Fire Chief

Thursday, November 20, 2008

Alan McArthur did a mountain of research, but only his summarized findings are available. I re-examined these findings and attempted to trace his logic through to his prediction system in both flame and spotting behavior. Some findings were accepted as correct, some were found to be not quite correct. I discovered that some theories upon which the forest fire prediction system is based have no significant supporting evidence. I have re-examined some of his findings to develop new understandings of flame and spotting behavior.

The practical outcome is a set of indicative fire behavior tables for each fuel type, all in similar format and each with common inputs. These have been tested against documented fires, both wildfires and prescribed fires. Their accuracy level can be classified as “operationally useful” for planning and decision purposes. In real fires, subtle changes in a large number of variables can influence on-site fire behavior to the point that prediction may seem to be an exercise in futility. These tables focus on the most significant influences. If observed fire behavior is different from predicted, the tables provide a starting point to begin the search for reasons why.

WINDY EFFECTS

It's well-known that litter fires spread in zero wind. According to McArthur, at zero wind speed:

ROS = 0.21kph at 3% FMC

ROS = 0.17kph at 4% FMC

ROS = 0.13kph at 5% FMC

ROS = 021kph at 6% FMC

ROS = 0.07kph at 7% FMC

ROS = 0.03kph at 10% FMC

McArthur and Harry Luke's moisture meter presents data from which zero wind speed rate of spread can be derived, but the speed for the lower moistures seem too high, for example 0.6 kph in zero wind at 3% FMC and 0.4kph at 4% FMC.

McArthur's research studies of rate of spread and fuel load have been done in low-intensity fires or with low-spread fires. At low fire intensities and low wind speed, spread rate and fuel load are probably related. Neal Burrows, the head of Western Australia's Department of Conservation and Land Management, Fire Research Group, found that rate of spread of backfires and zero wind fires was proportional to fuel load, whereas at higher wind speed, spread was independent of fuel load. The point where fuel load per se becomes less influential on rate of spread than wind speed occurs when wind speed overcomes vertical convection and causes lateral spread by direct flame contact.

There seems to be general agreement that rate of spread in mat fuel beds increases exponentially as wind speed at near flame level increases. McArthur equates to wind speed to the 1.5 power. Contemporary U.S. research in pine needle litter in wind tunnels also found an exponential relationship for mat type fuel bed. McArthur reported spread rate proportional to square of wind speed in the open at 10-meter height.

McArthur presented some original findings about low-intensity fires that seem to be appropriate for litter-only fires. It also has good data based on wind near forest floor. McArthur's later work has been adjusted for wind speed in the open, but there is no apparent uniformity with regard to wind reduction factor. “Rate of Spread,” opposite, presents stylized averages for 6% FMC and higher, and the relationship also seems reasonable for lower moisture content. Fine fuel load is deduced to be around 20 to 25 tons per hectare. The underlying formula for rate of spread is:

ROS₀ + (a + U₂ ^1.5)/b

Where ROS₀ = spread in in zero wind; a = 8.3, a constant, U₂ = wind speed near ground level, 1.5 meters; and b = 25 + 0.8 × FMC 2.5.

As we have seen, fuel load is not a significant factor in rate of spread, so this equation can be used for all litter fuel loads. Most of McArthur's examples refer to 20 to 25 tons per hectare fuel loads. The McArthur Meter has estimated spread and flame height in proportion to fuel load. Therefore, when deriving ROS figures from the meter, the values for 20 to 25 tons per hectare loads are more likely to reflect field measurements more accurately.

The possible weakness in this equation is its derivation by deduction and its reliance on hypothesis. Its strength is that it predicts verification wildfires with reasonable and consistent accuracy.

Recently, Burrows found spread rate in jarrah litter in the lab to be proportional to wind at the flame to the power 2.2 and in the field to be proportional to wind at 1.5 meters to the 2.67 power. The question arises, why is the response to wind exponential and not linear. The answer provides a remarkable insight into our general understanding of fire behavior. Burrows found these graphs were best-fit equations for data that showed a two stage reaction to wind at flame, negligible influence below 3kph, and linear response to wind above 3.5kph when fire spread by lateral flame contact becomes significant.

