{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,16]],"date-time":"2026-06-16T06:42:14Z","timestamp":1781592134882,"version":"3.54.5"},"reference-count":55,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2020,3,26]],"date-time":"2020-03-26T00:00:00Z","timestamp":1585180800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the Central Public-interest Scientific Institution Basal Research Fund","award":["Grant No. CAFYBB2016SZ003"],"award-info":[{"award-number":["Grant No. CAFYBB2016SZ003"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Rapidly advancing airborne laser scanning technology has become greatly useful to estimate tree- and stand-level variables at a large scale using high spatial resolution data. Compared with that of ground measurements, the accuracy of the inferred information of diameter at breast height (DBH) from a remotely sensed database and the models developed with traditional regression approaches (e.g., ordinary least square regression) may not be sufficient. Thus, this regression approach is no longer appropriate to develop accurate models and predict DBH from remotely sensed-related variables because DBH is subject to the random effects of forest stands. This study developed a generalized nonlinear mixed-effects DBH estimation model from remotely sensed imagery data. The light detection and ranging (LiDAR)-derived stand canopy density, crown projection area, and tree height were used as predictors in the DBH estimation model. These variables can be more readily measured over an extensive forest area with higher accuracy compared to the conventional field-based methods. The airborne LiDAR data for a total of 402 Picea crassifolia Kom trees on a sample plot that were divided into 16 sub-sample plots and located in the most important distribution region of western China were used. The leave-one sub-sample plot-out cross-validation method was applied to evaluate the model\u2019s prediction accuracy. The results indicated that the random effects of the sub-sample plot on the prediction of DBH were large and their inclusion into the DBH model significantly improved the prediction accuracy. The prediction accuracy of the proposed model at the mean (M) response was also substantially improved relative to the accuracy obtained from the base model. Among several tree selection alternatives evaluated, a sample size of the two largest trees per sub-sample plot used in estimating the random effects showed a significantly higher accuracy compared to other sampling alternatives. This sample size would balance both the measurement cost and potential prediction errors. The nonlinear mixed-effects DBH estimation model at the M response can also be applied if obtaining the estimates of individual tree DBH with a relatively lower cost, and a lower prediction accuracy was the purpose of the study.<\/jats:p>","DOI":"10.3390\/rs12071066","type":"journal-article","created":{"date-parts":[[2020,4,1]],"date-time":"2020-04-01T03:44:13Z","timestamp":1585712653000},"page":"1066","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":35,"title":["Prediction of Individual Tree Diameter Using a Nonlinear Mixed-Effects Modeling Approach and Airborne LiDAR Data"],"prefix":"10.3390","volume":"12","author":[{"given":"Liyong","family":"Fu","sequence":"first","affiliation":[{"name":"Research Center of Forestry Remote Sensing and Information Engineering, Central South University of Forestry and Technology, Changsha 410004, China"},{"name":"Research Institute of Forest Resource Information Techniques, Chinese Academy of Forestry, Beijing 100091, China"},{"name":"Key Laboratory of Forest Management and Growth Modeling, National Forestry and Grassland Administration, Beijing 100091, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Guangshuang","family":"Duan","sequence":"additional","affiliation":[{"name":"Research Institute of Forest Resource Information Techniques, Chinese Academy of Forestry, Beijing 100091, China"},{"name":"College of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qiaolin","family":"Ye","sequence":"additional","affiliation":[{"name":"College of Information Science and Technology, Nanjing Forestry University, Nanjing 210037, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiang","family":"Meng","sequence":"additional","affiliation":[{"name":"Research Institute of Forest Resource Information Techniques, Chinese Academy of Forestry, Beijing 100091, China"},{"name":"Key Laboratory of Forest Management and Growth Modeling, National Forestry and Grassland Administration, Beijing 100091, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Peng","family":"Luo","sequence":"additional","affiliation":[{"name":"Research Institute of Forest Resource Information Techniques, Chinese Academy of Forestry, Beijing 100091, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8623-6211","authenticated-orcid":false,"given":"Ram P.","family":"Sharma","sequence":"additional","affiliation":[{"name":"Institute of Forestry, Tribhuwan University, Kritipur, Kathmandu 44600, Nepal"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hua","family":"Sun","sequence":"additional","affiliation":[{"name":"Research Center of Forestry Remote Sensing and Information Engineering, Central South University of Forestry and Technology, Changsha 