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 ∼−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.

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The choice of an appropriate metric is mandatory to perform deformation analysis between two point clouds (PC)—the distance has to be trustworthy and, simultaneously, robust against measurement noise, which may be correlated and heteroscedastic. The Hausdorff distance (HD) or its averaged derivation (AHD) are widely used to compute local distances between two PC and are implemented in nearly all commercial software. Unfortunately, they are affected by measurement noise, particularly when correlations are present. In this contribution, we focus on terrestrial laser scanner (TLS) observations and assess the impact of neglecting correlations on the distance computation when a mathematical approximation is performed. The results of the simulations are extended to real observations from a bridge under load. Highly accurate laser tracker (LT) measurements were available for this experiment: they allow the comparison of the HD and AHD between two raw PC or between their mathematical approximations regarding reference values. Based on these results, we determine which distance is better suited in the case of heteroscedastic and correlated TLS observations for local deformation analysis. Finally, we set up a novel bootstrap testing procedure for this distance when the PC are approximated with B-spline surfaces.

For a trustworthy least-squares (LS) solution, a good description of the stochastic properties of the measurements is indispensable. For a terrestrial laser scanner (TLS), the range variance can be described by a power law function with respect to the intensity of the reflected signal. The power and scaling factors depend on the laser scanner under consideration, and could be accurately determined by means of calibrations in 1d mode or residual analysis of LS adjustment. However, such procedures complicate significantly the use of empirical intensity models (IM). The extent to which a point-wise weighting is suitable when the derived variance covariance matrix (VCM) is further used in a LS adjustment remains moreover questionable. Thanks to closed loop simulations, where both the true geometry and stochastic model are under control, we investigate how variations of the parameters of the IM affect the results of a LS adjustment. As a case study, we consider the determination of the Cartesian coordinates of the control points (CP) from a B-splines curve. We show that a constant variance can be assessed to all the points of an object having homogeneous properties, without affecting the a posteriori variance factor or the loss of efficiency of the LS solution. The results from a real case scenario highlight that the conclusions of the simulations stay valid even for more challenging geometries. A procedure to determine the range variance is proposed to simplify the computation of the VCM.

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