Modelling Stand Diameter Distribution by Using 3-Parameters Weibull Probability Density Function in Sarıçiçek-Vezirköprü Forest Enterprise

Year 2016, Volume: 2 Issue: 1-2, 13 - 24, 15.12.2016

İlker Ercanlı , Ferhat Bolat Aydın Kahriman

Abstract

In this study, it is aiming to model stand diameter distribution by using different parameter prediction methods for 3-Parameter Weibull probability density function in Sariciçek Forest Enterprise. The parameter of Weibull pdf were estimated by using five methods based on 25th, 31th, 50th, 63th and 95th percentiles obtained from data including 428 sample plots. In evaluations based on Rennolds et. al. (1988)’s error index values, the method using some equations including 31th, 50th and 63th percentiles were assessed to the most successful technique for modeling stand diameter in studied forest areas. When the relationships between the parameters of Weibull function and some stand attributes were analyzed, the statistical significant relationships were obtained for species admixtures and stand diameter classes. However, it is determined that stand crown closure has no effect on the value of the parameters of 3-Parameter Weibull probability density function.

Keywords

Stand diameter distribution models, 3-Parameter Weibull probability density function, Parameter prediction method based on percentile values

Vezirköprü-Sarıçiçek Orman İşletme Şefliği Sınırları İçerisinde Yer Alan Meşçerelerin Çap Dağılımlarının 3 Parametreli Weibull Olasılık Yoğunluk Fonksiyonu İle Modellenmesi

Abstract

Bu çalışmada, Sarıçiçek Orman İşletme Şefliğinde yayılış gösteren farklı meşcereleri için 3 parametreli Weibull olasılık yoğunluk fonksiyonun parametrelerinin tahmine ilişkin farklı eşitlikler ile çap dağılımlarının modellenmesi amaçlanmıştır. Bu amaçla, çalışmaya konu meşcerelerden alınmış 428 örnek alan verisi kullanılarak çap dağılımlarının %25,  %31, %50, %63 ve %95’lik değerlerine karşılık gelen çapları esas alan 5 farklı yüzdelik yöntemi ile 3 parametreli Weibull olasılık yoğunluk fonksiyonun parametreleri tahmin edilmiştir. Rennolds vd. (1988) tarafından geliştirilen hata indeksine bağlı olarak yapılan karşılaştırmada,  %31,  %50 ve %63’lük değerleri esas alan eşitliklere dayanan parametre tahmin yöntemi; çalışma alanındaki meşcerelerinin çap dağılımını modellemede en başarılı parametre tahmin yöntemi olarak belirlenmiştir. Ayrıca, olasılık yoğunluk fonksiyonun parametrelerinin çeşitli meşcere özelliklerine göre değişimleri değerlendirildiğinde; parametre değerleri ile ağaç tür karışımları ve çağ sınıfları arasında istatistiksel olarak anlamlı ilişkiler elde edilmiştir. Meşcere kapalılığının ise meşcere çap dağılımın modelleyen Weibull fonksiyonun parametre değeri üzerinde bir etkisinin olmadığı belirlenmiştir.

Keywords

Çap dağılım modelleri, 3 Parametreli Weibull olasılık yoğunluk fonksiyonu, Yüzdelikleri esas alan parametre tahmin yöntemi

