# Forest Canopy Height Estimation Using Multiplatform Remote Sensing Dataset

Authors: Won-Jin Lee; Chang-Wook Lee
Journal: Journal of Sensors
 (2018)

---

## Abstract

Recently, numerous studies have attempted to determine forest height using remote sensing techniques that not only have the benefits of fast data acquisition, processing, and analysis but are also cost-effective. However, if there was insufficient data to apply the latest remote sensing techniques, we need to consider many kinds of datasets as possible. In this study, we tried to determine forest height using discrete-return LiDAR data, SRTM, satellite L-band SAR data, and Optical data. We experimented with the differences between LiDAR DSM and DTM, as well as SRTM DSM and LiDAR DTM. In addition, we applied an SBAS algorithm and linear regression to the dataset. From the quantitative evaluation, the RMSE andR2 of the LiDAR-derived forest height (3.22 m and 0.43, resp.) and the SRTM-derived forest height (2.90 m and 0.50, resp.) were both reasonably good, especially when we consider data acquisition time differences and measurement errors in mountainous areas. Moreover, we slightly improved the RMSE and R2 from 2.90 m and 0.50, respectively, to 2.75 m and 0.54, respectively, by correcting the SRTM using the SBAS algorithm. Furthermore, we merged the datasets using linear regression and obtained improved forest heights with RMSE and R2 values of 2.68 m and 0.56, respectively. To generate a forest height map, we used NDVI from Optical imagery and masked heights below 2 m from each sensor. Thus, we excluded urban areas, “bare earth surfaces,” and mountain streams from each sensor’s imagery. Finally, we generated a forest height map by overlapping the datasets. The results of this study indicate that each sensor has the potential for not only determining forest height but also extracting complementary forest area information. Furthermore, this study demonstrates the potential for improvement using the SBAS algorithm and linear regression.


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## Body

## 1. Introduction

Recently, remote sensing techniques have received a lot of attention for extracting forest information. Remote sensing techniques are efficient methods for extracting forest information not only due to fast data acquisition, processing, and analysis but also because they are cost-effective. Of the forest information which can be acquired using remote sensing data, forest height plays an important role for estimation of forest volume and aboveground biomass [1]. For these reasons, numerous studies have attempted to estimate forest height using remote sensing data such as LiDAR (Light Detection and Ranging), Optical images, and SAR (Synthetic Aperture Radar).Each sensor has different wavelength band for data acquisition. For example, Optical images operate with a passive sensor that uses the visible spectrum, while on the other hand, LiDAR and SAR operate active sensors using near-infrared and microwave bands, respectively. In this sense, merging the various remote sensing data has the potential to provide reliable results for forest height extraction.LiDAR is one of the most powerful methods for estimating forest height; therefore, many studies have attempted to merge LiDAR with Optical imagery. Shendryk et al. [2] combined LiDAR data and multispectral image (SPOT-5) to estimate forest canopy height using linear regression. Erdody and Moskal [3] merged airborne LiDAR and high-resolution color near-infrared imagery to estimate canopy fuel metrics in a ponderosa pine. In addition to the fusion of LiDAR and Optical images, the merging of SAR and Optical imagery has been studied [4–8].It is worth mentioning that there are several drawbacks to each sensor. Though it has been successfully used for canopy height mapping, LiDAR data are difficult to update regularly because of the high cost [9]. Additionally, there have been studies concerned specifically with full-waveform LiDAR [10], but this data is generally not commercially available. In the case of Optical data, it has the benefit of extracting horizontal area rather than vertical structure. Meanwhile, most studies which use SAR data focus on polarimetric interferometry ([11], Damawan et al., 2014) or with using the difference in wavelengths sensitivity, such as the difference between the X-band and P-band, to calculate elevation [7]. However, it is difficult to acquire polarization and differing wavelength data, except from an airborne SAR system.In this paper, we used available data, such as discrete-return LiDAR data, SRTM (Shuttle Radar Topography Mission), satellite L-band SAR data, and Optical data, instead of the latest data, such as full-waveform LiDAR and X- and P-band SAR data, which have been shown in previous studies to be well-suited for forest height calculation. LiDAR DTM (Digital Terrain Model) provided us with consistent terrain for a base map, and SRTM, which was constructed from short 6 cm wavelength, provided reflections from the surface of the forest. Abundant SAR satellite data allowed us to update the SRTM using the SBAS (Small Baseline Subset) algorithm [12] for the terrain error. Generally, Optical images has been primarily used for land cover classification, especially, NDVI (Normalized Difference Vegetation Index) which has been validated as an effective measure for identifying pixels characterized as vegetation. In summary, the determination of forest height proceeded as follows: (1) we used a variety of remote sensing data, not only air-flight data but also SAR satellite data to overcome data insufficiencies in the absence of available state-of-the-art data. (2) By applying the SBAS algorithm to the SAR images to reduce the topography error and then estimate the forest height, we extended the application of SAR satellite images based on the SBAS algorithm.This paper is organized as follows. First, we describe the collection of the field data and provide details of the remote sensing data acquisition (LiDAR, SAR, and Optical image). We then present the methods used in the processing, and finally, we discuss the results.


