# Utilizing a Multi-Source Forest Inventory Technique, MODIS Data and Landsat TM Images in the Production of Forest Cover and Volume Maps for the Terai Physiographic Zone in Nepal

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials

#### 2.1. Study Area

#### 2.2. Image Materials

#### 2.3. Two-Phase Sampling and Visual Interpretation Data

^{st}phase sample. During this sampling process, more weight was given to the clusters comprising plots on forest area. Only the four-corner plots of the cluster in a square with a side length of 300 m were used in these analyses (see Figure 2(a)).

#### 2.4. Field Data

## 3. Methods

#### 3.1. Building a Satellite Image Mosaic

_{i}(x, y) is the corrected data for the pixel (x, y) in band i, f

_{i}(x, y) is the uncorrected data in band i, and a

_{i}(x, y) and b

_{i}(x, y) are the parameters computed for the given pixel (x, y) in band i.

_{Li}”, “sd

_{Li}”, avg

_{Mj}” and “sd

_{Mj}”—which represent the mean and standard deviation values of the Landsat TM data and the MODIS data in the compatible spectral wavelength bands i and j, respectively—were thereafter calculated using a moving window approach with a window size of w × w pixels. Here, a 21 × 21 window neighborhood was utilized (w = 21), representing approximately a 10 km neighborhood for each pixel with the size of c. The raster maps with a pixel size of c were computed for both image datasets: target images (Landsat TM) and reference images (MODIS).

_{i}and b

_{i}in the correction function (Equation (1)) were calculated for each pixel (x, y) as follows:

_{i}and b

_{i}(see Equation (2)) of the correction function (Equation (1)) were local, being based on statistics from the neighborhood of each pixel (x, y). As a result, the Landsat TM pixel values were rescaled according to the local distribution parameters (mean and standard deviation) of the pixel values in the reference image bands.

^{3}·ha

^{−1}).

#### 3.2. Nearest Neighbors Techniques

_{b}is the number of bands, i is the target set element for which a prediction is sought and j is a reference set element, b

_{ih}and b

_{jh}are spectral band values for the pixels i and j on band h, respectively, and p

_{h}is the empirical parameter for band h.

_{1}(i),…, j

_{k}(i)}) were sought. In the case of categorical variables, the mode value of a response variable from among the k-nearest neighbors was the predicted class for a target pixel. In the case of continuous response variables, on the contrary, the weight w

_{ij}of each neighbor j ∈ K(i) was determined to be inversely proportional to its distance to target pixel i:

_{i}) target pixel i was calculated as follows:

_{j}is the observed value of the response variable in reference pixel j ∈ K(i).

_{h}) was set to 1 for all bands). The mode value of a response variable, i.e., the FAO land use class, among the k-nearest neighbors was the predicted class for the given target pixel. We selected pixels from the Landsat TM mosaic from Terai as the set of target pixels using the physiographic zone raster map as a mask in the GRASS GIS package. The reference set consisted of the pixels covered by the center points of the 1st phase plots, where the observed value (FAO land use class) was known based on the visual interpretation. In order to clarify forest classification, the plots belonging to the land use categories “Agricultural area with tree cover” or “Built-up area with tree cover” were dropped out from the reference set, whereas the category “Roads”, having a very small number of observations, was combined with the category “Built-up land without tree cover”.

#### 3.3. Validation of Results

_{i}is the observed value, ŷ

_{i}the predicted value of the given characteristic, and n is the number of observations. The relative, i.e., percent, RMSEs (RMSE

_{%}) and biases (bias

_{%}) were calculated by dividing the absolute RMSEs and biases by the means of the respective values from the observations (ȳ) and multiplying the resulting quotients by 100.

_{1},…,b

_{6}) in the Landsat TM mosaic (referring to TM wavelength bands 1,..,5 and 7) together with the ratios of the band values and the value of the Normalized Difference Vegetation Index (NDVI).

^{3}·ha

^{−1}.

