# Investigating the Consistency of Uncalibrated Multispectral Lidar Vegetation Indices at Different Altitudes

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. The Titan Spectral Vegetation Indices

_{th}and m

_{th}channel/band. There is an obvious non-linear relation between these two indices [14]:

_{l},C

_{m}) and nδ(C

_{l},C

_{m}) with l, m indices corresponding to the Titan’s channel numbers or, for indicating the actual wavelengths, as $s{\rho}_{{\lambda}_{m}}^{{\lambda}_{l}}$ and $n{\delta}_{{\lambda}_{m}}^{{\lambda}_{l}}$.

#### 1.2. Lidar Radiometry

_{r}is received signal power, P

_{t}—transmitted power, D—aperture diameter, R—system range to target, μ

_{atm}—atmospheric transmission factor, μ

_{sys}—system transmission factor, θ

_{t}—transmitter beam width, and σ—effective target cross section.

_{fp}, illuminated by a circular beam at a range R at nadir, is:

_{t}is provided for only part of the spatial energy beam profile (e.g., Gaussian at 1/e or 1/e

^{2}), therefore, A

_{fp}only approximates the total illuminated area. If a target intercepts the entire beam, it is referred to as an extended target. If the target area is smaller than the transmitted footprint, it is referred to as a point target. Thus, for an extended Lambertian target substituting ∂A with A

_{fp}[27]:

#### 1.3. Lidar Intensity Metrics

^{i}> is used to denote rasterization of an attribute x associated with a point from the lidar point cloud by averaging (< >) through i numbers of attribute values from corresponding i points inside a grid cell. It is assumed that intensity DN (I) is a linear function of the received peak power (I = kP

_{r}) and range normalization to the range ℝ was applied to intensity DNs. Then, assuming that atmospheric losses, transmission power, and the system transmission factor are constant, the above equation can be re-written in the form of (denoting intensity normalized to inverse square range as ${\tilde{I}}_{i}={I}_{i}\frac{{R}_{i}^{2}}{{\mathbb{R}}^{2}}$):

_{fp}from Equation (9) as a normalization value:

#### 1.4. Angular Effects of Lidar Backscatter

#### 1.5. Relevant Studies and Impetus for the Experiment

#### 1.6. Hypothesis and Objectives

#### 1.6.1. Single Channel Intensity Ratios

^{−1}[27] for an increased range of 500 m–1000 m.

#### 1.6.2. Comparison of Point Density Distributions across Three Altitudes

#### 1.6.3. Consistency of Spectral Vegetation Indices through Different Altitudes

^{lm}:

^{lm}can be moved from inside the function) might be easier to compare to each other from different sensors and datasets. Thus, by calculating spectral ratios and normalized differences at three different altitudes, the consistency of both indices can be investigated.

#### 1.6.4. Comparing the Consistency of sρ vs. nδ

## 2. Data and Methods

#### 2.1. Study Area and Data Collection

#### 2.2. Scan Line Intensity Banding

#### 2.3. Comparative Analysis

#### 2.3.1. Point Density

#### 2.3.2. Single Channel Ratios

#### 2.3.3. Spectral Vegetation Indices Maps

#### 2.3.4. Spectral Vegetation Indices Ratios

## 3. Results

#### 3.1. Point Density Maps

#### 3.2. Single Channel Intensity Ratios

#### 3.3. Spectral Vegetation Indices Maps

#### 3.4. SVI Altitude Ratio Maps and Histograms

_{i}(500 m)/SVI

_{i}(1000 m) with the corresponding histograms for images, and maps of SVI

_{i}(500 m)/SVI

_{i}(1500 m) derived from single returns. The color ramp for all images is based on +/− two standard deviations of sρ (500 m)/sρ (1000 m) images. The ratio range for all histograms is from 0.0 to 2.0. Table 7 shows the mean, standard deviation, min, and max values for each image from Figure 9, Figure 10 and Figure 11.

