Abstract
Abstract. The time series of global radiation observed by a dense network of 99 autonomous pyranometers during the HOPE campaign around Jülich, Germany, are investigated with a multiresolution analysis based on the maximum overlap discrete wavelet transform and the Haar wavelet. For different sky conditions, typical wavelet power spectra are calculated to quantify the timescale dependence of variability in global transmittance. Distinctly higher variability is observed at all frequencies in the power spectra of global transmittance under broken-cloud conditions compared to clear, cirrus, or overcast skies. The spatial autocorrelation function including its frequency dependence is determined to quantify the degree of similarity of two time series measurements as a function of their spatial separation. Distances ranging from 100 m to 10 km are considered, and a rapid decrease of the autocorrelation function is found with increasing frequency and distance. For frequencies above 1∕3 min−1 and points separated by more than 1 km, variations in transmittance become completely uncorrelated. A method is introduced to estimate the deviation between a point measurement and a spatially averaged value for a surrounding domain, which takes into account domain size and averaging period, and is used to explore the representativeness of a single pyranometer observation for its surrounding region. Two distinct mechanisms are identified, which limit the representativeness; on the one hand, spatial averaging reduces variability and thus modifies the shape of the power spectrum. On the other hand, the correlation of variations of the spatially averaged field and a point measurement decreases rapidly with increasing temporal frequency. For a grid box of 10 km × 10 km and averaging periods of 1.5–3 h, the deviation of global transmittance between a point measurement and an area-averaged value depends on the prevailing sky conditions: 2.8 (clear), 1.8 (cirrus), 1.5 (overcast), and 4.2 % (broken clouds). The solar global radiation observed at a single station is found to deviate from the spatial average by as much as 14–23 (clear), 8–26 (cirrus), 4–23 (overcast), and 31–79 W m−2 (broken clouds) from domain averages ranging from 1 km × 1 km to 10 km × 10 km in area.
Highlights
The Sun is the primary source of energy for the Earth’s climate system
The time series of global radiation observed by a dense network of 99 autonomous pyranometers during the HOPE campaign around Jülich, Germany, are investigated with a multiresolution analysis based on the maximum overlap discrete wavelet transform and the Haar wavelet
As the time series of global transmittance results from a non-stationary process, the wavelet power spectrum is a suitable tool for the analysis of the variability contained within specific frequency intervals, and to study the effect of temporal and spatial averaging on the variability of the time series
Summary
The Sun is the primary source of energy for the Earth’s climate system. Clouds strongly modulate the radiation budget through reflection of solar radiation back to space, and by trapping terrestrial radiation within the atmosphere (Trenberth et al, 2009). According to the latest Intergovernmental Panel on Climate Change report, the impact of various cloud types on the net radiation budget is not fully understood to the extent that for some cloud types neither the magnitude nor even the sign is known (Boucher et al, 2013). This can be attributed to our currently still very limited understanding of cloud processes and the resulting cloud– radiation interactions, due to their complexity and the wide range of scales involved.
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