# Research on the Temporal and Spatial Distributions of Standing Wood Carbon Storage Based on Remote Sensing Images and Local Models

^{*}

^{†}

## Abstract

**:**

^{2}is increased to 0.52 compared with OLS. The local models based on geographically weighted regression, namely, GWR, MGWR, TWR, and GTWR, all have good performance. Compared with OLS, the R

^{2}is increased to 0.572, 0.589, 0.643, and 0.734, and the fitting effect of GTWR is the best. GTWR can overcome spatial autocorrelation and temporal autocorrelation problems, with a higher R

^{2}(0.734) and a more ideal model residual than other models. This study develops a model for carbon storage (CS) considering various influential factors in the Liangshui area and provides a possible solution for the estimation of long-term carbon storage distribution.

## 1. Introduction

_{2.5}estimation problem through effective sampling and fitting, and the proposed method effectively produced the relationship between the observed PM

_{2.5}and AOD data. It is also proved that GTWR has certain advantages in overcoming the influence of spatiotemporal heterogeneity. Wei [16] used GTWR to investigate the relationship between PM

_{2.5}and standard air pollutants (SO

_{2}, NO

_{2}, PM

_{10}, CO, and O

_{3}) in Heilongjiang Province, China, from 2015 to 2018, and compared the model with other basic models; they found that temporal and spatial heterogeneity influenced the distribution of data, and the GTWR fitting effect was better than that of other basic models such as OLS. Inspired by such work, we will investigate whether the distribution of forest standing tree carbon stocks is affected by spatial and temporal heterogeneity, and that the distribution of forest standing trees carbon storage also has a high degree of spatial and temporal heterogeneity, which has a great impact on the fitting and prediction of the model. How to overcome this impact has become the focus of research.

## 2. Materials and Methods

#### 2.1. Study Area and Research Process

#### 2.2. Data Sources

#### 2.2.1. Ground Survey Data

^{3}/ha) and carbon storage (Mg/ha). Carbon storage (Mg/ha) was calculated based on the aboveground biomass in the study area using the continuous function method for the biomass conversion coefficient of the main stand types [23]. The calculated biomass was multiplied by the carbon content coefficient to obtain carbon storage [24]. The carbon storage conversion coefficients of different tree species in the study area are shown in Table 1:

#### 2.2.2. Remote Sensing Data

#### 2.3. Methods

#### 2.3.1. Global OLS Model and LMM

^{2}) distribution.

#### 2.3.2. Spatial Local Models (GWR, MGWR, TWR and GTWR)

^{2}); and p is the total number of parameters to be estimated.

_{1}to perform classic GWR and find the optimal bandwidth 1 and a list of new parameter estimates ${\mathit{f}}_{1}$ and $\hat{\epsilon}$ to update the previous estimates. In the second step, the residual, the second additive term ${\mathit{f}}_{2}$ and the second independent variable X

_{2}are used to perform a second round of GWR and update the parameter estimates for the second variables ${\mathit{f}}_{2}$ and $\hat{\epsilon}$. This process is repeated until the k-th step calculation is completed for the last independent variable X

_{k}. The above steps form a complete loop process and are repeated until the estimate converges to the selected criterion.

#### 2.3.3. Model Evaluation

^{2}), and adjusted correlation coefficient (${\mathit{R}}_{\mathit{a}}^{2}$). Moran’s I and Z-score were used to evaluate the spatial autocorrelation of the residuals of each model. The sum of each squared residual is called the residual sum of squares (RSS), which represents the effect of random error. The smaller the RRS of a set of data is, the better the fit. The corresponding expression is as follows:

^{2}) represents the goodness of fit of a model, or the percentage of the total change in the observations explained by the model. The larger R

^{2}is, the better the model fitting result. R

^{2}tends to exaggerate the explained percentage because it is not reduced by adding more predictors [42]. The adjusted coefficient of determination (${\mathit{R}}_{\mathit{a}}^{2}$) overcomes this shortcoming by dividing the RSS and SST by their related degrees of freedom, and the corresponding formulas are as follows:

