Solar radiation assessment using Meteosat 4-VIS imagery

Pergamon PII: SOO38-092X(97)00001-7

Solar Energy Vol. 60, Nos. 314, 209-219, 1997 pp. 0 1997 Elsevier Science Ltd

All rights reserved. Printed in Great Britain 003&092X/97 $17.00+0.00

SOLAR RADIATION ASSESSMENT USING METEOSAT 4-VIS IMAGERY

JUAN CARLOS CEBALLOS*+ and GEBER BARBOSA DE A. MOURA**I * Departamento de Ci6ncias Atmosfiricas,

Centro de Ci&ncias e Tecnologia Universidade Federal da Paraiba, Brazil and ** LAMEPE/IPA, Instituto de Pesquisas Agropecuarias de Pernambuco, Recife, PE, Brazil

(Received 4 April 1995; revised version accepted 19 September 1996) (Communicated by Amos Zemel)

Abstract-Meteosat 4-VIS high-definition imagery was used for testing solar radiation assessment over northeast Brazil during January 1991 and 1994. Actinographs of solarimetric stations in Paraiba State provided proper ground reference. A simple physical model was developed, based on two basic hypotheses: visible and infrared intervals are decoupled, and radiation transfer in the visible interval is essentially conservative. Some ideas are borrowed from the well known model of Gautier et al. for cloudiness assessment. The resulting GL model can run on a personal microcomputer, processing targets of 5 x 5 pixels for all the region. It exhibits rather good behaviour on a monthly scale, reproducing the mean diurnal cycle and assessing mean irradiation with bias and mean standard deviation lower than 10 W m-*. Fifteen-day means exhibit similar accuracy. Ground albedo is a highly important parameter of the model. As expected, the main sources of error seem to be planetary reflectance and cloudiness assessment, because of the non-lambertian reflection and the different count thresholds for each kind of cloud cover. Further studies considering longer time series of images (VIS and IR channels) as well as the anisotropic properties of finite cloud fields may improve the model. 0 1997 Elsevier Science Ltd.

1. INTRODUCTION

A number of articles have been published on the assessment of daily solar irradiation at ground level. Intercomparisons show similar behaviour for a variety of models (Whitlock et al., 1990). Particularly important is the effort for operational monitoring of the radiative budget. For instance, the International Satellite Cloud Climatology Project (ISCCP) offers information on cloud cover, presently used for assessing monthly means of the shortwave radiation budget on a global scale, being available from NASA (Whitlock et al., 1995). Concerning Meteosat satellites, some pro- cedures using VIS imagery are operationally in use at several European institutions, such as HELIOSAT in France (Cano et al., 1986; DiabatC et al., 1989) and IGMK in Germany (Stuhlmann et al., 1990).

Authors typically claim 7-10% accuracy for monthly means of irradiation, which amounts to about 20-50 W mm2 for mean irradiance. Recommended mean standard errors are lower than 25 W rnp2 with bias errors lower than 10 W mm2 (Whitlock et al., 1995). Results of the IGMK method were reported by Rieland

‘Present address: CPTEC-INPE, 12630 Cachoeira Paulista, SP, Brazil. E-mail: [email protected].

*Formerly at: Divislo de Microfisica e Mesoescala, Funda@o Cearense de Meteorologia e Recursos Hidricos, (FUNCEME) Fortaleza, CE, Brazil.

and Stuhlmann (1993), describing geographical distributions of mean irradiance for July 1985 and January 1986. Although focused on Africa, their results include a region of the South American sector within the Meteosat field of view. For northeast Brazil, IGMK yielded mean daily irradiances of 175-200 W rnp2 for inner Paraiba State (about 7”S, 37”W) during July 1985; however, data from the solarimetric network operated by the Federal University of Paraiba (UFPB) reported values around 150 W rne2. Similarly, IGMK values for January 1986 were 250-275 W mm2 whilst UFPB obtained about 230 W rnp2. These results suggest that IGMK may overestimate the monthly mean solar irradiation by about 20-25% over an area of 2 000 000 km2.

As seen from the Brazilian northeast, Meteosat satellites located at 0”W have zenith angles of about 47”, i.e. of the same order as those corresponding to European countries. The above-mentioned bias errors suggest the impor- tance of testing the use of VIS channel ability for studies of solar radiation over that part of South America. Meteorological state agencies are potentially interested in monitoring solar irradiation, since they routinely save Meteosat 5 images in high definition formats. On the other hand, the UFPB solarimetric network (six stations) is able to provide the ground data required for validation over an area between 6--8”s and 34-39”W.

