# Mapping Tree Height in Burkina Faso Parklands with TanDEM-X

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## Abstract

**:**

## 1. Introduction

## 2. Method

#### 2.1. Phase Height

#### 2.2. Mean Canopy Elevation

#### 2.3. Estimation of Tree Height

#### 2.3.1. Effect of Crown Shape

#### 2.3.2. Effect of Vegetation Bias from the DTM

## 3. Experimental Data

#### 3.1. Test Site

#### 3.2. Reference Data

^{2}test site and equally divided between three canopy cover classes, derived using the WorldView-2 image [15,20,48]. This resulted in a total of 1125 measured trees.

^{2}test site.

#### 3.3. TanDEM-X Data Processing

#### 3.4. Estimation of Tree Height from Phase Height and Mean Canopy Elevation

- (i)
- Linear: $f\left(x\right)=x$
- (ii)
- Logarithmic: $f\left(x\right)=\mathrm{ln}\left(x\right)$

- (i)
- Calibrated phase height:$${h}^{\star}={h}_{\mathrm{pha}}^{\star}={\overline{h}}_{\mathrm{pha}}-{c}_{0}$$
- (ii)
- Calibrated mean canopy elevation:$${h}^{\star}={h}_{\mathrm{cnp}}^{\star}={\overline{h}}_{\mathrm{cnp}}-{c}_{1}$$

## 4. Results

#### 4.1. Geometric Distortion

#### 4.2. Tree Positioning Accuracy

#### 4.3. Tree Height Estimation

#### 4.4. Effect of Species/Genera on Mean Canopy Elevation

#### 4.5. Tree Height Estimation with Empirical Models

## 5. Discussion

#### 5.1. Tree Height Estimation Performance

#### 5.2. Implementation Aspects and InSAR Data Considerations

## 6. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Illustration of some quantities used in this paper. The top-of-canopy tree height ${h}_{top}$ is a purely geometrical quantity. Two InSAR quantities related to tree height are also shown: (1) Phase height (${h}_{\mathrm{pha}}$) is the estimated difference between a digital elevation model (DEM) and a digital terrain model (DTM). (2) Mean canopy elevation (${h}_{\mathrm{cnp}}$ ) is a model-based estimate of canopy height above the DTM. The ground range offset $\mathsf{\Delta}{r}_{\mathrm{gr}}$ is caused by geometrical distortion due to the slanted measurement geometry of SAR.${D}_{\mathrm{avg}}$ is the average diameter of the tree crown and ${d}_{\mathrm{bh}}$ is the stem diameter at breast height (1.3 m).

**Figure 2.**Acquisition geometry for a right-looking SAR system, with the incidence angle ($\theta $) and heading angle ($\alpha $) shown together with the principal axes of a SAR acquisition. $\left(E,N\right)$ are the respective east and north coordinates of a grid cell. (

**a**) Elevation plane; (

**b**) ground plane.

**Figure 3.**A simple geometric model is used to investigate the effect of crown shape on the observed difference between ${h}_{\mathrm{top}}$ and ${h}_{\mathrm{cnp}}$. (

**a**) Trees are modelled as ellipsoids and crown shape bias is the maximal height difference within a resolution cell centred on the treetop. (

**b**) Sample modelling results for ${\delta}_{\mathrm{DEM}}=3$ m.

**Figure 4.**The effect of vegetation bias from the DTM on tree height estimation. (

**a**) Vegetation bias is the offset between the DTM and the true ground surface, caused by vegetation objects. (

**b**) Sample results showing the effect of vegetation bias from the DTM on tree height estimation, as modelled by TLM for $\kappa =0.063$ ($\mathrm{HOA}\approx 100$ m).

**Figure 5.**Coverage of the data used in this study and location of the Saponé test site. Ouagadougou, the capital of Burkina Faso, is located about 30 km north of Saponé. The outline for optical data represents the coverage of the two high-resolution satellite images used in this study (one from WorldView-2 and one from Pléiades). Basemap: © OpenStreetMap contributors, CC-BY-SA.

