413
Views
7
Downloads
31
Crossref
N/A
WoS
35
Scopus
0
CSCD
The increasing availability of remotely sensed data has recently challenged the traditional way of performing forest inventories, and induced an interest in model-based inference. Like traditional design-based inference, model-based inference allows for regional estimates of totals and means, but in addition for wall-to-wall mapping of forest characteristics. Recently Light Detection and Ranging (LiDAR)-based maps of forest attributes have been developed in many countries and been well received by users due to their accurate spatial representation of forest resources. However, the correspondence between such mapping and model-based inference is seldom appreciated. In this study we applied hierarchical model-based inference to produce aboveground biomass maps as well as maps of the corresponding prediction uncertainties with the same spatial resolution. Further, an estimator of mean biomass at regional level, and its uncertainty, was developed to demonstrate how mapping and regional level assessment can be combined within the framework of model-based inference.
Through a new version of hierarchical model-based estimation, allowing models to be nonlinear, we accounted for uncertainties in both the individual tree-level biomass models and the models linking plot level biomass predictions with LiDAR metrics. In a 5005 km 2 large study area in south-central Sweden the predicted aboveground biomass at the level of 18 m ×18 m map units was found to range between 9 and 447 Mg· ha −1. The corresponding root mean square errors ranged between 10 and 162 Mg· ha −1. For the entire study region, the mean aboveground biomass was 55 Mg· ha −1 and the corresponding relative root mean square error 8%. At this level 75% of the mean square error was due to the uncertainty associated with tree-level models.
Through the proposed method it is possible to link mapping and estimation within the framework of model-based inference. Uncertainties in both tree-level biomass models and models linking plot level biomass with LiDAR data are accounted for, both for the uncertainty maps and the overall estimates. The development of hierarchical model-based inference to handle nonlinear models was an important prerequisite for the study.
The increasing availability of remotely sensed data has recently challenged the traditional way of performing forest inventories, and induced an interest in model-based inference. Like traditional design-based inference, model-based inference allows for regional estimates of totals and means, but in addition for wall-to-wall mapping of forest characteristics. Recently Light Detection and Ranging (LiDAR)-based maps of forest attributes have been developed in many countries and been well received by users due to their accurate spatial representation of forest resources. However, the correspondence between such mapping and model-based inference is seldom appreciated. In this study we applied hierarchical model-based inference to produce aboveground biomass maps as well as maps of the corresponding prediction uncertainties with the same spatial resolution. Further, an estimator of mean biomass at regional level, and its uncertainty, was developed to demonstrate how mapping and regional level assessment can be combined within the framework of model-based inference.
Through a new version of hierarchical model-based estimation, allowing models to be nonlinear, we accounted for uncertainties in both the individual tree-level biomass models and the models linking plot level biomass predictions with LiDAR metrics. In a 5005 km 2 large study area in south-central Sweden the predicted aboveground biomass at the level of 18 m ×18 m map units was found to range between 9 and 447 Mg· ha −1. The corresponding root mean square errors ranged between 10 and 162 Mg· ha −1. For the entire study region, the mean aboveground biomass was 55 Mg· ha −1 and the corresponding relative root mean square error 8%. At this level 75% of the mean square error was due to the uncertainty associated with tree-level models.
Through the proposed method it is possible to link mapping and estimation within the framework of model-based inference. Uncertainties in both tree-level biomass models and models linking plot level biomass with LiDAR data are accounted for, both for the uncertainty maps and the overall estimates. The development of hierarchical model-based inference to handle nonlinear models was an important prerequisite for the study.
