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Article

Estimating the Optimal Threshold for Accuracy Assessment of the Global Ecosystem Dynamics Investigation (GEDI) Data in a Gentle Relief Urban Area

by
Felipe Lima Ramos Barbosa
1,
Renato Fontes Guimarães
1,*,
Osmar Abílio de Carvalho Júnior
1,
Roberto Arnaldo Trancoso Gomes
1,
Osmar Luiz Ferreira de Carvalho
2 and
Thyego Pery Monteiro de Lima
3
1
Departamento de Geografia, Campus Universitário Darcy Ribeiro, Universidade de Brasília, Brasília 70910-900, Brazil
2
Departamento de Ciência da Computação, Campus Universitário Darcy Ribeiro, Universidade de Brasília, Brasília 70910-900, Brazil
3
Programa de Pós-Graduação em Ciências Ambientais, Campus Planaltina, Universidade de Brasília, Brasília 70910-900, Brazil
*
Author to whom correspondence should be addressed.
Remote Sens. 2022, 14(15), 3540; https://doi.org/10.3390/rs14153540
Submission received: 5 June 2022 / Revised: 11 July 2022 / Accepted: 13 July 2022 / Published: 24 July 2022
(This article belongs to the Section Urban Remote Sensing)
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Abstract

:
LiDAR is an excellent source of elevation data used in many surveys. The spaceborne handle system, Global Ecosystem Dynamics Investigation (GEDI), provides ground elevation information with high accuracy except for areas with steep slopes. GEDI data have a lot of noise from atmospheric conditions, and therefore filtering procedures are mandatory to select the best dataset. The dataset presents uncertainties of different magnitudes, with values reaching more than 100 m of difference between the reference data and the GEDI data. The challenge is to find a criterion to determine a threshold to filter accurate GEDI samples. This research aims to identify the threshold based on the difference values between the reference data and the GEDI data to select the maximum number of samples with low RMSE values. Therefore, we used the Kolmogorov–Smirnov (KS) non-parametric test to define the best threshold based on a normal distribution. Our results demonstrated a lower RMSE value with a high number of samples when compared with the quality flag parameter threshold, even using sensitivity parameter thresholds. This method is useful for achieving the best possible accuracy from GEDI data worldwide.

