698 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 19

A New Shadow-Ring Device for Measuring Diffuse Solar Radiation at the Surface

AMAURI P. DE OLIVEIRA AND ANTONIO J. MACHADO

Group of Micrometeorology, Department of Atmospheric Sciences. Institute of Astronomy. Geophysics and Atmospheric Sciences.University of São Paulo, Sao Paulo, Brazil

JOÃO E ESCOBEDO

Laboratory of Solar Radiation. Department of Environmelltal Sciences. State Universit)' of São Paulo. Botucatu. Brazil

(Manuscript received 21 May 2001, in final form 4 September 2001)

ABSTRACT

A new shadow-ring device for measuring diffuse solar radiation at the surface is presented. In this device theseasonal variation of shadow is followed by moving the detector horizontally. This unique characteristic facilitatesits application for long anâ continuous periods of time. The blocking effect caused by the ring and other relatedgeometric properties are formulated considering the diffuse solar radiation isotropic. The correction factor, shadowsize, and ring-detector distance are derived as a function of radius and width of the ring, sun position, and locallatitude. The largest blocking uccurs during summer, when the ring-detector distance and the shadow width arethe smallest, and it is compensated by a smaller blocking effect in the winter period. The performance of thenew device is verified comparing daily values of diffuse solar radiation measured simultaneously with a similardevice from Kipp & Zcnen, Inc. The results show a very good agreement (within 2.5%) between both devices.The new device was also able to reproduce the radiometric properties of the local atmosphere based on 3-yr-long measurements of direct solar radiation using a pyrheliometer. The new device can be applied to estimatedaily values of diffuse solar radiation at the surface in the range of 30oN-30oS with results comparable to othersimilar apparatuses.

1. Introduction

The diffuse component of the solar radiation over ahorizontal surface can be estimated by blocking the di-rect component of solar radiation. The most commondevice used to block the direct component is the shadowring. It is composed of a ring, or band, arranged to casta shadow over the detector, which in tum collects onlythe diffuse component of solar radiation (Robinson andStoch 1964; Drummond 1964; LeBaron et aI. 1980;Steven and Unsworth 1980; Stanhill 1985; Sirén 1987;Michalsky et aI. 1987; Battles et aI. 1995).

The major advantage of the shadow-ring is that it issimple to operate and provides a direct estimate of thesolar radiation diffuse component. The major disadvan-tage is the systematic underestimation of the diffusesolar radiation due to blocking effect caused by the ring(Steven and Unsworth 1980; LeRaron et aI. 1990). Thiseffect is difficult to take into consideration because itdepends not only on the geometrical characteristic ofthe device, but also on the hemispherical distribution of

Correspollding author address: Dr. Amauri P. Oliveira. Group ofMicrometeorology, Department of Atmospheric Sciences, Institute ofAstronomy, Geophysics and Atmospheric Sciences, University of SãoPaulo, Rua do Matão 1226, São Paulo 05508900, Brazil.E-mail: apdolive@usp.br

@ 2002 American Meteorological Society

solar radiation (Steven 1984; Burek et aI. 1988). Thecombination of these two factors makes the measure-ments of diffuse solar radiation an observational chal-lenge.

Correction of diffuse solar radiation measured underthe shadow (E~F)is estimated considering the ratio ofblocked part (Eb) to actual value of diffuse solar radi-ation (EDF),according to the following relation:

(I)

Expression (1) is known as correction factor (Fc) andit can be estimated analytically considering the diffusesolar radiation isotropic.

Since the field of diffuse solar radiation is seIdomisotropic, the use of shadow-ring devices call for a moregeneral and suitable way of taking into considerationthe effect caused by the anisotropy on the measurementscarried out with this kind of device. For instance, hor-izontal variation of surface albedo and uneven distri-bution of c10uds are the more important sources of an-isotropy (Battles et aI. 1995). The inc1usion of othereffects, such as anisotropy and multiple reflections fromelements of the ring, in the correction factor can onlybe done numerically and, most of the time, is heavily

MAy 2002 OLIVEIRA ET AL. 699

FIG. I. View of the shadow-ring devices used in Botucatu, Brazil. The device in the foreground is an MDD; behindthat is a KZD. The detector in the MDD is displaced manual1y in the north-south direction.

dependent on empirical expressions (LeBaron et aI.1980; Steven 1984; Rawlins and Readings 1986;LeBaron et aI. 1990; Battles et aI. 1995).