## 2. Study Area and Data

### 2.1. Study Area

The study area for this investigation was an approximately 20 km2 area within the Jangsan Mountain in Busan, Korea (Figure 1). The altitude of the mountain is 634 m and the shape of the mountain is entirely conical. This area is primarily composed of pine forest with reed grass at the top of the hill. Pine trees are easy to identify top of the tree because of its shape. Therefore, measuring pine tree height is easier than broad-leaved trees (Figure 2). Also, in the area, we could collect remote-sensed data such as SAR, LiDAR, and Optical data. An in situ forest height survey was conducted throughout the entire area during September and October 2012 using laser height measurements except for artificial construction (Table 1). We determined forest height by averaging laser height measurements taken three times in opposing directions. Also, tree species composition has a major effect on forest height measurements. Therefore, we measured 90 points of in situ tree heights to only pine trees to compare with remote-sensed datasets (Table 2).Figure 1
Study area and in situ locations indicated with red rectangles.Figure 2
Field photograph.Table 1
Laser measurement specification and geometry.
Specification
Value
Picture
Geometry of tree height measurement using laser
Distance accuracy
±30 cm
Max range to nonreflective targets
1000 m
Scope magnification
7xTable 2
In situ tree height measurements.
Number
Latitude (°)
Longitude (°)
Height (m)
Number
Latitude (°)
Longitude (°)
Height (m)
1
35.19082
129.1346
18.7
46
35.20826
129.1576
8.7
2
35.18935
129.1364
13
47
35.21124
129.16
10
3
35.1886
129.1405
11.9
48
35.21258
129.1615
10.2
4
35.18965
129.1414
12
49
35.21457
129.1645
9.3
5
35.19272
129.1444
2.2
50
35.21483
129.1649
10.1
6
35.19465
129.1447
4
51
35.20795
129.1579
3.3
7
35.1951
129.1451
9
52
35.20684
129.1607
3.6
8
35.19618
129.1471
6.6
53
35.20505
129.1642
10.5
9
35.19377
129.146
5.3
54
35.20261
129.1664
10
10
35.19627
129.1486
7.5
55
35.19725
129.1693
9.2
11
35.19613
129.1503
13
56
35.19587
129.1678
7.6
12
35.1921
129.1459
3.9
57
35.19429
129.1659
11
13
35.1913
129.1465
8.4
58
35.19275
129.1657
12.6
14
35.18977
129.148
10.3
59
35.18768
129.1629
13.8
15
35.1866
129.1503
8.9
60
35.21848
129.1575
12.67
16
35.18612
129.1535
12.2
61
35.21796
129.1588
14.83
17
35.18902
129.1584
9.4
62
35.21764
129.1611
13.38
18
35.18975
129.1604
13.4
63
35.21686
129.1649
12.13
19
35.1878
129.1612
14.4
64
35.21459
129.1707
12.33
20
35.18212
129.1669
14.4
65
35.21509
129.171
9.05
21
35.18043
129.1409
4.4
66
35.21716
129.1661
10.18
22
35.18015
129.1398
5
67
35.21669
129.1631
11.45
23
35.17964
129.1391
12.5
68
35.21707
129.1614
13.4
24
35.18095
129.1379
11
69
35.21963
129.1563
16.27
25
35.18169
129.1371
13
70
35.21953
129.1546
7.47
26
35.18513
129.1355
12
71
35.20605
129.1303
18.5
27
35.18654
129.1348
7.5
72
35.20568
129.132
15.45
28
35.18705
129.1342
13.5
73
35.20563
129.1329
14.183
29
35.18925
129.1346
12.5
74
35.20554
129.136
13.73
30
35.18907
129.1374
12.2
75
35.20508
129.1412
17.33
31
35.18844
129.1394
9.3
76
35.207
129.1443
11.73
32
35.18786
129.1407
7.7
77
35.20898
129.1461
10.57
33
35.18757
129.1414
7.2
78
35.21604
129.1512
12.7
34
35.19229
129.1455
2.5
79
35.21665
129.1539
17.53
35
35.19237
129.1458
3.2
80
35.21749
129.1559
13.58
36
35.18916
129.1458
3.5
81
35.20037
129.1418
6.55
37
35.1901
129.1561
12
82
35.2034
129.1416
13
38
35.18882
129.1616
16.5
83
35.20438
129.1418
12.92
39
35.19211
129.1586
7.8
84
35.20487
129.143
11.92
40
35.19514
129.1597
10.8
85
35.20452
129.145
8.1
41
35.1988
129.1615
11
86
35.20318
129.1465
7.98
42
35.20238
129.157
9
87
35.20212
129.1488
9.73
43
35.20337
129.1565
8.3
88
35.20053
129.1462
10.27
44
35.20377
129.1555
9.9
89
35.19975
129.1443
10.27
45
35.20377
129.1555
8
90
35.1983
129.1392
16.08


