.65 1.67 3.55 −2.95 −1.26 −3.53
Kolka a Jan 3.46 3.13 1.43 −1.80 −2.19 −1.19
Feb 2.40 1.69 1.64 −1.43 −1.25 −1.61
Ma 1.58 2.97 2.04 −0.04 −2.46 −2.01
Ap 1.94 5.49 3.55 −0.18 −4.99 −3.43
May 2.18 7.95 5.12 −0.73 −7.48 −5.06
Oc 2.73 7.32 3.73 −1.87 −7.16 −3.72
No 3.44 3.38 2.18 −2.61 −3.12 −2.11
Dec 3.85 2.46 1.25 −2.74 −2.04 −1.17
A e age 2.70 4.30 2.62 −1.43 −3.84 −2.54
Mumbai Jan 3.25 1.83 2.20 −2.57 −1.45 −2.19
Feb 2.82 1.67 2.44 −2.18 −1.23 −2.39
Ma 2.18 2.04 2.63 −1.77 −1.82 −2.60
Ap 1.72 2.86 2.84 −1.37 −2.75 −2.82
May 1.59 3.56 2.99 −1.26 −3.45 −2.98
Oc 2.21 6.50 3.87 −1.54 −6.41 −3.82
No 3.19 2.81 2.57 −2.73 −2.59 −2.55
Dec 5.12 3.50 3.15 −3.70 −2.68 −2.75
A e age 2.76 3.09 2.84 −2.14 −2.80 −2.76
Table 2 shows ha he minimum RMSE is 0.74% o MLWT2 model, in he mon h o Ap il, and o New Delhi
s a ion. Simila ly, able shows ha minimum MBE is –0.04% o MLWT2 model, in he mon h Ap il, o Jaipu .

576 L.N. Rohilla and D.K. Singh / Ene gy Repo s 6 (2020) 572–576
The nega i e sign shows ha he compu ed alue is unde es ima ed and he quan i y shows ha DNI compu ed by
MLWT2 model in his mon h o he men ioned s a ion is much close o measu ed alue.
The a e age o pe cen age RMSE, o he whole yea , a e he minimum o MLWT2 model and o s a ions
Jaipu , ollowed by New Delhi and Pune and he minimum alues a e 1.67, 2.33 and 2.49, espec i ely. While o
Kolka a he co esponding minimum alue is in CPCR2 model and he alue is 2.62 and o Mumbai he same is
in REST model ha is 2.76. This beha io is because o he Angs om’s u bidi y ac o being highe du ing some
o he mon hs o hese wo s a ions. He e i is obse ed ha he pe cen age RMSE is lesse in mos o he mon hs
o mos o he s a ions in MLWT2 model. This shows he sui abili y o MLWT2 model o mos o he Indian
s a ions.
5. Conclusions
The pe o mances o h ee models CPCR2, MLWT2 and REST ha e been s udied a i e Indian s a ions iz. New
Delhi, Kolka a, Mumbai, Pune and Jaipu . The beam adia ion a no mal incidence was compu ed. The compu ed
DNI was compa ed wi h measu ed DNI. Fo mos o he Indian s a ions, RMSE pe cen age, a e aged o e a yea , is
he minimum o MLWT2 model as compa ed o, CPCR2 and REST models. This s udy e eals he bes pe o mance
o MLWT2 model in Indian condi ions.
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