3.1. Vegetation Phenology
demonstrates a representative annual phenological progression of the region using a series of land cover fraction (first and third columns) and LST (second and fourth columns) images from the calendar year 2016. The subpixel fraction images use the colors Red, Green, and Blue to correspond to relative abundance of substrate (soil or non-photosynthetic vegetation), photosynthetic vegetation, and dark materials (shadow or water) for a given time. These relative abundances are computed using the 3-endmember spectral mixture model described in the Methods section. Each image is enhanced identically, so colors are directly comparable. Soils generally appear as red, photosynthetic vegetation as bright green, and standing water as blue. As vegetation senesces, its reflectance spectrum grades toward that of the substrate endmember, resulting in orange and yellow colors on the fraction images. Images are only shown from April through November, because winter months are generally covered in cloud and rice is not grown at this time.
Rice is generally grown in the clay rich soils to the east and west of the Sacramento and Feather River channels. The rice growing area can be visually identified as the area of standing water (dark blue/black) in the May 26 image. This is due to the rice crop phenology, summarized as follows:
Many, but not all, rice fields are flooded during winter (November through February or March) to provide habitat for migrating birds. In April, the flooded fields are drained, and all rice fields are plowed in preparation for the rice crop. Rice fields are then generally flooded in May and seeded by airplane into standing water. The rice then greens up during the summer months and begins to senesce in September, continuing to senesce and being harvested through September and October. By November, the harvest is complete. After harvest, some fields are left bare and others are flooded for winter bird habitat, and the cycle begins again. For more information on the rice cropping calendar in this region, see http://www.rice.ucanr.edu/
While rice dominates the landscape, other vegetation also exists. The foothills of the Sierra Nevada, Coast Ranges, and Sutter Buttes largely host rainfed grasslands used for grazing. The phenology of these regions is nearly opposite that of rice agriculture, because the grasslands are green during winter and generally senesced during the summer months. In addition, a wide range of other row crops and orchards are grown in the valley with a diversity of cropping systems and phenologies. Settlements also occupy a small portion of the landscape, hosting an even more complex mixture of evergreen and deciduous trees, shrubs, and grasses.
The time series in the lower right of Figure 4
show typical phenological progressions of rice crops (solid) versus native grassland (dashed) in terms of both vegetation abundance (green) and temperature (red). As expected from the image time series, the vegetation abundance curves for the rice and grassland pixels are nearly 180° out of phase. Rice has a strong peak in vegetation abundance during the summer growing season, and also a minor peak during the winter fallow season, presumably from non-rice vegetation growing in flooded fields. The grassland pixels have very low amounts of photosynthetic vegetation during the hot and dry summer months because they are rainfed, but reach broad peaks during the winter rainy season of comparable but somewhat smaller amplitude than the agriculture. In Figure 4
, dots correspond to Landsat Fv
and LST observations and continuous curves correspond to MODIS EVI and LST time series. The benefit of using both MODIS and Landsat for purposes of this illustration is evident, in that there were no cloud-free Landsat images available over a 3-month period during the wintertime, but sufficient usable MODIS images were acquired to produce composites approximating the full annual time series.
3.2. Thermal Phenology
The fundamental physical process driving the thermal phenology of the region is the sinusoidal seasonal insolation curve, with an annual minimum at the winter solstice. However, the biogeophysical properties of the landscape modify this insolation curve in both space and time. For instance, grassland achieves a much greater summer temperature than rice because the land surface dominated by dry soil and non-photosynthetic vegetation (or absence of vegetation) has low thermal inertia, and can support very little evapotranspirative cooling. On the other hand, rice agriculture is not only irrigated but grown in standing water for much of the summer, resulting in substantial cooling both from evaporation of the paddy water below the canopy and transpiration of the respiring and photosynthesizing vegetation. This results in a relatively stable LST during the summer months, yielding a flatter top to the temperature curve.
The phenological progression of the thermal image time series complements that of the fraction image time series. In late April, the only prominent spatial patterns in the thermal field are due to elevation, rivers and lakes, and transient clouds. However, as the spring progresses into summer, clear differences emerge between rice and grassland areas. In the September and October images, differences within the region of rice agriculture become apparent, likely on the basis of evapotranspiration decreasing at variable rates as some fields senesce sooner than others, and some fields are drained before others to prepare for harvest. Once the fields are harvested, differences between land cover types are greatly reduced. In fall, the remaining vegetation can be somewhat warmer than its dry surroundings due to the greater heat capacity of its leaf water.
