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Cotton is under the threat of climate and ecosystem change and has an essential role in the global textile industry. This makes its yield prediction essential for both economics and sustainability. The potential cotton yield can be predicted by integrating climatic factors, soil parameters, and biophysical parameters observed by high temporal and spatial resolution remote sensing satellites. This study used a multisource dataset to create an explainable and accurate predictive model for cotton yield prediction over the continental United States (CONUS). A recently proposed glass-box method called explainable boosting machine (EBM), which provides transparency, reliability, and ease of interpretation, was implemented. Accuracy performance was compared with the common machine learning (ML) methods for predicting cotton yields. The EBM showed higher accuracy against other glass-box methods and competitive results with black-box models. With the help of the EBM, the importance of individual features and their pairwise interactions was revealed without applying any post hoc methods. The study findings showed that precipitation (P), enhanced vegetation index (EVI), and leaf area index (LAI) are the three most important dynamic features. The dynamic features are the driver of the created model with 78% of the overall feature importance, followed by pairwise interactions of the features with 16% contribution. Finally, static features contribute 6% to the overall feature importance. The study highlights the importance of using multisource data and interactions of the input features and providing an interpretable model to understand the inner dynamics of cotton yield predictions. [ABSTRACT FROM AUTHOR]

Food security is at stake, with climate change heavily impacting agriculture and food production. In the present context of extreme events and changing conditions, developing advanced crop yield models can learn from all available information, and providing interpretable predictions for decision-making is of paramount relevance. This work explores the potential and limitations of developing interpretable crop yield models using long short-term memory (LSTM) neural networks, which typically excel at extracting information from time series. LSTMs were designed and trained with multisource satellite and meteorological time series over Continental US (CONUS) and corn, soybean, and wheat yield data from the US Department of Agriculture. Two recent attribution methods are used to interpret and extract knowledge from the developed models: integrated gradients (IG), based on back-propagation, and Shapley (SHAP) values, based on perturbations. Our results show that: 1) LSTM models achieved high accuracy ($\text {R}^{2}>0.56$); 2) multisource combinations outperformed single-variable models in all crop models; 3) both attribution methods were equivalent in detecting essential drivers and their contribution; 4) satellite estimates of enhanced vegetation index (EVI) and vegetation optical depth (VOD) together with meteorological estimates of maximum temperature (TMX) were the most relevant input features for crop yield estimations; and finally and 5) we discovered critical periods of the crop growth cycle for the corn, soybean, and wheat models. The suggested strategy constitutes an important step toward modeling and understanding crop production systems and advancing in automatic data-driven and accountable field management. [ABSTRACT FROM AUTHOR]

Learning the manifold structure of remote sensing images is of paramount relevance for modeling and understanding processes, as well as encapsulating the high dimensionality in a reduced set of informative features for subsequent classification, regression, or unmixing. Manifold learning methods have shown excellent performance when dealing with hyperspectral image (HSI) analysis, but, unless specifically designed, they cannot provide an explicit embedding map readily applicable to out-of-sample (OOS) data. A common assumption to deal with the problem is that the transformation between the high-dimensional input space and the latent space (typically low) is linear. This is a particularly strong assumption, especially when dealing with HSIs due to the well-known nonlinear nature of the data. To address this problem, a manifold learning method based on high-dimensional model representation (HDMR) is proposed, which enables a nonlinear embedding function to project OOS samples into the latent space. The proposed method is compared to manifold learning methods along with their linear counterparts and achieves promising performance in terms of classification accuracy for a representative set of HSIs. [ABSTRACT FROM AUTHOR]