Despite all these difficulties, devices using shadowrings are easier to operate than others that require specialsetups to track the sun position, such as pyrheliometersor even shadow disks. Even though they are more so-phisticated, tracking devices provide better estimates ofdiffuse solar radiation only under c1ear sky conditions.Under totally c10udyconditions the shadow-ring devicesoffer comparable results (Ineichen et aI. 1983). Besides,the shadow-ring devices require minimal adjustment tocompensate the annual evolution of shadow size andposition; therefore, they can be operated continuouslyfor a long period of time, as required for c1imatestudies.Moreover, because of their simplicity, the shadow-ringdevices cost much less than other more sophisticateddevices.

Most diffuse solar radiation measurements availableworldwide are based on shadow-ring devices proposedby Robinson (Robinson and Stoch 1964) or Drummond(Drummond 1964). The device proposed by Robinsonis composed of a set of rings covering different celestialsphere sectors. In Drummond's device, one single ringis displaced along the earth's axis direction to compen-sate the annual variation of the solar dec1ination. In bothcases the detectors are kept fixed.

Recently, a new shadow-ring device, named the mov-able detector device (MDD), has been developed in theLaboratory of Solar Radiation at the State Universityof São Paulo in Botucatu, Brazil (UNESP) (MeIo 1993;

Escobedo et aI. 1997). In this new device the ring isfixed and the annual variation of shadow position isfollowed by displacing the detector horizontally (Fig.1). The ring is sloped northward with an angle equal tothe local latitude, and the detector is displaced manually,in a horizontal plane, by a screw mechanism that allowsit to be centralized under the shadow cast by the ring.This unique characteristic makes the MDD simpler tooperate than other similar devices.

Although the MDD has been in continuous operationin Brazil since 1994, in two experimental sites locatedin a rural area of Botucatu (22°51' S) and in an urbanarea of São Paulo (23°32'S), its properties have not beenfully addressed in the literature (Escobedo et aI. 1997;Oliveira et aI. 2002).

Therefore, the main goal of this paper is to describethe MDD and verify its performance. A detailed deri-vation of the expressions used to correct the blockingeffect and other MDD relevant properties are presentedin section 2. The seasonal evolution for correction factor,ring-detector distance, and shadow size are presented insection 3 by comparing the behavior of the MDD withsimilar devices proposed by Drummond and Robinson.The effects of latitude upon these parameters are dis-cussed in section 4, showing how the MDD behaves ina site located in the Southern Hemisphere. Two perfor-mance tests for the MDD are described in section 5. Inthe first one, 192 daily values of diffuse solar radiationmeasured with the MDD are compared with equivalentmeasurements using a Kipp & Zonen, Inc., device asreference. The second test compares the MDD capacity

700

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JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 19

celestial sphere. Their shadows must also be wideenough to cover the detector for at least one day.

Assuming that the diffuse component of the solarradiation field is isotropic, the total diffuse irradianceincoming from the atmosphere and intercepted by thesurface can be written as EDF= 7TI,whereI is thediffusecomponent of the solar radiance and 7Tis 3.14.

Under these conditions, the amount of energy per unitof area and time, associated to the diffuse component of

Shadow(w) solar radiation blocked by a ring of width b, is given by

Eb = f I cos(z) dO., (2)

Suu

S

Suu trajectory

FIG. 2. Coordinates of the sun trajectory during a typical winterday for a shadow-ring device located in the Northern Hemisphere.The ring projection over the celestial sphere is indicated by b'. Theshadow of the ring at the solar meridian is indicated by w. Detectorposition is indicated by P. The other variables are solar declination(S), local latitude (eP), solar hour angle (w), solar zenithal angle (z),radius of the celestial sphere (r), and the radius of the circle formedby the sun trajectory (R).

to match the radiometric properties of the atmospherebased on three years of observations of global and directcomponents of solar radiation at the surface.

