Hilbert-Huang spectral analysis for the characterization of variability in satellite-derived time series of surface solar irradiance

International audienceIn the context of the ever increasing share of renewable energy in the global power mix, the thorough understanding of the variability of the solar resource is key to enable a smooth transition towards a carbon-free world energy scenario. Recently, several studies of the surface solar irradiance (SSI) have addressed the characteristic timescales of its temporal variability, by means of the Hilbert spectral analysis, with encouraging results. These works have focused primarily on high-quality measurements of the SSI from BSRN ground stations. Satellite-estimates of the SSI have become a popular alternative in supplementing ground measurements and offering a synoptic view of the SSI field. The present study aims at extending the previous analyses by dealing with time-series of satellite estimates of SSI. The approach adopted here is of increasing complexity in physical modelling of the SSI. First, a "clean source" synthetic signal, the simulated top-of-the atmosphere extraterrestrial solar irradiance is investigated. Second, to emphasize the role of atmospheric effects (scattering, absorption) on the variability, clear-sky, i.e. cloud-free, estimates of the SSI come under scrutiny. Third, in order to also account for the effects of the clouds, satellite-derived estimates of the SSI are analysed. Finally, a comparison is done with the intrinsic timescales of SSI variability found in ground measurements, which serve as "ground truth". By conducting a complete analysis of the variability of the satellite-derived SSI at each step in the modelling chain, fresh insight is gained into the complex atmospheric interactions at play, which could lead to the improvement of the models and eventually to better forecast

On the temporal variability of the surface solar radiation by means of spectral representations

International audienceThis work deals with the temporal variability of daily means of the global broadband surface solar irradiance (SSI) impinging on a horizontal plane by studying a decennial time-series of high-quality measurements recorded at a BSRN ground station. Since the data have a non-linear and non-stationary character, two time-frequency-energy representations of signal processing are compared in their ability to resolve the temporal variability of the pyranometric signal. First, the continuous wavelet transform is used to construct the wavelet power spectrum of the data. Second, the adaptive, noise-assisted empirical mode decomposition is employed to extract the intrinsic mode functions of the signal, followed by Hilbert spectral analysis. In both spectral representations , the temporal variability of the SSI is portrayed having clearly distinguishable features: a plateau between scales of two days and two-three months that has decreasing power with increasing scale, a large spectral peak corresponding to the annual variability cycle, and a low power regime in between the previous two. It is shown that the data-driven, noise-assisted method yields a somewhat more sparse representation and that it is a suitable tool for inspecting the temporal variability of SSI measurements

Assessing the temporal variability of the surface solar radiation with time-frequency-energy representations

International audienceThe share of solar photovoltaic (PV) energy in the global electricity mix is envisaged to rise in the coming decades. Yet, one major hurdle impeding its widespread penetration has been identified in the variability of the surface solar irradiance (SSI). Hence, a better understanding of the SSI variability can help lower costs for PV electricity producers, thus making solar power more economically attractive and speeding the addition of new production capacity. Here we report on a preliminary assessment of the temporal variability of the SSI by scrutinising long-term time-series of high-quality ground measurements from the BSRN network. Owing to the non-linearity and non-stationarity of the data, analysis is carried out with spectral methods that yield a time-frequency-energy representation of the signals. Two such techniques are employed and their ability in rendering an accurate picture of the temporal variability of the SSI is investigated. First, a scalogram is constructed by means of the continuous wavelet transform. Second, the empirical mode decomposition is used to elicit the embedded oscillatory modes of the signal, on which Hilbert spectral analysis is then applied. Results show that the adaptive nature of the second technique reduces spectral artefacts and yields a clearer image of the temporal variability of the SSI. In particular, the seasonal variability of the SSI is greatly emphasized, with two distinct spectral peaks showing

Assessment of Several Empirical Relationships for Deriving Daily Means of UV-A Irradiance from Meteosat-Based Estimates of the Total Irradiance

International audienceDaily estimates of the solar UV-A radiation (315–400 nm) at the surface, anywhere, anytime, are needed in many epidemiology studies. Satellite-derived databases of solar total irradiance, combined with empirical relationships converting totals into daily means of UV-A irradiance I UV , are a means to satisfy such needs. Four empirical relationships are applied to three different databases: HelioClim-3 (versions 4 and 5) and CAMS Radiation Service—formerly known as MACC-RAD—derived from Meteosat images. The results of these combinations are compared to ground-based measurements located in mid-latitude Europe, mostly in Belgium. Whatever the database, the relationships of Podstawczynska (2010) and of Bilbao et al. (2011) exhibit very large underestimation and RMSE on the order of 40%–50% of the mean I UV. Better and more acceptable results are attained with the relationships proposed by Zavodska and Reichrt (1985) and that of Wald (2012). The relative RMSE is still large and in the range 10%–30% of the mean I UV. The correlation coefficients are large for all relationships. Each of them captures most of the variability contained in the UV measurements and can be used in studies where correlation plays a major role

