Analysis of atmospheric turbidity levels at Taichung Harbor near the Taiwan Strait

Atmospheric Research 94 (2009) 168–177

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Atmospheric Research j o u r n a l h o m e p a g e : w w w. e l s e v i e r. c o m / l o c a t e / a t m o s

Analysis of atmospheric turbidity levels at Taichung Harbor near the Taiwan Strait Chih-Chung Wen ⁎, Hui-Hsuan Yeh Department of Safety, Health and Environmental Engineering, Hungkuang University, Sha-Lu, Taichung 433, Taiwan

a r t i c l e

i n f o

Article history: Received 3 March 2008 Received in revised form 20 January 2009 Accepted 14 May 2009 Keywords: Linke turbidity factor Angstrom turbidity Taichung Harbor Solar radiation

a b s t r a c t In this study, two universal turbidity parameters, the Angstrom turbidity coefficient and Linke turbidity factor, are applied to study the atmospheric turbidity characteristics of Taichung Harbor. Meteorological parameter values were measured during 2004 and 2005 at the Wuchi weather station of the Taiwan Central Weather Bureau, near the Taiwan Strait. Results based on the Angstrom turbidity models (β Lou, β Pin, and β Vis) indicated that annual mean values of the Angstrom turbidity coefficients were 0.174, 0.21 and 0.201, respectively. Four sets of Linke turbidity factors (TLin, TLou, TPin and T Vis) were calculated using the original Linke method and the Dogniaux method, incorporating the computed Angstrom turbidity coefficients (β Lou, β Pin and β Vis); the resultant values were 4.30, 6.40, 7.10 and 6.95, respectively. The monthly average values, frequency of occurrence, and cumulative frequency distributions were calculated using different models to describe the clear-sky atmospheric conditions at Taichung Harbor. The frequency results show that for over 50% of the dataset, three sets of Angstrom turbidity coefficients fell between 0.15 and 0.18, and four sets of Linke turbidity factors (TLin, TLou, TPin and T Vis) fell between 4.0 and 6.5. Thus, for 50% of cloudless days, the sky can be between turbid and clear over Taichung Harbor. Furthermore, the results reveal that for 30% of the dataset, three Angstrom sets of turbidity coefficients (β Lou, β Pin, and β Vis) exceed 0.2 and four sets of Linke turbidity factors (TLin, TLou, TPin and TVis) exceed 5.0. This indicates that 30% of cloudless sky conditions can be considered turbid to very turbid. © 2009 Published by Elsevier B.V.

1. Introduction Solar radiation and outdoor illuminance data are critical to a wide range of research areas, including pollution, climatology, and solar energy applications. More comprehensive solar radiation and daylight illuminance data would be invaluable to the reduction of cooling load in buildings, the evaluation of daylight, and the determination of the performance of photovoltaic plants (Li and Lam, 2000a,b; IT Power, 1996). The characteristics of the solar energy received in a given location depend on the solar position and prevailing climatic conditions at that site. The position of the sun can easily be determined from the solar geometry, specified solar altitude, and azimuth.

⁎ Corresponding author. Tel.: +886 4 26318652x4115; fax: +886 4 2652 5245. E-mail address: [email protected] (C.-C. Wen). 0169-8095/$ – see front matter © 2009 Published by Elsevier B.V. doi:10.1016/j.atmosres.2009.05.010

According to a previous study (Penner et al., 2001), the significant effects of aerosols on the climatic conditions stem from the fact that their radiative heating effects are caused by the aerosol absorption of short and long wave radiation. Accounting for the uncertainty in these ambient environmental factors (e.g. air molecules; water vapor; dust and aerosols), the total global radiation flux due to the direct and indirect effects of atmospheric aerosols is thought to be around −1.3 Wm − 2 (Shine and Forster, 1999). Turbidity is a dimensionless index of the opacity of a vertical column of the atmosphere. The attenuation of solar energy through the atmosphere is described by an index of the atmospheric turbidity, which is an important parameter in predicting the availability of solar radiation and daylight illuminance under cloudless skies. In recent decades, several atmospheric turbidity indices have been used to quantify the influence of aerosol content on direct normal irradiance through the earth's atmosphere. Among several turbidity coefficients, the most frequently used

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Fig. 1. The location of Taichung Harbor and Wuchi weather station near Taiwan Strait.

