SpringerLink
Log in

Fire frequency analysis for different climatic stations in Victoria, Australia

  • Original Paper
  • Published:
Natural Hazards Aims and scope Submit manuscript

Abstract

Frequent occurrence of fire events will have severe impact on Victoria’s water supply catchments. Hence, it is important to perform fire frequency analysis to obtain fire frequency curves (FFC) on fire intensity using Forest Fire Danger Index (FFDI) at different parts of Victoria. FFDI is a measure of fire initiation, spreading speed and containment difficulty. FFC will guide water harvesting by providing information with regard to future fire events and the subsequent impact on catchment yield. Five probability distributions, namely normal, Log Pearson Type III (LPIII), gamma, log-normal and Weibull distributions were used for the development of FFCs at ten selected meteorological stations spread all over Victoria. LPIII distribution was identified as the best fit distribution for Victoria and subsequently applied for an additional 30 more stations to show spatial variability for the entire Victoria.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  • Abernethy R (2006) The New Weibull handbook: reliability and statistical analysis for predicting life, safety, supportability, risk, cost and warranty claims, 5th edn. Barringer & Associates, Hickory

    Google Scholar 

  • Ahmed M, Sinclair C, Spurr B (1988) Assessment of flood frequency models using empirical distribution function statistics. Water Resour Res 24:1323–1328

    Article  Google Scholar 

  • Alexander A, Harald V, Herbert F, Alexander B (2010) A collection of possible fire weather indices (FWI) for alpine landscapes. www.alpffirs.eu/index.php?option=com_docman&task=doc. Accessed 5 June 2012

  • Allen C, Savage M, Falk D, Suckling K, Swetnam T, Schulke T, Stacey P, Morgan P, Hoffman M, Klingel J (2002) Ecological restoration of southwestern ponderosa pine ecosystems: a broad perspective. Ecol Appl 12:1418–1433

    Article  Google Scholar 

  • Arshad M, Rasool M, Ahmed M (2002) Power study for empirical distribution function tests for generalized Pareto distribution. Pak J Appl Sci 2:1119–1122

    Article  Google Scholar 

  • Australian Rainfall and Runoff (ARR) (1987) A guide to flood estimation, vol 1. Institution of Engineers, Australia, pp 195–235

    Google Scholar 

  • Bessie WC, Johnson EA (1995) The relative importance of fuels and weather on fire behavior in subalpine forests. Ecology 76:747–762

    Article  Google Scholar 

  • Blokhinov YG, Sarmanov IO (1968) Gamma correlation and its use in computations of long-term streamflow regulation. Sov Hydrol Sel Pap 1:36–54

    Google Scholar 

  • Catchpole WR, Bradstock R, Choate J, Fogarty L, Gellie N, McCarthy G, McCaw L, Marsden-Smedley J, Pearce G (1999) Cooperative development of prediction equations for fire behaviour in heathlands and shrublands. In: Proceedings of bushfire’99. Albury, New South Wales

  • Chandler C, Cheney P, Thomas P, Trabaud L, Williams D (1983) Fire in forestry, vol I. John Wiley and Sons, NewYork

    Google Scholar 

  • Cheney N, Gould J (1995) Separating fire spread prediction and fire danger rating. CALM Sci Suppl 4:3–8

    Google Scholar 

  • Chou Y, Minnich R, Chase R (1993) Map** probability of fire occurrence in San Jacinto mountains, California, USA. Environ Manag 17(1):129–140

    Article  Google Scholar 

  • Cohen A, Whitten B (1982) Modified moment and maximum likelihood estimators for parameters of the three-parameter gamma distribution. Commun Stat Simul Comput 11:197–216

    Article  Google Scholar 

  • Cohen AC, Whitten BJ (1988) Parameter estimation in reliability and life span models. Marcel Dekker Inc, New York

    Google Scholar 

  • Cox DR (1961) Tests of separate families of hypotheses. In: Proceedings of the fourth Berkeley symposium in mathematical statistics and probability, Berkeley, University of California Press, 105–123

