Predicting the vessel lumen area tree-ring parameter of  with linear and nonlinear machine learning algorithms

Jernej Jevšenak; Sašo Džeroski; Tom Levanič

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Predicting the vessel lumen area tree-ring parameter of Quercus robur with linear and nonlinear machine learning algorithms

| 05 nov. 2018

Édition 45 (2018): Edition 1 (January 2018)

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Article Category: Regular Articles

Publié en ligne: 05 nov. 2018

Pages: 211 - 222

Reçu: 26 janv. 2018

Accepté: 28 août 2018

DOI: https://doi.org/10.1515/geochr-2015-0097

Mots clés
dendroclimatology, artificial neural networks, multiple linear regression, machine learning, vessel lumen area,

© 2018 J. Jevšenak.

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

A) Locations of the research sites (circles) and the meteorological stations (triangles), B) location of Slovenia in Europe and climagraphs of C) Ljubljana and D) Maribor. The lines of climagraphs represent mean monthly temperature and the blocks represent monthly amounts of precipitation.

Individual sample lengths. The shaded area represents the analysed period used for model comparison for QURO-1 and QURO-2.

An example of a workflow of earlywood vessel analysis with ImageJ and macro EWVA: A) original image, B) image converted to a black and white mask for segmentation of the original image, vessels below the threshold were excluded from the analysis, C) recognised groups of earlywood vessels belonging to different years overlaid over the original image and D) measured earlywood vessels.

Chronologies of vessel lumen area (VLA) for QURO-1 and QURO-2 with 95% confidence interval of the mean.

Examples of the Model Tree (MT) for A) QURO-1 and B) QURO-2 sites.

Histograms of mean bias, calculated as the difference between observed and estimated mean responses for validation data.

Description of predictors of the VLA for QURO-1 and QURO-2.

	Predictor	Description
QURO-1	T_Jul_Sep	Average temperature from July to September, previous growing season
	T_MAR	Average March temperature, current growing season
	T_APR	Average April temperature, current growing season
	T_MAY	Average May temperature, current growing season
	T_JUN	Average June temperature, current growing season
	P_JAN-MAR	Sum of precipitation from January to March, current growing season
QURO-2	T_Jul-Nov	Average temperature from July to November, previous growing season
	T_JAN	Average January temperature, current growing season
	T_APR	Average April temperature, current growing season
	T_MAY	Average May temperature, current growing season
	T_JUN	Average June temperature, current growing season

Pearson correlation coefficients between vessel lumen area (VLA) and climate data: mean monthly temperatures (TEMP) and sum of monthly precipitation (PREC) for QURO-1 and QURO-2. Months with capital letters refer to the current growing season, while months with lowercase letters refer to the year of the previous growing season. Only correlation coefficients with p ≤ 0.01 are shown.

	Month	QURO-1		QURO-2
	Month	TEMP	PREC	TEMP	PREC
Previous growing season	Jul	0.45		0.53
	Aug	0.49		0.46
	Sep	0.37		0.38
	Oct			0.35
	Nov			0.37
	Dec
	Jul–Sep	0.57
	Jul–Nov			0.71
Current growing season	JAN		–0.41	0.44
	FEB
	MAR	0.38	–0.33
	APR	0.60		0.63
	MAY	0.32		0.47
	JUN	0.47		0.50
	JAN–MAR		–0.43

General description of the analysed sites.

Location / Site denotation	Year of sampling	Latitude	Longitude	Elevation (m)	Bedrock	Forest soil type	Meteorological station	Average age of measured tree
Mlace/ QURO-1	2012	N46°18′21′′	E15°30′35′′	280–315	Marl	Eutric brown soil	Maribor	150
Sorsko Plain / QURO-2	2015	N46°11′23′′	E14°25′26′′	360–365	Alluvial loams and clays	Dystric brown soil	Ljubljana	90

Characteristics of site chronologies: number of samples (N), chronology span, mean and standard deviation (Std) of vessel areas, minimum and maximum range of vessel areas (Min – Max), rbar (r̄) and autocorrelation with lag 1, 2 and 3 (AC).