## 4. Discussion

_{NIR-MIR}in the author’s notation) was the noisiest index among Titan’s normalized differences. The reason for this result might be in the type of the land cover—the average simple ratio of C2 and C1 channels for the AOI was ~0.8, while simple ratios of C2 and C3, and C1 and C3 combinations were ~4.5 and ~5.5 (Table 6). The channel dependent differences in atmospheric attenuation with altitude may lead to a change in intensity response from the scene, while the normalized difference may be oversensitive in areas where reflectance of C1 and C2 channels are close to each other. Thus, while it is possible to use combinations of nδ(C2,C3), nδ(C1,C3) and sρ(C2,C1) indices for interpretation and basic classification purposes, such as vegetation and land-cover within an urban environment, it is recommended to combine all three laser channels for more sophisticated classification needs (e.g., Hopkinson et al. [5]).

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) The area of interest (AOI) with highlighted classes; (

**b**) lidar point cloud colorized by passive RGB imagery. The thematic map was classified based on passive imagery and the familiarity of the field support team with the AOI. Virtual plots for a coniferous stand and a hay stubble field are 11.3 m radii circle areas chosen for additional analysis.

**Figure 3.**Point density maps from all returns at 2 m × 2 m grids. Top to bottom: C3, C2, and C1; left to right: 500 m, 1000 m, and 1500 m. White pixels represent no data. The explanation for density patterns is in the text.

**Figure 4.**The boxplot showing maximum values (with subtracted noise) of the digitized fraction of an outgoing pulse for subsamples of 21 pulses per flight line over the virtual hay stubble plot for channel C2 (1064 nm).

**Figure 5.**Single channels ratios of normalized to range 1000 m average intensity at 4 m × 4 m grid from all returns for each channel: C

_{i}(500 m)/C

_{i}(1000 m) in top figures, and C

_{i}(500 m)/C

_{i}(1500 m) in bottom figures. The channels are presented from left to right: C3, C2, and C1. White pixels represent no data.

**Figure 6.**Single channels ratios of normalized to range 1000 m average intensity at 4 m × 4 m grid from single returns for each channel: C

_{i}(500 m)/C

_{i}(1000 m) in top figures, and C

_{i}(500 m)/C

_{i}(1500 m) in bottom figures. The channels are presented from left to right: C3, C2, and C1. White pixels represent no data.

**Figure 7.**nδ (C2, C3) and sρ (C2, C3) for all returns (

**a–f**) and single returns (

**g–l**), averaged over 4 m × 4 m grid. White pixels represent no data.

**Figure 8.**nδ (C2, C1) and nδ (C1, C3) for single returns, averaged over 4 m × 4 m grid. White pixels represent no data.

**Figure 9.**Ratios derived from single return indices at 4 m × 4 m grid: (

**a**) ratio of sρ (C2, C3) at 500 m to sρ (C2, C3) at 1000 m; (

**b**) ratio of nδ (C2, C3) at 500 m to nδ (C2, C3) at 1000 m; (

**c**) Ratios of sρ (C2, C3) at 500 m to sρ (C2, C3) at 1500 m; (

**d**) ratio of nδ (C2, C3) at 500 m to nδ (C2, C3) at 1500 m. (

**e**) histograms for Figure 9a,b. White pixels represent no data.

**Figure 10.**Ratios derived from single return indices at 4 m × 4 m grid: (

**a**) ratio of sρ (C2, C1) at 500 m to sρ (C2, C1) at 1000 m; (

**b**) ratio of nδ (C2, C1) at 500 m to nδ (C2, C1) at 1000 m; (

**c**) Ratios of sρ (C2, C1) at 500 m to sρ (C2, C1) at 1500 m; (d) ratio of nδ (C2, C1) at 500 m to nδ (C2, C1) at 1500 m. (

