{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T11:14:27Z","timestamp":1780485267170,"version":"3.54.1"},"reference-count":47,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2018,11,19]],"date-time":"2018-11-19T00:00:00Z","timestamp":1542585600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"NASA's Carbon Monitoring System","award":["Healey CMS2016, Cohen CMS201"],"award-info":[{"award-number":["Healey CMS2016, Cohen CMS201"]}]},{"name":"ERA-GAS","award":["FORCLIMIT (grant number FR-2017\/0006)"],"award-info":[{"award-number":["FORCLIMIT (grant number FR-2017\/0006)"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Recent developments in remote sensing (RS) technology have made several sources of auxiliary data available to support forest inventories. Thus, a pertinent question is how different sources of RS data should be combined with field data to make inventories cost-efficient. Hierarchical model-based estimation has been proposed as a promising way of combining: (i) wall-to-wall optical data that are only weakly correlated with forest structure; (ii) a discontinuous sample of active RS data that are more strongly correlated with structure; and (iii) a sparse sample of field data. Model predictions based on the strongly correlated RS data source are used for estimating a model linking the target quantity with weakly correlated wall-to-wall RS data. Basing the inference on the latter model, uncertainties due to both modeling steps must be accounted for to obtain reliable variance estimates of estimated population parameters, such as totals or means. Here, we generalize previously existing estimators for hierarchical model-based estimation to cases with non-homogeneous error variance and cases with correlated errors, for example due to clustered sample data. This is an important generalization to take into account data from practical surveys. We apply the new estimation framework to case studies that mimic the data that will be available from the Global Ecosystem Dynamics Investigation (GEDI) mission and compare the proposed estimation framework with alternative methods. Aboveground biomass was the variable of interest, Landsat data were available wall-to-wall, and sample RS data were obtained from an airborne LiDAR campaign that produced simulated GEDI waveforms. The results show that generalized hierarchical model-based estimation has potential to yield more precise estimates than approaches utilizing only one source of RS data, such as conventional model-based and hybrid inferential approaches.<\/jats:p>","DOI":"10.3390\/rs10111832","type":"journal-article","created":{"date-parts":[[2018,11,21]],"date-time":"2018-11-21T11:23:27Z","timestamp":1542799407000},"page":"1832","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":89,"title":["Generalized Hierarchical Model-Based Estimation for Aboveground Biomass Assessment Using GEDI and Landsat Data"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9044-7249","authenticated-orcid":false,"given":"Svetlana","family":"Saarela","sequence":"first","affiliation":[{"name":"Faculty of Forest Sciences, Swedish University of Agricultural Sciences, SLU Skogsmarksgr\u00e4nd 17, SE-90183 Ume\u00e5, Sweden"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"S\u00f6ren","family":"Holm","sequence":"additional","affiliation":[{"name":"Faculty of Forest Sciences, Swedish University of Agricultural Sciences, SLU Skogsmarksgr\u00e4nd 17, SE-90183 Ume\u00e5, Sweden"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sean","family":"Healey","sequence":"additional","affiliation":[{"name":"Inventory and Monitoring, United States Department of Agriculture (USDA) Forest Service, 1400 Independence Ave, SW, Washington, DC 20250-1111, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hans-Erik","family":"Andersen","sequence":"additional","affiliation":[{"name":"Inventory and Monitoring, United States Department of Agriculture (USDA) Forest Service, 1400 Independence Ave, SW, Washington, DC 20250-1111, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hans","family":"Petersson","sequence":"additional","affiliation":[{"name":"Faculty of Forest Sciences, Swedish University of Agricultural Sciences, SLU Skogsmarksgr\u00e4nd 17, SE-90183 Ume\u00e5, Sweden"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wilmer","family":"Prentius","sequence":"additional","affiliation":[{"name":"Faculty of Forest Sciences, Swedish University of Agricultural Sciences, SLU Skogsmarksgr\u00e4nd 17, SE-90183 Ume\u00e5, Sweden"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Paul","family":"Patterson","sequence":"additional","affiliation":[{"name":"Inventory and Monitoring, United States Department of Agriculture (USDA) Forest Service, 1400 Independence