## 3. Results

#### 3.1. Comparison of Model Fitting Results

#### 3.2. OLS and LMM

#### 3.3. GWR, MGWR, TWR and GTWR

#### 3.4. Spatial Autocorrelation Analysis

#### 3.5. Optimal Model Space Analysis

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Informed Consent Statement

## Conflicts of Interest

## References

- Wen, D.; He, N. Forest Carbon Storage along the North-South Transect of Eastern China: Spatial Patterns, Allocation, and Influencing Factors. Ecol. Indic.
**2016**, 61, 960–967. [Google Scholar] [CrossRef] - Li, M. Carbon Stock and Sink Economic Values of Forest Ecosystem in the Forest Industry Region of Heilongjiang Province, China. J. For. Res.
**2021**, 1–8. [Google Scholar] [CrossRef] - Guo, Y.T.; Zhang, X.M.; Long, T.F.; Jiao, W.L.; He, G.J.; Yin, R.Y.; Dong, Y.Y. China forest cover extraction based on google earth engine. Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci.
**2020**, 42, 855–862. [Google Scholar] [CrossRef] [Green Version] - Gundersen, P.; Thybring, E.E.; Nord-Larsen, T.; Vesterdal, L.; Nadelhoffer, K.J.; Johannsen, V.K. Old-Growth Forest Carbon Sinks Overestimated. Nature
**2021**, 591, E21–E23. [Google Scholar] [CrossRef] [PubMed] - Anand, A.; Pandey, P.C.; Petropoulos, G.P.; Pavlides, A.; Srivastava, P.K.; Sharma, J.K.; Malhi, R.K.M. Use of Hyperion for Mangrove Forest Carbon Stock Assessment in Bhitarkanika Forest Reserve: A Contribution towards Blue Carbon Initiative. Remote Sens.
**2020**, 12, 597. [Google Scholar] [CrossRef] [Green Version] - Franki, V.; Višković, A.; Šapić, A. Carbon Capture and Storage Retrofit: Case Study for Croatia. Energy Sources Part A: Recovery Util. Environ. Eff.
**2021**, 43, 3238–3250. [Google Scholar] [CrossRef] - Tao, S.; Guo, Q.; Li, L.; Xue, B.; Kelly, M.; Li, W.; Xu, G.; Su, Y. Airborne Lidar-Derived Volume Metrics for Aboveground Biomass Estimation: A Comparative Assessment for Conifer Stands. Agric. For. Meteorol.
**2014**, 198–199, 24–32. [Google Scholar] [CrossRef] - Hu, T.; Sun, Y.; Jia, W.; Li, D.; Zou, M.; Zhang, M. Study on the Estimation of Forest Volume Based on Multi-Source Data. Sensors
**2021**, 21, 7796. [Google Scholar] [CrossRef] - Takagi, K.; Yone, Y.; Takahashi, H.; Sakai, R.; Hojyo, H.; Kamiura, T.; Nomura, M.; Liang, N.; Fukazawa, T.; Miya, H.; et al. Forest Biomass and Volume Estimation Using Airborne LiDAR in a Cool-Temperate Forest of Northern Hokkaido, Japan. Ecol. Inform.
**2015**, 26, 54–60. [Google Scholar] [CrossRef] - Narmada, K.; Annaidasan, K. Estimation of the Temporal Change in Carbon Stock of Muthupet Mangroves in Tamil Nadu Using Remote Sensing Techniques. JGEESI
**2019**, 19. [Google Scholar] [CrossRef] - Roy Chowdhury, P.K.; Maithani, S. Modelling Urban Growth in the Indo-Gangetic Plain Using Nighttime OLS Data and Cellular Automata. Int. J. Appl. Earth Obs. Geoinf.
**2014**, 33, 155–165. [Google Scholar] [CrossRef] - Krämer, W.; Bartels, R.; Fiebig, D.G. Another Twist on the Equality of OLS and GLS. Stat. Pap.
**1996**, 37, 277–281. [Google Scholar] [CrossRef] - Zhang, L.; Ma, Z.; Guo, L. Spatially assessing model errors of four regression techniques for three types of forest stands. Forestry
**2008**, 81, 209–225. [Google Scholar] [CrossRef] [Green Version] - Hajiloo, F.; Hamzeh, S.; Gheysari, M. Impact Assessment of Meteorological and Environmental Parameters on PM
_{2.5}Concentrations Using Remote Sensing Data and GWR Analysis (Case Study of Tehran). Environ. Sci. Pollut. Res.**2019**, 26, 24331–24345. [Google Scholar] [CrossRef] - Yu, H.; Fotheringham, A.S.; Li, Z.; Oshan, T.; Kang, W.; Wolf, L.J. Inference in Multiscale Geographically Weighted Regression. Geogr. Anal.