**e**) histograms for Figure 10a,b. White pixels represent no data.

**Figure 11.**Ratios derived from single return indices at 4 m × 4 m grid: (

**a**) ratios of sρ (C1, C3) at 500 m to sρ (C1, C3) at 1000 m; (

**b**) ratio of nδ (C1, C3) at 500 m to nδ (C1, C3) at 1000 m; (

**c**) Ratios of sρ (C1, C3) at 500 m to sρ (C1, C3) at 1500 m; (

**d**) ratio of nδ (C1, C3) at 500 m to nδ (C1, C3) at 1500 m. (

**e**) histograms for Figure 11a,b. White pixels represent no data.

**Table 1.**Lidar parameters for each swath. *PRF (Pulse Repetition Frequency) is given for one channel.

Flight Line (L) | L1 | L2 | L3 | L4 | L5 | L6 | L7 | L8 | L9 | L10 |
---|---|---|---|---|---|---|---|---|---|---|

<Range>, m | 491 | 540 | 547 | 546 | 536 | 942 | 1018 | 1475 | 1540 | 1555 |

PRF*, kHz | 75 | 75 | 75 | 75 | 75 | 75 | 75 | 75 | 75 | 75 |

SF, Hz | 40 | 40 | 40 | 40 | 40 | 38 | 38 | 32 | 32 | 32 |

Swath, deg | 40.0 | 40.0 | 40.0 | 40.0 | 40.0 | 40.0 | 40.0 | 40.0 | 40.0 | 40.0 |

<Speed>, m/s | 67 | 65 | 65 | 69 | 66 | 63 | 68 | 64 | 59 | 68 |

Heading, deg | 160 | 340 | 160 | 340 | 250 | 160 | 340 | 160 | 340 | 250 |

500 m | 1000 m | 1500 m | |||||||
---|---|---|---|---|---|---|---|---|---|

C1/C2/C3 | C1 | C2 | C3 | C1 | C2 | C3 | C1 | C2 | C3 |

Wavelength | 1550 nm | 1064 nm | 532 nm | 1550 nm | 1064 nm | 532 nm | 1550 nm | 1064 nm | 532 nm |

Point density all | 8.05 | 8.35 | 7.57 | 2.55 | 2.57 | 1.9 | 3.14 | 2.85 | 2.38 |

Point density last | 5.7 | 5.71 | 5.68 | 2 | 2 | 1.8 | 2.8 | 2.59 | 2.38 |

Spacing all, cm | 0.35 | 0.35 | 0.36 | 0.63 | 0.62 | 0.73 | 0.56 | 0.59 | 0.65 |

Number of returns | 6,468,902 | 6,709,651 | 6,083,545 | 2,050,152 | 2,059,638 | 1,502,604 | 2,525,347 | 2,291,578 | 1,337,302 |

Footprint diameter at nadir, cm | 18 | 18 | 35 | 35 | 35 | 70 | 53 | 53 | 105 |

Single | 3,269,931 | 3,151,688 | 3,344,283 | 1,236,739 | 1,231,412 | 1,347,771 | 1,984,104 | 1,887,007 | 1,336,696 |

Double | 1,741,204 | 1,822,086 | 1,903,834 | 591,220 | 606,513 | 153,513 | 518,169 | 368,437 | 606 |

Triple | 933,480 | 1,087,821 | 673,996 | 181,753 | 183,627 | 1,316 | 22,510 | 35,130 | 0 |

Quadruple | 524,287 | 648,056 | 161,432 | 40,440 | 38,086 | 4 | 564 | 1,004 | 0 |

First | 4,584,010 | 4,588,576 | 4,562,217 | 1,603,452 | 1,605,753 | 1,425,026 | 2,251,163 | 2,083,401 | 1,336,999 |

Second | 1,312,320 | 1,435,277 | 1,216,281 | 366,052 | 373,756 | 77,137 | 266,407 | 195,979 | 303 |

Third | 441,804 | 524,168 | 264,788 | 70,566 | 70,627 | 440 | 7,636 | 11,947 | 0 |

Fourth | 130,768 | 161,630 | 40,259 | 10082 | 9502 | 1 | 141 | 251 | 0 |

**Table 3.**Point density in points per square meter for lidar returns 0.5 m above ground for all returns and for single returns for different vegetation classes from Figure 1a. The density for the hay stubble class (i.e., ground) is presented for a reference to point density from extended targets.