The linear responses to wind were as follows (units kph):

3-4% FMC, ROS = .22 × U₂ - 0.73

4-8% FMC, ROS = .07 × U₂ - 0.2

8-10% FMC, ROS = .023 × U₂ - 0.04

At 4kph wind speed, Burrow's observations are lower than McArthur's, but at 8kph wind speed they correspond reasonably well. From 10-15 kph, Burrow's equations are close except for the 3-4% one which is approximately 40-50% higher than the 3% graph.

FLAME HEIGHT

Flame height has not been studied to the same extent as rate of spread. It has usually been noted in passing, and a total height often is given. The nature of total height is rarely noted.

McArthur conducted many experiments in litter-only fuel beds, but did not distinguish the effect of bark and shrubs on flame height. It is very helpful to our understanding of fire behavior if we separate them. When we examine the flame profile in a forest fire, we see an uneven height. Litter beds generate an identifiable flame height, patches of shrubs can cause an increase in flame height and flames can run high up the bark of tree trunks. This section focuses on the contribution of litter beds to flame height.

McArthur's flame height is average flame height in the forest, which means the sum of contributions of litter fuel, shrub fuel and bark fuel. We will firstly attempt to determine a causal relationship for his flame height findings and then adjust for litter only flame height.

We can deduce that for a given rate of spread, flame height is proportional to three-fourths the root of fuel load. The approximate formula is as follows:

Flame height = 3.7 × ROS × W^I

The problem with this equation is that if we keep fuel load constant, we find that flame height increases linearly with rate of spread. This is unrealistic when compared to other fuel types, and in fact a parabolic relationship is expected, approximate to the following function:

Flame height = A × ROSH

Even though rate of spread is a dependent variable that is determined by wind speed and fuel moisture content, it is a useful lead variable in fire behavior. Flame height in jarrah litter was related parabolically to rate of spread:

Flame height = 0.062 × ROS 0.687

When we combine the fuel load and rate of spread inputs, the flame height equation becomes:

Flame height = C × W^I × ROSH

where C is a constant that is determined by real life flame heights.

The next step is to assign a maximum flame height to litter-only fires and apply the above relationships to quantify it. Based on field data, a reasonable peak flame height for litter-only fuel beds at 3% FMC and 10t/ha fuel load is around 4 meters. Maximum wind at flame of 10-15kph is used. Using the H power relationship, the maximum flame height for 20 tons per hectare litter is around 7 meters.

Until better data becomes available, a 4-meter maximum flame seems a reasonable contribution by the litter fuel bed in very dry conditions.

Using the flame height references, left, a nominal formula for nominal flame height therefore computes as:

Flame height = 0.55 × W^I × ROSH

This represents a nominal base flame height for a litter-only fire. It explains the flame height due to litter fuel bed. Its role is conceptual because extensive litter only tracts are rare. It allows us to see the contributions of litter bed, shrubs and trunks in perspective. The presence of shrubs and tree trunk bark causes localized increases in flame height above the base (litter) flame height.

But this theory leads to some common misunderstandings.

1. Flame heights versus rate of spread

   Figure 3 is a reproduction Luke and McArthur's work. In this, fuel load is 20t/ha. The graph says that if spread stays constant, flame height reduces as wind speed increases. McArthur explains it as flame pushed over by a stronger wind. But this does not explain the graph.

   Consider this scenario. If wind speed is 8kph and the fire has a spread rate of 0.4kph, its flame height from the graph is approximately 7 meters. If wind speed increases to 14kph, spread probably doubles to 0.8kph, but the flame height from the graph is approximately 6 meters. This is not the behavior response expected when temperature and relative humidity are constant — flame height should increase substantially. The only plausible reason for reduced or same flame height as wind speed increases is higher fuel moisture content in the second example. Therefore this graph in reality presents data for a range of fuel moisture, and needs careful interpretation. A further example highlights this point. If spread remains constant at 0.4kph, how can flame height be 8 meters when wind is 8kph, but fall to 4 meters when wind is 14 kph? A much higher moisture content.