are the Linke turbidity factor, TL (Linke,1922), and the Angstrom turbidity coefficient, β (Angstrom,1961). Atmospheric turbidity coefficients have been estimated in various locations, either from broadband or spectral irradiance data (Kambezidis et al., 1998; Grenier et al., 1995; Sahsamanoglou and Bloutsos, 1989; Katz et al., 1982a). The effect of some atmospheric parameters on the annual variation in atmospheric turbidity has been investigated in several studies (Katz et al., 1982b; El-Hussainy, 1989; Maduekwe and Chendo, 1997; Stowe et al., 1997; Nakajima and Higurashi, 1998; Mishchenko et al., 1999; Higurashi et al., 2000). Studies of atmospheric turbidity have been undertaken mostly in North America (Gueymard and Garrison, 1998; Gueymard and Vignola, 1998), Europe (Bosca et al., 1996; Cucumo et al., 2000; Rapti, 2000; Kittler and Darula, 1998; Kambezidis et al., 1993; Gueymard and Kambezidis, 1997; Kambezidis et al., 2000; Kambezidis et al., 2001; Adamopoulos et al., 2002), the Indian sub-continent (Hussain et al., 2000), and Hong Kong (Lam and Li, 1996; Li and Lam, 2002). The present study investigates the atmospheric turbidity under clear skies in Taichung Harbor. Three sets of Angstrom turbidity coefficients (β Lou, β Pin, and β Vis) and four sets of Linke turbidity factors (TLin, TLou, TPin and TVis) are applied to determine various turbidity indices.

beach of the Ta-Chia stream; the southern boundary is the north beach of the Ta-Tu stream; the eastern boundary is Ling Kung Road; and the western boundary is the Taiwan Strait.

2.2. Meteorological conditions Table 1 lists the monthly mean meteorological measurements of various meteorological parameters from the period 2004–2005. The winter monsoon typically begins in September and ends in April of the following year; its intensive phase is from October to March. The winds in the monsoon season are strongest from October to March, and come from the NNE approximately 80% of the time. Winds stronger than 20 ms− 1 represent only 1.71% of all wind activity. The strongest gale recorded was a grade 10 on the Beaufort scale. In the summer most winds are from the South, with speeds generally under 10 ms− 1. Most typhoons occur from July to October, during which the maximum wind speed recorded was a grade 13 on the Beaufort wind scale. Sheltered by the Central Mountain Range, the Taichung Port is seldom subject to severe typhoon activity. The mean annual temperature is 22.9°C and the mean annual relative humidity is 77.8%.

2. Sampling sites and meteorological conditions

Table 1 Monthly average values of atmospheric parameters of 2004–2005.

2.1. Sampling sites

Month

Temperature (°C)

Taichung Harbor is one of four international commercial ports in Taiwan, located on the west coast of central Taiwan near the Taiwan Strait at a latitude of 24.17°N and a longitude of 120.29°E. Taichung Harbor is a relatively large port, with a total area of 3793 ha, forty-six wharfs, 17 specialized zones, and three free trade port zones. The Wuchi weather station of the Taiwan Central Weather Bureau is close to Taichung Harbor, which is located about 2 km to the east of the Taiwan Strait. Fig. 1 shows the locations of Taichung Harbor and the Wuchi weather station. The boundaries of the Port of Taichung are as follows: the northern boundary is the south

Solar radiation (MJm− 2)

Relative humidity (%)

Wind speed (ms− 1)

Atmospheric pressure (hPa)

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

8.27 6.32 10.72 13.23 15.19 12.17 18.01 13.93 16.05 13.14 10.38 8.11

15.53 15.58 16.75 23.56 26.92 27.97 29.36 28.80 28.61 25.46 23.19 16.42

78.2 86.4 73.1 76.2 80.0 78.9 74.2 78.3 75.3 73.0 73.4 72.4

6.04 5.48 5.07 3.75 3.77 4.03 4.12 3.81 3.59 5.93 4.84 6.79

1018.2 1007.8 1008.1 1010.3 1007.2 1010.3 1001.6 1012.8 1005.4 1011.3 1010.6 1015.7

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½

3. Turbidity models In this section each turbidity index is defined and the mathematical formulations are given. 3.1. Angstrom's turbidity coefficient Angstrom's turbidity coefficient (β) is a measure of the amount of aerosols in the atmosphere (Angstrom's, 1961). In this study, Louche's model (Louche et al., 1987) and Pinazo's model (Pinazo et al., 1995) are adopted to determine the Angstrom's turbidity coefficient (β Lou and β Pin). Both are based on the Iqbal C model (Iqbal, 1983) for calculating the solar irradiance data and the aerosol transmittance (τa). The τa is expressed as, τ a = ð0:12445α − 0:0162Þ + fð1:003 − 0:125α Þexp½−βma ð1:089α + 0:5123Þg

