A Bayesian model to estimate land surface phenology parameters with harmonized Landsat 8 and Sentinel-2 images

doi:10.1016/j.rse.2021.112471

Remote Sensing of Environment

Volume 261, August 2021, 112471

https://doi.org/10.1016/j.rse.2021.112471 Get rights and content

Highlights

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We develop a statistically rigorous Bayesian land surface phenology model.
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The approach allows for estimation of LSP parameters with associated uncertainty.
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We apply the method to EVI time series made from Harmonized Landsat Sentinel-2 data.
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We demonstrate how to propagate pixel-level uncertainty through subsequent analyses.
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We made the rsBayes R package to provide code for users to implement our methods.

Abstract

We develop a Bayesian Land Surface Phenology (LSP) model and examine its performance using Enhanced Vegetation Index (EVI) observations derived from the Harmonized Landsat Sentinel-2 (HLS) dataset. Building on previous work, we propose a double logistic function that, once couched within a Bayesian model, yields posterior distributions for all LSP parameters. We assess the efficacy of the Normal, Truncated Normal, and Beta likelihoods to deliver robust LSP parameter estimates. Three case studies are presented and used to explore aspects of the proposed model. The first case study, conducted over forested pixels within an HLS tile, explores choice of likelihood and space-time varying HLS data availability for long-term average LSP parameter point and uncertainty estimation. The second case study, conducted over the same pixels using only 2018 data, compares annual LSP parameter estimates from our proposed models with those generated using methods described in Bolton et al. (2020). The third case study, conducted on a small area of interest within the HLS tile on an annual time-step (2014–2019), further examines the impact of sample size and choice of likelihood on annual LSP parameter estimates in addition to assessing potential for the proposed models to inform LSP change detection analysis. Results indicate that while the Truncated Normal and Beta likelihoods are theoretically preferable when the vegetation index is bounded, all three likelihoods performed similarly when the number of index observations is sufficiently large and values are not near the index bounds. The case studies demonstrate how pixel-level LSP parameter posterior distributions can be used to propagate uncertainty through subsequent analysis. As a companion to this article, we provide an open-source R package rsBayes and supplementary data and code used to reproduce the analysis results. The proposed model specification and software implementation delivers computationally efficient, statistically robust, and inferentially rich LSP parameter posterior distributions at the pixel-level across massive raster time series datasets. Modeling functions in the rsBayes package and supplementary code sections are threaded, allowing for the use of multiple processing cores to further speed up model fitting for massive datasets. Using a 64 CPU workstation, the first case study analysis took ~3 days to run using the Beta likelihood model. However, processing time decreases linearly as the number of CPU cores increases. We expect that run times for this LSP modeling approach will decrease substantially as the power of new computing systems increases over time.

Introduction

From spring budbreak through winter dormancy, temperate forest vegetation changes seasonally. The timing and magnitude of phenological events that indicate transitions in vegetation behavior are primarily driven by temperature and water availability (Aber and Melillo, 2001). The vegetation phenology cycle shifts with changes in climatic variables, such as seasonal average temperatures and precipitation (Jeong et al., 2011). This makes tracking changes in vegetation phenology important for understanding how climate change will impact terrestrial ecosystems (Parmesan and Yohe, 2003). Improving climate model projections and monitoring ecosystem response to climate change require spatially and temporally accurate information about vegetation phenology (Piao et al., 2019). This need continues to motivate research activities aimed at collecting data and developing methods to provide high-quality spatio-temporal phenology information (Morisette et al., 2009).

Monitoring seasonal changes in vegetation using satellite imagery, i.e., land surface phenology (LSP), has a long history in remote sensing (Zeng et al., 2020). Exploration of the use of satellite remote sensing systems, such as the Advanced Very High Resolution Radiometer (AVHRR) and Landsat Mulitspectral Scanner (MSS), to estimate LSP parameters started in the 1970s (Rea and Ashley, 1976; Goward et al., 1985; Taylor et al., 1985). These early studies showed images from satellites could inform phenological parameter estimates for both natural and cultivated landscapes (Henderson and Badhwar, 1984; Spanner et al., 1990).