Graphical Abstract

1. Introduction

Advances in light detection and ranging (LiDAR) technology have produced accurate terrain altitude with airborne laser scanning (ALS). Many scientific studies use ground elevation and canopy heights in various applications such as urban environment mapping of Land Use and Land Cover (LULC) [1,2,3], extracting objects such as buildings [4], estimating urban tree canopy and heights [5,6], detecting roads [7], modeling floods and wetlands [8,9], quantifying urban landscape changes under a historical perspective [10], and investigating the Digital Elevation Model (DEM) generation process and upward fusion with another more generic DEM [11,12]. One problem is the high cost of ALS, with surveys covering small areas.
There are few experiences in the development of spaceborne LiDAR systems [13]. The first experiences started with Shuttle Laser Altimeter (SLA) [14], followed by ICESat [15]. Currently, the ICESat 2 altimeter mission [16] aims to estimate changes in polar ice-sheet volume to evaluate their impact on global sea level. Moreover, LiDAR data from space provides biomass quantification by measuring vegetation canopy heights, demonstrating its potential in forest studies.
In this way, the Global Ecosystem Dynamics Investigation (GEDI), launched in 2018, is an advanced spaceborne LiDAR system measuring the returned full waveform. The GEDI system comprises 3 lasers producing 8 tracks of data, separated by 600 m in the along-flight track direction, onboard the Japanese Experiment Module-Exposed Facility (JEM-EF) on the International Space Station (ISS). The lasers shoot fires at a frequency of 242 Hz and produce on-ground measurements over a 25 m-wide footprint. Each track’s footprint centers are separated by 60 m along-track direction, producing terrain and canopy information with an estimated accuracy of 10–20 m horizontally and about 50 cm vertically [13]. Future post-processing and pointing, ranging, and timing calibration updates improve data accuracy.
The GEDI data provide canopy heights, canopy vertical profile, Relative Heights (RH), and surface elevation. Data availability encourages the scientific community to produce several studies, such as: mapping 3D forest structure in the United States [17], forest stand volume estimation in a mixed forest area of northeast China [18], structural characterization of old-growth forests in the Ukrainian Carpathian Mountains [19], estimation of canopy heights and aboveground biomass (AGB) in Mediterranean forests [20], detection of ancient Maya buildings in a forested environment [21], slope-adaptive assessment of GEDI waveforms for AGB estimation over mountainous areas [22], and GEDI geolocation uncertainty impact to estimate tropical forest canopy height [23].
Studies also aim to calculate the terrain accuracy of the GEDI dataset compared with other reference elevation data. Spracklen and Spracklen [19] use the TanDEM-X 12 m as reference data to estimate the relative accuracy of GEDI terrain data. Otherwise, GEDI terrain information was the elevation reference to calculate the accuracy of the sub-canopy estimation from TanDEM-X 12 m using ALOS-2 PALSAR-2 InSAR Coherence [24]. Concerning measured elevations, few studies assessed the absolute accuracy of GEDI elevation data [25,26], mainly using ALS LiDAR.
GEDI is a near-infrared (IR) optical remote sensor and suffers disturbance due to cloud cover, solar illumination, system geometries, and atmospheric conditions, among others [13], producing two categories of noise: erroneous data with more than 100 m difference with reference data, and uncertainties of measurements. Most studies used the quality flag parameter provided as GEDI ancillary information to assess and remove erroneous data from distribution before their main accuracy assessment issues [18,19,20,21,24,27,28,29,30]. Other studies optimize the use of the quality flag parameter by adjusting the sensitivity beam value adopted as a complementary analytic threshold. This ancillary information establishes a signal-to-noise ratio related to the maximum canopy cover throughout the GEDI signal, enabling ground detection [17,31]. As height differences are typically not normally distributed, the accuracy estimate of the error using RMSE is often overestimated. Therefore, the data should be as close as possible to a goodness-of-fit distribution [32,33,34,35,36]. After elimination of erroneous data, the selection of the dataset closest to the normal distribution must consider the threshold value of the difference between the GEDI and LiDAR data.
Thus, this study aims to obtain the best threshold to select only GEDI data as close as possible to normal distribution to achieve low RMSE values. Therefore, we used a normality paradigm method to remove uncertainties using the Kolmogorov–Smirnov (KS) non-parametric test, based on a non-normal test trialed in a flat urban area of Federal District, Brazil.

2. Materials and Methods

2.1. Study Area

Brasília, the Federal capital of Brazil, has a population of approximately 3,000,000 inhabitants distributed in rural (3.38%) and urban (96.62%) areas [37]. Brasília’s urban environment has buildings and residences arranged in wooded areas, sparse green areas, commercial areas, and political buildings, among others. The study area is the center of Brasília and comprises the perimeter between the coordinates 47°57′19.62″W 15°43′34.62″S and 47°49′9.08″W 15°50′44.56″S (Figure 1). The relief is gentle with a mean slope of 3.07 and has ALS data available for absolute accuracy assessment. The vegetation belongs to the Cerrado biome, consisting mainly of grassland with sparse savanna and forest areas, normally located in urban conservation parks.

2.2. GEDI Data

GEDI data is available in the Land Processes Distributed Active Archive Center (LP DAAC, https://lpdaac.usgs.gov/tools/data-pool/ (accessed on 14 April 2021)) in three products, L1B, L2A [27,38], and L2B [39] processed to guarantee the useful part of the waveform after applying smoothing to reduce noise. The L1B data product contains geolocated raw transmitted and received waveforms and ancillary information about noise and acquisition time. The L2A data product contains elevation data and height metrics of the vertical structures inside the waveform. Other data about the L2B product are vegetation metrics, such as canopy cover, vertical profile metrics, and Leaf Area Index (LAI). We processed data from the L2A considering the following information (Table 1).

2.3. ALS Data

We used a digital terrain model (DTM) derived from discrete return ALS data to calculate the absolute accuracy of GEDI height estimates. The ALS data is a aero-photogrammetric product elaborated by a government campaign in the urban area, with 4 points per square meter density and 27 cm of vertical accuracy with 50 cm spatial resolution. Original ALS data has a horizontal reference system SIRGAS2000, UTM Zone 23S, ITRF2000-ellipsoid, referred vertically to MAPGEO2015.