ð1Þ where α is the wavelength exponent (dimensionless), and ma is the air mass at actual pressure (dimensionless). The factor ma is obtained as follows: ma =

mP P0

ð2aÞ

h i − 1:253 − 1 m = cos θ + 0:15ð93:885− θÞ

ð2bÞ

p = 1013:25expð−0:0001184zÞ

ð2cÞ

where m denotes the air mass (dimensionless), P is the pressure at vertical level (hPa), P0 is the standard pressure at sea level (1013.25 hPa), and 0 is the solar zenith angle (degrees). Modifying Eq. (1), yields β as, β=

 ln τ



a

A − B

D

ð4Þ

B = 0:12445α − 0:0162

ð5Þ

D = ma ð1:089α + 0:5123Þ

ð6Þ

For clear skies, the aerosol transmittance using the Louche method (τaLou) can be expressed as τaLou =

I 0:9751I0 τg τo τ r τ w

ð7Þ

where I is the direct normal solar irradiance at normal incidence (Wm− 2) I0 is the is the extraterrestrial solar irradiance at normal incidence (1367 Wm− 2), τg is the absorption transmittance of gases (dimensionless), τo is the ozone absorption transmittance (dimensionless), τr is the Rayleigh scattering transmittance (dimensionless), and τw is the water vapor scattering transmittance (dimensionless). For completeness, the various transmittances and other necessary formulae are presented below. τr is expressed as h  i 0:84 1:01 τr = exp −0:0903ma 1 + ma

ð8Þ



ð9Þ

ð10Þ

U3 = Lma

where L presents the vertical ozone layer thickness. The transmittance by uniformly mixed gases, τg is given by,   0:26 τg = exp −0:0127ma ð11Þ τw is the transmittance of water vapor which is expressed as: h i−1 0:682 τw = 1 − 2:4959wm ð1 + 79:034wmÞ + 6:385wm ð12Þ where w is the water thickness (cm) and can be estimated using the formula,  φ  5416 w = 0:493 exp 26:23 − ð13Þ TP TP where φ denotes the fractional relative humidity. TP is the ambient temperature (K). Integrating Eqs. (7) to (13), explicit expression for τaLou and βLou can be determined accordingly. Secondly, Pinazo et al. (1995) used the coefficient Kb = HG, which is defined as the ratio of the direct beam solar irradiance on a horizontal surface, H (Wm− 2), to the global solar irradiance on a horizontal surface, G (Wm− 2). Following Pinazo et al.' s method (1995), the aerosol transmittance τaPin is expressed as τaPin =

½ð1 − AÞC  ð1 − AC Þ

ð14Þ

where   1:06 C = C1 − C 2 A = ð1 − ω0 Þ 1 − MR + MR

ð3Þ

A = 1:003 − 0:125α

− 0:3035

τo = 1 − 0:1611U3 ð1 + 139:48U3 Þ   2 −1 − 0:002715U3 1 + 0:044U3 + 0:0003U

(" C1 =

1 + ðFc B −1ÞKb −ρg ð1:0685−Fc Þ 2ρg ð1 −Fc Þ

#2 + BKb

ð15Þ

" #)12 0:5ð1−τ r Þ + Fc ð1−Fc Þρg

ð16aÞ 1 + ðFc B − 1ÞKb − ρg ð1:0685 − Fc Þ ; 2ρg ð1 − Fc Þ h  i 1:02 B = 0:79 0:9751τr 1 − MR + MR Þ

C2 =

ð16bÞ

=

Fc =forward scattering of the fraction of radiation that is scattered in the forward half-space (dimensionless); ρg =albedo of the ground (dimensionless), and wo =single scattering albedo or ratio of the scattering coefficient to the extinction (scattering plus absorption) coefficient of aerosols that are high above the ground (dimensionless). Thirdly, the visibility is also an index of turbidity. The turbidity coefficients can be estimated from the visibility measured in the horizontal direction. In an earlier study (Iqbal, 1983), Iqbal noted that McClatchey and Selby established the correlation between hourly visibility and β. The Angstrom turbidity coefficient (β Vis ) is given by α

β Vis = ð0:55Þ ð3:912 = Vis − 0:0162Þ½0:02472ðVIS − 5Þ + 1:132; VIS > 5km

ð17Þ where VIS is the atmospheric visibility (km).