Time-frequency analysis of surface solar radiation data

Cette thèse traite de la variabilité temporelle intrinsèque de l'éclairement solaire reçu au sol. Les échelles caractéristiques de variabilité sont mises en évidence par l'analyse de longues séries temporelles de moyennes journalières de l'éclairement, pour différents endroits du monde, issues de mesures pyranométriques au sol, d'estimations satellitaires ou de réanalyses météorologiques .Compte-tenu de la nature non linéaire et non stationnaire des données, la transformée adaptative de Hilbert-Huang est utilisée comme outil d'analyse pour tenir compte de la diversité de ces échelles temporelles. On montre ainsi la nature variable des échelles caractéristiques et de leur intensité, ainsi que leur dépendance vis-à-vis du climat.L'application d'une technique adaptative de ré-échantillonnage fractionnaire montre la juxtaposition d'une composante déterministe et d'une stochastique. Pour tous les jeux de données, le cycle annuel déterministe représente la plus grande partie de la variabilité. Toutes les séries temporelle contiennent une composante de variabilité stochastique à haute fréquence, qui est modulée en amplitude par le cycle annuel.L'approche permet également d'évaluer, échelle par échelle, les performances des estimations satellitaires ou issues de ré-analyses par comparaison avec des mesures pyranométriques au sol. Une étude de cas confirme que les estimations satellitaires surpassent les ré-analyses à toutes les échelles temporelles.The center of focus for this PhD thesis is the intrinsic temporal variability of the surface solar irradiance (SSI). The characteristic time-scales of variability are revealed by analysing long-term time-series of daily means of SSI, such as ground measurements, satellite estimates, or radiation products from global atmospheric re-analyses, for different geographical locations around the world.To account for the wide range of the time-scales of variability, and given the non-linear and non-stationary nature of the data, the adaptive, data-driven Hilbert-Huang Transform is employed as an analysis tool. The time-varying nature of the characteristic time-scales of variability, along with variations in intensity, are thus revealed.An adaptive fractional re-sampling technique is used to discriminate between the deterministic and the stochastic variability constituents. For all datasets, the deterministic yearly cycle is found to account for the largest part of variability. Furthermore, all time-series are found to contain a high-frequency stochastic variability component, that exhibit cross-scale amplitude modulation by the yearly cycle.A refinement to existing methods for assessing the fitness for use of surrogate SSI products in lieu of ground measurements is also proposed. A case study confirms that satellite estimates outperform re-analyses across all time-scales

Analyse temps-fréquence des données de rayonnement solaire reçu au sol

The center of focus for this PhD thesis is the intrinsic temporal variability of the surface solar irradiance (SSI). The characteristic time-scales of variability are revealed by analysing long-term time-series of daily means of SSI, such as ground measurements, satellite estimates, or radiation products from global atmospheric re-analyses, for different geographical locations around the world.To account for the wide range of the time-scales of variability, and given the non-linear and non-stationary nature of the data, the adaptive, data-driven Hilbert-Huang Transform is employed as an analysis tool. The time-varying nature of the characteristic time-scales of variability, along with variations in intensity, are thus revealed.An adaptive fractional re-sampling technique is used to discriminate between the deterministic and the stochastic variability constituents. For all datasets, the deterministic yearly cycle is found to account for the largest part of variability. Furthermore, all time-series are found to contain a high-frequency stochastic variability component, that exhibit cross-scale amplitude modulation by the yearly cycle.A refinement to existing methods for assessing the fitness for use of surrogate SSI products in lieu of ground measurements is also proposed. A case study confirms that satellite estimates outperform re-analyses across all time-scales.Cette thèse traite de la variabilité temporelle intrinsèque de l'éclairement solaire reçu au sol. Les échelles caractéristiques de variabilité sont mises en évidence par l'analyse de longues séries temporelles de moyennes journalières de l'éclairement, pour différents endroits du monde, issues de mesures pyranométriques au sol, d'estimations satellitaires ou de réanalyses météorologiques .Compte-tenu de la nature non linéaire et non stationnaire des données, la transformée adaptative de Hilbert-Huang est utilisée comme outil d'analyse pour tenir compte de la diversité de ces échelles temporelles. On montre ainsi la nature variable des échelles caractéristiques et de leur intensité, ainsi que leur dépendance vis-à-vis du climat.L'application d'une technique adaptative de ré-échantillonnage fractionnaire montre la juxtaposition d'une composante déterministe et d'une stochastique. Pour tous les jeux de données, le cycle annuel déterministe représente la plus grande partie de la variabilité. Toutes les séries temporelle contiennent une composante de variabilité stochastique à haute fréquence, qui est modulée en amplitude par le cycle annuel.L'approche permet également d'évaluer, échelle par échelle, les performances des estimations satellitaires ou issues de ré-analyses par comparaison avec des mesures pyranométriques au sol. Une étude de cas confirme que les estimations satellitaires surpassent les ré-analyses à toutes les échelles temporelles

Characterizing Temporal Variability in Measurements of Surface Solar Radiation and its Dependence on Climate

