A methodology to generate spatially continuous fields of tree heights with an optimized Allometric Scaling and Resource Limitations (ASRL) model is reported in this first of a multi-part series of articles. Model optimization is performed with the Geoscience Laser Altimeter System (GLAS) waveform data. This methodology is demonstrated by mapping tree heights over forested lands in the continental USA (CONUS) at 1 km spatial resolution. The study area is divided into 841 eco-climatic zones based on three forest types, annual total precipitation classes (30 mm intervals) and annual average temperature classes (2 °C intervals). Three model parameters (area of single leaf, α, exponent for canopy radius, η, and root absorption efficiency, γ) were selected for optimization, that is, to minimize the difference between actual and potential tree heights in each of the eco-climatic zones over the CONUS. Tree heights predicted by the optimized model were evaluated against GLAS heights using a two-fold cross validation approach (R 2 = 0.59; RMSE = 3.31 m). Comparison at the pixel level between GLAS heights (mean = 30.6 m; standard deviation = 10.7) and model predictions (mean = 30.8 m; std. = 8.4) were also performed. Further, the model predictions were compared to existing satellite-based forest height maps. The optimized ASRL model satisfactorily reproduced the pattern of tree heights over the CONUS. Subsequent articles in this series will document further improvements with the ultimate goal of mapping tree heights and forest biomass globally.
References
[1]
Simard, M.; Pinto, N.; Fisher, J.B.; Baccini, A. Mapping forest canopy height globally with spaceborne lidar. J. Geophys. Res.-Biogeosci. 2011, 116, doi:10.1029/2011jg001708.
[2]
Lefsky, M.A. A global forest canopy height map from the Moderate Resolution Imaging Spectroradiometer and the Geoscience Laser Altimeter System. Geophys. Res. Lett. 2010, 37, doi:10.1029/2010gl043622.
[3]
Zhang, G.; Ganguly, S.; Nemani, R.; White, M.; Milesi, C.; Wang, W.; Saatchi, S.; Yu, Y.; Myneni, R.B. A simple parametric estimation of live forest aboveground biomass in California using satellite derived metrics of canopy height and Leaf Area Index. Geophys. Res. Lett. 2012. under review.
[4]
Saatchi, S.S.; Harris, N.L.; Brown, S.; Lefsky, M.; Mitchard, E.T.A.; Salas, W.; Zutta, B.R.; Buermann, W.; Lewis, S.L.; Hagen, S.; Petrova, S.; White, L.; Silman, M.; Morel, A. Benchmark map of forest carbon stocks in tropical regions across three continents. Proc. Natl. Acad. Sci. USA 2011, 108, 9899–9904, doi:10.1073/pnas.1019576108. 21628575
[5]
Chopping, M.; Schaaf, C.B.; Zhao, F.; Wang, Z.S.; Nolin, A.W.; Moisen, G.G.; Martonchik, J.V.; Bull, M. Forest structure and aboveground biomass in the southwestern United States from MODIS and MISR. Remote Sens. Environ 2011, 115, 2943–2953, doi:10.1016/j.rse.2010.08.031.
[6]
Sun, G.; Ranson, K.J.; Kimes, D.S.; Blair, J.B.; Kovacs, K. Forest vertical structure from GLAS: An evaluation using LVIS and SRTM data. Remote Sens. Environ 2008, 112, 107–117, doi:10.1016/j.rse.2006.09.036.
[7]
Mitchard, E.T.A.; Saatchi, S.S.; Lewis, S.L.; Feldpausch, T.R.; Gerard, F.F.; Woodhouse, I.H.; Meir, P. Comment on “A first map of tropical Africa’s above-ground biomass derived from satellite imagery”. Environ. Res. Lett. 2011, 6, doi:10.1088/1748-9326/6/4/049001.
[8]
Selkowitz, D.J.; Green, G.; Peterson, B.; Wylie, B. A multi-sensor lidar, multi-spectral and multi-angular approach for mapping canopy height in boreal forest regions. Remote Sens. Environ 2012, 121, 458–471, doi:10.1016/j.rse.2012.02.020.
[9]
Jung, S.-E.; Kwak, D.-A.; Park, T.; Lee, W.-K.; Yoo, S. Estimating crown variables of individual trees using airborne and terrestrial laser scanners. Remote Sens 2011, 3, 2346–2363, doi:10.3390/rs3112346.