Ave, SW, Washington, DC 20250-1111, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2460-5843","authenticated-orcid":false,"given":"Erik","family":"N\u00e6sset","sequence":"additional","affiliation":[{"name":"Faculty of Environmental Sciences and Natural Resource Management, Norwegian University of Life Sciences, P.O. Box 5003, NO-1432 \u00c5s, Norway"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2618-9369","authenticated-orcid":false,"given":"Timothy","family":"Gregoire","sequence":"additional","affiliation":[{"name":"School of Forestry and Environmental Studies, Yale University, 195 Prospect Street, New Haven, CT 06511, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9030-8057","authenticated-orcid":false,"given":"G\u00f6ran","family":"St\u00e5hl","sequence":"additional","affiliation":[{"name":"Faculty of Forest Sciences, Swedish University of Agricultural Sciences, SLU Skogsmarksgr\u00e4nd 17, SE-90183 Ume\u00e5, Sweden"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2018,11,19]]},"reference":[{"key":"ref_1","unstructured":"UNFCCC (2017, September 05). United Nations Framework Convention on Climate Change. Available online: http:\/\/unfccc.int\/resource\/convkp\/kpeng.html."},{"key":"ref_2","unstructured":"Europe, F., and Unece, F. (2017, September 05). State of Europe\u2019s Forests 2011. Available online: https:\/\/library.wmo.int\/index.php?lvl=notice_display&id=5268#.W_PPmcTNWUm."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"196","DOI":"10.1016\/j.rse.2012.02.001","article-title":"Lidar sampling for large-area forest characterization: A review","volume":"121","author":"Wulder","year":"2012","journal-title":"Remote Sens. Environ."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1016\/S0034-4257(01)00330-3","article-title":"Using a land cover classification based on satellite imagery to improve the precision of forest inventory area estimates","volume":"81","author":"McRoberts","year":"2002","journal-title":"Remote Sens. Environ."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1016\/j.rse.2014.11.020","article-title":"Model-assisted estimation of growing stock volume using different combinations of LiDAR and Landsat data as auxiliary information","volume":"158","author":"Saarela","year":"2015","journal-title":"Remote Sens. Environ."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Grafstr\u00f6m, A., Schnell, S., Saarela, S., Hubbell, S., and Condit, R. (2017). The continuous population approach to forest inventories and use of information in the design. Environmetrics, 28.","DOI":"10.1002\/env.2480"},{"key":"ref_7","first-page":"144","article-title":"Spatial Variation: Stochastic models and their applictation to some problems in forest surveys and other sampling investiagtions","volume":"49","year":"1960","journal-title":"Meddelanden fr\u00e5n Statens Skogsforskningsinstitut"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1429","DOI":"10.1139\/x98-166","article-title":"Design-based and model-based inference in survey sampling: Appreciating the difference","volume":"28","author":"Gregoire","year":"1998","journal-title":"Can. J. For. Res."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"3165","DOI":"10.1016\/j.rse.2011.07.002","article-title":"Parametric, bootstrap, and jackknife variance estimators for the k-Nearest Neighbors technique with illustrations using forest inventory and satellite image data","volume":"115","author":"McRoberts","year":"2011","journal-title":"Remote Sens. Environ."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"S\u00e4rndal, C.E., Swensson, B., and Wretman, J.H. (1992). Model Assisted Survey Sampling, Springer.","DOI":"10.1007\/978-1-4612-4378-6"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1139\/X10-195","article-title":"Model-assisted estimation of biomass in a LiDAR sample survey in Hedmark County, Norway","volume":"41","author":"Gregoire","year":"2011","journal-title":"Can. J. For. Res."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1177","DOI":"10.1139\/cjfr-2014-0152","article-title":"Integrating remote sensing and past inventory data under the new annual design of the Swiss National Forest Inventory using three-phase design-based regression estimation","volume":"44","author":"Massey","year":"2014","journal-title":"Can. J. For. Res."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.rse.2015.11.010","article-title":"Comparing echo-based and canopy height model-based metrics for enhancing estimation of forest aboveground biomass in a model-assisted framework","volume":"174","author":"Chirici","year":"2016","journal-title":"Remote Sens. Environ."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"3876","DOI":"10.1016\/j.rse.2008.06.003","article-title":"Regional aboveground forest biomass using airborne and spaceborne LiDAR in Qu\u00e9bec","volume":"112","author":"Boudreau","year":"2008","journal-title":"Remote Sens. Environ."