# A Simple Method for Retrieving Understory NDVI in Sparse Needleleaf Forests in Alaska Using MODIS BRDF Data

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## Abstract

**:**

^{2}and RMSE of 0.99 and 0.03, respectively. Using the MODIS BRDF data, we achieved an estimate of NDVIu close to the in situ measured value (0.61 vs. 0.66 for estimate and measurement, respectively) and reasonable seasonal patterns of NDVIu in 2010 to 2013. The results imply a potential application of the retrieved NDVIu to improve the estimation of overstory LAI for sparse boreal forests and ultimately to benefit studies on carbon cycle modeling over high-latitude areas.

## 1. Introduction

## 2. Study Area and Data Collection

#### 2.1. Study Area

**Figure 1.**Demonstration of the study area and land-cover types derived from MODIS data. PFRR denotes our investigation site, Poker Flat Research Range, and

**a**,

**b**, and

**c**indicate the locations of pixels selected as examples of shrubs, savanna, and evergreen needleleaf forest, respectively (see Section 4.2 for details).

#### 2.2. In Situ Data

**Figure 2.**Understory reflectance spectra collected at Poker Flat Research Range (PFRR), Alaska (N is the number of collected spectra.)

#### 2.3. MODIS Data

#### 2.4. Simulation Data Set

^{2}plot with stand density of 3978 trees∙ha

^{−1}(358 trees in the 30 × 30-m

^{2}plot). The average tree height and diameter at breast height (DBH) were 2.4 ± 1.1 m and 1.2 ± 0.079 cm, respectively. The crown diameters of all trees in the plot were determined through an empirical estimation equation based on DBH (i.e., crown diameter [m] = 0.044 DBH + 0.66, r

^{2}= 0.23, p < 0.01). The forest stand is composed of three layers: tree canopy, grass, and floor layers. The LAI for the tree canopy and the grass layer are denoted as LAIo (overstory) and LAIu (understory), respectively. The term “understory layer” here refers to the combination of the grass and floor layers. The LAIo changed from 0 to 2.0 at an interval of 0.1, and the LAIu varied from 0 to 2.5 at the same interval. Because we could not measure the bihemispherical reflectance and transmittance of the needle trees in this study, we instead used the bihemispherical reflectance and transmittance values of black spruce needle, which is the dominant species in our study area, reported by Hall et al. [29]. We also used the bihemispherical reflectance and transmittance values of grass reported by Myneni et al. [30], which are used for the MODIS global LAI product. Table 1 summarizes the optical parameters used in the simulation, where “floor reflectance” is the average reflectance of the non-vegetation objects collected in field investigations. Eight combinations of the solar-view angles were used: SZ = 45°, VZ = 0°, 10°, 20°, 30°, and RA = 40°, 140°. The BRF in red and near-infrared (NIR) bands for these angles were calculated from the FLiES.

Needle Reflectance ^{1} | Needle Transmittance ^{1} | Grass Reflectance ^{2} | Grass Transmittance ^{2} | Stem Reflectance | Floor Reflectance | |
---|---|---|---|---|---|---|

Red | 0.074 | 0.023 | 0.116 | 0.112 | 0.051 | 0.079 |

NIR | 0.466 | 0.387 | 0.427 | 0.479 | 0.091 | 0.225 |

## 3. Development of a New Method for Retrieving NDVIu

#### 3.1. Theory

**Figure 3.**Conceptual demonstration of the method for retrieving NDVIu (5 × 5 window with the center as target pixel; only the pixels with the same vegetation type as the target pixel are used for regression analysis. Grids with different format indicate different land-cover categories).

#### 3.2. Implementation Steps

_{i}= a

_{i}× NDVI

_{0}+ b

_{i}

_{0}denotes the NDVI values for a nadir-view position (SZ = 45°, VZ = 0° and RA = 140°), and NDVI

_{i}(i = 1, 2, …, 7) denotes the NDVI values for other seven solar-view angles.

_{i}has the lowest variation. Let the NDVI

_{0}change from 0 to 1.0 at an interval of 0.01. We calculated the standard deviation (SD) among the seven regression equations (shown as Equation (1)) corresponding to each value of NDVI

_{0}. Consequently, we obtained the value of NDVI

_{0}that corresponds to the lowest SD (denoted as NDVI

_{0,S}).

## 4. Results

#### 4.1. Results for Simulation Data Set

^{2}values higher than 0.99. The variation in the seven regression lines decreased from the higher tail of the NDVI values, then increased beyond the convergence point of the regression lines. This point is the position at which the SD of the seven regression lines has the smallest value (denoted by a red dashed line in Figure 4). Then, the estimation of NDVIu is calculated as the average of the seven regression lines corresponding to the position at which the SD is smallest. The cases corresponding to other levels of LAIu have similar outcomes. These results imply that the rationale of our proposed method is reasonable.