[10]
Straub, C.; Koch, B. Estimating single tree stem volume of Pinus sylvestris using airborne laser scanner and multispectral line scanner data. Remote Sens 2011, 3, 929–944, doi:10.3390/rs3050929.
[11]
Treuhaft, R.N.; Chapman, B.D.; dos Santos, J.R.; Goncalves, F.G.; Dutra, L.V.; Graca, P.M.L.A.; Drake, J.B. Vegetation profiles in tropical forests from multibaseline interferometric synthetic aperture radar, field, and lidar measurements. J. Geophys. Res.-Atmos. 2009, 114, doi:10.1029/2008jd011674.
[12]
Treuhaft, R.N.; Goncalves, F.G.; Drake, J.B.; Chapman, B.D.; dos Santos, J.R.; Dutra, L.V.; Graca, P.M.L.A.; Purcell, G.H. Biomass estimation in a tropical wet forest using Fourier transforms of profiles from lidar or interferometric SAR. Geophys. Res. Lett. 2010, 37, doi:10.1029/2010gl045608.
Kempes, C.P.; West, G.B.; Crowell, K.; Girvan, M. Predicting maximum tree heights and other traits from allometric scaling and resource limitations. Plos One 2011, 6, doi:10.1371/journal.pone.0020551.
[15]
Kozlowski, J.; Konarzewski, M. Is West, Brown and Enquist’s model of allometric scaling mathematically correct and biologically relevant? Funct. Ecol 2004, 18, 283–289, doi:10.1111/j.0269-8463.2004.00830.x.
[16]
Kozlowski, J.; Konarzewski, M. West, Brown and Enquist’s model of allometric scaling again: The same questions remain. Funct. Ecol 2005, 19, 739–743, doi:10.1111/j.1365-2435.2005.01021.x.
[17]
Zianis, D. Predicting mean aboveground forest biomass and its associated variance. Forest Ecol. Manage 2008, 256, 1400–1407, doi:10.1016/j.foreco.2008.07.002.
[18]
Etienne, R.S.; Apol, M.E.F.; Olff, H. Demystifying the West, Brown & Enquist model of the allometry of metabolism. Funct. Ecol 2006, 20, 394–399, doi:10.1111/j.1365-2435.2006.01136.x.
[19]
Brown, J.H.; Gillooly, J.F.; Allen, A.P.; Savage, V.M.; West, G.B. Response to forum commentary on “toward a metabolic theory of ecology”. Ecology 2004, 85, 1818–1821, doi:10.1890/03-0800.
[20]
Brown, J.H.; West, G.B.; Enquist, B.J. Yes, West, Brown and Enquist’s model of allometric scaling is both mathematically correct and biologically relevant. Funct. Ecol 2005, 19, 735–738, doi:10.1111/j.1365-2435.2005.01022.x.
[21]
Enquist, B.J.; West, G.B.; Brown, J.H. Extensions and evaluations of a general quantitative theory of forest structure and dynamics. Proc. Natl. Acad. Sci. USA 2009, 106, 7046–7051, doi:10.1073/pnas.0812303106. 19363161
[22]
West, G.B.; Enquist, B.J.; Brown, J.H. A general quantitative theory of forest structure and dynamics. Proc. Natl. Acad. Sci. USA 2009, 106, 7040–7045, doi:10.1073/pnas.0812294106. 19363160
[23]
Chojnacky, D.C. Allometric Scaling Theory Applied to FIA Biomass Estimation. In Proceedings of the Third Annual Forest Inventory and Analysis Symposium; McRoberts, R.E., Reams, G.A., Van Deusen, P.C., Moser, J.W., Eds.;. Gen. Tech. Rep. NC-230 North Central Research Station, USDA, Forest Service: St. Paul, MN, USA, 2002; Volume 230, pp. 96–102.
[24]
Cheng, D.L.; Li, T.; Zhong, Q.L.; Wang, G.X. Scaling relationship between tree respiration rates and biomass. Biol. Lett 2010, 6, 715–717, doi:10.1098/rsbl.2010.0070. 20356882
[25]
Choi, S.; Ni, S.; Shi, Y.; Ganguly, S.; Zhang, G.; Duong, H.V.; Lefsky, M.A.; Simard, M.; Saatchi, S.S.; Lee, S.; et al. Allometric scaling and resource limitations model of tree heights: Part 2. Site based testing of the model. Remote Sens 2013, 5, 202–223, doi:10.3390/rs5010202.
