Logic Model Design
We graphically designed the logic model for evaluating the relative danger of wildland fire (hereafter, fire danger) with the NetWeaver Developer (Rules of Thumb, Inc., North East, PA) modeling system. Note that the use of trade or firm names in this publication is for reader information and does not imply endorsement by the U.S. Department of Agriculture of any product or service. We present the formal logic specification both as a topic outline for readability and compactness (Table: Logic outline) and as a dendrogram (Figure 1). Each topic in a NetWeaver model represents a topic for which a premise or proposition is evaluated. For example, the overall fire danger topic, representing the top level in the model, evaluates the proposition that wildland fire danger is low (Table: Logic outline, Figure 1). All other propositions in the model similarly take the null form; i.e., the test for all topics is always for a low condition.
The complete evaluation of fire danger depends on three primary topics—fire hazard, fire behavior, and ignition risk—each of which incrementally contribute to the evaluation of fire danger, as indicated by the union operator (Table: Logic outline). Moreover, because the union operator specifies that premises incrementally contribute to the proposition of their parent topic, low strength of evidence for one topic can be compensated by strong evidence from others. Notice that if the fire danger topic is thought of as testing a conclusion, then the three topics on which it depends can be thought of as its logical premises. Similarly, each of the three topics under fire danger has its own logic specification that includes a set of secondary topics or premises. The full logic structure (Table: Logic outline), considered in its entirety, constitutes what we referred to earlier as the logical discourse. Note that this logic model represents one of many possible logical configurations, and the current configuration is readily adapted. Any of the primary and secondary topics may be modified, and topics may be added or removed with relative ease. Likewise, thresholds of elementary topics (discussed below) can be modified to fit customized or evolving evaluations as a function of adaptation and learning.
Primary Topic—Fire Hazard
Evaluation of fire hazard (Table: Logic outline, Figure 1) depends on the union of topics addressing surface fuels, canopy fuels, and fire regime condition class, each of which depends on two additional elementary topics that directly evaluate data (Table:Logic outline, Table:Definition of data inputs). Evaluation of each elementary topic under hazard involved two class metrics computed by the FRAGSTATS program: (1) the proportion of subwatershed area exceeding a specified threshold value, and (2) an index that shows the degree of spatial aggregation of observed values exceeding the threshold value. Threshold values were based on the fire literature, and, where literature values were lacking, were based on our judgment. Use of the metrics to evaluate the elementary topic for canopy bulk density (CBD) is presented below as an example; methods for evaluation of each of the other elementary topics under hazard are analogous.
Within the elementary topic for CBD, the logic first tests the value of CBDarea; the percentage of the subwatershed area with CBD exceeding a threshold value of 0.15 kg·m-3 (Table: Definition of data inputs):
- If CBDarea is < 0.29, (i.e., < 29 percent of the subwatershed area exhibits CBD values > 0.15 kg·m-3), then evidence for low CBD is fully satisfied, else
- If CBDarea is > 0.79, (i.e., > 79 percent of the subwatershed area exhibits CBD values > 0.15 kg·m-3), then there is no evidence for low CBD, else
- Evidence for low CBD is evaluated as a function of CBDaggregation.
The value 0.29 represents the lower bound of the median 80-percent range for the set of all CBDarea data in map zone 16. The value 0.79 represents the upper bound of the median 80-percent range (Table: Definition of data inputs). If the last condition above was satisfied, then we tested the observed value for CBDaggregation against a fuzzy membership function (Figure 2). This was done to determine the strength of evidence for a low degree of aggregation of high CBD values, (i.e., values of CBD exceeding the threshold value of 0.15 kg·m-3) relative to a set of reference conditions that defined the median 80-percent range of the CBDaggregation data from the set of all subwatersheds (Table: Definition of data inputs). Notice that each elementary topic (Table: Definition of data inputs) is similarly evaluated against the median 80-percent range of its associated datum, hence our characterization of fire danger as relative.