International audienceThe intrinsic temporal scales of the variability of the surface solar radiation are addressed by means of the empirical mode decomposition. High quality measurements of the solar radiation impinging on a horizontal plane at ground level, from different BSRN ground stations, are analysed. By first extracting all the embedded oscillations that share a common local timescale , followed by Hilbert spectral analysis, the characteristic scales of variability, along with the fluctuations in the intensity of the pyranometric signal, are revealed. It is shown that data from stations with different local climates share some common features, most notably a high-frequency plateau of variability whose amplitude is found to be modulated by the seasonal cycle. The study has possible implications on the modelling and the forecast of the surface solar radiation, at different local timescales

Adaptive data analysis for characterizing the temporal variability of the solar resource

International audienceOne of the key challenges associated with the large-scale penetration of solar power is the inherent spatio-temporal variability of the solar radiation impinging on the surface. Particular methods are currently employed to measure, estimate or forecast the extent and availability of the solar resource depending on the effective spatial and temporal scales of interest, such as numerical weather prediction models, satellite-based estimates, sky-imagers or in-situ ground measurements. Here we present a method for characterizing the intrinsic timescales of the solar resource variability. The study deals with decennial time-series of daily values of the surface solar irradiance (SSI) issued from high-quality BSRN ground measurement stations. Geophysical signals, such as the SSI time-series under scrutiny, are often the result of non-linear interactions of physical processes that are also often under natural or anthropogenic non-stationary forcings. Therefore, an adaptive data analysis technique is employed that makes no beforehand assumptions about the data: neither linearity, nor stationarity of the signal is assumed. The method, called the Hilbert-Huang transform, first extracts all the embedded oscillations that have a similar timescale , to which it then applies Hilbert spectral analysis. A time-frequency-energy representation of the signal is thus constructed, which reveals the time-varying character of the intrinsic temporal scales of variability (frequency modulation), along with any fluctuations in the intensity of the signal at the corresponding scale (amplitude modulation). In order to test whether the features extracted from the data are the expression of deterministic physical processes, as opposed to being stochastic realizations of various background processes (i.e. noise), a novel, adaptive null-hypothesis based on the statistical properties of noise is employed. It is shown that the data, irrespective of the geographical conditions, shares common timescales of variability, along with a plateau of noise-like features, whose amplitude is found to be modulated by variations in the intensity of the seasonal cycle

Hilbert-Huang spectral analysis for characterizing the intrinsic time-scales of variability in decennial time-series of surface solar radiation

International audienceAn analysis of the variability of the surface solar irradiance (SSI) at different local timescales is presented in this study. Since geophysical signals, such as long-term measurements of the SSI, are often produced by the non-linear interaction of deterministic physical processes that may also be under the influence of non-stationary external forcings, the Hilbert-Huang transform (HHT), an adaptive, noise-assisted, data-driven technique, is employed to extract locally – in time and in space – the embedded intrinsic scales at which a signal oscillates. The transform consists of two distinct steps. First, by means of the Empirical Mode Decomposition (EMD), the time-series is " de-constructed " into a finite number – often small – of zero-mean components that have distinct temporal scales of variability, termed hereinafter the Intrinsic Mode Functions (IMFs). The signal model of the components is an amplitude modulation-frequency modulation (AM-FM) one, and can also be thought of as an extension of a Fourier series having both time varying amplitude and frequency. Following the decomposition, Hilbert spectral analysis is then employed on the IMFs, yielding a time-frequency-energy representation that portrays changes in the spectral contents of the original data, with respect to time. As measurements of surface solar irradiance may possibly be contaminated by the manifestation of different type of stochastic processes (i.e. noise), the identification of real, physical processes from this background of random fluctuations is of interest. To this end, an adaptive background noise null hypothesis is assumed, based on the robust statistical properties of the EMD when applied to time-series of different classes of noise (e.g. white, red or fractional Gaussian). Since the algorithm acts as an efficient constant-Q dyadic, "wavelet-like", filter bank, the different noise inputs are decomposed into components having the same spectral shape, but that are translated to the next lower octave in the spectral domain. Thus, when the sampling step is increased, the spectral shape of IMFs cannot remain at its original position, due to the new lower Nyquist frequency, and is instead pushed toward the lower scaled frequency. Based on these features, the identification of potential signals within the data should become possible without any prior knowledge of the background noises

Do modelled or satellite-based estimates of surface solar irradiance accurately describe its temporal variability?

International audienceThis study investigates the characteristic timescales of variability found in long-term time-series of daily means of estimates of surface solar irradiance (SSI). The study is performed at various levels to better understand the causes of variability in the SSI. First, the variability of the solar irradiance at the top of the atmosphere is scrutinized. Then, estimates of the SSI in cloud-free conditions as provided by the McClear model are dealt with, in order to reveal the influence of the clear atmosphere (aerosols, water vapour, etc.). Lastly, the role of clouds on variability is inferred by the analysis of in-situ measurements. A description of how the atmosphere affects SSI variability is thus obtained on a timescale basis. The analysis is also performed with estimates of the SSI provided by the satellite-derived HelioClim-3 database and by two numerical weather re-analyses: ERA-Interim and MERRA2. It is found that HelioClim-3 estimates render an accurate picture of the variability found in ground measurements, not only globally, but also with respect to individual characteristic timescales. On the contrary, the variability found in re-analyses correlates poorly with all scales of ground measurements variability