Temporal Mixture Model Research Articles

Mapping multi-decadal wetland loss: Comparative analysis of linear and nonlinear spatiotemporal characterization

Wetlands provide critical habitat for birds and endangered species, and can be influenced by shifts in water availability and land use. The Landsat image archive can help both document historical wetland change and monitor current dynamics, but multi-decadal retrospective studies face two important challenges: 1) many important ecohydrological processes occur at scales finer than the field of view of a 30 m Landsat pixel, and 2) ecologically meaningful wetland response units frequently exhibit spatiotemporal complexity in both vegetation and surface water which may not be well-represented by a simple study area spatial mean. Here we explore a novel method for contending with these challenges with application to the rapidly changing Andrade Mesa wetlands along the US-Mexico border. Using a 26-year (1995–2021) Landsat image time series, we track changes in surface water and vegetation using green vegetation (V) and dark (D) fractions estimated from spectral mixture analysis (SMA). Spatiotemporal dynamics in both V and D fractions were characterized using two techniques: linear Principal Component Analysis (PCA) and nonlinear manifold learning (via Uniform Manifold Approximation and Projection; UMAP). Bounding temporal endmembers were identified from PCA and used to construct a temporal mixture model which quantified total area of surface water and vegetation loss, including an uncertainty estimate. UMAP clearly distinguished areas with differing onset of vegetation and water loss which were not identifiable using PCA. Change maps were then associated with different mechanisms and outcomes, including possible mechanical clearing of vegetation and unexpected greening of woody vegetation. The overall timing of surface water and vegetation decline follows the lining of the All-American Canal, suggesting a potential cross-border hydrologic association between loss of a wetland in Mexico and water efficiency measures implemented in the United States.

Predictive Ecological Land Classification From Multi-Decadal Satellite Imagery

Ecological land classifications serve diverse purposes including sample stratification, inventory, impact assessment and environmental planning. While popular, data-driven classification approaches can require large training samples, frequently with limited robustness to rapid environmental change. We evaluate the potential to derive useful, durable ecological land classifications from a synthesis of multi-decadal satellite imagery and geospatial environmental data. Using random forests and multivariate regression trees, we analyze 1982–2000 Landsat Thematic Mapper (L45) and 2013–2020 Harmonized Landsat Sentinel (HLS) imagery to develop and then test the predictive skill of an ecological land classification for monitoring Mediterranean-climate oak woodlands at the recently established Jack and Laura Dangermond Preserve (JLDP) near Point Conception, California. Image pixels were processed using spectral and temporal mixture models. Temporal mixture model residual scores were highly correlated with oak canopy cover trends between 2012 and 2020 (r2 = 0.74, p << 0.001). The resulting topoclimatic-edaphic land classification effectively distinguished areas of systematically higher or lower oak dieback during 2012–2020 severe drought, with a fivefold difference in dieback rates between land classes. Our results highlight the largely untapped potential for developing predictive ecological land classifications from multi-decadal satellite imagery to guide scalable, ground-supported monitoring of rapid environmental change.

