My Thesis Defence At Copenhagen University

Site Index and Height Growth Models for Japanese Larch & miscellaneous Larch Species in Denmark July, 2009

By:

Bidya Nath Jha SUFONAMA M.Sc. Student (EMN 08001) Thesis Supervisor

Dr. Thomas Nord-Larsen Senior Research Scientist Faculty of Life Sciences, University of Copenhagen

1. Research Context: Problem & Justifications 1.1 Larch: An Introduction & Importance. • Adaptation • Growth, Environment and Economy • Demand and Deficit 1.2 Site Index Model for Larch sp. does not exist in Denmark • Andersen, 1950.........Site B Japanese Larch • Schober, 1975.............German Yield Table 1.3 Existing yield table Ht. growth relation have methodological limitation: • Graphical interpretation • Statistical objectivity, flexibility or measure: No

2. Research Objectives 2.1. To develop dynamic site index models for Japanese larch and miscellaneous larch species in Denmark 2.2. To compare the predictive performance of the developed models with conventional height growth models for Japanese larch and miscellaneous larch species

Conceptual Research Framework for site index modelling Theoretical Background

Practical Process for Model development

Interaction abiotic factors (soil, climate) with biotic factors (biota)

Dominant Height as an indicator of site productivity

Variability of forest sites in their productive capacity

Establishment of Age Height Relationship for a given species and site from periodic growth data

forest growth = f (site factors, time)

Global and local parameter Estimation for given function to establish such relationship

Volume growth is the best indicator of productivity, but is impacted by management input.

Testing the predictive strength of given relationship (model)

Height growth is least impacted by management inputs

Model application and continuous monitoring and evaluation

3. Data for Modelling •Data Collection Summary of data used for site index and height growth Species

No. of

modelling. No. of Mean

Mean no.

Period of

Experimen

Plots

Plot

of

records

Area

Measurem (Years)

(ha)

ent per

0.1528

plot 9

ts

Jap. larch

19

25

19182008

Misc .larch

23

33

0.1505

11

19182008

4. Methods 4.1. Data Preparation • Regression

for the Height (Naslund, 1936; Johannsen,

2002) • Dominant Height Calculation (H100) Definition= 100 thickest trees/ha e.g. plot area =0.2 ha; then 0.2*100 = 20 thickest trees • Age

from records

4. Methods Approach and Equations 4.1. Algebraic Difference Approach-ADA (Bailey & Clutter,1974) • 1) Identification of suitable model:

• 2) Choose and solve for a site parameter:

• 3) Substitute the solution for the parameter:

4.2. Generalized Algebraic Difference Approach-GADA (Cieszewski and Bailey, 2000)

• 1) Identification of suitable longitudinal model • 2) Definition of model cross-sectional changes • 3) Finding solution for the unobservable variable • 4) Formulation of the implicitly defined equation

4.3. Selected Mathematical Functions: Model I

Model IV

Model II

Model V

Model III Model IV.1

4. Methods Model Development and Testing 4.4. PROC MODEL SAS 9.3.1. • Indicator Variable Method for Simultaneous estimation of site indexes and model parameter; • PROC MODEL 4.5. Model Evaluation • Performance Criteria • Residual Diagnostics • Linear Regression of Observed vs. Predicted Values • Leave-one-out Cross Evaluation

Criteria

Formula

Ideal

1. SSE

0

2. MSE

0

3. RMSE

0

4. R-Square

1

5. VR

1

6. MRes

0

7. |MRes|

0

8. RRes

0

9. IRRes

0

5. Results & Discussion

Model (Equation)

Estimates of Site Index (S), height in meter at age 50 years Mean Maximum Minimum Standard Deviation

Model I

23.5160

27.1972

17.4593

2.5565

Model II

23.8160

26.5424

19.5444

1.9471

Model III

23.9858

26.4363

19.6324

1.6215

Model IV

23.5716

26.7320

18.5599

2.2114

Model IV.1

23.5791

26.7266

18.6240

2.1934

Model V

23.5057

26.9726

17.8843

2.3907

Estimated parameter and related statistics for Japanese larch models Model and Parameters Estimates Standard Error t P value statistics Model I β 0.04957 0.00261 18.98 <0.001 γ 0.40916 0.0309 13.24 <0.001 Model II α 29.84222 0.4247 70.27 <0.001 γ 1.517837 0.0693 21.92 <0.001 Model III α 31.27321 0.6465 48.37 <0.001 β 0.036247 0.00243 14.89 <0.001 Model IV γ 15.9346 7.8048 2.04 0.0424 α 1.678773 0.0600 27.96 <0.001 β 7379.672 3762.1 1.96 0.0511 Model IV.1 (fixed a4) γ 17.44244 1.49 11.69 <0.001 α 1.674153 .0533 31.38 <0.001 Model V γ 4 3.99E85 1E85 <0.001 β 0.049175 0.00258 19.08 <0.001 α 5.462307 0.2645 20.65 <0.001

Model IV.1

Performance criteria of the applied models for Japanese Performanc Model I II

larch III

IV

IV.1

V

236.2

165.6

165.6

170.8

e Criteria SSE

175.6

177.4

MSE

0.7837 0.7922 1.0534

.7457

0.7425

0.7693

RMSE

0.8853 0.8900 1.0268

.8636

0.8617

0.8771

R-Square

0.9788 0.9786 0.9715

.9799

0.9799

0.9793

Adj. R-

0.9769 0.9767 0.9690

.9780

0.9781

0.9773

0.9756 0.9756 0.9656

.9796

0.9757

0.9767

Square Variance Ratio MRes

-0.002 5

-.0040 -0.0079 -0.0011 -0.0014

-0.002 4

Linear Regression of Observed vs. Predicted Values • Slope & intercept values very close to 1 and zero respectively • Simultaneous F tests reject the hypothesis • R-square above 97%

OLS Assumptions 1. Independence of Residuals First order autoregressive Model Structure was used; error term was expanded as

2. Normality of Residuals • • •

Statistical and graphical interpretation of model residuals Kolmogorov-Smirnov, Anderson-Darling and Shapiro-Wilk tests Visual Interpretation

3. Homoscedasticity ( Constant Variances) • • •

Statistical and graphical interpretation of model residuals White Tests Visual Interpretation

Miscellaneous Larch Model:

6. Comparisons of models Model IV (solid lines) and model IV.1 (dashed lines) for Jap. larch

Japanese Larch (blue-dotted) and Miscellaneous Larch (black-smooth)

Model IV.1 and Danish yield table age-ht. relation for Jap. larch (Andersen, 1950)

Model IV.1 and German yield table age-ht. relation for Jap. larch (Schober, 1975)

Model IV.1 and other models for Jap. larch from different countries and contents

•

7. Conclusions Dynamic site index and height growth models are

developed for Jap. larch and misc. larch species in Denmark. • They found to be predicting dominant height without any apparent bias. • Cieszewski models performed better than selected Chapman Richards function. • Traditional Japanese larch models were found to be predicting slightly higher than the developed models. Comparison of miscellaneous larch models with other species specific models produce contradicting results. • Japanese larch models can be applied in Danish and/or adjacent countries, for miscellaneous larch models external validation before wide applications will be a good recommendation.