{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,3]],"date-time":"2026-03-03T11:25:15Z","timestamp":1772537115600,"version":"3.50.1"},"reference-count":50,"publisher":"MDPI AG","issue":"23","license":[{"start":{"date-parts":[[2023,12,1]],"date-time":"2023-12-01T00:00:00Z","timestamp":1701388800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000104","name":"NASA Space Technology Graduate Research Opportunity (NSTGRO)","doi-asserted-by":"publisher","award":["80NSSC22K1213"],"award-info":[{"award-number":["80NSSC22K1213"]}],"id":[{"id":"10.13039\/100000104","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Early spaceborne laser altimetry mission development starts in pre-phase A design, where diverse ideas are evaluated against mission science requirements. A key challenge is predicting realistic instrument performance through forward modeling at an arbitrary spatial scale. Analytical evaluations compromise accuracy for speed, while radiative transfer modeling is not applicable at the global scale due to computational expense. Instead of predicting the arbitrary properties of a lidar measurement, we develop a baseline theory to predict only the distribution of uncertainty, specifically for the terrain elevation retrieval based on terrain slope and fractional canopy cover features through a deep neural network Gaussian mixture model, also known as a mixture density network (MDN). Training data were created from differencing geocorrected Global Ecosystem Dynamics Investigation (GEDI) L2B elevation measurements with 32 independent reference lidar datasets in the contiguous U.S. from the National Ecological Observatory Network. We trained the MDN and selected hyperparameters based on the regional distribution predictive capability. On average, the relative error of the equivalent standard deviation of the predicted regional distributions was 15.9%, with some anomalies in accuracy due to generalization and insufficient feature diversity and correlation. As an application, we predict the percent of elevation residuals of a GEDI-like lidar within a given mission threshold from 60\u00b0S to 78.25\u00b0N, which correlates to a qualitative understanding of prediction accuracy and instrument performance.<\/jats:p>","DOI":"10.3390\/rs15235594","type":"journal-article","created":{"date-parts":[[2023,12,1]],"date-time":"2023-12-01T08:36:59Z","timestamp":1701419819000},"page":"5594","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Modeling Uncertainty of GEDI Clear-Sky Terrain Height Retrievals Using a Mixture Density Network"],"prefix":"10.3390","volume":"15","author":[{"given":"Jonathan","family":"Sipps","sequence":"first","affiliation":[{"name":"Department of Aerospace Engineering and Engineering Mechanics, Cockrell School of Engineering, University of Texas at Austin, Austin, TX 78705, USA"},{"name":"Center for Space Research, University of Texas at Austin, Austin, TX 78759, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7564-1193","authenticated-orcid":false,"given":"Lori A.","family":"Magruder","sequence":"additional","affiliation":[{"name":"Department of Aerospace Engineering and Engineering Mechanics, Cockrell School of Engineering, University of Texas at Austin, Austin, TX 78705, USA"},{"name":"Center for Space Research, University of Texas at Austin, Austin, TX 78759, USA"}]}],"member":"1968","published-online":{"date-parts":[[2023,12,1]]},"reference":[{"key":"ref_1","unstructured":"Committee on the Decadal Survey for Earth Science and Applications from Space, Space Studies Board, Division on Engineering and Physical Sciences, and National Academies of Sciences, Engineering, and Medicine (2018). Thriving on Our Changing Planet: A Decadal Strategy for Earth Observation from Space, National Academies Press."},{"key":"ref_2","unstructured":"Donnellan, A., Harding, D., Lundgren, P., Wessels, K., Simard, M., Parrish, C., Jones, C., Lou, Y., Stoker, J., and Ranson, K.J. (2021). Observing Earth\u2019s Changing Surface Topography & Vegetation Structure: A Framework for the Decade, NASA\u2019s Surface Topography and Vegetation Incubation Study Team Report; Jet Propulsion Laboratory, California Institute of Technology, NASA Goddard Space Flight Center, George Mason University, Oregon State University, United States Geological Survey."