The Climatic Temporal Feature Space: Continuous and Discrete

Climatic zones, representing seasonal variations in temperature (T) and precipitation (P), are generally mapped geographically using discrete classifications with distinct boundaries. However, it is well known that global T and P vary continuously in space and time with steep gradients occurring infrequently. The objective of this analysis is to use complementary forms of dimensionality reduction to quantify the spatiotemporal dimensionality of the climate system and to produce a continuous representation of global climate based on the temporal feature space of historical T and P alone. We characterize the continuous global feature space using principal components (PCs) to identify a parsimonious set of temporal endmember T and P patterns bounding the feature space of all observed T and P patterns. These endmember T and P patterns provide the basis for a linear temporal mixture model that can represent decadal T and P patterns of any geographic location as fractions of the endmember T and P patterns. Inverting this linear mixture model for each geographic T+P time series gives an estimate of the fractional contribution of each endmember to the observed time series. The resulting temporal endmember fraction maps provide a continuous representation of the Euclidean proximity of T and P observations at every geographic location to each of the temporal endmember climates bounding the space. The spatiotemporal dimensionality implied by the variance partition of T + P time series for 67,420 land-based observations suggests that the T + P temporal feature space is effectively 3D, accounting for 92% of total variance. From the topology of the feature space, we identify 4 bounding temporal endmembers upon which to base the linear temporal mixture model. Inversion of the model for each normalized observed time series yields endmember fraction estimates and a model misfit distribution with 99% of misfit < 0.21. For comparison, we also render temporal feature spaces from ensembles of 2D manifolds within the T + P space derived from suites of t-distributed Stochastic Neighbor Embeddings (t-SNE) to identify discontinuities in the feature space. Comparison of spatial PC(t-SNE) across hyperparameter settings reveals consistent structure and little hyperparameter sensitivity to temporal feature spaces rendered by t-SNE. Combining the physically interpretable continuous global structure resolved by the PC feature space with the finer scale manifold structure resolved by the t-SNE feature space provides a continuous alternative to discrete classifications of climate that cannot represent the continuous character of its temporal feature space.

Scalable mapping and monitoring of Mediterranean-climate oak landscapes with temporal mixture models

Mediterranean-climate oak woodlands are prized for their biodiversity, aesthetics, and ecosystem services. Conservation and maintenance of these landscapes requires accurate observations of both present and historic conditions capable of spanning millions of hectares. Decameter optical satellite image time series have the observational coverage to meet this need, with almost 40 years of intercalibrated global observations from the Landsat program alone. However, the optimal approach to leverage these observations for oak ecosystem monitoring remains elusive. Temporal mixture models (TMMs) may offer a solution. TMMs use a linear inverse model based on temporal endmembers (tEMs) chosen to optimize both parsimony and information content by 1) possessing clear biophysical meaning, and 2) accurately representing the variance structure of the observations in the temporal feature space (TFS) composed of low-order Principal Components. We apply this approach to oak woodlands of the California Sierra Nevada foothills. Low-order TFS structure across the ≈1200 km2 study area is consistently bounded by 4 tEM phenologies: annual grasses, evergreen perennials, deciduous perennials + shadow, and unvegetated areas. Satellite-based tEM phenologies correspond to ground-based PhenoCam time series (correlations 0.8 to 0.9). Systematic temporal decimation is conducted to simulate years with varying numbers of cloud free measurements. Fractional cover of temporal endmembers is observed to scale linearly using as few as 6 images per year and coarse feature space topology is retained with as few as 4 well-timed images per year. In comparing 10 m versus 30 m pixel resolution, linear scaling is observed with correlations of 0.78–0.95. Comparison of 10 m Sentinel-2 and LiDAR-derived tree cover estimates at San Joaquin Experimental Range shows a correlation of 0.74. Visual orthophoto validation shows accuracies of annual, deciduous, and evergreen cover fractions of 74–88% (n = 102). Multi-year analysis of August imagery at Sequoia National Park to investigate dynamics associated with the 2012–2016 drought reveals 5 tEMs corresponding to: steady growth, steady decline, early decline then regrowth, persistent vegetation, and no vegetation. Validation images are sparse, but where available show accuracies in the 88 to 91% range for decrease, growth, and persistently vegetated multiyear endmembers (n = 102). Decreases are observed in areas with oak mortality documented in a recent field-based study. Overall, our results suggest the TMM approach has promise as an accurate, explainable, and linearly scalable method for retrospective analysis and prospective monitoring of Mediterranean-climate oak landscapes.