## 4. Results

#### 4.1. Forest Cover Mapping

#### 4.2. Thematic Map of a Forest Variable: Volume

_{1}, b

_{2}, b

_{4}/b

_{3}and b

_{5}/b

_{3}. The band weights (i.e., the parameters p

_{h}in Equation (3)) for the four variables in the weighted spectral Euclidean distance were as follows: 0.8537294, 0.9748646, 0.5139022 and 0.3661812, respectively. It was noted that several runs produced quite similar results. We used the values of 4 and 2 for parameters k and t, respectively, of which the former was obtained from the genetic algorithm. The RMSE and bias values obtained for the stand volume were 85.4 m

^{3}·ha

^{−1}(62.0%) and −0.541 m

^{3}·ha

^{−1}(slight overestimation effect), respectively. The boxplot [31] of residuals for the volume prediction categories of 50 m

^{3}·ha

^{−1}show the presence of some extreme observations, whereas the median of residuals is close to zero in all categories (Figure 6).

## 5. Discussion

## 6. Conclusions

## Acknowledgments

## References

- Acharya, K.P.; Dangi, R.B.; Tripathi, D.M.; Bushley, B.R.; Bhandary, R.R.; Bhattarai, B. (Eds.) Ready for REDD? Taking Stock of Experience, Opportunities and Challenges in Nepal; Nepal Foresters' Association: Kathmandu, Nepal, 2009.
- Pearson, T.; Walker, S.; Brown, S. Sourcebook for Land Use, Land-Use Change and Forestry Projects; Winrock International and the BioCarbon Fund of the World Bank: Washington, DC, USA, 2005; Available online: http://www.winrock.org/ecosystems/files/winrock-biocarbon_fund_sourcebook-compressed.pdf (accessed on 30 May 2012).
- GOFC-GOLD. A Sourcebook of Methods and Procedures for Monitoring and Reporting Anthropogenic Greenhouse Gas Emissions and Removals Caused by Deforestation, Gains and Losses of Carbon Stocks in Forests Remaining Forests, and Forestation, GOFC-GOLD Report version COP17-1; GOFC-GOLD Project Office, Natural Resources Canada: Edmonton, AB, Canada, 2011; Available online: http://www.gofcgold.wur.nl/redd/ (accessed on 20 September 2012).
- Tomppo, E. The Finnish Multi-Source National Forest Inventory—Small Area Estimation and Map Production. In Forest Inventory. Methodology and Applications; Managing Forest Ecosystems, Kangas, A., Maltamo, M., Eds.; Springer: Dordrecht, The Netherlands, 2006; Volume 10, pp. 195–224. [Google Scholar]
- Tomppo, E.; Haakana, M.; Katila, M.; Peräsaari, J. Multi-Source National Forest Inventory Methods and Applications; Managing Forest Ecosystems, Springer Science+Business Media: New York, NY, USA, 2008; Volume 18. [Google Scholar]
- Coppin, P.; Jonckheere, I.; Nackaerts, K.; Muys, B.; Lambin, E. Digital change detection methods in ecosystem monitoring: A review. Int. J. Remote Sens.
**2004**, 25, 1565–1596. [Google Scholar] - Tuominen, S.; Pekkarinen, A. Local radiometric correction of digital aerial photographs for multi source forest inventory. Remote Sens. Environ.
**2004**, 89, 72–82. [Google Scholar] - Tomppo, E.; Katila, M.; Mäkisara, K.; Peräsaari, J.; Malimbwi, R.; Chamuya, N.; Otieno, J.; Dalsgaard, S.; Leppänen, M. A Report to the Food and Agriculture Organization of the United Nations (FAO) in Support of Sampling Study for National Forestry Resources Monitoring and Assessment (NAFORMA) in Tanzania; FAO: Rome, Italy, 10 March 2010; Available online: http://www.mp-discussion.org/NAFORMA.pdf (accessed on 24 August 2012).
- Bodart, C.; Eva, H.; Beuchle, R.; Raši, R.; Simonetti, D.; Stibig, H.-J.; Brink, A.; Lindquist, E.; Achard, F. Pre-processing of a sample of multi-scene and multi-date Landsat imagery used to monitor forest cover changes over the tropics. ISPRS J. Photogramm.
**2011**, 66, 555–563. [Google Scholar] - Tomppo, E.; Czaplewski, R.L.; Mäkisara, K. FRA 2000 The Role of Remote Sensing in Global Forest Assessment. A Remote Sensing Background Paper for Kotka IV Expert Consultation 01.07–05.07.2002, Kotka, Finland; Working Paper 61; Forest Resources Assessment Programme (FRA) of FAO: Rome, Italy, 2002; Available online: ftp://ftp.fao.org/docrep/fao/006/ad650e/ad650e00.pdf (accessed on 20 November 2012).
- Tokola, T.; Löfman, S.; Erkkilä, A. Calibration of multitemporal landsat data for forest cover change detection. Remote Sens. Environ.
**1999**, 68, 1–11. [Google Scholar] - Open Foris Wiki. Available online: http://km.fao.org/OFwiki/index.php/Main_Page (accessed on 26 June 2012).
- Lillesø, J.-P.B.; Shrestha, T.B.; Dhakal, L.P.; Nayaju, R.P.; Shrestha, R. The Map of Potential Vegetation of Nepal: A Forestry/Agroecological/Biodiversity Classification System; Development and Environment Series 2–2005 and CFC-TIS Document Series No. 110; Forest & Landscape: Aalborg, Denmark, 2005. [Google Scholar]
