Assessment of some global solar radiation ... - Semantic Scholar

Journal of Atmospheric and Solar-Terrestrial Physics 64 (2002) 1631 – 1643

www.elsevier.com/locate/jastp

Assessment of some global solar radiation parameterizations M.G. Iziomon ∗ , H. Mayer Meteorological Institute, University of Freiburg, Werderring 10, D-79085 Freiburg, Germany Received 17 May 2001; received in revised form 14 January 2002; accepted 12 April 2002

Abstract In spite of their practicability, most classical models are not versatile but rather restrictive in their application. Consequently, their applicability for a particular location depends largely on validation against actual measurements. Global solar radiation parameterizations have been evaluated in this study for a lowland and a mountain site. Tested models were broadly categorised 4 as cloud-based (Kasten) and sunshine-based (Angstr5 om–Prescott, Garg and Garg, Sivkov). Data sets utilised for the evaluation extended from 1991 to 1994. Adjustable parameters in the models were determined. Observed monthly mean values of solar radiation G and those estimated using Kasten model agreed within 2.5% for the lowland site and 13% for the mountain site. Root mean square errors of estimated hourly values of G using Kasten model appreciated signi=cantly with fractional cloud 4 cover N (particularly for N ¿ 4 octals). For the study sites as well as other locations examined here, Angstr5 om–Prescott coe?cients did not show a distinctive trend with respect to season, geographical co-ordinate or altitude. Monthly mean values 4 of G estimated using Angstr5 om–Prescott model agreed with observation within 2.5% for the lowland site and 3.4% for 4 the mountain site. The e@ect of air mass, latitude and water vapour terms on the Angstr5 om–Prescott relation has also been 4 investigated. In general, Angstr5 om–Prescott as well as Garg and Garg models yielded the least RMSE (¡ 0:047) for the study c 2002 Elsevier Science Ltd. All rights reserved. sites and are thus recommended for estimating G for an arbitrary location. Keywords: Solar radiation; Cloud cover; Sunshine duration; Atmospheric transparency index; Water vapour; Air mass

1. Introduction By providing energy which may be converted into sensible, latent or ground heat Eux, solar radiation G arriving on the ground plays a key role in the energy balance of the Earth-Atmosphere system. Consequently, G is a major input to agronomic, ecological, hydrological and soil-vegetation-atmosphere transfer models, while also serving as a valuable resource for validating general circulation models (Garratt 1994; Hansen, 1999; Mariscal et al., 2000). In addition, solar energy systems (including high e?ciency solar heating panels, photovoltaic energy generation, solar dryers and solar sprayers) are currently being extensively ∗ Corresponding author. Present address: Department of Physics and Atmospheric Science, Dalhousie University, Halifax, Canada. Tel.: +1-902-494-1820; fax: +1-902-494-5191. E-mail addresses: [email protected] (M.G. Iziomon), [email protected] (H. Mayer).

utilised in the =eld of agriculture, architecture, photobiology and medicine (Hammonds, 2000; Ianetz et al., 2000). In spite of its signi=cance, solar radiation is infrequently measured compared to other variables such as temperature and rainfall (Wilks, 1999; Thornton and Running, 1999; Liu and Scott, 2001). Insu?cient solar radiation data has been reported in a number of countries including USA (Hook and McClendon, 1992; Augustine et al., 2000), Canada (De Jong and Stewart, 1993) and Australia (Liu and Scott, 2001). In addition, most of the existing radiation measurements on the globe cover mainly lowland areas so that most information available is inevitably biased towards lower elevation (Barry, 1992). Lack of adequate observations on solar radiation has been a persistent problem in studies of land-surface processes (Thornton and Running, 1999). Hence, alternative techniques are required to estimate solar radiation. In current practice, extrapolation from a nearby station, interpolation in networks (e.g. spline interpolation, Kriging or polynomial surface trend analysis) as well as

c 2002 Elsevier Science Ltd. All rights reserved. 1364-6826/02/$ - see front matter PII: S 1 3 6 4 - 6 8 2 6 ( 0 2 ) 0 0 1 3 1 - 1

1632

M.G. Iziomon, H. Mayer / Journal of Atmospheric and Solar-Terrestrial Physics 64 (2002) 1631 – 1643

Table 1 Monthly mean of meteorological variables at Bremgarten lowland site (Br) and Feldberg mountain site (Fe) in south-west Germany (1992– 1995) Month

January February March April May June July August September October November December

Temperature (◦ C)

Vapour pressure (hPa)

Relative humidity (%)

Wind speed (m s−1 ) Precipitation (mm)

