Trapezoidal Numerical Integration of Fire Radiative Power (FRP) Provides More Reliable Estimation of Fire Radiative Energy (FRE) and so Biomass Consumption Than Conventional Estimation Methods

The Fire Radiative Power (FRP) [MW] is a measure of the rate of biomass combustion and can be retrieved from ground based and satellite observations using middle infra-red measurements. The temporal integral of FRP is the Fire Radiative Energy (FRE) [MJ] and is related linearly to the total biomass consumption and so pyrogenic emissions. Satellite derived biomass consumption and emissions estimates have been derived conventionally by computing the summed total FRP, or the average FRP (arithmetic average of FRP retrievals), over spatial geographic grids for fixed time periods. These two methods are prone to estimation bias, especially under irregular sampling conditions such as provided by polar-orbiting satellites, because the FRP can vary rapidly in space and time as a function of the fire behavior. Linear temporal integration of FRP taking into account when the FRP values were observed and using the trapezoidal rule for numerical integration has been suggested as an alternate FRE estimation method. In this study FRP data measured rapidly with a dual-band radiometer over eight prescribed fires are used to compute eight FRE values using the sum, mean and trapezoidal estimation approaches under a variety of simulated irregular sampling conditions. The estimated values are compared to biomass consumed measurements for each of the eight fires to provide insights into which method provides more accurate and precise biomass consumption estimates. The three methods are also applied to continental MODIS FRP data to study their differences using polar orbiting satellite data. The research findings indicate that trapezoidal FRP numerical integration provides the most reliable estimator.