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Developing accurate models of crop stress, phenology and productivity is of paramount importance, given the increasing need of food. Earth observation remote sensing data provides a unique source of information to monitor crops in a temporally resolved and spatially explicit way. In this study, we propose the combination of multisensor (optical and microwave) remote sensing data for crop yield estimation and forecasting using two novel approaches. We first propose the lag between Enhanced Vegetation Index derived from MODIS and Vegetation Optical Depth derived from SMAP as a new joint metric combining the information from the two satellite sensors in a unique feature or descriptor. Our second approach avoids summarizing statistics and uses machine learning to combine full time series of EVI and VOD. This study considers two statistical methods, a regularized linear regression and its nonlinear extension called kernel ridge regression to directly estimate the county-level surveyed total production, as well as individual yields of the major crops grown in the region: corn, soybean and wheat. The study area includes the US Corn Belt, and we use agricultural survey data from the National Agricultural Statistics Service (USDA-NASS) for year 2015 for quantitative assessment., Comment: 53 pages, 8 figures, 3 tables

In many remote sensing applications one wants to estimate variables or parameters of interest from observations. When the target variable is available at a resolution that matches the remote sensing observations, standard algorithms such as neural networks, random forests or Gaussian processes are readily available to relate the two. However, we often encounter situations where the target variable is only available at the group level, i.e. collectively associated to a number of remotely sensed observations. This problem setting is known in statistics and machine learning as {\em multiple instance learning} or {\em distribution regression}. This paper introduces a nonlinear (kernel-based) method for distribution regression that solves the previous problems without making any assumption on the statistics of the grouped data. The presented formulation considers distribution embeddings in reproducing kernel Hilbert spaces, and performs standard least squares regression with the empirical means therein. A flexible version to deal with multisource data of different dimensionality and sample sizes is also presented and evaluated. It allows working with the native spatial resolution of each sensor, avoiding the need of match-up procedures. Noting the large computational cost of the approach, we introduce an efficient version via random Fourier features to cope with millions of points and groups.

Most problems in Earth sciences aim to do inferences about the system, where accurate predictions are just a tiny part of the whole problem. Inferences mean understanding variables relations, deriving models that are physically interpretable, that are simple parsimonious, and mathematically tractable. Machine learning models alone are excellent approximators, but very often do not respect the most elementary laws of physics, like mass or energy conservation, so consistency and confidence are compromised. In this paper, we describe the main challenges ahead in the field, and introduce several ways to live in the Physics and machine learning interplay: to encode differential equations from data, constrain data-driven models with physics-priors and dependence constraints, improve parameterizations, emulate physical models, and blend data-driven and process-based models. This is a collective long-term AI agenda towards developing and applying algorithms capable of discovering knowledge in the Earth system., Comment: 24 pages, 10 figures, 3 tables, expanded AAAI PGAI 2020 Symposium