**Figure 6.**Sample mapping results for a 1000 m × 200 m area in Saponé. The seven panels show: (

**a**) orthorectified satellite image from Pléiades, backscatter coefficient (${\mathsf{\sigma}}^{0}$) averaged across all images for the (

**b**) descending and (

**c**) ascending orbit directions, with red arrows indicating look directions; images of ${h}_{\mathrm{pha}}$ for the (

**d**) descending and (

**e**) ascending orbit directions; (

**f**) image of ${h}_{\mathrm{pha}}$ combined from ascending and descending data; and (

**g**) image of ${h}_{\mathrm{cnp}}$ combined from ascending and descending data. Solid lines outline the three areas A, B, and C discussed in Section 4.1.

**Figure 7.**Comparison of the estimated (

**a**) phase height (${\overline{h}}_{\mathrm{pha}}$) and (

**b**) mean canopy elevation (${\overline{h}}_{\mathrm{cnp}}$) with reference in situ tree height (${h}_{\mathrm{top}}$) for all 915 trees from 15 species/genera inventoried during three field campaigns in Saponé. Green dots indicate individual trees. The solid red line describes the bias in the data, and it was obtained by fitting a linear model to the data using orthogonal distance regression. The solid black line shows the zero-bias case. The corresponding estimation statistics are shown in Table 5.

**Figure 8.**Dependence of the estimated mean canopy elevation (${\overline{h}}_{\mathrm{cnp}}$) on the in situ-measured tree height (${h}_{\mathrm{top}}$) and species/genera for the 915 trees shown in Figure 6. $\langle {D}_{\mathrm{avg}}\rangle $ and $\langle {h}_{\mathrm{top}}\rangle $ are the average crown diameter and tree height for each species while $M$ is the number of trees. Marker sizes are proportional to ${D}_{\mathrm{avg}}$.

**Figure 9.**Bias (from Figure 8) versus average ${D}_{\mathrm{avg}}/{h}_{\mathrm{top}}$ for the 15 species/genera. Marker sizes are proportional to the average ${h}_{\mathrm{top}}$ (also given in parentheses for each species/genus). The vertical and horizontal bars indicate the 25th and 75th percentile values for each quantity.

**Figure 10.**Tree height estimation performance for the selected best-performing models using: (

**a**) TDM data only, (

**b**) ${D}_{\mathrm{avg}}$ only, (

**c**) ${d}_{\mathrm{bh}}$ only, (

**d**) ${D}_{\mathrm{avg}}$ and ${d}_{\mathrm{bh}}$, (

**e**) TDM data and species information, (

**f**) ${D}_{\mathrm{avg}}$, ${d}_{\mathrm{bh}}$, and species information. Mathematical expressions and estimation statistics are shown in Table 6. For (

**a**–

**d**), the models were fitted to data from all 915 trees, disregarding the species/genus of the trees. For (

**e**,

**f**), the models were fitted individually for each species/genus with at least ten times more trees than model parameters. In each panel, the first scatterplot from the left shows the estimated tree height (${\widehat{h}}_{\mathrm{top}}$) on the $y$ -axis against the reference tree height (${h}_{\mathrm{top}}$) on the $x$ -axis, while the second scatterplot shows the obtained tree height residual (${h}_{\mathrm{top}}-{\widehat{h}}_{\mathrm{top}}$) against average canopy diameter (${D}_{\mathrm{avg}}$).

Metric | Explanation |
---|---|

In situ-measured tree properties | |

${h}_{\mathrm{top}}$ | Top-of-canopy height |

${d}_{\mathrm{bh}}$ | Stem diameter at breast height (1.3 m) |

${D}_{\mathrm{avg}}$ | Crown diameter averaged across two perpendicular directions |

Raster data | |

DTM | Digital terrain model (estimated ground elevation above a reference surface) |

DEM | Digital elevation model (interferometric height above a reference surface) |

${h}_{\mathrm{pha}}$ | Phase height (DEM elevation above the DTM) |

${h}_{\mathrm{cnp}}$ | Mean canopy elevation (model-based estimate of canopy elevation above the DTM) |