### 2.2. Remote-Sensed Data

We obtained SAR images from ALOS PALSAR over the study area for the period between 2007 and 2010 (Table3). We produced 30 interferograms and used SRTM data not only to correct the topographic phase contribution but to also to estimate forest height as a DSM (Digital Surface Model). The LiDAR data were acquired in February 2007 with an LEICA ALS50 sensor, and aerial photography was acquired to generate NDVI data over the study area in April 2012. A variety of remote sensors has different resolution. In our study, we used a 5 m resolution LiDAR elevation model, 2.5 m aerial photography, 30 m SRTM DEM and 30 m SAR images using multi-look. Therefore, we conducted down- and upsampling for 5 m resolution after image processing.Table 3
SAR pairs for this study.
Master
Slave
Perp baseline (m)
Date difference
20070915
20071031
536
46
20071031
20071216
135
46
20071031
20080131
572
92
20071031
20080317
683.0
138
20071031
20100205
−353.0
828
20071031
20100508
115
920
20071216
20080131
437
46
20071216
20100205
−489
782
20071216
20100508
−20
874
20080131
20080317
110
46
20080131
20080502
750
92
20080131
20100205
−926
736
20080131
20101224
425
1058
20080317
20080502
639
46
20080617
20090202
−269
230
20080617
20090805
66
414
20080917
20090202
893
138
20090202
20090805
336
184
20090805
20090920
605
46
20090805
20091105
1037
92
20090920
20091105
432
46
20090920
20091221
658
92
20091105
20091221
225
46
20091105
20100205
754
92
20091105
20100508
1223
184
20091221
20100205
528
46
20091221
20100508
997
138
20100205
20100508
468
92
20100508
20100808
351
92
20100508
20101224
883
230During the processing, remote-sensed datasets include tree height error induced by acquisition time difference and sensor specification. However, these error sources are at cm level and do not need to be considered while ground-based tree height measurements might be more important, especially in mountain topography.