},{"key":"ref_3","unstructured":"Webb, C.E., Jay, Z.H., and Abdalati, W. (2012). The Ice, Cloud, and Land Elevation Satellite (ICESat) Summary Mission Timeline and Performance Relative to Pre-Launch Mission Success Criteria, NASA Goddard Space Flight Center."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"260","DOI":"10.1016\/j.rse.2016.12.029","article-title":"The Ice, Cloud, and Land Elevation Satellite-2 (ICESat-2): Science Requirements, Concept, and Implementation","volume":"190","author":"Markus","year":"2017","journal-title":"Remote Sens. Environ."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"100002","DOI":"10.1016\/j.srs.2020.100002","article-title":"The Global Ecosystem Dynamics Investigation: High-Resolution Laser Ranging of the Earth\u2019s Forests and Topography","volume":"1","author":"Dubayah","year":"2020","journal-title":"Sci. Remote Sens."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2374","DOI":"10.1109\/JSTARS.2023.3244866","article-title":"Large-Scale Forest Height Mapping by Combining TanDEM-X and GEDI Data","volume":"16","author":"Choi","year":"2023","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1971","DOI":"10.5194\/gmd-15-1971-2022","article-title":"Global Evaluation of the Ecosystem Demography Model (ED v3.0)","volume":"15","author":"Ma","year":"2022","journal-title":"Geosci. Model Dev."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"113367","DOI":"10.1016\/j.rse.2022.113367","article-title":"Quantifying Aboveground Biomass Dynamics from Charcoal Degradation in Mozambique Using GEDI Lidar and Landsat","volume":"284","author":"Liang","year":"2023","journal-title":"Remote Sens. Environ."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"102348","DOI":"10.1016\/j.ecoinf.2023.102348","article-title":"Combining GEDI and Sentinel Data to Estimate Forest Canopy Mean Height and Aboveground Biomass","volume":"78","author":"Guo","year":"2023","journal-title":"Ecol. Inform."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"211166","DOI":"10.1098\/rsos.211166","article-title":"Requirements for a Global Lidar System: Spaceborne Lidar with Wall-to-Wall Coverage","volume":"8","author":"Hancock","year":"2021","journal-title":"R. Soc. Open Sci."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Hansen, J.N., Hancock, S., Prade, L., Bonner, G.M., Chen, H., Davenport, I., Jones, B.E., and Purslow, M. (2022). Assessing Novel Lidar Modalities for Maximizing Coverage of a Spaceborne System through the Use of Diode Lasers. Remote Sens., 14.","DOI":"10.3390\/rs14102426"},{"key":"ref_12","unstructured":"Crisp, N.H., Mcgrath, C.N., Roberts, P.C.E., Edmondson, S., Haigh, S.J., Holmes, B.E.A., Rojas, A.M., Oiko, V.T.A., Sinpetru, L.A., and Smith, K.L. (2022, January 15). Very Low Earth Orbit Constellations for Earth Observation. Proceedings of the 73rd International Astronautical Congress, Paris, France."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"625","DOI":"10.1007\/s12567-022-00427-2","article-title":"Investigation of Very Low Earth Orbits (VLEOs) for Global Spaceborne Lidar","volume":"14","author":"McGrath","year":"2022","journal-title":"CEAS Space J."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"6687","DOI":"10.5194\/acp-13-6687-2013","article-title":"Performance of the Line-By-Line Radiative Transfer Model (LBLRTM) for Temperature, Water Vapor, and Trace Gas Retrievals: Recent Updates Evaluated with IASI Case Studies","volume":"13","author":"Alvarado","year":"2013","journal-title":"Atmos. Chem. Phys."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"112973","DOI":"10.1016\/j.rse.2022.112973","article-title":"DART-Lux: An Unbiased and Rapid Monte Carlo Radiative Transfer Method for Simulating Remote Sensing Images","volume":"274","author":"Wang","year":"2022","journal-title":"Remote Sens. Environ."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"112952","DOI":"10.1016\/j.rse.2022.112952","article-title":"Comprehensive LiDAR Simulation with Efficient Physically-Based DART-Lux Model (I): Theory, Novelty, and Consistency Validation","volume":"272","author":"Yang","year":"2022","journal-title":"Remote Sens. Environ."