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The Relevance of Forest Structure for Biomass and Productivity in Temperate Forests: New Perspectives for Remote Sensing

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Abstract

Forests provide important ecosystem services such as carbon sequestration. Forest landscapes are intrinsically heterogeneous—a problem for biomass and productivity assessment using remote sensing. Forest structure constitutes valuable additional information for the improved estimation of these variables. However, survey of forest structure by remote sensing remains a challenge which results mainly from the differences in forest structure metrics derived by using remote sensing compared to classical structural metrics from field data. To understand these differences, remote sensing measurements were linked with an individual-based forest model. Forest structure was analyzed by lidar remote sensing using metrics for the horizontal and vertical structures. To investigate the role of forest structure for biomass and productivity estimations in temperate forests, 25 lidar metrics of 375,000 simulated forest stands were analyzed. For the lidar-based metrics, top-of-canopy height arose as the best predictor for describing horizontal forest structure. The standard deviation of the vertical foliage profile was the best predictor for the vertical heterogeneity of a forest. Forest structure was also an important factor for the determination of forest biomass and aboveground wood productivity. In particular, horizontal structure was essential for forest biomass estimation. Predicting aboveground wood productivity must take into account both horizontal and vertical structures. In a case study based on these findings, forest structure, biomass and aboveground wood productivity are mapped for whole of Germany. The dominant type of forest in Germany is dense but less vertically structured forest stands. The total biomass of all German forests is 2.3 Gt, and the total aboveground woody productivity is 43 Mt/year. Future remote sensing missions will have the capability to provide information on forest structure (e.g., from lidar or radar). This will lead to more accurate assessments of forest biomass and productivity. These estimations can be used to evaluate forest ecosystems related to climate regulation and biodiversity protection.

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Acknowledgements

This study originates from the workshop “Space-based Measurement of Forest Properties for Carbon Cycle Research” at the International Space Science Institute in Bern during November 2017. We thank the Thünen Institute for providing the German national forest inventory data. We also want to thank Hans Pretzsch, Peter Biber and Michael Heym (TUM) for their input on forest structure and structure metrics. Kostas Papathanassiou, Victor Cazcarra-Bes, Matteo Pardini and Marivi Tello Alonso (DLR) gave useful insights into linking forest structure and remote sensing. We also thank the anonymous reviewers for their insightful comments and suggestions. This study was part of the HGF-Helmholtz-Alliance “Remote Sensing and Earth System Dynamics” HA-310 under the funding reference RA37012. NK was funded by the German Federal Ministry for Economic Affairs and Energy (BMWi) under the funding reference 50EE1416. FB was funded by the Deutsche Forschungsgemeinschaft (DFG) within the research unit FOR1246 (Kilimanjaro ecosystems under global change: linking biodiversity, biotic interactions and biogeochemical ecosystem processes). HHS was funded by NASA grants 14-TE14-0085 and 16-ESUSPI-16-0015.

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Appendices

Appendix 1: Estimation of Forest Attributes Using Structural Information

1.1 Describing Forest Structure from Field Data

The study examined a total of 13 field-based metrics to describe forest structure, which are listed in the following. Forest structure was described, for example, by basal area BA [m2], which is the sum of all tree basal area values BAi of a forest stand:

$${\text{BA}} = \sum \limits_{i} {\text{BA}}_{i} = \sum \limits_{i} \frac{\pi }{4}d_{i} ^{2} ,$$

where di (m) is the stem diameter of a tree i (in total n trees in a stand). Alternative metrics to describe the horizontal and vertical structures of a forest stand are:

  • standard deviation of stem diameters: \({\text{SD}}_{\text{DBH}} = \sqrt {\frac{1}{n - 1}\sum \limits_{i} \left( {d_{i} - \bar{d}} \right)^{2} }\)

  • coefficient of variation of all stem diameters: \({\text{CV}}_{\text{DBH}} = \frac{{{\text{SD}}_{\text{DBH}} }}{{\overline{{d_{i} }} }}\)

  • skewness of the diameter distribution: \({\text{Skew}}_{\text{DBH}} = \frac{{\frac{1}{n} \cdot \sum \nolimits_{i = 1}^{n} \left( {d_{i} - \bar{d}} \right)^{3} }}{{\left( {\frac{1}{n} \cdot \sum \nolimits_{i = 1}^{n} \left( {d_{i} - \bar{d}} \right)^{2} } \right)^{{\frac{3}{2}}} }}\)

  • Gini coefficient of the diameter distribution: \({\text{Gini}}_{\text{DBH}} = \frac{{2\sum \nolimits_{i} i \cdot d_{i} }}{{n\sum \nolimits_{i} d_{i} }} - \frac{n + 1}{n}\), where di is the sorted list of stem diameters.

\(\bar{d}\) is the mean diameter of all trees within a stand. The same metrics can be calculated also for the tree height distribution (where Hi (m) is the height of a tree) or basal area distribution. Especially for the tree height distribution, we have calculated further metrics.