## 2.1. Study Area

The study area for this investigation was an approximately 20 km2 area within the Jangsan Mountain in Busan, Korea (Figure 1). The altitude of the mountain is 634 m and the shape of the mountain is entirely conical. This area is primarily composed of pine forest with reed grass at the top of the hill. Pine trees are easy to identify top of the tree because of its shape. Therefore, measuring pine tree height is easier than broad-leaved trees (Figure 2). Also, in the area, we could collect remote-sensed data such as SAR, LiDAR, and Optical data. An in situ forest height survey was conducted throughout the entire area during September and October 2012 using laser height measurements except for artificial construction (Table 1). We determined forest height by averaging laser height measurements taken three times in opposing directions. Also, tree species composition has a major effect on forest height measurements. Therefore, we measured 90 points of in situ tree heights to only pine trees to compare with remote-sensed datasets (Table 2).Figure 1
Study area and in situ locations indicated with red rectangles.Figure 2
Field photograph.Table 1
Laser measurement specification and geometry.
Specification
Value
Picture
Geometry of tree height measurement using laser
Distance accuracy
±30 cm
Max range to nonreflective targets
1000 m
Scope magnification
7xTable 2
In situ tree height measurements.
Number
Latitude (°)
Longitude (°)
Height (m)
Number
Latitude (°)
Longitude (°)
Height (m)
1
35.19082
129.1346
18.7
46
35.20826
129.1576
8.7
2
35.18935
129.1364
13
47
35.21124
129.16
10
3
35.1886
129.1405
11.9
48
35.21258
129.1615
10.2
4
35.18965
129.1414
12
49
35.21457
129.1645
9.3
5
35.19272
129.1444
2.2
50
35.21483
129.1649
10.1
6
35.19465
129.1447
4
51
35.20795
129.1579
3.3
7
35.1951
129.1451
9
52
35.20684
129.1607
3.6
8
35.19618
129.1471
6.6
53
35.20505
129.1642
10.5
9
35.19377
129.146
5.3
54
35.20261
129.1664
10
10
35.19627
129.1486
7.5
55
35.19725
129.1693
9.2
11
35.19613
129.1503
13
56
35.19587
129.1678
7.6
12
35.1921
129.1459
3.9
57
35.19429
129.1659
11
13
35.1913
129.1465
8.4
58
35.19275
129.1657
12.6
14
35.18977
129.148
10.3
59
35.18768
129.1629
13.8
15
35.1866
129.1503
8.9
60
35.21848
129.1575
12.67
16
35.18612
129.1535
12.2
61
35.21796
129.1588
14.83
17
35.18902
129.1584
9.4
62
35.21764
129.1611
13.38
18
35.18975
129.1604
13.4
63
35.21686
129.1649
12.13
19
35.1878
129.1612
14.4
64
35.21459
129.1707
12.33
20
35.18212
129.1669
14.4
65
35.21509
129.171
9.05
21
35.18043
129.1409
4.4
66
35.21716
129.1661
10.18
22
35.18015
129.1398
5
67
35.21669
129.1631
11.45
23
35.17964
129.1391
12.5
68
35.21707
129.1614
13.4
24
35.18095
129.1379
11
69
35.21963
129.1563
16.27
25
35.18169
129.1371
13
70
35.21953
129.1546
7.47
26
35.18513
129.1355
12
71
35.20605
129.1303
18.5
27
35.18654
129.1348
7.5
72
35.20568
129.132
15.45
28
35.18705
129.1342
13.5
73
35.20563
129.1329
14.183
29
35.18925
129.1346
12.5
74
35.20554
129.136
13.73
30
35.18907
129.1374
12.2
75
35.20508
129.1412
17.33
31
35.18844
129.1394
9.3
76
35.207
129.1443
11.73
32
35.18786
129.1407
7.7
77
35.20898
129.1461
10.57
33
35.18757
129.1414
7.2
78
35.21604
129.1512
12.7
34
35.19229
129.1455
2.5
79
35.21665
129.1539
17.53
35
35.19237
129.1458
3.2
80
35.21749
129.1559
13.58
36
35.18916
129.1458
3.5
81
35.20037
129.1418
6.55
37
35.1901
129.1561
12
82
35.2034
129.1416
13
38
35.18882
129.1616
16.5
83
35.20438
129.1418
12.92
39
35.19211
129.1586
7.8
84
35.20487
129.143
11.92
40
35.19514
129.1597
10.8
85
35.20452
129.145
8.1
41
35.1988
129.1615
11
86
35.20318
129.1465
7.98
42
35.20238
129.157
9
87
35.20212
129.1488
9.73
43
35.20337
129.1565
8.3
88
35.20053
129.1462
10.27
44
35.20377
129.1555
9.9
89
35.19975
129.1443
10.27
45
35.20377
129.1555
8
90
35.1983
129.1392
16.08


## 2.2. Remote-Sensed Data

We obtained SAR images from ALOS PALSAR over the study area for the period between 2007 and 2010 (Table3). We produced 30 interferograms and used SRTM data not only to correct the topographic phase contribution but to also to estimate forest height as a DSM (Digital Surface Model). The LiDAR data were acquired in February 2007 with an LEICA ALS50 sensor, and aerial photography was acquired to generate NDVI data over the study area in April 2012. A variety of remote sensors has different resolution. In our study, we used a 5 m resolution LiDAR elevation model, 2.5 m aerial photography, 30 m SRTM DEM and 30 m SAR images using multi-look. Therefore, we conducted down- and upsampling for 5 m resolution after image processing.Table 3
SAR pairs for this study.
Master
Slave
Perp baseline (m)
Date difference
20070915
20071031
536
46
20071031
20071216
135
46
20071031
20080131
572
92
20071031
20080317
683.0
138
20071031
20100205
−353.0
828
20071031
20100508
115
920
20071216
20080131
437
46
20071216
20100205
−489
782
20071216
20100508
−20
874
20080131
20080317
110
46
20080131
20080502
750
92
20080131
20100205
−926
736
20080131
20101224
425
1058
20080317
20080502
639
46
20080617
20090202
−269
230
20080617
20090805
66
414
20080917
20090202
893
138
20090202
20090805
336
184
20090805
20090920
605
46
20090805
20091105
1037
92
20090920
20091105
432
46
20090920
20091221
658
92
20091105
20091221
225
46
20091105
20100205
754
92
20091105
20100508
1223
184
20091221
20100205
528
46
20091221
20100508
997
138
20100205
20100508
468
92
20100508
20100808
351
92
20100508
20101224
883
230During the processing, remote-sensed datasets include tree height error induced by acquisition time difference and sensor specification. However, these error sources are at cm level and do not need to be considered while ground-based tree height measurements might be more important, especially in mountain topography.