References

• Atıcı, E. 1998. Değişikyaşlı Doğu Kayını (Fagus orientalis Lipsly.) Ormanlarında Artım ve Büyüme, Doktora Tezi, İstanbul Üniversitesi, Fen Bilimleri Enstitüsü, İstanbul.
• Andrasev, S., Bobinac, M., Orlovic, S. 2009. Diameter structure models of Black Poplar selected clones in the section Aigeiros (Duby) obtained by the Weibull distribution. Sumarski List 133: 589-603
• Bailey RD (1980) Individual Tree Growth Derived From Diameter Distribution Models, Forest Science, 26, 626–632.
• Bailey RL, Dell TR (1973) Quantifying Diameter Distributions with The Weibull Function, Forest Science, 19, 97–104
• Bailey RL, Burgan TM, Jokela EJ (1989) Fertilized mid-rotation aged slash pine plantations—Stand structure and yield prediction models. South. J. Appl. For. 13:76-80.
• Baldwin VC, Feduccia DP (1987) Loblolly pine growth and yield prediction for managed West Gulf plantations. USDA For. Serv. Res. Pap. SO 236, 27 s.
• Bliss CI, ve Reinker KA (1964) A Lognormal Approach to Diameter Distributions in Even-Aged Stands, Forest Science, 10, 350–360.
• Borders BE, Patterson WD (1990) Projecting stand tables: a comparison of the weibull diameter distribution method, a percentile-based projection method and a basal area growth projection method, Forest Science, 36, 413– 424.
• Bullock B, Burkhart H (2005) Juvenile diameter distributions of loblolly pine characterized by the two-parameter Weibull function, New Forests 29, 233-244.
• Brooks JR, Borders BE, Bailey RL (1992) Predicting diameter distributions for site prepared loblolly and slash pine plantations. South. J. Appl. For. 16: 130-133
• Cao QV (2004) Predicting Parameters of A Weibull Function for Modelling Diameter Distribution. Forest Science, 50, 682 – 685.
• Carus S (1996) Aynı Yaşlı Doğu Kayını (Fagus orientalis Lipsly.) Meşcerelerinde Çap Dağılımın Bonitet ve Yaşa Göre Değişmi, İstanbul Orman Fakültesi Dergisi, 46, 171-181.
• Carus S, Çatal Y (2008) Kızılçam (Pinus Brutia Ten.) Meşcerelerinde 7-Ağaç Örnek Nokta Yöntemiyle Meşcere Ağaç Sayısının Çap Basamaklarına Dağılımının Belirlenmesi, Süleyman Demirel Üniversitesi, Orman Fakültesi Dergisi, 2, 158-169.
• Čavlović J, Božić M, Boncina A (2006) Stand Structure of An Uneven-Aged Fir–Beech Forest with An Irregular Diameter Structure: Modeling The Development of The Belevine Forest, Croatia, European Journal of Forest Research, 125, 4, 325-333.
• Clutter JL, Bennett FA (1965) Diameter Distributions in Old-Field Slash Pine Plantation, Georgia Forest Research Council, Report No.13.
• Clutter JL, Harms WR, Brister GH, Rhenney JW (1984) Stand structure and yields of site-prepared loblolly pine plantations in the lower coastal plain of the Carolinas, Georgia, and North Florida. USDA For. Serv. Gen. Tech. Rep. SE-27, 173 s.
• Coble DW, Lee YJ (2008) A new diameter distribution model for unmanaged slash pine plantations in East Texas. South. J. Appl. For. 32: 89-94.
• Ercanlı İ (2010) Trabzon ve Giresun orman bölge müdürlükleri sınırları içerisinde yer alan Doğu Ladini (Picea orientalis (l.) Link)-Sarıçam (Pinus sylvestris l.) Karışık meşcerelerine ilişkin büyüme modelleri, Doktora Tezi, K.T.Ü., Fen Bilimleri Enstitüsü, Trabzon.
• Ercanlı İ, Yavuz H (2010) Doğu Ladini (Picea Orientalis (L.) Link)-Sarıçam (Pinus Sylvestris L.) Karışık Meşcerelerinde Çap Dağılımlarının Olasılık Yoğunluk Fonksiyonları İle Belirlenmesi, Kastamonu Orman Fakültesi Dergisi, 10 (1), 68-83.
