Since the late 70’s, successive satellite missions have been monitoring the sun’s activity, recording the total solar irradiance (TSI). Some of these measurements last for more than a decade. It is then mandatory to merge them to obtain a seamless record whose duration exceeds that of the individual instruments. Climate models can be better validated using such long TSI records which can also help provide stronger constraints on past climate reconstructions (e.g.,back to the Maunder minimum). We propose a 3-stepmethod based on data fusion, including a stochastic noise model to take into account short and long-term correlations. Compared with previous products, the difference in terms of mean value over the whole time series and at the various solar minima are below 0.2W/m2. Next, we model the frequency spectrum of this 41-year TSI composite time series with a Generalized Gauss-Markov model to help describing an observed flattening at high frequencies. It allows us to fit a linear trend into these TSI time series by joint inversion with the stochastic noise model via a maximum-likelihood estimator. Our results show that the amplitude of such trend is∼−0.009±0.010 W/(m2.yr) for the period 1980-2021. These results are compared with the difference of irradiance values estimated from two consecutive solar minima. We conclude that the trend in these com-posite time series is mostly an artefact due to the coloured noise.

Microwave signals, for example, those from Global Navigation Satellite Systems (GNSS) and very long baseline interferometry, are affected by tropospheric turbulence in such a way that the random fluctuations of the atmospheric index of refraction correlate the phase measurements. These atmospheric correlations are an important error source in space geodetic techniques. For computational reasons, they are neglected in positioning applications, to the detriment of a trustworthy description of the precision, and rigorous test statistics. Fortunately, modelling such correlations is possible by combining concepts from electromagnetic wave propagation in a random medium and the Kolmogorov turbulence theory. In this contribution, we will process single differences GNSS phase observations from a 300 m baseline between two different receivers linked to a common clock. After a preprocessing to filter additional error contributions, such as multipath, we will study the power spectral density of the phase residuals. We will estimate its low and high cutoff frequencies with an adapted unbiased Whittle maximum likelihood estimator. These cutoff frequencies – as predicted by turbulence theory – are related directly to the scale lengths of turbulence, i.e. the size of the eddies that correlate the GNSS observations. The study of their dependencies with the satellite geometry, day of the year, or time of the day provides new insights into the two- and three-dimensional atmospheric turbulence in the atmosphere. In addition, it contributes to improving the stochastic description of random effects impacting GNSS phase observations.

Since the late 70’s, successive satellite missions have been monitoring the sun’s activity, recording total solar irradiance observations. These measurements provide estimates of the Earth’s energy imbalance, i.e. the difference of energy absorbed and emitted by our planet. With this amount of TSI data, solar irradiance reconstruction models can be better validated which can also improve studies looking at past climate reconstructions (e.g., Maunder minimum). Various algorithms have been proposed to merge the various TSI measurements recorded over the last 4 decades. We develop a 3-step algorithm based on data fusion, including a stochastic noise model to take into account the short and long-term correlations. We develop a wavelet filter in order to eliminate specific correlations introduced by the data fusion. Comparing with previous products,the mean value difference is below 0.1 W/m2and the discrepancy with the solar minima is mostly below 0.05 W/m2. Next, we model the frequency spectrum of this 40-year TSI composite time series with a Generalized Gauss-Markov model(with white noise) due to an observe flattening at high frequencies. It allows us to fit a linear trend in these TSI time series by joint inversion with the stochastic noise model via a maximum-likelihood estimator. Our results show that the amplitude of such trend is ∼ -0.009+/-0.01 W/(m2.yr). We conclude that the trend in these composite time series is mostly an artifact due to the solar noise.