2. Shadow-ring device

The common feature of ali shadow-ring devices is thetrajectory described by the Sun's direct beam on thecelestial sphere during daytime. The trajectory corre-sponds to a small circ1e with radius R over a sphere ofradius r centered in the point P (Fig. 2). To cast a shadowin point P ali shadow rings will have to contain thetrajectory described by the sun's direct beam on the

where z is the solar zênithal angle and dO. is the elementof solid angle for the ring, given by

dO. = dS/r2, (3)

where EDFis the element of area of the ring.Considering the geometric proprieties of the celestial

sphere (Table I), the area ring element can be written as

dS = br cos(8)dw, (4)

where w is the solar hour angle and 8 is the solar dec-lination.

a. Movable detector device

In the MDD, the ring is fixed and the detector isdisplaced horizontally in the north-south direction (seethe plane of displacement in Fig. 3a). In this device thering is sloped northward at an angle equal to the locallatitude. The detector is moved in the plane of displace-ment by a screw mechanism that allows it to be cen-tralized under the shadow of the ring. This displacement

TABLE 1. Summary of parameters for the MDD, and the Drummond and Robinson devices. The parameters in the first column are ring-detector distance (r), ring width projection on the celestial sphere (b'), ring area element (dS), element of ring solid angle (dO), energy fluxof diffuse component of solar radiation blocked by the ring (E.), fraction of diffuse solar radiation blocked by the ring (E.fEoF), and shadowsize (w).

MDD (Fig. 3a) Drummond (Fig. 3b) Robinson (Fig. 3c)

R [COS(eP)COS(S)]

Rr - R

cos(S) cos(eP+ S) cos(S)

b' b cos(S) b cos(S) b

dS bR cos(S)dw bR cos(S)dw br cos(S)dw

dOb S [COS(eP+ S)1'd

b

() cos(S)dw-cos() w -[cos(S)]3dwR cos(eP) R

E.(b) [cOS(eP+S)1'f' 2/()[COS(S)]3 f' cos(z) dw 2/() cos(S) fp cos(z) dw

2/ - cos(S) cos(z) dwR cos(cf:» o

(2b) [cOS(eP+S)1'fp (2b) fp Cb) fp- cos(S) cos(z) dw1TR [cos(S)]3 o cos(z) dw 1TR cos( S) o cos(z) dwEOF 1TR cos( eP) o

b cos( S) b cos(S) bw

cos(cf:>+ S) cos(eP + S)cos( eP + S)

MAy 2002

(a) Movable Detectar Device

OLIVEIRA ET AL. 701

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FIG. 3. Schematic representation of the shadow cast by the ring of the (a) MDD, (b) Drummond device, (c) Robinson device, and (d)MDD and Drummond device. The sun position corresponds to a winter day. The shadow rings are located in a Northern Hemisphere latitude(tjJ).

is carried out manually, and the position of the detectorrelative to the shadow is verified visually.

The only adjustments required to operate this deviceare the alignment of the sensor displacement in thenorth-south direction positioning of the ring so that itslopes northward at an angle equal to the local latitude.Given the fact that the diffuse solar radiation field isassumed isotropic, even if the detector is not perfectlycentralized under the shadow, the properties derivedhere for the MDD will still be valido

The effect of anisotropy certainly affects the diffuse

solar radiation measurements in shadow-ring devices.Even if the detector is kept under the shadow of theMDD, there is a source of error induced by the anisot-ropy portion of the diffuse solar radiation component.This type of error is also present in the other devices(e.g., that of Kipp & Zonen, Inc.). This problem willbe addressed in another future work.

The radius of the sphere that intercepts the centralcirc1e of the ring [and is centered in the detector (Fig.3a)] is equal to

rA = R{1 + [sin(ô) sin(cf»]/cos(ô + cf»}/cos(ô), (5)

702 JOURNAL OF ATMOSPHER1C AND OCEAN1C TECHNOLOGY VOLUME 19

where 4>is the local latitude. This radius defines thedistance ring detector.

The element of area in this case is given by

dS = bR cos( 8)dw,

while the element of solid angle is

[ ]

2

b cos(4) + 8)dO = - cos(8) dw.

