### 2.24.1.1. Fire counts[¶](#fire-counts "Permalink to this headline")

Fire counts \\(N\_{f}\\) is taken as

(2.24.2)[¶](#equation-23-2 "Permalink to this equation")\\\[N\_{f} = N\_{i} f\_{b} f\_{m} f\_{se,o}\\\]

where \\(N\_{i}\\) ( count s\-1) is the number of ignition sources due to natural causes and human activities; \\(f\_{b}\\) and \\(f\_{m}\\) (fractions) represent the availability and combustibility of fuel, respectively; \\(f\_{se,o}\\) is the fraction of anthropogenic and natural fires unsuppressed by humans and related to the socioeconomic conditions.

\\(N\_{i}\\) (count s\-1) is given as

(2.24.3)[¶](#equation-23-3 "Permalink to this equation")\\\[N\_{i} = \\left(I\_{n} +I\_{a} \\right) A\_{g}\\\]

where \\(I\_{n}\\) (count km\-2 s\-1) and \\(I\_{a}\\) (count km\-2 s\-1) are the number of natural and anthropogenic ignitions per km2, respectively; \\(A\_{g}\\) is the area of the grid cell (km2). \\(I\_{n}\\) is estimated by

(2.24.4)[¶](#equation-23-4 "Permalink to this equation")\\\[I\_{n} = \\gamma \\psi I\_{l}\\\]

where \\(\\gamma\\) =0.22 is ignition efficiency of cloud-to-ground lightning; \\(\\psi =\\frac{1}{5.16+2.16\\cos \[3min(60,\\lambda )\]}\\) is the cloud-to-ground lightning fraction and depends on the latitude \\(\\lambda\\) (degrees); \\(I\_{l}\\) (flash km\-2 s\-1) is the total lightning flashes. \\(I\_{a}\\) is modeled as a monotonic increasing function of population density:

(2.24.5)[¶](#equation-23-5 "Permalink to this equation")\\\[I\_{a} =\\frac{\\alpha D\_{P} k(D\_{P} )}{n}\\\]

where \\(\\alpha =0.01\\) (count person\-1 mon\-1) is the number of potential ignition sources by a person per month; \\(D\_{P}\\) (person km\-2) is the population density; \\(k(D\_{P} )=6.8D\_{P} ^{-0.6}\\) represents anthropogenic ignition potential as a function of human population density \\(D\_{P}\\); _n_ is the seconds in a month.

Fuel availability \\(f\_{b}\\) is given as

(2.24.6)[¶](#equation-23-6 "Permalink to this equation")\\\[\\begin{split}f\_{b} =\\left\\{\\begin{array}{c} {0} \\\\ {\\frac{B\_{ag} -B\_{low} }{B\_{up} -B\_{low} } } \\\\ {1} \\end{array} \\begin{array}{cc} {} & {} \\end{array}\\begin{array}{c} {B\_{ag} <B\_{low} } \\\\ {\\begin{array}{cc} {} & {} \\end{array}B\_{low} \\le B\_{ag} \\le B\_{up} } \\\\ {B\_{ag} >B\_{up} } \\end{array}\\right\\} \\ ,\\end{split}\\\]

where \\(B\_{ag}\\) (g C m\-2) is the biomass of combined leaf, stem, litter, and woody debris pools; \\(B\_{low}\\) = 105 g C m \-2 is the lower fuel threshold below which fire does not occur; \\(B\_{up}\\) = 1050 g C m\-2 is the upper fuel threshold above which fire occurrence is not limited by fuel availability.

