In order to observe the small-scale variability of cloud-induced shortwave surface radiation fields at a high spatiotemporal resolution, we have developed a set of 100 autonomous pyranometer stations equipped with meteorological sensors (relative humidity (RH) and air temperature) for the HOPE campaign. Each station is built with the following main components. i.

An EKO silicon photodiode pyranometer (model: ML-020VM) for measuring the shortwave global irradiance (G in Wm-2) in the spectral range 0.3–1.1 µm. The limited spectral range is a well-known constraint of this type of pyranometer due to the narrow spectral response of the photodiode. In comparison to thermopile pyranometers, silicon photodiode sensors have a superior response time enabling a sampling frequency of 10 Hz, which allows it to follow the rapid changes in the sky. Further specification details are listed in Table .

A pyranometer station in the field and the schematic data flow from pyranometer through logger to memory storage device is shown in Fig. . The data logger software has been modified to enable simultaneous recording of data from the GPS, pyranometer, temperature, and RH modules. The logger's internal real-time clock is synchronized with the GPS time frequently and all the data are stored on a micro-SD card (∼2 GB). The voltage signal detected by each pyranometer sensor ranges from 0 to 10 mV (∼ 0 to 1400 Wm-2) and an amplifier (INA333) enhances the signal by a factor of 300 to convert the signal in the range of 0–3 V. Note that the amplification of pyranometer signal is independent of the fading battery voltage because the stabilized output voltage (3.3 V) was used from the data logger board. If the battery voltage is too weak, then the whole logger board does not work anymore. In case of temperature and RH sensors, their respective measurement ranges are related with the output voltage from 0 to 2.5 V. These voltage signals are scaled to 10 bit counts ranging from 0 to 1023 and stored on the memory card.

During the HOPE campaign, we have set up 99 pyranometer stations covering the spatial domain of 50.85–50.95∘ N and 6.36–6.50∘ E (∼10km×12km area) around Jülich (mostly in open farm fields). Each measurement system was placed on a mounting rod, which is approximately 1.8 m high above the ground, and provides the measurements (in 10 bit counts) corresponding to the downward shortwave global irradiance, air temperature, and RH at 10 Hz frequency while the GPS information (latitude, longitude, time, etc.) is obtained at 1 s resolution. The spatial setup of pyranometer stations during the HOPE campaign is shown in Fig. . This network was continuously operational from 2 April to 24 July 2013 to capture the small-scale variability of cloud inhomogeneity fields at the surface.

Sites of the Research Center Jülich (FZJ) and the Karlsruhe Institute of Technology Hambach (KIT1, KIT2) were equipped with thermopile pyranometers, while the site of the Leipzig Aerosol and Cloud Research Observations System (LACROS) had an operational sky imager. These collocated sites with supplementary measurements are also shown in Fig. . With respect to the thermopile pyranometers at FZJ, KIT1, and KIT2, the nearest pyranometers from the network are spatially apart by 29.5, 227.5, and 343.5 m. Global horizontal irradiance measurements from thermopile pyranometers at FZJ were obtained as 1 min averages while those from KIT1 and KIT2 are available at 1 Hz resolution.

The EKO ML-020VM silicon photodiode pyranometers were calibrated against a reference ML-020VM sensor using an indoor solar simulator. This reference sensor was initially calibrated against another reference thermopile pyranometer. In our case, the sensor sensitivity is a single number determined under standard conditions with a specific spectrum that converts the narrowband response to an equivalent broadband response. The ML-020VM pyranometer sensors have calibration factors that range from 6.3 to 7.7 µVW-1m2 (provided by the manufacturer).

The raw data stored in the form of 10 bit counts are converted to global horizontal irradiance (G in Wm-2), ambient air temperature (Ta in K), and RH (in %) using the following equations: G=Ncounts⋅3.31023⋅1300⋅1Kc,Ta=Ncounts⋅3.31023⋅1002.5-20+273.15,RH=Ncounts⋅3.31023⋅12.5⋅100. Here Ncounts corresponds to the respective sensor data in 10 bit counts and Kc denotes the calibration factor (in VW-1m2) of a pyranometer sensor. Since our GPS did not provide sub-second information, both the pyranometer and meteorological measurements are averaged along 1 s time steps of the GPS. Additional information such as latitude, longitude, day, and time from the GPS was used to compute the solar zenith and azimuth angles as described in .