410004, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5419-4547","authenticated-orcid":false,"given":"Guangxing","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Geography and Environmental Resources, Southern Illinois University at Carbondale, Carbondale, IL 62901, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qingwang","family":"Liu","sequence":"additional","affiliation":[{"name":"Research Institute of Forest Resource Information Techniques, Chinese Academy of Forestry, Beijing 100091, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,3,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"943","DOI":"10.1016\/j.foreco.2009.11.036","article-title":"A generalized nonlinear mixed-effects height-diameter model for Eucalyptus globulus L. in northwestern Spain","volume":"259","author":"Soares","year":"2010","journal-title":"For. Ecol. Manag."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"839","DOI":"10.1007\/s00468-015-1325-x","article-title":"Comparison of seemingly unrelated regressions with multivariate errors-in-variables models for developing a system of nonlinear additive biomass equations","volume":"30","author":"Fu","year":"2016","journal-title":"Trees"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1016\/j.foreco.2016.09.012","article-title":"A generalized nonlinear mixed-effects height to crown base model for Mongolian oak in northeast China","volume":"384","author":"Fu","year":"2017","journal-title":"For. Ecol. Manag."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1016\/j.foreco.2016.09.012","article-title":"A generalized interregionalnonlinear mixed-effects crown width model for Prince Rupprecht larch in northern China","volume":"384","author":"Fu","year":"2017","journal-title":"For. Ecol. Manag."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"646","DOI":"10.1016\/j.biombioe.2007.06.022","article-title":"Estimating biomass of individual pine trees using airborne lidar","volume":"31","author":"Popescu","year":"2007","journal-title":"Biomass Bioenerg."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2602","DOI":"10.1016\/j.foreco.2008.01.044","article-title":"Spatial partitioning of biomass and diversity in a lowland Bolivian forest: Linking field and remote sensing measurements","volume":"255","author":"Broadbent","year":"2008","journal-title":"For. Ecol. Manag."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2416","DOI":"10.1016\/j.foreco.2008.01.022","article-title":"Automatic recognition and measurement of single trees based on data from airborne laser scanning over the richly structured natural forests of the Bavarian Forest National Park","volume":"255","author":"Heurich","year":"2008","journal-title":"For. Ecol. Manag."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"789","DOI":"10.1139\/x2012-019","article-title":"Evaluation of nonlinear equations for predicting diameter from tree height","volume":"42","author":"Bi","year":"2012","journal-title":"Can. J. For. Res."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"355","DOI":"10.5589\/m06-030","article-title":"A rigorous assessment of tree height measurements obtained using airborne lidar and conventional field methods","volume":"32","author":"Andersen","year":"2006","journal-title":"Can. J. Remote Sens."},{"key":"ref_10","first-page":"139","article-title":"Challenges to estimating tree height via LiDAR in closed-canopy forests: A parable from western Oregon","volume":"56","author":"Gatziolis","year":"2010","journal-title":"For. Sci."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1649","DOI":"10.1139\/x11-083","article-title":"Combining tree height samples produced by airborne laser scanning and stand management records to estimate plot volume in Eucalyptus plantations","volume":"41","author":"Vauhkonen","year":"2011","journal-title":"Can. J. For. Res."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"378","DOI":"10.1016\/j.rse.2013.07.044","article-title":"An efficient, multi-layered crown delineation algorithm for mapping individual tree structure across multiple ecosystems","volume":"154","author":"Duncanson","year":"2014","journal-title":"Remote Sens. Environ."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Aubry-Kientz, M., Dutrieux, R., Ferraz, A., Saatchi, S., Hamraz, H., Williams, J., Coomes, D., Piboule, A., and Vincent, G. (2019). A Comparative Assessment of the Performance of Individual Tree Crowns Delineation Algorithms from ALS Data in Tropical Forests. Remote Sens., 11.","DOI":"10.3390\/rs11091086"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"806","DOI":"10.1051\/forest\/2010042","article-title":"Allometric equations to predict the total aboveground biomass of radiata pine trees","volume":"67","author":"Moore","year":"2010","journal-title":"Ann. For. Sci."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1155","DOI":"10.1080\/01431160903380573","article-title":"Campaign and site effects in LiDAR prediction models for site-quality assessment of radiata pine plantations in South Australia","volume":"31","author":"Rombouts","year":"2010","journal-title":"Int. J. Remote Sens."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"295","DOI":"10.5424\/833","article-title":"Site productivity estimation using height-diameter relationships in Costa Rican secondary forests","volume":"13","author":"Campos","year":"2004","journal-title":"For. Syst."