Data Assimilation of Growing Stock Volume Using a Sequence of Remote Sensing Data from Different Sensors

Figures & data

Figure 1. Map of the study area in south-western Sweden. The Remningstorp forest estate covers 1,500 hectares of managed forest. A regular grid with 10 m radius sample plots was distributed over the property. The sample plots were measured in 2010 and re-measured in 2014.

Table 1. Mean and standard deviation per species category for the sample plots used in the study, measured in 2010 and 2014.

Species class	n	Age [years] 2010	Volume [m³/ha] measured 2010	SI [m]	Growth [m³/ha]	Volume [m³/ha] measured 2014
			(Mean/standard deviation)
Pine (Scots Pine)	29	85/33.6	212.8/72.2	22.8/4.5	6.5/6.9	238.8/80.3
Spruce (Picea Abies)	76	43/13.9	245.7/153.9	29.6/2.2	17.2/8.8	314.7/174.1
Deciduous^a	26	42.8/24.6	93.9/56.3	29.4/3.1	7.2/5.6	122.8/59
Mixed coniferous^b	6	96.4/44.0	251/45.8	24.0/5.7	11/10.4	295/48.5
Mixed^c	11	55.9/39.3	122.4/80.2	27.4/4.4	5.8/3.8	145.5/79
All plots	148	54.2/30.5	203.7/133.3	27.9/4.2	12.3/9.3	252.7/154

“All plots” refers to the entire set of 148 plots. Site Index (SI) and age were taken from field measurements in 2010. Growth is the difference between growing stock volume measured in 2014 and 2010, respectively, divided by the number of growing seasons (four).

^aThe deciduous class consists of over 65% of the total basal area with deciduous trees, mostly of Birch (Betula SPP), followed by Oak (Quercus Robur).

^bMixed coniferous is a mixture of Pine and Spruce summing to at least 65% of the total basal area.

^cMixed is a mixture of deciduous and coniferous trees where neither category has more than 65% of the total basal area.

Table 2. Remote sensing data was used in the study.

Acquisition No. and data type	Acquisition date	Season	Pixel size or point density
1 ALS	2010-08-29	Leaf-on	14.5 points/m²
2 OS	2011-06-06	Leaf-on	10 m
3 InSAR	2012-02-23	Leaf-off	5 m
4 DP	2012-05-23	Leaf-on	7.4 points/m²
5 InSAR	2012-08-28	Leaf-on	5 m
6 OS	2013-07-17	Leaf-on	10 m
7 InSAR	2013-11-18	Leaf-off	5 m
8 DP	2014-07-26	Leaf-on	11.2 points/m²
9 ALS	2014-09-14	Leaf-on	29.6 points/m²

Season refers to if deciduous trees had dropped their leaves or not.

Table 3. An overview of the DA methods and prediction methods used in this study, and the cases evaluated when the prediction types and DA methods were combined.

	Calibrated	Non-calibrated
EKF	Case 1	Case 2
EKFm	Case 3	Case 4
Forecast from 1 ALS	Case 5	Case 6
Single predictions	Case 7	Case 8

Figure 2. rRMSE, using DA with EKF or EKFm, forecast from first time point (ALS), and ALS for the last time point, for calibrated and non-calibrated predictions. Growth periods are marked with dotted vertical lines.

Figure 3. rBias using DA with EKF or EKFm, forecast from first time point (ALS), and ALS for the last time point, for calibrated and non-calibrated predictions. Growth periods are marked with dotted vertical lines.

Table 4. Accuracy for single predictions of growing stock volume, individually assessed by empirical evaluation against the field references.

Acquisition	RMSE (m³/ha)		rRMSE (%)		Bias (m³/ha)		rBias (%)
	Calibrated	Non-calibrated	Calibrated	Non-calibrated	Calibrated	Non-calibrated	Calibrated	Non-calibrated
1 ALS	71	63	34.9	30.8	0	0.06	0	0.03
2 OS	153	100	75.0	49.2	0	0.14	0	0.07
3 InSAR	101	82	46.6	37.9	0	−2.09	0	−0.97
4 DP	89	75	41.4	34.7	0	0.85	0	0.39
5 InSAR	154	105	67.3	45.9	0	−0.35	0	−0.15
6 OS	172	112	71.7	46.7	0	−0.03	0	−0.01
7 InSAR	147	104	61.0	43.3	0	0.46	0	0.19
8 DP	101	84	39.9	33.4	0	0.06	0	0.02
9 ALS	70	63	27.6	25.1	0	−0.11	0	−0.04

The evaluations were made at the time points of the individual acquisitions, with and without classical calibration.