## 3. Method

### 3.1. Extract NDVI Using Optical Images

Optical sensors give pixel values that represent only the intensity of the light that is directly reflected from the forest surface. Therefore, this sensor is usually used for horizontal forest parameters, such as forest area, by interacting with the entire tree in particular bands. These distinct bands allow us to classify land cover, especially using the NDVI method. NDVI is defined as [13]
(1)NDVI=ρnir−ρredρnir+ρred,where ρnir and ρred are spectral reflectance measurements acquired in the near-infrared and red (visible) regions, respectively.Several arguments have been made that NDVI is related not only to classification but also to tree height. Wang et al. [14] found that tree height increases are related to changes in NDVI from the previous year using NOAA/AVHRR (National Oceanic and Atmospheric Administration/Advanced Very High Resolution Radiometer) satellite imagery. Therefore, we used NDVI, calculated using high-geometrical-resolution multispectral aerial images to classify forest area and to extract forest height. We obtained an NDVI map, downsampled to 5 m resolution using cubic interpolation. After knowing that NDVI has considerable noise in complex urban areas, we applied 11 × 11 median filtering to remove this noise (Figure 3).Figure 3
NDVI map after median filtering.


### 3.2. LiDAR

LiDAR systems measure the range from a sensor to a target using the TOF (time of flight) of a high-frequency laser pulse. Each laser pulse is recorded as a point and provides the vertical difference between the last return (assumed as DTM) and the first return (assumed as DSM). Forest height can be determined using the difference between the DTM and the DSM [15] (Figure 4). We used discrete-return LiDAR data which was one of the available remote sensing datasets. Another role of LiDAR data is that it provides high precision DTM, which rarely changes compared to DSM.Figure 4
LiDAR height map by DSM-DTM.


### 3.3. SBAS Using L-Band SAR

As seen above, in cases of forest height estimation using SAR, most studies are focused on polarimetry and the penetration capabilities of the bands. Considered in this framework, it is necessary to use polarization data, such as TerraSAR-X, and air vehicles with long wavelengths, such as a P-band SAR sensor. These systems, however, are still experimental or generally are not commercially available in our study area; therefore, instead of these systems, we used ALOS PALSAR SAR imagery to overcome data deficiency and we increased accuracy using the SBAS algorithm. We generated a differential interferogram to apply the SBAS algorithm by using the interferograms simulated from the SRTM DEM that were multi-looked using three looks in range and twelve looks in azimuth, respectively. We used SRTM DEM for the differential interferogram, in spite of having higher accuracy LiDAR DTM because the latter covered only a small part of the SAR image. As a result, we estimated the topography error using the SBAS algorithm with the differential interferogram. For the SBAS algorithm, the differential phase is as follows:(2)∆φi,jx,r=∆φix,r−∆φjx,r≈4πλdix,r−djx,r+4πλB⊥i,j△zRsinθ+φiatmx,r−φjatmx,r+∆ni,j,where φ is the phase and i,j are time variables for master and slave acquisition time, d is surface displacement, x and r are azimuth and slant-range pixel coordinates, λ is radar wavelength, B⊥ is the perpendicular baseline, R is the slant-range distance from sensor to pixel, and θ is the look angle. The first term accounts for the deformation phase, the second term accounts for topography error, the third is the atmosphere effect on the phase, and the last term accounts for phase noise by decorrelation or noise effect.From (2), the first term of the deformation phase was not considered because the study area is stable and the third term of the atmosphere effect was neglected because we assumed that the sum of the atmospheric effects are random with respect to time similar to phase noise, so that is ∑iφiatmx,r≈0 and ∑i∆ni≈0. As a result, we defined topography error (Δz) iteratively as [16]
(3)∆z=λ4πRsinθ∆φi,jx,rB⊥i,j.The topography error shown in Figure5(b) from the SBAS algorithm represents the C-band-derived SRTM DEM error. Therefore, we estimated forest height from the difference between the SRTM DEM and the LiDAR DTM using a regression model (Figure 5(a)) and then we made a forest height map using DEM correction (Figure 5(c)). Moreover, we estimated and analyzed forest height using linear regression on combined LiDAR, SAR, and NDVI data.Figure 5
(a) SRTM DEM-LiDAR DTM, (b) topography error by SBAS, and (c) SRTM DEM-LiDAR DTM-SBAS topography error.
(a)
(b)
(c)