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Pinheiro, J.C., and Bates, D.M. (2000). Mixed-Effects Models in S and S-PLUS, Springer.","DOI":"10.1007\/978-1-4419-0318-1"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1139\/x03-199","article-title":"Interregional nonlinear height-diameter model with random coefficients for stone pine in Spain","volume":"34","author":"Calama","year":"2004","journal-title":"Can. J. For. Res."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"49","DOI":"10.14214\/sf.a9197","article-title":"A conspectus on estimating function theory and its application to recurrent modelling issues in forest biometry","volume":"29","author":"Schabenberger","year":"1995","journal-title":"Silva Fenn."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1016\/0378-1127(84)90068-9","article-title":"Problems of hypothesis testing of regressions with multiple measurements from individual sampling units","volume":"7","author":"West","year":"1984","journal-title":"For. Ecol. Manag."},{"key":"ref_21","first-page":"239","article-title":"Improved calibration of nonlinear mixed-effects models demonstrated on a height growth function","volume":"55","author":"Meng","year":"2009","journal-title":"For. Sci."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1016\/j.foreco.2013.03.036","article-title":"Nonlinear mixed-effects crown width models for individual trees of Chinese fir (Cunninghamia lanceolata) in south-central China","volume":"302","author":"Fu","year":"2013","journal-title":"For. Ecol. Manag."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"673","DOI":"10.2307\/2532087","article-title":"Nonlinear mixed effects models for repeated measures data","volume":"46","author":"Lindstrom","year":"1990","journal-title":"Biometrics"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Vonesh, E.F., and Chinchilli, V.M. (1997). Linear and Nonlinear Models for the Analysis of Repeated Measurements, Marcel Dekker.","DOI":"10.1201\/9781482293272"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1016\/j.foreco.2008.04.006","article-title":"A mixed nonlinear height diameter model for Pyrenean oak (Quercus pyrenaica Willd.)","volume":"256","author":"Adame","year":"2008","journal-title":"For. Ecol. Manag."},{"key":"ref_26","first-page":"43","article-title":"Law of the water transfer process of water\u2014Conversation forest in Qilian Mountains","volume":"12","author":"Dang","year":"2004","journal-title":"Chin. J. Eco-Agric."},{"key":"ref_27","first-page":"5","article-title":"Status of Forestry Ecosystem and Protection Countermeasure in the Protection Areas in Qilian Mountains","volume":"20","author":"Ma","year":"2005","journal-title":"J. Northwest For."},{"key":"ref_28","unstructured":"Pang, Y., Chen, E., Liu, Q., Xiao, Q., Zhong, K., Li, X., and Ma, M. (2008). WATER: Dataset of airborne LiDAR mission at the super site in the Dayekou watershed flight zone on Jun. 23, 2008. Chinese Academy of Forestry; Institute of Remote Sensing Applications, Chinese Academy of Sciences; Cold and Arid Regions Environmental and Engineering Research Institute, Chinese Academy of Sciences, Heihe Plan Science Data Center."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"872","DOI":"10.1109\/TGRS.2003.810682","article-title":"Aprogressive morphological filter for removing nonground measurements fromairborne LIDAR data","volume":"41","author":"Zhang","year":"2003","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"923","DOI":"10.14358\/PERS.72.8.923","article-title":"Isolating individual trees in asavanna Woodland using small footprint lidar data","volume":"72","author":"Chen","year":"2006","journal-title":"Photogramm. Eng. Remote Sens."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"170","DOI":"10.1080\/2150704X.2015.1117156","article-title":"Automated extraction of groundsurface along urban roads from mobile laser scanning point clouds","volume":"7","author":"Wu","year":"2016","journal-title":"Remote Sens. Lett."},{"key":"ref_32","unstructured":"Liu, Q. (2009). Study on the Estimation Method of Forest Parameters Using Airborne LiDAR. [Ph.D. Dissertation, Chinese Academy of Forestry]."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"357","DOI":"10.14358\/PERS.72.4.357","article-title":"Detection of Individual Tree Crowns in Airborne Lidar Data","volume":"72","author":"Koch","year":"2006","journal-title":"Photogramm. Eng. Remote Sens."},{"key":"ref_34","first-page":"83","article-title":"Extracting individual tree heights and crowns using airborne LIDAR data","volume":"30","author":"Liu","year":"2008","journal-title":"J. Beijing For. Univ."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"567","DOI":"10.1109\/TGRS.2019.2938017","article-title":"Improving Estimation of Forest Canopy Cover by Introducing Loss Ratio of Laser Pulses Using Airborne LiDAR","volume":"58","author":"Liu","year":"2019","journal-title":"IEEE Trans. Geosci. Remote"},{"key":"ref_36","unstructured":"Davidian, M., and Giltinan, D.M. (1995). Nonlinear Models for Repeated Measurement Data, Chapmanand Hall."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0034-4257(95)00224-3","article-title":"Estimation of tree heights and stand volume using an airborne lidar system","volume":"56","author":"Nilsson","year":"1996","journal-title":"Remote Sens. Environ."