Figure 4. Boxplots of residuals for three categories of true volumes on the x-axis. Each group contains roughly the same number of observations.

Figure 5. Correlation coefficients of residuals from predictions of growing stock volume using different sources of RS data. The left plot shows residuals after calibration while the right plot shows correlations of residuals for non-calibrated predictions.

Figure 6. Comparison of empirically evaluated rRMSEs (Equation 11[11] $$\mathit{rRMSE}=\frac{\mathit{RMSE}}{\overline{y}}\mathrm{\hspace{0.17em}}\mathrm{*}\mathrm{\hspace{0.17em}}100$$[11] ) and model-based rRMSEs (Equation 15[15] $$\mathit{rSD}=\frac{SD}{\overline{y}}\mathrm{\hspace{0.17em}}\mathrm{*}\mathrm{\hspace{0.17em}}100$$[15] ) from the filters. Growth periods are marked with dotted vertical lines.

Table A.1. Details about the ALS data.

Acquisition number	Acquisition date	Scanner	Flying altitude (m)	Point density (points/m²)
1 ALS	2010-08-29	TopEye s/N 700	400	14.5
9 ALS	2014-09-14	Riegl LMS Q680i	300	29.6

Table A.2. Details about the DP data.

Acquisition number	Acquisition date	Camera	Flying altitude (m)	Ground sampling distance (m)
4 DP	2012-05-23	Zeis/Integraph DMC	4,800	0.48
8 DP	2014-07-26	Vexcel UltraCamX	2,800	0.24

Table A.3. Details about the TanDEM-X InSAR data.

Acquisition number	Acquisition date	Orbit	Polarization	HOA
3 InSAR	2012-03-23	146	VV	79
5 InSAR	2012-08-28	146	VV	37
7 InSAR	2013-11-18	78	HH	72

Table A.4. Details about the OS data.

Acquisition number	Acquisition date	Satellite and sensor	Path/row	Ground sampling distance (m)
2 OS	2013-07-17	SPOT 5 HRG	053/231	10–20
6 OS	2011-06-06	SPOT 5 HRG	053/231	10–20

Estimated predictive modelsTable A.5. Coefficients and included variables for the estimated models predicting forest growing stock volume.

Acquisition number	Acquisition date	Variable	Coefficient	SE
1 ALS	2010-08-29	Intercept	2.4	7.29
		MeanH^2	1.5	0.199
		VR*P95	0.07	0.016
2 OS	2011-06-06	Intercept	520	83.4
		B4^2	1,400,000	239,000
		NDVI	−520	79.2
		B1/B4	−450	89.8
3 InSAR	2012-02-23	Intercept	46	8.94
		ISH^2	0.89	0.0566
4 DP	2012-05-23	Intercept	77	9.14
		CUBEmean^3	0.032	0.00323
		P95/CV	0.24	0.112
5 InSAR	2012-08-28	Intercept	33	17.3
		(ISH + 10)^2	0.35	0.0319
6 OS	2013-07-17	Intercept	790	126
		B4^2	4,800,000	723,000
		NDVI	−630	104
		B1/B4	−1,100	199
7 InSAR	2013-11-18	Intercept	350	69.2
		(ISH + 5)^2	0.6	0.074
		COH	−350	84.7
8 DP	2014-07-26	Intercept	70	10.5
		CUBEmean^3	0.034	0.00242
		VR/CV	0.035	0.0132
9 ALS	2014-09-14	Intercept	30	6.09
		MeanH^2	1.4	0.215
		VR*P95^2	4.1e-05	9.1e-06

Point cloud metrics abbreviated by: MeanH: mean of points heights above ground; VR: vegetation ratio; P95: height percentile 95; CUBEmean: cube-root of the mean of heights to the cube; CV: coefficient of variation.