  • maximum height: \(H_{\hbox{max} } = \hbox{max} \left( {H_{i} } \right)\)

  • mean height: \(H_{\text{mean}} = \frac{1}{n}\sum \nolimits_{i} H_{i}\)

  • quadratic mean height: \(H_{{{\text{quad}} \cdot {\text{mean}}}} = \sqrt {\frac{1}{n}\sum\nolimits_{i} {H_{i}^{{2_{i} }} } }\)

  • Lorey’s height: \(H_{\text{Lorey's}} = \frac{{\sum \nolimits_{i} H_{i} \cdot {\text{BA}}_{i} }}{{\sum \nolimits_{i} {\text{BA}}_{i} }}.\)

1.2 Describing Forest Structure from Remote Sensing Data

Estimating forest structure from remote sensing is more challenging as remote sensing data are not tree-based as in the field-based case. This study examined a total of 25 remote sensing-based metrics to describe forest structure. The basis for most metrics is the lidar-derived canopy height model (CHM) with a spatial resolution of 1 m × 1 m. In this study, we described horizontal structure for each 20 m × 20 m forest stand mainly by the mean top-of-canopy height TCH (m), which is the mean of the canopy height model (CHM):

$${\text{TCH}} = \frac{{\sum \nolimits_{i = 1}^{n} P_{{{\text{CHM}},i}} }}{n},$$

where PCHM,i is the forest height of the CHM in pixel i and n is the number of pixels. Alternative metrics based on the CHM are:

  • maximum height: \(H_{\hbox{max} } = {\hbox{max} } \left( {P_{{{\text{CHM}},i}} } \right)\)

  • quadratic TCH: \({\text{QTCH}} = \sqrt {\frac{{\sum \nolimits_{i = 1}^{n} P_{{{\text{CHM}},i}}^{2} }}{n}}\)

  • relative height of the CHM: \({\text{RH}}_{q} = {\text{quantile}}_{q} \left( {P_{{{\text{CHM}},i}} } \right)\)

It is also possible to calculate the standard deviation, the coefficient of variation and the skewness of the CHM (functions are described above in the field-based section). In this study, we considered further advanced metrics based on the CHM:

  • Shannon index of the CHM: \({\text{Shannon}}_{\text{CHM}} = - \sum \limits_{i = 1}^{{i_{\hbox{max} } }} {\text{CHM}}\left( {h_{i} } \right) \cdot \ln \left( {{\text{CHM}}\left( {h_{i} } \right)} \right),\)

  • with CHM (hi) being the CHM profile value (pixel count) in bin i. CHM (hi) has to be > 0, and CHM (hi) = 0 is ignored,

  • Kurtosis of the CHM: \({\text{Kurtosis}}_{\text{CHM}} = n \cdot \frac{{\sum \nolimits_{i = 1}^{n} \left( {P_{{{\text{CHM}},i}} - \overline{{P_{\text{CHM}} }} } \right)^{4} }}{{\left( {\sum \nolimits_{i = 1}^{n} \left( {P_{{{\text{CHM}},i}} - \overline{{P_{\text{CHM}} }} } \right)^{2} } \right)^{2} }},\)

with n being the total pixel number, PCHM,i the value of pixel i and \(\overline{{P_{\text{CHM}} }}\) the mean value of the CHM (which is the same as TCH),

  • the p–h ratio of the CHM: \(P:H_{{{\text{CHM}}}} = \frac{{h\left( {\mathop {{\text{max}}}\limits_{{i\epsilon \left[ {1,i_{{{\text{max}}}} } \right]}} \left( {{\text{CHM}}\left( {h_{i} } \right)} \right)} \right)}}{{\mathop {{\text{max}}}\limits_{{i\epsilon \left[ {1,i_{{{\text{max}}}} } \right]}} \left( {h_{i} } \right)}}\),

with CHM (hi) being the pixel count in height bin hi and imax is the highest height bin.

Another class of metrics calculates the fractional canopy cover above a certain threshold × (m) using the CHM: \({\text{FCC}}_{x} = \frac{{\sum \nolimits_{{h_{i} = x}}^{{h_{\hbox{max} } }} {\text{CHM}}\left( {h_{i} } \right)}}{{\sum \nolimits_{{h_{i} = 0}}^{{h_{\hbox{max} } }} {\text{CHM}}\left( {h_{i} } \right)}},\) with CHM (hi) the count of CHM pixels in height bin hi and × the height threshold to distinguish canopy from gap.

Instead of using the CHM as the basic information for calculating all these lidar metrics, we have used the vertical foliage profile (VFP) for a second class of metrics. All the above-described metrics can be calculated using the VFP. For this reason, the VFP was divided into 1-m height classes. This height classes can now be used in the equations described above by replacing the CHM. The generation of a VFP profile from a CHM is described below.

