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.

我们开发了贝叶斯陆地地表物候（LSP）模型，并使用增强的植被指数（EVI）观测值（其来自协调的Landsat Sentinel-2（HLS）数据集）来检查其性能。在以前的工作的基础上，我们提出了双重逻辑函数，一旦将其放入贝叶斯模型中，就可以得出所有LSP参数的后验分布。我们评估正常，截断正常和Beta可能性的功效，以提供可靠的LSP参数估计。提出了三个案例研究，并用于探索所提出模型的各个方面。第一个案例研究是在HLS磁贴内的森林像素上进行的，探讨了可能性的选择以及时空变化的HLS数据可用性，以用于长期平均LSP参数点和不确定性估计。第二个案例研究仅使用2018年数据在相同像素上进行，将我们提出的模型的年度LSP参数估算值与使用Bolton等人的方法生成的LSP参数估算值进行比较。（2020）。第三个案例研究以年度时间步长（2014-2019年）在HLS磁贴内的一小块感兴趣区域上进行，除了评估潜在的LSP潜力外，还研究了样本量和可能性选择对年度LSP参数估计的影响。提出的模型可以通知LSP变化检测分析。结果表明，当植被指数有界时，从理论上讲，截断正态和贝塔似然性是更可取的，但当指数观测值的数量足够大且值不在指数界附近时，这三种可能性的表现都相似。案例研究表明如何通过后续分析将像素级LSP参数的后验分布用于传播不确定性。作为本文的伴随，我们提供了一个开源R包rsBayes以及用于重现分析结果的补充数据和代码。所提出的模型规范和软件实现在整个栅格时间序列数据集中的像素级别上提供了计算有效，统计稳定且推断丰富的LSP参数后验分布。rsBayes中的建模功能包和补充代码部分是线程化的，从而允许使用多个处理核心来进一步加快模型对海量数据集的拟合速度。使用64 CPU工作站，使用Beta可能性模型进行的第一个案例研究分析耗时约3天。但是，处理时间随着CPU核心数量的增加而线性减少。我们预计，随着新计算系统功能的增强，这种LSP建模方法的运行时间将大大减少。