Spatiotemporal Characterization of Mangrove Phenology and Disturbance Response: The Bangladesh Sundarban

This work presents a spatiotemporal analysis of the phenology and disturbance response in the Sundarban mangrove forest on the Ganges-Brahmaputra Delta in Bangladesh. The methodological approach is based on an Empirical Orthogonal Function (EOF) analysis of the new Harmonized Landsat Sentinel-2 (HLS) BRDF and atmospherically corrected reflectance time series, preceded by a Robust Principal Component Analysis (RPCA) separation of Low Rank and Sparse components of the image time series. Low Rank components are spatially and temporally pervasive while Sparse components are transient and localized. The RPCA clearly separates subtle spatial variations in the annual cycle of monsoon-modulated greening and senescence of the mangrove forest from the spatiotemporally complex agricultural phenology surrounding the Sundarban. A 3 endmember temporal mixture model maps spatially coherent differences in the 2018 greening-senescence cycle of the mangrove which are both concordant and discordant with existing species composition maps. The discordant patterns suggest a phenological response to environmental factors like surface hydrology. On decadal time scales, a standard EOF analysis of vegetation fraction maps from annual post-monsoon Landsat imagery is sufficient to isolate locations of shoreline advance and retreat related to changes in sedimentation and erosion, as well as cyclone-induced defoliation and recovery.

Mapping and Monitoring Rice Agriculture with Multisensor Temporal Mixture Models

Rice is the staple food for more than half of humanity. Accurate prediction of rice harvests is therefore of considerable global importance for food security and economic stability, especially in the developing world. Landsat sensors have collected coincident thermal and optical images for the past 35+ years, and so can provide both retrospective and near-realtime constraints on the spatial extent of rice planting and the timing of rice phenology. Thermal and optical imaging capture different physical processes, and so provide different types of information for phenologic mapping. Most analyses use only one or the other data source, omitting potentially useful information. We present a novel approach to the mapping and monitoring of rice agriculture which leverages both optical and thermal measurements. The approach relies on Temporal Mixture Models (TMMs) derived from parallel Empirical Orthogonal Function (EOF) analyses of Landsat image time series. Analysis of each image time series is performed in two stages: (1) spatiotemporal characterization, and (2) temporal mixture modeling. Characterization evaluates the covariance structure of the data, culminating in the selection of temporal endmembers (EMs) representing the most distinct phenological cycles of either vegetation abundance or surface temperature. Modeling uses these EMs as the basis for linear TMMs which map the spatial distribution of each EM phenological pattern across study area. The two metrics we analyze in parallel are (1) fractional vegetation abundance (Fv) derived from spectral mixture analysis (SMA) of optical reflectance, and (2) land surface temperature (LST) derived from brightness temperature (Tb). These metrics are chosen on the basis of being straightforward to compute for any (cloud-free) Landsat 4-8 image in the global archive. We demonstrate the method using a 90 × 120 km area in the Sacramento Valley of California. Satellite Tb retrievals are corrected to LST using a standardized atmospheric correction approach and pixelwise fractional emissivity estimates derived from SMA. LST and Tb time series are compared to field station data in 2016 and 2017. Uncorrected Tb is observed to agree with the upper bound of the envelope of air temperature observations to within 3 °C on average. As expected, LST estimates are 3 to 5 °C higher. Soil T, air T, Tb and LST estimates can all be represented as linear transformations of the same seasonal cycle. The 3D temporal feature spaces of Fv and LST clearly resolve 5 and 7 temporal EM phenologies, respectively, with strong clustering distinguishing rice from other vegetation. Results from parallel EOF analyses of coincident Fv and LST image time series over the 2016 and 2017 growing seasons suggest that TMMs based on single year Fv datasets can provide accurate maps of crop timing, while TMMs based on dual year LST datasets can provide comparable maps of year-to-year crop conversion. We also test a partial-year model midway through the 2018 growing season to illustrate a potential real-time monitoring application. Field validation confirms the monitoring model provides an upper bound estimate of spatial extent and relative timing of the rice crop accurate to 89%, even with an unusually sparse set of usable Landsat images.