• Feduccia DP, Dell TR, Mann WF, Polmer BH (1979) Yields of unthinned loblolly pine plantations on cutover sites in the West Gulf region. USDA For. Serv. Res. Pap. So-148, 88 s.
• Gorgoso-Varela JJ, Alvarez-Gonzalez JG, Rojo A, Grandas-Arias JA (2007) Modelling diameter distributions of Betula alba L. stands in northwest Spain with the two-parameter Weibull function. Invest. Agrar. Sist. Recur. For. 16: 113-123.
• Hafley WL, Schreuder HT (1977) Statistical distributions for fitting diameter and height data in even-aged stands, Canadian Journal of Forest Reearcsh, 4, 481 – 487.
• Jiang LC, Brooks JR (2009) Predicting diameter distributions for young longleaf pine plantations in Southwest Georgia. South. J. Appl. For. 33: 25-28.
• Johnson NL (1949) Systems of Frequency Curves Generated By Methods of Translation, Biometrika, 36, 149-176.
• Kahriman A, Yavuz H (2011) Sarıçam (Pinus sylvestris L.)-Doğu Kayını (Fagus orientalis Lipsky) Karışık Meşcerelerinde Çap Dağılımlarının Olasılık Yoğunluk Fonksiyonları ile Belirlenmesi, Artvin Çoruh Üniversitesi Orman Fakültesi Dergisi, 12 (2), 109-125.
• Knoebel BR, Burkhart HE, Beck DE (1986) A Growth and Yield Model for Thinned Stands of Yellow-Poplar, Forest Science Monograph, 27, 39 s.
• Knowe SA (1992) Basal Area and Diameter Distribution Models for loblolly Pine Plantations with Hardwood Competition in The Piedmont And Upper Coastal Plain. South. J. Appl. For., 16, 93–98.
• Knowe SA, Ahrens GA, DeBell DS (1997) Comparison of diameter-distribution prediction, stand-table -projection and individual-tree growth modeling approaches for young red alder plantations. For. Ecol. Manage. 96: 207-216
• Knowe SA, Radosevich SR, Shula RG (2005) Basal area and diameter distribution prediction equations for young Douglas-Fir plantations with hardwood competition: Coast ranges. West. J. Appl. For. 20: 77-93.
• Leak WB (1965) The J-Shaped Probability Distribution, Forest Science, 11, 405–409.
• Lee YJ, Coble DW (2006) A new diameter distribution model for unmanaged loblolly pine plantations in East Texas. South. J. Appl. For. 30: 13-20.
• Liu C, Zhang SY, Lei Y, Newton PF, Zhang L (2004) Evaluation of Three Methods for Predicting Diameter Distributions of Black Spruce (Picea Mariana ) Plantations in Central Canada, Canadian Journal of Forest Research, 34 , 2424 – 2432
• Lohrey RE, Bailey RL (1977) Yield tables and stand structure for unthinned long leaf pine plantations in Louisiana and Texas. USDA For. Ser. Res. Pap. SO-133. 55 s
• Maltamo M (1997) Comparing basal area diameter distributions estimated by tree species and for the entire growing stock in a mixed stand. Silva Fenn 31(1); 53-65.
• Maltamo M, Puumalainen J, Paivinen R (1995) Comparison of Beta and Weibull Functions for Modeling Basal Area Diameter Distributions in Stands of Pinus Sylvestris and Picea Abies, Scandinavian Journal of Forest Research, 10, 184-295.
• Matney TG, Sullivan AD (1982) Compatible stand and stock tables for thinned and unthinned loblolly pine stands. For. Sci. 28: 161-171.
• McTague JP, Bailey RL (1987) Compatible basal area and diameter distribution models for thinned loblolly-pine plantations in Santa Catarina, Brazil. For. Sci. 33: 43-51.
• Meyer HA, Stevenson DD (1943) The structure and growth of virgin beech-birch-maplehemlock forests in northern Pennsylvania. J. Agr. Res. 67: 465-484
