{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,13]],"date-time":"2026-01-13T05:21:50Z","timestamp":1768281710711,"version":"3.49.0"},"reference-count":51,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2018,7,3]],"date-time":"2018-07-03T00:00:00Z","timestamp":1530576000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>The German National Forest Inventory consists of a systematic grid of permanent sample plots and provides a reliable evidence-based assessment of the state and the development of Germany\u2019s forests on national and federal state level in a 10 year interval. However, the data have yet been scarcely used for estimation on smaller management levels such as forest districts due to insufficient sample sizes within the area of interests and the implied large estimation errors. In this study, we present a double-sampling extension to the existing German National Forest Inventory (NFI) that allows for the application of recently developed design-based small area regression estimators. We illustrate the implementation of the estimation procedure and evaluate its potential for future large-scale operational application by the example of timber volume estimation on two small-scale management levels (45 and 405 forest district units respectively) over the entire area of the federal German state of Rhineland-Palatinate. An airborne laserscanning (ALS) derived canopy height model and a tree species classification map based on satellite data were used as auxiliary data in an ordinary least square regression model to produce the timber volume predictions. The results support that the suggested double-sampling procedure can substantially increase estimation precision on both management levels: the two-phase estimators were able to reduce the variance of the one-phase simple random sampling estimator by 43% and 25% on average for the two management levels respectively.<\/jats:p>","DOI":"10.3390\/rs10071052","type":"journal-article","created":{"date-parts":[[2018,7,3]],"date-time":"2018-07-03T11:12:58Z","timestamp":1530616378000},"page":"1052","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["A Double-Sampling Extension of the German National Forest Inventory for Design-Based Small Area Estimation on Forest District Levels"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6367-2256","authenticated-orcid":false,"given":"Andreas","family":"Hill","sequence":"first","affiliation":[{"name":"Department of Environmental Systems Science, ETH Zurich, 8092 Zurich, Switzerland"}]},{"given":"Daniel","family":"Mandallaz","sequence":"additional","affiliation":[{"name":"Department of Environmental Systems Science, ETH Zurich, 8092 Zurich, Switzerland"}]},{"given":"Joachim","family":"Langshausen","sequence":"additional","affiliation":[{"name":"State Forest Service Rhineland-Palatinate, 56281 Emmelshausen, Germany"}]}],"member":"1968","published-online":{"date-parts":[[2018,7,3]]},"reference":[{"key":"ref_1","unstructured":"Polley, H., Schmitz, F., Hennig, P., and Kroiher, F. (2010). National Forest Inventories\u2014Pathways for Common Reporting, Springer. Chapter 13."},{"key":"ref_2","unstructured":"Th\u00fcnen-Institut (2012, February 03). Dritte Bundeswaldinventur 2012, 2014. Available online: https:\/\/bwi.info."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"857","DOI":"10.1007\/s13595-016-0559-0","article-title":"Estimates of stem wood increments in forest resources: comparison of different approaches in forest inventory: Consequences for international reporting: case studyof European forests","volume":"73","author":"Tomter","year":"2016","journal-title":"Ann. For. Sci."},{"key":"ref_4","first-page":"298","article-title":"Neukonzeption und Weiterentwicklung der Forsteinrichtung in Niedersachsen","volume":"53","author":"Saborowski","year":"1998","journal-title":"Forst und Holz (Germany)"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1979","DOI":"10.1007\/s10342-012-0648-z","article-title":"A Three-Phase Sampling Procedure for Continuous Forest Inventory with Partial Re-measurement and Updating of Terrestrial Sample Plots","volume":"131","author":"Hansen","year":"2012","journal-title":"Eur. J. For. Res."},{"key":"ref_6","unstructured":"Von L\u00fcpke, N. (2013). Approaches for the Optimisation of Double Sampling for Stratification in Repeated Forest Inventories. [Ph.D. Thesis, University of G\u00f6ttingen]."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"De Vries, P.G. (1986). Sampling Theory for Forest Inventory: A Teach-Yourself Course, Springer.","DOI":"10.1007\/978-3-642-71581-5"},{"key":"ref_8","unstructured":"Cochran, W.G. (1977). Sampling Techniques, Wiley."},{"key":"ref_9","unstructured":"S\u00e4rndal, C.E., Swensson, B., and Wretman, J. (2003). Model Assisted Survey Sampling, Springer Science & Business Media."