[26]
ESRI. ArcGIS Desktop 9.2 Help Desk: Resampling Under Data Management. Available online: http://webhelp.esri.com/arcgisdesktop/9.2/index.cfm?TopicName=resample_(data_management ) (accessed on 12 July 2012).
[27]
Luo, W.; Taylor, M.C.; Parker, S.R. A comparison of spatial interpolation methods to estimate continuous wind speed surfaces using irregularly distributed data from England and Wales. Int. J. Climatol 2008, 28, 947–959, doi:10.1002/joc.1583.
[28]
DAYMET. Available online: http://www.daymet.org/ (accessed on 12 July 2012).
[29]
World Meteorological Organization (WMO). Guide to Meteorological Instruments and Methods of Observation, Appendix 4B. WMO-No. 8 (CIMO Guide); WMO: Geneva, Switzerland, 2008.
[30]
North American Regional Reanalysis (NARR). Available online: http://www.emc.ncep.noaa.gov/mmb/rreanl/ (accessed on 12 July 2012).
[31]
Gesch, D.; Evans, G.; Mauck, J.; Hutchinson, J.; Carswell, W.J. The National Map—Elevation: U.S. Geological Survey Fact Sheet 2009-3053, 2009, 4.
[32]
Yuan, H.; Dai, Y.J.; Xiao, Z.Q.; Ji, D.Y.; Wei, S.G. Reprocessing the MODIS Leaf Area Index products for land surface and climate modelling. Remote Sens. Environ 2011, 115, 1171–1187, doi:10.1016/j.rse.2011.01.001.
[33]
Fry, J.A.; Xian, G.; Jin, S.M.; Dewitz, J.A.; Homer, C.G.; Yang, L.M.; Barnes, C.A.; Herold, N.D.; Wickham, J.D. Completion of the 2006 National Land Cover Database for the Conterminous United States. Photogramm. Eng. Remote Sensing 2011, 77, 859–864.
[34]
Hansen, M.C.; DeFries, R.S.; Townshend, J.R.G.; Carroll, M.; Dimiceli, C.; Sohlberg, R.A. Global percent tree cover at a spatial resolution of 500 meters: First results of the MODIS Vegetation Continuous Fields Algorithm. Earth Interact 2003, 7, 1–10.
[35]
Zwally, H.J.; Schutz, B.; Abdalati, W.; Abshire, J.; Bentley, C.; Brenner, A.; Bufton, J.; Dezio, J.; Hancock, D.; Harding, D.; et al. ICESat’s laser measurements of polar ice, atmosphere, ocean, and land. J. Geodyn 2002, 34, 405–445, doi:10.1016/S0264-3707(02)00042-X.
[36]
Abshire, J.B.; Sun, X.L.; Riris, H.; Sirota, J.M.; McGarry, J.F.; Palm, S.; Yi, D.H.; Liiva, P. Geoscience Laser Altimeter System (GLAS) on the ICESat mission: On-orbit measurement performance. Geophys. Res. Lett. 2005, 32, doi:10.1029/2005gl024028.
[37]
Brenner, A.C.; Bentley, C.R.; Csatho, B.M.; Harding, D.J.; Hofton, M.A.; Minster, J.; Roberts, L.; Saba, J.L.; Schutz, R.; Thomas, R.H.; Yi, D.; Zwally, H.J. Derivation of Range and Range Distributions from Laser Pulse Waveform Analysis for Surface Elevations, Roughness, Slope, and Vegetation Heights. Algorithm Theoretical Basis Document Version 4.1; NASA Goddard Space Flight Center: Greenbelt, MD, USA, 2003; p. 12.
[38]
Neuenschwander, A.L.; Urban, T.J.; Gutierrez, R.; Schutz, B.E. Characterization of ICESat/GLAS waveforms over terrestrial ecosystems: Implications for vegetation mapping. J. Geophys. Res.-Biogeosci 2008, 113, doi:10.1029/2007jg000557.
[39]
Gong, P.; Li, Z.; Huang, H.B.; Sun, G.Q.; Wang, L. ICESat GLAS data for urban environment monitoring. IEEE Trans. Geosci. Remote Sens 2011, 49, 1158–1172, doi:10.1109/TGRS.2010.2070514.
