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Geostationary weather satellites collect high‐resolution data comprising a series of images. The Derived Motion Winds (DMW) Algorithm is commonly used to process these data and estimate atmospheric winds by tracking features in the images. However, the wind estimates from the DMW Algorithm are often missing and do not come with uncertainty measures. Also, the DMW Algorithm estimates can only be half‐integers, since the algorithm requires the original and shifted data to be at the same locations, in order to calculate the displacement vector between them. This motivates us to statistically model wind motions as a spatial process drifting in time. Using a covariance function that depends on spatial and temporal lags and a drift parameter to capture the wind speed and wind direction, we estimate the parameters by local maximum likelihood. Our method allows us to compute standard errors of the local estimates, enabling spatial smoothing of the estimates using a Gaussian kernel weighted by the inverses of the estimated variances. We conduct extensive simulation studies to determine the situations where our method performs well. The proposed method is applied to the GOES‐15 brightness temperature data over Colorado and reduces prediction error of brightness temperature compared to the DMW Algorithm.

 

Wind is a critical component of the Earth system and has unmistakable impacts on everyday life.The CYGNSS satellite mission improves observational coverage of ocean windsviaa fleet of eightmicro-satellites that use reflected GNSS signals to infer surface wind speed. We present analysescharacterizing variability in wind speed measurements among the eight CYGNSS satellites andbetween antennas, using a Gaussian process model that leverages comparisons between CYGNSSand Jason-3 during a one-year period from September 2019 to September 2020. The CYGNSS sen-sors exhibit a range of biases, mostly between1.0 m/s andþ0.2 m/s with respect to Jason-3,indicating that some CYGNSS sensors are biased with respect to one another and with respect toJason-3. The biases between the starboard and port antennas within a CYGNSS satellite aresmaller. Our results are consistent with, yet sharper than, a more traditional paired comparisonanalysis. We also explore the possibility that the bias depends on wind speed, finding some evi-dence that CYGNSS satellites have positive biases with respect to Jason-3 at low wind speeds.However, we argue that there are subtle issues associated with estimating wind speed-dependentbiases, so additional careful statistical modeling and analysis is warranted. 

We describe our implementation of the multivariate Matérn model for multivariate spatial datasets, using Vecchia’s approximation and a Fisher scoring optimization algorithm. We consider various pararameterizations for the multivariate Matérn that have been proposed in the literature for ensuring model validity, as well as an unconstrained model. A strength of our study is that the code is tested on many real-world multivariate spatial datasets. We use it to study the effect of ordering and conditioning in Vecchia’s approximation and the restrictions imposed by the various parameterizations. We also consider a model in which co-located nuggets are correlated across components and find that forcing this cross-component nugget correlation to be zero can have a serious impact on the other model parameters, so we suggest allowing cross-component correlation in co-located nugget terms. 

We derive a single-pass algorithm for computing the gradient and Fisher information of Vecchia’s Gaussian process loglikelihood approximation, which provides a computationally efficient means for applying the Fisher scoring algorithm for maximizing the loglikelihood. The advantages of the optimization techniques are demonstrated in numerical examples and in an application to Argo ocean temperature data. The new methods find the maximum likelihood estimates much faster and more reliably than an optimization method that uses only function evaluations, especially when the covariance function has many parameters. This allows practitioners to fit nonstationary models to large spatial and spatial–temporal datasets.