Br

Fe

Br

Fe

Br

Fe

Br

Fe

Br

Fe

3.25 3.55 6.79 9.93 14.60 17.18 20.65 19.70 14.31 10.45 5.84 3.73

− 2.30 − 1.16 − 1.81 2.53 7.28 8.93 12.48 12.55 7.55 4.86 1.38 − 0.68

6.77 6.82 7.47 8.69 11.92 14.16 16.97 15.89 13.06 11.00 8.47 7.11

4.81 4.63 4.71 6.12 7.76 9.80 11.79 11.63 8.96 7.12 5.61 5.13

86.03 85.88 75.30 72.16 73.63 73.60 71.34 71.48 80.59 84.95 87.63 87.36

88.78 83.20 81.13 80.35 77.24 85.69 81.49 80.12 83.97 82.76 83.74 87.79

4.4 3.6 4.2 3.8 3.0 3.1 3.0 3.1 3.0 2.9 2.9 4.3

9.9 6.9 6.8 6.7 5.8 5.9 5.3 6.1 6.7 6.7 6.9 8.7

41 35 36 53 105 67 59 71 88 56 38 56

104 78 103 94 159 133 155 122 174 130 141 181

satellite-based methods are often considered as reasonable techniques for estimating solar radiation (Gupta et al., 1999; Pinker et al., 2000). However, there are constraints with respect to the accuracy of estimated values and for regions characterised by pronounced heterogeneous terrain. Other alternative techniques for estimating solar radiation include stochastic weather generation using a continuous multivariate stochastic process or the application of empirical models. Stochastic method (Hansen, 1999; Wilks, 1999) may be useful in exploring theoretical model scenarios over a long time period. However, since this approach neither generates extreme weather condition (such as frost) reliably, nor produces data which match actual weather condition at a particular time of interest, its generated data are generally considered unsuitable for model validation (Wallis and Gri?ths, 1995; Liu and Scott, 2001). Apart from astronomical and geographical factors, incoming solar radiation is strongly modi=ed by cloud cover, albedo of the underlying surface, atmospheric turbidity, absorption and scattering. Empirical models which express global solar radiation as a function of these variables have been proposed by various investigators including Kasten (1983), Kamel et al. (1993), Thornton and Running (1999) and Meza and Varas (2000). In view of its practicability, empirical approach is generally preferred to other aforementioned methods (Badescu, 1997; Liu and Scott, 2001). However, since most proposed empirical models are not versatile but rather restrictive in their application, their suitability for a particular location would largely depend on validation against actual measurements. In light of this, this study is aimed at assessing some empirical solar radiation parameterizations with respect to a lowland and a mountain site. In particular, the capability of cloud-based and sunshine-based radiation models at reproducing actual measurements shall be evaluated.

2. Experimental sites and treatment of data The experimental sites used for this study are strategically located at Bremgarten (47◦ 54 35 N; 7◦ 37 18 E) within the Upper Rhine lowland area and at Feldberg (47◦ 52 31 N; 8◦ 00 11 E) on the mountain top of the Black Forest in south-west Germany. The surfaces of the experimental sites are grasslands. Bremgarten has an elevation of 212 m a.s.l. while Feldberg has an elevation of 1489 m a.s.l. Global solar radiation at the sites was measured by a horizontally positioned CM11 pyranometer (Kipp & Zonen, Delft, Netherlands) installed at 2 m above ground, while air temperature and humidity were measured by a wet and dry bulb psychrometer system at the same level. Measurement extended from January 1991 to September 1996 at Bremgarten lowland site and from July 1991 to September 1996 at Feldberg mountain site. However, the data set for 1994 at Feldberg was only restricted to the second half of the year (owing to storm-induced collapse of the measuring mast and the consequent lack of data from January to June 1994 for this mountain site). Data acquisition system was based on a Campbell Scienti=c 21X micro data logger with 10 s sampling rate and 10 min integration time. Hourly mean values were determined from the integrated values. Table 1 presents monthly mean of air temperature, vapour pressure, relative humidity, wind speed and total precipitation for the study sites over four years (1992–1995). Expectedly, monthly values of air temperature and vapour pressure, both of which reached a maximum in July at both sites, were greater at the lowland site relative to the mountain site. In addition, monthly mean values of wind speed and precipitation showed strong dependence on altitude, being higher at the mountain site throughout the year. For most months, the relative humidity at the mountain site exceeded that at the lowland site.