Finally, the scatterplots inset on the thermal images show the relationship between LST (x-axis) and Fv
(y-axis) for every pixel in the image. These scatterplots are an alternate coordinate system with which to understand the dataset. The scatterplots are color-coded so warmer colors represent more pixels and cooler colors represent fewer pixels. The grayscale background silhouette of the full multitemporal point cloud shows the composite space of all the images together. Because so many pixels in the image correspond to rice agriculture, they generally form the largest cluster in Temperature vs Vegetation (TV) space and are represented by warmer colors. In April, for instance, rice fields are recently plowed so they are cool and unvegetated, and the corresponding warm colored cluster plots at the bottom center of the space. In May, the fields are flooded and become even cooler, but remain unvegetated, so the cluster moves to the left in TV space. In late June, fields vary widely from just planted (late crop) to nearly mature (early crop), resulting in a wide range of Fv
. ET cools the crop so its temperature does not change appreciably, resulting in a vertically elongated cluster. For the rest of the summer, the fields do not change appreciably in vegetation abundance or temperature, so the cluster is stable until fields are drained and begin to senesce (September), resulting in the cluster elongating toward higher temperatures. Harvest of the rice crop results in a stepwise change of the TV properties of a rice field. The separation of the point cloud into two distinct clusters of approximately equal size (harvested & unharvested) in the October 1 image agrees with 2016 USDA estimates that 54% of the California rice crop was harvested by October 9 [52
]. By mid-November, rice harvest is complete, and the landscape shifts into its winter state. Interestingly, the few usable winter images that exist plot in a nearly disjoint portion of the vegetation temperature space, suggesting that the spatial relationship between vegetation and temperature during winter may be dominated by fundamentally different physical processes than during summer.
3.3. Characterization—EOF Analysis and tEM Selection
The preceding figures can be summarized by the following set of observations:
The thermal phenology of rice agriculture is substantially different in amplitude and shape from other land cover types in the region;
The parallel evolution of both thermal and vegetation phenology can be explained in terms of the surface hydrologic cycle and growth cycle of the multiple phases of rice crops;
The spatiotemporal variations in LST have substantial differences from those of the vegetation abundance, despite their interdependence; and
The spatiotemporal variations in both LST and Fv can be explained using fundamental physical principles.
Put together, observations 1, 2 and 3 suggest that including Landsat LST in a phenological analysis could add information that is not present using vegetation abundance alone. Observation 4 suggests that such a phenological analysis could be based on straightforward physical principles with a bare minimum of model complexity.
One potential approach to this mapping problem is the spatiotemporal analysis method of [18
]. A primary benefit of this approach is that it imposes no assumptions about the functional form of the phenology, but rather characterizes the temporal patterns based on the data itself. Other benefits to the method are its simplicity, robustness, and generalizability, as well as its ability to generate results with straightforward physical meaning. Because they are based on physical principles and easily identified tEMs representing known phenologies, maps derived from linear model inversion provide a degree of uniqueness of solution that is almost never provided by discrete thematic classifications which are based on ad hoc selection of land cover classes and training data.
In order to use this approach with a dual data stream, two decisions must be made. The first decision is whether to incorporate both streams into a single analysis or to analyze each in parallel. We present the results of parallel characterization method here because it is conceptually simpler and achieves the objectives of the current study. The combined characterization and analysis of thermal and vegetation phenology lends itself naturally to the study of ET dynamics, and is the focus of a separate study.
The second decision is whether to analyze the two years together or separately. Because significant benefits can result from either approach, we present results of both in Figure 5
and Figure 6
, respectively. Because the two single-year characterizations yielded similar results, we present only the 2016 results as characteristic of both years of the dataset.
For each case, we begin by first conducting an EOF analysis of the relevant image time series. We choose unnormalized (covariance-based) rotations in each instance. Normalized (correlation-based) rotations were also investigated, but the resulting feature spaces were less informative. In each case, over 65% of the variance is represented in the first 3 dimensions of the data. While this number is low enough to suggest that informative structure may be present in the higher dimensions of the dataset, the three low-order dimensions capture the most relevant phenological patterns necessary to distinguish rice from other crops and to characterize its seasonal and interannual variability.
