A stacking ensemble algorithm for improving the biases of forest aboveground biomass estimations from multiple remotely sensed datasets

Figures & data

Figure 1. Framework of stacking ensemble procedures for estimating forest AGB.

Table 1. Selected base learners, meta learner, and original features for stacking under five scenarios

Forest type	Base learners (from 1^st – 5^th)	Selected original features	Meta learner
All	CatBoost, MARS, MLP, GBRT, SVR	TC-Mean, CH, Temp, Prec, TC-Std, NPP	Ridge, RF
EBF	CatBoost, MLP, MARS, GBRT, SVR	TC-Mean, Prec, DEM, Temp, NPP, CH	Ridge, RF
DBF	CatBoost, MARS, GBRT, MLP, SVR	TC-Mean, Prec, Temp, DEM, NPP, TempChg	Ridge, RF
WSA	CatBoost, MARS, SVR, GBRT, MLP	TC-Mean, Prec, Temp, DEM, NPP, TempChg	Ridge, RF
SAV	CatBoost, MARS, MLP, GBRT, SVR	TC-Mean, Prec, NPP, DEM, Temp, TempChg	Ridge, RF

EBF, evergreen broadleaf forest; DBF, deciduous broadleaf forest; WSA, woody savanna; and SAV, savanna.

Table 2. Model assessments in R², RMSE and bias

Model	Meta-features			Meta- and original features			Relative improvement (%)
	R^2	RMSE(Mg/ha)	Bias(Mg/ha)	R^2	RMSE(Mg/ha)	Bias(Mg/ha)	R^2	RMSE	Bias
CatBoost	0.70	47.19	0.12	−	−	−	−	−	−
GBRT	0.69	48.01	0.07	−	−	−	−	−	−
MLP	0.62	53.43	−0.56	−	−	−	−	−	−
MARS	0.53	59.39	0.27	−	−	−	−	−	−
SVR	0.59	55.17	3.09	−	−	−	−	−	−
CatBoost + MARS + MLP (Ridge)	0.70	47.22	0.06	0.70	47.21	0.06	−0.05	−0.05	49.80
CatBoost + MARS + MLP (RF)	0.68	48.84	0.09	0.70	47.07	0.08	0.22	0.26	35.17
MARS + MLP + SVR (Ridge)	0.64	51.90	0.05	0.64	51.87	0.04	3.54	2.87	91.50
MARS + MLP + SVR (RF)	0.61	53.57	−0.02	0.67	49.44	0.04	8.96	7.46	92.70
CatBoost + MARS + MLP + GBRT (Ridge)	0.70	46.95	0.09	0.70	46.95	0.09	0.42	0.50	22.95
CatBoost + MARS + MLP + GBRT (RF)	0.69	47.93	0.11	0.70	46.82	0.13	0.66	0.78	−6.48
CatBoost + MARS + MLP + GBRT + SVR (Ridge)	0.70	46.96	0.09	0.70	46.96	0.09	0.40	0.48	22.12
CatBoost + MARS + MLP + GBRT+ SVR (RF)	0.69	47.66	0.10	0.70	46.85	0.13	0.62	0.72	−10.46

Figure 2. Comparing the performance of stacking using ridge (Ridge) and stacking using RF, as well as original features (RFOri) with those obtained by the optimal base learner.

Figure 3. Performance of stacking in estimating AGB in terms of R², RMSE, and bias for EBF, DBF, WSA, and SAV.

Figure 4. Boxplots depicting the relative improvement in R², RMSE, and bias achieved by stacking for AGB estimation in EBF, DBF, WSA, and SAV.

Figure 5. Spatial distributions of Stacking AGB for the 2000s (a), and difference maps obtained by subtracting the CatBoost AGB (b) and Fusion AGB (c) from Stacking AGB. Masked pixels denote areas with less than 10% forest cover.

Figure 6. Boxplot showing the AGB estimated by CatBoost, Stacking and Fusion (a) and AGB difference obtained by subtracting the CatBoost AGB and Fusion AGB from Stacking AGB (b) for different forest types.