209

210 J. C. Ceballos and G. B. De A. Moura

Given the complex structure of the IGMK procedure (Stuhlmann er al., 1990), a simple model (hereafter labelled GL) has been developed in order to perform preliminary analyses of global solar radiation assessment. Some com- plementary ideas were borrowed from the well known paper of Gautier et al. ( 1980) hereafter labelled G80. This model was originally applied to GOES VIS imagery. It is particularly interes- ting because of its simple but physically sound structure; moreover, it exhibits the same order of accuracy achieved by other models (Whitlock er al., 1990). Nevertheless, G80 considers that calibration based on VIS channel counts is fully representative of the total solar spectrum (Norton et al., 1980), while the particular spectral response of VIS sensors should be considered for a proper assessment of the information provided by the VIS channel (Dedieu et al., 1987). In this context, GL avoids this troubling scheme by splitting the solar spectrum into two physically independent wavebands (VIS and IR).

The following sections describe the structure and limitations of the GL and GXO models, discuss parameterizations and present GL preliminary results.

2. CL/G80 MODELS

A simple solar energy balance of the earth-atmosphere system can be written as

/JLso=&+E*+(l-Rg)Eg, (1)

where a direct beam (with directional flux S,) strikes the top of the atmosphere (“TOA”) with zenith angle Z(cos Z= p); E describes irradiance and subscripts R and A indicate exit at TOA and absorption (in the atmosphere). R, and Eg are ground level values for albedo and irradi- ante, respectively. Equation (1) describes a nearly-linear relationship between ER and ground-absorbed irradiance if EA is nearly constant or EA/& cc 1. This behaviour has recently been studied, being confirmed experimentally by Cess et al. ( 1991) for clear sky conditions and numerically by Li et al. ( 1993) for various cloud cover and precipitable water models.

The spectral range of the GOES VIS channel is 550-750 nm. Therefore, solar infrared fluxes and absorption effects due to clouds, water vapor and carbon dioxide are actually “invisi- ble” to the VIS sensor. This is nearly the case for the VIS Meteosat channel, which is sensitive within a wider interval but has a weak response

function for near infrared wavelengths (Kriebel and Amman, 1993). On the other hand, radiative transfer in the solar spectrum may be described in terms of definitely separated wavebands. Thus, eqn (1) will be split for the two intervals, identified as visible (VIS) and infrared (IR) in the following.

2.1. VIS GL model

The VIS spectral interval is defined here as A = 400- 1100 nm, appropriate for Meteosat 4. Nevertheless, it must be stressed that the spectral response is not constant in this interval (Kriebel and Amman, 1993), hence the sensor is not equally sensitive for all wavelengths in A. Incident and emerging irradiances for this interval will be labelled E, “is and E,i,, respectively. Ozone depletion is caused by Chappuis bands (450-750 nm), which are relatively weak; their effects may be included as a stratospheric correction (using an appropriate factor for correcting E,, “is and E,is). Only narrow and weak water vapor bands are present (centered at 720, 800 and 900 nm). The influence of the somewhat stronger 900 nm band on VIS counts can be disregarded because of the lower spectral response of the Meteosat sensor in this wave- length. Unless aerosol effects are considered, these facts suggest that we assume a conservative atmosphere in the VIS channel so that eqn ( 1) becomes

&% vis = ER vis + as f& vis + ( 1 - R, vis )Eg vis 3

1-a3=Rpvis+(1-Rgvis)GLvis. (2)

eqn (2) is non-dimensional where a3 is the ozone absorbance, R, the planetary reflectance and GL the global irradiance at ground level, nor- malized to VIS-interval TOA irradiance. Aerosol effects are neglected. Indeed, R, “is measurement is the main source of error for GLvis assessment. Note that the ground albedo becomes an important parameter, assuming that ground-absorbed irradiance is properly assessed from planetary reflectance.

2.2. Cloud and ground VIS properties The G80 model can be useful for determining

some cloud and ground properties. Figure 1 illustrates its basic structure. Two atmospheric layers (I and II) are considered, interfaced by a third layer (C) containing a cloud field. A direct (VIS interval) sunbeam strikes the top of layer I (zenith angle Z), while the satellite looks at a site (pixel P) with zenith angle Z,(cos Z, = p,). Radiance upwelling towards the

Solar radiation assessment using Meteosat 4-VIS imagery 211

sun El E2 E3

I

Fig. 1. Radiance components arriving at the satellite sensor in the VIS interval, as considered in the G80 model.

satellite is composed of three sources: L, is produced by atmospheric reflection in layer I, while reflection in layer C generates component L,. The original beam also yields a component L, after transmission through layers I, C and II, reflection at ground (point P) and further transmission through II, C and I.

