a. Clouds and radiation

Atmospheric radiation is strongly influenced by clouds. Since the former determines climate on earth, clouds are major actors in all climate studies, the more so since the radiation budget is very sensitive to small variations in cloud cover and characteristics. Most modeling and observational efforts related to climate concern the net upwelling radiation, which is a complex convolution of radiative scattering and absorption processes in clear sky, clouds, and at the earth's surface. The description of these complex processes contains numerous uncertainties of microphysical (single photon scattering by liquid water, aerosol particles, and ice crystals) and macrophysical (vertical and horizontal inhomogeneity in cloud distribution and composition) nature, which still inhibit an accurate assessment of the climate impact.

In atmospheric modeling of radiation transfer, clouds are often represented as extended homogeneous layers of constant thickness. Homogeneity is assumed in for example, droplet size, liquid water content, and droplet number concentration. In reality these quantities may strongly vary on all scales, even in stratiform cloud types. This variance in cloud properties has a distinct influence on the radiation transfer process (Los and Duynkerke 2001). One of the consequences is that the horizontal divergence of radiative fluxes cannot always be neglected. Also, in regions with scattered clouds, a full 3D analysis of radiation transfer is required. The albedo of a broken cloud field can be quite different from a similar, but homogeneous cloud layer (albedo bias; Barker 1992; Barker et al. 1996; Cahalan et al. 1994). This is a matter of concern since in all numerical climate studies the horizontal resolution is (and will be) much larger than the scale of the cloud inhomogeneity which, as a consequence, has to be parameterized.

What apparently is required is an insight in cloud-radiative properties, based on experimental evidence as a function of azimuthal and zenith angle (radiances) under conditions where simplifications such as the plane parallel approximation are likely to be invalid. Measurements of the angular distribution of scattered radiation (relative to the solar incidence) yield bidirectional reflectance distribution functions, which provide the required information on radiative scattering processes in clouds.

In this article we describe the design, development, calibration, validation, and airborne testing of a device that enables the measurement of scattered solar radiation in a number of directions relative to the solar incidence angle. The instrument is based on an original design by Davis et al. (1982), but equipped with sensors with a unique collimation system consisting of solid PERSPEX cylinders which combines simplicity with robustness and that yields both a strong light signal and a high discrimination with respect to the angle of incidence. The main difference with the earlier instrument is that Directional Radiance Distribution Measurement (DIRAM) device can operate with a small field of view, while maintaining a high signal-to-noise ratio (∼1%), so that the angular distribution of the scattered radiation can be better resolved. The detecting photodiodes are sufficiently sensitive to measure radiance from cloudless regions of the sky.

b. Historical background

The design and scientific use of shortwave radiation measurements devices at the Institute for Marine and Atmospheric Research (IMAU) goes back to the 1980s. Instruments were designed to measure the radiation in vegetation (van der Hage 1984), the actinic flux above grassland (van der Hage 1992), and the horizontal component of radiation (van der Hage 1993). More recently, IMAU participated in a number of field experiments (Azores, Antarctic, and Netherlands) in order to study the interaction of clouds and radiation (Duynkerke and van Weele 1993; de Arellano et al. 1994; van der Hage and de Roode 1999). For this purpose a special sensor was designed and built to determine actinic fluxes as a function of height in cloudy and clear-sky conditions up to altitudes of 1.5 km under different surface albedos (van der Hage et al. 1994); van der Hage and de Roode 1999). The obtained results were used to validate radiative transfer models in clear-sky and overcast conditions. The combination of the current scientific interest in scattering of shortwave radiation by clouds and atmospheric (photo) chemistry, and our expertise with simple radiation instruments has initiated the development of the present DIRAM instrument.

a. Experimental design

The present concept (Fig. 1) consists of two hemispherical domes, one to be mounted on top of an aircraft and one under it. Each dome has 24 cylindrical holes (8-mm diameter); each hole contains a collimator and a detector.

