Abstract
This study addresses long-term sea level variability in Macaronesia from a holistic perspective using all available instrumental records in the region, including a dense network of GPS continuous stations, tide gauges and satellite observations. A detailed assessment of vertical movement from GPS time series underlines the influence of the complex volcano-tectonic setting of the Macaronesian islands in local uplift/subsidence. Relative sea level for the region is spatially highly variable, ranging from -1.1 to 5.1 mm yr(-1). Absolute sea level from satellite altimetry exhibits consistent trends in the Macaronesia, with a mean value of 3.0 +/- 0.5 mm yr(-1). Typically, sea level trends from tide gauge records corrected for vertical movement using the estimates from GPS time series are lower than uncorrected estimates. The agreement between satellite altimetry and tide gauge trends corrected for vertical land varies substantially from island to island. Trends derived from the combination of GPS and tide gauge observations differ by less than 1 mm yr(-1) with respect to absolute sea level trends from satellite altimetry for 56 per cent of the stations, despite the heterogeneity in length of both GPS and tide gauge series, and the influence of volcanic-tectonic processes affecting the position of some GPS stations.

Abstract
This work addresses the short-term variability of gamma radiation measured continuously at the Eastern North Atlantic (ENA) facility located in the Graciosa island (Azores, 39N; 28W), a fixed site of the Atmospheric Radiation Measurement programme (ARM). The temporal variability of gamma radiation is characterized by occasional anomalies over a slowly-varying signal. Sharp peaks lasting typically 2-4 h are coincident with heavy precipitation and result from the scavenging effect of precipitation bringing radon progeny from the upper levels to the ground surface. However the connection between gamma variability and precipitation is not straightforward as a result of the complex interplay of factors such as the precipitation intensity, the PBL height, the cloud's base height and thickness, or the air mass origin and atmospheric concentration of sub-micron aerosols, which influence the scavenging processes and therefore the concentration of radon progeny. Convective precipitation associated with cumuliform clouds forming under conditions of warming of the ground relative to the air does not produce enhancements in gamma radiation, since the drop growing process is dominated by the fast accretion of liquid water, resulting in the reduction of the concentration of radionuclides by dilution. Events of convective precipitation further contribute to a reduction in gamma counts by inhibiting radon release from the soil surface and by attenuating gamma rays from all gamma-emitting elements on the ground. Anomalies occurring in the absence of precipitation are found to be associated with a diurnal cycle of maximum gamma counts before sunrise decreasing to a minimum in the evening, which are observed in conditions of thermal stability and very weak winds enabling the build-up of near surface radon progeny during the night.

Abstract
This article presents an optimal estimator for discrete-time systems disturbed by output white noise, where the proposed algorithm identifies the parameters of a Multiple Input Single Output LPV State Space model. This is an LPV version of a class of algorithms proposed elsewhere for identifying LTI systems. These algorithms use the matchable observable linear identification parameterization that leads to an LTI predictor in a linear regression form, where the ouput prediction is a linear function of the unknown parameters. With a proper choice of the predictor parameters, the optimal prediction error estimator can be approximated. In a previous work, an LPV version of this method, that also used an LTI predictor, was proposed; this LTI predictor was in a linear regression form enablin, in this way, the model estimation to be handled by a Least-Squares Support Vector Machine approach, where the kernel functions had to be filtered by an LTI 2D-system with the predictor dynamics. As a result, it can never approximate an optimal LPV predictor which is essential for an optimal prediction error LPV estimator. In this work, both the unknown parameters and the state-matrix of the output predictor are described as a linear combination of a finite number of basis functions of the scheduling signal; the LPV predictor is derived and it is shown to be also in the regression form, allowing the unknown parameters to be estimated by a simple linear least squares method. Due to the LPV nature of the predictor, a proper choice of its parameters can lead to the formulation of an optimal prediction error LPV estimator. Simulated examples are used to assess the effectiveness of the algorithm. In future work, optimal prediction error estimators will be derived for more general disturbances and the LPV predictor will be used in the Least-Squares Support Vector Machine approach.

Abstract
This article presents four state-space models for high pressure gas pipelines, departing from a system of nonlinear partial differential equations. The models were derived taking advantage of an electrical analogy and are very accurate and simple, therefore suitable for network simulation and analysis. The models' simulation is compared with the data obtained with Simone (R), a commercial simulator of gas transport and distribution networks used by many european companies, and exhibit similar accuracy.

Abstract
While most physical systems or phenomena occur in continuous-time, identification methods based on discrete-time models are more widespread among practitioners and academic community, possibly due to the discrete-time nature of the data records. There has been a growing interest in estimating continuous-time (CT) models in the last decade. This work develops algorithms to estimate the parameters of multivariable state-space CT models from input-output samples using a method based on the recently developed MOLI-ZOFT approach. The performance of the algorithm is evaluated using real data from an industrial winding process.

Abstract
A cost-effective, accurate, and robust leak detection method is essential in gas network management in order to reduce inspection time and to increase reliability in the system. This work presents a model-based leakage detection method; the gas dynamics are described by a linearized system of partial differential equations that is further reduced to a one-dimensional spatial model. By using an electrical analogy, a pipeline can be represented by a two-port network, where mass flow behaves like current and pressure like voltage. Four transfer function quadripole models are then established to describe the gas pipeline dynamics, depending on the variables of interest at the pipeline boundaries. A leak detection method is devised by employing mass flow data at boundaries and pressure data at some point of the pipeline, as well as by assessing the effects of the leakage on the pressure and mass flow along the pipeline. A case study has been built from operational data supplied by REN Gasodutos (the Portuguese gas company) to show the advantages of the proposed models. © Springer International Publishing AG 2017.