**2020**, 52, 87–106. [Google Scholar] [CrossRef] - Wei, Q.; Zhang, L.; Duan, W.; Zhen, Z. Global and Geographically and Temporally Weighted Regression Models for Modeling PM2.5 in Heilongjiang, China from 2015 to 2018. IJERPH
**2019**, 16, 5107. [Google Scholar] [CrossRef] [Green Version] - Cohen, J.P.; Coughlin, C.C.; Zabel, J. Time-Geographically Weighted Regressions and Residential Property Value Assessment. J. Real Estate Financ. Econ.
**2020**, 60, 134–154. [Google Scholar] [CrossRef] [Green Version] - Fotheringham, A.S.; Crespo, R.; Yao, J. Geographical and Temporal Weighted Regression (GTWR): Geographical and Temporal Weighted Regression. Geogr. Anal.
**2015**, 47, 431–452. [Google Scholar] [CrossRef] [Green Version] - Chu, H.-J.; Bilal, M. PM
_{2.5}Mapping Using Integrated Geographically Temporally Weighted Regression (GTWR) and Random Sample Consensus (RANSAC) Models. Environ. Sci. Pollut. Res.**2019**, 26, 1902–1910. [Google Scholar] [CrossRef] - Feng, G.; Mi, X.; Yan, H.; Li, F.Y.; Svenning, J.-C.; Ma, K. CForBio: A Network Monitoring Chinese Forest Biodiversity. Sci. Bull.
**2016**, 61, 1163–1170. [Google Scholar] [CrossRef] [Green Version] - Duveneck, M.J.; Thompson, J.R.; Gustafson, E.J.; Liang, Y.; de Bruijn, A.M.G. Recovery Dynamics and Climate Change Effects to Future New England Forests. Landsc. Ecol.
**2017**, 32, 1385–1397. [Google Scholar] [CrossRef] - Usinowicz, J.; Chang-Yang, C.-H.; Chen, Y.-Y.; Clark, J.S.; Fletcher, C.; Garwood, N.C.; Hao, Z.; Johnstone, J.; Lin, Y.; Metz, M.R.; et al. Temporal Coexistence Mechanisms Contribute to the Latitudinal Gradient in Forest Diversity. Nature
**2017**, 550, 105–108. [Google Scholar] [CrossRef] [PubMed] - Dong, L. Study on Biomass Model of Main Tree Species and Stand Types in Northeast Forest Region. Ph.D. Thesis, Northeast Forestry University, Harbin, China, 2015. [Google Scholar]
- Widagdo, F.R.A.; Dong, L.; Li, F. Biomass Functions and Carbon Content Variabilities of Natural and Planted Pinus Koraiensis in Northeast China. Plants
**2021**, 10, 201. [Google Scholar] [CrossRef] [PubMed] - Rehman, A.U.; Ullah, S.; Shafique, M.; Khan, M.S.; Badshah, M.T.; Liu, Q.-J. Combining Landsat-8 spectral bands with ancillary variables for land cover classification in mountainous terrains of northern Pakistan. J. Mt. Sci.
**2021**, 18, 2388–2401. [Google Scholar] [CrossRef] - Huang, X.; Li, J.; Yang, J.; Zhang, Z.; Li, D.; Liu, X. 30 m global impervious surface area dynamics and urban expansion pattern observed by Landsat satellites:From 1972 to 2019. Sci. China Earth Sci.
**2021**, 64, 1922–1933. [Google Scholar] [CrossRef] - Qu, L.A.; Li, M.; Chen, Z.; Zhi, J. A Modified Self-adaptive Method for Mapping Annual 30-m Land Use/Land Cover Using Google Earth Engine: A Case Study of Yangtze River Delta. Chin. Geogr. Sci.
**2021**, 31, 782–794. [Google Scholar] [CrossRef] - Beguet, B.; Guyon, D.; Boukir, S.; Chehata, N. Automated Retrieval of Forest Structure Variables Based on Multi-Scale Texture Analysis of VHR Satellite Imagery. ISPRS J. Photogramm. Remote Sens.
**2014**, 96, 164–178. [Google Scholar] [CrossRef] - Chen, C.; Liu, F.; Li, Y.; Yan, C.; Liu, G. A Robust Interpolation Method for Constructing Digital Elevation Models from Remote Sensing Data. Geomorphology
**2016**, 268, 275–287. [Google Scholar] [CrossRef] - Sassi, M. OLS and GWR Approaches to Agricultural Convergence in the EU-15. Int. Adv. Econ. Res.