2. McArthur Meter flame height predictions

   McArthur Meter lists flame heights for each fire danger index and fuel load. If the danger index is held constant, flame height increases by 2.3 to 2.5 times when fuel load doubles. Unfortunately, this relationship is too inaccurate because there is no direct link to wind speed and moisture content. For example, an FDI of 40 can mean a low moisture content and a low wind speed or a high moisture content and a strong wind. The flame heights for both will be quite different in real life.

The equation for flame height links spread and fuel load as follows.

Ht = - 2 + 13 × ROS + 0.24 × W

The equation is an accurate representation of the meter, except for the 100 m/hr range, where the meter curiously underestimates flame height above 15t/ha.

As can be seen in the flame heights from the McArthur Meter, this does not help determine actual flame height. The equation and the McArthur Meter fall short because they do not provide a direct link between flame height, wind and moisture content. Moreover, their linear relationship with spread disagrees with the parabolic shapes of “Flame Height vs. Rate of Spread,” page 24. A parabolic shape is more credible than a linear one.

SPOT FIRE DEVELOPMENT

A spot fire expands at an increasing rate of spread until is reaches a steady state. This is the acceleration stage of the fire's development. For example, a line of fire in litter has three to four times the rate of spread of a spot fire in the same conditions.

This principle can be demonstrated with the following hypothetical example. Under a given set of conditions, the steady-state spread of a line of fire is 360 meters per hour. A point source begins life at a slower average spread, but in this case it reaches steady state after about 10 minutes. The current spread is the rate at each time interval. (See “Hypothetical Rate of Spread, page 25.”)

The graph shows the average rate rising gradually to an asymptote at 360m/hr after 10 minutes. The current spread rises above the average rate but then falls as it approaches the equilibrium rate.

In real life, the exact timing of steady state could depend on weather conditions. For example, in mild weather, the spread and flame height tend to be more or less constant from the start, but in severe weather, spread and flame height tend to increase with time.

Or it could depend on fuel structure. In a forest with dense shrub layer, the steady-state spread can proceed as a series of steps. McArthur shows an example of a litter fire reaching a peak rate of 140 meters per hour after 15-20 minutes. The shrub layer then ignites and its spread rate peaks around 360 meters per hour after another 10 minutes. Then the convection column forms, spot fires occur and the tree canopy burns, lifting the spread to more than 500 meters per hour.

McArthur seemed to regard 24 minutes after ignition as the time to measure steady-state spread, at least in low-intensity fires. He actually presented the following data to support his belief that spread is proportional to fuel load, but it is re-analyzed here to explore the how a spot fire develops to steady state.

Consider two fires lit in the same conditions of slope and very mild weather, but they varied in fuel load. Distance measurements were shown up to 36 minutes after origin, together with a map of their shape. By deduction, he seems to have calculated steady-state spread for each as the average current rate from 24 to 36 minutes, and has found values of 20 meters per hour for 8 tons per hectare and 43 meters per hour for 15 tons per hectare fuel loads. (See “Development of Two Spot Fires,” opposite.)

When these trend curves are compared to the hypothetical graph on page 25, we see that the current rate of spread for 15t/ha fuel load seems to be falling toward the average rate of spread, and will probably meet around 40 meters per hour. However, the curves for the 8t/ha fuel load don't seem to fit the pattern, and both the current and the average spread rate seem to be surging at the 36-minute mark. His conclusion that the steady state for the 8t/ha fuel load is 20 meters per hour is heroic, because the 30-36 minute segment has a current spread of 42 meters per hour, which is remarkably close to the steady-state rate for 15 tons per hectare.

In mild weather conditions, higher intensity fires may achieve steady-state rate of spread before low-intensity fires. It is likely that in severe weather conditions, steady state is achieved more rapidly than in mild weather. For operational guideline purposes, a range of 30-60 minutes seems reasonable.

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