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"862","DOI":"10.1139\/X09-002","article-title":"Estimating Quebec provincial forest resources using ICESat\/GLAS","volume":"39","author":"Nelson","year":"2009","journal-title":"Can. J. For. Res."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"274","DOI":"10.1016\/j.rse.2013.06.019","article-title":"Taking stock of circumboreal forest carbon with ground measurements, airborne and spaceborne LiDAR","volume":"137","author":"Neigh","year":"2013","journal-title":"Remote Sens. Environ."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"895","DOI":"10.1007\/s13595-016-0590-1","article-title":"Hierarchical model-based inference for forest inventory utilizing three sources of information","volume":"73","author":"Saarela","year":"2016","journal-title":"Ann. For. Sci."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1016\/j.rse.2017.04.004","article-title":"Hybrid three-phase estimators for large-area forest inventory using ground plots, airborne lidar, and space lidar","volume":"197","author":"Holm","year":"2017","journal-title":"Remote Sens. Environ."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1016\/j.rse.2012.01.025","article-title":"Estimating biomass in Hedmark County, Norway using national forest inventory field plots and airborne laser scanning","volume":"123","author":"Gobakken","year":"2012","journal-title":"Remote Sens. Environ."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1016\/j.rse.2017.10.007","article-title":"Combining UAV and Sentinel-2 auxiliary data for forest growing stock volume estimation through hierarchical model-based inference","volume":"204","author":"Puliti","year":"2018","journal-title":"Remote Sens. Environ."},{"key":"ref_21","unstructured":"Dubayah, R., Goetz, S., Blair, J.B., Fatoyinbo, T., Hansen, M., Healey, S.P., Hofton, M., Hurtt, G., Kellner, J., and Luthcke, S. (2018, July 03). The Global Ecosystem Dynamics Investigation. Available online: http:\/\/adsabs.harvard.edu\/abs\/2014AGUFM.U14A.07D."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Tomppo, E., Gschwantner, T., Lawrence, M., McRoberts, R., Gabler, K., Schadauer, K., Vidal, C., Lanz, A., St\u00e5hl, G., and Cienciala, E. (2010). National Forest Inventories. Pathways for Common Reporting, Springer.","DOI":"10.1007\/978-90-481-3233-1"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1524","DOI":"10.1139\/cjfr-2015-0077","article-title":"Effects of sample size and model form on the accuracy of model-based estimators of growing stock volume","volume":"45","author":"Saarela","year":"2015","journal-title":"Can. J. For. Res."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1139\/X10-161","article-title":"Model-based inference for biomass estimation in a LiDAR sample survey in Hedmark County, Norway","volume":"41","author":"Holm","year":"2011","journal-title":"Can. J. For. Res."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1016\/j.rse.2006.03.005","article-title":"A model-based approach to estimating forest area","volume":"103","author":"McRoberts","year":"2006","journal-title":"Remote Sens. Environ."},{"key":"ref_26","unstructured":"Cassel, C.M., S\u00e4rndal, C.E., and Wretman, J.H. (1977). Foundations of Inference in Survey Sampling, Wiley."},{"key":"ref_27","first-page":"1","article-title":"Use of models for improved estimation in sample-based large-area forest surveys: A review","volume":"3","author":"Saarela","year":"2016","journal-title":"For. Ecosyst."},{"key":"ref_28","unstructured":"Davidson, R., and MacKinnon, J.G. (1993). Estimation and Inference in Econometrics, Oxford University Press."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1007\/s13253-015-0205-6","article-title":"Improving the efficiency and precision of tree counts in pine plantations using airborne LiDAR data and flexible-radius plots: Model-based and design-based approaches","volume":"20","author":"Melville","year":"2015","journal-title":"J. Agric. Biol. Environ. Stat."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Saarela, S., Holm, S., and Yang, Z. (2018). HMB: Hierarchical Model-Based Estimation Approach, R package version 1.0.","DOI":"10.32614\/CRAN.package.HMB"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1","DOI":"10.21105\/joss.00026","article-title":"Armadillo: A template-based C++ library for linear algebra","volume":"1","author":"Sanderson","year":"2016","journal-title":"J. Open Source Softw."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"2509","DOI":"10.1029\/1999GL010484","article-title":"Modeling laser altimeter return waveforms over complex vegetation using high-resolution elevation data","volume":"26","author":"Blair","year":"1999","journal-title":"Geophys. Res. Lett."