- If CBDaggregation is ≤ 76, (i.e., ≤ 76 percent of the maximum value of aggregation), then evidence for low aggregation of high CBD values is fully satisfied, else
- If CBDaggregation is ≥ 93, (i.e., ≥ 93percent of the maximum value of aggregation), then there is no evidence for low aggregation of high CBD values, else
- Observed values of CBDaggregation fall within the open interval (76, 93), and evaluate to partial support for the proposition, based on a linear interpolation between 76 and 93. The open interval (76, 93) represents the median 80-percent range of the data.
Primary Topic—Fire Behavior
Evaluation of fire behavior depends on the union of topics addressing spread rate, flame length, fireline intensity, and crown fire potential (Table: Logic outline), each of which is an elementary topic that directly evaluates data (Table:Logic outline, Table:Definition of data inputs). The spread rate topic evaluates the proposition that likelihood of spread rate of surface fire > 8.0 kph within the subwatershed is low. The flame length topic evaluates the proposition that likelihood of flame length > 1.2 m within the watershed is low. The fireline intensity topic evaluates the proposition that likelihood of fireline intensity > 400 kW·m-1 within the watershed is low. The crown fire potential topic evaluates the proposition that likelihood of crown fire spread potential > 7 within the watershed is low. This last metric is an index based on crown fire ignition and crown fire spread potentials (Keane and others 2004) and represents the ratio of crown fire behavior to surface fire behavior based on Rothermel (1972, 1991) surface and crown fire algorithms.
None of the fire behavior elementary topics are entirely independent of the other topics; rather, one or more of these topics is used in the calculation of the others. For example, flame length influences the spread rate calculation, and fireline intensity influences flame length. In fact, fireline intensity is double weighted in our model because of the equivalence of flame length and fireline intensity (Chandler and others 1983). We used both in the model because intensity relates best to fire effects, and flame length is easily observed and often asked for. Each selected elementary topic is used here to provide a more comprehensive picture of expected fire behavior. Whereas complete independence among the topics would be desirable, there is no set of fire behavior attributes with such independence, and there is also no independent set that provides a comprehensive picture of expected fire behavior.
Primary Topic—Ignition Risk
Evaluation of ignition risk depends on the union of four elementary topics—Palmer drought severity index (Palmer 1965), the Keetch-Byram drought index (Keane and others 2004), the AVHRR-NDVI relative greenness index (Keane and others 2004), and lightning strike probability (Table:Logic outline, Table:Definition of data inputs). First, the probability of a summer Palmer drought severity index value < −2 is evaluated. A value of −2 corresponds to moderate drought in the Palmer rating system. This elementary topic is included because it allows consideration of the effects of long-term drought on vegetation and fuels. Second, the probability of a Keetch-Byram drought index value > 400 is evaluated. The topic considers the short-term effects of precipitation and temperature on duff, litter, and soil moisture in the top 20 cm. An index value of 400 corresponds to a deficit of 10 cm of water in the top 20 cm; Burgan (1993) suggested that severe fire behavior often occurs when the KBDI exceeds this value.
The AVHRR-NDVI relative greenness value on Julian day 152 (June 1, 2004) is then considered as a topic that indirectly represents fuel condition by incorporating vegetation drying or curing in a measure of relative greenness. June 1 is used to represent the height of the growing season in the study area; the greenest values indicate lesser chance for fire ignition. Future versions of this modeling system would include dates to capture the span of the fire season of each unique map zone.
Finally, lightning strike probability is evaluated, which we base on actual strikes triangulated and recorded over 15 years (1990 to 2004). The probability of human-caused ignitions is also important but omitted in this implementation. We constructed a logic module for evaluating the likelihood of human-caused ignitions, but it is not implemented in this version because wall-to-wall human ignition density data were unavailable for map zone 16. In a future version, we will incorporate a direct evaluation based on recorded human-ignition densities, or an indirect measure of likelihood involving road density maps and maps of human congregation sites.
Encyclopedia ID: p3639