Tree height estimates | |

${\overline{h}}_{\mathrm{pha}}$ | $\mathrm{Maximal}{h}_{\mathrm{pha}}$ within the extent of the crown for a single tree |

${\overline{h}}_{\mathrm{cnp}}$ | $\mathrm{Maximal}{h}_{\mathrm{cnp}}$ within the extent of the crown for a single tree |

${h}_{\mathrm{pha}}^{\star}$ | $\mathrm{Calibrated}{\overline{h}}_{\mathrm{pha}}$ (shifted by a constant so that a regression line for all trees goes through zero) |

${h}_{\mathrm{cnp}}^{\star}$ | Calibrated ${\overline{h}}_{\mathrm{cnp}}$ (shifted by a constant so that a regression line for all trees goes through zero) |

${\widehat{h}}_{\mathrm{top}}$ | Top-of-canopy height estimate from an empirical model |

Model parameters | |

${h}_{\mathrm{TLM}}$ | Distance between ground and vegetation levels in the two-level model (TLM) |

**Table 2.**Summary of the in situ data from Saponé, Burkina Faso, used in this study. The second column from the left contains the number of trees fulfilling the conditions described in Section 3.2, as well as the total number of trees sampled in field.

Dates | Used Trees (Total) | ${\mathit{h}}_{\mathbf{top}}\left(\mathbf{m}\right)$ | ${\mathit{D}}_{\mathbf{avg}}\left(\mathbf{m}\right)$ | ||||
---|---|---|---|---|---|---|---|

Min | Mean | Max | Min | Mean | Max | ||

October–December 2012 | 401 (1125) | 2.5 | 7.0 | 20.0 | 1.0 | 6.0 | 28.0 |

October 2017 | 241 (637) | 2.0 | 9.9 | 25.0 | 2.0 | 9.3 | 27.7 |

June 2018 | 273 (321) | 3.5 | 11.1 | 23.9 | 2.0 | 8.2 | 25.0 |

All | 915 (2083) | 2.0 | 9.0 | 25.0 | 1.0 | 7.5 | 28.0 |

**Table 3.**Summary of the SAR acquisitions over Saponé, Burkina Faso used in this study. “No” refers to the relative orbit number, “Dir” refers to orbit direction (“dsc” is descending and “asc” is ascending), $\alpha $ and $\theta $ are the flight heading and incidence angles, respectively (see Figure 2), “Pol” refers to polarisation, “Res” refers to resolution (“grg” is ground range and “az” is azimuth), and “Temp” refers to temperature.

Date | Time (UTC): | Orbit | Pol | HOA (m) | Res (m) | Temp (°C) | ||||
---|---|---|---|---|---|---|---|---|---|---|

No | Dir | $\mathit{\alpha}{(}^{\circ})$ | $\mathit{\theta}{(}^{\circ})$ | grg | az | |||||

24 January 2018 | 6:03 AM | 63 | dsc | 191 | 32 | HH | 39 | 2.1 | 1.1 | 16 |

26 February 2018 | 47 | 24 | ||||||||

31 March 2018 | 55 | 25 | ||||||||

9 February 2018 | 6:09 PM | 147 | asc | 349 | 25 | 49 | 2.8 | 1.1 | 28 | |

20 February 2018 | 59 | 36 | ||||||||

25 March 2018 | 79 | 33 | ||||||||

5 April 2018 | 87 | 37 |

**Table 4.**Tree positioning performance for phase height and mean canopy elevation images, individually for ascending and descending data and for the final, combined images. The results are provided separately for three tree height groups: short (below 8 m), medium (8–16 m), and tall (above 16 m), as well as for all trees. The biases (mean offsets) between measured and reference tree positions in the east and north directions are denoted with ${\mu}_{E}$ and ${\mu}_{N}$, respectively, while the corresponding standard deviations are ${\sigma}_{E}$ and ${\sigma}_{N}$. The highlighted values are discussed in Section 4.2.

$$\mathbf{Phase}\mathbf{height}\left({\mathit{h}}_{\mathbf{pha}}\right)$$
| ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Orbit Direction: | Ascending | Descending | Combined | |||||||||