**2010**, 16, 96–108. [Google Scholar] [CrossRef] - Schneider, M.B.; Knapp, D.A.; Chen, M.H.; Scofield, J.H.; Beiersdorfer, P.; Bennett, C.L.; Henderson, J.R.; Levine, M.A.; Marrs, R.E. Measurement of the LMM Dielectronic Recombination Resonances of Neonlike Gold. Phys. Rev. A
**1992**, 45, R1291–R1294. [Google Scholar] [CrossRef] - Zhou, A.; Wang, S.; Wan, S.; Qi, L. LMM: Latency-Aware Micro-Service Mashup in Mobile Edge Computing Environment. Neural Comput. Appl.
**2020**, 32, 15411–15425. [Google Scholar] [CrossRef] - Liu, C.; Zhang, L.; Li, F.; Jin, X. Spatial Modeling of the Carbon Stock of Forest Trees in Heilongjiang Province, China. J. For. Res.
**2014**, 25, 269–280. [Google Scholar] [CrossRef] - Hu, X.; Xu, H. Spatial Variability of Urban Climate in Response to Quantitative Trait of Land Cover Based on GWR Model. Environ. Monit. Assess.
**2019**, 191, 194. [Google Scholar] [CrossRef] - Wang, Q.; Feng, H.; Feng, H.; Yu, Y.; Li, J.; Ning, E. The Impacts of Road Traffic on Urban Air Quality in Jinan Based GWR and Remote Sensing. Sci. Rep.
**2021**, 11, 15512. [Google Scholar] [CrossRef] - Diniz-Filho, J.A.F.; Soares, T.N.; de Campos Telles, M.P. Geographically Weighted Regression as a Generalized Wombling to Detect Barriers to Gene Flow. Genetica
**2016**, 144, 425–433. [Google Scholar] [CrossRef] - Taghadosi, M.M.; Hasanlou, M. Developing Geographic Weighted Regression (GWR) Technique for Monitoring Soil Salinity Using Sentinel-2 Multispectral Imagery. Environ. Earth Sci.
**2021**, 80, 75. [Google Scholar] [CrossRef] - Zhang, S.; Wang, L.; Lu, F. Exploring Housing Rent by Mixed Geographically Weighted Regression: A Case Study in Nanjing. IJGI
**2019**, 8, 431. [Google Scholar] [CrossRef] [Green Version] - Shabrina, Z.; Buyuklieva, B.; Ng, M.K.M. Short-Term Rental Platform in the Urban Tourism Context: A Geographically Weighted Regression (GWR) and a Multiscale GWR (MGWR) Approaches. Geogr. Anal.
**2021**, 53, 686–707. [Google Scholar] [CrossRef] - Oshan, T.M.; Smith, J.P.; Fotheringham, A.S. Targeting the Spatial Context of Obesity Determinants via Multiscale Geographically Weighted Regression. Int. J. Health Geogr.
**2020**, 19, 11. [Google Scholar] [CrossRef] - Wu, B.; Li, R.; Huang, B. A Geographically and Temporally Weighted Autoregressive Model with Application to Housing Prices. Int. J. Geogr. Inf. Sci.
**2014**, 28, 1186–1204. [Google Scholar] [CrossRef] - Naderi, A.; Delavar, M.A.; Kaboudin, B.; Askari, M.S. Assessment of Spatial Distribution of Soil Heavy Metals Using ANN-GA, MSLR and Satellite Imagery. Environ. Monit. Assess.
**2017**, 189, 214. [Google Scholar] [CrossRef] - Hayes, A.F.; Matthes, J. Computational Procedures for Probing Interactions in OLS and Logistic Regression: SPSS and SAS Implementations. Behav. Res. Methods
**2009**, 41, 924–936. [Google Scholar] [CrossRef] [Green Version] - Xu, X.; Ding, S.; Jia, W.; Ma, G.; Jin, F. Research of Assembling Optimized Classification Algorithm by Neural Network Based on Ordinary Least Squares (OLS). Neural Comput. Appl.
**2013**, 22, 187–193. [Google Scholar] [CrossRef] - Shan, Y.; Guan, D.; Liu, J.; Mi, Z.; Liu, Z.; Liu, J.; Schroeder, H.; Cai, B.; Chen, Y.; Shao, S.; et al. Methodology and Applications of City Level CO
_{2}Emission Accounts in China. J. Clean. Prod.**2017**, 161, 1215–1225. [Google Scholar] [CrossRef] [Green Version] - Song, G.; Dong, X.; Wu, J.; Wang, Y.-G. Blockwise AICc for Model Selection in Generalized Linear Models. Environ. Model Assess.
