Model-assisted inference for mean estimation of forest volume and biomass in Mexico
DOI:
https://doi.org/10.29298/rmcf.v17i96.1646Keywords:
Horvitz-Thompson estimator, quasi-systematic sampling, Sentinel-2, ecosystem services, variance, forest volume and biomassAbstract
Accurate estimation of timber volume and above-ground biomass in terms of variance reduction is essential for sustainable forest management and for the estimation of above-ground carbon. This study evaluated the performance of the Model-assisted estimator (MAE) across different functional forms, given a single continuous auxiliary variable derived from Sentinel-2A, and a model that regards the treatment as a categorical variable, compared to the Horvitz–Thompson estimator (HTE) in its simple form. Eight models (linear, generalized, and nonlinear) were analyzed using a quasi-systematic field sampling scheme in a managed temperate forest in Puebla, Mexico. The Green Normalized Difference Vegetation Index (GNDVI) was selected as an auxiliary variable using regularization methods (LASSO and Elastic Net, with cross-validation as the selection criterion). The population means estimated using MAE were consistent across models and comparable to the Horvitz–Thompson estimator. Significant differences in relative efficiency were observed in both volume and above-ground biomass estimations when analyzing the variance of MAE relative to the HTE. For harvestable volume, the model using GNDVI and silvicultural management achieved a 37.65 % reduction in variance; for above-ground biomass, the reduction was 30.21 %. The findings show that model-assisted estimation significantly improves accuracy without compromising unbiasedness.
Downloads
References
Ameztegui, A., Rodrigues, M., & Granda, V. (2022). Uncertainty of biomass stocks in Spanish forests: a comprehensive comparison of allometric equations. European Journal of Forest Research, 141, 395-407. https://doi.org/10.1007/s10342-022-01444-w DOI: https://doi.org/10.1007/s10342-022-01444-w
Arias-Téllez, A., & García-Martínez, R. (2017). Almacén de carbono en plantaciones de Pinus patula y Pinus ayacahuite en San Miguel Tenextepec, Amanalco, Estado de México. En V. J. C. Vinay, V. A. Esqueda E., O. H. Tosquy V., A. Ríos U., M. V. Vázquez H. & C. Perdomo M. (Comps.), Avances en investigación agrícola, pecuaria, forestal, acuícola, pesquera, desarrollo rural, transferencia de tecnología, biotecnología, ambiente, recursos naturales y cambio climático 2017 (pp. 1057-1065). Instituto Nacional de Investigaciones Forestales, Agrícolas y Pecuarias. https://www.researchgate.net/publication/322448012_Almacen_de_carbono_en_plantaciones_de_Pinus_patula_y_Pinus_ayacahuite_en_San_Miguel_Tenextepec_Amanalco_Estado_de_Mexico
Avendaño-Hernández, D. M., Acosta-Mireles, M., Carrillo-Anzures, F., & Etchevers-Barra, J. D. (2009). Estimación de biomasa y carbono en un bosque de Abies religiosa. Revista Fitotecnia Mexicana, 32(3), 233-238. https://revfitotecnia.mx/index.php/RFM/article/view/756 DOI: https://doi.org/10.35196/rfm.2009.3.233-238
Besic, N., Picard, N., Vega, C., Bontemps, J.-D., Hertzog, L., Renaud, J.-P., Fogel, F., Schwartz, M., Pellissier-Tanon, A., Destouet, G., Mortier, F., Planells-Rodriguez, M., & Ciais, P. (2025). Remote-sensing-based forest canopy height mapping: some models are useful, but might they provide us with even more insights when combined? Geoscientific Model Development, 18(2), 337-362. https://doi.org/10.5194/gmd-18-337-2025 DOI: https://doi.org/10.5194/gmd-18-337-2025
Breidenbach, J., & Astrup, R. (2012). Small area estimation of forest attributes in the Norwegian National Forest Inventory. European Journal of Forest Research, 131, 1255-1267. https://doi.org/10.1007/s10342-012-0596-7 DOI: https://doi.org/10.1007/s10342-012-0596-7
Comisión Nacional Forestal. (2017). Inventario Nacional Forestal y de Suelos. Procedimientos de muestreo. Versión 19.0. Comisión Nacional Forestal. https://www.conafor.gob.mx/apoyos/docs/externos/2022/DocumentosMetodologicos/2019/ANEXO_Procedimientos_de_muestreo_2019.pdf
Correa-Díaz, A., Villanueva-Díaz, J., Gutiérrez-García, J. V., Velasco-Bautista, E., Moreno-Sánchez, F., & Zamora-Morales, B. P. (2025). Efecto del clima y el manejo forestal en el crecimiento radial de un bosque de coníferas en Puebla, México. Madera y Bosques, 31, Artículo e312717. https://doi.org/10.21829/myb.2025.312717 DOI: https://doi.org/10.21829/myb.2025.312717