500 m | 1000 m | 1500 m | |||||||
---|---|---|---|---|---|---|---|---|---|

C1/C2/C3Wavelength, nm | C1 1550 | C2 1054 | C3 532 | C1 1550 | C2 1064 | C3 532 | C1 1550 | C2 1064 | C3 532 |

Hay stubble | 5.3 | 5.35 | 5.0 | 2.5 | 2.4 | 2.0 | 3.2 | 2.9 | 2.6 |

Coniferous all | 9.9 | 10.8 | 9.7 | 4.0 | 3.6 | 2.6 | 2.6 | 2.2 | 0.1 |

Coniferous single | 3.4 | 2.7 | 3.6 | 2.0 | 1.5 | 2.1 | 2.2 | 1.5 | 0.1 |

Deciduous all | 14.3 | 15.1 | 12.0 | 3.3 | 3.3 | 1.3 | 3.4 | 2.7 | <0.1 |

Deciduous single | 2.3 | 1.9 | 3.2 | 0.9 | 0.9 | 1.1 | 2.0 | 1.6 | <0.1 |

Mixed all | 12.7 | 14.0 | 11.4 | 3.7 | 3.8 | 1.8 | 3.0 | 2.6 | 0.1 |

Mixed singles | 3.1 | 2.6 | 3.5 | 1.4 | 1.3 | 1.6 | 2.1 | 1.7 | 0.1 |

Crop all | 5.0 | 5.2 | 5.1 | 1.3 | 1.6 | 1.3 | 2.7 | 2.3 | 0.2 |

Crop singles | 1.1 | 1.0 | 0.8 | 0.4 | 0.6 | 0.8 | 1.1 | 1.5 | 0.2 |

**Table 4.**The comparison of range and incidence angle normalized intensities for the same altitudes for a virtual hay stubble plot (Figure 1a) for selected flight lines (Table 1). KS test comparing range-normalized intensity from two flight lines at the same altitude (note difference in the Range column). The number of points (N) presented for each flight line and channel. The single channel ratios presented for all altitudes and channels and compared to single channel ratios for different altitudes.

Range, m | C1 (1550 nm) | C2 (1064 nm) | C3 (532 nm) | |||||||
---|---|---|---|---|---|---|---|---|---|---|

N | $\tilde{\mathit{I}}$ | $\frac{\tilde{\mathit{I}}}{\mathbf{cos}\mathit{\alpha}}$ | N | $\tilde{\mathit{I}}$ | $\frac{\tilde{\mathit{I}}}{\mathbf{cos}\mathit{\alpha}}$ | N | $\tilde{\mathit{I}}$ | $\frac{\tilde{\mathit{I}}}{\mathbf{cos}\mathit{\alpha}}$ | ||

L3 | 515 | 580 | 772.2 (51.9) | 778,0 (54.0) | 486 | 394.0 (30.5) | 396.5 (30.7) | 556 | 136.6 (11.0) | 137.5 (11.1) |

KS test | D = 0.133 p < 0.01 | D = 0.095 p = 0.012 | D = 0.132 p < 0.01 | D = 0.094 p = 0.018 | D = 0.038 p = 0.997 | D = 0.205 p < 0.01 | ||||

L4 | 525 | 536 | 759.6 (52.7) | 790.2 (54.7) | 591 | 383.9 (28.6) | 389.4 (29.0) | 418 | 137.1 (10.8) | 142.3 (11.2) |

L3/L4 | 1.07 | 0.98 | 1.03 | 1.02 | 1.00 | 1.00 | ||||

L6 | 916 | 280 | 643.7 (41.6) | 646.8 (41.8) | 294 | 328.6 (22.7) | 330.2 (22.8) | 289 | 114.6 (8.2) | 115.0 (8.3) |

KS test | D = 0.688 p < 0.01 | D = 0.544 p < 0.01 | D = 0.436 p < 0.01 | D = 0261 p < 0.01 | D = 0.630 p < 0.01 | D = 0.461 p < 0.01 | ||||

