Adaptation of the Nelson Dead Fuel Moisture Model for Fire Behavior and Fire Danger Software Application

Transcription

1 Adaptation of the Nelson Dead Fuel Moisture Model for Fire Behavior and Fire Danger Software Application April 2005 Collin D. Bevins Systems for Environmental Management Page 1

2 0. Introduction This document describes the procedures and results of an effort to adapt Nelson's (2000) dead fuel moisture model for use in fire behavior and fire danger software applications. The following steps were undertaken: 1. All available dead fuel moisture content field data and associated weather observations were collected, reviewed, and edited into a common format. The data included measurements for 1-h, 10-h, 100-h, and 1000-h dead fuel dowels. 2. A preliminary C++ class, DeadFuelMoisture, was written based upon Bevins' Fuel Moisture Stick C library, incorporating the most recent parameter values available from Ralph Nelson and J. D. Carlson (Carlson 2003, 2004a, 2004b). 3. A C++ test platform was written to perform iterative statistical analysis of observed and predicted dead fuel moisture contents using the DeadFuelMoisture class. 4. Model logic and radius-dependent model parameters were tuned to provide best fit with the field data. 5. Functions were developed to estimate radius-dependent parameters, enabling DeadFuelMoisture to be used for arbitrary fuel sizes. 1. Field Data Table 1 summarizes the moisture content field data and associated weather observations gathered from various sources. The data were in a variety of formats, with a range of documentation and data integrity. Obvious data errors such as dropped digits were corrected. The data were edited into a common test format. A large number of files were created representing various groupings and weather patterns during model testing. The individual data sets have been archived in the deadfuelmoisture.xls spreadsheet file using the format described in Table 2. The spreadsheet file is included in the accompanying compact disc Page 2

3 Table 1 Field Data Sources Location- Year Radius Weather Fuel Moisture (cm) Obs Frequency Obs Frequency Slapout, OK min :00 & 17:00 Slapout, OK min :00 & 17:00 Slapout, OK min :00 & 17:00 Slapout, OK Std.5 Sticks min :00 & 17:00 Unknown, April min min Burnsville, NC min min Unknown, March min min Mio, MI min min Missoula, MT min 66 Variable Unknown, April min min Unknown, April min min Missoula, MT min min Missoula, MT min min Slapout, OK min :00 & 17:00 Table 2 Field Data Spreadsheet Format Column Content Units A Elapsed time H B Year YYYY C Month MM (Jan=1, Dec=12) D Day DD E Hour MM F Minute MM G Second MM H Air temperature C I Relative Humidity G/g J Solar Radiation W/m2 K Cumulative rainfall Cm L Observed fuel moisture contents G/g (<=0 indicates no observation) M Predicted fuel moisture content G/g N Fuel moisture content prediction error G/g O Fuel moisture state at end of update() Index Page 3

4 2. DeadFuelMoisture C++ Class The DeadFuelMoisture class is an ANSI/ISO standard C++ class implementing Nelson's (2000) dead fuel moisture model as modified by Carlson (2003, 2004a, 2004b) and the results of this study. It requires no other code libraries besides the C++ Standard Template Library (STL) available in all C++ development environments. The class header file DeadFuelMoisture.h contains the class interface and description, while the source code file DeadFuelMoisture.cpp contains the class implementation and definition. The source code is heavily commented with extensive Doxygen markup for automatic generation of on-line and PDF manuals. 3. Model Parameter Testing and Selection The parameters listed in Table 3 vary by stick radius in the Nelson model. Nelson selected his parameter values based upon a series of ad hoc trials with a limited set of field data until a good fit was found (Nelson, personal communication). One objective of the current study was to reselect parameter values based upon a larger body of field data using a more systematic approach. A C++ test application based upon the DeadFuelMoisture class was developed to assist in the parameter value selection process. The test application could read one or more of the various data sets, generate predicted fuel moisture contents, accumulate observed v predicted statistics, and produce various output data, statistical, and graphics files. The parameters in Table 3 were iteratively varied to find a combination of values yielding the best observed v predicted results. This was repeated for the combined field data sets for each of the 1-h, 10-h, 100-h, and 1000-h time lag fuel size classes. The result of these trials was set of model parameters for each of the 4 fuel size classes yielding the minimum prediction error. Page 4

