A General Mathematical Framework for Modeling Two-Dimensional Wildland Fire Spread

1995 ◽  
Vol 5 (2) ◽  
pp. 63 ◽  
Author(s):  
GD Richards
Keyword(s):  
Differential Equations ◽  
Wildland Fire ◽  
Fire Spread ◽  
Meteorological Conditions ◽  
Mathematical Framework ◽  
Two Dimensional ◽  
Affecting Factors ◽  
Modelling Framework ◽  
Rate Of Spread ◽  
The Relationship

This work considers the modelling of two dimensional fire spread for heterogeneous fuel and meteorological conditions. Differential equations are used as the modelling form, and a set of partial differential equations that describes fire growth in terms of the rate of spread at each point on the perimeter is derived. These equations require the specification of the rate of spread as a function of the variables affecting it, and form a general modelling framework into which such a function can be placed. To model the relationship between the rate of spread and its affecting factors an analysis of point source ignition fires for homogeneous fuel and meteorological conditions is made. Based on this analysis a spread rate model for heterogeneous conditions is proposed. The resulting differential equations require a sophisticated computer solution, however there are a number of nontrivial fire situations for which solutions can relatively easily be obtained, and example solutions are presented.

A cellular automata model to link surface fires to firebrand lift-off and dispersal

2013 ◽  
Vol 22 (4) ◽  
pp. 428 ◽  
Author(s):  
Holly A. Perryman ◽  
Christopher J. Dugaw ◽  
J. Morgan Varner ◽  
Diane L. Johnson
Keyword(s):  
Wind Speed ◽  
Wildland Fire ◽  
Fire Spread ◽  
Fuel Moisture ◽  
Fuel Loading ◽  
Cellular Automata Model ◽  
Rate Of Spread ◽  
Lift Off ◽  
Fuel Moisture Content ◽  
Spot Fires

In spite of considerable effort to predict wildland fire behaviour, the effects of firebrand lift-off, the ignition of resulting spot fires and their effects on fire spread, remain poorly understood. We developed a cellular automata model integrating key mathematical models governing current fire spread models with a recently developed model that estimates firebrand landing patterns. Using our model we simulated a wildfire in an idealised Pinus ponderosa ecosystem. Varying values of wind speed, surface fuel loading, surface fuel moisture content and canopy base height, we investigated two scenarios: (i) the probability of a spot fire igniting beyond fuelbreaks of various widths and (ii) how spot fires directly affect the overall surface fire’s rate of spread. Results were averages across 2500 stochastic simulations. In both scenarios, canopy base height and surface fuel loading had a greater influence than wind speed and surface fuel moisture content. The expected rate of spread with spot fires occurring approached a constant value over time, which ranged between 6 and 931% higher than the predicted surface fire rate of spread. Incorporation of the role of spot fires in wildland fire spread should be an important thrust of future decision-support technologies.

Exploring fire response to high wind speeds: fire rate of spread, energy release and flame residence time from fires burned in pine needle beds under winds up to 27 ms−1

2020 ◽  
Vol 29 (1) ◽  
pp. 81
Author(s):  
Bret Butler ◽  
Steve Quarles ◽  
Christine Standohar-Alfano ◽  
Murray Morrison ◽  
Daniel Jimenez ◽  
...  
Keyword(s):  
Wind Speed ◽  
Energy Release ◽  
Residence Time ◽  
Wildland Fire ◽  
Ground Level ◽  
Fire Spread ◽  
Convective Heating ◽  
Atmospheric Conditions ◽  
Wind Speeds ◽  
Rate Of Spread

The relationship between wildland fire spread rate and wind has been a topic of study for over a century, but few laboratory studies report measurements in controlled winds exceeding 5ms−1. In this study, measurements of fire rate of spread, flame residence time and energy release are reported for fires burning under controlled atmospheric conditions in shallow beds of pine needles subject to winds ranging from 0 to 27ms−1 (measured 5m above ground level). The data suggested that under constant flow conditions when winds are less than 10ms−1, fire rate of spread increases linearly at a rate of ~3% of the wind speed, which generally agrees with other laboratory-based models. When wind speed exceeds 10ms−1, the fire rate of spread response to wind remains linear but with a much stronger dependence, spreading at a rate of ~13% of the wind speed. Radiative and convective heating correlated directly to wind speed, with radiant heating increasing approximately three-fold as much as convective heating over the range of winds explored. The data suggested that residence time is inversely related to wind speed and appeared to approach a lower limit of ~20s as wind exceeded 15ms−1. Average flame residence time over the range of wind speeds was nominally 26s.