2.4. Methods

The present research has four methodological sections (Figure 2): data preparation, orthometric height transformation, pre-processing, and statistical analysis.

2.4.1. GEDI Data Preparation

The GEDI Finder web service provides all available GEDI L2A products to the study area, totaling 13 orbits files within the boundary box. Table 2 lists the GEDI L2A products downloaded and the acquisition dates.
We used a GEDI Subsetter python code to clip the GEDI products spatially and performed the data conversion from the GeoJSON format to shapefile using QGIS 3.16. The total number of processed footprints in the study area was 7619 between 2 June 2019 and 4 August 2020.

2.4.2. GEDI Orthometric Height Conversion

The analysis between GEDI and reference data elevations requires all height metrics to be in the same vertical reference system. The original GEDI height data are relative to the WGS 84 ellipsoid, while DTM-ALS is in the MAPGEO2015 geoid system. According to Nicacio and Dalazoana [40], the relative approach using EGM 2008 produces better results than MAPGEO2015. Thus, the conversion to orthometric heights of GEDI data used the following Equation (1):
HEGM2008 = hWGS84 − NEGM2008
where HEGM2008 is the derived orthometric height of GEDI data, hWGS84 is the original GEDI footprint heights referenced to the WGS84 ellipsoid, and NEGM2008 represents the EGM 2008 gravimetric geoid heights (≈ -12.5 m for study area). We used VDatum 4.2 software developed by the National Oceanic and Atmospheric Administration (NOAA) to convert the vertical datum of GEDI data, ensuring compatibility with the ALS LiDAR reference.

2.4.3. GEDI Pre-Processing

Each terrain height of GEDI data is a mean terrain height from the interaction between the signal and the objects within a 25 m footprint, represented by a point-shaped polygon. We extracted to every GEDI footprint attribute table the median of the intercepted cell values from DTM-ALS, regarding the difference between the spatial resolutions of both datasets. The median reduces the influence of potential uncertainties in the DTM-ALS [25].
For further statistical analysis and absolute accuracy assessment, we defined as the error the difference in height (dh) between GEDI elevation of the center of the lowest mode (ELM) value and the DTM-ALS median value (henceforth called “dh-DTM”) within each GEDI footprint.

2.4.4. Statistical Analysis

Kolmogorov–Smirnov (KS)

The statistical Kolmogorov–Smirnov (KS) non-parametric test estimates the normality in the error distribution. Applied in many remote sensing studies, the KS test, from two sets of values, compares an observed cumulative frequency distribution based on randomly collected samples and an empirical cumulative frequency distribution based on a normal distribution, expressed as F x i   and   S x i . The KS test identifies the point at which these two distributions show the maximum divergence [41], calculated through estimation of absolute divergence values D1 and D2, according to Equations (2)–(4):
D 1 = | F x i − S x i |
D 2 = | F x i − S x i − 1 |
K S = n   m a x ( | D 1 | , | D 2 | )
The KS test has the advantage of not assuming the previous normality distribution of the samples [42], increasing the ability to explain the normality of data with larger sample sizes and matching the powerful Shapiro–Wilk (SW), Anderson–Darling (AD), and Lilliefors (LF) tests [43,44]. The KS curve estimates used the dh-DTM distribution according to two groups of pre-defined absolute thresholds. The first group admitted a 10 m interval (100, 90, 80, 70, 60, 50, 40, 30, 20, and 10 m) and the second more detailed considered a 1 m interval below the 10 m absolute dh-DTM threshold (9, 8, 7, 6, 5, 4, 3, 2, and 1 m). These interval thresholds allowed us to find the optimal point for data normality with reduced uncertainties. Assuming a similar approach, around 99.92% of samples above the first absolute threshold (<100 m) have amplitude errors from 1668.69 to 14,709.78 m, indicating coarse data error. Therefore, the statistical analysis started from this threshold for further accuracy comparison since the presence of such data errors in the distribution affects it negatively.
The performance analysis of the proposed uncertainties elimination method considered the RMSE of each pre-selected threshold and the RMSE curve (Equation (5)) [45]:
R M S E = 1 n ∑ i = 1 n Δ h i 2
where Δhi is the difference between ith values of dh-DTM.
In addition, we also removed uncertainties from the total GEDI distribution using the quality flag indicator with 0 for further comparison and discussion.