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1016\/j.foreco.2006.12.024","article-title":"Stand-level growth models for young scots pine stands in Finland","volume":"241","author":"Huuskonen","year":"2007","journal-title":"For. Ecol. Manag."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Venables, W.N., and Ripley, B.D. (1999). Modern Applied Statistics with S-PLUS, Springer. [3rd ed.].","DOI":"10.1007\/978-1-4757-3121-7"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"2203","DOI":"10.1139\/X09-123","article-title":"A multilevel individual tree basal area increment model for aspen in boreal mixedwood stands","volume":"39","author":"Yang","year":"2009","journal-title":"Can. J. For. Res."},{"key":"ref_41","first-page":"287","article-title":"Nonlinear mixed-effect modeling for Slash pine dominant height growth following intensive silvicultural treatments","volume":"47","author":"Fang","year":"2001","journal-title":"For. Sci."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"37","DOI":"10.14214\/sf.394","article-title":"Multilevel linear mixed model for tree diameter increment in stone pine (pinus pinea): A calibrating approach","volume":"39","author":"Calama","year":"2005","journal-title":"Silva Fenn."},{"key":"ref_43","unstructured":"Tang, S.Z., Li, Y., and Fu, L.Y. (2015). Statistical Foundation for Biomathematical Models, Higher Education Press. [2nd ed.]."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"1383","DOI":"10.1139\/x2012-090","article-title":"Evaluating marginal and conditional predictions of taper models in the absence of calibration data","volume":"42","author":"Shater","year":"2012","journal-title":"Can. J. For. Res."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"553","DOI":"10.1139\/X07-104","article-title":"Analysis and comparison of nonlinear tree height prediction strategies for Douglas-fir forests","volume":"38","author":"Temesgen","year":"2008","journal-title":"Can. J. For. Res."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"194","DOI":"10.1080\/02827580902795036","article-title":"Site-specific height growth models for six common tree species in Denmark","volume":"24","author":"Meilby","year":"2009","journal-title":"Scand. J. For. Res."},{"key":"ref_47","first-page":"27","article-title":"Individual tree-based diameter growth model of slash pine in Florida using nonlinear mixed modeling","volume":"59","author":"Timilsina","year":"2013","journal-title":"For. Sci."},{"key":"ref_48","first-page":"319","article-title":"Study on biomass of water conservation forest on North Slope of Qilian Mountains","volume":"18","author":"Wang","year":"1998","journal-title":"J. Fujian Coll. For."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"1547","DOI":"10.1139\/x11-068","article-title":"Using the dummy variable model approach to construct compatible single-tree biomass equations at different scales\u2014A case study for Masson pine (Pinus massoniana) in southern China","volume":"41","author":"Zeng","year":"2011","journal-title":"Can. J. For. Res."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"114","DOI":"10.5558\/tfc65114-2","article-title":"A Comparison of existing models for DBH estimation for large-scale photos","volume":"65","author":"Hall","year":"1989","journal-title":"For. Chron."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1093\/sjaf\/19.4.177","article-title":"The relationship of diameter at breast height and crown diameter for four species groups in Hardin county, Tennessee","volume":"19","author":"Gering","year":"1995","journal-title":"South. J. Appl. For."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1016\/j.foreco.2014.04.003","article-title":"An allometric model for estimating DBH of isolated and clustered Eucalyptus trees from measurements of crown projection area","volume":"326","author":"Verma","year":"2014","journal-title":"For. Ecol. Manag."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1093\/forestry\/cpx049","article-title":"Comparing height\u2013age and height\u2013diameter modelling approaches for estimating site productivity of natural uneven-aged forests","volume":"91","author":"Fu","year":"2018","journal-title":"Forestry"},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"202","DOI":"10.1016\/j.foreco.2006.04.028","article-title":"A generalized height-diameter model including random components for radiate pine plantations in northwestern Spain","volume":"229","author":"Anta","year":"2006","journal-title":"For. Ecol. Manag."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"1095","DOI":"10.1139\/X10-073","article-title":"Using error-in-variable regression to predict tree diameter and crown width from remotely sensed imagery","volume":"40","author":"Zhang","year":"2010","journal-title":"Can. J. For. Res."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/12\/7\/1066\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:11:48Z","timestamp":1760173908000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/12\/7\/1066"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,3,26]]},"references-count":55,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2020,4]]}},"alternative-id":["rs12071066"],"URL":"https:\/\/doi.org\/10.3390\/rs12071066","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,3,26]]}}}