Using symbols R, T and A for reflectance, transmittance and absorptance, and assuming that radiance leaving the atmosphere at the top of layer I is isotropic, the emerging irradiance at satellite level is given by

E=7c(L, +L, +L,)=E, SE2 +E3, (3a)

E, = R,E,, (3b)

EZ = T,& T;,E,, (3c)

E, = T, T, T,, R, T;,T;T;E,. (3d)

Equations (3b)-(3d) no longer refers to the radiative properties of the directional flux but of the irradiances. T,, T;, R,, T,, and T;, refer to properties of the layers I and II, while R,, T, and TL refer to properties of the cloud layer (but not of a single cloud). Aerosol optical load is disregarded, as well as stratospheric ozone depletion (as before, the latter could be included by assuming TOA transmittance factors T, for correcting incident irradiance E, and T; for correcting the emerging irradiance E). The prime denotes the returning beam; note that transfer properties might not be the same for incident (that is, nearly direct) and returning (diffuse) beams. Multiple reflections between ground and layer C are disregarded. SE 60:3,4-O

The original G80 model is based on three assumptions:

(1) (2)

(3)

T, = T;; T,, = T;,; T, = T;. For each layer, the transmittance is given

by T=(l-R)(l-A) instead of T=l-R-A. The absorptance A, within layer C is a linear function of pixel count B (“brightness”), between extreme cases Bmin and B max. The pair (B,in; A,=O) corresponds to a cloud-free pixel and (B,,,; A, = A, ,J corresponds to overcast sky. A, o is the absorptance of a single extended cloud, for which G80 assumes the value 0.2. Extremes Bmin and B,,, for each target are assessed through a statistical analysis of brightness time series.

A and A, are null as seen by satellite VIS sensors. Therefore, T, + R, = 1 and eqn (3a) becomes a quadratic equation with the unknown R, = 1 - T,, as follows:

(4)

As mentioned above, R, is the cloud-layer reflectance within the VIS interval. If the fractional area covered by clouds (C= “cloudiness”) were known, a measure of typical single-cloud reflectance R, o = R,/C could be obtained. The original GSO model implicitly defines

C=(B-Bmi,)/‘(B,,, -Bmi,) (5)

through hypothesis (3), since it assumes that the cloud layer absorptance is given by A, = CA, o. This is the same estimate used by HELIOSAT (Diabate et al., 1989) and IGMK (Stuhlmann et al., 1990).

Finally, eqn (4) allows an assessment of the ground reflectance within the VIS interval (R, “is) from cloud-free pixels, for which T,, = 1, T, = 1 and R, “is are found from the minimal count Bmin in an extended time series. This provides a first-order approximation, usu- ally accurate enough for R, assessment. A model considering multiple ground reflections leads to

R, “is(min) = R, vis o +&(l-&.i,o)(l-R*)l

(1 -R*R,), (6)

where R, “is o is the expected R, value for a Rayleigh atmosphere and non-reflecting surface, and R* is the atmospheric reflectance for a diffuse flux (“counter-reflectance”).


2.3. IR GL model

Only clouds have relevant scattering effects within the IR interval. For cloud-free scenes, the global IR irradiance at ground level can be written as

Eg ir = ~(SO ir - ASI > (7)

where S, ir refers to extraterrestrial solar directional flux in the IR interval and AS is the absorption by water vapour and CO, bands. In tropical atmospheres, these bands are considerably depleted before the solar beam reaches the ground. In a cloudy scene (Fig. 1) IR sunbeam is partially absorbed in layer I; after reaching the clouds, the fraction of the original beam that arrives at the bottom level as downwelling diffuse radiation can also be considered satu- rated (that is, the flux in the absorption bands has been exhausted). This means that further radiative processes can be thought of as conservative. Therefore, the primary direct plus diffuse irradiance Eg ir O reaching the ground generates an infrared global irradiance Eg ir such that

Eg 0 ir =~(Sir -AS)( 1 -C) +~ssi,Ti,(ClOud)C,

(8)

Egir=EgOir/(l-CRgi,Rci,), (9)

where C is the cloudiness (fractional area cover- age). AS refers to the total atmospheric column [as in eqn (6)]. SSi, refers to the IR subinterval free of absorption bands and Ti,(cloud) is cloud (conservative) transmittance in this subinterval. As a matter of fact, the latter is a second-order term and will be disregarded. Equation (9) describes the enhancement of primary global irradiance by multiple reflection between the ground and the cloud layer. It is worthwhile to note that ground reflectance within the IR interval (Rg ir) is considerably higher than within VIS.

Some physical parameters are needed, such as precipitable water (u) and ground IR reflectance (Rg ir) as well as the (modelled or mea- sured) IR conservative reflectance of cloud base (R, ir). The cloudiness C is obtained from eqn (5).

2.4. Target irradiance Eg

In order to compare model results with ground data, it is worthwhile to consider the integrated irradiances on an hourly basis (i.e. irradiation), yielding mean irradiances rather than instantaneous local values; therefore, not single pixels but satellite targets with N x N

elements will be processed. This involves an “ergodic hypothesis”: it is assumed that spa- tially averaged irradiance over a target- obtained by means of satellite imagery-is a reliable estimate of the mean irradiance mea- sured at any point within the target, averaged over a certain time interval. This time interval must be coherent with the target size N. Models GL and G80 are built in this context.