In addition to the aforementioned variables, which were directly measured at the study sites, hourly data on cloud cover and visibility for Feldberg (January 1991–October 1994) as well as data on sunshine duration for Feldberg (January 1991–October 1994) and Bremgarten (January 1991–February 1995) were obtained from the German Weather Service, which runs observation stations at these locations. Furthermore, hourly cloud cover data for Bremgarten extending from January 1991 to February 1993 was obtained from German Geophysical Consultant Services. 3. Solar radiation parameterizations Kasten (1983) proposed the following parameterization for estimating solar radiation as a function of fractional cloud cover N (octal) for solar elevation 6 66◦ :

G(N ) = G(0) 1 − a

N 8

b

;

(1)

where a and b are empirical coe?cients and G(0) represents the potential (clear-sky) solar radiation. G(0) was computed in this study according to DIN-VDI (1999) G(0) = 0:84I0 sin exp

−0:027

P P0

TL

sin ;

(2)

where I0 represents the intensity of the extraterrestrial solar radiation, TL is the Linke turbidity factor (given as 0:84 + 39=(Vm ), with Vm been the visibility in km), P=P0 denotes the pressure correction factor for reducing optical thickness of the standard atmosphere P0 to the current atmospheric pressure P at altitude z. The pressure correction factor was obtained as P z = exp − ; P0 8434:5m

(3)

1 [sin + a ( + b )−c ]

S S0

(6)

where G represents monthly global radiation (originally expressed in cal cm−2 ) and noon denotes noon solar elevation on the 15th day of the month. Although water vapour content of the atmosphere absorbs mainly in the longwave bands, it also attenuates a small portion of direct solar radiation by absorption. Water vapour inEuences atmospheric transmissivity through refraction e@ects. Calculations by Tamm and Thormalla (1992), for example, show that increase in water vapour from 1.0 to 4:0 cm H2 O in the vertical column reduces daily mean of G by 5.6% for a cloudless sky. Garg and Garg (1982) proposed a relation of the type G S + ZWat ; (7) = X +Y E0 S0 for obtaining monthly mean daily global radiation where Wat (g m−3 ) is the atmospheric water vapour content per unit volume of air and X; Y; Z are variable coe?cients. Wat for the study sites was computed according to Hussain (1984) viz. Wat = RH(4:7923 + 0:3647Ta + 0:0055Ta2 + 0:0003Ta3 )

(8)

4. Results and discussion ◦

;

G = 4:9(S)1:31 + 10; 550(sin noon )2:1 ;

(4)

and a = 0:50572, b = 6:07995 and c = 1:6364. 4 4 Angstr5 om–Prescott (Angstr5 om, 1924; Prescott, 1940) model for estimating global solar radiation has gained much popularity over the years. This model is given in its original form as G =A+B E0

respectively, and S and S0 denote the corresponding sunshine duration (h) and day length (h). A and B are re4 ferred to as Angstr5 om–Prescott coe?cients. These coe?cients are a@ected by the optical properties of cloud cover 4 and ground reEectivity. In particular, the sum of Angstr5 om– Prescott coe?cients (i.e. A + B) for a particular location could be termed its atmospheric transparency index (ATI) (Dogniaux, 1994). The path length of solar beam through the atmosphere is determined by the optical air mass, which is the reciprocal of the sine of solar elevation. An empirical model for estimating G based on sunshine duration and optical air mass was proposed by Sivkov (1964) as

where air temperature Ta is in ◦ C and relative humidity RH is a fraction (0.0 –1.0). These variables were determined from surface measurements.

where the relative optical air mass m is given by m=

1633

(5)

where G and E0 represent daily total of global solar radiation (MJ m−2 d −1 ) and extraterrestrial radiation (MJ m−2 d −1 ),

4.1. Solar radiation parameterization based on cloud-cover On inputting hourly values of solar radiation data, cloud cover and G(0) for the study sites into Eq. (1), coe?cients a and b were determined as a = 0:79 (Bremgarten); a = 0:69 (Feldberg) and b = 3:21 (Bremgarten); b = 3:62 (Feldberg) with the standard errors being 0.0063 (a, Bremgarten), 0.0079 (a, Feldberg), 0.050 (b, Bremgarten) and 0.083 (b, Feldberg). Fig. 1 presents the quotient G(N )=G(0) versus fractional cloud cover for Bremgarten lowland site,

1634

M.G. Iziomon, H. Mayer / Journal of Atmospheric and Solar-Terrestrial Physics 64 (2002) 1631 – 1643 1.0 Feldberg a = 0.69, b = 3.62

G (N)/G(0)

0.8

Bremgarten a = 0.79, b = 3.21

0.6

Kasten (1983) a = 0.72, b = 3.20

0.4

0.2

0.0 0

2

4

6

8

N (octal) Fig. 1. Ratio of incoming solar radiation to potential (i.e. clear sky) solar radiation (G(N )=G(0)) as a function of fractional cloud cover N for Bremgarten lowland site and Feldberg mountain site as well as that originally proposed by Kasten (1983).

