| Abstract: |
The goal of this paper is to use SMOS data to provide new information about crop phenology. The SMOS satellite carries an L-band radiometer. Its primary mission is to observe soil moisture, but it is also sensitive to vegetation. We consider the SMOS tau product, also called the vegetation optical depth (VOD), which has been shown to be directly proportional to the mass of water in vegetation.
Because we are interested in applications relevant to Midwestern agriculture, we analyze SMOS data restricted to an area in the US Corn Belt. Since this region is primarily rural and predominantly covered by corn and soybean, the information contained in tau should be relatively easy to interpret. We hypothesize that differences in tau from year-to-year are due to changes in weather conditions and/or crop management.
Previous research has shown a relationship between SMOS tau and the growth and senescence of crops (Patton and Hornbuckle, 2013). In situ data indicate that tau in this region should reach its maximum value during the R3 reproductive stage of corn (Hornbuckle et al., 2016). If this is true, then retrospectively estimating the peak timing of tau with a statistical measure of uncertainty will provide useful information about changes in crop development and management across growing seasons.
We use the SMOS data from 2011 - 2016 to answer four main questions. One, how can we accurately model the seasonal patterns of crop development as measured by SMOS? Two, how can we estimate, and quantify the uncertainty, for when tau reaches its maximum value each year? Three, how does this estimate of peak tau compare to USDA ground-based surveys? Four, what can the uncertainty in the timing of maximum tau tell us about crop management?
To accommodate the noise and missing values in SMOS data, we model tau at 28 pixel locations in Western Iowa using a Dynamic Linear Model (DLM) within a Bayesian framework. This class of model is well suited to model tau as it provides a single mechanism to analyze the data retrospectively, at the current time point, and in the future. A DLM can also quickly adapt to changes in the data generating process; for example, non-stationary data or changes in environmental conditions that alter the level or seasonal pattern in the time series. In addition, using Bayesian estimation allows straightforward computation of uncertainty intervals for any functionals of interest, such as the day of the year when tau reaches its maximum value.
We find that the DLM approach is able to identify a time of peak tau and its uncertainty. While there were no significant differences in the timing of peak tau across pixels within a growing season, there was significant variation in the timing of peak tau across years. In seasons with hotter weather, such as 2012, tau reached its peak much earlier in the summer. Accumulated thermal time (also known as growing degree days) is the main explanatory variable driving the rate at which crops reach their maximum growth stage, and our estimates of peak tau are consistent with this result. There was also variation in the uncertainty interval for the peak. Some seasons, such as 2012, the peak was more acute, compared to other years when tau reaches a plateau rather than a peaked quadratic shape. We compare this to USDA data on crop development as well as planting and harvesting. Finally, we suggest ways that the timing of peak tau and its uncertainty could be used by farmers and agronomists to make crop management decisions, and to better understand and forecast weather and climate.
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