Tree height group: | <8 | 8–16 | >16 | All | <8 | 8–16 | >16 | All | <8 | 8–16 | >16 | All |

${\mu}_{E}$ | −0.1 | 1.0 | 6.0 | 0.4 | 0.2 | −0.5 | −3.9 | −0.2 | −0.0 | 0.3 | 1.0 | 0.1 |

${\mu}_{N}$ | 0.2 | 0.2 | 0.9 | 0.2 | 0.0 | −0.1 | −0.5 | −0.1 | 0.0 | −0.1 | 1.3 | 0.0 |

${\sigma}_{E}$ | 1.5 | 2.8 | 4.1 | 2.3 | 1.5 | 3.0 | 5.1 | 2.4 | 1.5 | 2.9 | 7.3 | 2.3 |

${\sigma}_{N}$ | 2.4 | 2.9 | 3.4 | 2.6 | 1.5 | 2.8 | 4.1 | 2.2 | 1.6 | 2.8 | 3.3 | 2.1 |

Mean canopy elevation (${h}_{\mathrm{cnp}}$) | ||||||||||||

Orbit direction: | Ascending | Descending | Combined | |||||||||

Tree height group: | <8 | 8–16 | >16 | All | <8 | 8–16 | >16 | All | <8 | 8–16 | >16 | All |

${\mu}_{E}$ | −0.2 | −1.2 | −0.6 | −0.6 | 0.1 | 1.5 | 2.8 | 0.6 | −0.0 | 0.2 | 0.4 | 0.1 |

${\mu}_{N}$ | 0.2 | 0.6 | −0.2 | 0.3 | 0.1 | 0.6 | 2.2 | 0.4 | 0.1 | 0.7 | 0.5 | 0.3 |

${\sigma}_{E}$ | 1.6 | 2.5 | 5.5 | 2.2 | 1.4 | 2.8 | 3.7 | 2.2 | 1.5 | 2.5 | 3.5 | 2.0 |

${\sigma}_{N}$ | 1.6 | 2.8 | 3.3 | 2.2 | 1.6 | 2.8 | 3.9 | 2.2 | 1.5 | 2.7 | 3.1 | 2.1 |

**Table 5.**Tree height estimation statistics for ${\overline{h}}_{\mathrm{pha}}$ and ${\overline{h}}_{\mathrm{cnp}}$. “Figure” refers to the figure with the corresponding scatterplot, $N$ is the number of available tree measurements, and $S$ is the number of species/genera represented in the available tree measurements. Bias and standard error metrics are given in three tree height categories: short trees (below 8 m), medium trees (8–16 m), and tall trees (above 16 m), as well as for all trees.

Figure | Tree Height Estimate | N | S | r_{p} (%) | Bias (m) | SE (m) | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

<8 | 8–16 | >16 | All | <8 | 8–16 | >16 | All | |||||

Figure 7a | ${\overline{h}}_{\mathrm{cnp}}$ | 915 | 15 | 75 | −0.7 | −1.5 | −3.9 | −1.3 | 2.6 | 3.1 | 2.9 | 3.0 |

Figure 7b | ${\overline{h}}_{\mathrm{pha}}$ | 915 | 15 | 73 | −2.7 | −4.2 | −7.7 | −3.7 | 2.2 | 2.8 | 2.9 | 2.9 |

**Table 6.**Tree height estimation statistics for selected empirical models of TDM data and in situ-measurements. “Figure” refers to the figure with the corresponding scatterplot, $P$ is the total number of estimated parameters, $N$ is the number of available tree measurements, and $S$ is the number of species/genera represented in the available tree measurements. For the species-specific models, the ratio between the number of trees within each species/genus and the number of model parameters to-be-estimated was required to be at least 10, thus reducing the number of included species and the total number of trees. Bias and standard error metrics are given in three tree height categories: short trees (below 8 m), medium trees (8–16 m), and tall trees (above 16 m), as well as for all trees. This table is an excerpt from the full results that can be found in Supplementary Materials.

