# Fire Spread Analysis from Raw Time-of-Arrival (TOA) Rasters

## Overview

This document outlines a comprehensive workflow for analyzing wildfire progression using high-resolution time-of-arrival (TOA) rasters. The approach leverages empirical TOA data—typically encoded per-pixel in raster images—to derive local rate of spread (ROS), direction vectors, fire zone segmentation, and quantitative front complexity metrics. It adapts modern wildfire modeling and spatial data science techniques for both operational and research uses.

## 1. TOA Raster Structure

- **Input:** Raster where each pixel encodes fire arrival time (seconds since ignition).
- **Typical encoding:** RGB channels with blue as least significant, allowing high temporal precision.
- **Spatial resolution:** Matches the underlying perimeters or satellite-derived fronts; precise across large burned areas.


## 2. Calculating Local Rate of Spread (ROS) \& Direction

### 2.1. Directional ROS Calculation

For each pixel:

- Identify its 8-connected neighbors (N, NE, E, SE, S, SW, W, NW).
- For each neighbor:
    - Calculate distance (pixel size or pixel size × √2 for diagonals).
    - Compute time interval: $|TOA_{neighbor} - TOA_{center}|$ in seconds.
    - Compute ROS:

$$
ROS_{dir} = \frac{distance_{dir}}{|TOA_{neighbor} - TOA_{center}|}
$$
- Result: 8-directional local ROS vector for every pixel.


### 2.2. Continuous Gradient (Sobel/Laplace Analysis)

- Apply a Sobel or equivalent spatial gradient operator to the TOA raster:
    - **Direction:** Angle of steepest TOA decrease = direction of fastest local fire advance.
    - **Magnitude:** Inverse of the spatial gradient = estimated local ROS.
- This provides a continuous-valued direction and physically meaningful ROS metric per pixel.


## 3. Time-Windowed Front Analysis

- Segment analysis into **time windows** (e.g., every 10, 30, or 60 minutes) using arrival time thresholds or bins.
- For each time window, extract the set of "active" fire front pixels.
- Enables granular, interval-based analysis as fire behavior and conditions change dynamically.


## 4. Head, Flank, and Backing Fire Segmentation

- For each pixel within a time window:
    - Compare the local spread direction (from the gradient) to the overall fire run direction (or wind, if known).
    - **Head fire:** Direction aligns closely with main spread/wind (angle difference < 30°, or by ROS percentile).
    - **Backing fire:** Direction opposite to head (angle difference > 150°, lowest ROS).
    - **Flanking fire:** Direction roughly perpendicular to head (angle ≈ 60–120°).
- Outputs a classified raster of head, flank, and backing fire for each time window.
- Use for zone-specific analysis of flame length, intensity, and prescribed burn evaluation.


## 5. Front Complexity Quantification via Cluster Analysis

- For each time windowed fire front:
    - Create a binary mask for all front pixels.
    - Apply cluster analysis (e.g., connected components labeling, DBSCAN) to group contiguous fronts ("heads" or "fingers").
    - Calculate metrics:
        - **Number of clusters:** Distinct heads/fingers.
        - **Cluster size and shape:** Area, elongation, fragmentation.
- Quantifies spatial complexity and dynamic evolution of the fire front.


## 6. Integration with Landscape Features

- For every pixel, link local terrain features (slope, aspect), fuel type, and ignition pattern with calculated ROS and front classification.
- Enables analysis of environmental controls on fire behavior at each time step.


## 7. Applications and Outputs

- **Map outputs:** ROS rasters, direction rasters, classified head/flank/backing fire zones, front complexity maps.
- **Operational uses:** Model validation, hazard assessment, prescribed burn effectiveness, risk mapping, scenario simulation.
- **Research uses:** Fire dynamics benchmarking, understanding landscape and ignition impacts, training data for advanced machine learning models.


## 8. Recommended Terminology

- Use **“time-windowed fire front analysis”** or **“time-sliced fire behavior analysis”** to describe per-interval evaluation.
- Refer to **front complexity** and **cluster analysis** for quantifying heads, fingers, and front fragmentation.


### Example Summary Table

| Step | Method/Algorithm | Output |
| :-- | :-- | :-- |
| Local ROS \& direction | Gradient analysis, neighbor differencing | Per-pixel ROS and direction vectors |
| Time window segmentation | Arrival time binning | Active fire front mask per window |
| Fire zone classification | Angle/percentile thresholds | Head, flank, backing fire segmentation |
| Front complexity | Cluster analysis | Metrics: \#heads, shape, continuity |

## 9. References to Best Practice

- This workflow is conceptually consistent with industry-leading models (Spark, FARSITE, FlamMap) and state-of-the-art fire science and geospatial literature.
- Adaptable to both operational and research needs, with full compatibility for integration with existing and emerging machine learning frameworks.

**Contact:** Adapt this markdown template for your own event documentation, scientific publication, or operational fire reporting.