Feldberg mountain site and that originally reported by Kasten (1983). With increasing fractional cloud cover, the depletion of solar radiation becomes more pronounced for N ¿ 5 octa particularly at the lowland site. Fig. 2 presents monthly mean of daily total of G for two years period computed using Kasten model versus measured values for the lowland and mountain sites. The coe?cients used in Kasten model are those obtained for the respective sites. Measured and computed monthly mean values of G agreed within 2.5% for Bremgarten lowland site while those for Feldberg mountain site agreed within 13%. Observed lower accuracy of estimates for Feldberg mountain site could imply that the dependence of solar radiation on cloud cover (particularly for high altitude) is not entirely deterministic (see also Fig. 3, which presents a case of computed and measured values of G for N = 4 octals). For instance, high daily sums of global radiation can result from broken clouds due to reEection from the sides of the clouds. Fig. 4 presents mean bias error MBE and root mean square error RMSE of estimated hourly global solar radiation as a function of fractional cloud cover at the study sites. Although measured values of G and those obtained using Kasten model are in fairly good agreement particularly for N 6 4 octals (where RMSE ≈ 0:24), systematic larger differences between observed and computed values at small solar elevation and as N →8 octals, however, present a major limitation of this model. Correlation of G=E0 (where E0 =I0 sin ) with daily mean of fractional cloud cover NT (octal) for the lowland site (Br) and mountain site (Fe) yielded Eqs. (9) and (10), with a

standard error of 0.08 for the lowland site and 0.12 for the mountain site G 2 (Br) = 0:631 + 0:0382NT − 0:0133NT ; E0 G 2 (Fe) = 0:737 + 0:014NT − 0:0077NT : E0

(9) (10)

From Eqs. (9) and (10) (obtained from this study), it follows that given a clear sky day (NT = 0) at both study locations, daily atmospheric clearness index (G=E0 ) at the mountain grassland site exceeds that at the lowland grassland site with an order of 10%. This could be owing to the e@ect of reduced air mass and shorter path length at the high elevation. 4.2. Solar radiation parameterizations based on sunshine duration Fig. 5 presents correlation of four years (1991–1994) hourly values of G=E0 with S=S0 at the study sites. The coe?cients of Eq. (5) were determined as A = 0:19 (Bremgarten); A = 0:20 (Feldberg) and B = 0:60 (Bremgarten); B = 0:59 (Feldberg). These coe?cients shall afterwards 4 be referred to as annual Angstr5 om–Prescott coe?cients. Table 2 presents annual coe?cients A, B and resulting ATI for the study sites as well as those reported for some other locations (Dogniaux, 1994) in Germany. Also included in Table 2 is the calculated latitude-dependent ATI (Dogniaux, 1994) for each of the sites. For the locations presented in Table 2, the magnitude of the annual coef=cient A ranged between 0.19 and 0.24, while B ranged


1635

25

Bremgarten

-2 -1

Computed G (MJ m d )

20

15

10 Kasten model 5

0 0

5

10

15

20

25

25

Feldberg

-2 -1

Computed G (MJ m d )

20

15

10 Kasten model 5

0 0

5

10

15 -2

20

25

-1

Measured G (MJ m d )

Fig. 2. Monthly mean of daily total of global solar radiation G computed using Kasten model versus measured values for Bremgarten lowland site (1991–1992) and Feldberg mountain site (1992–1993).

4 between 0.55 and 0.61. Although Angstr5 om–Prescott coe?cients did not show any distinctive trend with respect to altitude or geographical co-ordinate, observed ATI for most of the locations (including those examined here) was 0.79. It is also noteworthy that the di@erence between observed and calculated ATI for both Bremgarten lowland and Feldberg mountain sites amounted to only 0.01. 4 Angstr5 om–Prescott coe?cients were also determined on monthly basis for the study sites. Fig. 6 presents monthly 4 values of Angstr5 om–Prescott coe?cients A and B as well as ATI for the study sites and two other nearby locations namely: Freiburg (48◦ 00 09 N; 7◦ 51 33 E, 286 m a.s.l.) and Hartheim (47◦ 56 04 N; 7◦ 36 04 E, 201 m a.s.l.). The former is an urban meteorological station while the latter is