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3.2. Turbidity factors In the present work, Linke's model (Linke, 1922) and Dogniaux's model (Dogniaux, 1975) are adopted to determine Angstrom's turbidity coefficient. First, Linke (1922) recommended that the total optical thickness of a cloudless atmosphere be represented as the product of two terms — the clear and dry atmosphere (δR) and the Linke turbidity factor (TL) — in order to represent a clean and dry atmosphere that produce the observed extinction. The normal-incidence irradiance (I) over all wavelengths received at the earth's surface under clear sky conditions can be expressed as (Hussain et al., 2000) I = FI0 e

− TL δR ma

ð18Þ

 2 R0 F= = 1 + 0:03344 cosð 0:9856J − 28Þ R

ð19Þ

  2 3 4 −1 δR = 6:5567 + 1:7513ma −0:1202ma + 0:0065ma −0:00013ma

ð20Þ

where R is the instantaneous sun–earth distance, R0 is the mean sun–earth distance, and J is the day number of the year, I0 is the extraterrestrial solar irradiance at normal incidence (=1367 Wm− 2 ), and ma is the relative optical air mass. Rearranging Eq. (18) yields TL as     1 FI ln 0 ð21Þ TL = I δR ma The direct beam irradiance can be determined directly through pyrheliometic measurements. The minimal value of TL from Eq. (21) is somewhat greater than the theoretical value of 1 which is reported in Molineaux et al. (1995). Some authors have tried to overcome this difficulty with various methods, the most popular of which is to normalize the measured values of TL at ma = 2 (Kasten, 1988; Grenier et al., 1995). Dogniaux (1975) developed another common approach for estimating the turbidity factor TL. The formula can be expressed as  TL =

 90 − Z + 85 + 0:1 + ð16 + 0:22wÞβ 39:5e − w + 47:4

ð22Þ

Eq. (22) expresses the Dogniaux turbidity factor as a function of solar zenith angle Z, precipitable water thickness w, and Angstrom turbidity coefficients (β Lou or β Pin, or β Vis). Therefore, three different estimations of Linke turbidity factors (TLou, TPin and T Vis) can be made based on β Lou, β Pin and β Vis using the Dogniaux method. 4. Results and discussion 4.1. Comparison of seasonal series of aerosol optical characteristics at Taichung Harbor According to the analysis results of Zakey et al. (2004), daily variations were obtained by averaging the hourly calculated values and monthly values were obtained by average these values in each month. Turbidity is an important index of clear atmospheric conditions. Daily turbidity indices

171

TL and β are statistically analyzed to describe the atmospheric turbidity at Taichung Harbor. In this investigation, following the suggestion of Karayel et al. (1984), the criteria adopted for a clear sky are a normal-incidence irradiance that exceeds 200 Wm− 2 and a ratio of diffuse irradiance to global irradiance of less than 1/3. In this study, clear sky data that meet these criteria were applied to analyze the Linke turbidity factors and Angstrom's turbidity coefficients. The values of the two turbidity indices depend on numerous measurements, including direct solar irradiance (H), atmospheric pressure (P), relative humidity (φ), temperature (TP), vertical ozone layer thickness (L), ground albedo (ρg), forward scattering (Fc), single scattering albedo (ω0), and wavelength exponent (α). Direct solar irradiance can be determined by subtracting the measured diffuse irradiance from the corresponding measured global values. The direct solar irradiance, the atmospheric pressure, the relative humidity, and the temperature were obtained from the Wuchi Weather Station. Following the methods presented by Iqbal (1983), the thickness of the vertical ozone layer (L) was taken from the tabulated monthly mean values. Results based on Li and Lam (2002), the values of ρg, Fc, ω0 and α were adopted 0.2, 0.84, 0.9 and 1.3, respectively. In this study, the hourly solar irradiance data from 2004 and 2005 were used along with other meteorological parameters (solar radiation, temperature, relative humidity, wind speed, and atmospheric pressure) to determine turbidity. Table 2 presents monthly averages of daily Angstrom turbidity coefficients (i.e. β Lou, β Pin, and β Vis). Given a set of Angstrom's turbidity data, the Linke turbidity factor, TLou, can be determined from Eq. (16) (Dogniaux's formula). The Linke turbidity, TLin, can also be determined from the original Linke's expression in Eq. (15), requiring only solar irradiance and air mass data. Table 2 reveals that the monthly mean of β Lou ranges from 0.102 in June to 0.307 in December, β Pin ranges from 0.075 in April to 0.308 in February, and β Vis ranges from 0.169 in July to 0.272 in February. All Angstrom turbidity coefficients are based on the Louche's model (1987) peak during the winter months (December to February). The values of β Lou, β Pin, and β Vis are lowest in the spring. Dust storms generally occur between February and April. According to Lee et al. (2001), the origin of dust, its transport path and duration time, the inland meteorology, and the local source pattern may influence the results of a Table 2 Monthly averages (ave) and standard derivaftion (S.D.) of Angstrom turbidity coefficients and Linke turbidity factors based on different methods in 2004 and 2005. Month

β Lou (ave, S.D.)

