Statistical properties of hybrid estimators proposed for GEDI—NASA’s global ecosystem dynamics investigation

Paul L Patterson,Sören Holm,Warren B Cohen,Göran Ståhl,Sean P Healey,John Armston,Steven Hancock,Laura Duncanson,Hans-Erik Andersen,James R Kellner,Svetlana Saarela,Ralph O Dubayah,Zhiqiang Yang

doi:10.1088/1748-9326/ab18df

Abstract

NASA’s Global Ecosystem Dynamics Investigation (GEDI) mission will collect waveform lidar data at a dense sample of ∼25 m footprints along ground tracks paralleling the orbit of the International Space Station (ISS). GEDI’s primary science deliverable will be a 1 km grid of estimated mean aboveground biomass density (Mg ha−1), covering the latitudes overflown by ISS (51.6 °S to 51.6 °N). One option for using the sample of waveforms contained within an individual grid cell to produce an estimate for that cell is hybrid inference, which explicitly incorporates both sampling design and model parameter covariance into estimates of variance around the population mean. We explored statistical properties of hybrid estimators applied in the context of GEDI, using simulations calibrated with lidar and field data from six diverse sites across the United States. We found hybrid estimators of mean biomass to be unbiased and the corresponding estimators of variance appeared to be asymptotically unbiased, with under-estimation of variance by approximately 20% when data from only two clusters (footprint tracks) were available. In our study areas, sampling error contributed more to overall estimates of variance than variability due to the model, and it was the design-based component of the variance that was the source of the variance estimator bias at small sample sizes. These results highlight the importance of maximizing GEDI’s sample size in making precise biomass estimates. Given a set of assumptions discussed here, hybrid inference provides a viable framework for estimating biomass at the scale of a 1 km grid cell while formally accounting for both variability due to the model and sampling error.

Highlights

The NASA GEDI (Global Ecosystem Dynamics Investigation) mission mounted a full-waveform us cri lidar instrument on the International Space Station (ISS) in late 2018
“scale up” from field data to spatially coincident lidar footprints using one level of models, apply those models to all lidar footprints, and use the lidar-based AGBD predictions to calibrate pte another level of models that predict AGBD using coarse-resolution optical or radar data (e.g.,(Baccini et al 2017))
We propose the use of hybrid inference ((Fattorini, 2012); (Ståhl et al 2016)) to estimate mean AGBD, with associated uncertainty, at the level of the GEDI grid cell while us cri explicitly accounting for both field-to-lidar model error as well as sampling uncertainty

Summary

Introduction

The NASA GEDI (Global Ecosystem Dynamics Investigation) mission mounted a full-waveform us cri lidar instrument on the International Space Station (ISS) in late 2018. One approach has been to “scale up” from field data to spatially coincident lidar footprints using one level of models, apply those models to all lidar footprints, and use the lidar-based AGBD predictions to calibrate pte another level of models that predict AGBD using coarse-resolution optical or radar data (e.g.,(Baccini et al 2017)) While diagnostics such as Root Mean Square Error from the latter model can be used to indicate confidence for predictions at the scale of each coarsece resolution grid cell under such an approach, ignoring residual variance in the field-to-lidar model can hide substantial uncertainty (Saarela et al 2016), as can discounting the sampling uncertainty involved with associating fine-grain lidar measurements with coarser remote sensing data

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