Atmospheric transmittance characterizes the fraction of radiation that passes through the column atmosphere under variable sky conditions at different solar zenith angles (θ0). As this is derived from the global irradiance measurements by normalizing with a fixed value of extraterrestrial irradiance at the TOA corrected for geometrical factors, we also refer as global transmittance (T). While the observed transmittance is sensitive to aerosols and cloud optical thickness, information on cloud thermodynamic phase and cloud droplet effective radius is outside the spectral range of our silicon photodiode pyranometer.

We convolute the standard solar spectrum of with the EKO silicon photodiode spectral sensitivity (see Fig. ) and then integrate the weighted EKO solar spectrum over the range of sensitivity to calculate the sensor-specific extraterrestrial irradiance (S0′) using the following equation: S0′=∫λ1λ2ϕ(λ)⋅η(λ)dλ, where λ1 and λ2 are the lower and upper spectral limits (in µm), λ is the wavelength (in µm), ϕ is the extraterrestrial solar spectrum (in Wm-2µm-1) at a Sun–Earth distance of 1 AU (or astronomical units), and η denotes the spectral sensitivity of the EKO silicon photodiode sensor. Since the EKO pyranometers used in this study were calibrated to the full solar spectrum and not to the spectral range of the sensor, we use the climate significant total solar irradiance value of 1360.8 ± 0.5 Wm-2 at the TOA for deriving the global transmittance (T) as given below: T=G′S0′⋅rr02⋅cos⁡θ0. Here S0′ (=617.48 Wm-2) is the sensor-specific extraterrestrial irradiance, G′=617.481360.8⋅G is the scaled global horizontal irradiance in the spectral sensitivity range of the sensor, r is the actual Sun–Earth distance (in AU), and r0 is the mean Sun–Earth distance (=1.0 AU). If there is no atmosphere, then the global transmittance will be unity.

Global irradiance measurements from each pyranometer station may be influenced by various operational sources of uncertainty, namely horizontal misalignment of the sensor leveling plate, cleanliness of glass dome, short-time resting of birds or insects, water droplets (during rain, fog, or dew) on the glass dome, instrument malfunctioning, and shadowing due to close by structures (i.e., obstructions to free the horizon). A spirit (or bubble) level was available on the leveling plate, which mounts the pyranometer sensor. The screws of the leveling plate were adjusted on the mounting rod such that the bubble in the spirit level is always enclosed within the marked circle for perfect horizontal alignment (see Fig. S1 in the Supplement). During the campaign period, batteries were replaced every week and a record of the physical information, such as (i) cleanliness of the pyranometer glass dome (i.e., cleanliness flag on a scale of 1–10, with 1 denoting perfectly clean and 10 representing complete blocking) and (ii) horizontal alignment status based on the position of bubble in the spirit level of the leveling plate (i.e., tilt flag on a scale of 1–3), were noted for each station. The tilt flag 1 denotes perfect alignment with bubble located within the marked circle, 2 is medium alignment with bubble partially located in and out of the marked circle, and 3 represents bad alignment with the bubble completely located out of the marked circle. Examples of level reading warranting tilt flags 1, 2, and 3 are shown in Fig. S1. In case of missing or no observation of both cleanliness and horizontal misalignment status, they were assigned zero flags. This information was then used to assign an observational flag (on a scale of 1–4) to the entire previous week's data of corresponding station. Table  outlines the criteria adopted for assigning these observational flags. Over the entire HOPE period, it was observed that more than 80 stations (∼80%) always had good data (i.e., observational flag =1) on any day.

The accuracy of global irradiance measurements from an EKO silicon photodiode pyranometer depends not only on the specifications of the sensor (including the calibration procedure) but also on the measurement and maintenance protocol along with the prevailing environmental conditions. The measurement system includes a pyranometer sensor, analog-to-digital conversion (ADC) modules including an amplifier, and a data logger unit as described in Sect. 2.1. The uncertainty of the whole system is a combination of uncertainties from various components. In general, the measurement system is assumed to have intrinsic, calibration, and operational uncertainties. These uncertainty calculations are dependent on the distribution of uncertainty sources . If a Gaussian distribution is assumed for measurement values, then the “standard uncertainty” is equivalent to the standard deviation (∼ 68 % values are included in ±1 standard deviation interval around the true value). When the limits of deviation encompasses a large fraction of the distribution of the measured values (∼ 95 % values, which in case of a Gaussian distribution of the measured values is about twice the standard uncertainty), this is referred as “expanded uncertainty”. Hereafter, we denote the standard uncertainties with “u” and expanded uncertainties by “U”. Further information on uncertainty calculations for different distributions of measurement values are given in and . Detailed description about the uncertainty assessment of measurements from an EKO photodiode pyranometer was included in the Supplement, while a brief overview of the methods adopted for estimating these uncertainties from different sources and resulting estimates is presented in the following subsections.