β Pin (ave, S.D.)

β Vis (ave, S.D.)

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

(0.226, 0.089) (0.160, 0.072) (0.150, 0.070) (0.116, 0.056) (0.107, 0.054) (0.102, 0.034) (0.138, 0.040) (0.120, 0.052) (0.169, 0.044) (0.219, 0.058) (0.272, 0.072) (0.307, 0.069)

(0.250, 0.145) (0.308, 0.154) (0.176, 0.026) (0.175, 0.024) (0.227, 0.067) (0.225, 0.073) (0.170, 0.047) (0.227, 0.096) (0.227, 0.103) (0.203, 0.058) (0.251, 0.052) (0.280, 0.071)

(0.207, 0.026) (0.272, 0.104) (0.206, 0.047) (0.216, 0.035) (0.182,0.032) (0.170, 0.035) (0.169, 0.033) (0.187, 0.036) (0.196, 0.032) (0.177, 0.023) (0.232, 0.081) (0.194, 0.026)

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Fig. 2. Monthly average variations for Angstrom turbidity coefficients (β Lou, β Pin and β Vis) in 2004 and 2005 at Taichung Harbor.

dust storm. During a dust storm, only local pollutant sources affect coarse particulates, whereas fine particulates can be carried long distances. Dust storms may make the Angstrom turbidity coefficients higher in the spring. Fig. 2 presents the monthly mean variation in Angstrom turbidity coefficients, β Lou, β Pin, and β Vis in 2004 and 2005. The ranking of Angstrom turbidity coefficients was β Pin >β Vis >β Lou from May to September. Throughout the year the monthly average values of β Pin were similar to those of β Vis and β Lou, but varied more than other two Angstrom turbidity coefficients. The Linke turbidity can also be determined using the original Linke's expression (TLin), requiring only solar irradiance and air mass data (Eq. (23)). The Linke turbidity factors (TLou, TPin and TVis) can be computed using Dogniaux's formula, Eq. (24), from Louche's set (1987) of Angstrom's turbidity data. Table 3 presents the monthly mean values of TLin, TLou, TPin, and TVis. The results reveal the TLin values to be smaller than the other values determined by Dogniaux's approach, and that the turbidity factors TPin and TVis were highest in February. Fig. 3 plots the monthly mean variation of turbidity factors TLin, TLou, TPin and T Vis from 2004 to 2005. According to Fig. 3, these turbidity factors (TLou, TPin and TVis) ranked in the same order as the Angstrom turbidity coefficients (β Lou, βPin and β Vis). Under wet weather conditions, the model may yield higher turbidity factors at higher solar altitudes. 4.2. A statistical analysis for Angstrom's turbidity coefficient β and turbidity factor TL In this investigation, several statistical methods (coefficients of skewness and kurtosis, T-test method and non-parametric (Spearman) correlation analysis) are applied to elucidate the characteristics of the Angstrom's turbidity coefficient β and the Linke turbidity factor TL. The analyses of the skewness in Angstrom's turbidity coefficients (β Lou, β Pin, and β Vis) result in skewness coefficients equal −0.598, 14.35, and 11.653, respectively. According to these results β Pin and β Vis are skewed to the right, while β Lou is almost symmetrical. Additionally, the skewness coefficients of the Linke turbidity factors (TLin, TLou,

TPin and T Vis) equal − 0.276, 0.343, 13.276 and 10.613, respectively. The results reveal that, like the Angstrom's turbidity coefficients, the Linke turbidity factors TPin and TVis also have higher skewness coefficients values with distributions skewed to the right. The distributions of the other turbidity factors, TLin and TLou, are almost normal. The kurtosis coefficients of the Angstrom's turbidity coefficients (β Lou, β Pin and β Vis) are 0.307, 2.507, and 2.524, respectively. That the kurtosis of β Pin and β Vis exceed 2.0 indicates that these coefficients exhibit leptokurtic distributions. The kurtosis of coefficient β Lou follows an almost mesokurtic distribution. Moreover, the kurtosis coefficients of the Linke turbidity factors (TLin, TLou, TPin and TVis) are −0.183, −0.028, 2.358, and 2.389, respectively. The high kurtosis coefficients of turbidity factors TPin and TVis indicate their distributions are leptokurtic. The distributions of the other turbidity factors TLin and TLou are mesokurtic, like that of β Lou. The t-test method was performed to determine whether the different estimated groups exhibited the same characterizations in 2004 and 2005. The critical value α is equal to α=1 − 0.99= 0.01 , the sampling number n =651 , and the t-test values in the range of −2.576 ≤t 651 ≤2.576 for Angstrom's

Table 3 Monthly averages (ave) and standard derivation (S.D.) of turbidity factors based on different methods in 2004 and 2005. Month

TLin (ave, S.D.) TLou (ave, S.D.) TPin (ave, S.D.) T Vis (ave, S.D.)

