Investigation of parametric and artificial neural network modeling approaches for total tree height prediction in cedar plantations

doi:10.21203/rs.3.rs-96662/v2

Download PDF

Research

Investigation of parametric and artificial neural network modeling approaches for total tree height prediction in cedar plantations

https://doi.org/10.21203/rs.3.rs-96662/v2

This work is licensed under a CC BY 4.0 License

Version 2

posted

You are reading this latest preprint version

Background: Height-diameter relationships are of critical importance in tree and stand volume estimation. Stand description, site quality determination and proper forest management decisions originate from reliable stem height predictions.

Methods: In the context of this work, the prediction ability of the developed height-diameter models was investigated for cedar (Cedrus libani A. Rich.) plantations in Western Mediterranean Region of Turkey. Towards this direction, parametric modeling methods such as fixed-effects, generalized models, and mixed-effects were evaluated. Furthermore, in an effort to come up with the construction of more reliable stem-height prediction models, artificial neural networks were employed using two different modeling algorithms: the Levenberg-Marquardt and the resilient back-propagation.

Results: Taking into account the prediction behavior of each respective modelling strategy while using a new validation data set, the mixed-effects model with calibration using 3 trees for each plot seems to be a reliable alternative to the rest standard modelling approaches given the evaluation statistics regarding the predictions of tree heights.

Conclusion: Finally, as for providing the most reliable results as compared to the remaining, the resilient propagation algorithm showed its capability of providing more accurate predictions of the tree stem height and thus it can be a reliable alternative to pre-existing modelling methodologies.

Forestry

Height model prediction

mixed-effects models

Levenberg-Marquardt algorithm

resilient propagation

Table 1. Summary statistics for fitting and validation data sets.

Variable	Fitting data (70%)				Validation data (30%)
	Mean	Min.	Max.	S.D.	Mean	Min.	Max.	S.D.
	Cedar (630 trees in 21 plots)				Cedar (270 trees in 9 plots)
d (cm)	10.31	3.20	20.00	3.12	11.37	5.40	20.00	3.50
h (m)	6.12	3.00	11.75	1.42	6.66	3.20	11.00	1.81
Age (years)	26.00	17.00	35.00	6.30	31.00	23.00	35.00	4.70
D₀	13.96	9.72	18.30	2.38	14.86	7.82	19.24	3.49
H₀	7.51	5.44	10.02	1.21	8.30	5.66	10.65	1.67
G	30.30	12.75	50.70	10.86	36.96	12.01	58.25	15.02
d_m	10.29	6.68	13.53	2.02	11.35	6.74	14.64	2.51
h_m	6.10	4.31	7.93	1.03	6.66	4.50	8.65	1.37
D_g	10.57	6.98	13.92	2.08	11.60	6.77	14.92	2.59

d, diameter at breast height (1.3 m above ground level); h, total tree height; H₀, dominant height; D₀, dominant diameter; G, basal area; d_m, mean diameter; h_m, mean height; D_g, quadratic mean diameter.

Table 2. Fit statistics for equation (1) for different combinations of random parameters.

Random Parameters	AIC (smaller is better)	BIC (smaller is better)
Cedar
None (Fixed-effects)	2503	2522
β₁	1617	1624
β₂	1821	1828
β₃	1605	1612
β₁ and β₂	1540	1550
β₁ and β₃	1539	1548
β₂ andβ₃	1714	1724
β₁,β₂ and β₃	1656	1670

Table 3. Parameter estimates and standard errors in parentheses for the fixed- and mixed-effects regression models.

Parameter estimates	Generalized Model	Fixed-effects	Mixed-effects
Parameter estimates
β₁	-6.90872 (0.5670)	7.8237 (0.6187)	24.7062 (11.3829)
β₂	-0.02937 (0.0045)	0.1348 (0.0315)	0.01597 (0.01127)
β₃		1.5604 (0.2998)	0.8643 (0.07504)
		0.8311 (0.0468)	0.2216 (0.0129)
			73.9740 (113.22)
			0.04480 (0.0176)
			1.6671 (1.3800)

s², residual variance of the model; variance of the random-effect , variance of the random-effect , covariance of the random-effects and .

Table 4. Fit statistics results for the constructed basic h–d mixed-model, generalized h-d model and artificial neural network models (LMANN and RPANN), for a) the fitting, b) the validation data sets and c) the calibrated adjusted fixed and mixed models, using 1, 2, and 3 sampled trees for calibration.

Fitting data set (630 trees in 21 plots)
Model	Type	RMSE	FI	MD	MAD
LMANN Model: 3-2-1	ANN	0.5512	0.8241	-0.0174	0.4306
RPANN Model: 3-2-1	ANN	*0.5387*	0.8353	0.0074	*0.4155*
Chapman-Richards (Eq. 1)	Fixed	0.9116	0.5912	*-0.0019*	0.7088
Chapman-Richards (Eq. 14)	Mixed	0.6316	0.8059	0.1905	0.4684
Krumland and Wensel (1982) (Eq.13)	Generalized	0.5677	0.8422	-0.0429	0.4299
Validation data set (270 trees in 9 plots)
Model	Type	RMSE	FI	MD	MAD
LMANN Model: 3-2-1	ANN	0.6839	0.8000	-0.1138	0.5673
RPANN Model: 3-2-1	ANN	*0.6671*	0.8176	*-0.0995*	*0.5500*
Chapman-Richards (Eq. 1)	Fixed	1.1401	0.6017	0.2101	0.8943
Krumland and Wensel (1982) (Eq. 13)	Generalized	0.7210	0.7825	-0.2272	0.5985
Validation data (270 trees in 9 plots) after using localization
Chapman-Richards (Eq. 3)	Fixed-Calibrated (1)	0.8759	0.7649	0.3114	0.6417
Chapman-Richards (Eq. 3)	Fixed-Calibrated (2)	0.7427	0.8310	-0.1683	0.5937
Chapman-Richards (Eq. 3)	Fixed-Calibrated (3)	0.7348	0.8346	-0.1778	0.5809
Chapman-Richards (Eq. 14)	Mixed-Calibrated (1)	0.7573	0.8243	0.2129	0.5798
Chapman-Richards (Eq. 14)	Mixed-Calibrated (2)	0.6799	0.8585	-0.1335	0.5377
Chapman-Richards (Eq. 14)	Mixed-Calibrated (3)	*0.6773*	*0.8594*	-0.1523	*0.5242*

RMSE, root mean square error; FI, fit index; MD, mean difference; MAD, mean absolute difference; ANN, artificial neural network model. ^aA bold, italic number denotes the best method for cedar plantations.

Download PDF

Version 2

posted

You are reading this latest preprint version

Investigation of parametric and artificial neural network modeling approaches for total tree height prediction in cedar plantations

Status:

Version 2

Abstract

Figures

Full Text

Tables

Status:

Version 2