Dettmann, G. T., MacFarlane, D. W., Radtke, P. J., Weiskittel, A. R., Affleck, D. L. R., Poudel, K. P., & Westfall, J. (2022). Testing a generalized leaf mass estimation method for diverse tree species and climates of the continental United States. Ecological Applications, 32(7), Article e2646. https://doi.org/10.1002/eap.2646 DOI: https://doi.org/10.1002/eap.2646
Dhiman, V., & Kumar, A. (2025). Species exhibiting positive association demonstrate high above-ground biomass accumulation in the subtropical Himalayan forest ecosystem, India. Applied Ecology and Environmental Research, 23(1), 1433-1452. https://doi.org/10.15666/aeer/2301_14331452 DOI: https://doi.org/10.15666/aeer/2301_14331452
Díaz-Ríos, M. de J., Vázquez-Alarcón, A., Uribe-Gómez, M., Sánchez-Vélez, A., Lara-Bueno, A., & Cruz-León, A. (2016). Ecuaciones alométricas para estimar biomasa y carbono en aile obtenidas mediante un método no destructivo. Revista Mexicana de Ciencias Agrícolas, (Pub. Esp. 16), 3235-3249. https://www.scielo.org.mx/scielo.php?script=sci_arttext&pid=S2007-09342016001203235 DOI: https://doi.org/10.29312/remexca.v0i16.393
Frank, B., & Monleon, V. J. (2021). Comparison of variance estimators for systematic environmental sample surveys: Considerations for post-stratified estimation. Forests, 12, Article 772. https://doi.org/10.3390/f12060772 DOI: https://doi.org/10.3390/f12060772
Gitelson, A. A., Kaufman, Y. J., & Merzlyak, M. N. (1996). Use of a green channel in remote sensing of global vegetation from EOS-MODIS. Remote Sensing of Environment, 58(3), 289-298. https://doi.org/10.1016/S0034-4257(96)00072-7 DOI: https://doi.org/10.1016/S0034-4257(96)00072-7
González-Rosales, A., & Ortiz-Paniagua, C. F. (2022). Superficie forestal afectada por incendios en México: Apuntes iniciales hacia un modelo de manejo preventivo. Revista de Ciencias Ambientales, 56(1), 1-27. https://www.scielo.sa.cr/scielo.php?pid=S2215-38962022000100001&script=sci_abstract&tlng=es DOI: https://doi.org/10.15359/rca.56-1.1
Hernández-Ramos, J., García-Cuevas, X., Pérez-Miranda, R., González-Hernández, A., & Martínez-Ángel, L. (2020). Inventario y mapeo de variables forestales mediante sensores remotos en el estado de Quintana Roo, México. Madera y Bosques, 26(1), Artículo e2611884. https://myb.ojs.inecol.mx/index.php/myb/article/view/e2611884 DOI: https://doi.org/10.21829/myb.2020.2611884
Horvitz, D. G., & Thompson, D. J. (1952). A generalization of sampling without replacement from a finite universe. Journal of the American Statistical Association, 47(260), 663-685. https://doi.org/10.1080/01621459.1952.10483446 DOI: https://doi.org/10.1080/01621459.1952.10483446
Hu, Y., & Sun, Z. (2022). Assessing the capacities of different remote sensors in estimating forest stock volume based on high-precision sample plot positioning and the random forest method. Nature Environment and Pollution Technology, 21(3), 1113-1123. https://doi.org/10.46488/nept.2022.v21i03.016 DOI: https://doi.org/10.46488/NEPT.2022.v21i03.016
Khan, M. N., Tan, Y., Gul, A. A., Abbas, S., & Wang, J. (2024). Forest aboveground biomass estimation and inventory: evaluating remote sensing-based approaches. Forests, 15, Article 1055. https://doi.org/10.3390/f15061055 DOI: https://doi.org/10.3390/f15061055
López-Serrano, P. M., Vega-Nieva, D. J., Ramírez-Aldaba, H., García-Montiel, E., & Corral-Rivas, J. J. (2021). Estimación de parámetros forestales mediante datos de Sentinel 2A en Pueblo Nuevo, Durango. Revista Mexicana de Ciencias Forestales, 12(68), 81-106. https://doi.org/10.29298/rmcf.v12i68.1075 DOI: https://doi.org/10.29298/rmcf.v12i68.1075
Matiza, C., Mutanga, O., Peerbhay, K., Odindi, J., & Lottering, R. (2023). A systematic review of remote sensing and machine learning approaches for accurate carbon storage estimation in natural forests. Southern Forests: A Journal of Forest Science, 85(3-4), 123-141. https://doi.org/10.2989/20702620.2023.2251946 DOI: https://doi.org/10.2989/20702620.2023.2251946
McConville, K. S., Moisen, G. G., & Frescino, T. S. (2020). A tutorial on model-assisted estimation with application to forest inventory. Forests, 11(2), Article 244. https://doi.org/10.3390/f11020244 DOI: https://doi.org/10.3390/f11020244
McRoberts, R. E., Holden, G. R., Nelson, M. D., Liknes, G. C., & Gormanson, D. D. (2006). Using satellite imagery as ancillary data for increasing the precision of estimates for the Forest Inventory and Analysis program of the USDA Forest Service. Canadian Journal of Forest Research, 36, 2968-2980. https://doi.org/10.1139/x05-222 DOI: https://doi.org/10.1139/x05-222