- MODIS Products Table. Available online: https://lpdaac.usgs.gov/products/modis_products_table (accessed on 18 June 2012).
- MODIS Reprojection Tool. Available online: https://lpdaac.usgs.gov/tools/modis_reprojection_tool (accessed on 26 June 2012).
- GDAL: Geospatial Data Abstraction Library. Available online: http://www.gdal.org/index.html (accessed on 18 June 2012).
- Quantum GIS. Available online: http://www.qgis.org/ (accessed on 18 June 2012).
- Neteler, M.; Mitasova, H. Open Source GIS: A GRASS GIS Approach, 3rd ed.; Springer Science+Business Media: New York, NY, USA, 2008. [Google Scholar]
- Kleinn, C. Forest Resources Inventories in Nepal: Status Quo, Needs, Recommendations; FRIS Project Paper No. 1; Forest Resource Information System Project (FRISP), HMGN/FINNIDA, Finnish Forest and Park Service: Kathmandu, Nepal, 1994. [Google Scholar]
- Forest Resource Assessment of Nepal. Draft Field Manual 2010; Version of October 16, 2010; Forest Resource Assessment of Nepal Project: Kathmandu, Nepal, 2010. [Google Scholar]
- Google Earth. Available online: http://www.google.com/earth/index.html (accessed on 26 June 2012).
- van Laar, A.; Akça, A. Forest Mensuration; Cuvillier Verlag: Göttingen, Germany, 1997. [Google Scholar]
- Sharma, E.R.; Pukkala, T. Volume Equations and Biomass Prediction of Forest Trees of Nepal; Publication 47; Forest Survey and Statistics Division, Ministry of Forests and Soil Conservation: Kathmandu, Nepal, 1990. [Google Scholar]
- Pinheiro, J.C.; Bates, D.M. Mixed-Effects Models in S and S-PLUS; Corrected third printing; Springer-Verlag: New York, NY, USA, 2002. [Google Scholar]
- McRoberts, R.E. Estimating forest attribute parameters for small areas using nearest neighbors techniques. Forest Ecol. Manag.
**2012**, 272, 3–12. [Google Scholar] - Tokola, T. The Influence of Field Sample Data Location on Growing Stock Volume Estimation in Landsat TM-based Forest Inventory in Eastern Finland. Remote Sens. Environ.
**2000**, 74, 422–431. [Google Scholar] - Congalton, R.G.; Green, K. Assessing the Accuracy of Remotely Sensed Data: Principles and Practices, 2nd ed.; CRC Press: Boca Raton, FL, USA, 2009. [Google Scholar]
- Hyvönen, P.; Anttila, P. Change detection in boreal forests using bi-temporal aerial photographs. Silva Fenn.
**2006**, 40, 303–314. [Google Scholar] - Katila, M.; Tomppo, E. Selecting estimation parameters for the Finnish multisource National Forest Inventory. Remote Sens. Environ.
**2001**, 76, 16–32. [Google Scholar] - Haapanen, R.; Tuominen, S. Data combination and feature selection for multi-source forest inventory. Photogramm. Eng. Remote Sensing
**2008**, 74, 869–880. [Google Scholar] - R Development Core Team. R: A Language and Environment for Statistical Computing; R Foundation for Statistical Computing: Vienna, Austria, 2011; Available online: http://www.R-project.org/ (accessed on 2 December 2011).
- Landis, J.R.; Koch, G.G. The measurement of observer agreement for categorical data. Biometrics
**1977**, 33, 159–174. [Google Scholar] - McRoberts, R.E. Diagnostic tools for nearest neighbors techniques when used with satellite imagery. Remote Sens. Environ.
**2009**, 113, 489–499. [Google Scholar] - Varjo, J. Change detection and controlling forest information using multi-temporal Landsat TM imagery. Acta For. Fenn.
**1997**, 258, 1–64. [Google Scholar] - Olsson, H. Regression functions for multitemporal relative calibration of Thematic Mapper data over boreal forest. Remote Sens. Environ.
**1993**, 46, 89–102. [Google Scholar] - Tokola, T.; Sarkeala, J.; van der Linden, M. Use of topographic correction in Landsat TM-based forest interpretation in Nepal. Int. J. Remote Sens.
**2001**, 22, 551–563. [Google Scholar] - Katila, M.; Tomppo, E. Sampling Simulation on Multi-Source Output Forest Maps—An Application for Small Areas. Proceedings of 7th International Symposium on Spatial Accuracy Assessment in Natural Resources and Environmental Sciences, Lisbon, Portugal, 5–7 July 2006; pp. 614–623.
- Tuominen, S.; Eerikäinen, K.; Schibalski, A.; Haakana, M.; Lehtonen, A. Mapping biomass variables with a multi-source forest inventory technique. Silva Fenn.
**2010**, 44, 109–119. [Google Scholar] - Eerikäinen, K. A multivariate linear mixed-effects model for the generalization of sample tree heights and crown ratios in the Finnish National Forest Inventory. Forest Sci.
**2009**, 55, 480–493. [Google Scholar]

