Algorithm Theoretical Basis Document (ATBD) for GEDI Transmit and Receive Waveform Processing for L1 and L2 Products Michelle Hofton1, J Bryan Blair2 Contributions by Sarah Story3, Donghui Yi3 1. University of Maryland, College Park, MD 2. NASA Goddard Space Flight Center, Greenbelt, MD 3. KBR Greenbelt MD Version 1.0 Release date: December, 4th, 2019 Goddard Space Flight Center, Greenbelt, MD Authors: Principal Investigator: ________________________________ ________________________________ ________________________________ Abstract The GEDI instrument consists of 3 lasers producing a total of 8 beam ground transects that are spaced approximately 600 m apart on the Earth’s surface in the cross-track direction. Each beam transect consists of ~30 m footprint samples approximately spaced every 60 m along track. The “coverage” laser is split into two transects that are then each dithered producing four ground transects. The other two lasers are dithered only, producing two ground transects each. The fundamental footprint observations made by the GEDI instrument are received waveforms of energy (number of photons) as a function of receive time. When combined with laser pointing and positioning information, these waveforms precisely georeference the 3-dimensional surface within each laser footprint relative to a reference ellipsoid. Within each waveform the vertical distribution of intercepted surfaces is captured (e.g., ground, canopy surfaces, ocean etc.). The relative locations of each reflecting surface within the footprint is identified during postprocessing, then combined with the geolocation of each waveform provided in the L1B product to generate the geolocation product in the L2 group. This ATBD details the algorithms and approaches used to determine various ranging and other metrics within the GEDI waveforms. Version 1.0 2 Foreword This document is the Algorithm Theoretical Basis Document for the GEDI Transmit and Receive Waveform Processing for L1 and L2 Products. The GEDI Science Team assumes responsibility for this document and updates it, as required, as algorithms are refined. Reviews of this document are performed when appropriate and as needed updates to this document are made. This document is a GEDI ATBD controlled document. Changes to this document require prior approval of the project. Proposed changes shall be noted in the change log, as well as incrementing the document version number. Questions or comments concerning this document should be addressed to: Michelle Hofton University of Maryland, and NASA Goddard Space Flight Center, Code 61A [email protected] 301-286-4488 Version 1.0 3 Change History Log Revision Date Description of Change Level Approved 1.0 Major revision to focus ATBD on waveform analysis Nov 29 2019 congruent with the GEDI data products Version 1.0 4 Table of Contents Abstract ................................................................................................................................... 2 Foreword ................................................................................................................................. 3 Change History Log .............................................................................................................. 4 Table of Contents ................................................................................................................. 1 List of Tables ......................................................................................................................... 1 1.0 INTRODUCTION ....................................................................................................... 3 1.1 GEDI Data Products Overview ...................................................................................... 3 1.2 GEDI Configuration ......................................................................................................... 4 1.3 Document Overview and Objective ............................................................................ 4 1.4 GEDI Waveform Overview ............................................................................................. 5 1.5 Algorithm Objectives ...................................................................................................... 6 1.6 Related Documentation ................................................................................................. 6 1.6.1 Parent Documents ................................................................................................................................ 6 1.6.2 Applicable Documents ....................................................................................................................... 6 2.0 GEDI Transmit Waveform Analysis and Generation of the Range Vector for input to the L1B ............................................................................................................. 7 2.1 Outline of the Procedure ............................................................................................... 7 2.2 Transmit Waveform Characterization....................................................................... 7 2.2.1 Waveform Maximum and Minimum Amplitudes ................................................................. 7 2.2.2 Transmit pulse peak amplitude location .................................................................................. 8 2.2.3 Transmit Pulse Energy ....................................................................................................................... 8 2.2.4 Waveform background noise standard deviation ............................................................... 8 2.2.5 Saturation and Digitizer Artifacts ................................................................................................ 8 2.2.6 Ringing ....................................................................................................................................................... 9 2.2.7 Pulse flag ................................................................................................................................................... 9 2.2.8 Average pulse ......................................................................................................................................... 9 2.3 Transmit Waveform Interpretation: Least Squares Gaussian Fitting ............... 10 2.3.1 Overview ................................................................................................................................................ 10 2.3.2 Gaussian fit parameters.................................................................................................................. 10 2.4 Transmit Waveform Interpretation: Least Squares Extended Gaussian Fitting 11 2.4.1 Overview ................................................................................................................................................ 11 2.4.2 Extended Gaussian Fit Parameters........................................................................................... 11 2.5 Calculating Window Ranges for Subsequent Geolocation ...................................... 12 2.6 Required Inputs .............................................................................................................. 13 2.7 Summary of Parameters Output by the Transmit Waveform Processing ............ 13 3.0 Correcting Telemetered Transmit and Receive Waveforms for Known Artifacts ................................................................................................................................ 14 3.1 Outline of the Procedure ............................................................................................ 14 3.2 Approach ......................................................................................................................... 15 3.2.1 Mean noise level, mean ................................................................................................................... 15 3.2.2 Noise standard deviation, sd_corrected .................................................................................. 15 3.2.3 Corrected transmit and receive waveforms, Txwaveform and rxwaveform ....... 16 3.3 Required Inputs ............................................................................................................ 16 3.4 Summary of Output Parameters............................................................................... 16 4.0 GEDI Receive Waveform Analysis..................................................................... 16 4.1 Outline of the Procedure ............................................................................................ 16 4.2 Receive Waveform Characterization ...................................................................... 17 4.2.1 Precise noise mean and noise standard deviation for each rxwaveform ............. 17 4.2.2 Maximum and minimum amplitudes of the waveform.................................................. 17 4.2.3 Location of maximum amplitude return within waveform ......................................... 17 4.2.4 Waveform amplitude clipping .................................................................................................... 17 4.2.5 Waveform total energy ................................................................................................................... 18 4.2.6 Mean signal value within the 10k range window ............................................................. 18 4.2.7 Laser shot used in measurement model calculations ....................................................