**Figure 4.**An example of scatterplots of the relationship between the nadir-view NDVI and NDVI for other bidirectional angles from the simulation data set.

^{2}and RMSE of 0.99 and 0.013 and the slope and intercept very close to “1” and “0”, respectively. This is an idealized case without contamination caused by measurement errors, and the simulated conditions totally satisfy the basic assumptions of the proposed method. The high accuracy of the retrieval results demonstrates that the proposed method is theoretically reasonable.

**Figure 5.**Comparison between true and retrieved NDVIu values for cases with LAIu ranging from 0 to 2.5.

**Figure 6.**RSME for NDVIu retrieval corresponding to different levels of coefficient of variation (CV) for LAIo.

#### 4.2. Results of MODIS Data

- (1)
- The number of pixels used for regression analysis should be greater than nine.
- (2)
- All the R
^{2}values for the linear regression should be higher than 0.7. - (3)
- The retrieval values of NDVIu should not be larger than the minimum NDVI within the 5 × 5 window.

**Figure 7.**Examples of scatterplots of the relationship between the nadir-view NDVI and NDVI for other bidirectional angles from the MODIS BRDF data for three different biomes: (

**a**) shrubs; (

**b**) savanna; and (

**c**) evergreen needleleaf forest (ENF).

**Figure 8.**Three examples of the spatial distribution of retrieved understory NDVI (NDVIu) on (

**a**) 10 June; (

**b**) 20 July; and (

**c**) 29 August 2013, using the 5 × 5 window.

**Figure 9.**Time series of the average NDVIu for different biome types (shrubs, savanna, and evergreen needleleaf forest) in years (

**a**) 2013; (

**b**) 2012; (

**c**) 2011; and (

**d**) 2010 (The average of in situ measured understory NDVI on 17 July 2013, at PFRR is also shown in (a) for comparison).

## 5. Discussion

#### 5.1. Angular Variations in BRF for the Stands with Variable LAIo Values

#### 5.2. How to Determine the Window Size

**Figure 10.**Coefficient of variation (CV) in BRF at red and NIR bands, and NDVI for the stands with different values of LAIo.

**Figure 11.**An example of NDVIu retrieval using window sizes of (

**a**) 5 × 5 and (

**b**) 7 × 7. (The 3 × 3 window size cannot provide satisfactory samples for regression analysis; thus, is not shown here).

**Figure 12.**Spatial distribution of retrieved understory NDVI (NDVIu) on (

**a**) 10 June; (

**b**) 20 July; and (

**c**) 29 August 2013, using the 7 × 7 window.

#### 5.3. Toward Practical Applications of the Retrieved NDVIu

^{2}) is similar to its two ambient pixels (i.e., 5 × 5 pixel window). This assumption may not be satisfied for some forests. Therefore, we cannot expect that our method can be applicable everywhere. Consequently, we cannot derive the retrieval of NDVIu in some cases. Improving the retrieval rate of NDVIu will be carried out in future works. However, the present approach can be regarded as an alternative to the data bank method for dealing with the background properties (e.g., [12,14]), and it provides a much larger number of samples than conventional in situ methods do by covering wide areas and long periods. It is also worth noting that the performance of the proposed method would be influenced by the accuracy of land-cover products. Use of more accurate land-cover data than MODIS products can possibly improve the estimation of NDVIu.

## 6. Conclusions

^{2}) and root-mean-square-error (RMSE) of 0.99 and 0.03, respectively. Using the MODIS BRDF data, we achieved an estimate of NDVIu close to the in situ measured value (0.61 vs. 0.66 for estimate and measurement, respectively) and reasonable seasonal patterns of NDVIu during 2010–2013. The retrieval of NDVIu can be used to improve the estimation of leaf area index (LAI) in sparsely vegetated areas, and also possibly be used to study the phenology of understory layer.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Yang, W.; Kobayashi, H.; Suzuki, R.; Nasahara, K.N.
A Simple Method for Retrieving Understory NDVI in Sparse Needleleaf Forests in Alaska Using MODIS BRDF Data. *Remote Sens.* **2014**, *6*, 11936-11955.
https://doi.org/10.3390/rs61211936

**AMA Style**

Yang W, Kobayashi H, Suzuki R, Nasahara KN.
A Simple Method for Retrieving Understory NDVI in Sparse Needleleaf Forests in Alaska Using MODIS BRDF Data. *Remote Sensing*. 2014; 6(12):11936-11955.
https://doi.org/10.3390/rs61211936

**Chicago/Turabian Style**

Yang, Wei, Hideki Kobayashi, Rikie Suzuki, and Kenlo Nishida Nasahara.
2014. "A Simple Method for Retrieving Understory NDVI in Sparse Needleleaf Forests in Alaska Using MODIS BRDF Data" *Remote Sensing* 6, no. 12: 11936-11955.
https://doi.org/10.3390/rs61211936