**2017**, 22, 523–533. [Google Scholar] [CrossRef] [Green Version] - Fotheringham, A.S.; Yang, W.; Kang, W. Multiscale Geographically Weighted Regression (MGWR). Ann. Am. Assoc. Geogr.
**2017**, 107, 1247–1265. [Google Scholar] [CrossRef] - Chen, X. A Spatial and Temporal Analysis of the Socioeconomic Factors Associated with Breast Cancer in Illinois Using Geographically Weighted Generalized Linear Regression. J. Geovis. Spat. Anal.
**2018**, 2, 5. [Google Scholar] [CrossRef] - Qin, K.; Rao, L.; Xu, J.; Bai, Y.; Zou, J.; Hao, N.; Li, S.; Yu, C. Estimating Ground Level NO
_{2}Concentrations over Central-Eastern China Using a Satellite-Based Geographically and Temporally Weighted Regression Model. Remote Sens.**2017**, 9, 950. [Google Scholar] [CrossRef] [Green Version] - Jordan, J.H.; Hamilton, C.A.; D’Agostino, R.B.; Lawrence, J.; Vasu, S.; Hundley, W.G. Dispersion of Hyperenhancement in Late Gadolinium Enhancement Cardiovascular Magnetic Resonance Measured with Moran’s I Is Associated with a Decrement in LVEF 6 Months after Cardiotoxic Chemotherapy. J. Cardiovasc. Magn. Reson.
**2013**, 15, P156. [Google Scholar] [CrossRef] [Green Version] - Li, Z.; Fotheringham, A.S.; Li, W.; Oshan, T. Fast Geographically Weighted Regression (FastGWR): A Scalable Algorithm to Investigate Spatial Process Heterogeneity in Millions of Observations. Int. J. Geogr. Inf. Sci.
**2019**, 33, 155–175. [Google Scholar] [CrossRef] - Guo, Y.; Tang, Q.; Gong, D.-Y.; Zhang, Z. Estimating Ground-Level PM
_{2.5}Concentrations in Beijing Using a Satellite-Based Geographically and Temporally Weighted Regression Model. Remote Sens. Environ.**2017**, 198, 140–149. [Google Scholar] [CrossRef] - Luo, Y.; Wang, X.; Ouyang, Z.; Lu, F.; Feng, L.; Tao, J. A Review of Biomass Equations for China’s Tree Species. Earth Syst. Sci. Data
**2020**, 12, 21–40. [Google Scholar] [CrossRef] [Green Version] - Sun, Y.; Ao, Z.; Jia, W.; Chen, Y.; Xu, K. A Geographically Weighted Deep Neural Network Model for Research on the Spatial Distribution of the down Dead Wood Volume in Liangshui National Nature Reserve (China). iForest
**2021**, 14, 353–361. [Google Scholar] [CrossRef] - Li, Y.; Jiao, Y.; Browder, J.A. Modeling Spatially-Varying Ecological Relationships Using Geographically Weighted Generalized Linear Model: A Simulation Study Based on Longline Seabird Bycatch. Fish. Res.
**2016**, 181, 14–24. [Google Scholar] [CrossRef] [Green Version] - Gao, J.; Li, S. Detecting Spatially Non-Stationary and Scale-Dependent Relationships between Urban Landscape Fragmentation and Related Factors Using Geographically Weighted Regression. Appl. Geogr.
**2011**, 31, 292–302. [Google Scholar] [CrossRef] - Rani, M.; Kumar, P.; Pandey, P.C.; Srivastava, P.K.; Chaudhary, B.S.; Tomar, V.; Mandal, V.P. Multi-Temporal NDVI and Surface Temperature Analysis for Urban Heat Island Inbuilt Surrounding of Sub-Humid Region: A Case Study of Two Geographical Regions. Remote Sens. Appl. Soc. Environ.
**2018**, 10, 163–172. [Google Scholar] [CrossRef] - Evin, G.; Kavetski, D.; Thyer, M.; Kuczera, G. Pitfalls and Improvements in the Joint Inference of Heteroscedasticity and Autocorrelation in Hydrological Model Calibration: Technical Note. Water Resour. Res.
**2013**, 49, 4518–4524. [Google Scholar] [CrossRef] [Green Version] - Dong, L.; Du, H.; Mao, F.; Han, N.; Li, X.; Zhou, G.; Zhu, D.; Zheng, J.; Zhang, M.; Xing, L.; et al. Very High Resolution Remote Sensing Imagery Classification Using a Fusion of Random Forest and Deep Learning Technique—Subtropical Area for Example. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens.
**2020**, 13, 113–128. [Google Scholar] [CrossRef] - Dong, F.; Li, J.; Zhang, S.; Wang, Y.; Sun, Z. Sensitivity Analysis and Spatial-Temporal Heterogeneity of CO
_{2}Emission Intensity: Evidence from China. Resour. Conserv. Recycl.**2019**, 150, 104398. [Google Scholar] [CrossRef]

