EFIMED Advanced course on MODELLING MEDITERRANEAN FOREST STAND DYNAMICS FOR FOREST MANAGEMENT

1. EFIMED Advanced course on MODELLING MEDITERRANEAN FOREST STAND DYNAMICS FOR FOREST MANAGEMENT SITE INDEX MODELLING MARC PALAHI Head of EFIMED Office

2. Forest stand development affected by • Regeneration • Growth of trees • Mortality • Models should be able to predict these processes which are affected by factors like • Productive capacity of an area • Degree to which the site is occupied • Point in time in stand development

3. Site quality • Defined as the yield potential for specific tree species on a given growing site • key to explain and predict forest growth and yield and therefore for defining optimal forest management. Certain investments might be only justify in certain sites…

4. Assesing site quality • Might be assessed directly or indirectly • Indirect methods: topographic descriptors, location descriptors, soil types, presence of plant species, etc • Direct methods: require the presence of the species at the location where site is evaluated • - Why not using the volume-age relationship? • m3ha-1 at a given age • Site index, dominant height at an specified reference age; the height development of dominant trees in even-aged stands is not affected by stand density = in good sites height growth rates are high

5. Site index curves 26 23 20 17 13 A family of height development patterns with a qualitative symbol or number associated with each curve usually the height achieved at a reference age Site index curves are the graphic representations of mathematical equations obtained by applying regression analysis to height age data

6. Many equations used Non-linear regression required

7. Data for site index modelling • Derived from three sources: • 1. Meaurement of height and age on temporary plots • - Inexpensive, full range should be represented • 2. Measurement of height and age over time: permanent plots • - Many years, good dynamic data, expensive • 3. Reconstruction of height/age through stem analysis • - Immediately, expensive, good dynamic data

8. Methods for site index modelling • The guide curve method • The difference equation method • The parameter prediction method • The guide curve method produces anamporphic site index curves and is usually used when only temporary plots are available • The difference equation method requieres permanent plots or stem analysis data

9. Amamorphic versus Polymorphic

10. The guide curve method (1) Boi= constant associate with the ith curve B1= constant for all curves

11. The guide curve method (2) • Produces a set of anamorphic curves (proportional curves) • Needs to be algebraically adjusted after fitting the equation, • - such site index equations varies depending on which reference age is chosen

12. The difference equation method (1) • Requires permanent plots or stem analysis data • Flexible method, can be used with any equation to produce anamorphic or polymorphic curves • First step: developing a difference form of the heigh/age equation being fitted • Expressing Height at remeasurement (H2) as a function of remeasurement age (A2), initial measurement age (A1), and heigh at initial measurement (H1)

13. The difference equation method (4) • Makes direct use of the fact that observations in a give plot should belong to the same site index curve • Difference equtions traditionally obtained through substituting one parameter, which is site-specific, by dynamic information • Substitution of the asymptote = anamorphic curves • Substitution of other parameters = polymorphic curves • Different approaches to obtain them ADA, GADA, equating… • Dynamic equations representing a continuos four variable prediction system directly interpreting three dimensional surfaces without explicit knowledge of the third dimension

14. The difference equation method (2) • A family of curves with a general mathematical form A = asymptotic parameter K= growth rate parameter m= shape parameter Where each individual height/Age curve has its own unique value of A (but we could also do it for k or m depending on which we assume is the site dependent parameter)

15. The difference equation method (3) - Example of obtaining the difference form, ADA approach

16. Final remarks • Difference equation methods: • Can compute predictions directly from any age-dominant height pair without compromising consistency of the predictions, which are unaffected by changes in the base age • - Better than guide curve method • Evaluating site index models: • -Biological realism (asymptote, growth pattern, quality of extrapolations out of the age and site range of the data) • - Fitting statistics (Mef, Mres, Amres, etc)

17. Exercise I 1. Derive a difference equation from the Hossfeld model assuming that parameter is b is the site dependent one

18. Exercise II • 1.Open the SPSS file Site_stems and fit a non-linear regression model using the difference form of the Hossfeld model. • Based on previous studies, initial values for a (between 10 and 10) and c (between 0,02 and 0,04). • The asymptote of the model is equal 1/c • 2.Fit now the McDill-Amateis equation (M= asymptote) • - How we decide which one is better? Which model is better?