It is assumed that the mean hourly irradiance corresponds to the mean of E,(VIS) +E,( IR) over the target [eqns (2) and (9)]. Taking 5 x 5-pixel targets (about 25 km sized regions), the mean over 25 pixels accounts for displace- ments and life cycles of clouds within an hour. Similar numerical values are obtained with 5 x 5 and 3 x 3 targets.

A VIS brightness threshold for discriminating cloud-free from cloudy pixels is needed. It must be assessed from previous statistics of minimal counts (&,,) over the region. There may exist a daily cycle as well as an annual cycle for these minima. In addition, a proper climatology of the &,, parameter allows improvement of the cloudiness assessment by eqn (5).

3. DATA PROCESSING AND PARAMETERIZATIONS

3.1. Satellite and ground data

Meteosat 4 VIS channel hourly images were provided by the Brazilian Fundacao Cearense de Meteorologia e Recursos Hidricos (FUNCEME, at Fortaleza) as binary files. They were available for even days of December 1990 to January 1991 and for all the days of January 1994, only from 10:00 to 17:00 GMT (07:OO to 14:00 Brazilian time). Some cases could correspond to half-hour time intervals. The pixel size is 2.5 km x 2.5 km at satellite nadir; the actual east-west width of a pixel is about 1.47 times larger at Paraiba State, since the sites are located around 7”S, 38”W. VIS images recorded by Funceme include pixels of only alternate lines and columns (global picture of 2500 x 2500 pixels); thus, single-pixel information at nadir is assigned to a 5 km x 5 km area.

In order to perform detailed comparisons with actual ground data, two 5 x 5-pixel reference targets were considered at Paraiba, centred respectively at Cabaceiras (CAB =7.48’S, 36.28”W, altitude 390 m) and at Belem do Brejo do Cruz (BEL = 6.18”S, 37.53”W, altitude 200 m). Both Paraiban sites have solarimetric stations held by UFPb, measuring global and


diffuse radiation with Fuess bimetallic actinographs (model 58cd, installed in 1975). Negative comments are found in the literature concerning the performance of older models (Robinson, 1966). However, calibrations of Fuess models manufactured after 1955 indicate good linearity and accuracies better than 4% for daily irradiation and better than 20% for hourly records (Fattori and Ceballos, 1988; Ceballos et al., 1992). We employed a calibration constant previously found for several actinographs in the UFPb network. Areas in actinographic records were assessed by planimetry of l-h intervals between 06:OO and 14:00 local time, as well as the full interval 07:00-14:OO for global and diffuse irradiations.

Mean cloudiness C for each pixel in a target was determined using eqn (5). Previously, reference extremes B,i, and B,,,,, were defined for each target (eighth hourly values within time interval 07:00-14:OO). Bmin values were found by determining the lowest counts in a target from two-month imagery (total of 30 images). Concerning maxima, the time series of highest counts in the 5 x 5-pixel target was considered and the mean value was assumed as B,,,. This procedure avoids excessively bright counts typical of cumulonimbus (Cb clouds) but not of usual homogeneous cloudiness. It should be noted that a short observation period might fail to include cases of overcast sky.

3.2. Use of satellite calibration

The VIS spectral interval was defined as ;L= 400-l 100 nm and the IR region limited to ;1= 1100-2000 nm. This allowed comparison of the planetary reflectances as viewed by satellite (limited to the VIS region) with global irradi- ante as deduced from actinographic records, covering the spectral range il=400-2000 nm. It also implies the assumption for the TOA solar directional fluxes the values of S,, vis= 906 W rnp2 (visible) and So ,=270 W mm2 (infrared), thus S,,(actin) = 1176 W rnp2 for actinographs at the mean Sun-Earth distance (Iqbal, 1983).

Concerning the outgoing flux as seen by the VIS channel, Kriebel and Amman (1993) have reported calibration factors KS ranging from 1.16 (crop field scenes) to 0.99 (overcast) in units of W m -2 ster-’ count-l. Planetary reflectance may be assessed by

R, =~&B/(cLS~ “is), (10)

where B is the pixel count. Equation (10) assumes lambertian radiance. These figures suggest that counts B= 50 (typical of partially cloudy scenes) for sun position p =0.8 and isotropic reflectance should correspond to planetary (visible) reflectances R, = 0.25. However, the spectral response ~(2) for the Meteosat 4 VIS sensors is not constant but nearly trapezoi- dal (Kriebel and Amman, 1993), with v] =0 for AI 350 nm, ‘I= 1 within 1=650-800 nm, and q =0 for II 2 1070 nm. A response factor of q 20.5 is attained within the interval ,? = 420-950 nm, hereafter labelled the VI&, (i.e. effective VIS) interval. Radiation outside the VI&r interval is poorly detected by the VIS sensors, suggesting that R, in eqn (10) could be better assessed assuming q = 1 within VI&, and r] = 0 elsewhere, thus S, “is US, “is ef = 690 W rnm2. This choice of effective interval should improve the assessment of cloud reflectances, which are nearly constant in the VIS interval (Welch and Cox, 1980; King et al., 1993). In the above-mentioned example, this criterion leads to R,=0.35, which is considerably higher than the former value of 0.25. Note that this new value may be assumed as valid for the entire VIS interval.