a forest (Scots pine) meteorological station (Mayer et al., 2000). Although slight inter-site similarities in annual features of these indices can be observed, no general systematic seasonal trend was found. The latter could be attributed to variation in local climatic conditions. In general, A and B vary inversely for most of the year, with A varying more rapidly than B. Annually, A showed a variability of 11% for Bremgarten lowland site and 16% for Feldberg mountain site while B exhibited a variability of 7.4% and 5.5% for the respective sites. Fig. 7 presents observed monthly mean of daily totals of G and those estimated using annual and monthly 4 Angstr5 om–Prescott coe?cients at the study sites. The use of 4 monthly Angstr5 om–Prescott coe?cients in Eq. (5) produced

1636

M.G. Iziomon, H. Mayer / Journal of Atmospheric and Solar-Terrestrial Physics 64 (2002) 1631 – 1643 1000 Bremgarten

−2

Computed G (W m )

800

600

400

Computed G (Kasten) = 0.94 Measured G R 2 = 0.886

200

0 0

200

400

600

800

1000

1000 Feldberg

Computed G (W m−2)

800

600

400

Computed G (Kasten) = 0.93 Measured G R2 = 0.800

200

0 0

200

400

600

800

1000

−2

Measured G (W m )

Fig. 3. Hourly global solar radiation G computed using Kasten model (with N = 4 octals) versus measured values for Bremgarten (January 1991–February 1993) and Feldberg (July 1991–October 1994).

estimates of higher accuracy and coe?cient of determination than annual coe?cients. Observed and estimated 4 monthly values of G (using monthly Angstr5 om–Prescott coe?cients) agreed within 2.5% for lowland site and 3.4% 4 for the mountain site, while those from annual Angstr5 om– Prescott coe?cients agreed within 3.7% for the lowland site and 6.0% for the mountain site. 4 Incorporating latitude term into Angstr5 om–Prescott yields G S ; (11) = C cos + D S0 E0

where the constants C and D for the study sites amounted to C = 0:29 (Bremgarten); C = 0:30 (Feldberg) and D = 0:60 (Bremgarten); D = 0:59 (Feldberg) with overall standard error of 6% for Bremgarten and 7.1% for Feldberg. The closeness of obtained constants for the sites is indicative of 4 the little e@ect of a latitude adjustment term on Angstr5 om– Prescott relation (see also Table 2). On inputting monthly mean values of G, E0 , S=S0 , Wat into Eq. (7), the coe?cients X; Y and Z of Garg and Garg model were determined as X = 0:212 (Bremgarten), X = 0:257 (Feldberg); Y = 0:629


1637

0.8 MBE (Bremgarten) MBE (Feldberg) RMSE (Bremgarten) RMSE (Feldberg)

0.6

MBE, RMSE

0.4

0.2

0.0

-0.2

-0.4 1

2

3

4

5

6

7

8

N (octal)

Fig. 4. Mean bias error (MBE) and root mean square error (RMSE) of estimated hourly global solar irradiance as a function of fractional cloud cover N for Bremgarten (January 1991–February 1993) and Feldberg (July 1991–October 1994).

Table 2 4 Angstr5 om–Prescott coe?cients A, B and atmospheric transparency index ATI for study sites (Bremgarten and Feldberg) and those reported for other sites in Germany in decreasing order of latitude (see text) Site

Latitude (degree and minute)

Longitude (degree and minute)

Altitude (m a.s.l.)

A

B

ATIa

ATIb

||c

Nordeney Hamburg Braunschweig Braunlage W5urzburg Trier Weihenstephan Bremgartend Feldbergd Hohenpeissenberg

53 53 52 51 49 49 48 47 47 47

07 10 10 10 09 06 11 07 08 11

13 14 81 601 259 265 467 212 1489 975

0.22 0.19 0.19 0.19 0.23 0.20 0.24 0.19 0.20 0.22

0.58 0.55 0.55 0.59 0.56 0.59 0.55 0.60 0.59 0.61

0.80 0.74 0.74 0.78 0.79 0.79 0.79 0.79 0.79 0.83

0.79 0.79 0.79 0.79 0.79 0.79 0.78 0.78 0.78 0.78

0.01 0.05 0.05 0.01 0.00 0.00 0.01 0.01 0.01 0.05

43 38 18 43 48 45 24 54 52 48

N N N N N N N N N N

09 00 27 37 54 40 44 37 00 01

E E E E E E E E E E

a Observed

ATI. ATI. c Di@erence between observed and calculated ATI. d Results emanating from present study. b Calculated