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Gregoire, T.G., and Valentine, H.T. (2007). Sampling Strategies for Natural Resources and the Environment, CRC Press.","DOI":"10.1201\/9780203498880"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"K\u00f6hl, M., Magnussen, S.S., and Marchetti, M. (2006). Sampling Methods, Remote Sensing and GIS Multiresource Forest Inventory, Springer Science & Business Media.","DOI":"10.1007\/978-3-540-32572-7"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Mandallaz, D. (2008). Sampling Techniques for Forest Inventories, CRC Press.","DOI":"10.1201\/9781584889779"},{"key":"ref_13","unstructured":"Gillis, M., Boudewyn, P., Power, K., and Russo, G. (2010). Canada. National Forest Inventories\u2014Pathways for Common Reporting, Springer. Chapter 4."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Chojnacky, D.C. (1998). Double Sampling for Stratification: A Forest Inventory Application in the Interior West, US Department of Agriculture, Forest Service, Rocky Mountain Research Station Ogden. Technical Report.","DOI":"10.2737\/RMRS-RP-7"},{"key":"ref_15","unstructured":"Lanz, A., Br\u00e4ndli, U.B., Brassel, P., Ginzler, C., Kaufmann, E., and Th\u00fcrig, E. (2010). Switzerland. National Forest Inventories\u2013Pathways for Common Reporting, Springer. Chapter 36."},{"key":"ref_16","unstructured":"Gasparini, P., Tosi, V., and DiCosmo, L. (2010). Italy. National Forest Inventories\u2014Pathways for Common Reporting, Springer. Chapter 19."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1886","DOI":"10.1016\/j.foreco.2010.08.035","article-title":"Double sampling for stratification in periodic inventories\u2014Infinite population approach","volume":"260","author":"Saborowski","year":"2010","journal-title":"For. Ecol. Manag."},{"key":"ref_18","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_19","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_20","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1139\/cjfr-2013-0449","article-title":"A three-phase sampling extension of the generalized regression estimator with partially exhaustive information","volume":"44","author":"Mandallaz","year":"2013","journal-title":"Can. J. For. Res."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Rao, J.N. (2015). Small-Area Estimation, Wiley Online Library.","DOI":"10.1002\/9781118735855"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1255","DOI":"10.1007\/s10342-012-0596-7","article-title":"Small area estimation of forest attributes in the Norwegian National Forest Inventory","volume":"131","author":"Breidenbach","year":"2012","journal-title":"Eur. J. For. Res."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1189","DOI":"10.1139\/x11-033","article-title":"A comparison of small-area estimation techniques to estimate selected stand attributes using LiDAR-derived auxiliary variables","volume":"41","author":"Goerndt","year":"2011","journal-title":"Can. J. For. Res."},{"key":"ref_24","first-page":"373","article-title":"Small area estimations of proportion of forest and timber volume combining Lidar data and stereo aerial images with terrestrial data","volume":"28","author":"Steinmann","year":"2013","journal-title":"Can. J. For. Res."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1023","DOI":"10.1139\/cjfr-2013-0181","article-title":"New regression estimators in forest inventories with two-phase sampling and partially exhaustive information: A design-based monte carlo approach with applications to small-area estimation","volume":"43","author":"Mandallaz","year":"2013","journal-title":"Can. J. For. Res."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"581","DOI":"10.1016\/j.isprsjprs.2010.09.001","article-title":"Status and future of laser scanning, synthetic aperture radar and hyperspectral remote sensing data for forest biomass assessment","volume":"65","author":"Koch","year":"2010","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Naesset, E. (2014). Area-Based Inventory in Norway\u2014From Innovation to an Operational Reality. Forest Applications of Airborne Laser Scanning\u2014Concepts and Case Studies, Springer. Chapter 11.","DOI":"10.1007\/978-94-017-8663-8_11"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"839","DOI":"10.1007\/s10342-017-1074-z","article-title":"Area-level analysis of forest inventory variables","volume":"136","author":"Magnussen","year":"2017","journal-title":"Eur. J. For. Res."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1079","DOI":"10.1139\/cjfr-2013-0448","article-title":"National forest inventories in the service of small area estimation of stem volume","volume":"44","author":"Magnussen","year":"2014","journal-title":"Can. J. For. Res."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1139\/cjfr-2012-0381","article-title":"Design-based properties of some small-area estimators in forest inventory with two-phase sampling","volume":"43","author":"Mandallaz","year":"2013","journal-title":"Can. J. For. Res."},{"key":"ref_31","unstructured":"Bundesministerium f\u00fcr Ern\u00e4hrung, L.u.V. (2011). Aufnahmeanweisung f\u00fcr die Dritte Bundeswaldinventur BWI3 (2011\u20132012), BMELV."},{"key":"ref_32","unstructured":"Bitterlich, W. (1984). The Relascope Idea. Relative Measurements in Forestry, Commonwealth Agricultural Bureaux."