McRoberts, R. E., Næsset, E., & Gobakken, T. (2013). Inference for lidar-assisted estimation of forest growing stock volume. Remote Sensing of Environment, 128, 268-275. https://doi.org/10.1016/j.rse.2012.10.007 DOI: https://doi.org/10.1016/j.rse.2012.10.007
R Core Team. (2025). R: A language and environment for statistical computing (Version 4.5.0) [Computer software]. R Foundation for Statistical Computing. https://www.r-project.org/
SAS Institute Inc. (2024). SAS/STAT® User’s guide: The GLIMMIX Procedure 2024.04-2024.09*. SAS Institute Inc. https://documentation.sas.com/api/collections/pgmsascdc/v_052/docsets/statug/content/glimmix.pdf
Soriano-Luna, M. de los Á., Ángeles-Pérez, G., Martínez-Trinidad, T., Plascencia-Escalante, F. O., & Razo-Zárate, R. (2015). Estimación de biomasa aérea por componente estructural en Zacualtipán, Hidalgo, México. Agrociencia, 49(4), 423-438. https://www.agrociencia-colpos.org/index.php/agrociencia/article/view/1156
Ståhl, G., Saarela, S., Schnell, S., Holm, S., Breidenbach, J., Healey, S. P., Patterson, P. L., Magnussen, S., Næsset, E., McRoberts, R. E., & Grégoire, T. G. (2016). Use of models in large-area forest surveys: Comparing model-assisted, model-based and hybrid estimation. Forest Ecosystems, 3, Article 5. https://doi.org/10.1186/s40663-016-0064-9 DOI: https://doi.org/10.1186/s40663-016-0064-9
Tanase, M., Martini, J. P., Miranda, P., García-García, D., Wilke, V., Diez, J., Natal, S., & San Martín, D. (2025). Estimación de variables forestales a partir de sensores Lidar y ópticos e inteligencia artificial. Cuadernos de Investigación Geográfica, 51(2), 121-132. https://doi.org/10.18172/cig.6767 DOI: https://doi.org/10.18172/cig.6767
Valbuena, R., Hernando, A., Manzanera, J. A., Görgens, E. B., Almeida, D. R. A., Mauro, F., García-Abril, A., & Coomes, D. A. (2017). Enhancing of accuracy assessment for forest above-ground biomass estimates obtained from remote sensing via hypothesis testing and overfitting evaluation. Ecological Modelling, 366, 15-26. https://doi.org/10.1016/j.ecolmodel.2017.10.009 DOI: https://doi.org/10.1016/j.ecolmodel.2017.10.009
Zadbagher, E., Marangoz, A. M., & Becek, K. (2024). Estimation of above-ground biomass using machine learning approaches with InSAR and LiDAR data in tropical peat swamp forest of Brunei Darussalam. iForest, 17(3), 172-179. https://doi.org/10.3832/ifor4434-017 DOI: https://doi.org/10.3832/ifor4434-017
Zhang, M., Zhu, J., Song, L., Qi, K., Zheng, X., Zhang, X., Ge, J., & Tian, H. (2025). How to characterize the decline of natural Pinus sylvestris var. mongolica forests on sandy land? Global Ecology and Conservation, 64, Article e03955. https://doi.org/10.1016/j.gecco.2025.e03955 DOI: https://doi.org/10.1016/j.gecco.2025.e03955
Zhao, A., Cheng, X., Cao, R., Huang, L., & Hou, Z. (2024). Continuous monitoring of forests in wetland ecosystems with remote sensing and probability sampling. Remote Sensing, 16(18), Article 3508. https://doi.org/10.3390/rs16183508 DOI: https://doi.org/10.3390/rs16183508
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2026 Revista Mexicana de Ciencias Forestales
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
The authors who publish in Revista Mexicana de Ciencias Forestales accept the following conditions:
In accordance with copyright laws, Revista Mexicana de Ciencias Forestales recognizes and respects the authors’ moral right and ownership of property rights which will be transferred to the journal for dissemination in open access.
All the texts published by Revista Mexicana de Ciencias Forestales –with no exception– are distributed under a Creative Commons License Attribution-NonCommercial 4.0 International (CC BY-NC 4.0), which allows third parties to use the publication as long as the work’s authorship and its first publication in this journal are mentioned
The author(s) can enter into independent and additional contractual agreements for the nonexclusive distribution of the version of the article published in Revista Mexicana de Ciencias Forestales (for example, include it into an institutional repository or publish it in a book) as long as it is clearly and explicitly indicated that the work was published for the first time in Revista Mexicana de Ciencias Forestales.
For all the above, the authors shall send the form of Letter-transfer of Property Rights for the first publication duly filled in and signed by the author(s). This form must be sent as a PDF file to: ciencia.forestal2@inifap.gob.mx
This work is licensed under a Creative Commons Attribution-Noncommercial 4.0 International license.
