Short-Wave Solar Radiation in the Earth’s Atmosphere Part 4 potx

84 Spectral Measurements of Solar Irradiance and Radiance in Clear and Cloudy Atmospheres

Table 3.1. Evaluation of the uncertainty (standard deviation) of airborne measurements of

the radiative characteristics

Uncertainty source Uncertainty

type

Observations, which

the uncertainty

influences

Uncertainty estimation

Displacement of the Systematic All observations 1 nm

wavelength scale Random All observations 1 nm

Deviation from the

cosine dependence

Systematic The irradiance

observations

Look at Fig. 3.1

Calibration Systematic All observations 15% within UV, 10%

within VD and NIR

K-3 spectrometer Random All observations 5% within UV, 1% within

VD and NIR

Aircraft pitch Systematic Observations of the

downwelling irradi￾ance in the clear

atmosphere

5% within UV, 10%

within VD and NIR for

the azimuths 0 and 180◦

Aircraft bumps Random Observations of the

downwelling irradi￾ance in the clear

atmosphere below

the bumps level

5% within UV, 10%

within VD and NIR for

the azimuths 90 and 270◦

Illumination

heterogeneity

Random Observations below

the inhomogeneous

clouds

10%

Surface heterogeneity Random Observations of the

upwelling radiance

and irradiance

below the bumps

level

10%

area in the field of view of the instrument is smoothing the surface hetero￾geneity. It is especially distinct during the upwelling irradiance observations:

the corresponding estimations indicated that the surface heterogeneity could

be neglected if the flight altitude was higher than the bumps level. Table 3.1

concludes the reasons and estimations of the uncertainties of the airborne

observations with the information-measuring system based on the K-3 instru￾ment.

Airborne Observation of Vertical Profiles of Solar Irradiance and Data Processing 85

3.2

Airborne Observation of Vertical Profiles

of Solar Irradiance and Data Processing

The concern of the spectral observations of solar irradiances was to calculate

radiative flux divergences and it conditions both the observational scheme and

the methodology of data processing. It is necessary to distinguish two different

cases: observations under overcast and clear sky conditions. The observations

either of upwelling or of downwelling irradiance were accomplished using one

instrument through the upper and lower opal glasses in turn.

The observations of the solar irradiances in the overcast sky were accom￾plished out of the cloud (above the cloud top and below the cloud bottom) and

within the cloud layer at every 100 m. As the implementation of the experiment

under the overcast conditions needed both a horizontal homogeneity of the

cloud and its stability in time, the observations were accomplished as fast as

possible with measuring of only one pair of the irradiances (upwelling and

downwelling) at every altitude level. Besides, only one circle of observations

was needed as usual. We need to stress that cases of homogeneous and stable

cloudiness are rare so the quantity of observations for the overcast sky are less

than in the clear sky.

The main component of the uncertainty during irradiance observations

under overcast conditions is the random error due to the heterogeneity of

illumination (Table 3.1). It leads to distortions of the vertical profiles of the

spectrum, as Fig. 3.2 demonstrates. The filtration of these distortions was

possible using the smooth procedures, but the standard algorithms (Anderson

1971; Otnes and Enochson 1978) turned out to be ineffective in this case. Thus,

it was necessary to elaborate the special one (Vasilyev A et al. 1994).

The smooth procedure of distortions of the spectral downwelling and up￾welling irradiances provides the replacement of the irradiance value at every

altitude level with the weighted mean value over this level and two neighbor

(upper and below) levels:

F↓(zi) =



1

j=−1

βjf ↓(zi+j) , F↑(zi) =



1

j=−1

βjf ↑(zi+j) , 

1

j=−1

βj = 1 , (3.2)

where βj are the weights of smoothing (common for all wavelengths, altitudes

and types of the irradiances); f ↓(zi), f ↑(zi) are the observational results of the

downwelling and upwelling irradiances at level zi; F↓(zi), F↑(zi) are the values

of the irradiances calculated during the secondary data processing. Weights βj

in (3.2) have been obtained from the demands of the physical laws.

As the radiative flux divergence has to be positive, the net radiant flux does

not increase with the optical thickness increasing (from the top to the bottom

of the cloud) according to Sect. 1.1. That is to say, the following condition has

to be fulfilled for the results of (3.2):

F↓(zi) − F↑(zi) ≥ F↓(zi−1) − F↑(zi−1) (3.3)

86 Spectral Measurements of Solar Irradiance and Radiance in Clear and Cloudy Atmospheres

Fig. 3.2. Vertical profile of net, downward, and upward fluxes of solar radiation in the

cloud for three wavelengths. Solid lines are the original measurements; dashed lines are

the smoothed values. Observation 20th April 1985, overcast stratus cloudiness. Cloud top

1400 m, cloud bottom – 900 m, solar incident zenith angle ϑ0 = 49◦ (µ0 = 0. 647), snow

surface

The substituting of (3.3) to (3.2) provided the conditions for obtaining weights

βj



1

j=−1

βj(f ↓(zi+j) − f ↓(zi−1+j)) ≥ 

1

j=−1

βj(f ↑(zi+j) − f ↑(zi−1+j)) , 

1

j=−1

βj = 1.

(3.4)

The equation system (3.4) was solved with the iteration method. Firstly, weights

βj for measured values f ↓(zi), f ↑(zi) were obtained after the conversion of the

inequality to the equality in (3.4). Only three spectral points in the interval cen￾ters (UV – 370 nm,VD – 550 nm, NIR – 850 nm)were considered as a smoothing

condition for all other wavelengths. Equation system (3.4) was solved using the

Least-Squares Technique (LST) (Anderson 1971; Kalinkin 1978). The formulas

and features of the LST in applying to atmospheric optics will be considered

in Chap. 4 and here we are presenting the results only.

Then values F↓(zi), F↑(zi) were calculated using (3.2), and conditions (3.3)

were verified for all wavelengths and altitudes. The iterations were broken in

the case of satisfying the conditions, otherwise the above-described procedure

was repeated after substituting values F↓(zi), F↑(zi) to f ↓(zi), f ↑(zi) in (3.4). One