**Figure 1.**The geographical location of the study area: China, Heilongjiang Province, Liangshui National Nature Reserve.

**Figure 2.**Research flow chart: Data processing and model fitting process, which includes two parts: data processing and model fitting.

**Figure 3.**(

**a**–

**d**) are the location distributions of the specific plots in 1989, 1999, 2009, and 2019, respectively.

**Figure 4.**(

**a**) The spatial distribution of variables in different years in latitude. In the solid wireframe is the spatial distribution map of independent variables obtained through stepwise regression screening, and in the red dotted wireframe is the spatial distribution map of the actual measured and calculated carbon storage. (

**b**) The spatial distribution of variables in different years in longitude. In the same way, in the solid wireframe is the spatial distribution map of independent variables obtained through stepwise regression screening, and in the red dotted wireframe is the spatial distribution map of the actual measured and calculated carbon storage.

**Figure 5.**Temporal and spatial distributions of carbon storage based on observation data and model fitting results.

**Figure 6.**(

**a**) Moran’s I values of the global model residual under different bandwidths; (

**b**) Moran’s I values of the local model residual under different bandwidths.

**Figure 7.**(

**a**) Z-score of the global model residual under different bandwidths; (

**b**) Z-score of the local model residual under different bandwidths.

**Figure 8.**(

**a**–

**d**) are the carbon storage heat maps in 1989, 1999, 2009, and 2019 fitted by the GTWR model and the average carbon storage error analysis maps at different longitudes and latitudes, respectively.