## 3.1. Extract NDVI Using Optical Images

Optical sensors give pixel values that represent only the intensity of the light that is directly reflected from the forest surface. Therefore, this sensor is usually used for horizontal forest parameters, such as forest area, by interacting with the entire tree in particular bands. These distinct bands allow us to classify land cover, especially using the NDVI method. NDVI is defined as [13]
(1)NDVI=ρnir−ρredρnir+ρred,where ρnir and ρred are spectral reflectance measurements acquired in the near-infrared and red (visible) regions, respectively.Several arguments have been made that NDVI is related not only to classification but also to tree height. Wang et al. [14] found that tree height increases are related to changes in NDVI from the previous year using NOAA/AVHRR (National Oceanic and Atmospheric Administration/Advanced Very High Resolution Radiometer) satellite imagery. Therefore, we used NDVI, calculated using high-geometrical-resolution multispectral aerial images to classify forest area and to extract forest height. We obtained an NDVI map, downsampled to 5 m resolution using cubic interpolation. After knowing that NDVI has considerable noise in complex urban areas, we applied 11 × 11 median filtering to remove this noise (Figure 3).Figure 3
NDVI map after median filtering.


## 3.2. LiDAR

LiDAR systems measure the range from a sensor to a target using the TOF (time of flight) of a high-frequency laser pulse. Each laser pulse is recorded as a point and provides the vertical difference between the last return (assumed as DTM) and the first return (assumed as DSM). Forest height can be determined using the difference between the DTM and the DSM [15] (Figure 4). We used discrete-return LiDAR data which was one of the available remote sensing datasets. Another role of LiDAR data is that it provides high precision DTM, which rarely changes compared to DSM.Figure 4
LiDAR height map by DSM-DTM.


## 3.3. SBAS Using L-Band SAR

As seen above, in cases of forest height estimation using SAR, most studies are focused on polarimetry and the penetration capabilities of the bands. Considered in this framework, it is necessary to use polarization data, such as TerraSAR-X, and air vehicles with long wavelengths, such as a P-band SAR sensor. These systems, however, are still experimental or generally are not commercially available in our study area; therefore, instead of these systems, we used ALOS PALSAR SAR imagery to overcome data deficiency and we increased accuracy using the SBAS algorithm. We generated a differential interferogram to apply the SBAS algorithm by using the interferograms simulated from the SRTM DEM that were multi-looked using three looks in range and twelve looks in azimuth, respectively. We used SRTM DEM for the differential interferogram, in spite of having higher accuracy LiDAR DTM because the latter covered only a small part of the SAR image. As a result, we estimated the topography error using the SBAS algorithm with the differential interferogram. For the SBAS algorithm, the differential phase is as follows:(2)∆φi,jx,r=∆φix,r−∆φjx,r≈4πλdix,r−djx,r+4πλB⊥i,j△zRsinθ+φiatmx,r−φjatmx,r+∆ni,j,where φ is the phase and i,j are time variables for master and slave acquisition time, d is surface displacement, x and r are azimuth and slant-range pixel coordinates, λ is radar wavelength, B⊥ is the perpendicular baseline, R is the slant-range distance from sensor to pixel, and θ is the look angle. The first term accounts for the deformation phase, the second term accounts for topography error, the third is the atmosphere effect on the phase, and the last term accounts for phase noise by decorrelation or noise effect.From (2), the first term of the deformation phase was not considered because the study area is stable and the third term of the atmosphere effect was neglected because we assumed that the sum of the atmospheric effects are random with respect to time similar to phase noise, so that is ∑iφiatmx,r≈0 and ∑i∆ni≈0. As a result, we defined topography error (Δz) iteratively as [16]
(3)∆z=λ4πRsinθ∆φi,jx,rB⊥i,j.The topography error shown in Figure5(b) from the SBAS algorithm represents the C-band-derived SRTM DEM error. Therefore, we estimated forest height from the difference between the SRTM DEM and the LiDAR DTM using a regression model (Figure 5(a)) and then we made a forest height map using DEM correction (Figure 5(c)). Moreover, we estimated and analyzed forest height using linear regression on combined LiDAR, SAR, and NDVI data.Figure 5
(a) SRTM DEM-LiDAR DTM, (b) topography error by SBAS, and (c) SRTM DEM-LiDAR DTM-SBAS topography error.
(a)
(b)
(c)