The launch of satellite remote sensing systems near the turn of the 21st century, e.g., SPOT (Satellite Pour l'Observation de la Terre)-VEGETATION and the Moderate Resolution Imaging Spectroradiometer (MODIS), spurred a new wave of LSP research. These studies aimed to exploit the higher temporal and spatial resolution reflectance data products offered by these satellites (Ahl et al., 2006; Zhang et al., 2003; Ganguly et al., 2010; Verhegghen et al., 2014; Verger et al., 2016). Currently, the United States National Aeronautics and Space Administration (NASA) hosts the MODIS Land Cover Dynamics product (MCD12Q2 C6) that provides global annual LSP parameter estimates at a 500 m spatial resolution from 2001 to present (Sulla-Menashe et al., 2019). In 2011, the Visible Infrared Imaging Radiometer Suite (VIIRS) was launched. This sensor system was designed as a replacement for the aging MODIS Aqua and Terra satellites. NASA also hosts the VIIRS Global Land Surface Phenology Product (VNP22Q2) that provides annual 500 m resolution LSP parameters from 2013 through 2018 (Zhang et al., 2018).

Over the past decade, remote sensing technology has advanced tremendously and, with it, the ability to collect imagery useful for higher spatial resolution LSP parameter estimation (Melaas et al., 2013; An et al., 2018). NASA's Landsat 8 and the European Space Agency's (ESA) Sentinel-2 A and B satellites now collect and make publicly available reflectance data for the entire globe at unprecedented spatial, temporal, and radiometric resolutions. Combined, Landsat 8 and Sentinel-2 provide global coverage imagery at a nearly 3 day repeat interval (Li and Roy, 2017). The Harmonized Landsat Sentinel-2 (HLS) project is an effort by NASA to bring Landsat 8 Operational Land Imager (OLI) and Sentinel-2 Multispectral Instrument (MSI) reflectance data together (Claverie et al., 2018). The HLS dataset offers analysis-ready imagery with temporal density sufficient to estimate LSP parameters at 30 m resolution annually (Bolton et al., 2020; Kowalski et al., 2020).

Along with improvements to remote sensing data collection, there have been methodological advancements for translating reflectance readings into meaningful LSP parameters. Vorobiova and Chernov (2017) and Zeng et al. (2020) provide an extensive survey of approaches used to extract LSP parameters from vegetation index (VI) time series. We focus our attention on the double logistic curve fitting technique (Zhang et al., 2003; Elmore et al., 2012; Melaas et al., 2013). The approach generally involves fitting spring and autumn logistic functions to a VI time series for a pixel using a nonlinear model fitting algorithm. The spring function is designed to model VI behavior from winter dormancy to the midsummer growing season, and the autumn logistic function is designed to model VI behavior from midsummer back to dormancy. A key strength of the double logistic phenology curve fitting approach is the spring and autumn function coefficients can be meaningfully interpreted as LSP parameters (Melaas et al., 2013; Elmore et al., 2012). Many other approaches require further manipulation of the fitted curve to derive ecologically relevant metrics (e.g., derivatives to find inflection points, minimums, and maximums).

Some double logistic LSP approaches combine the spring and autumn functions into a single equation for modeling (Beck et al., 2006; Fisher et al., 2006; Elmore et al., 2012). While a single equation simplifies model fitting, some flexibility is lost because the autumn function can affect spring phenology curve behavior and vice versa. Other approaches fit the spring and autumn functions separately to remove the potential for the two logistic curves to adversely interact (Melaas et al., 2013). However, when fitting the logistic functions separately, a decision needs to be made about the day of year (DOY) to transition from the spring to autumn function. It is common for the transition DOY to be set based on VI time series exploratory analysis conducted prior to model fitting. For instance, to determine the transition DOY, Melaas et al. (2013) calculated slopes for moving windows across the time series. The earliest (after DOY = 90) detection of a negative slope in a moving window was set as the transition DOY for the pixel. This approach (among others) does not guarantee the spring and autumn functions will meet, often leading to a ‘step’ in the phenology curve at the transition DOY. This behavior can be problematic when calculating higher-order LSP parameters, such as area-under-the-curve (AUC). To date, we have found no published double logistic approach that seamlessly combines the two logistic functions into one smooth equation and ensures the spring (autumn) function cannot adversely affect autumn (spring) LSP curve behavior. Building upon Melaas et al. (2013), Senf et al. (2017) placed the spring logistic function in a Bayesian model to estimate the LSP parameters and demonstrated this statistical paradigm's utility for quantifying parameter uncertainty. Senf et al. (2017), however, left for future research the derivation of a single Bayesian LSP model to fit both spring and autumn functions and algorithms to deliver Bayesian inference on more than a few hundred pixels. Our work presented here addresses both points.

The overarching objective of this paper is to advance model development work detailed in Melaas et al. (2013) and Senf et al. (2017). Specifically, we propose an approach to simultaneously estimate spring and autumn logistic function parameters for a VI time series within a single Bayesian model. Casting these functions in a single Bayesian model allows estimation of the entire phenology curve with statistical rigor and yields full uncertainty quantification for LSP parameters. Delivering probabilistic uncertainty for all LSP parameters as part of the model fitting process, opposed to post hoc cross-validation or bootstrapping, is a central contribution of the methods detailed in this paper. Additionally, we developed an open-source package rsBayes (Finley and Babcock, 2020) that provides functions for efficiently sampling from the proposed LSP model parameters' posterior distributions using a Markov chain Monte Carlo (MCMC) algorithm.