3. Results

3.1. Proposed KS Uncertainties Removal Method and Absolute Accuracy Assessment

Table 3 lists the number of GEDI footprints, calculated KS, and RMSE from each selected threshold. Figure 3 shows comparisons between calculated KS, the number of GEDI footprints, and RMSE curves with 10 and 1 m intervals.
Figure 3a indicates a decrease in calculated KS and RMSE values between thresholds of differences <100 and <10 m, around 68.26% and 78.67%, as expected. However, Figure 4b shows a reduction in only 120 GEDI samples, indicating few differences above 10 m absolute dh-DTM. The KS and RMSE values showed a pronounced reduction between thresholds <100 and <30 m, registering better goodness-of-fit data distribution with the removal of 97 high differences that ensured a better absolute accuracy (8.91 to 2.33 m).
Figure 3c,d show the KS curves, RMSE, and the number of GEDI samples in more detail, considering the 1 m interval between the <9 and <1 m absolute dh-DTM thresholds. A function inflection point occurs in <3 m absolute dh-DTM distribution, where the dispersion of data found its optimal normal fit distribution. Calculated KS decreased from 0.1109 to 0.0172 until the identified inflection point, at an approximately constant rate in each 1 m decrease in absolute dh-DTM. Moreover, there is no gain in absolute accuracy (1.82 to 1.33 m), and the number of GEDI samples decreased by 7.07% with the removal of 253 smaller differences from the distribution. However, absolute dh-DTM thresholds lower than 3 m have increased KS values, a high reduction in the number of samples, around 53.08% (3325 to 1560), and a small gain of approximately 0.75 m in absolute accuracy. Therefore, minor differences in dh-DTM do not produce a better fit to the Gaussian distribution.
Figure 4 shows the optimal threshold considering calculated KS, RMSE values, and the number of GEDI samples. The optimal goodness-of-fit threshold converges with the best GEDI sample arrangement, reaching an RMSE value of 1.33 m. Figure 5 shows the histograms of <4, <3, <2, and <1 m absolute difference thresholds (dh-DTM). The <3 m threshold fit with the best normal distribution (Figure 5b). Below 2 m, data tends to non-normal distribution, as shown by calculated KS values.
Figure 6 shows the normal quantile–quantile (QQ) plots graphical method for diagnosing differences between the probability distribution of the GEDI dataset and theoretical normal distribution. We observed a slightly sigmoid shape of the empirical distribution compared to the straight line of the normal curve. The analysis of the QQ plots reveals the improvement in goodness fit with reduction in absolute thresholds dh-DTM and the optimal normal behavior of the threshold of 3 m. Moreover, absolute dh-DTM distributions lower than 3 m show a non-normal statistical distribution.
Figure 7 and Figure 8 show the GEDI uncertainty footprints eliminated above and below the optimal dh-DTM distribution threshold identified. It is possible to observe the spatial distribution of the 385 and 1765 uncertainty samples eliminated, respectively, above the inflection point identified on the KS curve and below it. Although there is no spatial pattern in the eliminated GEDI samples, we can observe a significant loss of accurate data from the GEDI distribution.