(Bremgarten), Y = 0:5984 (Feldberg) and Z = −0:00334 (Bremgarten), Z = −0:00911 (Feldberg). Of the three coe?cients in Eq. (7), it is noteworthy that water vapour coe?cient Z di@ered considerably for both lowland and mountain sites, thus indicating the obvi4 ous e@ect of water vapour term on Angstr5 om–Prescott relation. Observed monthly mean values of daily total of G and those computed using Garg and Garg model agree closely to 3% for Bremgarten lowland site

and 5% for Feldberg mountain site (see Fig. 8 and Table 3). The test of Sivkov model with experimental data for the study sites showed the need for a multiplying factor of 0.00228 for the right hand side of Eq. (4). Subsequent application of Sivkov model produced monthly mean estimates of G (MJ m−2 d −1 ) which agreed with observation within 4.5% for the lowland site and 10% for the mountain site (see Fig. 8 and Table 3).

1638

M.G. Iziomon, H. Mayer / Journal of Atmospheric and Solar-Terrestrial Physics 64 (2002) 1631 – 1643 1.0

Bremgarten 0.8

G /EO

0.6

0.4

0.2

0.0 0.0

0.2

0.4

0.2

0.4

0.6

0.8

1.0

0.6

0.8

1.0

1.0

Feldberg

0.8

G /EO

0.6

0.4

0.2

0.0 0.0

S/SO

Fig. 5. Plot of daily total of G=E0 versus S=S0 for Bremgarten lowland site and Feldberg mountain site (1991–1994).

4.3. Statistical assessment of examined models Table 3 presents MBE and RMSE of monthly estimates of tested empirical models for the study sites as well as regression equations for Figs. 2, 6 and 8, which relate computed monthly solar radiation Gc to measured solar radiation Gm . Negative MBE implies 4 an underestimation of G. Angstr5 om–Prescott and Garg and Garg models yielded the lowest RMSE, highest coe?cient of determination and the best regression equations followed by Kasten model. Sivkov model, which require only sunshine duration and solar elevation as input parameters, gave the worst RMSE for

both sites. In particular, it is noteworthy that the inclu4 sion of water vapour and air mass terms in Angstr5 om– Prescott relation did not signi=cantly improve estimates of G. 5. Concluding remarks Accurate computer simulation of terrestrial ecosystem process depend largely on reliable estimates of solar radiation. In view of this requirement, this study examines the suitability of some cloud-based and sunshine based radiation models for the


1639

0.3 Bremgarten

Feldberg

Hartheim

Freiburg

A

0.2

0.1

0.0

(a)

Jan

Mar

May

Jul

Sep

Nov

Jan

Mar

May

Jul

Sep

Nov

Jan

Mar

May

Jul

Sep

Nov

0.8

B

0.6

0.4

0.2

0.0

(b)

Atmospheric transparency index

0.90

0.85

0.80

0.75

0.70

0.65

(c)

Month

4 Fig. 6. Annual variation of coe?cients A and B of Angstr5 om–Prescott model, and atmospheric transparency index for Bremgarten (1991–1994), Feldberg (1991–1994), Hartheim (1976 –1989) and Freiburg (1976 –1989) in south-west Germany.

1640

M.G. Iziomon, H. Mayer / Journal of Atmospheric and Solar-Terrestrial Physics 64 (2002) 1631 – 1643 25

Computed G (MJ m−2 d −1)

20

Ångström-Prescott model using monthly coefficients Ångström-Prescott model using annual coefficients

15

Bremgarten

10

5

0 0

5

10

15

20

25

25

Computed G (MJ m −2 d−1)

20

Ångström-Prescott model using monthly coefficients

15

Feldberg

Ångström-Prescott model using annual coefficients 10

5

0 0

5

10

15

20

25

4 Fig. 7. Observed monthly mean of daily totals of G and those estimated using annual and monthly Angstr5 om–Prescott coe?cients for the period 1991–1994 at Bremgarten lowland site and Feldberg mountain site. Thin and broken lines mark 1 : 1 data to projection ratio resulting 4 from the use of annual and monthly coe?cients respectively in the Angstr5 om–Prescott model.

estimation of solar radiation at two strategic locations of di@erent altitude. Although observed values of solar radiation and those estimated using cloud-based Kasten model are in a fairly good agreement, the accuracy of the estimated G declined as N →8 octals and for the mountain site. This presents a major limitation to this model. One advantage of Kasten model, however, is that it can be used to simulate various time scales (ranging from hourly to monthly values) of G.