  • Cox D (1962) Renewal theory. Wiley, London

    Google Scholar 

  • Cunnane C (1973) A particular comparison of annual maxima and partial duration series methods of flood frequency prediction. J Hydrol 18:257–271

    Article  Google Scholar 

  • Dayananda A (1977) Stochastic models for forest fires. Ecol Model 3(4):309–313

    Article  Google Scholar 

  • Finkele K, Mills GA, Beard G, Jones DA (2006) National gridded drought factors and comparison of two soil moisture deficit formulations used in prediction of forest fire danger index in Australia. BMRC research report 119, Bureau of Meteorology, Melbourne, Australia

    Google Scholar 

  • Fisher RA, Tippett LHC (1928) Limiting forms of the frequency distribution of the largest or smallest member of a sample. In: Proceedings of the Cambridge philosophical society, vol 24, no II, pp 180–191

  • Gordon N, McMahon T, Finlayson B, Gippel C, Nathan R (2004) Stream hydrology: an introduction for ecologists, 2nd edn. John Wiley and Sons Ltd, West Sussex

    Google Scholar 

  • Grissino-Mayer HD (1999) Modeling fire interval data from the American Southwest with the Weibull distribution. Int J Wildland Fire 9:937–950

    Article  Google Scholar 

  • Grubbs FE, Beck G (1972) Extension of sample sizes and percentage points for significance tests of outlying observations. Technometrics 14(4):847–854

    Article  Google Scholar 

  • Gumbel EJ (1958) Statistics of extremes. Columbia University Press, New York

    Google Scholar 

  • Johnson E (1979) Fire recurrence in the subarctic and its implications for vegetation composition. Can J Bot 57:1374–1379

    Article  Google Scholar 

  • Johnson E, Wagner C (1985) The theory and use of two fire history models. Can J For Res 15:214–219

    Article  Google Scholar 

  • Johnson N, Kotz S, Balakrishnan N (1995) Continuous univariate distributions, 2nd edn. Wiley, New York

    Google Scholar 

  • Karoly DJ (2009) Bushfires and extreme heat wave in southeast Australia. www.RealClimate.org. Accessed 16 Feb 2016

  • Keetch J, Byram G (1968) A drought index for forest fire control. USDA forest service research paper No. SE-38, pp 1–32

  • Kundu D, Manglick A (2005) Discriminating between the log-normal and gamma distributions. J Appl Stat Sci 14:175–187

    Google Scholar 

  • Landres P, Morgan P, Swanson F (1999) Overview of the use of natural variability concepts in managing ecological systems. Ecol Appl 9:1179–1188

    Google Scholar 

  • Lang M, Ouarda T, Bobee B (1999) Towards operational guidelines for over-threshold modelling. J Hydrol 225:103–117

    Article  Google Scholar 

  • Madsen H, Pearson C, Rosbjerg D (1997) Comparison of annual maximum series and partial duration series methods for modeling extreme hydrologic events, 2. Regional modelling. Water Resour Res 33:759–769

    Article  Google Scholar 

  • Mandallaz D, Ye R (1997) Prediction of forest fires with Poisson models. Can J For Res 27:1685–1694

    Article  Google Scholar 

  • McArthur A (1966) Weather and grassland fire behaviour. Department of National Development, Forestry and Timber Bureau Leaflet No. 100, Canberra

    Google Scholar 

  • McArthur A (1967) Fire behaviour in eucalypt forests. Department of National Development, Forestry and Timber Bureau Leaflet No. 107, Canberra

    Google Scholar 

  • McArthur AG (1973) Forest fire danger meter, Mark V. Forest Research Institute, Forest and Timber Bureau of Australia, Leaflet No. 107, Canberra

    Google Scholar 

  • Moran PAP (1970) Simulation and evaluation of complex water systems operations. Water Resour Res 6(6):1737–1742

    Article  Google Scholar 

  • Mount AB (1972) The derivation and testing of a soil dryness index using run-off data. Tasmanian Forestry Commission Bulletin, no 4. pp 31