},{"key":"ref_17","first-page":"1","article-title":"Analytical Formula to Investigate the Modulation of Sloped Targets Using LiDAR Waveform","volume":"60","author":"Hu","year":"2022","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"25026","DOI":"10.1364\/OE.24.025026","article-title":"Analytical and Numerical Approaches to Study Echo Laser Pulse Profile Affected by Target and Atmospheric Turbulence","volume":"24","author":"Hao","year":"2016","journal-title":"Opt. Express"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"294","DOI":"10.1029\/2018EA000506","article-title":"The GEDI Simulator: A Large-Footprint Waveform Lidar Simulator for Calibration and Validation of Spaceborne Missions","volume":"6","author":"Hancock","year":"2019","journal-title":"Earth Space Sci."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Huettermann, S., Jones, S., Soto-Berelov, M., and Hislop, S. (2022). Intercomparison of Real and Simulated GEDI Observations across Sclerophyll Forests. Remote Sens., 14.","DOI":"10.3390\/rs14092096"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2509","DOI":"10.1029\/1999GL010484","article-title":"Modeling Laser Altimeter Return Waveforms over Complex Vegetation Using High-Resolution Elevation Data","volume":"26","author":"Blair","year":"1999","journal-title":"Geophys. Res. Lett."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"112477","DOI":"10.1016\/j.rse.2021.112477","article-title":"Modelling Lidar-Derived Estimates of Forest Attributes over Space and Time: A Review of Approaches and Future Trends","volume":"260","author":"Coops","year":"2021","journal-title":"Remote Sens. Environ."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"112760","DOI":"10.1016\/j.rse.2021.112760","article-title":"Global Canopy Height Regression and Uncertainty Estimation from GEDI LIDAR Waveforms with Deep Ensembles","volume":"268","author":"Lang","year":"2022","journal-title":"Remote Sens. Environ."},{"key":"ref_24","unstructured":"Bishop, C.M. (1994). Mixture Density Networks, Neural Computing Research Group; Department of Computer Science and Applied Mathematics."},{"key":"ref_25","unstructured":"Brando Guillaumes, A. (2017). Mixture Density Networks for Distribution and Uncertainty Estimation. [Master\u2019s Thesis, Universitat Polit\u00e8cnica de Catalunya]."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"032002","DOI":"10.1088\/1361-6501\/abc867","article-title":"Airborne LiDAR: State-of-the-Art of System Design, Technology and Application","volume":"32","author":"Li","year":"2021","journal-title":"Meas. Sci. Technol."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"112571","DOI":"10.1016\/j.rse.2021.112571","article-title":"Performance Evaluation of GEDI and ICESat-2 Laser Altimeter Data for Terrain and Canopy Height Retrievals","volume":"264","author":"Liu","year":"2021","journal-title":"Remote Sens. Environ."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"7718","DOI":"10.1109\/JSTARS.2023.3298991","article-title":"Improving GEDI Footprint Geolocation Using a High-Resolution Digital Elevation Model","volume":"16","author":"Schleich","year":"2023","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Xu, Y., Ding, S., Chen, P., Tang, H., Ren, H., and Huang, H. (2023). Horizontal Geolocation Error Evaluation and Correction on Full-Waveform LiDAR Footprints via Waveform Matching. Remote Sens., 15.","DOI":"10.3390\/rs15030776"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"975","DOI":"10.1080\/15481603.2022.2085354","article-title":"Factors Affecting Relative Height and Ground Elevation Estimations of GEDI among Forest Types across the Conterminous USA","volume":"59","author":"Wang","year":"2022","journal-title":"GISci. Remote Sens."},{"key":"ref_31","unstructured":"(2023, April 08). NEON (National Ecological Observatory Network) Discrete Return LiDAR Point Cloud (DP1.30003.001), RELEASE-2023 2015. Available online: https:\/\/data.neonscience.org\/data-products\/DP1.30003.001."},{"key":"ref_32","unstructured":"Krause, K., and Goulden, T. (2015). NEON L0-to-L1 Discrete Return LiDAR Algorithm Theoretical Basis Document (ATBD), National Ecological Observatory Network."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"5844","DOI":"10.1002\/2017GL072874","article-title":"A High-accuracy Map of Global Terrain Elevations","volume":"44","author":"Yamazaki","year":"2017","journal-title":"Geophys. Res. Lett."},{"key":"ref_34","unstructured":"Buchhorn, M., Smets, B., Bertels, L., Roo, B.D., Lesiv, M., Tsendbazar, N.