R cos(4))

The amount of diffuse solar radiation intercepted by thering is given by

I ]

2

[J ]

b cos(4) + 8) Wp

Eb = 2/(R) cos(8) cos(4)) o cos(z) dw,

where Wp is a half-day.The fraction intercepted by the ring is

[ ]

'

[J ]

Eb 2b cos(4) + 8) - Wp_E

=(-

) cos(8) 4> cos(z) dw.DF 71"R cos( ) o

The width of the shadow cast by the ring can be esti-mated by the projection of b' (Fig. 2) over the horizontalplane (Fig. 3a) and expressed as

w = [b cos(8)]/cos(4>+ 8). (10)

Finally, the expression used to correct the blocking ef-fect in the MDD is

F ={

I _(

2b

)COS(8)

[

cOS(4> + 8)12

c 71"R cos( 4»

X [iWPcos(z) dW]r1. (11)

b. The Drummond and Robinson devices

As mentioned before, most of diffuse solar radiationmeasurements available worldwide are based on shad-ow-ring devices proposed by Robinson or Drummond.The device proposed by Robinson is composed of a setof rings covering different celestial sphere sectors (Rob-inson and Stoch 1964). In Drummond's device, one sin-gle ring is displaced along the earth's axis direction tocompensate the annual variation of the solar declination(Drummond 1964). In both cases the detectors are keptfixed and the rings are moved (Drummond) or replacedby others (Robinson). Therefore is worthwhile to lookat the properties of these two devices and compare themwith the MDD.

In the Drummond device (Fig. 3b), the ring is dis-placed along the earth's axis to compensate the annualvariation of the sun declination. This characteristic sim-plifies the construction and the operation of this device.In this case, the correction factor is

(6)

Fc = {I - (~~)rCOS(8)]3 iWP cos(z) dW} -I. (12)

In the Robinson device the blocking procedure is ac-complished by a set of rings corresponding to "slices"of a sphere with radius r and centered on the detector.The ring-sensor distance does not vary as the sun changesits trajectory during the year.This characteristic simplifiesthe expression to correct the blocking effect (13). Gn theother hand, this device requires a continuous replacementof the rings to take into account the annual evolution ofthe solar declination. The correction factor is

(7)

(8) Fc = {I - (~~) cos(8) iWP cos(z) dWr1. (13)

The expressions used in the derivation of the correc-tion factors (12) and (13) are indicated in Table 1.

(9)c. The MDD and Drummond's device

Visually, the relative movements of the detector withrespect to the ring for the MDD (Fig. 3a) and Drum-mond's device (Fig. 3b) seem to be similar. In bothdevices the axes of the ring are oriented along the earth'saxis (in the north-south direction) and the planes definedby the rings are parallel to the earth's equator in thecelestial sphere (Fig. 2).

However, when these two devices are overlaid, asindicated in Fig. 3d, the important differences betweenthem become more clear. In the MDD, the detector isdisplaced in the horizontal plane, as indicated by thered double arrow horizontalline in Fig. 3d. In the Drum-mond device, the ring is displaced in the direction ofthe earth's axis, as indicated by the black double arrowin Fig. 3d. The differences in the ring-detector distances(rs and rA) are clearer when the circles (red and black)are compared (Fig. 3d). The impact of the ring is lessintense in the case of the MDD in the situation depictedin Fig. 3b, because for winter conditions the ring-de-tector distance is larger than in the case of the Drum-mond device. A more detailed comparison betweenthese devices, including Robinson's device, will be donein section 3.

From the practical point of view, the MDD has ad-vantages when compared with the other two devicesdiscussed here. It requires only an initial alignment inthe north-south direction and an adjustment of the ringangle to the local latitude. The operation is easily ac-complished by keeping the detector under the shadow.This can be carried out manually without any adjustmentof ring angle or alignment direction.

3. Seasonal evolution of MDD correction factor

Annual variation of correction factor for the MDDhas a larger amplitude compared to the Drummond andRobinson devices (Fig. 4a). In this comparison, all three

OLIVEIRA ET AL. 703

-MDDDrummond

- - - - Robinson

122 183 305 366244

Yearday

Yearday

FIG. 4. Seasonal evolution of (a) correction factor, Fc; (b) ring-detector distance normalized by the ring radius, r/R; and (c) shadowwidth normalized by the ring width, w/h, for the MDD, and theDrummond and Robinson devices. The results are valid for the lat-

itude of Botucatu (22051 'S). Vertical dotted lines in (a) correspondto the equinoxes and solstices.

deviees are hypothetieally setup with their rings' radiiand widths equal to 24 and 6 em, respeetively. Thelatitude used in this eomparison is 22°51' S, eorrespond-ing to the local latitude where the diffuse solar radiationhas been measured by the MDD. Ali the observationalresults presented in this work were gathered in thisplaee.