Prediction of Fire Spread in Grasslands

1998 ◽  
Vol 8 (1) ◽  
pp. 1 ◽  
Author(s):  
NP Cheney ◽  
JS Gould ◽  
WR Catchpole
Keyword(s):  
Wind Speed ◽  
Linear Relationship ◽  
Power Function ◽  
Fire Spread ◽  
Fuel Moisture ◽  
Critical Wind Speed ◽  
Rate Of Spread ◽  
The Relationship ◽  
Potential Rate

This pager describes a model to predict fire spread in grasslands from wind speed at 10 m, dead fuel moisture, and degree of grass curing in three defined pasture types, The model was developed from spread measurements of experimental fins that were adjusted to their potential rate of spread at wide fronts. Extrapolations of the model were compared with spread data from 20 major wildfires in Australia. This model uses different functions to describe the relationship between rate of spread and wind speed above and below a critical wind speed of 5 km h-1. A linear relationship is used below 5 km h-1; above 5 km h-1 rate of spread is described by a power function of wind speed with an exponent of less than 1.

A Computer Algorithm for Simulating the Spread of Wildland Fire Perimeters for Heterogeneous Fuel and Meteorological Conditions

1995 ◽  
Vol 5 (2) ◽  
pp. 73 ◽  
Author(s):  
GD Richards ◽  
RW Bryce
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Wildland Fire ◽  
Meteorological Conditions ◽  
Simple Method ◽  
Reasonable Time ◽  
Method Of Solution ◽  
Fire Scenarios ◽  
Computer Based ◽  
The Mathematical Model

This work describes a computer based technique for simulating the spread of wildland fire for heterogeneous fuel and meteorological conditions. The mathematical model is in the form of a pair of partial differential equations, and can model fuels whose fire perimeter for homogeneous conditions is any given shape, such as ellipses, double ellipses, lemniscates etc. Provided the fire does not attempt to burn into an already burnt out region, then the differential equations are easily solved and a simple method of solution is presented. To identify regions that are internal to the fire perimeter an algorithm that uses the turning number of a point in the plane relative to the fire perimeter is used. The algorithm is found to be reliable, and allows for the simulation of highly complex fire scenarios in a reasonable time. Example simulations are presented that involve variations in fuel, barriers, wind direction changes and multiple fires.

scholarly journals Resolving vorticity-driven lateral fire spread using the WRF-Fire coupled atmosphere–fire numerical model

2014 ◽  
Vol 14 (9) ◽  
pp. 2359-2371 ◽  
Author(s):  
C. C. Simpson ◽  
J. J. Sharples ◽  
J. P. Evans
Keyword(s):  
High Spatial Resolution ◽  
Wildland Fire ◽  
Fire Spread ◽  
Weather Research And Forecasting ◽  
Grid Spacing ◽  
Fire Behaviour ◽  
Model Framework ◽  
Rate Of Spread ◽  
Fire Front ◽  
Vertical Grid

