Fire behavior and smoke modeling: Model improvement and measurement needs for next-generation smoke research and forecasting systems.

There is an urgent need for next-generation smoke research and forecasting (SRF) systems to meet the challenges of the growing air quality, health, and safety concerns associated with wildland fire emissions. This review paper presents simulations and experiments of hypothetical prescribed burns with a suite of selected fire behavior and smoke models and identifies major issues for model improvement and the most critical observational needs. The results are used to understand the new and improved capability required for the next-generation SRF systems and to support the design of the Fire and Smoke Model Evaluation Experiment (FASMEE) and other field campaigns. The next-generation SRF systems should have more coupling of fire, smoke, and atmospheric processes to better simulate and forecast vertical smoke distributions and multiple sub-plumes, dynamical and high-resolution fire processes, and local and regional smoke chemistry during day and night. The development of the coupling capability requires comprehensive and spatially and temporally integrated measurements across the various disciplines to characterize flame and energy structure (e.g., individual cells, vertical heat profile and the height of well mixing flaming gases), smoke structure (vertical distributions and multiple sub-plumes), ambient air processes (smoke eddy, entrainment and radiative effects of smoke aerosols), fire emissions (for different fuel types and combustion conditions from flaming to residual smoldering), as well as night-time processes (smoke drainage and super-fog formation).

Bayesian tracking of emerging epidemics using ensemble optimal statistical interpolation.

We present a preliminary test of the Ensemble Optimal Statistical Interpolation (EnOSI) method for the statistical tracking of an emerging epidemic, with a comparison to its popular relative for Bayesian data assimilation, the Ensemble Kalman Filter (EnKF). The spatial data for this test was generated by a spatial susceptible-infectious-removed (S-I-R) epidemic model of an airborne infectious disease. Both tracking methods in this test employed Poisson rather than Gaussian noise, so as to handle epidemic data more accurately. The EnOSI and EnKF tracking methods worked well on the main body of the simulated spatial epidemic, but the EnOSI was able to detect and track a distant secondary focus of infection that the EnKF missed entirely.

ON THE CONVERGENCE OF THE ENSEMBLE KALMAN FILTER.

Convergence of the ensemble Kalman filter in the limit for large ensembles to the Kalman filter is proved. In each step of the filter, convergence of the ensemble sample covariance follows from a weak law of large numbers for exchangeable random variables, the continuous mapping theorem gives convergence in probability of the ensemble members, and Lp bounds on the ensemble then give Lp convergence.

Data driven computing by the morphing fast Fourier transform ensemble Kalman filter in epidemic spread simulations.

The FFT EnKF data assimilation method is proposed and applied to a stochastic cell simulation of an epidemic, based on the S-I-R spread model. The FFT EnKF combines spatial statistics and ensemble filtering methodologies into a localized and computationally inexpensive version of EnKF with a very small ensemble, and it is further combined with the morphing EnKF to assimilate changes in the position of the epidemic.

Exact calculations of average power for the Benjamini-Hochberg procedure.

Exact analytic expressions are developed for the average power of the Benjamini and Hochberg false discovery control procedure. The result is based on explicit computation of the joint probability distribution of the total number of rejections and the number of false rejections, and expressed in terms of the cumulative distribution functions of the p-values of the hypotheses. An example of analytic evaluation of the average power is given. The result is confirmed by numerical experiments and applied to a meta-analysis of three clinical studies in mammography.