Figure | Model Properties | ${\mathit{r}}_{\mathit{P}}(\%)$ | Bias (m) | SE (m) | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Formula | $\mathit{P}$ | $\mathit{N}$ | $\mathit{S}$ | <8 | 8–16 | >16 | All | <8 | 8–16 | >16 | All | ||

Empirical models and species-independent parameters | |||||||||||||

Figure 10a | $\mathrm{ln}\left({\widehat{h}}_{\mathrm{top}}^{\prime}\right)={p}_{1}\mathrm{ln}\left({h}_{\mathrm{cnp}}^{\star}\right)$ | 1 | 915 | 15 | 75 | 0.8 | −0.3 | −3.0 | 0.0 | 2.4 | 2.9 | 2.8 | 2.8 |

Figure 10b | ${\widehat{h}}_{\mathrm{top}}^{\prime}={p}_{0}+{p}_{2}{D}_{\mathrm{avg}}$ | 2 | 915 | 15 | 76 | 1.5 | −1.0 | −3.3 | 0.0 | 1.3 | 2.4 | 4.0 | 2.6 |

Figure 10c | $\mathrm{ln}\left({\widehat{h}}_{\mathrm{top}}^{\prime}\right)={p}_{3}\mathrm{ln}\left({d}_{\mathrm{bh}}\right)$ | 1 | 915 | 15 | 79 | 1.0 | −0.4 | −4.2 | 0.0 | 1.8 | 2.5 | 2.2 | 2.5 |

Figure 10d | $\mathrm{ln}\left({\widehat{h}}_{\mathrm{top}}^{\prime}\right)={p}_{2}\mathrm{ln}\left({D}_{\mathrm{avg}}\right)+{p}_{3}\mathrm{ln}\left({d}_{\mathrm{bh}}\right)+{p}_{4}{\mathrm{ln}}^{2}\left({D}_{\mathrm{avg}}\right)$ | 3 | 915 | 15 | 82 | 1.1 | −0.6 | −3.5 | 0.0 | 1.4 | 2.3 | 2.6 | 2.3 |

Empirical models and species-specific parameters | |||||||||||||

Figure 10e | ${\widehat{h}}_{\mathrm{top}}^{\prime}={p}_{0}+{p}_{1}{h}_{\mathrm{cnp}}^{\star}$ | 16 | 853 | 8 | 79 | 0.7 | −0.3 | −2.4 | 0.0 | 2.2 | 2.7 | 3.2 | 2.6 |

Figure 10f | $\mathrm{ln}\left({\widehat{h}}_{\mathrm{top}}^{\prime}\right)={p}_{2}\mathrm{ln}\left({D}_{\mathrm{avg}}\right)+{p}_{3}\mathrm{ln}\left({d}_{\mathrm{bh}}\right)$ | 16 | 853 | 8 | 87 | 0.7 | −0.3 | −3.0 | 0.0 | 1.4 | 2.0 | 3.0 | 2.0 |

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**MDPI and ACS Style**

Soja, M.J.; Karlson, M.; Bayala, J.; Bazié, H.R.; Sanou, J.; Tankoano, B.; Eriksson, L.E.B.; Reese, H.; Ostwald, M.; Ulander, L.M.H.
Mapping Tree Height in Burkina Faso Parklands with TanDEM-X. *Remote Sens.* **2021**, *13*, 2747.
https://doi.org/10.3390/rs13142747

**AMA Style**

Soja MJ, Karlson M, Bayala J, Bazié HR, Sanou J, Tankoano B, Eriksson LEB, Reese H, Ostwald M, Ulander LMH.
Mapping Tree Height in Burkina Faso Parklands with TanDEM-X. *Remote Sensing*. 2021; 13(14):2747.
https://doi.org/10.3390/rs13142747

**Chicago/Turabian Style**

Soja, Maciej J., Martin Karlson, Jules Bayala, Hugues R. Bazié, Josias Sanou, Boalidioa Tankoano, Leif E. B. Eriksson, Heather Reese, Madelene Ostwald, and Lars M. H. Ulander.
2021. "Mapping Tree Height in Burkina Faso Parklands with TanDEM-X" *Remote Sensing* 13, no. 14: 2747.
https://doi.org/10.3390/rs13142747