3.2. Comparison with Uncertainties Removal by Quality Flag Parameter and GEDI Sensitivity Beam Data Dispersion

Table 4 lists the number of GEDI samples, KS, and RMSE values for dh-DTM distribution after removing uncertainties by quality flag and the IQR threshold approach. Figure 9 shows its respective boxplots of dh-DTM uncertainties.
For the total GEDI dataset (7619 samples), with the erroneous data, the absolute accuracy is 5946.73 m. Even after removing all data with quality flag value “0”, the RMSE value is 260.46 m, indicating high GEDI dh-DTM distribution errors (Table 4). Thus, we applied another step to remove remaining erroneous data using thresholds of 1.5 times the interquartile range (IQR) minus the first quartile plus third quartile, establishing a benchmark. Results indicated a better dh-DTM distribution with RMSE of 1.40 m considering 2883 GEDI footprints (Table 4). The proposed uncertainties removal method reached 1.33 m of RMSE selecting 3325 GEDI footprints. This result is 15.33% higher than the quality flag method benchmark in dh-DTM distribution with an absolute difference < 3 m.
The boxplot in Figure 10a shows data selection using the 0.9 sensitivity threshold. Figure 10b shows dh-DTM <3 m in all sensitivity ranges. Those data are useful and should not be disregarded.
We divided into two groups the differences between GEDI footprints derived from both uncertainty removal methods for analysis. Group 1 represents GEDI samples present in our method but not in the dataset from the quality flat removal method (with a value equal to 1). Group 2 is the opposite. Table 5 lists the number of samples and RMSE from both GEDI groups, and Figure 11 presents the spatial distribution of these GEDI groups in the study area.
The results indicate that 502 GEDI samples remain when applying our method to remove uncertainties, reaching an RMSE value of 1.32 m suitable for use. In contrast, the quality flag removal method keeps only 60 samples (RMSE of 3.28 m). Furthermore, the proposed method did not select the 60 GEDI samples captured by the quality flag removal method because the absolute dh-DTM is greater than 3 m. As shown in Figure 11, the increase in useful GEDI samples can assist in the DEM interpolation processes or even as reference points to support other terrain applications in the study area. These results reinforce the importance of statistical analysis of the Gaussian distribution before removing uncertainties, evidencing that the use of the quality flag parameter alone may not be sufficient to select the appropriate GEDI data. This is because the quality flag parameter disregards error distribution analysis but considers the energy, sensitivity, amplitude, and real-time surface tracking for each GEDI sample separately [27].

4. Discussion

Atmospheric conditions and system geometries influence the GEDI data and affect its quality flag measurements [13]. Thus, all related GEDI studies have an uncertainty removal approach. The challenge is to find the best threshold that can separate the signal from the noise. Articles using GEDI data determine this threshold based on the quality flag parameter. However, this procedure does not adequately consider points with low RMSE that could be used, especially in the interpolation process.
Using a quality flag threshold, Quiros et al. [28] compared GEDI data with airborne LiDAR in 10 different areas with a mean slope varying between 3.4 and 25.5 degrees and found a global RMSE of 6.05 m and 1.25 in gentle relief. Guerra-Hernández and Pascual [30] applied the quality flag parameter to remove uncertainties and reached a total of 3566 valid observations to assess height growth dynamics in fast-growing species in Spain. They found an RMSE value of 4.48 m, compatible with a higher canopy cover in their GEDI samples.
Spracklen and Spracklen [19] filtered GEDI data distribution in old-growth forests in Ukraine using the quality flag parameter. In addition, the authors had to apply a second step to remove uncertainty samples based on field data. Our study also had to apply a second step based on the IQR threshold to guarantee a useful dataset without erroneous data after quality flag filtering. Kokalj and Mast [21] used GEDI data for archaeological exploration in a forest area, considering two steps to eliminate uncertainties data: (a) visual inspection and (b) quality flag parameter followed by IQR threshold filtering. Despite obtaining an RMSE of 0.98 m, the procedure removed many GEDI samples, creating a significant data gap. Differently, our results showed similar absolute precision with a larger number of GEDI samples.
Sensitivity is ancillary GEDI information used to optimize the outlier removal data approach, where studies use a conservative threshold equal to or higher than 0.9 [17,46]. Boucher et al. [47] analyzed different sensitivity thresholds to identify ground information in various forest canopies and found that values higher than 0.95 guaranteed that 60–80% of waveforms could detect true ground heights. Our results show that it is insufficient to establish an empirical sensitivity threshold to remove GEDI uncertainties. The KS test has been widely used in remote sensing studies to verify data normality [42,48,49,50,51,52,53]. Especially in error removal, few studies used the KS test, but these have demonstrated improvements in different sensors [54,55,56,57,58]. Our approach innovates by using KS testing to analyze the error distribution and improve outlier removal, leveraging all valid GEDI data. The high sample size of the analyzed GEDI data ensures a significant performance of the adopted normality test by matching it with more robust tests, such as Shapiro-Wilk.

