Jan Mandel

Jan Mandel, Jonathan D. Beezley, Janice L. Coen et al.

Two wildland fire models are described, one based on reaction-diffusion-convection partial differential equations, and one based on semi-empirical fire spread by the level let method. The level set method model is coupled with the Weather Research and Forecasting (WRF) atmospheric model. The regularized and the morphing ensemble Kalman filter are used for data assimilation.

Bedřich Sousedík, Jan Mandel

After a short historical review, we present four popular substructuring methods: FETI-1, BDD, FETI-DP, BDDC, and derive the primal versions to the two FETI methods, called P-FETI-1 and P-FETI-DP, as proposed by Fragakis and Papadrakakis. The formulation of the BDDC method shows that it is the same as P-FETI-DP and the same as a preconditioner introduced by Cros. We prove the equality of eigenvalues of a particular case of the FETI-1 method and of the BDD method by applying a recent abstract result by Fragakis.

Jan Mandel

This is an introductory document surveying several results in polynomial approximation, known as the Bramble-Hilbert lemma.

Bryan Shaddy, Deep Ray, Angel Farguell et al.

Increases in wildfire activity and the resulting impacts have prompted the development of high-resolution wildfire behavior models for forecasting fire spread. Recent progress in using satellites to detect fire locations further provides the opportunity to use measurements to improve fire spread forecasts from numerical models through data assimilation. This work develops a method for inferring the history of a wildfire from satellite measurements, providing the necessary information to initialize coupled atmosphere-wildfire models from a measured wildfire state in a physics-informed approach. The fire arrival time, which is the time the fire reaches a given spatial location, acts as a succinct representation of the history of a wildfire. In this work, a conditional Wasserstein Generative Adversarial Network (cWGAN), trained with WRF-SFIRE simulations, is used to infer the fire arrival time from satellite active fire data. The cWGAN is used to produce samples of likely fire arrival times from the conditional distribution of arrival times given satellite active fire detections. Samples produced by the cWGAN are further used to assess the uncertainty of predictions. The cWGAN is tested on four California wildfires occurring between 2020 and 2022, and predictions for fire extent are compared against high resolution airborne infrared measurements. Further, the predicted ignition times are compared with reported ignition times. An average Sorensen's coefficient of 0.81 for the fire perimeters and an average ignition time error of 32 minutes suggest that the method is highly accurate.

Jonathon Hirschi, Jan Mandel, Adam Kochanski

This paper proposes a time-warping transfer learning method, a technique for temporally rescaling the learned dynamics of a recurrent neural network (RNN) with a Long Short-Term Memory (LSTM) layer to enable task transfer across fuel moisture classes. Fuel moisture content (FMC) is divided into idealized classes based on characteristic lag time. Large quantities of real-time data are available for 10h fuels from sensors on weather stations, but observations of other fuel classes are sparse in space and time. We use transfer learning to adapt an RNN pretrained on 10h FMC to predict FMC for 1h, 100h, and 1000h fuels. We validate this method using data from a landmark field study conducted in Oklahoma that was used to calibrate the state-of-the-art Nelson fuel moisture model.

Bryan Shaddy, Brianna Binder, Agnimitra Dasgupta et al.

Increasing wildfire occurrence has spurred growing interest in wildfire spread prediction. However, even the most complex wildfire models diverge from observed progression during multi-day simulations, motivating need for data assimilation. A useful approach to assimilating measurement data into complex coupled atmosphere-wildfire models is to estimate wildfire progression from measurements and use this progression to develop a matching atmospheric state. In this study, an approach is developed for estimating fire progression from VIIRS active fire measurements, GOES-derived ignition times, and terrain height data. A conditional Generative Adversarial Network is trained with simulations of historic wildfires from the atmosphere-wildfire model WRF-SFIRE, thus allowing incorporation of WRF-SFIRE physics into estimates. Fire progression is succinctly represented by fire arrival time, and measurements for training are obtained by applying an approximate observation operator to WRF-SFIRE solutions, eliminating need for satellite data during training. The model is trained on tuples of fire arrival times, measurements, and terrain, and once trained leverages measurements of real fires and corresponding terrain data to generate samples of fire arrival times. The approach is validated on five Pacific US wildfires, with results compared against high-resolution perimeters measured via aircraft, finding an average Sorensen-Dice coefficient of 0.81. The influence of terrain height on the arrival time inference is also evaluated and it is observed that terrain has minimal influence when the inference is conditioned on satellite measurements.

Jonathan Beezley, Mavin Martin, Paul Rosen et al.

We introduce several useful utilities in development for the creation and analysis of real wildland fire simulations using WRF and SFIRE. These utilities exist as standalone programs and scripts as well as extensions to other well known software. Python web scrapers automate the process of downloading and preprocessing atmospheric and surface data from common sources. Other scripts simplify the domain setup by creating parameter files automatically. Integration with Google Earth allows users to explore the simulation in a 3D environment along with real surface imagery. Postprocessing scripts provide the user with a number of output data formats compatible with many commonly used visualization suites allowing for the creation of high quality 3D renderings. As a whole, these improvements build toward a unified web application that brings a sophisticated wildland fire modeling environment to scientists and users alike.