The geometrie properties of the three deviees (TableI) were derived based on the Northern Hemisphere geo-graphie and astronomieal eharaeteristies (Figs. 2 and3a-d). These expressions ean be applied to estimate the

properties of these three deviees in the Southern Hemi-sphereby ehangingonly the latitude (cp)and solardee-lination (8) signals. The results shown hereafter are ap-plieations of these expressions for the Southern Hemi-sphere.

The eorreetion faetor for the MDD (Fig. 4a) variesfrom a maximum of 1.236 in the summer (yeardays 19and 328) to a minimum of 1.054 in the winter solstiee(yearday 173). Similarly, the Robinson deviee showstwo maximum values of 1.194 during summer (yeardays30 and 317) and one minimum of 1.099 in the wintersolstiee. In the case of Drummond, the eorreetion faetorvaries from a maximum value of 1.183 in the summer(yeardays 57 and 290) to a minimum value of 1.083 inthe winter solstiee. In the equinoxes ali three devieesreaeh the same value, 1.174 (yeardays 80 and 267).

This behavior is re1atedto the annual evo1utionof ring-deteetor distanee for the MDD and Drummond's deviee(rAand rB;Fig. 3d). For the MDD, the ratio rAIRvariesfrom 0.92 (rA = 22.1 em) in the summer to 1.33 (rA =31.9 em) in the winter. For the Drummond deviee, rBIR varies from 1.09 (rB = 26.13 em) in the winter andsummer solstiees to 1 (rB = 24 em) in the equinoxes.In the Robinson deviee, the annua1 evolution of Fc isdetermined on1yby the relative projeetion of b over thehorizontal plane (rc in Fig. 3e) sinee the ratio reIR re-mains eonstant (equal to 1) ali year long (Fig. 4b).

Another important feature of these deviees is the sizeof the shadow east by the ring over the horizontal plane(Fig. 4e). This parameter will determine the operationa1autonomy (time without manual adjustment) of theshadow ring. The annua1 evolution of the size of theshadow east by the MDD is identieal to that obtainedby the Drummond deviee. The shadow ratio (wlb) variesfrom a maximum of 1.32 (w = 7.96 em) in the winterto a minimum of 0.92 (w = 5.51 em) in the summer.In the case of Robinson, this ratio varies from 1.44 (w= 8.66 em) in the winter to 1.00 (w = 6 em) duringthe summer. Based on this analysis it may be eoncludedthat the MDD has the same operational autonomy ofthe Drummond deviee.

4. Effect of latitude on seasonal evolution of theMDD correction factor

The annual variation of the Fc for the MDD is in-dieated in Fig. 5a for latitudes varying from 0° to 300S.At the equator the MDD behaves exaetly like the Drum-mond deviee. There, Fc for both deviees shows a max-imum of 1.189 in fali and spring equinoxes (yeardays80 and 267 in Table 2) to a minimum of 1.128 in thewinter and summer solstiees (yeardays 173 and 356).At this latitude, the ratio of ring-deteetor distanee toradius of the ring (riR in Fig. 5b) shows two maximumvalues, 1.089 in the winter solstiee (yearday 173) and1.088 in the summer solstice (yearday 356), and twominimum values in the fali and spring equinoxes (year-days 80 and 267). The annual evolution of the shadow

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JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY

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FIG. 5. Seasonal evolution of (a) eorreetion faetor, F c; (b) ring-deteetor distanee normalized by the ring radius, rA/R; and (e) shadowwidth normalized by ring width, w/b, for the MDD loeated at 0°, 10°,20°, and 300S latitude (4)).

width (east by the ring on the horizontal plane) nor-malized by the ring width (w/b in Fig. 5e) indicates thatthe size of the shadow at the equator remains eonstantand equal to b during the whole year.

Far from the equator the MDD behavior departs sig-nifieantly from that of the other deviees. The amplitudeof Fc inereases and the annual distribution of maximumand minimum diverges from the pattern found at theequator (Fig. 5a). At 300S, Fc reaehes a maximum of1.277 in the summer (yeardays 1 and 356 in Table 2)and a minimum of 1.037 in the winter solstiee. At thislatitude, the ratio of ring-deteetor distanee to ring radius(rA/R in Figo 6b) varies from 0.872 in the summer to1.448 in the winter solstice. The shadow width to ring

VOLUME 19

TABLE 2. Correetion faetor (Fd (top) maximum and (bottom) min-imum values as a funetion of yeardays. They eorrespond to an MDDwith b/R = 0.25 and loeated at latitudes (4)) varying from 0° to 300S(Fig. 5). The latitude of 22°51' S eorresponds to Botueatu.

