Soil moisture plays a key role in the Earth’s water and carbon cycles, but acquisition of continuous (i.e., gap-free) soil moisture measurements across large regions is a challenging task due to limitations of currently available point measurements. Satellites offer critical information for soil moisture over large areas on a regular basis (e.g., European Space Agency Climate Change Initiative (ESA CCI), National Aeronautics and Space Administration Soil Moisture Active Passive (NASA SMAP)); however, there are regions where satellite-derived soil moisture cannot be estimated because of certain conditions such as high canopy density, frozen soil, or extremely dry soil. We compared and tested three approaches, ordinary kriging (OK), regression kriging (RK), and generalized linear models (GLMs), to model soil moisture and fill spatial data gaps from the ESA CCI product version 4.5 from January 2000 to September 2012, over a region of 465,777 km2 across the Midwest of the USA. We tested our proposed methods to fill gaps in the original ESA CCI product and two data subsets, removing 25% and 50% of the initially available valid pixels. We found a significant correlation (r = 0.558, RMSE = 0.069 m3m−3) between the original satellite-derived soil moisture product with ground-truth data from the North American Soil Moisture Database (NASMD). Predicted soil moisture using OK also had significant correlation with NASMD data when using 100% (r = 0.579, RMSE = 0.067 m3m−3), 75% (r = 0.575, RMSE = 0.067 m3m−3), and 50% (r = 0.569, RMSE = 0.067 m3m−3) of available valid pixels for each month of the study period. RK showed comparable values to OK when using different percentages of available valid pixels, 100% (r = 0.582, RMSE = 0.067 m3m−3), 75% (r = 0.582, RMSE = 0.067 m3m−3), and 50% (r = 0.571, RMSE = 0.067 m3m−3). GLM had slightly lower correlation with NASMD data (average r = 0.475, RMSE = 0.070 m3m−3) when using the same subsets of available data (i.e., 100%, 75%, 50%). Our results provide support for using geostatistical approaches (OK and RK) as alternative techniques to gap-fill missing spatial values of satellite-derived soil moisture.
The current availability of soil moisture data over large areas comes from satellite remote sensing technologies (i.e., radar-based systems), but these data have coarse resolution and often exhibit large spatial information gaps. Where data are too coarse or sparse for a given need (e.g., precision agriculture), one can leverage machine-learning techniques coupled with other sources of environmental information (e.g., topography) to generate gap-free information and at a finer spatial resolution (i.e., increased granularity). To this end, we develop a spatial inference engine consisting of modular stages for processing spatial environmental data, generating predictions with machine-learning techniques, and analyzing these predictions. We demonstrate the functionality of this approach and the effects of data processing choices via multiple prediction maps over a United States ecological region with a highly diverse soil moisture profile (i.e., the Middle Atlantic Coastal Plains). The relevance of our work derives from a pressing need to improve the spatial representation of soil moisture for applications in environmental sciences (e.g., ecological niche modeling, carbon monitoring systems, and other Earth system models) and precision agriculture (e.g., optimizing irrigation practices and other land management decisions).
Word $W$ is an instance of word $V$ provided there is a homomorphism $\phi$ mapping letters to nonempty words so that $\phi(V) = W$. For example, taking $\phi$ such that $\phi(c)=fr$, $\phi(o)=e$ and $\phi(l)=zer$, we see that "freezer" is an instance of "cool". Let $\mathbb{I}_n(V,[q])$ be the probability that a random length $n$ word on the alphabet $[q] = \{1,2,\cdots q\}$ is an instance of $V$. Having previously shown that $\lim_{n \rightarrow \infty} \mathbb{I}_n(V,[q])$ exists, we now calculate this limit for two Zimin words, $Z_2 = aba$ and $Z_3 = abacaba$. Comment: 25 pages
The PRIMAD model with its six components (i.e., Platform, Research Objective, Implementation, Methods, Actors, and Data), provides an abstract taxonomy to represent computational experiments and enforce reproducibility by design. In this paper, we assess the model applicability to a set of Laser Interferometer Gravitational-Wave Observatory (LIGO) workflows from literature sources (i.e., published papers). Our work outlines potentials and limits of the model in terms of its abstraction levels and application process.
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