## 4. Results and Discussion

### 4.1. Estimated Forest Height

We conducted comparisons between the SRTM-derived forest height and the topographically corrected SRTM-derived forest height with respect to in situ dataset (Figures6(a) and 6(b)). The root mean square error of the estimated forest height from the first method to the second method was a little improved, from 2.90 to 2.75 as well as the R2 increasing from 0.50 to 0.54. In the case of the LiDAR data, the RMSE and R2 were calculated at 3.22 m and 0.43, respectively (Figure 6(c)); however, when the data acquisition differences between LiDAR and the in situ data are taken into consideration, particularly for the mountainous topography of the study area, these results show that this method is viable for determining forest height.Figure 6
(a) Tree height derived by SRTM-DTM, (b) tree height derived by SRTM-DTM-height error, and (c) tree height derived by LiDAR.
(a)
(b)
(c)To improve the results, we merged the data through linear combination as follows:(4)HTreeHeight_1=α·HSARHeight+β·HLiDARHeight+c,(5)HTreeHeight_2=d·HSARHeight+e·HLiDARHeight+f·HNDVIHeight+g,where α,β,d,e, and f are coefficients and c and f are offset values obtained from each tree height data and a least squares technique.From (4), the RMSE of the forest height derived from the combined data improved by approximately 10 cm and 50 cm from the SAR-derived forest height and the LiDAR-derived forest height, respectively. This approach may be the most viable method to determine forest height (Figure 7(a)). In the case of NDVI, there have been accounts that there is a relationship between NDVI and tree height [14]; however, it was not possible to estimate forest height using this method for this study because most of the trees in the study area have minor stem diameters and tree rings (Figure 7(b)).Figure 7
(a) Tree height derived by SAR and LiDAR and (b) tree height derived by SAR and LiDAR and NDVI.
(a)
(b)


### 4.2. Forest Area Mapping

We extracted forest height based on LiDAR DTM; however, this method led to unexpected forest areas such as urban area (artificial buildings) or field of reeds. To remove urban areas from the forest height map, we calculated NDVI values using aerial Optical imagery which has NIR and R-bands. First, we masked below 2 m in height from LiDAR- and SAR-derived height maps because we only collect over 2 m in height trees. From the first masking results, the urban area remained as a forest area having both LiDAR- and SAR-derived height maps in common because artificial structures were above the threshold. Furthermore, SAR dataset excluded mountain streams in valley areas. To be precise, there are thin forest areas along the streams that the L-band penetrates more deeply than dense forest areas. Additionally, the “bald earth surface” areas signified construction dated after the SRTM DEM was acquired because the “bald earth surfaces” are not presented in the SAR-derived forest area map. Second, we used an NDVI value for threshold 0.4 as a nonforest area to remove the urban area.Finally, we generated a forest area map by overlapping three datasets (Figure8) and generated a forest height map using LiDAR, SAR, NDVI data, and a linear combination of each dataset and forest area (Figure 9). To compare results, we generated a height profile (Figure 10). The profile shows that LiDAR-derived forest height well represents detailed changes while SAR-derived forest height represents the overall pattern well. If we used two merged datasets, we represent not only overall pattern but also detailed change over the forest area. However, NDVI factor have no influence to forest height retrieval.Figure 8
Masking forest area map by overlapping LiDAR, SAR, and NDVI and the yellow box represents “bare earth surfaces”.Figure 9
Forest height map derived by (a) LiDAR, (b) SAR, (c) LiDAR + SAR, and (d) LiDAR + SAR + NDVI.
(a)
(b)
(c)
(d)Figure 10
Forest height profile presented in Figure9. Grey line represents LiDAR-derived height, black line represents SAR-derived line, black bold line represents LiDAR + SAR-derived height. LiDAR + SAR + NDVI-derived height has same profile value with black bold line.


