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In this paper, a stochastic model is proposed for a joint statistical description of solar photovoltaic (PV) power and outdoor temperature. The underlying correlation emerges from solar irradiance that is responsible in part for both the variability in solar PV power and temperature. The proposed model can be used to capture the uncertainty in solar PV power and its correlation with the electric power consumption of thermostatically controlled loads. First, a model for solar PV power that explicitly incorporates the stochasticity due to clouds via a regime-switching process between the three classes of sunny, overcast and partly cloudy is proposed. Then, the relationship between temperature and solar power is postulated using a second-order Volterra model. This joint modeling is leveraged to develop a joint probabilistic forecasting method for solar PV power and temperature. Real-world datasets that include solar PV power and temperature measurements in California are analyzed and the effectiveness of the joint model in providing probabilistic forecasts is verified. The proposed forecasting methodology outperforms several reference methods thus portraying that the underlying correlation between temperature and solar PV power is well defined and only requires a simple lower-complexity sampling space. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of obtaining a reduced-dimension parameterization of a propagation medium for the purpose of estimating the medium from transmission data. The application addressed is microwave remote sensing of tropospheric index-of-refraction profiles over the sea surface, using radar clutter returns. The proposed parameterization balances the desire to represent features prominent in the a priori statistics of the profiles versus the need to capture elements of the profile that significantly affect the observed clutter data. In linear estimation problems, basis vectors for the unknown parameter vector that optimizes this tradeoff have been derived as the reduced-rank Wiener filter or, equivalently, the generalized Karhunen-Loeve transform (GKLT). In this paper, we reinterpret the linear result, producing an extension to the nonlinear refractivity estimation problem. The resulting procedure produces basis vectors for tropospheric refractivity that are less dependent on features that have little effect on the clutter measurements. This results in a more efficient parameterization and reduces mean-square estimation error relative to an approach driven purely by the statistical prior. Application of the generalized KL technique to finding efficient basis vectors for refractivity profiles taken off the southern California coast is presented. [ABSTRACT FROM AUTHOR]