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

(5.019, 1.192) (4.063, 1.138) (3.994, 0.997) (3.413, 1.050) (3.201, 1.080) (3.295, 0.661) (3.903, 0.755) (3.546, 1.010) (4.394, 0.641) (5.019, 0.820) (5.691, 0.953) (6.066, 0.887)

(7.126, 1.396) (6.050, 1.317) (5.889, 1.139) (5.365, 1.163) (5.163, 1.224) (5.250, 0.755) (5.957, 0.831) (5.551, 1.078) (6.543, 0.735) (7.258, 0.969) (8.137, 1.197) (8.525, 1.098)

(7.528, 0.561) (8.610, 1.776) (6.080, 0.899) (5.871, 0.609) (7.519, 0.546) (7.483, 0.588) (6.577, 0.572) (7.558, 0.624) (7.547, 0.542) (7.000, 0.439) (7.783, 1.427) (8.086, 0.490)

(6.828, 2.414) (8.017, 2.496) (6.836, 0.451) (7.248, 0.415) (6.760, 1.131) (6.549, 1.253) (6.559, 0.801) (6.880, 1.642) (7.004, 1.780) (6.557, 1.004) (7.471, 0.848) (6.650, 1.216)

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Fig. 3. Monthly average variations for Linke turbidity factors (TLin, TLou,TPin and T Vis) in 2004 and 2005 at Taichung Harbor.

turbidity coefficients β and Linke turbidity factors TL. T-test statistical analysis shows that β Lou −β Pin, β Lou −β Vis and β Vis − β Pin at the Taichung Harbor site yielded t-test statistics of −5.41, −4.65 and 2.482, respectively. According to the t-test results, Angstrom's turbidity coefficients β Pin and β Vis have the same mean average Angstrom's turbidity coefficient. However, the Angstrom's turbidity coefficient βLou did not fall in the t-test value range (−2.576≤t651 ≤2.576), indicating that the means were not equal to those of the other coefficients. With respect to the Linke turbidity factor TL, the t-test values of various turbidity factors, TLin − TPin, TLin − TLou, TLin −TVis, TPin − TLou, TPin − TVis, and TVis − TLou, were −29.53, −177.54, −37.156, −6.77, 2.50, and −6.08, respectively. The turbidity factors TPin and TVis fell between the t-test values (−2.576≤t500 ≤2.576), suggesting that their mean values are closed. A non-parametric (Spearman) correlation analysis was also conducted to study the correlation between the Angstrom turbidity coefficients (i.e. β Lou, β Pin, and β Vis) and turbidity

factors (i.e. TLou, TPin, and TVis) with the meteorological conditions. Table 4 presents the results of the correlative analysis between the Angstrom turbidity coefficients and meteorological parameters (temperature, average wind velocity). According to the spearman ranking, the Angstrom turbidity coefficients β Lou are inversely correlated with visibility (VIS), solar radiation (SR), temperature (TP), and relative humidity (RH), with correlation coefficients rsp ranging from −0.629 to −0.524. The coefficients are positively correlated with wind speed (WS) and atmospheric pressure (AP), with correlation coefficients ranging from 0.455 to 0.671. β Pin and β Vis are also inversely correlated with visibility, solar radiation, and temperature, with correlation coefficients rsp from −0.755 to −0.462. TLin and TLou are also inversely correlated with visibility (VIS), solar radiation (SR), temperature (TP), and relative humidity (RH), with correlation coefficients rsp from −0.629 to −0.476. They are positively correlated with wind speed (WS)

Table 4 Spearman rank correlation coefficients of Angstrom turbidity coefficients and Linke turbidity factors and meteorological factors.