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"983","DOI":"10.1007\/s10342-013-0715-0","article-title":"A flexible stem taper and volume prediction method based on mixed-effects B-spline regression","volume":"132","author":"Kublin","year":"2013","journal-title":"Eur. J. For. Res."},{"key":"ref_34","unstructured":"Schmitz, F., Polley, H., Hennig, P., Dunger, K., and Schwitzgebel, F. (2008). Die Zweite Bundeswaldinventur-BWI2: Inventur- und Auswertmethoden, Bundesministerium fur Ernahrung, Land-Wirtschaft und Verbraucherschutz (Hrsg), BMELV."},{"key":"ref_35","unstructured":"Mandallaz, D., Hill, A., and Massey, A. (2016). Design-Based Properties of Some Small-Area Estimators in Forest Inventory with Two-Phase Sampling\u2014Revised Version, Department of Environmental Systems Science, ETH Zurich. Technical Report."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Hill, A., and Massey, A. (2017, October 16). Forestinventory: Design-Based Global and Small-Area Estimations for Multiphase Forest Inventories. Available online: https:\/\/cran.r-project.org\/web\/packages\/forestinventory\/forestinventory.pdf.","DOI":"10.32614\/CRAN.package.forestinventory"},{"key":"ref_37","unstructured":"R Core Team (2018). R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing."},{"key":"ref_38","first-page":"281","article-title":"Wald\u00f6kologische Naturr\u00e4ume Deutschlands-Wuchsgebiete","volume":"43","author":"Gauer","year":"2005","journal-title":"Mitt. Ver. Forstliche Standortskunde Forstpflanzenz\u00fcchtung"},{"key":"ref_39","unstructured":"LWaldG (2000). Landeswaldgesetz Rheinland-Pfalz (Forest Act Rhineland-Palatinate), Rhineland."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Lamprecht, S., Hill, A., Stoffels, J., and Udelhoven, T. (2017). A Machine Learning Method for Co-Registration and Individual Tree Matching of Forest Inventory and Airborne Laser Scanning Data. Remote Sens., 9.","DOI":"10.3390\/rs9050505"},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Hill, A., Buddenbaum, H., and Mandallaz, D. (2018). Combining canopy height and tree species map information for large-scale timber volume estimations under strong heterogeneity of auxiliary data and variable sample plot sizes. Eur. J. For. Res.","DOI":"10.1007\/s10342-018-1118-z"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1982","DOI":"10.3390\/f6061982","article-title":"Satellite-Based Derivation of High-Resolution Forest Information Layers for Operational Forest Management","volume":"6","author":"Stoffels","year":"2015","journal-title":"Forests"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"1071","DOI":"10.1007\/s10342-011-0577-2","article-title":"Satellite-based stand-wise forest cover type mapping using a spatially adaptive classification approach","volume":"131","author":"Stoffels","year":"2012","journal-title":"Eur. J. For. Res."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"619","DOI":"10.1080\/07038992.2016.1207484","article-title":"Remote sensing technologies for enhancing forest inventories: A review","volume":"42","author":"White","year":"2016","journal-title":"Can. J. Remote Sens."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1023\/A:1010933404324","article-title":"Random forests","volume":"45","author":"Breiman","year":"2001","journal-title":"Mach. Learn."},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Congalton, R.G., and Green, K. (2008). Assessing the Accuracy of Remotely Sensed Data: Principles and Practices, CRC Press.","DOI":"10.1201\/9781420055139"},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Fahrmeir, L., Kneib, T., Lang, S., and Marx, B. (2013). Regression: Models, Methods and Applications, Springer Science & Business Media.","DOI":"10.1007\/978-3-642-34333-9"},{"key":"ref_48","first-page":"171","article-title":"Critical values and probability levels for the Wilcoxon rank sum test and the Wilcoxon signed rank test","volume":"1","author":"Wilcoxon","year":"1970","journal-title":"Sel. Tables Math. Stat."},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Kirchhoefer, M., Schumacher, J., Adler, P., and K\u00e4ndler, G. (2017). Considerations towards a Novel Approach for Integrating Angle-Count Sampling Data in Remote Sensing Based Forest Inventories. Forests, 8.","DOI":"10.3390\/f8070239"},{"key":"ref_50","unstructured":"ESA (2017, March 29). Sentinel-2 Earth Observation Mission, 2017. Available online: https:\/\/sentinel.esa.int\/web\/sentinel\/missions\/sentinel-2."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"1775","DOI":"10.1139\/cjfr-2015-0266","article-title":"Design-based regression estimation of net change for forest inventories","volume":"45","author":"Massey","year":"2015","journal-title":"Can. J. For. Res."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/10\/7\/1052\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:11:11Z","timestamp":1760195471000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/10\/7\/1052"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,7,3]]},"references-count":51,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2018,7]]}},"alternative-id":["rs10071052"],"URL":"https:\/\/doi.org\/10.3390\/rs10071052","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,7,3]]}}}