Highest values of ATI for the lowland site occurred during winter while those for the mountain site were ob4 tained in March and April. Although Angstr5 om–Prescott coe?cients did not show any particular trend with respect to altitude, season or geographical co-ordinate, observed ATI for most locations (including those examined here) averaged 0.79. In comparison with Kasten 4 cloud-based model, Angstr5 om–Prescott as well as Garg and Garg sunshine-based models predicted monthly values of G with higher accuracy, yielding lower RMSE


1641

25

Computed G (MJ m−2 d −1)

20

15 Garg and Garg model

Bremgarten

Sivkov model 10

5

0 0

5

10

15

20

25

25

Computed G (MJ m −2 d−1)

20

15 Garg and Garg model Sivkov model

Feldberg

10

5

0 0

5

10

15 −2

20

25

−1

Measured G (MJ m d )

Fig. 8. Monthly mean of daily total of global solar radiation G computed using Sivkov model and Garg and Garg model for Bremgarten lowland site (1991–1994) and Feldberg mountain site (1991–1994) versus measured values. Solid and broken lines mark 1 : 1 data to projection ratio for Garg and Garg model and Sivkov model, respectively.

for both the lowland and mountain sites examined. Thus, while solar radiation can be estimated from both cloud cover and sunshine duration, the latter appears to be a more realistic index of solar radiation for an arbitrary location. Future study shall explore the predictability of solar radiation from additional variables including air temperature and precipitation, both of which are routinely measured at most radiometric sites.

Acknowledgements This study was carried out within the framework of a regional climate project (REKLIP) funded by the Ministry of Science and Research, Baden-Wuerttemberg, Germany. Thanks are due to the awarding agency as well as to Prof. em. A. Kessler, Prof. Dr. L. Jaeger and Mr. W. Wicke for their participation in REKLIP on behalf of the Meteorological Institute, University of Freiburg, Germany. We also thank

1642


Table 3 Regression equations relating computed monthly solar radiation Gc to measured solar radiation Gm , coe?cient of determination R2 as well as mean bias error (MBE) and root mean square error (RMSE) of monthly estimates of tested models Model

Bremgarten lowland site Gc (MJ m−2 d −1 ); Gm (MJ m−2 d −1 )

Feldberg mountain site Gc (MJ m−2 d −1 ); Gm (MJ m−2 d −1 )

Kasten (see Fig. 2)

Gc = 0:97Gm ; R2 = 0:992 MBE = −0:014; RMSE = 0:062

Gc = 0:90Gm ; R2 = 0:971 MBE = −0:104; RMSE = 0:13

4 Angstr5 om–Prescott (using monthly coe?cients) (see Fig. 7)

Gc = 0:99Gm ; R2 = 0:998 MBE = −0:0075; RMSE = 0:0092

Gc = 1:00Gm ; R2 = 0:991 MBE = −0:0025; RMSE = 0:046

4 Angstr5 om–Prescott (using annual coe?cients) (see Fig. 7)

Gc = 0:98Gm ; R2 = 0:994 MBE = −0:016; RMSE = 0:026

Gc = 1:000Gm ; R2 = 0:978 MBE = −0:0031; RMSE = 0:074

Garg and Garg (see Fig. 8)

Gc = 0:99Gm ; R2 = 0:994 MBE = −0:0030; RMSE = 0:045

Gc = 0:99Gm ; R2 = 0:991 MBE = −0:0074; RMSE = 0:046

Sivkov (see Fig. 8)

