Extended optimal estimation techniques for sea surface temperature from the Spinning Enhanced Visible and Infra-Red Imager (SEVIRI)

Sea surface temperature (SST) can be estimated from day and night observations of the Spinning Enhanced Visible and Infra-Red Imager (SEVIRI) by optimal estimation (OE). We show that exploiting the 8.7 μm channel, in addition to the “traditional” wavelengths of 10.8 and 12.0 μm, improves OE SST retrieval statistics in validation. However, the main benefit is an improvement in the sensitivity of the SST estimate to variability in true SST. In a fair, single-pixel comparison, the 3-channel OE gives better results than the SST estimation technique presently operational within the Ocean and Sea Ice Satellite Application Facility. This operational technique is to use SST retrieval coefficients, followed by a bias-correction step informed by radiative transfer simulation. However, the operational technique has an additional “atmospheric correction smoothing”, which improves its noise performance, and hitherto had no analogue within the OE framework. Here, we propose an analogue to atmospheric correction smoothing, based on the expectation that atmospheric total column water vapour has a longer spatial correlation length scale than SST features. The approach extends the observations input to the OE to include the averaged brightness temperatures (BTs) of nearby clear-sky pixels, in addition to the BTs of the pixel for which SST is being retrieved. The retrieved quantities are then the single-pixel SST and the clear-sky total column water vapour averaged over the vicinity of the pixel. This reduces the noise in the retrieved SST significantly. The robust standard deviation of the new OE SST compared to matched drifting buoys becomes 0.39 K for all data. The smoothed OE gives SST sensitivity of 98% on average. This means that diurnal temperature variability and ocean frontal gradients are more faithfully estimated, and that the influence of the prior SST used is minimal (2%). This benefit is not available using traditional atmospheric correction smoothing.

Extended factorizations of exponential functionals of Lévy processes

Pardo, Patie, and Savov derived, under mild conditions, a Wiener-Hopf type factorization for the exponential functional of proper Lévy processes. In this paper, we extend this factorization by relaxing a finite moment assumption as well as by considering the exponential functional for killed Lévy processes. As a by-product, we derive some interesting fine distributional properties enjoyed by a large class of this random variable, such as the absolute continuity of its distribution and the smoothness, boundedness or complete monotonicity of its density. This type of results is then used to derive similar properties for the law of maxima and first passage time of some stable Lévy processes. Thus, for example, we show that for any stable process with $\rho\in(0,\frac{1}{\alpha}-1]$, where $\rho\in[0,1]$ is the positivity parameter and $\alpha$ is the stable index, then the first passage time has a bounded and non-increasing density on $\mathbb{R}_+$. We also generate many instances of integral or power series representations for the law of the exponential functional of Lévy processes with one or two-sided jumps. The proof of our main results requires different devices from the one developed by Pardo, Patie, Savov. It relies in particular on a generalization of a transform recently introduced by Chazal et al together with some extensions to killed Lévy process of Wiener-Hopf techniques. The factorizations developed here also allow for further applications which we only indicate here also allow for further applications which we only indicate here.