Species | Betula platyphylla Suk. | Ulmus pumila L. | Tilia amurensis Rupr. | Quercus mongolica Fisch. ex Ledeb | Picea asperata Mast. | Larix gmelinii (Rupr.) Kuzen. | Pinus koraiensis Sieb. et Zucc. |
---|---|---|---|---|---|---|---|

Conversion coefficients | 0.4656 | 0.4331 | 0.4373 | 0.453 | 0.4805 | 0.4674 | 0.4809 |

Vegetation Index | Formula |
---|---|

Blue | B2 |

Green | B3 |

Red | B4 |

Near Infrared | B5 |

Ratio Vegetation Index (RVI) | $B5/B4$ |

Difference Vegetation Index (DVI) | $B5-B4$ |

Weighted Difference Vegetation Index (WDVI) | $B5-0.5\times B4$ |

Infrared Percentage Vegetation Index (IPVI) | $B5/(B5+B4)$ |

Perpendicular Vegetation Index (PVI) | $\mathrm{sin}(45\xb0)\times B5-\mathrm{cos}(45\xb0)\times B4$ |

Normalized Difference Vegetation Index (NDVI) | $(B5-B4)/(B5+B4)$ |

Transformed Normalized Difference Vegetation Index (TNDVI) | ${[(B5-B4)/(B5+B4)+0.5]}^{1/2}$ |

Soil-Adjusted Vegetation Index (SAVI) | $1.5\times (B5-B4)/8\times (B5+B4+0.5)$ |

Modified Soil-Adjusted Vegetation Index (MSAVI) | $\begin{array}{l}(2-\mathrm{NDVI}\times \mathrm{WDVI})\times (B5-B4)/\\ 8\times (B5+B4+1-\mathrm{NDVI}\times \mathrm{WDVI})\end{array}$ |

Modified Soil-Adjusted Vegetation Index 2 (MSAVI2) | $\begin{array}{l}0.5\times (2\times (B5+1))-sqrt[(2\times B5+1)\\ \times (2\times B5+1)-8\times (B5-B4)]\end{array}$ |

Atmospheric Ratio Vegetation Index (ARVI) | $[B5-(2\times B4-B2)]/[B5+(2\times B4-B2)]$ |

Model | RSS | RMSE | AICc | R^{2} | ${\mathit{R}}_{\mathit{a}}^{2}$ |
---|---|---|---|---|---|

OLS | 889,784 | 48.52 | 4026 | 0.464 | 0.454 |

LMM | 778,693 | 45.39 | 3995 | 0.527 | 0.519 |

GWR | 710,468 | 43.35 | 3989 | 0.572 | 0.536 |

MGWR | 681,806 | 42.47 | 3988 | 0.589 | 0.547 |

TWR | 594,131 | 39.65 | 3953 | 0.643 | 0.637 |

GTWR | 443,198 | 34.24 | 3912 | 0.734 | 0.729 |

Parameter | Estimate | Std. Error | t Test | p Value | ||||
---|---|---|---|---|---|---|---|---|

OLS | LMM | OLS | LMM | OLS | LMM | OLS | LMM | |

Intercept | 36.187 | 47.556 | 20.306 | 20.162 | 1.78 | 2.36 | 0.075 | 0.046 |

Slope | −2.936 | −2.862 | 0.952 | 0.942 | −3.08 | −3.04 | 0.002 | 0.016 |

Age | 0.353 | 0.362 | 0.091 | 0.098 | 3.87 | 3.7 | 0.000 | 0.006 |

DBH | 1.775 | 1.622 | 0.259 | 0.321 | 6.84 | 5.06 | 0.000 | 0.001 |

RVI | −3.075 | −3.840 | 1.047 | 1.016 | −2.94 | −3.78 | 0.003 | 0.005 |

B3-Mean | 8.805 | 9.2573 | 1.900 | 1.808 | 4.63 | 5.12 | 0.000 | 0.001 |

B4-Mean | −7.196 | −8.077 | 1.745 | 1.780 | −4.12 | −4.54 | 0.000 | 0.002 |

B4-Entropy | 11.984 | 12.415 | 5.646 | 5.476 | −2.12 | −2.27 | 0.034 | 0.053 |

Parameter | Models | Mean | STD | Min | Median | Max |
---|---|---|---|---|---|---|