The proposed model's ability to deliver robust LSP parameter estimates is assessed using three case studies. The case studies consider an Enhanced Vegetation Index (EVI) time series for cloud-free forested pixels within an HLS tile. In the first case study, we pool EVI time series across years (2013–2019) to estimate long-term average LSP curves as was done in Fisher et al. (2006) and Elmore et al. (2012). We examine how EVI observation sample size and data variability contribute to LSP parameter uncertainty at the pixel level. In the second case study, we produce LSP parameter estimates for 2018 (use only 2018 EVI observations to inform the LSP model). We compare our 2018 parameter estimates to published 2018 estimates created using the LSP modeling approach detailed in Bolton et al. (2020). In the third case study, we fit the proposed LSP model using annual EVI observations to assess reliability of LSP parameter estimates given differing sample sizes. Using an abbreviated forest change detection analysis, this case study also demonstrates how the proposed error propagation approach is useful for estimating the posterior distribution of new parameters computed from the LSP model's original parameters.

Supplementary material includes the data and software needed to reproduce our results and additional R functions that facilitate efficient fitting of the proposed model over massive pixel arrays (e.g., entire HLS tiles) for multi-core processor computer systems. We conclude by discussing potential ways to further improve the proposed Bayesian LSP approach through model refinement and increased posterior sampling efficiency.

Section snippets

Land surface phenology function

We develop an LSP function by building on the approaches outlined in Melaas et al. (2013) and Senf et al. (2017). Here, for a given spatial location, e.g., pixel, we denote y(t) as the observed VI at time t. As in Melaas et al. (2013), the first order behavior of y over a year, i.e., t = 1, 2, …, T with T = 365, can be modeled using two logistic functions. The spring function is $S (t) = α_{1} + \frac{α_{2} - α_{5} t}{1 + e^{- α_{3} (t - α_{4})}},$ where α₁ is seasonal minimum greenness, α₂ is the seasonal amplitude, α₃ controls the green-up

Analyses of forest phenology inferred from Harmonized Landsat Sentinel-2 (HLS) data

The proposed modeling approach efficacy was assessed by estimating and analyzing key LSP characteristics using multi-year and multi-pixel reflectance data from the HLS tile described in Section 3.1. The subsequent analyses consider the performance of the proposed phenology function (3) and estimation of its parameters using the Bayesian model (4). Posterior summaries for model parameters, along with derived quantities such as the maximum greenness and area under the phenology curve (AUC) were

Discussion and conclusions

We propose a new approach to estimate LSP parameters that builds on Melaas et al. (2013) and Senf et al. (2017). Specifically, we adapt and combine the separate spring and autumn logistic functions found in Melaas et al. (2013) into a unified equation using a step function. In our model, the date where the two logistic functions meet is a random variable and hence its uncertainty can be estimated. We adopt a Bayesian mode of inference, as was done in Senf et al. (2017), to estimate LSP model

Declaration of Competing Interest

None.

Acknowledgments

The work of the first and second author was supported, in part, by the USDA Forest Service Forest Inventory and Analysis (FIA) and Forest Health Monitoring (FHM) programs, and National Aeronautics and Space Administration's Carbon Monitoring System project. The first author's work was also supported through the Minnesota Agricultural Research, Education and Extension Tech Transfer program (AGREETT). The second author received additional support from the National Science Foundation (NSF) NSF/EF

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A Bayesian model to estimate land surface phenology parameters with harmonized Landsat 8 and Sentinel-2 images

Highlights

Abstract

Introduction

Section snippets

Land surface phenology function

Analyses of forest phenology inferred from Harmonized Landsat Sentinel-2 (HLS) data

Discussion and conclusions

Declaration of Competing Interest

Acknowledgments

Remote Sens. Environ.

Remote Sens. Environ.

Remote Sens. Environ.

Remote Sens. Environ.

Remote Sens. Environ.

Remote Sens. Environ.

Remote Sens. Environ.

Int. J. Appl. Earth Obs. Geoinf.

Remote Sens. Environ.

Remote Sens. Environ.

Remote Sens. Environ.

Remote Sens. Environ.

Remote Sens. Environ.

Proc. Eng.

ISPRS J. Photogramm. Remote Sens.

Remote Sens. Environ.

Remote Sens. Environ.

Remote Sens. Environ.

Terrestrial Ecosystems