L7 | 1023 | 253 | 571.3 (36.8) | 595.5 (38.0) | 266 | 304.6 (19.0) | 317.6 (19.8) | 290 | 102.3 (6.7) | 106.7 (7.0) |

L6/L7 | 1.13 | 1.09 | 1.08 | 1.04 | 1.12 | 1.08 | ||||

(L3+L4)/(L6+L7) | 1.26 | 1.26 | 1.23 | 1.21 | 1.26 | 1.26 | ||||

L8 | 1460 | 250 | 553.4 (30.8) | 553.4 (30.8) | 218 | 301.5 (16.7) | 301.5 (16.7) | 881 | 100.8 (7.4) | 100.8 (7.4) |

KS test | D = 0.506 p < 0.01 | D = 0.425 p < 0.01 | D = 0.330 p < 0.01 | D = 0.220 p < 0.01 | D = 0.233 p < 0.01 | D = 0.184 p < 0.01 | ||||

L9 | 1514 | 212 | 514.1 (29.6) | 522.6(30.1) | 198 | 289.4 (16.7) | 294.3 (17.0) | 190 | 97.0 (7.1) | 98.7 (7.2) |

L8/L9 | 1.08 | 1.06 | 1.04 | 1.02 | 1.04 | 1.02 | ||||

(L3+L4)/(L8+L9) | 1.43 | 1.46 | 1.32 | 1.32 | 1.38 | 1.40 |

**Table 5.**The mean values and standard deviation for single-channel ratios for the whole AOI. One sample t-test (for the mean equals to one) p-values are given for 0.95 confidence interval. Two sample Mann-Whitney test p-values are given for 0.95 confidence interval.

All Returns | Paired Test, p-Value | Single Returns | ||||||
---|---|---|---|---|---|---|---|---|

MEAN | SD | p | MEAN | SD | p | |||

a) | C3(500 m)/C3(1000 m) | 1.08 | 0.20 | <0.01 | <0.01 | 1.31 | 0.23 | <0.01 |

d) | C3(500 m)/C3(1500 m) | 1.14 | 0.30 | <0.01 | <0.01 | 1.30 | 0.18 | <0.01 |

b) | C2(500 m)/C2(1000 m) | 1.19 | 0.15 | <0.01 | <0.01 | 1.31 | 0.23 | <0.01 |

e) | C2(500 m)/C2(1500 m) | 1.20 | 0.17 | <0.01 | <0.01 | 1.51 | 0.33 | <0.01 |

c) | C1(500 m)/C1(1000 m) | 1.22 | 0.20 | <0.01 | <0.01 | 1.34 | 0.27 | <0.01 |

f) | C1(500 m)/C1(1500 m) | 1.29 | 0.20 | <0.01 | <0.01 | 1.60 | 0.33 | <0.01 |

**Table 6.**The mean values and standard deviation (in brackets) for nδ and sρ for the whole AOI at three altitudes, derived from all returns and from single returns. P-values and D-statistics from Kolmogorov-Smirnov test are given for comparisons of 500 m products to 1000 m products, and 1500 m products. All p-values are low because of the large sample size (~80,000) and D-statistics provide values of practical significance for interpretation.

Index | AGL, m | (C2,C3) | (C2,C1) | (C1,C3) | |||
---|---|---|---|---|---|---|---|

(1064 nm, 532 nm) | (1064 nm, 1550 nm) | (1550 nm, 532 nm) | |||||

<all> | <single> | <all> | <single> | <all> | <single> | ||

nδ | 500 | 0.57 (0.10) | 0.60 (0.12) | −0.14 (0.13) | −0.12 (0.16) | 0.66 (0.06) | 0.68 (0.07) |