This work introduces a novel method that makes use of machine learning (ML) techniques to classify hyper- and multi spectral observations into optical water types (OWTs). Classification was done using $k$ -means clustering, which was followed by a feature relevance step based on the sensitivity analysis (SA) of the predictive mean and variance function of a Gaussian process (GP) regression model. The method was used both in training and predictive mode. The latter allows applying the approach for new unlabeled observations, so that the OWTs and the associated relevant features can automatically be assessed. The methods were studied on hyperspectral synthesized and in situ Arctic data, and were further evaluated on a test image acquired over Arctic seas. Good empirical results encourage wide adoption of the methodology to be applied in operational processing and assessment of water types. [ABSTRACT FROM AUTHOR]

This work introduces the use of Gaussian processes (GPs) for the estimation and understanding of crop development and yield using multisensor satellite observations and meteorological data. The proposed methodology combines synergistic information on canopy greenness, biomass, soil, and plant water content from optical and microwave sensors with the atmospheric variables typically measured at meteorological stations. A composite covariance is used in the GP model to account for varying scales, nonstationary, and nonlinear processes. The GP model reports noticeable gains in terms of accuracy with respect to other machine learning approaches for the estimation of corn, wheat, and soybean yields consistently for four years of data across continental U.S. (CONUS). Sparse GPs allow obtaining fast and compact solutions up to a limit, where heavy sparsity compromises the credibility of confidence intervals. We further study the GP interpretability by sensitivity analysis, which reveals that remote sensing parameters accounting for soil moisture and greenness mainly drive the model predictions. GPs finally allow us to identify climate extremes and anomalies impacting crop productivity and their associated drivers. [ABSTRACT FROM AUTHOR]

In many inference problems, the evaluation of complex and costly models is often required. In this context, Bayesian methods have become very popular in several fields over the last years, in order to obtain parameter inversion, model selection, or uncertainty quantification. Bayesian inference requires the approximation of complicated integrals involving (often costly) posterior distributions. Generally, this approximation is obtained by means of Monte–Carlo (MC) methods. In order to reduce the computational cost of the corresponding technique, surrogate models (also called emulators) are often employed. Another alternative approach is the so-called approximate Bayesian computation (ABC) scheme. ABC does not require the evaluation of the costly model but the ability to simulate artificial data according to that model. Moreover, in ABC, the choice of a suitable distance between real and artificial data is also required. In this work, we introduce a novel approach where the expensive model is evaluated only in some well-chosen samples. The selection of these nodes is based on the so-called compressed MC scheme. We provide theoretical results supporting the novel algorithms and give empirical evidence of the performance of the proposed method in several numerical experiments. Two of them are real-world applications in astronomy and satellite remote sensing. (Corresponding author: Luca Martino.) [ABSTRACT FROM AUTHOR]

Current anomaly detection (AD) algorithms are typically challenged by either accuracy or efficiency. More accurate nonlinear detectors are typically slow and not scalable. In this letter, we propose two families of techniques to improve the efficiency of the standard kernel Reed–Xiaoli (KRX) method for AD by approximating the kernel function with either the data-independent random Fourier features or the data-dependent basis with the Nyström approach. We compare all methods for both real multi- and hyperspectral images. We show that the proposed efficient methods have a lower computational cost, and they perform similar to (or outperform) the standard KRX algorithm thanks to their implicit regularization effect. Last but not least, the Nyström approach has an improved power of detection. [ABSTRACT FROM AUTHOR]