366

366

width ratio (w/b in Figo 5e) varies from 0.925 in thesummer to 1.536 in the winter solstiee.

The maximum diffuse solar radiation bloeking oeeursduring the summer period and is eompensated by thesmaller bloeking during winter. The faet that the pres-enee of cloud makes the diffuse solar radiation fieldmore isotropie (Steven and Unsworth 1980) seems toindieate that the MDD is more suitable to regions wherethere is more cloud aetivity in summer than in winter.For latitudes greater than 30°, the behavior of Fc forthe MDD (not shown here) diverges eonsiderably fromthat for other deviees, and its applieation is not ree-ommended.

366

5. Performance of the MDD

During 7 months the MDD and the Kipp & Zonendeviee (KZD) were used to measure diffuse solar ra-diation at the surfaee in order to verify the MDD per-formaneeo These measurements took plaee in the eity

1.05

1.00O 122 183 244

Yearday

305 36661

FIG. 6. Seasonal evolution of eorreetion faetor (F c) eorrespondingto the MDD and the KZD at the latitude of Botueatu (22°51' S). The

shadow width and ring radius were set equal to 6 and 24 em, re-speetively.

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lOoS 1.197 58 and 289200S 1.223 30 and 31722°51'S 1.236 19 and 328300S 1.277 01 and 356

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OLIVEIRA ET AL. 705

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3 6 9 12 15d 2

(E DF)KZD(MJ/m )

FIG. 7. Seatter diagram for diffuse solar radialion daily valuesmeasured by the MDD vs lhe KZD. The rings used in both devieeshave b = 6 em and R = 24 em. The data eorresponds to 192 daysof observation in Botueatu, from 17 Dee 1999 (yearday 351) to 7lul 2000 (yearday 192). The eontinuous line eorresponds to a linearregression eoeffieient equal to 0.99.

of Botucatu between 17 December 1999 (yearday 351)and 11 July 2000 (yearday 192) and both devices wereset up at 2 m above the surface. This site correspondsto a rural area characterized by homogeneous horizon-tally distributed green short grass surrounded by spotsof deciduous forest at the south (Fig. 1).

In the MDD, the diffuse component was measuredwith a CM21 pyranometer modeI (SN 980.537) built byKipp & Zonen, Inc., with a calibration constant equalto 11.99 :t 0.12 J.LVW-l m-2. The KZD correspondsto a CM121B shadow-ring modeI, and the diffuse solarradiation was measured with a CM21 pyranometer mod-el (SN 980.017) also built by Kipp & Zonen, with acalibration constant equal to 9.93 :t 0.10 J.LVW-l m-2.

The geometric dimensions of the MDD were set sim-ilar to the KZD, with both rings having a radius andwidth equal to 24 and 6 em, respectively. The correctionfactors are indicated in Fig. 6. The smooth and contin-uous annual evolution of Fc for the KZD was obtainedby fitting a sixth-degree polynomial to the table of val-ues proposed by the manufacturer. In Fig. 6 one noticesthat, despite the geometric simi1arity of both devices,their Fc annual evolution differs significantly. The larg-est difference occurs during the summer period, whenthe ring is closest to the pyranometer in the MDD.

The comparison carried out here is based on 192 dailyvalues of diffuse solar radiation (EiF)' All solar radiationquantities used in this part of the work are expressedin units of 106 Joules per square meter (MJ m-2). Theparameters KT and Kd, clearness index and diffuse frac-tion, respectively, were estimated as E'/:;/E1and Ei;E'/:;.Here, E'/:;corresponds to the daily value of globalsolar radiation at the surface (available from a modei 2pyranometer designed by Eppley, Inc.), and E1 to thedaily value of solar radiation at the top of the atmo-

.. .., " .:. ~ ..Ir . ,. .. ..e I'. ·

~ .. .. ... . ..., .1 .!. #.. .~ . .... .-. .

15 186 9 12

d 2

, (E DF)KZD(MJ/m )

FIG. 8. Seatter diagram of absolute deviation of diffuse solar ra-diation daily values measured with the MDD and the KZD, [(E~F)KZD- (E~F)MDD],in Botueatu.