Andersen H-E, McGaughey RJ, Reutebuch SE (2005) Estimating forest canopy fuel parameters using LIDAR data. Remote Sens Environ 94(4):441–449
Axelsson A, Lindberg E, Olsson H (2018) Exploring multispectral ALS data for tree species classification. Remote Sens 10(2):183
Bellassen V, Luyssaert S (2014) Carbon sequestration: Managing forests in uncertain times. Nat News 506(7487):153
Breidenbach J, Astrup R (2012) Small area estimation of forest attributes in the Norwegian National Forest Inventory. Eur J For Res 131(4):1255–1267
Davidson R, MacKinnon JG (1993) Estimation and inference in econometrics. Oxford University Press
Esteban J, McRoberts RE, Fernández-Landa A, Tomé JL, Næsset E (2019) Estimating forest volume and biomass and their changes using random forests and remotely sensed data. Remote Sens 11(16):1944
Franco-Lopez H, Ek AR, Bauer ME (2001) Estimation and mapping of forest stand density, volume, and cover type using the k-nearest neighbors method. Remote Sens Environ 77(3):251–274
Fridman J, Holm S, Nilsson M, Nilsson P, Ringvall A, Ståhl G (2014) Adapting National Forest Inventories to changing requirements — the case of the Swedish National Forest Inventory at the turn of the 20th century. Silv Fenn 48:1–29
Gobakken T, Næsset E, Nelson R, Bollandsås OM, Gregoire TG, Ståhl G, Holm S, Ørka HO, Astrup R (2012) Estimating biomass in Hedmark County, Norway using national forest inventory field plots and airborne laser scanning. Remote Sens Environ 123(0):443–456
Grafström A, Schnell S, Saarela S, Hubbell S, Condit R (2017a) The continuous population approach to forest inventories and use of information in the design. Environmetrics 28(8). https://doi.org/10.1002/env.2480
Grafström A, Zhao X, Nylander M, Petersson H (2017b) A new sampling strategy for forest inventories applied to the temporary clusters of the Swedish national forest inventory. Can J For Res 47(9):1161–1167
Gregoire TG (1998) Design-based and model-based inference in survey sampling: appreciating the difference. Can J For Res 28(10):1429–1447
Gregoire TG, Næsset E, McRoberts RE, Ståhl G, Andersen H-E, Gobakken T Ene, Nelson R (2016) Statistical rigor in LiDAR-assisted estimation of aboveground forest biomass. Remote Sens Environ 173:98–108
Gregoire TG, Ståhl G, Næsset E, Gobakken T, Nelson R, Holm S (2011) Model-assisted estimation of biomass in a LiDAR sample survey in Hedmark County, Norway. Can J For Res 41(1):83–95
Haakana H, Heikkinen J, Katila M, Kangas A (2019) Efficiency of post-stratification for a large-scale forest inventory—case Finnish NFI. Ann For Sci 76(1):9
Hansen MC, DeFries RS, Townshend JR, Carroll M, DiMiceli C, Sohlberg RA (2003) Global percent tree cover at a spatial resolution of 500 meters: First results of the MODIS vegetation continuous fields algorithm. Earth Interac 7(10):1–15
Hudak AT, Crookston NL, Evans JS, Hall DE, Falkowski MJ (2008) Nearest neighbor imputation of species-level, plot-scale forest structure attributes from LiDAR data. Remote Sens Environ 112(5):2232–2245
Katila M, Tomppo E (2002) Stratification by ancillary data in multisource forest inventories employing k-nearest-neighbour estimation. Can J For Res 32(9):1548–1561
Ku HH (1966) Notes on the use of propagation of error formulas. J Res Natl Bur Stand 70(4):263–273
Lindberg E, Olofsson K, Holmgren J, Olsson H (2012) Estimation of 3D vegetation structure from waveform and discrete return airborne laser scanning data. Remote Sens Environ 118:151–161
Magnussen S (2015) Arguments for a model-dependent inference? For Int J For Res 88(3):317–325
Magnussen S, Mandallaz D, Breidenbach J, Lanz A, Ginzler C (2014) National forest inventories in the service of small area estimation of stem volume. Can J For Res 44(9):1079–1090
McRoberts RE (2006) A model-based approach to estimating forest area. Remote Sens Environ 103(1):56–66
McRoberts RE (2010) Probability- and model-based approaches to inference for proportion forest using satellite imagery as ancillary data. Remote Sens Environ 114(5):1017–1025
McRoberts RE, Chen Q, Domke GM, Ståhl G, Saarela S, Westfall JA (2016) Hybrid estimators for mean aboveground carbon per unit area. Forest Ecol Manag 378:44–56
McRoberts RE, Næsset E, Gobakken T, Chirici G, Condés S, Hou Z, Saarela S, Chen Q, Ståhl G, Walters BF (2018) Assessing components of the model-based mean square error estimator for remote sensing assisted forest applications. Can J For Res 48(6):642–649
McRoberts RE, Tomppo E, Schadauer K, Vidal C, Ståhl G, Chirici G, Lanz A, Cienciala E, Winter S, Smith WB (2009) Harmonizing national forest inventories. J For 107(4):179–187
McRoberts RE, Wendt DG, Nelson MD, Hansen MH (2002) Using a land cover classification based on satellite imagery to improve the precision of forest inventory area estimates. Remote Sens Environ 81(1):36–44