## 4.1. Estimated Forest Height

We conducted comparisons between the SRTM-derived forest height and the topographically corrected SRTM-derived forest height with respect to in situ dataset (Figures6(a) and 6(b)). The root mean square error of the estimated forest height from the first method to the second method was a little improved, from 2.90 to 2.75 as well as the R2 increasing from 0.50 to 0.54. In the case of the LiDAR data, the RMSE and R2 were calculated at 3.22 m and 0.43, respectively (Figure 6(c)); however, when the data acquisition differences between LiDAR and the in situ data are taken into consideration, particularly for the mountainous topography of the study area, these results show that this method is viable for determining forest height.Figure 6
(a) Tree height derived by SRTM-DTM, (b) tree height derived by SRTM-DTM-height error, and (c) tree height derived by LiDAR.
(a)
(b)
(c)To improve the results, we merged the data through linear combination as follows:(4)HTreeHeight_1=α·HSARHeight+β·HLiDARHeight+c,(5)HTreeHeight_2=d·HSARHeight+e·HLiDARHeight+f·HNDVIHeight+g,where α,β,d,e, and f are coefficients and c and f are offset values obtained from each tree height data and a least squares technique.From (4), the RMSE of the forest height derived from the combined data improved by approximately 10 cm and 50 cm from the SAR-derived forest height and the LiDAR-derived forest height, respectively. This approach may be the most viable method to determine forest height (Figure 7(a)). In the case of NDVI, there have been accounts that there is a relationship between NDVI and tree height [14]; however, it was not possible to estimate forest height using this method for this study because most of the trees in the study area have minor stem diameters and tree rings (Figure 7(b)).Figure 7
(a) Tree height derived by SAR and LiDAR and (b) tree height derived by SAR and LiDAR and NDVI.
(a)
(b)


## 4.2. Forest Area Mapping

We extracted forest height based on LiDAR DTM; however, this method led to unexpected forest areas such as urban area (artificial buildings) or field of reeds. To remove urban areas from the forest height map, we calculated NDVI values using aerial Optical imagery which has NIR and R-bands. First, we masked below 2 m in height from LiDAR- and SAR-derived height maps because we only collect over 2 m in height trees. From the first masking results, the urban area remained as a forest area having both LiDAR- and SAR-derived height maps in common because artificial structures were above the threshold. Furthermore, SAR dataset excluded mountain streams in valley areas. To be precise, there are thin forest areas along the streams that the L-band penetrates more deeply than dense forest areas. Additionally, the “bald earth surface” areas signified construction dated after the SRTM DEM was acquired because the “bald earth surfaces” are not presented in the SAR-derived forest area map. Second, we used an NDVI value for threshold 0.4 as a nonforest area to remove the urban area.Finally, we generated a forest area map by overlapping three datasets (Figure8) and generated a forest height map using LiDAR, SAR, NDVI data, and a linear combination of each dataset and forest area (Figure 9). To compare results, we generated a height profile (Figure 10). The profile shows that LiDAR-derived forest height well represents detailed changes while SAR-derived forest height represents the overall pattern well. If we used two merged datasets, we represent not only overall pattern but also detailed change over the forest area. However, NDVI factor have no influence to forest height retrieval.Figure 8
Masking forest area map by overlapping LiDAR, SAR, and NDVI and the yellow box represents “bare earth surfaces”.Figure 9
Forest height map derived by (a) LiDAR, (b) SAR, (c) LiDAR + SAR, and (d) LiDAR + SAR + NDVI.
(a)
(b)
(c)
(d)Figure 10
Forest height profile presented in Figure9. Grey line represents LiDAR-derived height, black line represents SAR-derived line, black bold line represents LiDAR + SAR-derived height. LiDAR + SAR + NDVI-derived height has same profile value with black bold line.


## 5. Conclusion

Remote sensing techniques are efficient methods of extracting forest height quickly, with cost-effective tools. However, there is data insufficiency for our study area with regard to the latest data, such as full-waveform LiDAR and X- and P-band SAR data. Instead, we determined forest height using common remote data, such as discrete-return LiDAR data, SRTM, satellite L-band SAR data, and Optical data. Moreover, in order to improve the results, we applied the SBAS algorithm for SRTM DEM error correction and combined each dataset using linear regression. We then extracted the forest areas by overlapping NDVI and forest height data above 2 m allowing the sensors to complement each other. Using this procedure, we generated a forest height map as an end product with an RMSE accuracy of 2.68 m.In general terms, this study shows the various ways in generating a forest height map using limited data. In spite of different acquisition times, it should be noted that each sensor has the potential for not only determining forest height but also extracting complementary forest area. Furthermore, there is potential for improvement using the SBAS algorithm and linear regression. For those who may encounter a lack of available of data to generate forest height map, this study offers one possible approach.



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*Source: 1593129-2018-04-11.xml*