In order to better use the calibration constant, KS assumes values between 1.16 and 0.99 for each pixel, linearly interpolated according to the cloudiness C [eqn (5)].

3.3. Aerosols

No aerosol was considered in the GL model. Spectral determinations of direct irradiance by PSP pyranometers (global and diffuse fluxes) and measurements with actinographs suggest a light aerosol load (optical depth Z, ~0.2) over the Paraiban region (Ceballos et al., 1992).

3.4. Atmospheric and ground albedo

The parameterization of Lacis and Hansen ( 1974), considered valid within 1% for the entire solar spectrum (100-4000 nm), was used as reference:

R, = 0.28/( 1 + 6.43~). (11)

Equation ( 11) describes planetary reflectance assuming a black ground surface at the 1000 HPa level. However, it should be noted that the IR interval has negligible Rayleigh scattering, so that the scattered flux assessed by eqn (11) must be spectrally limited to the VIS channel. Therefore, R, must be corrected by a


factor Se/S, “is =y= 1.50 in order to be representative of VIS reflectance.

Equation ( 11) corrected for the VIS channel was used together with eqn (6) in order to deduce ground reflectance R, “is from counts of cloud-free pixels. For the IR interval a typical value of R, ir =0.4 was assumed, intermediate between soil and vegetated surfaces for I > 800 nm (Richards, 1986). Also, R, ir = 0.4 was assumed for cloud reflectances as adequate for diffuse radiation incident on a cloud base.

3.5. Atmospheric absorption: water vapor

Lacis and Hansen (1974) proposed a parameterization for the absorptance of solar directional flux by atmospheric water vapor, valid for the whole solar spectral range, given by

a(w*) =2.9w*/[( 1 + 141.5~*)~~~~~ + 5.925w*],

(12)

based on a paper of Yamamoto (1962), who in turn used (among others) experimental results of Howard et al. ( 1956a,b). Equation ( 12) assesses absorptance over the whole solar spectrum; w* (g cme2) is the equivalent optical path through water vapour, reduced (“scaled”) to 1013 HPa pressure conditions. The use of eqn (12) implies the calculation of a scaled value precipitable water u*, such that w* = u*/P. To do this, knowledge of the vertical profile of moisture is needed.

In order to compare model results with actinographic, only bands in 400-2000 nm are to be considered. Howard et al. describe the absorption within each band by means of an equivalent bandwidth function A(P,w), which depends on total pressure P (considered constant along the light path) and on optical path w. Joint absorption by (non-overlapping) bands is calculated using

AS=C Ai(P,w)Si, I

(13)

where Si is the incident spectral directional flux for a representative frequency within the ith band. Zuev (1970) showed that, in atmospheric (vertically inhomogeneous) conditions, eqn ( 13) can be used with actual optical path w =u/,u, but considering an equivalent pressure P*, obtained by vertically weighting pressure P with the profile of moisture content. Assuming this criterion and including two additional bands in i = 700-800 nm we obtain the parameteriza-

tions (Ceballos et al., 1992)

AS= 109.7+84.21 log,,w

+ 2.1 w (700-2000 nm),

AS= 133+92 log,,w+2.lw (700-2800 nm).

(14)

These expressions are appropriate for actinograph and pyranometer spectral intervals, respectively, with w > 2 g cm-‘. Equivalent pressure P” = 800 HPa is typical of the northeast region, as well as precipitable water amounts u = 4.3 g cmp2. Equation ( 14) is fairly consistent with eqn (12) for reduced precipitable water U* = 3.5 g cm -’ (Ceballos et al., 1992).

3.6. Atmospheric absorption: carbon dioxide and ozone

Absorption by CO2 bands in the I%= 700-2000 nm interval is fairly weak. Parameterizations published by Howard et al. (1956a) show that absorption lies between 13 and 28 W rnp2 for zenith angles 0 <Z< 75”.

The ozone Chappuis bands are active within the ;1= 450-760 nm interval. The optical depth is not higher than 0.05 through the atmosphere or 0.04 between the top and 10 km height (Elterman, 1970). The maximum is at 2 = 600 nm. Considering a mean value of 0.02 for the optical depth and zenith angle Z=30”, less than 13 W mm2 is depleted in the upper atmosphere up to 10 km height.

