with the development and application of new modeling ap-
proaches. With the increased use of non-parametric modeling
and classification approaches increased effort is required to
provide uncertainty approaches for machine learning tech-
niques. We developed a relatively straightforward approach
to approximate prediction uncertainty for continuous maps
developed from random forest models, tested the approach in
a simulation environment and provided a case example. The
results were reasonable but the method typically provided
conservative confidence intervals for new observation. The
approach is applicable to a broad range mapping efforts that
use random forest models. This general approach may also be
applicable to other ensemble modeling techniques.
References
Baccini, A.N. Laporte, S.J. Goetz, M. Sun, and H. Dong, 2008. A first
map of tropical Africa’s above-ground biomass derived from
satellite imagery,
Environmental Research Letters
, 3:045011, 9 p.
Bacini, A., M.A. Friedl, C.E. Woodcock, and Z. Zhu, 2007. Scaling
field data to calibrate and validate moderate spatial resolution
remote sensing models,
Photogrammetric Engineering & Remote
Sensing
, 73(8):945–954.
Blackard, J.A., M.V. Finco, E.H. Helmer, G.R. Holden, M.L. Hoppus,
D.M. Jacobs, A.J. Lister, G.G. Moisen, M.D. Nelson, R. Riemann,
B. Ruefenacht, D. Salajanu, D.L. Weyermann, K.C. Winterberger,
T.J. Brandeis, R.L. Czaplewski, R.E. McRoberts, P.L. Patterson,
and R.P. Tymcio, 2008. Mapping U.S. forest biomass using
nationwide forest inventory data and moderate resolution
information,
Remote Sensing of Environment
, 112(4):1658–1677.
Breiman, L., 2001. Random forests,
Machine Learning
, 45(1):5–32.
Congalton, R.G., and K. Green, 2008.
Assessing the Accuracy of
Remotely Sensed Data: Principles and Practices
, Second edition,
CRC Press, 183 p.
Coulston, J.W., G.G. Moisen, B.T. Wilson, M.V. Finco, W.B. Cohen,
and C.K. Brewer, 2012. Modeling percent tree canopy cover: a
pilot study,
Photogrammetric Engineering & Remote Sensing
,
78(7):715–727.
Cracknell, M.J., and A.M. Reading. 2014. Geological mapping using
remote sensing data: A comparison of five machine learning
algorithms, their responses to variation in the spatial distribution
of training data and the use of explicit spatial information,
Computers & Geosciences
, 63:22–33.
Draper, N., and H. Smith, 1981.
Applied Regression Analysis
, Second
edition, John Wiley & Sons, 709 p.
Dungan, J.L., D.L. Kao, and A. Pang, 2003. Modeling and visualizing
uncertainty in continuous variables predicted using remotely
sensed data,
Proceedings of the IEEE Geoscience and Remote
Sensing Symposium
, 5:3017–3019.
Efron, B., and R.J. Tibshirani, 1993.
An Introduction to the Bootstrap
,
Chapman & Hall, 436 p.
Englund, E., 1993. Spatial simulations: Environmental applications,
Environmental Modeling with GIS
, Oxford University Press, pp.
432–437.
Evans, J.S., and S.A. Cushman, 2009. Gradient modeling of conifer
species using random forests,
Landscape Ecology
, 24: 673–683.
Fernandes, R.A., J.R. Miller, J.M. Chen, and I.G. Rubinstein, 2004.
Evaluating image-based estimates of leaf area index in boreal
conifer stands over a range of scales using high-resolution CASI
imagery,
Remote Sensing of Environment
, 89(2):200–216.
Foody, G.M., and P.M. Atkinson, 2002.
Uncertainty in Remote
Sensing and GIS
, John Wiley & Sons, 326 p.
Hernandez, P.A., I. Franke, S.K. Herzog, V. Pacheco, L. Paniagua, H.L.
Quintana, A. Soto, J.J. Swenson, C. Tovar, T.H. Valqui, J. Vargas,
and B.E. Young. 2008. Predicting species distributions in poorly-
suited landscapes,
Biodiversity and Conservation
, 17:1353–1366.
Homer, C., C. Huang, L. Yang, B. Wylie, and M. Coan, 2004.
Development of a 2001 National Land Cover Database for the
United States,
Photogrammetric Engineering & Remote Sensing
,
70(7):829–840.