-E., Li, L., and Tarko, A. (2020). Copernicus Global Land Service: Land Cover 100m: Version 3 Globe 2015-2019: Product User Manual, Zenodo."},{"key":"ref_35","unstructured":"Luthcke, S.B., Rebold, T., Thomas, T., and Pennington, T. (2019). Algorithm Theoretical Basis Document (ATBD) for GEDI Waveform Geolocation for L1 and L2 Products, Version 1.0; Goddard Space Flight Center."},{"key":"ref_36","unstructured":"Hofton, M., and Blair, J.B. (2019). Algorithm Theoretical Basis Document (ATBD) for GEDI Transmit and Receive Waveform Processing for L1 and L2 Products, Version 1.0; Goddard Space Flight Center."},{"key":"ref_37","unstructured":"Beck, J., Writ, B., Luthcke, S.B., Hofton, M., and Armston, J. (2021). Global Ecosystem Dynamics Investigation (GEDI) Level 1B User Guide, Version 2.0; Goddard Space Flight Center."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Neuenschwander, A.L., and Magruder, L.A. (2019). Canopy and Terrain Height Retrievals with ICESat-2: A First Look. Remote Sens., 11.","DOI":"10.3390\/rs11141721"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"112110","DOI":"10.1016\/j.rse.2020.112110","article-title":"Validation of ICESat-2 Terrain and Canopy Heights in Boreal Forests","volume":"251","author":"Neuenschwander","year":"2020","journal-title":"Remote Sens. Environ."},{"key":"ref_40","unstructured":"Tang, H., and Armston, J. (2019). Algorithm Theoretical Basis Document (ATBD) for GEDI L2B Footprint Canopy Cover and Vertical Profile Metrics, Version 1.0; Goddard Space Flight Center."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"5285","DOI":"10.1109\/JSTARS.2021.3080711","article-title":"GEDI Elevation Accuracy Assessment: A Case Study of Southwest Spain","volume":"14","author":"Polo","year":"2021","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1109\/18.61115","article-title":"Divergence Measures Based on the Shannon Entropy","volume":"37","author":"Lin","year":"1991","journal-title":"IEEE Trans. Inform. Theory"},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Nielsen, F. (2019). On the Jensen\u2013Shannon Symmetrization of Distances Relying on Abstract Means. Entropy, 21.","DOI":"10.3390\/e21050485"},{"key":"ref_44","unstructured":"(2023, November 10). Institut National de L\u2019information Jura Department, France 2023. Available online: https:\/\/geoservices.ign.fr\/lidarhd."},{"key":"ref_45","unstructured":"(2023, November 10). OpenTopography Tasman, New Zealand 2020. Available online: https:\/\/opentopography.org\/meta\/OT.052022.2193.2."},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Snyder, J.P. (1987). Map Projections: A Working Manual, U.S. Government Printing Office.","DOI":"10.3133\/pp1395"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1080\/17538947.2013.786146","article-title":"Global, 30-m Resolution Continuous Fields of Tree Cover: Landsat-Based Rescaling of MODIS Vegetation Continuous Fields with Lidar-Based Estimates of Error","volume":"6","author":"Sexton","year":"2013","journal-title":"Int. J. Digit. Earth"},{"key":"ref_48","unstructured":"DiMiceli, C., Carroll, M., Sohlberg, R., Kim, D.-H., Kelly, M., and Townshend, J. (2023, November 10). MOD44B MODIS\/Terra Vegetation Continuous Fields Yearly L3 Global 250m SIN Grid V006 2015, Available online: https:\/\/lpdaac.usgs.gov\/products\/mod44bv006\/."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"024016","DOI":"10.1088\/1748-9326\/ac4d4f","article-title":"A 30 m Global Map of Elevation with Forests and Buildings Removed","volume":"17","author":"Hawker","year":"2022","journal-title":"Environ. Res. Lett."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"2798","DOI":"10.1016\/j.rse.2010.08.025","article-title":"Impact of Footprint Diameter and Off-Nadir Pointing on the Precision of Canopy Height Estimates from Spaceborne Lidar","volume":"115","author":"Pang","year":"2011","journal-title":"Remote Sens. Environ."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/23\/5594\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:36:05Z","timestamp":1760132165000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/23\/5594"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,12,1]]},"references-count":50,"journal-issue":{"issue":"23","published-online":{"date-parts":[[2023,12]]}},"alternative-id":["rs15235594"],"URL":"https:\/\/doi.org\/10.3390\/rs15235594","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,12,1]]}}}