},{"key":"ref_33","unstructured":"Andersen, H.E., Cohen, W.B., Yang, Z., Healey, S.P., Patterson, P.L., and Dubayah, R. (2018). Model-assisted estimation of carbon using Landsat and a designed sample of lidar data. Environ. Res. Lett., in press."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1109\/LGRS.2005.857030","article-title":"A Landsat surface reflectance dataset for North America, 1990\u20132000","volume":"3","author":"Masek","year":"2006","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"6481","DOI":"10.3390\/rs5126481","article-title":"Seasonal composite Landsat TM\/ETM+ images using the medoid (a multi-dimensional median)","volume":"5","author":"Flood","year":"2013","journal-title":"Remote Sens."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1016\/j.rse.2014.12.014","article-title":"Improvement and expansion of the Fmask algorithm: Cloud, cloud shadow, and snow detection for Landsats 4\u20137, 8, and Sentinel 2 images","volume":"159","author":"Zhu","year":"2015","journal-title":"Remote Sens. Environ."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1016\/j.rse.2017.06.031","article-title":"Google Earth Engine: Planetary-scale geospatial analysis for everyone","volume":"202","author":"Gorelick","year":"2017","journal-title":"Remote Sens. Environ."},{"key":"ref_38","first-page":"345","article-title":"Completion of the 2011 National Land Cover Database for the conterminous United States\u2014Representing a decade of land cover change information","volume":"81","author":"Homer","year":"2015","journal-title":"Photogramm. Eng. Remote Sens."},{"key":"ref_39","unstructured":"CMS (2015). Carbon Monitoring System (CMS) Field Guide 2015, Pacific Northwest Research Station, USDA Forest Service."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1379","DOI":"10.14358\/PERS.74.11.1379","article-title":"Conterminous US and Alaska forest type mapping using forest inventory and analysis data","volume":"74","author":"Ruefenacht","year":"2008","journal-title":"Photogramm. Eng. Remote Sens."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Cohen, W.B., Healey, S.P., Yang, Z., Stehman, S.V., Brewer, C.K., Brooks, E.B., Gorelick, N., Huang, C., Hughes, M.J., and Kennedy, R.E. (2017). How similar are forest disturbance maps derived from different Landsat time series algorithms?. Forests, 8.","DOI":"10.3390\/f8040098"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1017","DOI":"10.1016\/j.rse.2009.12.013","article-title":"Probability- and model-based approaches to inference for proportion forest using satellite imagery as ancillary data","volume":"114","author":"McRoberts","year":"2010","journal-title":"Remote Sens. Environ."},{"key":"ref_43","unstructured":"McGaughey, R. (2012, August 24). FUSION\/LDV: Software for LIDAR Data Analysis and Visualization, Version 3.01. Available online: http:\/\/forsys.cfr.washington.edu\/fusion\/fusionlatest.html."},{"key":"ref_44","unstructured":"Legner, K., Andersen, H.E., Dobelbower, K., Cooke, A., Cohen, W., and Healey, S.P. (2018). A cost-effective field measurement protocol to support carbon monitoring\u2014Implementing a prototype design at six different US sites (SC, NJ\/PA, ME, MN, CO, OR). Gen. Tech. Rep., in press."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1185","DOI":"10.1109\/26.8924","article-title":"Gaussian approximation versus nearly exact performance analysis of optical communication systems with PPM signaling and APD receivers","volume":"36","author":"Davidson","year":"1988","journal-title":"IEEE Trans. Commun."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"3286","DOI":"10.1016\/j.rse.2011.07.012","article-title":"A threshold insensitive method for locating the forest canopy top with waveform lidar","volume":"115","author":"Hancock","year":"2011","journal-title":"Remote Sens. Environ."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/S0924-2716(99)00002-7","article-title":"The Laser Vegetation Imaging Sensor: A medium-altitude, digitisation-only, airborne laser altimeter for mapping vegetation and topography","volume":"54","author":"Blair","year":"1999","journal-title":"ISPRS J. Photogramm. Remote Sens."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/10\/11\/1832\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:30:42Z","timestamp":1760196642000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/10\/11\/1832"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,11,19]]},"references-count":47,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2018,11]]}},"alternative-id":["rs10111832"],"URL":"https:\/\/doi.org\/10.3390\/rs10111832","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,11,19]]}}}