ECONOMIC AND SOCIAL DETERMINANTS OF AN ADEQUATE LEVEL OF FOREST FIRE CONTROL by Richard Keith Arnold A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the University of Michigan 1949 Committee in charge: Professor Shirley W• Allen, Chairman Associate Professor Gardner Ackley Professor Samuel T. Dana Professor Willett F* Ramsdell Copyrighted by Richard Keith Arnold 1950 i - ii ACKNOWLEDGMENTS In addition to effective guidance by the committee the author wishes to express appreciation to others who contributed to the study which produced this dissertation, Charles C. Buck, In Charge, Division of Forest Fire Research, California Forest and Range Experiment Station, spent con­ siderable time in 1946 helping the author prepare a course in forest fire protection. Some proposals which appear in this study have been developed from those discussions with Mr. Buck. Professor Kenneth C. Davis, School of Forestry, University of Michigan, was particularly helpful and con­ structive in his critioism of parts of the manuscript. Lawrence A. Jehu, Teaching Fellow in Mathematics, University of Michigan, advised the author concerning the mathematical appendix. i iii - TABLE OF CONTENTS Page LIST OF TABLES.................................. vi LIST OF ILLUSTRATIONS........................... vii Chapter I. INTRODUCTION............................. 1 Conditions under which Forest Fire Con­ trol Must Function The Work of the Fire Control Organization Fire, a Public Problem The Importance of Economic Studies Deal­ ing with Fire Objectives of the Study II. THE DEVELOPMENT OF FOREST FIRE PROTECTION IN THE UNITED STATES....................... 11 General Considerations The Prevention Era— Fire, a Reoognized Danger The Suppression Era— Fire, the Principal Forestry Problem The Present--Fire, a Recognized Tool in Forest Management III. ANALYSIS OF OBJECTIVES OF ADEQUATE FIRE CONTROL................................. 70 General Critique i Area and Size Objectives Time Goals Miscellaneous Objectives Lea st-Cost-Plus-Damage IV. A "MODEL*1 APPROACH TO THE LEAST-COST-PLUS- DAMAGE SOLUTION......................... 107 Basis for the Model Approach The Model The Synthesis Implications of the Model Least-Cost- Plus-Damage Solution - iv - Chapter Page V. FACTORS AFFECTING THE LEAST-COST-PLUS- DAMAGE SOLUTION ....................... 150 Difficulties in Practical Application Conflagration Potential A Balanced Fire Control Effort Fire Control and Depression Fire Control and Forest Management Appendix I. MEANING OF SYMBOLS................... 186 II. MATHEMATICS OF THE LEAST-COST-PLUS-DAMAGE SOLUTION ............................. 188 LITERATURE CITED ............................. 200 LIST OF TABLES Table Page 1. Historic Forest Fires in the United States and Canada.......................... 25 2* Area of National Forest in the United States, Exclusive of Alaska and Porto Rico, Burned » over from 1904 to 1907 Inclusive.......... 28 3. Expenditures for Cooperative Fire Protection on Private and State Forest Lands, 1911-47................................... 40 4« Importance of Unprotected Land to the Forest Protection Problem......................... 68 5« Fire Occurrence on Protected Forest Lands by State Groups and by Cause............... 69 6* Indexes of Effective Fire Control for Various Forest Types........................ 77 7* Average Run-off and Erosion Damage from Future Fires on Selected Watersheds of the Angeles National Forest..................... 118 8* Average Suppression Cost and Damage per Fire in Dollars...................................190 9* Total Suppression Cost and Damage per Million Acfhes per Year............................... 192 10* Damage Plus Suppression Cost Plus Presuppres­ sion Cost per Million Aores per Year Assuming No Prevention Effort • • • • • • • • • • • • • 193 11* Total Damage and Protection Costs per Million Acres per Year Assuming Optimum "Shotgun” Prevention Effort........................... 196 12* Total Damage and Protection Costs per Million Acres per Year Assuming Optimum "Concentrated” Prevention Effort......... 198 vi - LIST OF ILLUSTRATIONS Figure Page . 1 The Forest Fire Situation in the United States ............................... 67 . 2 Sparhawk’s Illustration of the Least-Cost- Plus-Damage Analysis......................... 93 Flint*s Least-Cost-Plus-Damage Analysis . . . 97 3. 