Neither 0, nor CO2 absorption are included in this work, inducing an overestimation of about 30 W m-’ for ground-level irradiance in cloud-free situations.

4. ANALYSIS OF RESULTS

4.1. Extreme countsjelds

Figure 2 illustrates the minimum count (interpolated) distribution in December 1990 at 10:00 local time. An extreme image was built with minimum counts for each of 150 x 200 pixels (10 days were considered). Sampling points were taken each 0.25” of latitude and longitude, and an interpolated grid file with 0.4” x 0.4” resolution was built. A fairly homogeneous field of Bmin approximations is found over the continent (B,i” =35-40), except for brighter (shadowed) areas where airmass convection (hence cloud formation) is very frequent. The eastern shadowed area corresponds to a plateau 500 m high where the tradewind blows from the ocean; the region located at about 6”S, 4O”W is a


Atlantic

-8 -

Fig. 2. Regional distribution of minimal counts at IO:00 local time (IO-day sample). Six solarimetric stations are marked by stars. Cabaceiras and Belem do Brejo do Cruz are labelled CAB and BEL. Shadowed areas indicate remaining cloudiness after masking. Continental minima compatible with water-land transition (dotted rectangles)

identify extended watersheds along San Francisco river.

mountainous area, seeming to present local convection. The boundary between continent and ocean is well defined. Typical ocean values are Bmin = 12. Bmin = 20 corresponds to the water-land transition; it is also observed on the continent, associated with extended watersheds of the Sao Francisco river (dotted squares). The minimal values for two months (December 1990 to January 1991) are similar, but cloudy areas (B,i, > 45) become smaller, as expected. In these areas Bmin was assumed as being equal to that of the neighbouring homogeneous region. The maximum distribution, obtained as described in Section 3.1, made evident typical B,,,,, values of about 120 over the region.

Figure 2 includes the position of six solarimetric stations (which might provide ground references). Cabaceiras and Belem do Brejo do Cruz are labelled CAB and BEL. For the period December 1990 to January 1991, CAB and BEL showed the following extreme pairs (Bmin, B,,,) between 07:OO and 14:00 local time: (18, 50), (19, 50), (35, 110) (35, 120), (33, 140), (28, 140) and (28, 145). Comparison with Fig. 2 suggests that even the rough approximation obtained with a sample of 10 days yields useful information about extreme counts.

4.2. GL model versus ground measurements

Two effective intervals were tested for apply- ing the GL model: /z =420-950 nm and 1, =

450-820 nm. The latter exhibited a definitely biased behaviour with higher planetary reflectances [eqn (lo)] inducing lower GL values in eqn (2). Hereafter, only results for effective interval 1. = 420-950 nm are described.

Figure 3 illustrates regional distributions of irradiation for two days in December 1990 (08:00- 12:OO local time), obtained using the GL model. Typical cloud-system behaviours are observed. Both days exhibit extended convective cloudiness over the western region (area with irradiation lower than 9 MJ mm2 is shadowed). For December 4th, a South Atlantic anticyclone blows from the southeast inducing cloud formation and low irradiation (shadowed area over southern region). The ocean-continent boundary is well delimited by a high-valued threshold (10.8811 MJ m-‘). On December 12th, normal flow from the ocean tends to generate clouds by elevation up to the Borborema plateau; nevertheless, only a small nucleus with values of 10 MJ mm2 or less appears and high irradiations are observed over inland Paraiba. Several ground station values are also included. A good fit is observed for most cases. Generally speak- ing, the GL model reproduces the regional behaviour of solar radiation within a scale of 40 km and seems to present errors lower than 20% for a single day.

Fig. 3. Distribution of solar irradiation in MJ mm2 (08:OO to 12:OO local time) on 4 and 12 December 1990. Values near the stars indicate actinographic data. Lower irradiation

regions affected by clouds are shadowed.


Two particular situations can be noted where cloudiness seems to have local characteristics: at 36”W, 7”s (Dec. 4th) and 38.5”W, 7”s (Dec. 12th). Biases from regional behaviour could be associated with the formation of vertically well developed clouds after 09:OO local time, which are not horizontally large enough to have a strong influence on R,, but are efficient for interception of the direct solar beam just over a solarimetric station. This kind of discrepancy between pixel brightness and ground level irradiation was also commented on by Djemaa and Delorme (1992) concerning Meteosat images of Tunisia.