**Figure 1.**Map of Nepal with borders of the physiographic zones. The study area, i.e., Terai, is denoted by the grey-fill color.

**Figure 2.**Layout of the inventory cluster (

**a**) and Concentric Circular Sample Plot (CCSP) (

**b**) used in the FRA Nepal project. In the case of Terai, one cluster comprises four CCSPs (1, 3, 4 and 6) in a square with 300 m sides, i.e., plots number 2 and 5 of the basic cluster, which are used in the visual interpretation (first stage sample) and are excluded from the field inventory (second stage sample). In (b), the symbols r

_{1},..., r

_{4}are for the radii of the four circular plots (4, 8, 15 and 20 m, respectively) within the CCSP.

**Figure 3.**(

**a**) Subsets of two original Landsat TM images from a region in Eastern Terai (Feb-4- 2010 for the image on the left and Jan-28- 2010 for the image on the right), a composite of TM bands 3, 2 and 1 (rgb). (

**b**) A subset of the corrected Landsat TM image mosaic, a composite of TM bands 3, 2 and 1 (rgb). (

**c**) A subset of the corrected Landsat TM image mosaic, a composite of TM bands 5, 3 and 2 (rgb). (Coordinate reference system: WGS 84/ UTM zone 45N).

**Figure 4.**Distributions of KHAT statistic values at different k values in the western (upper figure) and eastern (lower figure) parts of Terai. In the boxplot, the grey region is the area between the 1st and 3rd quartiles (including 50% of the observations), the thick line is the median and the outer lines extend to the data point, which is no more than 1.5 times the area between the 1st and 3rd quartiles away from the box. The most extreme individual observations are also plotted [31].

**Figure 5.**A forest cover map (forest: bright green color) for the Terai physiograhic zone produced by the k-NN technique and overlaid on a composite of MODIS image bands 1, 4 and 3 (rgb).

**Figure 7.**Mean observation versus mean prediction for volume (m

^{3}·ha

^{−1}). The observations have been sorted and grouped into groups of 20 observations at the minimum based on the observed volume (m

^{3}·ha

^{−1}).

**Figure 8.**At left: forest cover map (vector boundaries) and a field sample plot cluster, (plotnr = sample plot number; zone = UTM zone number; ba_ha = basal area, m

^{2}·ha

^{−1}; vol_ha = volume, m

^{3}·ha

^{−1}; tmcl1–tmcl6 = pixel values in the Landsat TM mosaic bands 1–6). At right: A thematic map of the volume. An example from eastern Terai (background: a composite of Landsat TM mosaic bands 5, 3 and 2 (rgb)). (Coordinate reference system: WGS 84/UTM zone 45N).