To register the angular distribution of radiance in the atmosphere, a regularly distributed, spherical array of radiance sensors is required. To this end the holes were positioned in an icosahedral geometry of 20 equal triangles. Holes were drilled at each vertex and at the middle of each edge (see Fig. 2). In this way 42 sensors can be distributed over a full sphere in an approximately equidistant way. The distance between two adjacent sensors is a/2 when a is the length of an edge. When the fields of view of the six sensors on the triangular face are not allowed to overlap then the maximum aperture, ϕ (defined as the ratio of the radius of the circles in figure 2, a/4, and the radius of the enveloping sphere R) can then be found from

View Expanded

Thus, ϕ is just over 15°. With this aperture a coverage of 95% can be obtained. In Table 1 we have listed the azimuthal ψ and zenith angle θ of all holes.

b. Collimating system

The collimating system¹ consists of light-conducting PERSPEX (polymethyl-methacrylate) cylinders. This material has a very high transparency in the window 400–1200 nm. The aperture of the cylinders is determined by the length (l) of the tube and the diameter (d) of the collimating diaphragms (Fig. 3).

When both diaphragms have the same diameter d, we find: tanϕ = 2d/l, corresponding to an aperture of 10°. One extra diaphragm is required to screen reflections by the inside of the cylinder, since oblique reflection from the wall, even when the wall is treated with a low reflection coating, is a significant source of stray light. The extra diaphragm works two ways: it shields the view of the detector of the front part of the tube wall, and it prevents light with an angle of incidence >ψ to enter the rear compartment of the tube (see Fig. 3a). Finally, light incident at angles between ϕ and ψ is reflected by the walls of the rear compartment but these reflections are screened from the detector by the detector diaphragm. The collimators were machined from a solid PERSPEX rod of 8-mm diameter, the sides covered with a black coating, attached to photodiodes and finally fitted in the holes in the DIRAM sphere.

a. Viewing angles

A check of the azimuthal and zenith angles (see Table 1) of each of the 42 sensors after they were mounted in the holes in the aluminium spheres was made. This was done by mounting a laser in a spherical construction (∼1-m radius) with the sphere positioned in the center. The laser could be moved in azimuthal and zenith directions. The direction of the laser beam was also adjustable. The position where the laser produced a maximum in the detector signal defined the viewing angle of the sensor. This could be done with an estimated accuracy of approximately 0.25° for ψ, while θ could be determined with an error of ∼0.1°. In Fig. 4 we show (an average of) the measured deviations in azimuthal and zenith direction, respectively. Nearly all the sensors are placed into the holes in the spheres with an accuracy better than 1°. Only three sensors are misaligned just over 1° (no. 6 and no. 15 of the upper DIRAM sphere and no. 2 of the lower DIRAM sphere). The error in the alignment is sufficiently small to enable the determination of angular radiation distributions.

b. Angular response and stray light

The angular response of each individual collimating system was determined by irradiating it with a laser beam as a function of incident angle α relative to the centerline of the sensor. A typical result of a collimator is given in Fig. 5. The full-width half-maximum is 7.14°, which is somewhat less than the geometrical aperture (10°) found in section 2b. There is a strong decrease in response toward large angles, up to 4–5 orders of magnitude for α > 35°. In the absence of direct (solar) radiation, stray light² can be neglected. However, above the clouds a correction to the signal may be necessary due to stray light from the sun. An estimate of this correction can be obtained as follows. Suppose that the direct solar radiation yields a signal in a sensor of Sf_att(α) (in V), where S is the signal when the sensor is pointed toward the sun³ and f_att(α) is the attenuation factor depending on the solar incidence angle α on the sensor. The attenuation factor can be directly obtained from Fig. 5 and is defined as the ratio between the output at angle zero and α, respectively. Since S is of the order of 800 V, corrections up to 80 mV are required for angles larger than 10°. For smaller angles of incidence, that is, for sensors almost pointing toward the sun, larger corrections are required. For comparison we note that blue sky radiation yields a signal of ∼25 mV in the detector. From clouds the signal is at least an order of magnitude larger. Correction for stray light must therefore be applied for sensors exposed to the sun.