			Mean ± Std	Min – Max
Site	N	Chronology span	(μm² 10⁴)	(μm² 10⁴)	r̄	AC_1	AC_2	AC_3
QURO-1	6	2012–1961	6.259 ± 0.603	5.133–7.743	0.44	0.42	0.40	0.31
QURO-2	8	2015–1961	4.691 ± 0.395	4.072–5.756	0.32	0.61	0.52	0.46

Comparison of the performance of five predictive modelling methods for A) QURO.1 and B) QURO.2 sites. Methods were evaluated by 3-fold cross-validation repeated 100 times. The five predictive modelling methods were Multiple Linear Regression (MLR), Artificial Neural Networks (ANN), Model Trees (MT), Bagging of Model Trees (BMT) and Random Forests of Regression Trees (RF). The performance measures were the correlation coefficient (r), root relative squared error (RRSE), root mean squared error (RMSE), index of agreement (d), reduction of error (RE), coefficient of efficiency (CE) and detrended efficiency (DE), calculated on the training (train) and testing (test) data of cross-validation splits. Across the 100 runs of cross-validation, we present the mean, standard deviations (Std), mean rank and share of rank 1 for each performance measure. The best values of each performance measure on the test set are highlighted in bold.

	MLR		ANN		MT		BMT
	mean	std	mean	std	mean	std	mean	std	mean	std
(A) QURO-1
rtrain	0.797	0.037	0.815	0.043	0.789	0.059	0.810	0.030	0.898	0.018
rtest	0.694	0.103	0.726	0.095	0.633	0.134	0.692	0.112	0.689	0.097
RMSE_train	0.356	0.027	0.343	0.042	0.359	0.047	0.360	0.025	0.302	0.022
RMSE_test	0.453	0.063	0.428	0.066	0.488	0.079	0.447	0.065	0.453	0.066
RRSE_train	0.601	0.048	0.580	0.077	0.606	0.080	0.608	0.041	0.510	0.035
RRSE_test	0.786	0.134	0.741	0.123	0.845	0.148	0.771	0.106	0.778	0.083
d_train	0.877	0.026	0.878	0.059	0.871	0.042	0.851	0.030	0.898	0.019
d_test	0.794	0.066	0.808	0.073	0.753	0.081	0.757	0.067	0.723	0.069
RE_test	0.405	0.227	0.473	0.184	0.312	0.257	0.435	0.158	0.429	0.110
CE_test	0.364	0.237	0.436	0.202	0.265	0.273	0.394	0.174	0.387	0.132
DE_test	0.317	0.249	0.394	0.215	0.210	0.289	0.348	0.188	0.339	0.155
	rank	rank1	rank	rank1	rank	rank1	rank	rank1	rank	rank1
r_train	3.92	0.00	2.67	0.02	4.16	0.03	2.95	0.00	1.05	0.95
r_test	2.91	0.11	1.85	0.50	3.93	0.06	2.93	0.15	3.12	0.20
RMSE_train	3.45	0.00	2.33	0.05	3.93	0.07	3.90	0.00	1.13	0.88
RMSE_test	2.95	0.14	1.89	0.49	3.86	0.06	2.82	0.12	3.22	0.21
RRSE_train	3.45	0.00	2.33	0.05	3.93	0.07	3.90	0.00	1.13	0.88
RRSE_test	2.95	0.14	1.89	0.49	3.86	0.06	2.82	0.12	3.22	0.21
d_train	2.64	0.07	2.52	0.13	3.39	0.13	4.71	0.00	1.49	0.68
d_test	2.18	0.24	1.50	0.65	3.32	0.09	3.45	0.02	4.29	0.03
RE_test	2.96	0.14	1.89	0.49	3.86	0.06	2.82	0.12	3.22	0.21
CE_test	2.96	0.14	1.89	0.49	3.86	0.06	2.82	0.12	3.22	0.21
DE_test	2.95	0.14	1.89	0.49	3.86	0.06	2.82	0.12	3.22	0.21
Overall_train	3.37	0.02	2.46	0.06	3.85	0.08	3.86	0.00	1.20	0.85
Overall_test	2.75	0.16	1.79	0.53	3.74	0.07	3.00	0.11	3.46	0.16
(B) QURO-2
r_train	0.796	0.044	0.843	0.035	0.800	0.039	0.839	0.028	0.907	0.020
r_test	0.717	0.093	0.781	0.084	0.687	0.104	0.740	0.087	0.747	0.094
RMSE_train	0.232	0.019	0.209	0.027	0.232	0.019	0.216	0.015	0.180	0.013
RMSE_test	0.293	0.041	0.257	0.042	0.297	0.040	0.278	0.040	0.274	0.043
RRSE_train	0.601	0.058	0.541	0.080	0.602	0.052	0.560	0.044	0.465	0.044
RRSE^_test	0.792	0.164	0.694	0.150	0.801	0.147	0.745	0.126	0.733	0.107
d_train	0.874	0.032	0.899	0.059	0.866	0.030	0.883	0.024	0.921	0.018
d_test	0.793	0.057	0.839	0.077	0.765	0.068	0.789	0.052	0.782	0.058
RE_test	0.410	0.253	0.546	0.202	0.401	0.234	0.483	0.189	0.503	0.142
CE_test	0.346	0.299	0.496	0.248	0.337	0.283	0.428	0.230	0.451	0.179
DE_test	0.297	0.356	0.457	0.295	0.286	0.359	0.384	0.300	0.409	0.236
	rank	rank1	rank	rank1	rank	rank1	rank	rank1	rank	rank1
r_train	4.54	0.00	2.44	0.00	4.30	0.00	2.72	0.00	1.00	1.00
r_test	3.61	0.06	1.70	0.61	4.21	0.04	2.82	0.07	2.65	0.22
RMSE_train	4.42	0.00	2.22	0.01	4.26	0.00	3.08	0.00	1.01	0.99
RMSE_test	3.70	0.03	1.75	0.64	4.05	0.03	2.78	0.11	2.72	0.20
RRSE_train	4.42	0.00	2.22	0.01	4.26	0.00	3.08	0.00	1.01	0.99
RRSE_test	3.70	0.03	1.75	0.64	4.05	0.03	2.78	0.11	2.72	0.20
d_train	4.05	0.00	1.99	0.11	4.34	0.00	3.49	0.00	1.13	0.89
d_test	3.09	0.03	1.30	0.85	4.02	0.03	3.15	0.04	3.44	0.05
RE_test	3.70	0.03	1.75	0.64	4.05	0.03	2.78	0.11	2.72	0.20
CE_test	3.70	0.03	1.75	0.64	4.05	0.03	2.78	0.11	2.72	0.20
DE_test	3.70	0.03	1.75	0.64	4.05	0.03	2.78	0.11	2.72	0.20
Overall_train	4.36	0.00	2.22	0.03	4.29	0.00	3.09	0.00	1.04	0.97
Overall_test	3.53	0.04	1.62	0.68	4.08	0.03	2.88	0.08	2.88	0.17