3

sphere, estimated theoretically considering the solarconstant equal to 1366 W m-2 (Fr61ichand Lean 1998).

Figure 7 shows the scatter diagram of daily values ofdiffuse solar radiation measured by the MDD and theKZD. There one can see that despite the difference inthe seasonal evolution of Fc (Fig. 6), there is very goodagreement between the measurements obtained with thetwo devices. The linear correlation coefficient is 0.99,and the diagonal (dotted line) and the fitted curve ob-tained by linear regression (continuous line) show asmall mismatch near to the diagram origino

The scatter diagram of the absolute deviation, AD =[(EiF)KZD- (EiF)MOO]'as a function of diffuse solarradiation daily values measured by the KZD is shownin Fig. 8. The distribution of the absolute deviation in-dicates that the MDD underestimates the daily valuesof diffuse solar radiation compared to the KZD forEiF < 6 MJ m -2, as pointed out by the vertical dottedline in Fig. 8. This behavior shows that the MDD un-derestimates the KZD measurements under clear skyconditions. Above this limit there is no visually de-tectable pattern in the distribution of absolute deviation.

Frequency distribution of relative deviation betweenthe MDD and the KZD is shown in Fig. 9. The relativedeviation, RD = 100% [AD/(EiF)KZO]'has a distributionthat is approximately Gaussian around 2.5%, indicatingthat the MDD has a tendency to underestimate diffusesolar radiation daily values in comparison to the KZD.There is also a secondary peak around -1.5%, indi-cating that there is also a condition when the MDD hasa tendency to overestimate EiF'

This bimodal distribution is related to the combina-tion of climate conditions in Botucatu and the seasonaldistribution of Fc. Botucatu is located in the countrysideof Brazil, at 750 m above the mean sea leveI and 250km away from the Atlantic Oceano It is characterizedby mild and dry winters (June-August) and warm andwet summers (December-February). The first peak

MAy 2002

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JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY

FIG. 9. Frequency distribution of relative deviation for diffuse solarradiation daily values measured with the MDD in Botucatu. Thedeviation was carried out considering KZD measurements as refer-ence. The most probable relative deviation is +2.5%. Normal curvewas adjusted by linear regression.

(2.5%) is related to the larger frequency of c1ear skydays and partially c10udy days during the period of ob-servation. The second peak (-1.5%) is related to thesmaller frequency of totally c10udy days.

The distribution of relative deviation as a function ofthe c1earness index indicates that the relative deviationdoes not depend on the c10ud cover conditions in theinterval 0.25 < KT < 0.6 (shown in Fig. 10 by twovertical dotted lines) because the linear correlation co-efficient (0.54) is not conc1usive. In this interval, bothpositive and negative relative deviations are equally dis-tributed. Under totally c10udy conditions (KT < 0.30)the MDD overestimates EiF because this condition oc-curs during summer period, when the solar dec1inationis negative (Fig. 11). The correction factor for the MDDduring summertime in the Southern Hemisphere is larg-er than that for the KZD (Fig. 6).

It is important to emphasize that the c1earness indexis directly proportional to the intensity of global solarradiation at the surface; therefore values of KT c10seto1 indicate not only c1ear sky conditions but also largerintensity of solar radiation and vice versa. Thus, thebehaviorof the relative deviationwithrespectto KT canbe extended to the intensity of global solar radiation atthe surface.

The distribution of relative deviation as a function ofsolar dec1ination is indicated in Fig. 11. The maximumrelative deviation (- + 5%) occurs during spring andpart of winter, when there is less c10ud activity in Bo-tucatu. On the other hand, the minimum relative devi-ation (- -2.5%)occurs during summer. This behaviorindicates that seasonal distribution of relative deviationresults from the combined effect of seasonal variationof c10ud activity and correction factor. During summer(8 < -10) there is more c10udactivity, and, as explainedbefore, the effect of the correction factor dominates thebehavior of relative deviation. During spring and winter

VOLUME 19

0.0 0.2 004 0.6 1.00.8

FIG. 10. Scatter diagram of relative deviation for diffuse solarradiation daily values vs cIearness index (Kr) in Botucatu.

c10ud activity is smaller, and correction factors for thetwo devices are comparable. Therefore, the relative de-viation reaches a maximum (-+5%) and stays at thisleveI. The pattern displayed in Fig. 11 is statisticallysignificant once the linear correlation for the interpo-lated curve (second-degree polynomial) is equal to 0.86.

