## 2 Methods
### Fuel Dynamics Estimated from MODIS Products
First, we estimated the live fuel loads from MODIS NPP. The amount of annual live herbaceous fuel is estimated from the grass NPP as follows:  
\[Livefuel_{herb}(t)=NPP_{grass}(t)\times\frac{1}{1+f_{F\text{FCC},\text{LC}}} \tag{2}\]The allocation parameter \(f_{FRC:LC}\) is the ratio of new fine root carbon to new leaf carbon for grass. This formula assumed that all the previous year's live herbaceous fuel was transferred to the dead fuel load. The amount of live woody fuel is estimated based on the shrub NPP and the woody fuel load from the previous year:  
\[\mathit{Livefuel_{x woody}(t)}=\mathit{NPP_{slrub}(t)}\times\frac{1+f_{SC,LC}}{1 +f_{FRC:LC}+f_{SC,LC}}+\mathit{Livefuel_{woody}(t-1)-\mathit{litter}(t)_{produce}} \tag{3}\]  
The allocation parameter \(f_{FRC:LC}\) is the ratio of new fine root carbon to new leaf carbon allocation and the allocation parameter \(f_{SC:LC}\) is the ratio of new stem carbon to new leaf carbon allocation for shrub biomes. Both Equations (1) and (2) are used to calculate the live herbaceous fuel load and live woody fuel load changes in the grass-shrub fuel type. Second, we calculated the dead fuel load using the live fuel load information. The change of the dead fuel load is controlled by three major processes:  
\[\mathit{Deadfuel}(t)=\mathit{litter}(t)_{produce}-\mathit{litter}(t)_{ decomp}-\mathit{litter}(t)_{removal}+\mathit{Deadfuel}(t-1) \tag{4}\]  
\[\mathit{litter}(t)_{produce}=\mathit{Livefuel}(t-1)\times\left(f_{ turnover}+f_{mortality}\right) \tag{5}\]  
where \(\mathit{litter}_{\mathrm{produce}}\) is the production of litter from the live vegetation, \(\mathit{litter}_{\mathrm{decomp}}\) is the loss of litter through decomposition, and \(\mathit{litter}_{\mathrm{removal}}\) is the removal of litter from the surface by disturbances other than decomposition, such as grazing and fire. \(\mathit{Litter}_{\mathrm{produce}}\) includes two processes: turnover and mortality [37]. \(\mathit{Deadfuel}_{(t-1)}\) is the turnover portion of the live plant pools that are replaced each year. \"t\" is yearly steps. The typical turnover time of grass was set to 1.0 yr\({}^{-1}\), which means that all the aboveground live biomass will turn into litter in the next year. For shrubs, the live leaf biomass turnover time was estimated as the inverse of the leaf longevity time. We set the leaf turnover rate of shrub to 1.0 yr\({}^{-1}\)[38] and the woody turnover rate to 0.01 yr\({}^{-1}\)[39]. Mortality is the portion of the plant pool that is lost because of vegetation death. The whole plant mortality rate of grass was set to 0.4 and the mortality rate of shrub was set to a constant 0.02 [37]. To simplify the calculation, we assumed that the live biomass only changed to dead biomass at the end of the growing season and all the dead biomass was 1 h dead fuel load. \(\mathit{Litter}_{\mathrm{produce}}\) is determined by the surface litter amount and the litter decomposition rate. The litter decomposition rate is impacted not only by the different components of the litter but also by environmental conditions such as soil temperature and moisture. We simplified the calculation by using a decay constant for all the litter pools. Generally, the mass loss of litter can be approximated by a simple model with an exponential decay function:  
\[\mathit{litter}(t)=\mathit{litter}(t-1)\times e^{-kt} \tag{6}\]  
_Litter(t-1)_ is the aboveground litter mass in the previous year, _litter(t)_ is the litter mass remaining at the current year without considering the new litter production and removal, k is the decay constant, and t is time. We reviewed the literature and used the mean decay constant (0.5 yr\({}^{-1}\)) of the litter from several studies in the western USA [40; 41; 42; 43]. \(\mathit{Litter}_{\mathrm{removal}}\) was set to 0 when no disturbance was detected (fire, grazing, etc.). When there was a fire event, we assumed the fraction of litter removed by the fire to be 90% [44].