β Lou β Pin β Vis TLin TLou TPin T Vis VIS SR TP RH WS P

β Lou

β Pin

β Vis

TLin

TLou

TPin

T Vis

VIS

SR

TP

RH

WS

P

1.0 0.573 0.392 0.993⁎⁎ 0.993⁎⁎ 0.503 0.182 −0.629⁎ −0.524 − 0.545 − 0.622⁎ 0.671 0.455

1.0 0.413 0.559 0.580⁎ 0.951⁎⁎ 0.322 −0.755⁎⁎ −0.573 − 0.462 0.175 0.392 0.245

1.0 0.378 0.343 0.364 0.881⁎⁎ − 0.678⁎ − 0.594 − 0.706⁎ 0.105 0.126 0.175

1.0 0.986⁎⁎ 0.497 0.154 −0.615 −0.552 − 0.538 − 0.629⁎ 0.685⁎ 0.480

1.0 0.510 0.154 − 0.580⁎ − 0.476 −0.490 −0.608 0.657⁎ 0.427

1.0 0.371 − 0.706⁎ −0.497 −0.301 0.175 0.301 0.266

1.0 −0.531 − 0.231 −0.315 0.238 − 0.231 − 0.402

1.0 0.706⁎ 0.678⁎ −0.014 −0.497 − 0.245

1.0 0.895⁎ 0.063 − 0.755⁎⁎ − 0.560

1.0 0.091 −0.685⁎ −0.473

1.0 − 0.406 − 0.256

1.0 0.571

1.0

⁎Correlation is significant at the 0.01 level (2-tailed); ⁎⁎correlation is significant at the 0.05 level (2-tailed). VIS: visibility, SR: solar radiation, TP: temperature, RH: relative humidity, WS: wind speed, P: atmospheric pressure.

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Fig. 4. Frequency of occurrence for turbid and very turbid conditions with different wind directions.

and atmospheric pressure (AP), with coefficients from 0.427 to 0.685. TPin is more strongly inversely correlated with the visibility (VIS), and T Vis is inversely correlated with all meteorological parameters. Both Angstrom turbidity coefficients (β Lou, β Pin and β Vis) and Linke turbidity factors (TLou, TPin and TVis) are inversely correlated with visibility (VIS), solar radiation (SR) and temperature (TP). 4.3. Comparison of the frequency of different wind directions and wind speeds on Angstrom's turbidity coefficient β and turbidity factor TL The local weather conditions (temperature, relative humidity, solar radiation and atmospheric pressure) constitute the major parameters determining the Angstrom's turbidity coefficient β and the turbidity factor TL. The prevailing wind direction and wind speed may be important in governing the temporal

variation in turbidity (Hamdy et al., 2006). This section investigates the atmospheric turbidity model and incorporates prevailing wind direction and wind speed. The daily mean wind direction was adopted to analyze the frequency of different wind directions and the wind speeds for their effects on Angstrom's turbidity coefficient β and turbidity factor TL. Fig. 4 plots the frequency of atmospheric turbidity coefficients in the ranges of 0.2<β<0.4 (turbid) and 0.4<β (very turbid) for various wind directions. The results reveal that for very turbid conditions, most of the winds that influence the Taichung Harbor environment were northerly (NNW and N), and the mean frequency of Angstrom's turbidity coefficient β in these two bins was: for NNW: 26.6% (β Pin), and 85.7% (β Vis); and for N: 60.0% (β Pin). The lowest frequency was seen with the southerly winds (SSE, S and WWS), for which cases the mean frequencies in those two bins were: SSE: 6.67% (β Pin), S: 6.67% (β Pin), and WWS: 14.3% (β Vis). Winds did not blow in any other directions in this analysis. The

Fig. 5. Frequency of occurrence for Angstrom turbidity coefficients (β Lou, β Pin, and β Vis) during 2004 and 2005 at Taichung Harbor.

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Fig. 6. Cumulative frequency distribution for Angstrom turbidity coefficients (β Lou, β Pin and β Vis) in 2004 and 2005 at Taichung Harbor.

results show that under turbid conditions, most of the wind influencing the Taichung Harbor environment is northerly (NNW and N), as determined by the mean frequency of Angstrom's turbidity coefficients β Pin, β Lou and β Vis. The lowest frequency is associated with the southerly winds (SE, SSE, S, SSW, SW, and WWS).

4.4. Comparison of the frequency of Angstrom's turbidity coefficient β and turbidity factor TL In this work, the frequency of computed turbidity is analyzed during 2004 and 2005. The cumulative frequency of turbidity values is adopted to indicate the percentage of clear days on which a given turbidity threshold is exceeded. Typical frequency curves of the prevailing climatic conditions should

be based on long-term measurement data to broadly elucidate the general characteristics. Fig. 5 plots the frequency distributions of occurrence distributions for β Lou, β Pin and β Vis values at intervals of 0.01. The results reveal that βLou has a high peak near 0.16, around which the distribution is not quite symmetrical, ranging in value from 0.02 to 0.37. The distribution of β Pin has a high peak near 0.17, also with an asymmetrical distribution. The β Pin distribution has a second peak at 0.22, and ranges in value from 0.03 to 0.44. The β Vis distribution has a high peak near 0.18, and spreads more symmetrically and widely than the above models, perhaps because β Vis depends strongly on visibility. Fig. 5 displays a major peak of 11% at 0.18, which corresponds to the visibility of 28 km. Fig. 6 plots the cumulative frequency distributions of calculated β Lou, β Pin and β Vis values. The results indicate that

Fig. 7. Frequency of occurrence for Linke turbidity factors (TLin, TLou, TPin, and T Vis) in 2004 and 2005 at Taichung Harbor.