4* Sum of Damage Plus Suppression Plus Prevention Plus Presuppression Costs for Various Levels of Variable Prevention Plus Presuppression Cost, Private Land, Southwest Virginia, 1940- 4 4 .......................................... 101 5. Relation of Sum of Variable Costs and Damage to Total Variable Costs for Prevention, Pre­ suppression and Suppression, South Carolina Coastal Area, 1941-45 102 . 6 Rate of Held Line Construction for Suppression Forces of Various Sizes .................... 114 7. Suppression Cost and Damage per Fire in Relation to Intensity of Suppression ......... 127 . 8 The Sum of Suppression Cost and Damage in Relation to Intensity of Suppression ......... 128 9. Least-Cost-Plus-Damage Solution Based on Annual Sums of Suppression Cost, Damage, and Presuppression Cost for One Million Acres • • 130 . 10 Determination of the Least Annual Sum per Million Acres of Suppression Cost, Damage, and "Shotgun" Prevention Cost for Various Attack Times in Relation to Percentage Reduction in Number of Fires................. 133 11. Least-Cost-Plus-Damage Solution Based on Suppression Cost, Damage, Presuppression Cost, and "Shotgun" Prevention Cost per Million Acres per Year....................... 135 - vii - Figure Page 12* Determination of the Least Annual Sum per Million Acres of Suppression Cost, Damage, Presuppression Cost, and "Concentrated" Prevention Cost for Various Attack Times in Relation to Percentage Reduction in Number of Fires........................ 136 13« Least-Cost-Plus-Damage Solution Based on Prevention Cost, Damage, Presuppression Cost, and "Concentrated" Prevention Cost per Million Acres per Y e a r ............... 138 14* Relation of Damage to the Sum of Suppression Cost and Damage........................... 144 15. Comparison of Least-Cost-Plus-Damage Solutions................................. 147 » - viii - CHAPTER I INTRODUCTION Conditions under whioh Forest Fire Control Must Function Forest fire oontrol1 has been defined as the "pro­ tection of wild land and the growth thereon from fire," (U.S. Forest Service, 1939:8) but like many general definitions this is useful only as the foundation for a frame of referenoe whioh delineates the problem area of the field in question. An im­ portant part of the frame of reference of forest fire control is the description of limiting assumptions or conditions under which it operates. The first oonditlon is that the wild land and growth thereon must have value. Unless these resources provide directly for the creation of utilities whioh are soaroe and which satisfy human wants their protection oannot be justi­ { fied. However in practice this oondltion is easily satis- fied: for forest values derived from products such as lum­ ber, fuel wood, pulpwood, naval stores, forage for livestock, wildlife, recreation; and indirect values derived from the forest as a oondltion (regulation of stream-flow, erosion Fire protection is used synonymously with fire con­ trol in this work. - 1 - control, reduction of wind velocity, and social values) are well established. (U.S. Forest Servloe, 1948:13-21) (U.S. Forest Service, 1933*91-117) The second condition is that the effeot of fire oust be to decrease these forest values. Damage from oomplete de­ struction of merchantable timber, or any forest raw material, or of improvements is dearly a harmful effeot of fire. But other types of fire losses such as the reduotion in quantity or quality of growth, deorease in soil productivity, incep­ tion of inseot and disease attaoks, increase in flood and erosion damage, and their resultant eoonomio and sooial mal­ adjustments, though not always so evident, may in the aggre­ gate deorease forest values more than oomplete destruction of raw materials. As an extreme example, on some southern Cal­ ifornia watersheds, damage from inoreased run-off and erosion has been oomputed to be greater than $300 per aore, when the brush cover has been removed by fire. (Buck, Fons, and Countryman, 1948b) The third condition is readily established by ooour- renoe reoords: there must be fire, and aocording to the U.S. Forest Servioe, there is fire. 1 From 1946 to 1948, inclusive, the average number of forest fires in the United States per year was 182,415» whioh is equal to 280 fires per *U.S. Forest Servioe, Div. of State Cooperation, jj0r??t Fire Statistics. Calendar Year (published annually, Washington) • Hereafter in this worV data from this souroe will be acknowledged by the title, Forest Fire Statistics.