Multiresolution analysis of the spatiotemporal variability in global radiation observed by a dense network of 99 pyranometers

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.

The HD(CP)<sup>2</sup> Observational Prototype Experiment (HOPE) – an overview

“…Based on the autonomous pyranometer network described in Madhavan et al (2016), the representativeness of a single station measurement for spatially extended domains with different area sizes has been investigated (Madhavan et al, 2017). This is an important aspect for the evaluation of model results with observations, where point measurements are mostly compared to grid-box means and are thus implicitly assumed to have similar statistical properties.…”

Evaluation of Himawari-8 surface downwelling solar radiation by ground-based measurements

“…Previous studies have found that the correlation between sites decreases with distance and increases with temporal aggregation (Engeland et al, 2017). Although time series of spatially averaged irradiance fields generally resemble behavior point measurements, their power spectra are strongly attenuated at higher frequencies and for large domains (Madhavan et al, 2017). Therefore, variation in spatial averages (or satellite pixels) and in point measurements is often poorly correlated at high frequencies (Perez et al, 2016).…”

Evaluation of Himawari-8 surface downwelling solar radiation by SKYNET observations

“…Previous studies have found that the correlation between sites decreases with distance and increases with temporal aggregation (Engeland et al, 2017). Although time series of spatially averaged irradiance fields generally resemble behaviour point measurements, 5 their power spectra are strongly attenuated at higher frequencies and for large domains (Madhavan et al, 2017). Therefore, variation in spatial averages (or satellite pixels) and in point measurements are often poorly correlated at high frequencies.…”