**Table 1.**Information about the Landsat TM satellite imagery used in this study. Path and row information is given in the WRS-2 system.

Area | Date | Path | Row |
---|---|---|---|

Western Terai | 2011-03-07 | 144 | 40 |

2010-02-25 | 143 | 41 | |

2010-02-18 | 142 | 41 | |

Eastern Terai | 2010-02-11 | 141 | 41 |

2010-02-04 | 140 | 41 | |

2010-02-04 | 140 | 42 | |

2010-01-28 | 139 | 42 |

**Table 2.**Descriptive statistics for the CCSP data, (n = 217): D

_{g}is the basal area weighted mean diameter at breast height (cm), H

_{g}is the basal area weighted mean height (m), N is the number of living trees (ha

^{−1}), G is the stand basal area of living trees (m

^{2}·ha

^{−1}) and V is the stand volume of living trees (m

^{3}·ha

^{−1}).

Variable | Minimum | Median | Mean | Standard Deviation | Maximum |
---|---|---|---|---|---|

D_{g} | 0.00 | 35.64 | 36.95 | 25.70 | 145.11 |

H_{g} | 0.00 | 17.44 | 16.13 | 9.23 | 40.00 |

N | 0 | 288.5 | 473.6 | 546.3 | 2735.5 |

G | 0.00 | 16.09 | 15.00 | 10.45 | 43.31 |

V | 0.00 | 130.94 | 137.53 | 112.66 | 499.59 |

**Table 3.**Statistics (mean and standard deviation (sd)) by the four indicators of classification accuracy (ICA): (1) the user’s accuracy of forest class (FUA), (2) the producer’s accuracy of forest class (FPA), (3) overall accuracy (OA) and (4) Kappa statistic (KHAT) based on the test samples for each value of k.

Area | ICA | Value of k | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

1 | 3 | 5 | 7 | 9 | 11 | 13 | 15 | |||

Western Terai | FUA | mean | 0.866 | 0.886 | 0.889 | 0.891 | 0.891 | 0.891 | 0.889 | 0.888 |

sd | 0.017 | 0.016 | 0.015 | 0.015 | 0.016 | 0.016 | 0.016 | 0.016 | ||

FPA | mean | 0.870 | 0.901 | 0.908 | 0.910 | 0.911 | 0.912 | 0.912 | 0.911 | |

sd | 0.017 | 0.015 | 0.014 | 0.013 | 0.013 | 0.013 | 0.013 | 0.013 | ||

OA | mean | 0.905 | 0.923 | 0.926 | 0.928 | 0.928 | 0.928 | 0.927 | 0.927 | |

sd | 0.007 | 0.007 | 0.007 | 0.007 | 0.007 | 0.007 | 0.007 | 0.007 | ||

KHAT | mean | 0.793 | 0.832 | 0.840 | 0.843 | 0.845 | 0.845 | 0.843 | 0.841 | |

sd | 0.016 | 0.015 | 0.014 | 0.014 | 0.014 | 0.015 | 0.015 | 0.015 | ||

Eastern Terai | FUA | mean | 0.857 | 0.897 | 0.905 | 0.908 | 0.908 | 0.908 | 0.907 | 0.906 |

sd | 0.026 | 0.024 | 0.023 | 0.023 | 0.023 | 0.023 | 0.023 | 0.024 | ||

FPA | mean | 0.852 | 0.871 | 0.876 | 0.877 | 0.878 | 0.877 | 0.877 | 0.877 | |

sd | 0.026 | 0.024 | 0.024 | 0.024 | 0.024 | 0.024 | 0.024 | 0.024 | ||

OA | mean | 0.953 | 0.963 | 0.966 | 0.966 | 0.966 | 0.966 | 0.966 | 0.966 | |

sd | 0.005 | 0.005 | 0.005 | 0.005 | 0.005 | 0.005 | 0.005 | 0.005 | ||

KHAT | mean | 0.826 | 0.862 | 0.870 | 0.872 | 0.872 | 0.872 | 0.871 | 0.870 | |

sd | 0.020 | 0.019 | 0.019 | 0.019 | 0.019 | 0.019 | 0.019 | 0.019 |

**Table 4.**Confusion matrices between the forest cover delineations derived from the visual interpretation (Visual), the forest cover map and the field observations (Obs.). (UA = User’s accuracy, PA = producer’s accuracy, OA = overall accuracy, KHAT = Kappa statistic).