  • National Fire Warning System (2009) New warning system explained. http://www.cfaconnect.net.au/index.php?option=com_k2&view=item&id=873. Accessed on 2 Dec 2009

  • Nesterov V (1949) Forest fires and methods of fire risk determination. Goslesbumizdat, Moscow

    Google Scholar 

  • Noble I, Bary G, Gill A (1980) McArthur’s fire-danger meters expressed as equations. Aust J Ecol 5:201–203

    Article  Google Scholar 

  • Onoz B, Bayazit M (1995) Best-fit distributions of largest available flood samples. J Hydrol 167:195–208

    Article  Google Scholar 

  • Pearson K (1893) Contributions to the mathematical theory of evolution. Proc R Soc Lond 54:329–333

    Article  Google Scholar 

  • Pearson K (1895) Contributions to the mathematical theory of evolution, II: skew variation in homogeneous material. Philos Trans R Soc Lond 186:343–414

    Article  Google Scholar 

  • Peng R, Schoenberg F (2001) Estimation of wildfire hazard using spatial-temporal fire history data. Technical report, Statistics Department, UCLA

  • Schoenberg FP, Peng R, Woods J (2003) On the distribution of wildfire sizes. Environmetrics 14:583–592

    Article  Google Scholar 

  • Schoennagel T, Veblen T, Romme W (2004) The interaction of fire, fuels, and climate across Rocky Mountain forests. Bioscience 54:661–676

    Article  Google Scholar 

  • Sivandran G (2002) Effects of rising water tables and climate change on annual and monthly flood frequencies. Department of Environmental Engineering, University of Western Australia

  • Skvarenina J, Mindas J, Holecy J, Tucek J (2003) Analysis of the natural and meteorological conditions during two large forest fire events in the Slovak Paradise National Park. In: International bioclimatological workshop, p 11

  • Sneeuwjagt J, Peet B (1985) Forest fire behaviour table for Western Australia. WA Department of Conservation and Land Management, Perth

    Google Scholar 

  • Stedinger JR, Vogel RM, Foufoula-Georgiou E (1993) Frequency analysis of extreme events. McGraw-Hill, New York

    Google Scholar 

  • Stephens M (1986) Tests based on EDF statistics. Goodness-of-Fit techniques, New York, pp 97–193

    Google Scholar 

  • Takeuchi K (1984) Annual maximum series and partial duration series—evaluation of Langbein’s formula and Chow’s discussion. J Hydrol 68:275–284

    Article  Google Scholar 

  • Van Wagner C (1978) Age class distributions and forest fire cycle. Can J For Res 8:220–227

    Article  Google Scholar 

  • Van Wagner C (1987) Development and structure of the Canadian forest fire weather index system. Canadian forest service technology report no. 35

  • Weibull W (1951) A statistical distribution function of wide applicability. J Appl Mech Trans ASME 18(3):293–297

    Google Scholar 

  • Wiens BL (1999) When log-normal and gamma models give different results: a case study”. Am Stat 53(2):89–93

    Google Scholar 

  • **aowei L, Guobin F, Zeppel MJB, **ubo Y, Gang Z, Eamus D, Qiang Y (2012) Probability models of fire risk based on forest fire indices in contrasting climates over China. J Resour Ecol 3(2):105–117

    Article  Google Scholar 

  • Yue S (2000) The bivariate log-normal distribution to model a multivariate flood episode. Hydrol Process 14:2575–2588

    Article  Google Scholar 

  • Yue S (2001) A bivariate gamma distribution for use in multivariate flood frequency analysis. Hydrol Process 15:1033–1045

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Vocational Engineering, Health and Sciences, RMIT University, Melbourne, Australia

    Anirban Khastagir

Authors
  1. Anirban Khastagir
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Anirban Khastagir.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Khastagir, A. Fire frequency analysis for different climatic stations in Victoria, Australia. Nat Hazards 93, 787–802 (2018). https://doi.org/10.1007/s11069-018-3324-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11069-018-3324-x

Keywords

Search

Navigation