1000 | 0.54 (0.09) D = 0.19, p < 0.01 | 0.60 (0.12) D = 0.02, p < 0.01 | −0.13 (0.14) D = 0.05, p < 0.01 | −0.11 (0.16) D = 0.03, p < 0.01 | 0.62 (0.08) D = 0.24, p < 0.01 | 0.67 (0.07) D = 0.03, p < 0.01 | |

1500 | 0.50 (0.09) D = 0.33, p < 0.01 | 0.54 (0.08) D = 0.31, p < 0.01 | −0.11 (0.13) D = 0.10, p < 0.01 | −0.09 (0.14) D = 0.11, p < 0.01 | 0.60 (0.10) D = 0.31, p < 0.01 | 0.62 (0.08) D = 0.26, p < 0.01 | |

sρ | 500 | 3.91 (1.11) | 4.54 (2.03) | 0.78 (0.23) | 0.82 (0.27) | 5.12 (1.05) | 5.53 (1.60) |

1000 | 3.47 (0.85) D = 0.19, p < 0.01 | 4.49 (1.85) D = 0.02, p < 0.01 | 0.80 (0.23) D = 0.05, p < 0.01 | 0.84 (0.28) D = 0.03, p < 0.01 | 4.51 (1.09) D = 0.24, p < 0.01 | 5.42 (1.55) D = 0.03, p < 0.01 | |

1500 | 3.16 (0.75) D = 0.33, p < 0.01 | 3.44 (0.73) D = 0.31, p < 0.01 | 0.83 (0.21) D = 0.10, p < 0.01 | 0.87 (0.24) D = 0.11, p < 0.01 | 4.24 (1.17) D = 0.31, p < 0.01 | 4.49 (1.04) D = 0.26, p < 0.01 |

500 m/1000 m | 500 m/1500 m | ||||||
---|---|---|---|---|---|---|---|

Mean(SD) | min | max | Mean(SD) | min | max | ||

(C2,C3) | sρ | 1.02(0.20) | 0.15 | 10.10 | 1.13(0.40) | 0.29 | 11.13 |

nδ | 1.00(0.62) | −11.95 | 130.06 | 1.05(0.33) | −35.06 | 28.14 | |

(C2,C1) | sρ | 1.00(0.18) | 0.08 | 6.09 | 0.96(0.16) | 0.07 | 5.78 |

nδ | 0.80(3.83) | −103.06 | 118.32 | 0.95(4.14) | −126.80 | 123.60 | |

(C1,C3) | sρ | 1.03(0.21) | 0.08 | 12.68 | 1.21(0.41) | 0.16 | 12.30 |

nδ | 1.01(0.09) | −5.92 | 8.43 | 1.09(0.22) | −15.81 | 12.07 |

**Table 8.**Point density m

^{−2}of vegetated area in comparison to an open area (second value) at one flight line averaged over 11.3 m radii circle area (virtual plots in Figure 1a).

532 nm | 1064 nm | 1550 nm | |

500 m | ~ 4.2/2.4 | ~ 4.5/2.5 | ~4.2/2.4 |

1000 m | ~ 1.0 /1.3 | ~2.0/1.3 | ~ 2.1/1.3 |

1500 m | ~ 0.04/0.8 | ~0.8/0.8 | ~ 0.9/0.9 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Okhrimenko, M.; Hopkinson, C. Investigating the Consistency of Uncalibrated Multispectral Lidar Vegetation Indices at Different Altitudes. *Remote Sens.* **2019**, *11*, 1531.
https://doi.org/10.3390/rs11131531

**AMA Style**

Okhrimenko M, Hopkinson C. Investigating the Consistency of Uncalibrated Multispectral Lidar Vegetation Indices at Different Altitudes. *Remote Sensing*. 2019; 11(13):1531.
https://doi.org/10.3390/rs11131531

**Chicago/Turabian Style**

Okhrimenko, Maxim, and Chris Hopkinson. 2019. "Investigating the Consistency of Uncalibrated Multispectral Lidar Vegetation Indices at Different Altitudes" *Remote Sensing* 11, no. 13: 1531.
https://doi.org/10.3390/rs11131531