Multiple linear regression summary statistics for QURO-1 and QURO-2.

	Variable	Coefficients	t value	p value
QURO-1	Intercept	0.496164	0.418	0.67767
	T_Jul–Sep	0.165491	2.617	0.01196
	T_MAR	0.042491	1.437	0.15744
	T_APR	0.159552	3.474	0.00113
	T_JUN	0.064903	1.422	0.16164
	P_JAN–MAR	–0.00598	–2.294	0.02639
	R²	Adj R²
	0.6304	0.5903
QURO-2	Intercept	1.08324	1.792	0.07914
	T_Jul–Nov	0.12812	2.570	0.01319
	T_JAN	0.03792	2.501	0.01569
	T_APR	0.08273	2.879	0.00586
	T_ JUN	0.04669	1.800	0.07782
	R²	Adj R²
	0.6241	0.5941

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Predicting the vessel lumen area tree-ring parameter of Quercus robur with linear and nonlinear machine learning algorithms

Article Category: Regular Articles

Publié en ligne: 05 nov. 2018

Pages: 211 - 222

Reçu: 26 janv. 2018

Accepté: 28 août 2018

DOI: https://doi.org/10.1515/geochr-2015-0097

Mots clés
dendroclimatology, artificial neural networks, multiple linear regression, machine learning, vessel lumen area,

© 2018 J. Jevšenak.

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Description of predictors of the VLA for QURO-1 and QURO-2.

General description of the analysed sites.

Characteristics of site chronologies: number of samples (N), chronology span, mean and standard deviation (Std) of vessel areas, minimum and maximum range of vessel areas (Min – Max), rbar (r̄) and autocorrelation with lag 1, 2 and 3 (AC).

Multiple linear regression summary statistics for QURO-1 and QURO-2.

Predicting the vessel lumen area tree-ring parameter of Quercus robur with linear and nonlinear machine learning algorithms

Article Category: Regular Articles

Publié en ligne: 05 nov. 2018

Pages: 211 - 222

Reçu: 26 janv. 2018

Accepté: 28 août 2018

DOI: https://doi.org/10.1515/geochr-2015-0097

Mots clésdendroclimatology, artificial neural networks, multiple linear regression, machine learning, vessel lumen area,

© 2018 J. Jevšenak.

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Description of predictors of the VLA for QURO-1 and QURO-2.

General description of the analysed sites.

Characteristics of site chronologies: number of samples (N), chronology span, mean and standard deviation (Std) of vessel areas, minimum and maximum range of vessel areas (Min – Max), rbar (r̄) and autocorrelation with lag 1, 2 and 3 (AC).

Multiple linear regression summary statistics for QURO-1 and QURO-2.

Mots clés
dendroclimatology, artificial neural networks, multiple linear regression, machine learning, vessel lumen area,