McRoberts RE, Westfall JA (2016) Propagating uncertainty through individual tree volume model predictions to large-area volume estimates. Ann For Sci 73(3):625–633
Melville G, Welsh A, Stone C (2015) 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. J Agric Biol Environ Stat 20(2):229–257
Næsset E (2002) Predicting forest stand characteristics with airborne scanning laser using a practical two-stage procedure and field data. Remote Sens Environ 80(1):88–99
Nelson R, Krabill W, Tonelli J (1988) Estimating forest biomass and volume using airborne laser data. Remote Sens Environ 24(2):247–267
Nilsson M, Nordkvist K, Jonzén J, Lindgren N, Axensten P, Wallerman J, Egberth M, Larsson S, Nilsson L, Eriksson J, Olsson H (2017) A nationwide forest attribute map of Sweden predicted using airborne laser scanning data and field data from the National Forest Inventory. Remote Sens Environ 194:447–454
Olofsson K, Holmgren J (2014) Forest stand delineation from lidar point-clouds using local maxima of the crown height model and region merging of the corresponding Voronoi cells. Remote Sens Lett 5(3):268–276
Patterson PL, Healey SP, Ståhl G, Saarela S, Holm S, Andersen H-E, Dubayah RO, Duncanson L, Hancock S, Armston J, Kellner JR, Cohen WB, Yang Z (2019) Statistical properties of hybrid estimators proposed for GEDI—NASA's Global Ecosystem Dynamics Investigation. Environ Res Lett 14(6):065007
Petersson H, Breidenbach J, Ellison D, Holm S, Muszta A, Lundblad M, Ståhl GR (2017) Assessing uncertainty: sample size trade-offs in the development and application of carbon stock models. For Sci 63(4):402–412
Qi W, Dubayah RO (2016) Combining Tandem-X InSAR and simulated GEDI lidar observations for forest structure mapping. Remote Sens Environ 187:253–266
Qi W, Saarela S, Armston J, Ståhl G, Dubayah RO (2019) Forest biomass estimation over three distinct forest types using TanDEM-X InSAR data and simulated GEDI lidar data. Remote Sens Environ 232:111, 283
Repola J (2009) Biomass equations for scots pine and norway spruce in finland. Silv Fenn 43(4):625–647
Saarela S, Grafström A, Ståhl G, Kangas A, Holopainen M, Tuominen S, Nordkvist K, Hyyppä J (2015a) Model-assisted estimation of growing stock volume using different combinations of LiDAR and Landsat data as auxiliary information. Remote Sens Environ 158:431–440
Saarela S, Holm S, Grafström A, Schnell S, Næsset E, Gregoire TG, Nelson RF, Ståhl G (2016) Hierarchical model-based inference for forest inventory utilizing three sources of information. Ann For Sci 73(4):895–910
Saarela S, Holm S, Healey SP, Andersen H-E, Petersson H, Prentius W, Patterson PL, Næsset E, Gregoire TG, Ståhl G (2018) Generalized Hierarchical model-based estimation for aboveground biomass assessment using GEDI and Landsat data. Remote Sens 10(11):1832
Saarela S, Schnell S, Grafström A, Tuominen S, Nordkvist K, Hyyppä J, Kangas A, Ståhl G (2015b) Effects of sample size and model form on the accuracy of model-based estimators of growing stock volume. Can J For Res 45:1524–1534
Saatchi SS, Harris NL, Brown S, Lefsky M, Mitchard ET, Salas W, Zutta BR, Buermann W, Lewis SL, Hagen S, Petrova S, White L, Silman M, Morel A (2011) Benchmark map of forest carbon stocks in tropical regions across three continents. PNAS 108(24):9899–9904
Santoro M, Pantze A, Fransson JE, Dahlgren J, Persson A (2012) Nation-wide clear-cut mapping in Sweden using ALOS PALSAR strip images. Remote Sens 4(6):1693–1715
Ståhl G, Holm S, Gregoire TG, Gobakken T, Næsset E, Nelson R (2011) Model-based inference for biomass estimation in a LiDAR sample survey in Hedmark County, Norway. Can J For Res 41(1):96–107
Ståhl G, Saarela S, Schnell S, Holm S, Breidenbach J, Healey SP, Patterson PL, Magnussen S, Næsset E, McRoberts RE, Gregoire TG (2016) Use of models in large-area forest surveys: comparing model-assisted, model-based and hybrid estimation. Forest Ecosyst 3(5):1–11
Tomppo E, Olsson H, Ståhl G, Nilsson M, Hagner O, Katila M (2008b) Combining national forest inventory field plots and remote sensing data for forest databases. Remote Sens Environ 112(5):1982–1999
Wulder M, White J, Fournier R, Luther J, Magnussen S (2008) Spatially explicit large area biomass estimation: three approaches using forest inventory and remotely sensed imagery in a GIS. Sensors 8(1):529–560
Zald HS, Wulder MA, White JC, Hilker T, Hermosilla T, Hobart GW, Coops NC (2016) Integrating Landsat pixel composites and change metrics with lidar plots to predictively map forest structure and aboveground biomass in Saskatchewan, Canada. Remote Sens Environ 176:188–201
The authors are thankful to the two anonymous Reviewers, whose comments helped to improve the clarity of the article.
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.