and Figure 6
summarize the characterization stage of the parallel analyses for single year (2016) and dual year (2016 + 2017) time series, respectively. Characterization is based on the 24 × 24 km subset shown in the white box in Figure 4
. We use this spatial subset because it is dominated by rice agriculture with a wide range of crop timing. In every case, the loadings of the first 3 spatial PCs are shown as scatterplots. These scatterplots represent the location of each geographic pixel in the image time series in a 3-dimensional space, known as the Temporal Feature Space (TFS), in which the axes represent the relative contributions of the first 3 EOFs (uncorrelated temporal patterns of maximum variance). Clusters in this space correspond to sets of geographic pixels with similar temporal trajectories over the course of the two years of the study. Apexes in the space correspond to temporal endmembers (tEMs), pixels with the most distinctive temporal patterns in the image time series. Pixel time series lying inside a convex hull connecting the tEMs can be represented as linear combinations of the tEM time series.
shows a comparison of the TFS for image time series of both Fv
and LST for the year 2016. The TFS of the Fv
image time series shows four distinct apexes representing the tEMs: Early Rice, Late Rice, Wetlands/Evergreen, and Water/Fallow. Time series of Fv
corresponding to these tEMs are shown in the lower right. All 4 tEMs are clearly distinct on the PC 3 vs. 2 scatterplot. The point cloud in this scatterplot forms a cross shape, with the axis between tEMs 1 and 2 corresponding to phenological timing and the axis between tEMs 3 and 4 corresponding to overall vegetation abundance. The Water/Fallow tEM forms the sharpest corner, as expected given the small amount of variability expected in the Fv
of water bodies and fallow fields through time. Early and Late tEMs are less sharp but still clearly defined, indicating substantial variability in the timing of the phenological signal. However, the Early and Late clusters are also visibly distinct, indicating two clear phenological groups. The Wetlands tEM is the most diffuse, as expected given the wide range of vegetation types, hydrological regimes, and land management strategies for wetlands in the area.
The TFS of the LST image time series shows substantially more clustering than that of the Fv time series. This indicates that more pixels have more similar LST trajectories than Fv trajectories. At least 7 tEMs are identifiable. The most distinct from each other are Water (EM 4; blue) and fallow fields (3; gray). Water time series are particularly distinctive as their very low PC 2 and very high PC 1 and 3 values position them as disjoint from the remainder of the dataset. The remainder of the space partitions into (a) differences in timing of rice phenology, and (b) differences between rice, non-rice agriculture, and wetlands. Wetlands (EM6) occupy the corner of the point cloud closest to water, and also form an axis grading into fallow fields (EM3). The Fallow-Wetland axis is nearly orthogonal to the Early-Late axis of rice phenology, most clearly seen in the PC 1 vs. 3 projection. Non-rice agriculture (EM5) plots on a continuum between the Early Rice and Fallow tEMs. Finally, double cropping (D) is clearly identifiable in both the Fv and LST feature spaces. Few fields in the spatial subset used for this rotation practice double cropping, so this tEM is sparsely populated.
shows a characterization of the dual year 2016 + 2017 image time series. In both time series, the early/late phase information that dominated the single year time series is suppressed (though still present), and the structure of the TFS is dominated by year-to-year differences in crop presence or absence. In the Fv
space, both Wetlands (EM4; green) and Water/Fallow (EM5; blue) are still clear tEMs. The largest cluster, however, is now that of fields cropped in both 2016 and 2017 (EM3; red). This cluster is clearly distinct from the small cluster of fields cropped in 2017 only (EM2; gray) and the much larger cluster of fields cropped in 2016 only (EM1; yellow). The fact that the 2016-only cluster is much larger than the 2017-only cluster is concordant with official USDA estimates of 42,000 fewer acres of California rice planted in 2017 than 2016 due to higher prices for competing commodities and severe early season flooding [53
The dual year LST space again shows more clustering and overall complexity than the corresponding Fv space. At least 6 tEMs are identifiable. Again, the greatest distinction exists between water and fields that are fallow in both years (F/F). Water time series are again particularly distinctive as their very low PC 1 and PC 3 values position them as disjoint from the remainder of the dataset. The remainder of the space partitions into (a) differences in timing of phenology for fields under rice cultivation in both years, and (b) the presence and absence of a rice crop in each year. The axis corresponding to phenology is nearly orthogonal to the axis corresponding to presence/absence of crop in each year. The potential utility of this information is discussed below.
While information about the phase of the rice is clearly present in both single year datasets, the Fv space tEMs capture more end-of-season variability than the LST tEMs. This could be due to gradual browning of the top canopy layer over weeks to months (resulting in progressive decline in Fv over the second half of the growing season) being accompanied by continual cooling by ET of the green vegetation and paddy water below (resulting in minimal change of LST). However, the LST dataset clearly shows enhanced ability to discriminate between rice and non-rice crops, likely due to early season paddy water producing a unique signature in LST but not Fv. For the dual year characterization, both Fv and LST clearly discriminate between areas cropped both years versus each individual year, but again LST shows superior ability to discriminate between rice and non-rice crops. Clearly, analyzing both datasets in parallel may yield substantial benefit over only using one, especially given that the two are co-acquired in all standard Landsat image acquisitions.