Area | Obs. | Visual Interpretation | Forest Cover Map | ||||||
---|---|---|---|---|---|---|---|---|---|

Forest | Non-Forest | Total | PA, % | Forest | Non-Forest | Total | PA, % | ||

Western Terai | Forest | 103 | 5 | 108 | 95.4 | 100 | 8 | 108 | 92.6 |

Non-Forest | 4 | 28 | 32 | 87.5 | 5 | 27 | 32 | 84.4 | |

Total | 107 | 33 | 140 | 105 | 35 | 140 | |||

UA, % | 96.3 | 84.8 | 95.2 | 77.1 | |||||

OA, % | 93.6 | 90.7 | |||||||

KHAT | 0.820 | 0.745 | |||||||

Eastern Terai | Forest | 61 | 2 | 63 | 96.8 | 61 | 2 | 63 | 96.8 |

Non-Forest | 2 | 12 | 14 | 85.7 | 2 | 12 | 14 | 85.7 | |

Total | 63 | 14 | 77 | 63 | 14 | 77 | |||

UA, % | 96.8 | 85.7 | 96.8 | 85.7 | |||||

OA, % | 94.8 | 94.8 | |||||||

KHAT | 0.825 | 0.825 |

**Table 5.**Confusion matrices between the forest cover map and the forest cover delineation derived from the visual interpretation (Visual). (UA = User’s accuracy, PA = producer’s accuracy, OA = overall accuracy, KHAT = Kappa statistic).

Area | Visual | Forest Cover Map | |||
---|---|---|---|---|---|

Forest | Non-Forest | Total | PA, % | ||

Western Terai | Forest | 97 | 10 | 107 | 90.7 |

Non-Forest | 8 | 25 | 33 | 75.8 | |

Total | 105 | 35 | 140 | ||

UA, % | 92.4 | 71.4 | |||

OA, % | 87.1 | ||||

KHAT | 0.650 | ||||

Eastern Terai | Forest | 61 | 2 | 63 | 96.8 |

Non-Forest | 2 | 12 | 14 | 85.7 | |

Total | 63 | 14 | 77 | ||

UA, % | 96.8 | 85.7 | |||

OA, % | 94.8 | ||||

KHAT | 0.825 |

## Appendix: Height Prediction Model

#### A1.1. Modeling Data

**Table A1.**Descriptive statistics for the tree-level and plot-level characteristics of the height modeling data: h is the total tree height (m); z

_{dominated}and z

_{dominant}are dummy variables for the dominated and dominant tree, respectively; G is the stand basal area at the plot-level (m

^{2}·ha

^{−1}); z

_{KS/SK}, z

_{SB}and z

_{TMH}are plot-level dummy variables for the forest types of Khair Sissoo Forest, Shrub, and Terai Mixed Hardwood Forest, respectively; z

_{SG1}–z

_{SG4}are tree-level dummy variables for species groups 1–4, respectively; and d is the tree diameter at breast height (cm).

Variable | Minimum | Median | Mean | Standard Deviation | Maximum |
---|---|---|---|---|---|

h | 2.00 | 15.95 | 16.88 | 7.671 | 41.10 |

z_{dominated} | 0 | 0 | 0.05 | 0.225 | 1 |

z_{dominant} | 0 | 1 | 0.82 | 0.385 | 1 |

G | 0.51 | 19.93 | 20.58 | 7.908 | 43.31 |

z_{KS/SK} | 0 | 0 | 0.02 | 0.126 | 1 |

z_{SB} | 0 | 0 | 0.00 | 0.053 | 1 |

z_{TMH} | 0 | 1 | 0.60 | 0.491 | 1 |

z_{SG1} | 0 | 0 | 0.43 | 0.495 | 1 |

z_{SG2} | 0 | 0 | 0.13 | 0.333 | 1 |

z_{SG3} | 0 | 0 | 0.25 | 0.432 | 1 |

z_{SG4} | 0 | 0 | 0.20 | 0.400 | 1 |

d | 5.0 | 27.4 | 32.30 | 21.516 | 187.9 |

#### A1.2. Model Specification

_{ijk}, m) having a random intercept and slope terms with respect to the cluster (u