Abstract. Vorticity-driven lateral fire spread (VLS) is a form of dynamic fire behaviour, during which a wildland fire spreads rapidly across a steep leeward slope in a direction approximately transverse to the background winds. VLS is often accompanied by a downwind extension of the active flaming region and intense pyro-convection. In this study, the WRF-Fire (WRF stands for Weather Research and Forecasting) coupled atmosphere–fire model is used to examine the sensitivity of resolving VLS to both the horizontal and vertical grid spacing, and the fire-to-atmosphere coupling from within the model framework. The atmospheric horizontal and vertical grid spacing are varied between 25 and 90 m, and the fire-to-atmosphere coupling is either enabled or disabled. At high spatial resolutions, the inclusion of fire-to-atmosphere coupling increases the upslope and lateral rate of spread by factors of up to 2.7 and 9.5, respectively. This increase in the upslope and lateral rate of spread diminishes at coarser spatial resolutions, and VLS is not modelled for a horizontal and vertical grid spacing of 90 m. The lateral fire spread is driven by fire whirls formed due to an interaction between the background winds and the vertical circulation generated at the flank of the fire front as part of the pyro-convective updraft. The laterally advancing fire fronts become the dominant contributors to the extreme pyro-convection. The results presented in this study demonstrate that both high spatial resolution and two-way atmosphere–fire coupling are required to model VLS with WRF-Fire.

Examination of the wind speed limit function in the Rothermel surface fire spread model

2013 ◽  
Vol 22 (7) ◽  
pp. 959 ◽  
Author(s):  
Patricia L. Andrews ◽  
Miguel G. Cruz ◽  
Richard C. Rothermel
Keyword(s):  
Wind Speed ◽  
Wildland Fire ◽  
Fire Spread ◽  
Speed Limit ◽  
Limit Function ◽  
Surface Fire ◽  
Rate Of Spread ◽  
Fire Modelling ◽  
Spread Model ◽  
Fire Spread Model

The Rothermel surface fire spread model includes a wind speed limit, above which predicted rate of spread is constant. Complete derivation of the wind limit as a function of reaction intensity is given, along with an alternate result based on a changed assumption. Evidence indicates that both the original and the revised wind limits are too restrictive. Wind limit is based in part on data collected on the 7 February 1967 Tasmanian grassland fires. A reanalysis of the data indicates that these fires might not have been spreading in fully cured continuous grasslands, as assumed. In addition, more recent grassfire data do not support the wind speed limit. The authors recommend that, in place of the current wind limit, rate of spread be limited to effective midflame wind speed. The Rothermel model is the foundation of many wildland fire modelling systems. Imposition of the wind limit can significantly affect results and potentially influence fire and fuel management decisions.

Barley seed storage under controlled conditions

2019 ◽  
pp. 140-150 ◽  
Author(s):  
O. A. Zadorozhna ◽  
T. P. Shyianova ◽  
M.Yu. Skorokhodov
Keyword(s):  
Hordeum Vulgare ◽  
Moisture Content ◽  
Spring Barley ◽  
Seed Storage ◽  
Growing Season ◽  
Storage Conditions ◽  
Meteorological Conditions ◽  
Hordeum Vulgare L ◽  
The Relationship ◽  
And Storage

Seed longevity of 76 spring barley gene pool samples (Hordeum vulgare L. subsp. distichon, convar. distichon: 56 nutans Schubl., two deficience (Steud.) Koern., two erectum Rode ex Shuebl., two medicum Koern.; convar. nudum (L.) A.Trof.: one nudum L. та subsp. vulgare: convar. vulgare: nine pallidum Ser., three rikotense Regel.; convar. coeleste (L.) A.Trof.: one coeleste (L.) A.Trof.) from 26 countries, 11 years and four places of reproduction was analyzed. Seeds with 5–8% moisture content were stored in chamber with unregulated and 4oC temperature. The possibility of seed storage under these conditions for at least 10 years without significant changes in germination has been established. The importance of meteorological conditions in the formation and ripening of seeds for their longevity is confirmed. The relationship between the decrease of barley seeds longevity and storage conditions, amount of rainfall, temperature regime during the growing season of plants is discussed.

scholarly journals A Deep Learning Approach to Downscale Geostationary Satellite Imagery for Decision Support in High Impact Wildfires

Forests ◽  
2021 ◽  
Vol 12 (3) ◽  
pp. 294
Author(s):  
Nicholas F. McCarthy ◽  
Ali Tohidi ◽  
Yawar Aziz ◽  
Matt Dennie ◽  
Mario Miguel Valero ◽  
...  
Keyword(s):  
Deep Learning ◽  
Decision Support ◽  
Real Time ◽  
Forest Fires ◽  
Wildland Fire ◽  
Fire Spread ◽  
Low Earth Orbit ◽  
Practical Implementation ◽  
Spatiotemporal Resolution ◽  
Active Fire