A second performance test was undergone comparingthe KT - Kd distribution obtained by the MDD with thedistribution representative of the local c1imate.This laterdistribution is indicated by a curve (Fig. 12), obtainedfrom a polynomial fitting of KT - Kd values based on3-yr-long measurements of direct solar radiation (usinga pyrheliometer) and global solar radiation (using a pyr-anometer), as described by Ricieri (1999).

The values of Kd obtained by the MDD are sym-metrically distributed around the polynomial, indicatingthat, for 0.25 < KT< 75, the device is able to reproducethe c1imatological behavior. For KT < 0.25, the MDD

Solar Declination (degree)

FIG. 11. Scatter diagram of relative deviation distribution for dailyvalues of diffuse solar radiation as a function of solar decIination (8)in Botucatu. The fitted curve corresponds to a linear regression co-efficient of 0.86.

. [(EdOF)KZO- (EdOF)MDD]/(EdDf)KZO

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OLIVEIRA ET AL. 707

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FIG. 12. A Kr - Kd diagram based on diffuse solar radialion dailyvalues measured with the MDD and the KZD in Botucatu. The solid

line corresponds to the adjusted curve through the Kr - Kd valuesobtained from diffuse solar radiation measured with a pyrheliometerduring 3 yr in Botucatu (Ricieri 1999).

yields slightly larger values of Kd due to the correctionfactor effects discussed before. As expected, the KT -Kddistribution obtained by the MDD is comparable withthe KZD distribution.

6. Conclusions

In this work major features of a new shadow-ringdevice have been presented. This device, called the mo-bile detector device, was developed in the Laboratoryof Solar Radiation at UNESP (MeIo 1993) and has beenused continuously to measure diffuse solar radiation inBotucatu (Escobedo et aI. 1997) and São Paulo citysince 1994 (Oliveira et aI. 1996, 2002).

In the MDD the ring is fixed, and the annual variationof shadow position is followed by displacing the de-tector horizontally. The ring is sloped northward at anangle equal to the local latitude, and the detector isdisplaced manually, in a horizontal plane, by a screwmechanism that allows it to be centralized under theshadow cast by the ring. This unique characteristicmakes this device simpler to operate compared to otherdevices in which the detector is fixed.

Considering the diffuse solar radiation isotropic, thecorrection factor for the MDD is given by

The ring-detector distance and shadow size are given by

rA = R{1 + [sin(8) sin(cP)]/cos(8 + cP)}/cos(8),

w = [b cos(8)]!cos(cP+ 8).

1.0

Major geometric properties of the MDD were com-pared with the ones for the Robinson and Drummonddevices, indicating that Fc for the MDD is higher duringsummer and smaller during winter. In latitudes between0° and 300S,the maximum value of Fc varies from 1.189to 1.277, and the minimum from 1.128 to 1.037. Thehighest correction factors occur during summer whenthe ring-detector distance and shadow width are smaller.

The comparison between diffuse solar radiation dailyvalues measured by the new device and the Kipp &Zonen device indicates a good agreement, with a linearcorrelation coefficient of 0.99. The deviation betweenthe MDD and the KZD is due to the combined effectof annual distribution of cloud and Fc; the relative de-viation distribution varies from -3% to +6%.

The comparison between values of Kd, obtained withboth devices (MDD and KZD), shows that the perfor-mance of the prototype is similar to that of the Kipp &Zonen device for atmospheric conditions varying frompartially cloudy to totally clear (0.25 < KT< 75), whilefor totally cloudy sky the performance of the MDD isslightly inferior to that of the KZD.

The MDD was able to reproduce the climatologicalbehavior obtained from a polynomial fitting of KT - Kdvalues based on 3-yr-long measurements of direct andglobal solar radiation. The results presented here indi-cate that the MDD can be applied, with results com-parable to other similar apparatus, to estimate diffusesolar radiation daily values at the surface in the rangeof 300N-300S.

Acknowledgments. The authors acknowledge finan-cial support provided by "Conselho Nacional de De-senvolvimento Científico e Tecnológico-CNPq" andby "Fundação de Amparo à Pesquisa do Estado de SãoPaulo-Fapesp. "

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