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Abstract Predicting dissolved oxygen (DO) in lakes is important for assessing environmental conditions as well as reducing water treatment costs. High levels of DO often precede toxic algal blooms, and low DO causes carcinogenic metals to precipitate during water treatment. Typically, DO is predicted from limited data sets using hydrodynamic modeling or data‐driven approaches like neural networks. However, functional data analysis (FDA) is also an appropriate modeling paradigm for measurements of DO taken vertically through the water column. In this analysis, we build FDA models for a set of profiles measured every 2 hours and forecast the entire DO percent saturation profile from 2 to 24 hours ahead. Functional smoothing and functional principal component analysis are applied first, followed by a vector autoregressive model to forecast the empirical functional principal component (FPC) scores. Rolling training windows adapt to seasonality, and multiple combinations of window sizes, model variables, and parameter specifications are compared using both functional and direct root mean squared error metrics. The FPC method outperforms a suite of comparison models, and including functional pH, temperature, and conductivity variables improves the longer forecasts. Finally, the FDA approach is useful for identifying unusual observations. 

Abstract The heavy‐tailed behavior of the generalized extreme‐value distribution makes it a popular choice for modeling extreme events such as floods, droughts, heatwaves, wildfires and so forth. However, estimating the distribution's parameters using conventional maximum likelihood methods can be computationally intensive, even for moderate‐sized datasets. To overcome this limitation, we propose a computationally efficient, likelihood‐free estimation method utilizing a neural network. Through an extensive simulation study, we demonstrate that the proposed neural network‐based method provides generalized extreme value distribution parameter estimates with comparable accuracy to the conventional maximum likelihood method but with a significant computational speedup. To account for estimation uncertainty, we utilize parametric bootstrapping, which is inherent in the trained network. Finally, we apply this method to 1000‐year annual maximum temperature data from the Community Climate System Model version 3 across North America for three atmospheric concentrations: 289 ppm (pre‐industrial), 700 ppm (future conditions), and 1400 ppm , and compare the results with those obtained using the maximum likelihood approach. 

In many practical applications, spatial data are often collected at areal levels (i.e., block data), and the inferences and predictions about the variable at points or blocks different from those at which it has been observed typically depend on integrals of the underlying continuous spatial process. In this paper, we describe a method based onFourier transformsby which multiple integrals of covariance functions over irregular data regions may be numerically approximated with the same level of accuracy as traditional methods, but at a greatly reduced computational expense.