5 Table 3 Radius-Dependent Model Parameters Parameter Moisture computation radial nodes Moisture computation time steps per observation Moisture diffusivity time steps per observation Maximum local moisture content Planar heat transfer rate Surface mass transfer rate for adsorption Surface mass transfer rate for desorption Rainfall runoff factor during first hour of rain event Rainfall runoff factor during subsequent hours of rain event Storm transition value (precipitation rate) Water film contribution to stick moisture content Units count count count g/g cal/cm2-h-c (cm3/cm2)/h (cm3/cm2)/h dl dl cm rain/h g/g 4. Model Modifications As a result of testing the model against all the field data sets, a series of modifications were made to DeadFuelMoisture to produce the best predictions. 4.1 Storm Transition Value Nelson's model categorized rainfall into non-storm and storm events. The distinction between the two depended upon a precipitation rate threshold called the storm transition value. Testing showed that raising this threshold to an arbitrarily high value (such as cm/h) yielded the best predictions for all data sets. Because of this, the storm transition state logic was removed from the DeadFuelMoisture class. 4.2 Rainfall Runoff Factors Similarly, Nelson applied one rainfall runoff factor during the first hour of a rainfall event, and a second factor during subsequent periods for the same rainfall event. Not only did this produce a disjoint moisture content prediction curve throughout a rainfall event, it also increased prediction error. Removing the subsequent rainfall runoff factor logic from the DeadFuelMoisture class yielded improved predictions for all data sets. 4.3 Water Film Contribution Setting the water film contribution to zero resulted in the best predictions for all size classes. Page 5

6 4.4 Maximum Local Moisture Content Setting the maximum local moisture content to 0.6 g/g resulted in the best predictions for all size classes. It especially improved the responsiveness and accuracy of 1000-h fuel moisture content predictions. 4.5 Surface Mass Transfer Rate for Desorption Model results were relatively insensitive to the surface mass transfer rate for desorption. Fixing its value to 0.06 (cm3/cm2)/h did not significantly degrade any of the model predictions. 4.6 Radius-Dependent Parameters The remaining model parameters were determined to be radius-dependent: number of moisture computation radial nodes, number of moisture content computation steps per weather update, number of moisture diffusivity computation steps per weather update, planar heat transfer rate, surface mass transfer rate for adsorption, and rainfall runoff factor. 5. Radius-Dependent Model Parameter Functions Optimal model parameter sets for the four idealized 1-h, 10-h, 100-h, and 1000-h fuel size classes are generally adequate for most fire danger uses. Fire behavior applications, however, typically deal with dead fuels whose surface area-to-volume ratio range from ft -1 ( cm radius). A method of estimating the 6 radiusdependent parameters is therefore desirable for fire behavior modeling. Inverse power functions (Tables 4-9) were fitted to the optimal parameter sets; parameter values become asymptotic as radius increases, and approach infinity as the radius approaches zero. The function values and charts are archived in the deadfuelmoisture.xls spreadsheet file. Page 6

7 Table 4 Number of Moisture Computation Radial Nodes N = / radius 1.0 Radius (cm) Surface area-to-volume (ft -1 ) Parameter Value (n) Table 5 Number of Moisture Computation Steps per Update N = / radius 1.4 Radius (cm) Surface area-to-volume (ft -1 ) Parameter Value (n) Table 6 Number of Moisture Diffusivity Computation Steps per Update N = / radius 1.3 Radius (cm) Surface area-to-volume (ft -1 ) Parameter Value (n) Page 7

8 Table 7 Planar Heat Transfer Rate Rate = / radius 2.5 Radius (cm) Surface area-to-volume (ft -1 ) Parameter Value (cal/cm 2 -h-c) Table 8 Surface Mass Transfer Rate for Adsorption Rate = / radius 2.6 Radius (cm) Surface area-to-volume (ft -1 ) Parameter Values ((cm 3 /cm 2 )/h) Table 9 Rainfall Runoff Factor Factor = / radius 2.2 Radius (cm) Surface area-to-volume (ft -1 ) Parameter Values (dl) Page 8

