Search

Since the late 1970s, successive satellite missions have been monitoring the sun's activity and recording the total solar irradiance (TSI). Some of these measurements have lasted for more than a decade. In order to obtain a seamless record whose duration exceeds that of the individual instruments, the time series have to be merged. Climate models can be better validated using such long TSI time series which can also help to provide stronger constraints on past climate reconstructions (e.g., back to the Maunder minimum). We propose a 3-step method based on data fusion, including a stochastic noise model to take into account short and long-term correlations. Compared with previous products scaled at the nominal TSI value of 1361 W/m2, the difference is below 0.2 W/m2 in terms of solar minima. Next, we model the frequency spectrum of this 41-year TSI composite time series with a Generalized Gauss-Markov model to help describe 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 $\sim$ -0.004 +/- 0.004 W/(m2yr) 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 composite time series is mostly an artifact due to the colored noise., Comment: accepted for publication in JGR Atmospheres; in Special Section: Monitoring the Earth radiation budget and its implication to climate simulations: Recent Advances and Discussions

The Global Navigation Satellite System (GNSS) daily position time series are often described as the sum of stochastic processes and geophysical signals which allow studying global and local geodynamical effects such as plate tectonics, earthquakes, or ground water variations. In this work we propose to extend the Generalized Method of Wavelet Moments (GMWM) to estimate the parameters of linear models with correlated residuals. This statistical inferential framework is applied to GNSS daily position time series data to jointly estimate functional (geophysical) as well as stochastic noise models. Our method is called GMWMX, with X standing for eXogeneous variable: it is semi-parametric, computationally efficient and scalable. Unlike standard methods such as the widely used Maximum Likelihood Estimator (MLE), our methodology offers statistical guarantees, such as consistency and asymptotic normality, without relying on strong parametric assumptions. At the Gaussian model, our results show that the estimated parameters are similar to the ones obtained with the MLE. The computational performances of our approach has important practical implications. Indeed, the estimation of the parameters of large networks of thousands of GNSS stations quickly becomes computationally prohibitive. Compared to standard methods, the processing time of the GMWMX is over $1000$ times faster and allows the estimation of large scale problems within minutes on a standard computer. We validate the performances of our method via Monte-Carlo simulations by generating GNSS daily position time series with missing observations and we consider composite stochastic noise models including processes presenting long-range dependence such as power-law or Mat\'ern processes. The advantages of our method are also illustrated using real time series from GNSS stations located in the Eastern part of the USA., Comment: 30 pages, 11 figures, 3 tables

In this contribution, we introduce a multilevel approximation method with T-splines for fitting scattered point clouds iteratively, with an application to land remote sensing. This new procedure provides a local surface approximation by an explicit computation of the control points and is called a multilevel T-splines approximation (MTA). It is computationally efficient compared with the traditional global least-squares (LS) approach, which may fail when there is an unfavourable point density from a given refinement level. We validate our approach within a simulated framework and apply it to two real datasets: (i) a surface with holes scanned with a terrestrial laser scanner, and (ii) a patch on a sand-dune in the Netherlands. Both examples highlight the potential of the MTA for rapidly fitting large and noisy point clouds with variable point density and with similar results compared to the global LS approximation., Comment: 28 pages, 10 figures