5. Conclusions

GEDI data are an important source of altimetry data used in several areas of knowledge. This study innovates by presenting an improved method to remove uncertainties from GEDI elevation data distribution using the KS non-parametric test and absolute accuracy assessment with a reference terrain elevation derived from ALS-DTM in an urban area with gentle relief in Federal District, Brazil. The proposed outlier removal method was better than the method using the quality flag threshold, with wide application in GEDI-related studies. Results indicate a better absolute accuracy (RMSE of 1.33) with a reduction of 56.36% (3325) of the total GEDI dataset, 15.33% higher than the sample reduction from the quality flag benchmark (2883). In addition, the quality flag procedure benchmark removed low RMSE data and selected data with RMSE that would have to be discarded. Calculating KS curves according to pre-defined absolute thresholds allows us to find the optimal inflection point where the dh-DTM distribution has a normal behavior, which occurred in <3 m. This methodology is useful for defining a threshold capable of selecting the maximum GEDI data with a low RMSE value.
This study disregards the influence of high slope and landcover on the altimetric quality of the GEDI data. Thus, future approaches in mountainous and forested areas should be conducted to determine GEDI LiDAR performance under different environmental and acquisition conditions. Furthermore, additional efforts should be conducted by adapting this methodology with other probability distribution assumptions, given that it has been demonstrated that the Laplace distribution could better represent the distribution of the terrain elevation bias [59].

Author Contributions

Conceptualization, F.L.R.B., R.F.G., O.A.d.C.J. and T.P.M.d.L.; methodology, F.L.R.B., R.F.G., O.A.d.C.J. and T.P.M.d.L.; software, F.L.R.B., R.F.G. and O.L.F.d.C.; validation, R.F.G., O.A.d.C.J. and R.A.T.G.; formal analysis, F.L.R.B., R.F.G., O.A.d.C.J. and R.A.T.G.; investigation, F.L.R.B., R.F.G., O.L.F.d.C. and T.P.M.d.L.; resources, R.F.G., O.A.d.C.J. and R.A.T.G.; data curation, F.L.R.B., R.F.G. and T.P.M.d.L.; writing—original draft preparation, F.L.R.B., R.F.G. and T.P.M.d.L.; writing—review and editing, O.A.d.C.J. and R.A.T.G.; supervision, R.F.G., O.A.d.C.J. and R.A.T.G.; project administration, F.L.R.B., R.F.G., O.A.d.C.J., R.A.T.G. and T.P.M.d.L.; funding acquisition, R.F.G., O.A.d.C.J. and R.A.T.G. All authors have read and agreed to the published version of the manuscript.

Funding

Financial support from National Council for Scientific and Technological Development—CNPq; Regulatory Agency for Water, Energy and Sewage of the Federal District—ADASA; Federal District Research Foundation—FAP/DF; and Coordination for the improvement of Higher Education Personnel (CAPES).