As described in the Methods section, tEMs selected from each TFS were then used as the basis for two separate linear temporal mixture models. These models were then inverted to produce maps of thermal and vegetation phenology. Figure 7
shows the result of these inversions. In this figure, the saturation of each color corresponds to the similarity of each pixel to each of the tEM time series. Greater saturation implies greater similarity to the corresponding tEM (or binary mixtures for subtractive colors), while less saturation implies less similarity of the corresponding pixel to any of the tEMs. The latter is associated with higher model misfit, and is expected for pixels with phenologies not included in the model. Individual fields are clearly identifiable as either very early (pure green), very late (pure blue) or a mixture of the two (dark cyan). Intrafield heterogeneity in phenology is also clearly present in some cases, showing portions of individual fields growing faster than other portions. The potential utility of Landsat’s ability to resolve intrafield spatiotemporal variability is discussed below. Overall, RMS misfits were comparable but somewhat higher for the Fv
(μ = 0.15, 90% < 0.25) than the LST (μ = 0.07, 90% < 0.12) models. While these model misfit values are higher than generally observed for spectral mixture models, this is expected given the phenological complexity of the landscape and the relatively low number of tEMs used.
The right column shows the result of a 3 tEM temporal mixture model of 2016 + 2017 thermal phenology showing crops in both years (cyan), only 2016, magenta, or neither (dark yellow/orange). The unique temporal signature of rice thermal phenology allows it to be readily identified from other types of agriculture, which map as dull colors corresponding to combinations of tEMs. Field-to-field variations in the similarity of each pixel time series to the tEMs are present, likely due to a combination of soil moisture during the fallow year and/or greenup phase during the cropped year. Some intrafield variability is also present, likely for similar reasons.
While the Fv TMM maps crop timing with high accuracy, it does not explicitly distinguish between rice and non-rice agriculture. As a result, non-rice agriculture maps in a variety of ways, potentially mimicking rice, depending on its phenological characteristics. Fortunately, the thermal image time series can explicitly capture the phenological signature of rice by leveraging the large early-season difference between cold, flooded, recently planted rice fields and hot, dry, recently planted non-rice fields. Interpreting the two of these phenology maps together therefore provides maximum information about both the location and timing of rice agriculture.
3.5. Near-Realtime Monitoring & Field Validation
To illustrate one potential application of this methodology, we present the results of a TMM generated in the middle of the current (2018) growing season. 2018 presents an unusually challenging case for the model, because only the first part of the growing season is available, with only 2/3 as many usable images as the same period in 2016 and 2017. This is due to the prevalence of cloud cover in many spring images and smoke plumes from multiple severe wild fires in late summer images. Through the end of July, only 4 usable thermal images were collected, in comparison to 6 images through the end of July for each of the 2016 and 2017 growing seasons.
shows false color composite and thermal image time series for these 4 images. The false color composite images show a clear difference in crop timing between the rice growing areas in the eastern versus western portions of the valley, with the dividing line located approximately at the Sacramento River channel in the north and the Sutter Bypass in the south. The wide range of planting times in 2018, and the overall unusually late crop, is due to complex water management circumstances. Because of the relatively dry winter and associated low reservoir levels, uncertainty existed in early spring about expected water allocations. Heavy April rains then boosted allocations, but also forced farmers to wait for the clay-rich soils to dry before it was possible to bring tractors onto the fields for leveling. The fields which had already been prepared could be flooded and planted on time, but those which had not were forced to plant significantly later than usual. This is described in brief by [55
], and expected impacts of this situation are broadly described by [56
A TMM condenses the information from these 4 LST images into a single map, shown in Figure 9
. In this model, red corresponds to grasslands and fallow fields, green corresponds to early rice, and blue corresponds to water and non-rice crops. Despite the limited data availability in 2018, and the fact that this map is produced mid-season with no data on senescence or harvest, the areas growing rice are clearly identifiable. The broad east-west dichotomy in planting date described by [55
] is evident in the discrepancy between bright and dull green map color. Field validation with 1650 km of driving transects, 8500 field photos, and 380 field spectra verifies that 527 of 592 fields (89%) are correctly mapped as rice. Validation details are given in the Appendix