^{(1)}) and sample plot (u

^{(2)}) effects as well as the tree species effects for the four crown layer groups can now be described under conditions of normality (N) as follows:

_{1}, β

_{2},..., β

_{8.4}, β

_{9}and λ

_{d}are fixed model parameters; i, j and k refer to the cluster, plot and tree, respectively; z

_{dominatedijk}and z

_{dominantijk}are dummy variables for the dominated and dominant tree, respectively; G

_{ij}is the stand basal area at the plot j of cluster i (m

^{2}·ha

^{−1}); z

_{KS/SKij}, z

_{SBij}and z

_{TMHij}are dummy variables for three forest types, a Khair Sissoo Forest, a Shrub Forest and a Terai Mixed Hardwood Forest, respectively; d

_{ijk}is the diameter at breast height (cm); z

_{SG1ijk},z

_{SG3ijk}and z

_{SG4ijk}are dummy variables for the species groups 1, 3 and 4, respectively (note: when z

_{SG1ijk}, z

_{SG3ijk}and z

_{SG4ijk}are set to zero, the predictions are obtained for species group 2 (SG2)); and e

_{ijk}is the random error term of the model.

_{d}in Equation (A1) was added to the independent variable “d

_{ijk}” in order to decrease the residual variation among small-sized trees. The selection of fixed values for λ

_{d}and for the form parameter β

_{9}was based on the analysis of residuals as well as the Akaike Information Criterion (AIC) values (see [24]) and Root Mean Square Errors (RMSEs, see Equation (6)) obtained using different values for the two parameters (see also Eerikäinen et al. [A2]). A combination of values of 10 and 0.65 for the respective parameters λ

_{d}and β

_{9}was found to provide the best model fit in the PSP data from Terai.

_{ijk}is a weighting variable, e.g., the diameter at breast height or its transformation, and δ

_{m}is an unrestricted, group-dependent parameter that needs to be estimated and which assumes values according to the stratification variable m respective to the four species effect groups (i.e., SG1–SG4). The appropriate weighting variable (v

_{ijk}) of the variance function was found to be (d

_{ijk}+5).

#### A1.3. Parameter Estimation and Model Validation

**Table A2.**Parameter estimates for the fixed independent variables of the NLME model for tree height (Equation (A1)).

Parameter | Estimate | Standard Error | t-value | p-value |
---|---|---|---|---|

β_{1} | 20.10056 | 3.47697 | 5.78 | <0.001 |

β_{2} | −10.93493 | 1.83761 | −5.95 | <0.001 |

β_{3} | 5.39272 | 1.07708 | 5.01 | <0.001 |

β_{4} | 8.31991 | 0.95719 | 8.69 | <0.001 |

β_{5} | −8.46984 | 2.99058 | −2.83 | 0.005 |

β_{6} | 14.15576 | 5.56316 | 2.54 | 0.011 |

β_{7} | −3.13794 | 0.99325 | −3.16 | 0.002 |

β_{8} | 11.79772 | 0.37590 | 31.39 | <0.001 |

β_{8.1} | −1.02356 | 0.21786 | −4.70 | <0.001 |

β_{8.3} | 1.29069 | 0.24134 | 5.35 | <0.001 |

β_{8.4} | 2.28025 | 0.25112 | 9.08 | <0.001 |

**Table A3.**Estimated Variances (diagonal), covariances (lower triangle) and correlations (upper triangle) for the random parameters of Equation (A1) at the cluster, plot and tree levels, respectively, and estimates for the power parameters of the variance function respective to the four species groups, i.e., SG1–SG4 (Equation (A3)).

Cluster Level | |||||

${u}_{1}^{(1)}$ | ${u}_{8}^{(1)}$ | ${u}_{8.1}^{(1)}$ | ${u}_{8.3}^{(1)}$ | ${u}_{8.4}^{(1)}$ | |