Acknowledgments

The authors are grateful for financial support from CNPq, ADASA, FAP/DF and CAPES fellowship (Osmar Abílio de Carvalho Júnior, Renato Fontes Guimarães and Roberto Arnaldo Trancoso Gomes). Special thanks are given to the research group of the Laboratory of Spatial Information System of the University of Brasília for technical support. The authors thank the Brazilian Ministry of Environment, who encouraged research and guaranteed all necessary support. Finally, the authors acknowledge the contribution of anonymous reviewers.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. Study area located in Federal District. The red line represents the center of Brasília city and the black dots are GEDI data used in this study.
Figure 1. Study area located in Federal District. The red line represents the center of Brasília city and the black dots are GEDI data used in this study.
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Figure 2. Methodological flowchart.
Figure 2. Methodological flowchart.
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Figure 3. Comparison between calculated KS (red color), number of GEDI samples (grey color), and RMSE (orange color) curves from absolute dh-DTM thresholds. (a) Calculated KS and RMSE values—10 m interval from |dh| < 100 m and |dh| < 10 m; (b) calculated KS value and number of GEDI samples—10 m interval from |dh| < 100 m and |dh| < 10 m; (c) calculated KS and RMSE values—1 m interval from |dh| < 9 m and |dh| < 1 m; (d) calculated KS value and number of GEDI samples —1 m interval from |dh| < 9 m and |dh| < 1 m.
Figure 3. Comparison between calculated KS (red color), number of GEDI samples (grey color), and RMSE (orange color) curves from absolute dh-DTM thresholds. (a) Calculated KS and RMSE values—10 m interval from |dh| < 100 m and |dh| < 10 m; (b) calculated KS value and number of GEDI samples—10 m interval from |dh| < 100 m and |dh| < 10 m; (c) calculated KS and RMSE values—1 m interval from |dh| < 9 m and |dh| < 1 m; (d) calculated KS value and number of GEDI samples —1 m interval from |dh| < 9 m and |dh| < 1 m.
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Figure 4. Optimal threshold of calculated KS (red color), RMSE (red dashed line) values, and the number of GEDI samples (grey color).
Figure 4. Optimal threshold of calculated KS (red color), RMSE (red dashed line) values, and the number of GEDI samples (grey color).
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Figure 5. Histograms showing the dh-DTM distribution: (a) |dh| < 4 m; (b) |dh| < 3 m; (c) |dh| < 2 m; (d) |dh| < 1 m. The shaded grey curve is the normal distribution.
Figure 5. Histograms showing the dh-DTM distribution: (a) |dh| < 4 m; (b) |dh| < 3 m; (c) |dh| < 2 m; (d) |dh| < 1 m. The shaded grey curve is the normal distribution.
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Figure 6. Quantile–quantile plots showing distributions of: (a) |dh| < 4 m; (b) |dh| < 3 m; (c) |dh| < 2 m; (d) |dh| < 1 m. The light grey line indicates the reference of the QQ plot.
Figure 6. Quantile–quantile plots showing distributions of: (a) |dh| < 4 m; (b) |dh| < 3 m; (c) |dh| < 2 m; (d) |dh| < 1 m. The light grey line indicates the reference of the QQ plot.
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Figure 7. Location of the GEDI samples excluded from <100 to <3 m thresholds. The yellow dots are the GEDI samples.
Figure 7. Location of the GEDI samples excluded from <100 to <3 m thresholds. The yellow dots are the GEDI samples.
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Figure 8. Location of the GEDI samples excluded from <3 to <1 m threshold. The yellow dots are the GEDI samples.
Figure 8. Location of the GEDI samples excluded from <3 to <1 m threshold. The yellow dots are the GEDI samples.
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Figure 9. Boxplots showing the distribution of dh-DTM of the total GEDI dataset. (a) Original distribution of dh-DTM; (b) resulted distribution of dh-DTM after applying a second step based on IQR thresholds.
Figure 9. Boxplots showing the distribution of dh-DTM of the total GEDI dataset. (a) Original distribution of dh-DTM; (b) resulted distribution of dh-DTM after applying a second step based on IQR thresholds.
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Figure 10. Boxplots showing the distribution of dh-DTM. Data selection with 0.9 sensitivity threshold (a). Useful data along all sensitivity ranges (b).