It is essential to understand the consistency in the clear-sky global transmittance among a large number of measurement stations as it offers the possibility for validating the existing clear-sky models. These models are required to study the more complicated cloudy skies in terms of the cloud radiative forcing.

In Fig. a, the instantaneous spatial distribution of the derived global transmittance on a clear-sky day (4 May 2013) is shown along with the corresponding sky image (Fig. b) obtained at the LACROS site. On this day, a few high-altitude cirrus clouds were observed in the morning and thereafter perfect clear-sky conditions prevailed with weak westerly winds. The difference between minimum and maximum values in the spatial distribution of RH and ambient air temperature measurements varied from 10 to 20 % and 6 to 8 K, respectively, during the day. At noon (∼ 14:00 UTC), RH varied from 35 to 55 %, while ambient air temperatures ranged from 289 to 295 K in the observation domain.

The temporal variability of the mean, median, minimum, and maximum values of the derived global transmittance from the spatial distribution is shown in Fig. c. During this day, the relative standard deviation (or the ratio of standard deviation to the mean) of the derived global transmittance measurements from the pyranometer network varied from 2.6 to 19.7 %. Apart from the contribution due to aerosols on a clear-sky day, the large spread in the morning and evening times can be attributed to the larger directional errors associated with an EKO pyranometer at lower solar elevation angles. We have also observed that a few stations were influenced by the background shadowing from surrounding obstructions (see movie01.avi in the Supplement) in spite of limiting the data analysis to solar zenith angles larger than 75∘. Additional short-time decrements in transmittance from some stations may result from random resting of birds. Absolute differences between the mean and median values of derived global transmittance in the spatial domain are spread between 0.0 and 0.03 as a function of time. This implies that the spatial distribution is evenly centered around the mean with few outliers.

The time series comparison of derived global transmittance values from collocated thermopile pyranometers (i.e., FZJ, KIT1, KIT2) with our close-by stations showed a very good matchup (see Table ). Though the linear correlation (r > 0.92) and the slope of regression (> 0.80) are always high and complemented each other, the root mean square error (RMSE) varied from 4.2 to 11.1 %. Further, an approximate difference of 5 % was observed consistently between the mean spatial transmittance from the network and the measurements from the collocated thermopile pyranometers especially during 09:00–15:00 UTC. The frequency distribution of instantaneous global transmittance values from the spatial domain (shown in Fig. d) indicated a dominant peak varying between 0.4 and 0.7.

Under broken-cloud conditions, the pyranometer views a portion of the clear-sky or even direct sunlight. As a result of this, the intensity of diffuse irradiance is mainly determined by the presence or absence of cloud patches in the vicinity of the Sun and their optical thickness. If the clouds are not too thick, then the diffuse irradiance from a clear sky is smaller than that of a cloudy sky. Broken clouds vary considerably in their horizontal and vertical extents. A nonhomogeneous thicker cloud (or a portion of the cloud that is relatively thick) loses solar energy due to scattering at the cloud edges, eventually complicating the determination of flux absorbed in a cloud layer due to net horizontal photon transport. Consequently, both the reflection and transmission are reduced relative to a plane-parallel cloud of the same cloud thickness and microphysics. However, under clear or partially cloudy conditions, both reflection and transmission are enhanced by the incoming photons scattered by the neighboring thick clouds. Subsequently, the uncertainties in the input parameters required for radiative transfer calculations result in errors that are comparable or even larger than the discrepancies between the observed and computed cloud absorptions. Thus, the cloud inhomogeneity has a significant influence on the broadband solar fluxes e.g.,.