${u}_{1}^{(1)}$ | 50.249045 | 0.836 | 0.604 | −0.175 | 0.529 |

${u}_{8}^{(1)}$ | 7.790949 | 1.728385 | 0.076 | −0.663 | 0.548 |

${u}_{8.1}^{(1)}$ | 0.856461 | 0.019987 | 0.040014 | 0.589 | 0.056 |

${u}_{8.3}^{(1)}$ | −0.770911 | −0.541671 | 0.073219 | 0.386193 | −0.037 |

${u}_{8.4}^{(1)}$ | 2.014978 | 0.387125 | 0.006019 | −0.012355 | 0.288736 |

Plot Level | |||||

${u}_{1}^{(2)}$ | ${u}_{8}^{(2)}$ | ${u}_{8.1}^{(2)}$ | ${u}_{8.3}^{(2)}$ | ${u}_{8.4}^{(2)}$ | |

${u}_{1}^{(2)}$ | 27.894114 | 0.406 | 0.953 | 0.638 | 0.762 |

${u}_{8}^{(2)}$ | 0.434241 | 0.041011 | 0.659 | 0.946 | −0.268 |

${u}_{8.1}^{(2)}$ | 4.870331 | 0.129135 | 0.936308 | 0.839 | 0.536 |

${u}_{8.3}^{(2)}$ | 0.980705 | 0.055757 | 0.236283 | 0.084708 | 0.012 |

${u}_{8.4}^{(2)}$ | 1.141066 | −0.015388 | 0.147053 | 0.000990 | 0.080389 |

Tree Level | |||||

e | |||||

e | 0.194484 | ||||

Estimates for the Power Parameters | |||||

δ_{SG1} | δ_{SG2} | δ_{SG3} | δ_{SG4} | ||

0.545992 | 0.492496 | 0.499664 | 0.503056 |

### References

- Lappi, J. Calibration of height and volume equations with random parameters. Forest Sci.
**1991**, 37, 781–801. [Google Scholar] - Eerikäinen, K.; Mabvurira, D.; Nshubemuki, L.; Saramäki, J. A calibrateable site index model for Pinus kesiya plantations in southeastern Africa. Can. J. Forest Res.
**2002**, 32, 1916–1928. [Google Scholar] - Lappi, J. A longitudinal analysis of height/diameter curves. Forest Sci.
**1997**, 43, 555–570. [Google Scholar] - Hall, D.B.; Clutter, M. Multivariate multilevel nonlinear mixed effects models for timber yield predictions. Biometrics
**2004**, 60, 16–24. [Google Scholar] - Wutzler, T.; Wirth, C.; Schumacher, J. Generic biomass functions for Common beech (Fagus sylvatica) in Central Europe: predictions and components of uncertainty. Can. J. Forest Res.
**2008**, 38, 1661–1675. [Google Scholar] - Vonesh, E.F.; Chinchilli, V.G. Linear and Nonlinear Models for the Analysis of Repeated Measurements; Chapman and Hall: London, UK, 1997. [Google Scholar]
- Crecente-Campo, F.; Tomé, M.; Soares, P.; Diéguez-Aranda, U. A generalized nonlinear mixed-effects height–diameter model for Eucalyptus globulus L. in northwestern Spain. Forest Ecol. Manag.
**2010**, 259, 943–952. [Google Scholar]

## Share and Cite

**MDPI and ACS Style**

Muinonen, E.; Parikka, H.; Pokharel, Y.P.; Shrestha, S.M.; Eerikäinen, K.
Utilizing a Multi-Source Forest Inventory Technique, MODIS Data and Landsat TM Images in the Production of Forest Cover and Volume Maps for the Terai Physiographic Zone in Nepal. *Remote Sens.* **2012**, *4*, 3920-3947.
https://doi.org/10.3390/rs4123920

**AMA Style**

Muinonen E, Parikka H, Pokharel YP, Shrestha SM, Eerikäinen K.
Utilizing a Multi-Source Forest Inventory Technique, MODIS Data and Landsat TM Images in the Production of Forest Cover and Volume Maps for the Terai Physiographic Zone in Nepal. *Remote Sensing*. 2012; 4(12):3920-3947.
https://doi.org/10.3390/rs4123920

**Chicago/Turabian Style**

Muinonen, Eero, Heikki Parikka, Yam P. Pokharel, Sahas M. Shrestha, and Kalle Eerikäinen.
2012. "Utilizing a Multi-Source Forest Inventory Technique, MODIS Data and Landsat TM Images in the Production of Forest Cover and Volume Maps for the Terai Physiographic Zone in Nepal" *Remote Sensing* 4, no. 12: 3920-3947.
https://doi.org/10.3390/rs4123920