[40]
Lee, S.; Ni-Meister, W.; Yang, W.Z.; Chen, Q. Physically based vertical vegetation structure retrieval from ICESat data: Validation using LVIS in White Mountain National Forest, New Hampshire, USA. Remote Sens. Environ 2011, 115, 2776–2785, doi:10.1016/j.rse.2010.08.026.
[41]
Chen, Q. Retrieving vegetation height of forests and woodlands over mountainous areas in the Pacific Coast region using satellite laser altimetry. Remote Sens. Environ 2010, 114, 1610–1627, doi:10.1016/j.rse.2010.02.016.
[42]
Lefsky, M.A.; Keller, M.; Pang, Y.; de Camargo, P.B.; Hunter, M.O. Revised method for forest canopy height estimation from Geoscience Laser Altimeter System waveforms. J. Appl. Remote Sens 2007, 1, doi:10.1117/1.2795724.
[43]
Duncanson, L.I.; Niemann, K.O.; Wulder, M.A. Estimating forest canopy height and terrain relief from GLAS waveform metrics. Remote Sens. Environ 2010, 114, 138–154, doi:10.1016/j.rse.2009.08.018.
[44]
Pang, Y.; Lefsky, M.; Sun, G.Q.; Ranson, J. Impact of footprint diameter and off-nadir pointing on the precision of canopy height estimates from spaceborne lidar. Remote Sens. Environ 2011, 115, 2798–2809, doi:10.1016/j.rse.2010.08.025.
[45]
Harding, D.J.; Carabajal, C.C. ICESat waveform measurements of within-footprint topographic relief and vegetation vertical structure. Geophys. Res. Lett. 2005, 32, doi:10.1029/2005gl023471.
[46]
Neuenschwander, A.L. Evaluation of waveform deconvolution and decomposition retrieval algorithms for ICESat/GLAS data. Can. J. Remote Sens 2008, 34, S240–S246, doi:10.5589/m08-044.
[47]
Rosette, J.A.B.; North, P.R.J.; Suarez, J.C.; Los, S.O. Uncertainty within satellite LiDAR estimations of vegetation and topography. Int. J. Remote Sens 2010, 31, 1325–1342, doi:10.1080/01431160903380631.
[48]
Lagerloef, G.S.E.; Bernstein, R.L. Empirical orthogonal function-analysis of Advanced Very High-Resolution Radiometer surface-temperature patterns in Santa-Barbara Channel. J. Geophys. Res.-Oceans 1988, 93, 6863–6873, doi:10.1029/JC093iC06p06863.
[49]
Choi, S.; Lee, W.K.; Son, Y.; Yoo, S.; Lim, J.H. Changes in the distribution of South Korean forest vegetation simulated using thermal gradient indices. Sci. China Life Sci 2010, 53, 784–797, doi:10.1007/s11427-010-4025-1. 20697868
[50]
Powell, M.J.D. An efficient method for finding the minimum of a function of several variables without calculating derivatives. Comput. J 1964, 7, 155–162, doi:10.1093/comjnl/7.2.155.
[51]
Press, W.H.; Teukolsky, S.A.; Vetterling, W.T.; Flannery, B.P. Minimization or Maximization of Functions. In Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed.. Chapter 10 ed.; Cambridge University Press: Cambridge, UK/New York, NY, USA, 1992; pp. 394–445.
[52]
Kuusk, A.; Nilson, T. A directional multispectral forest reflectance model. Remote Sens. Environ 2000, 72, 244–252, doi:10.1016/S0034-4257(99)00111-X.
[53]
TRY. Plant Trait Database. Available online: http://www.try-db.org/TryWeb/Home.php (accessed on 12 July 2012).
[54]
Kattge, J.; Diaz, S.; Lavorel, S.; Prentice, C.; Leadley, P.; Bonisch, G.; Garnier, E.; Westoby, M.; Reich, P.B.; Wright, I.J.; et al. TRY—A global database of plant traits. Glob. Change Biol 2011, 17, 2905–2935, doi:10.1111/j.1365-2486.2011.02451.x.
[55]
West, G.B.; Brown, J.H.; Enquist, B.J. A general model for the structure and allometry of plant vascular systems. Nature 1999, 400, 664–667, doi:10.1038/23251.
[56]
Ridler, M.E.; Sandholt, I.; Butts, M.; Lerer, S.; Mougin, E.; Timouk, F.; Kergoat, L.; Madsen, H. Calibrating a soil–vegetation–atmosphere transfer model with remote sensing estimates of surface temperature and soil surface moisture in a semi arid environment. J. Hydrol. 2012, 436–437, 1–12.