Figure 4 shows the daily cycle of mean irradi- ante for CAB and BEL (obtained by actinographs) together with GL results. Hourly integrations over (t, t + 1 h) time intervals are represented at (t+ l/2) instants, whilst GL results correspond to instantaneous t = abcissas. It is seen that mean cycles are higher for BEL between 09:30 and 12:30, and the GL model seems to overestimate CAB and BEL irradiance at 12:O0. In particular, overestimation at BEL remains apparent until 14:O0. This behaviour suggests a systematic bias in the planetary reflectance estimates for the interval 12:00-14:O0. This is consistent with the theoreti- cal results of Lubin and Weber (1995) concerning correction factors for the lambertian hypothesis in reflectance assessment [eqn (lo)]. For instance, the solar beam arrives from the south at solar noon in January while Meteosat

loo0 : p 800

i 3 8 600

S 5 2 400

.L

6 7 8 9 10 11 12 13 14 15 16 17 Local time

Fig. 4. Daily cycle of monthly mean irradiance at ground level for January 1991, including the GL model (open symbols) and actinographic measurements (lines). The sites are

Cabaceiras (CAB) and Belem do Brejo do Cruz (BEL).

line-of-sight is more or less towards the west, resulting in a satellite azimuth angle of about 90” related to the sun. This angle is definitely different for European countries or even for African areas. Following Lubin and Weber (1995), the anisotropy of plane-parallel cloud bidirectional reflectance implies a correction factor of about 1.08 for the VIS channels in eqn (10). For local times 10:00 and 14:00, the correction factor is 1.03-l .04. These would also be the factors correcting overestimation in the GL model. In the case of finite cloud fields, Ebel and McKee (1983) also showed that asymmetry must be observed between morning and afternoon reflected sunbeams (as seen by geostationary satellites).

Figure 5 illustrates the results for daily integ- ration of solar irradiance (not exceeding 14:00 local time). The time interval 08:00-14:00 was adopted for January 1991, in order to include lower irradiations. The model exhibits promis- ing behaviour concerning linearity, fitting clear- sky (highest) irradiations well. Overestimation is suggested for BEL and CAB, January 1994, although not exceeding 20%. The reasons for this deviation are not clear, but it could be due to the anisotropy of the reflected beam. Figure 5 suggests a satisfactory behaviour of the estimates, considering that daily (rather than monthly) results are shown.

In order to discuss monthly means, let us state some previous definitions. Let X0 be the “true monthly mean” of N daily values _$ of actual irradiation between local time 07:OO and

I I I I

I ??CAB91:08m14a

,’ ??BELW’aaol‘lm 0 CA9 94 07GSl CO 0 EEL94 07CC14CO

I I I I 5 10 15 20

irradiation - actinograph MJlm”2

Fig. 5. Daily irradiation in MJ rn-’ (local time interval 07:00~14:00): comparison between actinographic and GL results. Epochs: January 1991 and January 1994. The sites are Cabaceiras (CAB) and Belem do Brejo do Cruz (BEL).


14:OO. The circumflex indicates random behaviour. Actinographic records provide daily values _?g with random errors Zi-, (hopefully with no bias), so that 8= Jg +P,. Model values are _%GL, each one with error 9 composed of a systematic bias b and a random fluctuation 2, such that 8= &GL + b + R.

The true mean X0 is actually estimated by the arithmetic mean _i?, of a sample of N values X,, with standard deviation S, for x, and estimated sB = S,/N li2 for the mean zg (itself a random variable); sg is the “mean standard error” (mse) of the estimator for X0. It can be stated that mathematical expectations make

E{Z-,} =E{i} =o,

E{&--GL}=E{y,-XGL}=b, (15)

and variances behave as follows:

var{i} = Sx’,

var{fg - kGL> = S2 = Si + Sx2 .

var{z, -XGL} =S~/N+Sx2/N=s~ +sx2.

(16)

sg and sx are the mean standard errors (mse) associated with fluctuations of means x, and XGL. In particular, sg z 0.04X,, for actinographs (Fattori and Ceballos, 1988). Equation ( 15) shows that XGL values can be corrected for bias b if ground truth is available. The observed standard deviation between these variables allows the assessment of the errors Sx and sx associated with individual values and means of the GL model. Reference ground truth is not always available; in these cases, bias reduction cannot be operated and efictiue (and biased) errors of $GL become z^ = b + $, with expected mean b and mean square (z’) = b2 +Si. The mean of model values will have an effective mean standard error of

(Xg)=[b2 +S;/N]“2. (17)

This equation makes evident how biases signifi- cantly higher than random deviations would control the overall quality of the model.

The numerical behaviour of the GL model is summarized in Table 1. Mean irradiations refer to 8-h sums. In order to assess daily mean irradiances, the S-h mean irradiations were con- verted to daily sums by a correction factor of 1.28 based on observed main daily cycle behaviour (Fig. 4). The standard deviation of the reference measurements (about 0.8 MJ me2 and even less) was neglected, thus becoming included in S, estimates. It is seen that:

(a) The mean bias lies in the interval (-0.4, + 0.5) MJ rnd2. Changes may be due to particular weather conditions in 1991 and 1994. Biases are apparent from the regression coefficients (considering GL values proportional to actinographic results), particularly for CAB in 1991. Nevertheless, the mean irradiance presents biases lower than the recommended value of 10 W mm2 and mean standard errors lower than 25 W mm2 (Whitlock et al., 1995).