It is clear that a sharply restricted field of view is required and we believe that the current construction is one of the few that yields narrow and restricted views. All collimators were tested and those with a significantly worse relative sensitivity or angular response than presented in Table 2 or Fig. 5 were rejected.

c. Sensitivity and dynamic range

On the surface of the DIRAM domes a circular groove is cut around each sensor. The function of these grooves is to enable the exact positioning of a reference light source on the optical axis of each sensor. A plain diffuse electric light source was applied to simultaneously illuminate both a “reference sensor” and any one sensor in the DIRAM domes. For the reference sensor, an arbitrary sensor, similar to the ones in the dome was selected and kept in the laboratory. These measurements were repeated in reverse direction in order to remove possible linear trends in time of the light source, yielding a relative sensitivity factor s_i for each sensor i. The sensitivity factors are listed in Table 2. They may change in time due to aging of the diodes and the optics and therefore determination of sensitivity should be regularly repeated.

The absolute calibration was done by comparing the integrated DIRAM signal with the signal of a calibrated climatological global radiation meter (Kipp & Zonen CM5).⁴ This was done in a campaign in France during the solar eclipse in August 1999. This occasion offered a large range of values of diffuse radiation, as we shall see shortly. Measurements were done in cloudy, almost overcast conditions. All observations where direct solar radiation was significant (i.e., when the solar disk was visible) were excluded from calibration. We denote the diffuse radiance by R(θ, ψ) (in W m⁻² sr⁻¹). Then the global radiation G is by definition

View Expanded

where Ω denotes the solid angle (=sinθdθdϕ). The integration extends to the upper hemisphere. The output V_i (in V) from a sensor i pointing in direction θ_i, ψ_i can be expressed as

V_is_iRθ_iψ_ic(3)

where c is the conversion factor [V (W m⁻²)⁻¹], s_i's are the sensitivity factors (see Table 2) and ΔΩ is the field of view of the sensor (sr). The latter was taken constant for each sensor and equal to 9.71 × 10⁻⁴ sr, corresponding with an aperture of 3.57° (the half-width half-maximum value from Fig. 5). The 21 values of the sensors of each dome, normalized with their relative sensitivity (V_i/s_i) were interpolated to a regular grid with N grid points, yielding V_n(n = 1, N). After summation we obtain V_tot according to

View Expanded

Note that the summation is over the N grid points of the interpolation grid and that Δθ and Δψ denote the grid size. The global radiation as measured by the DIRAM can now be expressed as

View Expanded

From the regression with the Kipp & Zonen global radiation radiometer the constant cΔΩ was determined (Fig. 6). The relationship is linear over a large range of values. The correlation coefficient is 0.994. From the regression a value for cΔΩ is obtained of 7.58 × 10⁻⁴ V sr (W m⁻²)⁻¹. Varying the number of grid points (N) or the interpolation method has little effect on the value of cΔΩ. With the above value for the field of view, c equals 0.781 V (W m⁻²)⁻¹.

In the present DIRAM, BPW 21 diodes are used, which detect only a filtered fraction of the solar radiation. The spectral sensitivity of the DIRAM instrument has an optimum around 550 nm and a bandwidth of ∼300 nm. The global radiation meter has a constant spectral sensitivity over the range from 400 to 1200 nm. Though the spectral response is different, we estimate that this does not affect the calibration significantly. (The spectral distribution of the solar radiation originating from areas close to the edge of the solar disk is considered to be not very different from that of the central part.)

d. Spectral response

The spectral sensitivity of the PERSPEX sensor is completely determined by the specifications of the BPW 21 (Siemens) silicon photodiode. This diode only responds to light in the range of 400–1200 nm, a range where PERSPEX is perfectly transparent (Touloukian et al. 1972). The spectral response is shown in Fig. 7. Weiss and Norman (1985) have shown that the relative spectral distribution in global radiation under a cloudy sky is practically identical to that under a clear sky, which justifies the assumption that the effects of different spectral responses of the Kipp & Zonen radiometer and the BPW 21 photodiode on the value of regression constant c are small in variable cloudiness. However, for blue sky conditions c may be somewhat different due to the deviating spectral response. This has to be looked into in further experiments.