1.3 Calculating the Vertical Foliage Profile from a CHM

The vertical foliage profile (VFP) was reconstructed from the CHM profile at 1 m vertical resolution following the approach described by Harding et al. (2001).

$${\text{VFP}}\left( {h_{i} } \right) = \frac{1}{k*\Delta h}*\ln \left( {\frac{{P\left( {h_{i} } \right)}}{{P\left( {h_{i + 1} } \right)}}} \right),$$

with k being the light extinction coefficient, Δh the width of one height bin and P(hi) the value of the cumulative CHM profile in height bin hi. The method reconstructs the vertical leaf profile by giving more weight to lower parts of the profile. All pixels below 5 m height were regarded as ground and the light extinction coefficient was set to 0.3 which has been shown to result in good LAI estimations (Getzin et al. 2017).

1.4 Estimation of Forest Biomass and Productivity Using Forest Structure

See Figs. 9 and 10.

Fig. 9
figure 9

Relationship between observed biomass and estimated biomass derived by three different approaches (see Table 1). Each point represents one of 375,000 forest stands from the forest factory data set. The observed biomass have been derived by summing up the biomass values of all trees in the 20 m × 20 m stand. The estimated biomass was determined using the structural information for each forest stand. a Estimation of biomass using only information from the horizontal structural index TCH (AGB = 9.49 * TCH1.22, r2 = 0.90), b using the vertical structural index SDVFP (AGB = 34.77 * SD 0.48VFP , r2 = 0.01) and c using the vertical and horizontal structural index (AGB = 7.55 * TCH1.20 * SD 0.23VFP , r2 = 0.90). A comparison of the estimated biomass values for the different approaches is shown in Fig. 6a

Fig. 10
figure 10

Relationship between observed and estimated aboveground woody productivity (AWP) for 375,000 forest stands (forest factory data set). Each dot represents one forest stand. a Estimation of productivity using only the horizontal structural index TCH (AWP = 1.68 * TCH0.31, r2 = 0.14), b only the vertical structural index SDVFP (AWP = 4.03 * SD −0.34VFP , r2 = 0.09) and c using the vertical and horizontal structural index (AWP = 2.55 * TCH0.34 * SD −0.39VFP , r2 = 0.31). A comparison of the estimated productivity values with the different approaches is shown in Fig. 6b

Appendix 2: Analysis of the German Forest Inventory Data Set

All analyses so far referred to the forest factory data set. This Appendix reproduces all analyses with the empirical BWI data set. For each forest stand of the BWI data set, a virtual lidar campaign was carried out and the remote sensing-based metrics were then calculated.

See Figs. 11, 12, 13, 14, 15, 16 and 17.

Fig. 11
figure 11

Remote sensing-based estimation of the forest structure using the BWI data set. Each dot represents one stand of the BWI. The figure shows the estimate of a the horizontal forest structure (basal area) from lidar using top-of-canopy height and b the vertical forest structure (tree height heterogeneity) from lidar using the standard deviation of the vertical foliage profile

Fig. 12
figure 12

Overview of all correlations between field-based structural metrics and remote sensing-based metrics based only on the BWI data set. Numbers and gray scale indicate the coefficient of determination. All structural metrics are explained in Appendix 1

Fig. 13
figure 13

Role of forest structure for biomass, derived from the BWI data set (more than 45,000 field plots, 20 m × 20 m). Forest structure is estimated from remote sensing. As horizontal forest structure descriptor the top-of-canopy height (TCH) was used and as vertical structure descriptor the standard deviation of the vertical foliage profile (SDVFP). Shown is the mean aboveground biomass in relation to the forest structure classes. Error bars indicate the standard deviation

Fig. 14
figure 14

Relationship between observed biomass and estimated biomass. Each point represents one forest stand from the forest inventory data set BWI. The observed biomass has been taken from the BWI data set. The estimated biomass values were determined using different approaches (cf. Table 1) and information on forest structure. a Estimation of biomass using only the horizontal structural index TCH, b only the vertical structural index SDVFP and c using the vertical and horizontal structural index. A comparison of the estimated values with the different approaches is shown in Fig. 15

Fig. 15
figure 15

Histogram for forest biomass estimates for Germany based on the BWI data set. The biomass was estimated using three different approaches: H—horizontal structure (blue), V—vertical structure (green) and H + V—horizontal and vertical structures (red). The histogram was compared with the measured values from the BWI data set (black line)

Fig. 16
figure 16

Forest structure of Germany over different gradients. Mean value of the horizontal structure (TCH) from a south to north, c west to east in Germany and e over the altitudinal gradient. Mean value of the vertical structure (SDVFP) from a south to north, c west to east in Germany and e over the altitudinal gradient. The structure values correspond to Fig. 7 (forest structure maps of Germany)

Fig. 17
figure 17

Histograms of structural metrics for forests outside of national parks and inside national parks. As horizontal forest structure descriptor, the top-of-canopy height (TCH, left) was used, and as vertical structure descriptor, the standard deviation of the vertical foliage profile (SDVFP, right) was used

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Fischer, R., Knapp, N., Bohn, F. et al. The Relevance of Forest Structure for Biomass and Productivity in Temperate Forests: New Perspectives for Remote Sensing. Surv Geophys 40, 709–734 (2019). https://doi.org/10.1007/s10712-019-09519-x

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