(b) Neglecting ozone and carbon dioxide absorption, the daily mean irradiance ,?? is over- estimated by about 15 W mm2 (or about 6% of i?). Another source of overestimation may be the assessment of R, (actually bidirectional) without a correction for asymmetry. Table 1 suggests that their influences are partially bal- anced by other sources of error in the model (for instance, precipitable water absorption, cloudiness assessment and IR ground albedo).

5. CONCLUSIONS

Meteosat images are currently recorded once per hour, and are available at FUNCEME (Fortaleza, CE) in high definition formats (one pixel for a two-line-and-two-column target in the original image). Other state meteorological agencies for northeast Brazil are also capable of such a recording schedule, covering an area of about 2 000 000 km. A simple model was developed for assessing daily solar irradiation over Paraiba State based on hourly Meteosat 4 (VIS channel) imagery; the required files for covering the northeast region do not exceed 120 kbytes, so that complete processing can be performed on a microcomputer.

Irradiation data from the solarimetric network of the Federal University of Paraiba show that regional variations are well described by the model for 4-h sums in a given day. Detailed comparison with two solarimetric stations for January 1991 and 1994 show that: ( 1) the GL model provides mean monthly irradiations within recommended standards for the mean bias and mean standard deviation; (2) the mean daily cycle is well reproduced by the model.

The basic hypotheses (VIS and IR intervals are physically decoupled, and radiation transfer is essentially conservative in the VIS interval) allow the model to be dramatically simplified; on the other hand, the quality of irradiation assessment becomes highly dependent on the proper determination of: ( 1) planetary reflectance (influenced by asymmetry in bidirectional


Table 1. GL model results for time interval 07:00-14:00 (8-h sums) on a monthly basis. Effective mean error includes the effect of the bias b and the mse SG

Month: January Year

Number of days, N

Irradiation (MJ mm’) Monthly mean (effective days only) Mean model bias, b Standard deviation of errors, SC Standard error of the mean, SC/N”* =sg Standard error of the mean (%) Regression coefficient in CL = a.,4 CTINOG Effective error, (b’ +$)1’2

Equivalent mean irradtance (W m-‘) Monthly mean (effective days only), E Model mean bias Standard deviation of daily errors Standard error of the mean

CAB BEL

1991 1994 1991 1994 13 26 15 26

15.1 16.8 15.0 17.9 -0.38 0.49 0.07 0.43

1.7 2.4 2.2 2.1 0.47 0.47 0.57 0.41 3.1 2.8 3.7 2.3

0.93 kO.02 1.01+0.03 0.98 & 0.01 1.01+0.02 0.60 0.68 0.57 0.60

227 252 226 270 -6 7 1 6 25 35 32 31

7 7 8 6

reflectance); (2) ground VIS albedo (which requires convenient cloud masking in order to detect clear-sky conditions. However, the albedo may be highly variable during the rainy season). It is expected that a proper climatology of count extrema (minima and maxima) will allow improvement of information on ground reflectance and cloudiness, leading to lower mean biases and standard errors. Low regional turbidity may contribute to the success of the model.

Further refinements may be introduced, such as an explicit account of ozone and carbon dioxide absorption, as well as conservative flux transfer by clouds within solar infrared and aerosol attenuation. All of these refinements can be easily included in the model; however, preliminary results suggest that they are only of second order for the proper assessment of cloudiness and corrected (bidirectional) cloud reflectances. It seems convenient to use IR channel images in order to obtain a more precise definition of cloudiness; perhaps the B,,,,, parameter should be stratified allowing for different types of clouds present in a scene. On the other hand, simultaneous observations by two geostationary satellites (Meteosat 3 and 5 were available in part of 1994-95) can help to develop ad hoc corrections of R, allowing for anisotropic cloud reflection. This procedure can be readily adapted for the present image recording in the region (Meteosat 5 over 0”W as well as GOES over IYW).

Validation of the GL model must be carried out for longer time series, including the rainy season. Nevertheless, this version appears to be a useful tool for solar radiation monitoring,

yielding reliable means for at least 15-day periods.

Acknowledgements-The Brazilian CNPq partially sup- ported this work. The authors also recognize the persistent enthusiasm of the authorities from FUNCEME (Fundacao Cearense de Meteorologia e Recursos Hidricos), who provided satellite imagery as well as some of the computer facilities.

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Solar radiation assessment using Meteosat 4-VIS imagery