• Nelson TC (1964) Diameter Distribution and Growth of Loblolly Pine, Forest Science, 10, 105–115.
• Nord-Larsen T, Cao QV (2006) A Diameter Distribution Model for Even-Aged Beech in Denmark, Forest Ecology and Management, 231, 218–225.
• Packard KC (2000) Modeling Tree Diameter Distributions for Mixed-Species ConiferForests in The Northeast United States, Master Thesis, State University of New York, New York, USA., 129 s.
• Palahi M, Pukkala T, Trasobares A (2006) Calibrating Predicted Tree Diameter Distributions in Catalonia (Spain), Silva Fennica, 40, 3, 487–500.
• Palahi M, Pukkala T, Trasobares A (2007) Modelling The Diameter Distribution of Pinus Sylvesris, Pinus Nigra and Pinus Halepensis Forest Stands in Catalonia Using The Truncated Weibull Function, Forestry, 79, 5, 553-562.
• Podlaski R (2006) Suitability of The Selected Statistical Distributions for Fitting Diameter Data in Distinguished Development Stages and Phases of Near-Natural Mixed Forests in The Świętokrzyski National Park (Poland), Forest Ecololgy and Management, 236, 393–402
• Poudel KP (2011) Evaluatıon of methods to predıct weıbull parameters for characterızıng dıameter dıstrıbutıons, MSc. Graduate Faculty of the Louisiana State University and Agricultural and Mechanical College, 60 s.
• Poudel KP, Cao QV (2013) Evaluatıon of methods to predıct weıbull parameters for characterızıng dıameter dıstrıbutıons, Forest Science, 59 (2), 243-252
• Pukkala T, Saramaki J, Mubita O (1990) Management Planning System For Tree Plantations; A Case Study for Pinus Kesiya in Zambia, Silva Fennica, 24, 171–180
• Rennolls K, Geary DN, Rollinson TJD (1985) Characterizing diameter distributions by the use of the Weibull distribution, Forestry, 58, 58–66.
• Reynolds MR, Burke TE, Huang W (1988) Goodness-of-Tests and Model Sselection Procedures for Diameter Distribution models, Forest Science, 34, 373-379.
• Saraçoğlu Ö (1988) Karadeniz Yöresi Göknar Meşçerelerinde Artım ve Büyüme, O. G. M. Yayınları, No: 25, 312.
• Smalley GW, Bailey RL (1974) Yield Tables and Stand Structure for Shortleaf Pine Plantations in The Tennessee, Alabama and Georgia Highlands. USDA Forest Service Research Paper, 97 s.
• Samaraki J (1992) A Growth and Yield Prediction Model of Pinus Kesiya in Zambia, Acta Forestalia Fennica, 230, 68.
• Sönmez T, Günlü A, Karahalil U, Ercanl İ, Şahin A (2010) Saf Doğu Ladini Meşcerelerinde Çap Dağılımının Modellenmesi, "III. Ulusal Karadeniz Ormancılık Kongresi Bildiriler Kitabı. 20-22 Mayıs 2010, Artvin", Cilt: I, 388-398
• SPSS Institute Inc., 2005. SPSS Base 12.0 User’s Guide, 688 s.
• Yavuz H, Gül AU, Mısır N, Özçelik R, Sakıcı OE (2002) Meşcerelerde Çap Dağılımlarının Düzenlenmesi ve Bu Dağılımlara İlişkin Parametreler ile Çeşitli Meşcere Öğeleri Arasındaki İlişkilerin Belirlenmesi, Orman Amenajmanında Kavramsal Açılımlar ve Yeni Hedefler Sempozyumu, 18-19 Nisan İstanbul
• van Lear A, Akça A (2007) Forest mensuration: in: Managing Forest Ecosystems, Dordrecht, The Netherlands: Springer, 383 s.
• Weibull W (1951) A Statistical Distribution Function of Wide Applicability, J. Appl. Mech., 18, 293–297.
• Zhang L, Liu C (2006) Fitting Irregular Diameter Distributions of Forest Stands By Weibull, Modified Weibull and Mixture Weibull Models, Journal Forest Research, 11, 369–372.