# Biomass Growth from Multi-Temporal TanDEM-X Interferometric Synthetic Aperture Radar Observations of a Boreal Forest Site

^{1}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Main Dataset

#### 2.2. Method for Interpretation of TanDEM-X Dataset

_{gr}, and the vegetation layer, σ

_{veg}, the two-way attenuation, α, back and forth through the medium with a height h, exp(−αh), and η, the area-fill, which is the fraction of the area covered by vegetation which attenuates the microwaves.

_{sys}, and is due to system noise. The phase height and coherence are expressed in IWCM as functions of α, σ

_{gr}, σ

_{veg}, γ

_{sys}, HoA, and the stem volume, V, and the backscatter as function of α, σ

_{gr}, σ

_{veg}, and V.

^{3}was used, a factor that varies with species composition and age [29]. For η(V), an expression based on ALS observations of the vegetation ratio in Remningstorp was used [3], cf. also [30],

#### 2.3. Supporting Dataset

#### 2.3.1. Field Data from 2008

#### 2.3.2. Field Data from 2015

^{2}density.

#### 2.3.3. Methods for Biomass Estimates from 2015

## 3. Results

#### 3.1. Linear Regression Results

#### 3.2. Interpretation of Linear Regression Results

#### AGB Approximately Proportional to Phase Height

_{pr}Ph with κ

_{pr}= 10.3, and on the other hand AGB as determined from IWCM from (3), and based on the first TanDEM-X acquisition. The difference in growth for the individual stands varies from −40% to +20%. Assuming AGB proportional to phase height means that the AGB growth is proportional to phase height growth. The difference in expected AGB growth relative IWCM results is seen to vary with AGB, due to the non-linear variation between Ph and AGB of the stands.

_{pr}, and for that purpose, we need to know the phase height. Since the phase height is related to the product of vegetation density and height, phase height will vary between different forest types. In addition, we have changes associated with changes in radar scattering, change of HoA, etc. For the 12 summer acquisitions from Krycklan, we have a variation of κ

_{pr}between 9.5 and 10.8, indicating the variability of the relation between AGB and phase height.

#### 3.3. Ratio between AGB Change and Phase Height Change Using IWCM

_{gr}, σ

_{veg}, and HoA (most influential of the model parameters is α). We now introduce the ratio factor RF, cf. [20], the ratio between the AGB growth rate and the Ph growth rate according to IWCM

#### 3.4. Changes Related to Manual Impact and to Tree Species

#### 3.4.1. TanDEM-X Observations of Change, e.g., Clear Cutting or Thinning

#### 3.4.2. TanDEM-X Growth Related to Tree Types and Age

#### 3.5. Comparison with Other Datasets

## 4. Discussion

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Illustration of the observed phase heights of each of the 31 stands. Five stands are shown per plot, except the first plot, which includes six stands. Each stand is illustrated in separate color.

**Figure 2.**

**Upper row**: location of test site Krycklan and relation between stem volume and aboveground dry biomass (AGB) data from BIOSAR 2008.

**Lower row**: illustration of the allometries; dotted lines and local data from Krycklan regarding Lorey’s height vs. AGB, and area-fill η(V) vs. AGB. Note that η(V) is expected to be higher than ALS estimated vegetation ratio, due to the difference between laser and radar frequencies.

**Figure 3.**HoA and phase height estimated by the model for the 12 summer acquisitions, including the phase height for the mean parameters in Table 1 (black line).

**Figure 4.**Illustrates the phase height measured 17 June 2011 compared with the other measurements of phase height (x) and the corresponding Interferometric Water Cloud Model (IWCM) expressions (dotted lines), in order to illustrate the stability of the observations and the accuracy of the model.

**Figure 5.**(

**a**) Biomass estimates for 2008 using Petersson’s, P, and Marklund’s, M, model; (

**b**) the same for 2015; (

**c**) biomass 2008 compared with 2015 using Petersson’s model; and (

**d**) the same as (

**c**) using Marklund’s model. Note that the 2008 values are based on in situ data, whereas the biomass estimates for 2015 are based on ALS data, and in situ data from different plots compared to 2008.

**Figure 7.**Linear regression curves of phase height, Ph, and curves representing one standard deviation, σPh, around the regression line for two stands with maximum and minimum phase height growth (stand 21580: age = 35 years, AGB = 43 Mg/ha, stand 3611: age = 157 years, AGB = 117 Mg/ha.). Relative spread for all stands around a linear regression line for Ph is illustrated with the two stands marked (upper right). Ph 2011 in upper and lower right figures are observations from 17 June 2011.