Figure 10. Boxplots showing the distribution of dh-DTM. Data selection with 0.9 sensitivity threshold (a). Useful data along all sensitivity ranges (b).
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Figure 11. Location of GEDI footprint groups derived from both uncertainty removal methods. GEDI footprints from group 1 is represented in yellow dots and group 2 in red dots.
Figure 11. Location of GEDI footprint groups derived from both uncertainty removal methods. GEDI footprints from group 1 is represented in yellow dots and group 2 in red dots.
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Table
Table 1. GEDI metrics used in this study.
Table 1. GEDI metrics used in this study.
MetricsGEDI SourceDescription
Quality flagL2AQuality assessment parameter related to good adjustment between energy, sensitivity, amplitude, and real-time surface tracking. The value “1” means usable information in GEDI data.
SensitivityL2AMaximum canopy cover throughout, the GEDI signal can detect the ground. This ancillary information is concerned with the signal-to-noise ratio.
Elev_lowestmodeL2AElevation of center of lowest mode (ELM) relative to WGS84 ellipsoid.
Table
Table 2. GEDI L2A products downloaded and acquisition dates.
Table 2. GEDI L2A products downloaded and acquisition dates.
GEDI ISS OrbitsAcquisition Dates
GEDI02_A_2019153141419_O02667_T05383_02_001_01.h52 June 2019
GEDI02_A_2019161000303_O02782_T04978_02_001_01.h510 June 2019
GEDI02_A_2019226215413_O03805_T02285_02_001_01.h514 August 2019
GEDI02_A_2019268053258_O04446_T02132_02_001_01.h525 September 2019
GEDI02_A_2019279121858_O04621_T02690_02_001_01.h56 October 2019
GEDI02_A_2019302032210_O04972_T01114_02_001_01.h529 October 2019
GEDI02_A_2019317100329_O05209_T00709_02_001_01.h513 November 2019
GEDI02_A_2019328165040_O05384_T03960_02_001_01.h524 November 2019
GEDI02_A_2020103220644_O07558_T00709_02_001_01.h512 April 2020
GEDI02_A_2020123141942_O07863_T03555_02_001_01.h52 May 2020
GEDI02_A_2020162101244_O08465_T05536_02_001_01.h510 June 2020
GEDI02_A_2020209042759_O09190_T04978_02_001_01.h527 July 2020
GEDI02_A_2020217012015_O09312_T02285_02_001_01.h54 August 2020
Table
Table 3. Statistics from pre-defined thresholds of absolute value of dh-DTM.
Table 3. Statistics from pre-defined thresholds of absolute value of dh-DTM.
Absolute Thresholds |dh|Number of GEDI FootprintsCalculated KSRMSE (m)
10 m interval<100 m37100.38888.91
<90 m37100.38888.91
<80 m37080.38698.67
<70 m36960.37527.55
<60 m36840.36206.60
<50 m36670.33815.41
<40 m36380.28323.70
<30 m36130.18492.33
<20 m36080.16072.13
<10 m35900.12341.90
1 m interval<9 m35780.11091.82
<8 m35640.09721.75
<7 m35550.08911.71
<6 m35340.07381.64
<5 m35040.05711.56
<4 m34330.03731.42
<3 m33250.01721.33
<2 m29070.05421.09
<1 m15600.07370.58
Table
Table 4. Statistics from the dh-DTM quality flag to remove uncertainties and its IQR threshold improvement.
Table 4. Statistics from the dh-DTM quality flag to remove uncertainties and its IQR threshold improvement.
Number of GEDI FootprintsCalculated KSRMSE (m)
Total GEDI dataset76190.30985946.73
Uncertainty removal method by quality flag30900.4965260.46
Uncertainty removal method by quality flag after IQR threshold28830.03201.40
Table
Table 5. Statistics from GEDI footprint groups.
Table 5. Statistics from GEDI footprint groups.
Number of GEDI FootprintsRMSE (m)
GEDI group 15021.32
GEDI group 2603.28
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Barbosa, F.L.R.; Guimarães, R.F.; de Carvalho Júnior, O.A.; Gomes, R.A.T.; de Carvalho, O.L.F.; de Lima, T.P.M. Estimating the Optimal Threshold for Accuracy Assessment of the Global Ecosystem Dynamics Investigation (GEDI) Data in a Gentle Relief Urban Area. Remote Sens. 2022, 14, 3540. https://doi.org/10.3390/rs14153540

AMA Style

Barbosa FLR, Guimarães RF, de Carvalho Júnior OA, Gomes RAT, de Carvalho OLF, de Lima TPM. Estimating the Optimal Threshold for Accuracy Assessment of the Global Ecosystem Dynamics Investigation (GEDI) Data in a Gentle Relief Urban Area. Remote Sensing. 2022; 14(15):3540. https://doi.org/10.3390/rs14153540

Chicago/Turabian Style

Barbosa, Felipe Lima Ramos, Renato Fontes Guimarães, Osmar Abílio de Carvalho Júnior, Roberto Arnaldo Trancoso Gomes, Osmar Luiz Ferreira de Carvalho, and Thyego Pery Monteiro de Lima. 2022. "Estimating the Optimal Threshold for Accuracy Assessment of the Global Ecosystem Dynamics Investigation (GEDI) Data in a Gentle Relief Urban Area" Remote Sensing 14, no. 15: 3540. https://doi.org/10.3390/rs14153540

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