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Fig. 8. Cumulative frequency distribution for Linke turbidity factors (TLin, TLou, TPin, and T Vis) in 2004 and 2005 at Taichung Harbor.

the β Lou values were lower than β Pin, revealing that the Louche method yields a clear cloudless condition. Notably, for Angstrom turbidity coefficients (β Lou, β Pin and β Vis) between 0.1 and 0.3, the cumulative percentage falls rapidly, presenting between 70% and 95% cloudless days. This result indicates that the sky over Taichung Harbor on cloudless days is between clear and turbid. Based on the four modes (TLin, TLou, TPin and T Vis), the frequency of Linke turbidity values were computed and plotted in Fig. 7. The figure reveals that TLin ranged from 0.5 to 7, TLou ranged from 2 to 10, TPin ranged from 4 to 10, and T Vis ranged from 5 to 10. Furthermore, the distribution of TLou, TPin, and T Vis values are slightly skewed to the left with peak values between 5 and 8. TLin values are lower, and the associated cumulative percentages are smaller than those obtained using the other three models for all turbidity values. For TLou, TPin, and TVis values, similar tendencies were seen in the turbidity factor distributions. Fig. 8 plots the cumulative frequency distributions of calculated TLin, TLou, and TVis showing that they follow similar trends. Interestingly, TVis has the same cumulative percentages as TLou and TPin at 30% and 75%, corresponding to turbidity values of 7.0 and 6.5, respectively. The cumulative frequency distribution of β and the turbidity data reveal the percentage of cloudless days on which a given turbidity level is exceeded. On 50% of cloudless days, the β values obtained using the four models are between 0.15 and 0.18 and the turbidities found using the four associated methods are between 4.0 and 6.5; this indicates that on over 50% of cloudless days, the sky over Taichung Harbor was turbid to clear. Moreover, on 30% of the

Table 5 Parameter for various degrees of atmospheric cleanliness (Leckner, 1978). Atmosphere

α

β

Visibility (km)

Clean Clear Turbid Very turbid

1.3 1.3 1.3 1.3

0 0.1 0.2 0.4

340 28 11 <5

cloudless days, the β values obtained using the four models exceed 0.2 and the turbidities obtained using the associated four methods exceed 5.0; this reveals that on 30% of cloudless days, the sky over Taichung Harbor was turbid (Table 5). 5. Conclusion The Angstrom turbidity coefficient (β) and the Linke turbidity factor (TL) were calculated from two years (2004– 2005) of meteorological data measured at the Wuchi weather station of the Taiwan central weather bureau, near Taiwan Strait. The annual mean values of the Angstrom turbidity coefficients obtained using the Louche, Pinazo, and visibility methods were 0.152, 0.2, and 0.15, respectively. Based on the above methods, β Pin yields the highest mean monthly average values, followed by β Vis and β Lou. Four sets of Linke turbidity factors (TLin, TLou, TPin and T Vis) were determined using the original Linke method and the Dogniaux method from the computed Angstrom data (β Lou, β Pin and β Vis). TLin has the lowest monthly average values of the four models (in May), and TPin has the highest monthly average values of the four models (in February). The data on Angstrom coefficient β show that β Pin and β Vis are skewed to the right, and the other coefficient β Lou is almost symmetrical. The kurtosis coefficients for Angstrom's turbidity coefficients (β Lou, β Pin and β Vis) show that β Pin and β Vis exhibit leptokurtic distributions and that β Lou follows an almost mesokurtic distribution. The turbidity factors TPin and T Vis exhibit the same skewness and kurtosis as β Pin and β Vis, and the turbidity factors TLin and TLou exhibit the same skewness and kurtosis as β Lou. Overall, 50% of the data yield Angstrom coefficients between 0.15 and 0.18 and Linke turbidity factors between 4.0 and 6.5. The results demonstrate that, in Taichung Harbor, clear sky conditions can be defined as being between turbid and clear. Further, 30% of the Angstrom coefficients exceed 0.2 and 5.0, indicating that, for 30% of those clear sky days over Taichung Harbor, conditions could be considered turbid to very turbid in 2004 and 2005.

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