**Figure 8.**Measured relative phase height growth in percent and the associated relative AGB and hM growth as determined from IWCM with mean of dPh/dt = 0.16 m/yr. (AGB and Lorey’s height, hL, from 2008.).

**Figure 9.**Illustrating growth rate with AGB proportional to the phase height or determined using IWCM. The figure to the left compares growth determined by assuming proportionality between AGB and phase height, and by IWCM. The figure to the right illustrates the growth difference between the expression in (3) and κ

_{pr}dPh/dt in Mg/ha/year versus AGB 2008.

**Figure 10.**(

**a**) RF, the ratio between biomass change per year relative phase height change per year, determined from linear regression over all acquisitions of phase height and estimated biomass as derived by IWCM (x), or according to (4), as function of Ph_mean(V) (dotted line); (

**b**) the ratio as function of AGB derived by IWCM 17 June 2011, and (

**c**) the growth rate of AGB versus the growth rate of Ph (x). In (

**a**–

**c**) the dashed line represents proportionality between AGB and Ph with the factor 10.3.

**Figure 11.**Illustrating estimated AGB with ± one standard deviation from the linear slope over the observation period of 3.2 years for stands with possible manual effects. Lower right figure illustrates dates for three storms (triangle), aerial photo (

**+**) and SPOT-5 image (•).

**Figure 12.**Growth rate for 27 stands with no specific indication of manual influence (growth rate > 0) as function of AGB from 2015 and age updated from BIOSAR 2008 and for different species mixture. ▲ > 60% Picea, ● > 60% Pinus, ♦ > 30% deciduous.

**Figure 13.**TanDEM-X/IWCM growth rates have been used for updating the biomass from 2008 to 2015, (

**a**) using Marklund’s model and in situ data, 08M, and compared with the biomass in 2015 using Marklund’s model and ALS, (

**b**) the same with Petersson’s model. (

**c**) Estimates of AGB from in situ measurements according to Petersson’s model, 08P, compared with BIOSAR 2008 reported AGB from in situ. Stands marked by o are discussed in the text.

**Figure 14.**(

**a**) AGB estimated from ALS compared to AGB estimated from in situ, booth from BIOSAR 2008, and (

**b**) AGB in situ—AGB ALS illustrated for each stand, and (

**c**) AGB growth according to TanDEM-X/IWCM, marked TDM, compared to growth according to ALS using the model by Petersson, marked P. Lines marking 40% and 100% of GR P. ▲ > 60% Picea, ● > 60% Pinus, ♦ > 30% deciduous.

**Figure 15.**(

**a**) Results for stem volume growth from [43] determined by multi-temporal ALS in Kalkkinen and (

**b**) by TanDEM-X and IWCM in Krycklan. (V 2015 from AGB P 15 using conversion factor BF).

**Table 1.**Mean values and standard deviation for the 12 TanDEM-X observations of the related IWCM parameters.

α | σ_{gr} | σ_{veg} | γ_{sys} | |
---|---|---|---|---|

mean | 0.12 | 0.15 | 0.31 | 0.94 |

stddev | 0.01 | 0.03 | 0.03 | 0.03 |

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**MDPI and ACS Style**

Askne, J.I.H.; Persson, H.J.; Ulander, L.M.H.
Biomass Growth from Multi-Temporal TanDEM-X Interferometric Synthetic Aperture Radar Observations of a Boreal Forest Site. *Remote Sens.* **2018**, *10*, 603.
https://doi.org/10.3390/rs10040603

**AMA Style**

Askne JIH, Persson HJ, Ulander LMH.
Biomass Growth from Multi-Temporal TanDEM-X Interferometric Synthetic Aperture Radar Observations of a Boreal Forest Site. *Remote Sensing*. 2018; 10(4):603.
https://doi.org/10.3390/rs10040603

**Chicago/Turabian Style**

Askne, Jan I. H., Henrik J. Persson, and Lars M. H. Ulander.
2018. "Biomass Growth from Multi-Temporal TanDEM-X Interferometric Synthetic Aperture Radar Observations of a Boreal Forest Site" *Remote Sensing* 10, no. 4: 603.
https://doi.org/10.3390/rs10040603