Gc = 0:95Gm ; R2 = 0:962 MBE = −0:0024; RMSE = 0:12

Gc = 1:00Gm ; R2 = 0:889 MBE = −0:040; RMSE = 0:37

the German academic exchange service (DAAD) and the Killam Trust for supporting this study. References 4 Angstr5 om, A., 1924. Solar and terrestrial radiation. Quarterly Journal of the Royal Meteorological Society 50, 121–125. Augustine, J.A., DeLuisi, J.J., Long, C.N., 2000. SURFRAD-A national surface radiation budget network for atmospheric research. Bulletin of the American Meteorological Society 81, 2341–2356. Badescu, V., 1997. Veri=cation of some very simple clear and cloudy sky models to evaluate global solar irradiance. Solar Energy 61, 251–264. Barry, R.G., 1992. Mountain weather and climate. USA, Methuen and Co. Ltd., 402pp. De Jong, R., Stewart, D.W., 1993. Estimating global solar radiation from common meteorological observations in Western Canada. Canadian Journal of Plant Science 73, 509–518. DIN-VDI, 1999. Environmental meteorology, Meteorological measurements, Part 2—Global radiation, turbidity, visual weather observations, meteorological measuring stations for agric purposes. Handbook 333, Beuth Verlag, Berlin. Dogniaux, R., 1994. Prediction of Solar Radiation in Areas with a Speci=c Microclimate. Commission of the European communities. Kluwer Academic Publishers, Dordrecht. Garratt, J.R., 1994. Incoming shortwave Euxes at the surface—A comparison of GCM results observations. Journal of Climate 7, 72–80. Garg, H.P., Garg, S.T., 1982. Prediction of global solar radiation from bright sunshine hours and other meteorological parameters. Solar-India, Proceedings of the National Solar Energy convention. Allied Publishers, New Delhi, pp. 1.004 – 1.007. Gupta, S.K., Ritchey, N.A., Wilber, A.C., Whitlock, C.H., Gibson, G.G., Stackhouse Jr., W.P., 1999. A climatology of surface

radiation budget derived from satellite data. Journal of Climate 12, 2691–2710. Hammonds, M., 2000. Solar photovoltaics. Renewable Energy Focus July=August 2000, pp. 28–29. Hansen, J.W., 1999. Stochastic daily solar irradiance for biological modeling applications. Agricultural and Forest Meteorology 94, 53–63. Hook, J.E., McClendon, R.W., 1992. Estimation of solar radiation data missing from long-term meteorological records. Agronomy Journal 84, 739–742. Hussain, M., 1984. Estimation of global and di@use irradiation from sunshine duration and atmospheric water vapour content. Solar Energy 33, 217–220. Ianetz, A., Lyubansky, V., Setter, I., Evseev, E.G., Kudish, A.I., 2000. A method for characterization of sites with regard to solar energy utilization by statistical analysis of their solar radiation data as performed for three sites in the Israel Negev Region. Solar Energy 69, 283–293. Kamel, M.A., Shalaby, S.A., Mostafa, S.S., 1993. Solar radiation over Egypt: comparison of predicted and measured meteorological data. Solar Energy 50, 463–467. Kasten, F., 1983. Parametriserung der Globalstrahlung durch Bedeckungsgrad und Tr5ubungsfaktor.-Annal. Annalen der Meteorologie 20, 49–50. Liu, D.L., Scott, B.J., 2001. Estimation of solar radiation in Australia from rainfall and temperature observations. Agricultural and Forest Meteorology 106, 41–59. Mariscal, M.J., Orgaz, F., Villalobos, F.J., 2000. Modelling and measurement of radiation interception by olive canopies. Agricultural and Forest Meteorology 100, 183–197. Mayer, H., Jaeger, L., Matzarakis, A., Fernbach, G., Redepenning, D., 2000. Forstmeteorologische Messtelle Hartheim des Meteorologischen Institut der Universit5at Freiburg. Bericht des Meteorologischen Institutes der Universit5at Freiburg 5, 55–83. Meza, F., Varas, E., 2000. Estimation of mean monthly solar global radiation as a function of temperature. Agricultural and Forest Meteorology 100, 231–241.

M.G. Iziomon, H. Mayer / Journal of Atmospheric and Solar-Terrestrial Physics 64 (2002) 1631 – 1643 Pinker, R.T., Laszlo, I., Goodrich, D., Pandithurai, G., 2000. Satellite estimates of surface radiative Euxes for the extended San Pedro Basin: sensitivity to aerosols. Agricultural and Forest Meteorology 105, 43–54. Prescott, J.A., 1940. Evaporation from a water surface in relation to solar radiation. Transactions of the Royal Society of Science, Australia 64, 114–125. Sivkov, S.I., 1964. To the method of computing possible radiation in Italy. Transaction of the Main Geophysical Observatory 160. Tamm, E., Thormalla, E., 1992. Handbook of Helionda: a program to simulate the e@ects of Meteorology, Place and Time. J5ulich: BMFT-Forschungsprojekt 0328932A.

1643

Thornton, P.E., Running, S.W., 1999. An improved algorithm for estimating incident daily solar radiation from measurements of temperature, humidity, and precipitation. Agricultural and Forest Meteorology 93, 211–228. Wallis, T.W.R., Gri?ths, J.F., 1995. An assessment of the weather generator (WXGEN) used in the erosion=productivity impact calculator. Agricultural and Forest Meteorology 73, 115–133. Wilks, D.S., 1999. Simultaneous stochastic simulation of daily precipitation, temperature and solar radiation at multiple sites in complex terrain. Agricultural and Forest Meteorology 96, 85–101.