Homer, C., J. Dewitz, J. Fry, M. Coan, N. Hossain, C. Larson, N.
Herold, A. McKerrow, J.N. VanDriel, and J. Wickham, 2007.
Completion of the 2001 National Land Cover Database for the
conterminous United States,
Photogrammetric Engineering &
Remote Sensing
, 73(4):337–341.
Huang, C., L. Yang, B. Wylie, and C. Homer, 2001. A strategy for
estimating tree canopy density using Landsat-7 ETM and
high resolution images over large areas,
Proceedings of the
Third International Conference on Geospatial Information in
Agriculture and Forestry
, 05-07 November, Denver, Colorado,
unpaginated CD-ROM.
Isaaks, E.H., and R.M. Srivastava, 1989.
An Introduction to Applied
Geostatistics
, Oxford University Press, pp 561.
Liaw, A., and M. Wiener, 2002. Classification and regression by
RandomForest,
R News
, 2(3):18–22.
Moisen, G.G., J.W. Coulston, B.T. Wilson, W.B. Cohen, and M.V.
Finco, 2012. Choosing appropriate subpopulations for modeling
tree canopy cover nationwide,
Proceedings of Monitoring
Across Borders: 2010 Joint Meeting of the Forest Inventory and
Analysis (FIA) Symposium and the Southern Mensurationists
(W. McWilliams and F.A. Roesch editors), e-General Technical
Report, SRS-157, Asheville, NC, U.S. Department of Agriculture,
Forest Service, Southern Research Station, pp. 195–200.
Moisen, G.G., and T.S. Frescino, 2002. Comparing five modelling
techniques for predicting forest characteristics,
Ecological
Modelling
, 157:209–225.
Molinaro, A.M., 2005. Prediction error estimation: A comparison of
resampling methods,
Bioinformatics
, 21(15):3301–3307.
Popescu, S.C., R.H. Wynne, and J.A. Scrivani, 2004. Fusion of small-
footprint lidar and multispectral data to estimate plot level
volume and biomass in deciduous and pine forests in Virginia,
USA,
Forest Science
, 50(4):551–565.
Powell, S.L., S.P. Healey, W.B. Cohen, R.E. Kennedy, G.G. Moisen,
K.B. Pierce, and J.L. Ohmann, 2010. Quantification of live
aboveground forest biomass dynamics with Landsat time-series
and field inventory data: A comparison of empirical modeling
approaches.
Remote Sensing of Environment
, 114(5):1053–1068.
Rollins, M.G., and C.K Frame (editors), 2006.
The LANDFIRE
Prototype Project: Nationally Consistent and Locally Relevant
Geospatial Data for Wildland Fire Management
, USDA Forest
Service, General Technical Report RMRS-GTR-175, Rocky
Mountain Research Station, Fort Collins, Colorado, 416 p.
Schlather, M., A. Malinowski, M. Oesting, D. Boecker, K. Strokorb,
S. Engelke, J. Martini, F. Ballani, P.J. Menck, S. Gross, U. Ober,
K. Burmeister, J. Manitz, P. Ribeiro, R. Singleton, B. Pfaff, and
R Core Team, 2014.
RandomFields: Simulation and Analysis of
Random Fields
, R package version 3.0.44, URL:
-
project.org/package=RandomFields
(last date accessed: 06
January 2016)
Wang, G., G.Z. Gertner, S. Fang, and A.B. Anderson, 2005. A
methodology for spatial uncertainty analysis of remote sensing
and GIS Products,
Photogrammetric Engineering & Remote
Sensing
, 71(12):1423–1432.
Weisberg, S., 1985.
Applied Linear Regression
, John Wiley & Sons, 324 p.
Wieland, M., and M. Pittore, 2014. Performance evaluation of
machine learning algorithms for urban pattern recognition from
multi-spectral satellite images,
Remote Sensing
, 6:2912–2939:
doi:10.3390/rs6042912
Wilson, B.T., C.W. Woodall, and D.M Griffith, 2013. Imputing forest
carbon stock estimates from inventory plots to a nationally
continuous coverage,
Carbon Balance and Management
, 8:1,
URL:
(last date
accessed: 06 January 2016).
(Received 25 January 2015; accepted 12 May 2015; final ver-
sion 21 September 2015)
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