[57]
Gholz, H.L. Environmental limits on aboveground net primary production, leaf area, and biomass in vegetation zones of the Pacific Northwest. Ecology 1982, 63, 469–481, doi:10.2307/1938964.
[58]
Smith, T.M.; Shugart, H.H.; Bonan, G.B.; Smith, J.B. Modeling the potential response of vegetation to global climate change. Adv. Ecol. Res 1992, 22, 93–116.
[59]
Obrien, S.T.; Hubbell, S.P.; Spiro, P.; Condit, R.; Foster, R.B. Diameter, height, crown, and age relationships in 8 neotropical tree species. Ecology 1995, 76, 1926–1939, doi:10.2307/1940724.
[60]
Shugart, H.H.; Saatchi, S.; Hall, F.G. Importance of structure and its measurement in quantifying function of forest ecosystems. J. Geophys. Res-Biogeo. 2010, 115, doi:10.1029/2009jg000993.
[61]
Ryan, M.G.; Yoder, B.J. Hydraulic limits to tree height and tree growth. Bioscience 1997, 47, 235–242, doi:10.2307/1313077.
[62]
Pan, Y.; Chen, J.M.; Birdsey, R.; McCullough, K.; He, L.; Deng, F. Age structure and disturbance legacy of North American forests. Biogeosciences 2011, 8, 715–732, doi:10.5194/bg-8-715-2011.
[63]
Nadeau, C.; Bengio, Y. Inference for the generalization error. Mach. Learn 2003, 52, 239–281, doi:10.1023/A:1024068626366.
[64]
Wu, J.; Jelinski, D.E.; Luck, M.; Tueller, P.T. Multiscale Analysis of Landscape Heterogeneity: Scale Variance and Pattern Metrics. Geogr. Inf. Sci 2000, 6, 6–19.
[65]
Wu, H.; Li, Z.L. Scale issues in remote sensing: A review on analysis, processing and modeling. Sensors 2009, 9, 1768–1793, doi:10.3390/s90301768. 22573986
[66]
Seong, J.C. Modelling the accuracy of image data reprojection. Int. J. Remote Sens 2003, 24, 2309–2321, doi:10.1080/01431160210154038.
[67]
Pandey, G.R.; Cayan, D.R.; Dettinger, M.D.; Georgakakos, K.P. A hybrid orographic plus statistical model for downscaling daily precipitation in northern California. J. Hydrometeorol 2000, 1, 491–506, doi:10.1175/1525-7541(2000)001<0491:AHOPSM>2.0.CO;2.
[68]
Lundquist, J.D.; Cayan, D.R. Surface temperature patterns in complex terrain: Daily variations and long-term change in the central Sierra Nevada, California. J. Geophys. Res.-Atmos. 2007, 112, doi:10.1029/2006jd007561.
[69]
Parkhurst, D.F.; Loucks, O.L. Optimal leaf size in relation to environment. J. Ecol 1972, 60, 505–537, doi:10.2307/2258359.
[70]
Grier, C.C.; Running, S.W. Leaf area of mature Northwestern Coniferous Forests—Relation to site water-balance. Ecology 1977, 58, 893–899, doi:10.2307/1936225.
[71]
Westoby, M.; Falster, D.S.; Moles, A.T.; Vesk, P.A.; Wright, I.J. Plant ecological strategies: Some leading dimensions of variation between species. Annu. Rev. Ecol. Syst 2002, 33, 125–159, doi:10.1146/annurev.ecolsys.33.010802.150452.
[72]
Golluscio, R.A.; Oesterheld, M. Water use efficiency of twenty-five co-existing Patagonian species growing under different soil water availability. Oecologia 2007, 154, 207–217, doi:10.1007/s00442-007-0800-5. 17641918
[73]
Goldstein, G.; Rada, F.; Rundel, P.; Azocar, A.; Orozco, A. Gas-exchange and water relations of evergreen and deciduous tropical savanna trees. Ann. Sci. Forest 1989, 46, S448–S453, doi:10.1051/forest:198905ART0100.
[74]
Medina, E.; Francisco, M. Photosynthesis and water relations of savanna tree species differing in leaf phenology. Tree Physiol 1994, 14, 1367–1381, doi:10.1093/treephys/14.12.1367. 14967610