Scarcity in wildland fire progression data as well as considerable uncertainties in forecasts demand improved methods to monitor fire spread in real time. However, there exists at present no scalable solution to acquire consistent information about active forest fires that is both spatially and temporally explicit. To overcome this limitation, we propose a statistical downscaling scheme based on deep learning that leverages multi-source Remote Sensing (RS) data. Our system relies on a U-Net Convolutional Neural Network (CNN) to downscale Geostationary (GEO) satellite multispectral imagery and continuously monitor active fire progression with a spatial resolution similar to Low Earth Orbit (LEO) sensors. In order to achieve this, the model trains on LEO RS products, land use information, vegetation properties, and terrain data. The practical implementation has been optimized to use cloud compute clusters, software containers and multi-step parallel pipelines in order to facilitate real time operational deployment. The performance of the model was validated in five wildfires selected from among the most destructive that occurred in California in 2017 and 2018. These results demonstrate the effectiveness of the proposed methodology in monitoring fire progression with high spatiotemporal resolution, which can be instrumental for decision support during the first hours of wildfires that may quickly become large and dangerous. Additionally, the proposed methodology can be leveraged to collect detailed quantitative data about real-scale wildfire behaviour, thus supporting the development and validation of fire spread models.

The Geometry of d2y1/dt2 = f (y, ẏ, t) and d2y2/dt2 = g(y, ẏ, t), and Euclidean Spaces

2006 ◽  
Vol 49 (2) ◽  
pp. 170-184
Author(s):  
Richard Atkins
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Shortest Paths ◽  
Equivalence Problem ◽  
Second Order ◽  
System Of Differential Equations ◽  
Lagrange Equations ◽  
Invariant Functions ◽  
Underlying Geometry ◽  
The Relationship

AbstractThis paper investigates the relationship between a system of differential equations and the underlying geometry associated with it. The geometry of a surface determines shortest paths, or geodesics connecting nearby points, which are defined as the solutions to a pair of second-order differential equations: the Euler–Lagrange equations of the metric. We ask when the converse holds, that is, when solutions to a system of differential equations reveals an underlying geometry. Specifically, when may the solutions to a given pair of second order ordinary differential equations d2y1/dt2 = f (y, ẏ, t) and d2y2/dt2 = g(y, ẏ, t) be reparameterized by t → T(y, t) so as to give locally the geodesics of a Euclidean space? Our approach is based upon Cartan's method of equivalence. In the second part of the paper, the equivalence problem is solved for a generic pair of second order ordinary differential equations of the above form revealing the existence of 24 invariant functions.

scholarly journals Template-Free Self-Assembly of Two-Dimensional Polymers into Nano/Microstructured Materials

Molecules ◽  
2021 ◽  
Vol 26 (11) ◽  
pp. 3310
Author(s):  
Shengda Liu ◽  
Jiayun Xu ◽  
Xiumei Li ◽  
Tengfei Yan ◽  
Shuangjiang Yu ◽  
...  
Keyword(s):  
Self Assembly ◽  
Recent Progress ◽  
Two Dimensional ◽  
Subsequent Removal ◽  
The Past ◽  
2D Polymers ◽  
Template Free ◽  
Self Assembled ◽  
The Relationship ◽  
Polymer Tubes

In the past few decades, enormous efforts have been made to synthesize covalent polymer nano/microstructured materials with specific morphologies, due to the relationship between their structures and functions. Up to now, the formation of most of these structures often requires either templates or preorganization in order to construct a specific structure before, and then the subsequent removal of previous templates to form a desired structure, on account of the lack of “self-error-correcting” properties of reversible interactions in polymers. The above processes are time-consuming and tedious. A template-free, self-assembled strategy as a “bottom-up” route to fabricate well-defined nano/microstructures remains a challenge. Herein, we introduce the recent progress in template-free, self-assembled nano/microstructures formed by covalent two-dimensional (2D) polymers, such as polymer capsules, polymer films, polymer tubes and polymer rings.

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