The instantaneous spatial distribution of the derived global transmittance on a broken cloudy day (5 May 2013) is shown in Fig. a along with the corresponding sky image (Fig. b). During this day, clear-sky conditions prevailed until 09:00 UTC. Thereafter, slightly increasing cloudiness with cumulus humilis was observed. The winds turned from the south in the morning to west during noon and then to the north. The differences between minimum and maximum values in the spatial distribution of RH and ambient air temperature measurements varied from 10 to 20 % and 6 to 8 K, respectively, during the day. At noon (∼14:00 UTC), the RH and air temperature measurements varied from 35 to 60 % and 291 to 297 K, respectively, in the observation domain.

The temporal variability in the mean, median, minimum, and maximum values of the derived global transmittance from the spatial domain is shown in Fig. c. During this day, the relative standard deviation in the derived global transmittance measurements from the pyranometer network varied from 4.0 to 40.9 % (see movie02.avi in the Supplement). The large spatial heterogeneity in global transmittance values is more pronounced through the incoherent variability between different thermopile pyranometers (at FZJ, KIT1, and KIT2) in addition to the large deviation observed from the pyranometer network. Occasional decoupling between the mean and median time series occurred when the sky was covered with broken clouds. As a result, absolute differences between the mean and median values of the derived global transmittance values varied between 0.0 and 0.14 as a function of time, indicating the presence of skewed distributions with outliers that are not symmetrical.

The time series comparison of the derived global transmittance values from collocated thermopile pyranometers with our close-by stations indicated remarkable differences in the observed statistical parameters during the periods of broken-cloud cover (Table ). This implies that the spatial collocation distance between the comparison pyranometers is sensitive under nonhomogeneous sky conditions. As the distance between the comparison pyranometers increases, the linear correlation (r) and the slope of the regression decreases while the RMSE increases. The frequency distribution of instantaneous spatial global transmittance values (Fig. d) indicate a bimodal distribution with a dominant peak at higher transmittance value (∼0.7) and an insignificant peak at lower transmittance value (∼0.2). The dominance of a peak at higher transmittance values possibly indicate the prevalence of a more open clear-sky portions relative to the cloud cover.

An overcast sky is characterized by relatively lower global irradiance than that of a clear-sky situation at any wavelength. Atmospheric transmission can be reduced to less than 10 % of its clear-sky value under thick overcast conditions and the downward radiance distribution is almost independent of the direction.

The instantaneous spatial distribution of the derived global transmittance on an almost overcast day (30 May 2013) is shown in Fig. a along with the corresponding sky image (Fig. b). During this day, strong cloudiness prevailed mostly with few clearings in between. Winds from the south were prevailing throughout the day. As there was rain in the previous night and early morning, significant differences between the minimum and maximum values of RH were observed (20 to 40 %) while ambient air temperature remained consistent and homogeneous (∼ 6 K) throughout the day. Though RH measurements varied between 40 and 80 %, ambient air temperature measurements were less variable (280 to 286 K) during the day in the observation domain.

The temporal variability in the mean, median, minimum, and maximum values of the derived global transmittance from the spatial domain is shown in Fig. c. On this day, the relative standard deviation in the derived global transmittance measurements from the pyranometer network varied from 7.6 to 75.1 % (movie03.avi in the Supplement). Large deviations indicate the prevalence of nonhomogeneous and variable conditions in the sky. The absolute differences between the mean and median values of the derived global transmittance varied similar to broken cloudy conditions (between 0.0 and 0.14) indicating the presence of skewed distributions with outliers that are not symmetrical. Throughout the day, the dominance of lower global transmittance values (<0.5) in the spatial domain indicate thick overcast cloud cover in the sky. Very high global transmittance values (>1.0) were also observed in the morning before 08:30 UTC during the periods of short clearances in the sky (i.e., broken clouds). At this time, the global horizontal irradiance observed at the surface was higher for some stations than the corresponding values at the TOA. It is possible that for short time periods under broken cloudy conditions, the downward global irradiance at the surface can be larger than that at the TOA due to the scattering of photons from the cloud edges (i.e., broken-cloud effect) that are not in the way of incident solar beam . This was also pronounced with the collocated thermopile pyranometers (at KIT1 and KIT2).

The time series comparison of the derived global transmittance from thermopile pyranometers with nearby network stations indicated a high linear correlation, r >0.82 (Table ). The frequency distribution of instantaneous global transmittance values from the network (Fig. d) indicated a monomodal distribution with one dominant peak lying towards lower transmittance values (∼0.3) during overcast conditions. However, during shorter clearances (before 08:30 UTC) with broken clouds a bimodal distribution was observed with a dominant peak towards lower transmittance values.