Fuel combustibility \\(f\_{m}\\) is estimated by

(2.24.7)[¶](#equation-23-7 "Permalink to this equation")\\\[f\_{m} = {f\_{RH} f\_{\\beta}}, \\qquad T\_{17cm} > T\_{f}\\\]

where \\(f\_{RH}\\) and \\(f\_{\\beta }\\) represent the dependence of fuel combustibility on relative humidity \\(RH\\) (%) and root-zone soil moisture limitation \\(\\beta\\) (fraction); \\(T\_{17cm}\\) is the temperature of the top 17 cm of soil (K) and \\(T\_{f}\\) is the freezing temperature. \\(f\_{RH}\\) is a weighted average of real time \\(RH\\) (\\(RH\_{0}\\)) and 30-day running mean \\(RH\\) (\\(RH\_{30d}\\)):

(2.24.8)[¶](#equation-23-8 "Permalink to this equation")\\\[f\_{RH} = (1-w) l\_{RH\_{0}} + wl\_{RH\_{30d}}\\\]

where weight \\(w=\\max \[0,\\min (1,\\frac{B\_{ag}-2500}{2500})\]\\), \\(l\_{{RH}\_{0}}=1-\\max \[0,\\min (1,\\frac{RH\_{0}-30}{80-30})\]\\), and \\(l\_{{RH}\_{30d}}=1-\\max \[0.75,\\min (1,\\frac{RH\_{30d}}{90})\]\\). \\(f\_{\\beta}\\) is given by

(2.24.9)[¶](#equation-23-9 "Permalink to this equation")\\\[\\begin{split}f\_{\\beta } =\\left\\{\\begin{array}{cccc} {1} & {} & {} & {\\beta\\le \\beta\_{low} } \\\\ {\\frac{\\beta\_{up} -\\beta}{\\beta\_{up} -\\beta\_{low} } } & {} & {} & {\\beta\_{low} <\\beta<\\beta\_{up} } \\\\ {0} & {} & {} & {\\beta\\ge \\beta\_{up} } \\end{array}\\right\\} \\ ,\\end{split}\\\]

where \\(\\beta \_{low}\\) =0.85 and \\(\\beta \_{up}\\) =0.98 are the lower and upper thresholds, respectively.

For scarcely populated regions (\\(D\_{p} \\le 0.1\\) person km \-2), we assume that anthropogenic suppression on fire occurrence is negligible, i.e., \\(f\_{se,o} =1.0\\). In regions of \\(D\_{p} >0.1\\) person km\-2, we parameterize the fraction of anthropogenic and natural fires unsuppressed by human activities as

(2.24.10)[¶](#equation-23-10 "Permalink to this equation")\\\[f\_{se,o} =f\_{d} f\_{e}\\\]

where \\({f}\_{d}\\) and \\({f}\_{e}\\) are the effects of the demographic and economic conditions on fire occurrence. The demographic influence on fire occurrence is

(2.24.11)[¶](#equation-23-11 "Permalink to this equation")\\\[f\_{d} =0.01 + 0.98 \\exp (-0.025D\_{P} ).\\\]

For shrub and grass PFTs, the economic influence on fire occurrence is parameterized as a function of Gross Domestic Product GDP (k 1995US$ capita\-1):

(2.24.12)[¶](#equation-23-12 "Permalink to this equation")\\\[f\_{e} =0.1+0.9\\times \\exp \[-\\pi (\\frac{GDP}{8} )^{0.5} \]\\\]

which captures 73% of the observed MODIS fire counts with variable GDP in regions where shrub and grass PFTs are dominant (fractional coverage of shrub and grass PFTs \\(>\\) 50%). In regions outside tropical closed forests and dominated by trees (fractional coverage of tree PFTs \\(>\\) 50%), we use

(2.24.13)[¶](#equation-23-13 "Permalink to this equation")\\\[\\begin{split}f\_{e} =\\left\\{\\begin{array}{c} {0.39} \\\\ {0.79} \\\\ {1} \\end{array} \\begin{array}{cc} {} & {} \\end{array}\\begin{array}{c} {GDP > 20 } \\\\ { 8 < GDP \\le 20 } \\\\ { GDP \\le 8 } \\end{array}\\right\\} \\ ,\\end{split}\\\]

to reproduce the relationship between MODIS fire counts and GDP.