9 The power functions for estimating the 6 radius-dependent model parameters were incorporated into DeadFuelMoisture. A final run of the modified model against all the field data sets produced results (Tables 10-13) whose standard errors were within g/g of the optimal parameter sets. Table h Predicted v Observed Fuel Moisture Content Results Data Set Samples Mean Abs Diff Std Error R2 Y intercept Slope Std Err Est Slapout, OK Table h Predicted v Observed Fuel Moisture Content Results Data Set Samples Mean Abs Diff Std Error R2 Y intercept Slope Std Err Est Slapout,OK Table h Predicted v Observed Fuel Moisture Content Results Data Set Samples Mean Abs Diff Std Error R2 Y intercept Slope Std Err Est April Burnsville, NC March Mio, MI Missoula, MT Slapout, OK Slapout, OK Std Dowels All Data Sets Table h Predicted v Observed Fuel Moisture Content Results Data Set Samples Mean Abs Diff Std Error R2 Y intercept Slope Std Err Est April April March Missoula, MT Missoula, MT Slapout, OK All Data Sets Page 9

10 The DeadFuelMoisture model performed well on the trial data sets with R 2 's in the range and standard errors of prediction generally around g/g. Standard errors of prediction were inflated by larger errors under wetter conditions. Of concern was the behavior of the DeadFuelMoisture model for fuels less than 0.2 cm and greater than 6.4 cm radii; i.e., outside the range of the test data sets. This was especially true for the finer fuels, whose model parameters (based on the inverse power functions of Tables 4-9) become exponentially large. Furthermore, it has been noted by Nelson, Carlson, and Bevins that the model projections become unstable for smaller fuels if an insufficient number of radial nodes, moisture content steps, or moisture diffusivity steps are applied. The 1-h fuel weather observations were used to generate moisture content predictions for fuels with 2000 ft -1 and 3500 ft -1 surface area-to-volume ratios. The parameter functions were adjusted until all computational instabilities were overcome (these modifications are incorporated into Tables 4-9). In all cases, predictions for these two fine fuel sizes appeared reasonable, generally following the 0.2 cm prediction curve but responding more rapidly to changes in relative humidity. For most (but not all) weather observations, the 2000 ft -1 and 3500 ft -1 predictions were the same. Modeling finer fuel moisture content carries a fairly heavy computational burden. The model is cpu-bound, with computation time t proportional to: t = n ( m + d ) where t is the relative time, n is the number of radial nodes, m is the number of moisture content computation time steps, and d is the number of moisture diffusivity time steps. Radius (cm) Table 14 DeadFuelMoisture Relative Computation Times Radial Nodes (n) Moisture Content Steps (m) Moisture Diffusivity Steps (d) Computation Time Factor (t) Relative Computation Time , , , , , Page 10

11 6. Conclusions The DeadFuelMoisture model performed well in predicting moisture content for the 15 field data sets covering 1-h, 10-h, 100-h, and 1000-h fuel size classes. Observed v predicted R 2 s ranged from 0.70 to 0.99, with standard errors generally in the 0.02 to 0.08 g/g range. The inverse power functions for estimating the 6 radius-dependent model parameters also performed well, yielding computationally stable results that appear reasonable for very fine fuels. The DeadFuelMoisture C++ class has been fairly well exercised during the testing process, and appears stable and ready for use in larger applications. 7. References Cited Carlson, J.D Evaluation of a new dead fuel moisture model in a near-real-time data assimilation and forecast environment. Progress report on file at USDA Forest Service, Rocky Mountain Research Station, Fire Sciences Lab, Missoula, MT. Sep 15, pp. Carlson, J.D. 2004a. Evaluation of a new dead fuel moisture model in a near-real-time data assimilation and forecast environment. Progress report on file at USDA Forest Service, Rocky Mountain Research Station, Fire Sciences Lab, Missoula, MT. Feb 10, pp. Carlson, J.D. 2004b. Evaluation of a new dead fuel moisture model in a near-real-time data assimilation and forecast environment. Progress report on file at USDA Forest Service, Rocky Mountain Research Station, Fire Sciences Lab, Missoula, MT. Jul 13, pp. Nelson, Ralph M. Jr Prediction of diurnal change in 10-h fuel stick moisture content. Can. J. For. Res. 30: Page 11

12 8. CD-ROM The contents of the accompanying cd-rom are: DfmReport doc this document in MS Word doc format DfmReport pdf this document in Adobe PDF formats DeadFuelMoisture.xls archival field data, observed v predicted, and charts DeadFuelMoisture.cpp DeadFuelMoisture C++ class source code file DeadFuelMoisture.h DeadFuelMoisture C++ class header file Docs Directory containing DeadFuelMoisture HTML Doxygen documentation for developers (start with the index.html file) Page 12