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Given the increasing prevalence of wildland fires in the Western US, there is a crit- ical need to develop tools to understand and accurately predict burn severity. We develop a novel machine learning model to predict post-fire burn severity using pre- fire remotely sensed data. Hydrological, ecological, and topographical variables col- lected from four regions of California — the site of the Kincade fire (2019), the CZU Lightning Complex fire (2020), the Windy fire (2021), and the KNP Fire (2021) — are used as predictors of the differenced normalized burn ratio. We hypothesize that a Super Learner (SL) algorithm that accounts for spatial autocorrelation using Vec- chia’s Gaussian approximation will accurately model burn severity. We use a cross- validation study to show that the spatial SL model can predict burn severity with reasonable classification accuracy, including high burn severity events. After fitting and verifying the performance of the SL model, we use interpretable machine learn- ing tools to determine the main drivers of severe burn damage, including greenness, elevation, and fire weather variables. These findings provide actionable insights that enable communities to strategize interventions, such as early fire detection systems, pre-fire season vegetation clearing activities, and resource allocation during emer- gency responses. When implemented, this model has the potential to minimize the loss of human life, property, resources, and ecosystems in California. 

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.

 

Geostatistical modeling for continuous point‐referenced data has extensively been applied to neuroimaging because it produces efficient and valid statistical inference. However, diffusion tensor imaging (DTI), a neuroimaging technique characterizing the brain's anatomical structure, produces a positive‐definite (p.d.) matrix for each voxel. Currently, only a few geostatistical models for p.d. matrices have been proposed because introducing spatial dependence among p.d. matrices properly is challenging. In this paper, we use the spatial Wishart process, a spatial stochastic process (random field), where each p.d. matrix‐variate random variable marginally follows a Wishart distribution, and spatial dependence between random matrices is induced by latent Gaussian processes. This process is valid on an uncountable collection of spatial locations and is almost‐surely continuous, leading to a reasonable way of modeling spatial dependence. Motivated by a DTI data set of cocaine users, we propose a spatial matrix‐variate regression model based on the spatial Wishart process. A problematic issue is that the spatial Wishart process has no closed‐form density function. Hence, we propose an approximation method to obtain a feasible Cholesky decomposition model, which we show to be asymptotically equivalent to the spatial Wishart process model. A local likelihood approximation method is also applied to achieve fast computation. The simulation studies and real data application demonstrate that the Cholesky decomposition process model produces reliable inference and improved performance, compared to other methods.

 

Spatial extremes are common for climate data as the observations are usually referenced by geographic locations and dependent when they are nearby. An important goal of extremes modeling is to estimate the T-year return level. Among the methods suitable for modeling spatial extremes, perhaps the simplest and fastest approach is the spatial generalized extreme value (GEV) distribution and the spatial generalized Pareto distribution (GPD) that assume marginal independence and only account for dependence through the parameters. Despite the simplicity, simulations have shown that return level estimation using the spatial GEV and spatial GPD still provides satisfactory results compared to max-stable processes, which are asymptotically justified models capable of representing spatial dependence among extremes. However, the linear functions used to model the spatially varying coefficients are restrictive and may be violated.We propose a flexible and fast approach based on the spatial GEV and spatial GPD by introducing fused lasso and fused ridge penalty for parameter regularization. This enables improved return level estimation for large spatial extremes compared to the existing methods. Supplemental files for this article are available online. 

We study the problem of sparse signal detection on a spatial domain. We propose a novel approach to model continuous signals that are sparse and piecewise-smooth as the product of independent Gaussian (PING) processes with a smooth covariance kernel. The smoothness of the PING process is ensured by the smoothness of the covariance kernels of the Gaussian components in the product, and sparsity is controlled by the number of components. The bivariate kurtosis of the PING process implies that more components in the product results in the thicker tail and sharper peak at zero. We develop an efficient computation algorithm based on spectral methods. The simulation results demonstrate superior estimation using the PING prior over Gaussian process prior for different image regressions. We apply our method to a longitudinal magnetic resonance imaging dataset to detect the regions that are affected by multiple sclerosis computation in this domain. Supplementary materials for this article are available online. 

High spatiotemporal resolution maps of surface vegetation from remote sensing data are desirable for vegetation and disturbance monitoring. However, due to the current limitations of imaging spectrometers, remote sensing datasets of vegetation with high temporal frequency of measurements have lower spatial resolution, and vice versa. In this research, we propose a space-time dynamic linear model to fuse high temporal frequency data (MODIS) with high spatial resolution data (Landsat) to create high spatiotemporal resolution data products of a vegetation greenness index. The model incorporates the spatial misalignment of the data and models dependence within and across land cover types with a latent multivariate Matérn process. To handle the large size of the data, we introduce a fast estimation procedure and a moving window Kalman smoother to produce a daily, 30-m resolution data product with associated uncertainty.