Intercept | GWR | 59.122 | 14.526 | 31.178 | 66.296 | 80.532 |

MGWR | 42.777 | 0.363 | 42.055 | 42.849 | 43.510 | |

TWR | 19.721 | 41.639 | −35.698 | 26.179 | 66.296 | |

GTWR | 25.408 | 56.280 | −113.552 | 30.221 | 196.112 | |

Slope | GWR | −3.425 | 1.522 | −5.925 | −3.688 | −0.035 |

MGWR | −2.017 | 0.077 | −2.081 | −2.067 | −1.808 | |

TWR | −3.103 | 0.425 | −3.688 | −2.926 | −2.736 | |

GTWR | −2.869 | 1.615 | −7.173 | −2.796 | 2.006 | |

Age | GWR | 0.236 | 0.371 | −0.426 | 0.18 | 0.912 |

MGWR | 0.369 | 0.183 | 0.034 | 0.341 | 1.024 | |

TWR | 0.444 | 0.296 | 0.180 | 0.297 | 0.922 | |

GTWR | 0.428 | 0.316 | −0.021 | 0.350 | 1.182 | |

DBH | GWR | 2.264 | 1.497 | 0.432 | 1.469 | 4.982 |

MGWR | 1.633 | 0.035 | 1.571 | 1.636 | 1.694 | |

TWR | 2.219 | 2.296 | −0.256 | 1.469 | 5.432 | |

GTWR | 1.810 | 1.762 | −0.764 | 1.380 | 6.481 | |

RVI | GWR | −4.889 | 1.628 | −10.281 | −4.799 | −3.117 |

MGWR | −3.166 | 0.375 | −3.734 | −3.220 | −2.472 | |

TWR | −1.322 | 1.482 | −3.347 | −0.594 | 0.191 | |

GTWR | −1.501 | 5.905 | −18.245 | −0.324 | 12.037 | |

B3-Mean | GWR | 9.977 | 2.213 | 5.484 | 10.983 | 11.7 |

MGWR | 7.227 | 0.042 | 7.142 | 7.225 | 7.337 | |

TWR | 5.942 | 4.192 | 1.951 | 3.959 | 11.665 | |

GTWR | 7.328 | 8.908 | −4.139 | 4.086 | 34.291 | |

B4-Mean | GWR | −9.94 | 3.406 | −15.417 | −10.35 | −3.572 |

MGWR | −6.508 | 0.082 | −6.613 | −6.550 | −6.285 | |

TWR | −5.238 | 4.067 | −10.350 | −4.783 | −0.395 | |

GTWR | −9.008 | 9.704 | −40.573 | −6.802 | 5.123 | |

B4-Entropy | GWR | −9.398 | 4.682 | −17.063 | −10.178 | 1.933 |

MGWR | −11.405 | 0.506 | −11.962 | −11.640 | −10.092 | |

TWR | −4.052 | 9.373 | −11.391 | −10.178 | 9.593 | |

GTWR | 1.475 | 14.355 | −41.318 | 0.415 | 36.677 |

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**MDPI and ACS Style**

Zhang, X.; Sun, Y.; Jia, W.; Wang, F.; Guo, H.; Ao, Z.
Research on the Temporal and Spatial Distributions of Standing Wood Carbon Storage Based on Remote Sensing Images and Local Models. *Forests* **2022**, *13*, 346.
https://doi.org/10.3390/f13020346

**AMA Style**

Zhang X, Sun Y, Jia W, Wang F, Guo H, Ao Z.
Research on the Temporal and Spatial Distributions of Standing Wood Carbon Storage Based on Remote Sensing Images and Local Models. *Forests*. 2022; 13(2):346.
https://doi.org/10.3390/f13020346

**Chicago/Turabian Style**

Zhang, Xiaoyong, Yuman Sun, Weiwei Jia, Fan Wang, Haotian Guo, and Ziqi Ao.
2022. "Research on the Temporal and Spatial Distributions of Standing Wood Carbon Storage Based on Remote Sensing Images and Local Models" *Forests* 13, no. 2: 346.
https://doi.org/10.3390/f13020346