Remote sensing observations, products, and simulations are fundamental sources of information to monitor our planet and its climate variability. Uncovering the main modes of spatial and temporal variability in Earth data is essential to analyze and understand the underlying physical dynamics and processes driving the Earth System. Dimensionality reduction methods can work with spatio-temporal data sets and decompose the information efficiently. Principal component analysis (PCA), also known as empirical orthogonal functions (EOFs) in geophysics, has been traditionally used to analyze climatic data. However, when nonlinear feature relations are present, PCA/EOF fails. In this article, we propose a nonlinear PCA method to deal with spatio-temporal Earth system data. The proposed method, called rotated complex kernel PCA (ROCK-PCA for short), works in reproducing kernel Hilbert spaces to account for nonlinear processes, operates in the complex kernel domain to account for both space and time features, and adds an extra rotation for improved flexibility. The result is an explicitly resolved spatio-temporal decomposition of the Earth data cube. The method is unsupervised and computationally very efficient. We illustrate its ability to uncover spatio-temporal patterns using synthetic experiments and real data. Results of the decomposition of three essential climate variables are shown: satellite-based global gross primary productivity (GPP), soil moisture (SM), and reanalysis sea surface temperature (SST) data. The ROCK-PCA method allows identifying their annual and seasonal oscillations, as well as their nonseasonal trends and spatial variability patterns. The main modes of variability of GPP and SM match expected distributions of land-cover and eco-hydrological zones, respectively; the interannual component of SM is shown to be highly correlated with El Niño Southern Oscillation (ENSO) phenomenon; and the SST annual oscillation is perfectly uncoupled in magnitude and phase from the global warming trend and ENSO anomalies, as well as from their mutual interactions. We provide the working source code of the presented method for the interested reader in https://github.com/DiegoBueso/ROCK-PCA. [ABSTRACT FROM AUTHOR]

Gaussian processes (GPs) are a class of Kernel methods that have shown to be very useful in geoscience and remote sensing applications for parameter retrieval, model inversion, and emulation. They are widely used because they are simple, flexible, and provide accurate estimates. GPs are based on a Bayesian statistical framework which provides a posterior probability function for each estimation. Therefore, besides the usual prediction (given in this case by the mean function), GPs come equipped with the possibility to obtain a predictive variance (i.e., error bars, confidence intervals) for each prediction. Unfortunately, the GP formulation usually assumes that there is no noise in the inputs, only in the observations. However, this is often not the case in earth observation problems where an accurate assessment of the measuring instrument error is typically available, and where there is huge interest in characterizing the error propagation through the processing pipeline. In this letter, we demonstrate how one can account for input noise estimates using a GP model formulation which propagates the error terms using the derivative of the predictive mean function. We analyze the resulting predictive variance term and show how they more accurately represent the model error in a temperature prediction problem from infrared sounding data. [ABSTRACT FROM AUTHOR]

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 the 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 with a number of remotely sensed observations. This problem setting is known in statistics and machine learning as multiple instance learning (MIL) or distribution regression (DR). This article introduces a nonlinear (kernel-based) method for DR 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 for matchup 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. Real experiments involve the Soil Moisture Active Passive (SMAP) vegetation optical depth (VOD) data for the estimation of crop production in the U.S. Corn Belt and the Moderate Resolution Imaging Spectroradiometer (MODIS) and Multi-angle Imaging SpectroRadiometer (MISR) reflectances for the estimation of aerosol optical depth (AOD). An exhaustive empirical evaluation of the method is done against naive (linear and nonlinear) approaches based on input-space means as well as previously presented methods for MIL. We provide source code of our methods in http://isp.uv.es/code/dr.html. [ABSTRACT FROM AUTHOR]

Anomalous change detection (ACD) is an important problem in remote sensing image processing. Detecting not only pervasive but also anomalous or extreme changes has many applications for which methodologies are available. This paper introduces a nonlinear extension of a full family of anomalous change detectors. In particular, we focus on algorithms that utilize Gaussian and elliptically contoured (EC) distribution and extend them to their nonlinear counterparts based on the theory of reproducing kernels’ Hilbert space. We illustrate the performance of the kernel methods introduced in both pervasive and ACD problems with real and simulated changes in multispectral and hyperspectral imagery with different resolutions (AVIRIS, Sentinel-2, WorldView-2, and Quickbird). A wide range of situations is studied in real examples, including droughts, wildfires, and urbanization. Excellent performance in terms of detection accuracy compared to linear formulations is achieved, resulting in improved detection accuracy and reduced false-alarm rates. Results also reveal that the EC assumption may be still valid in Hilbert spaces. We provide an implementation of the algorithms as well as a database of natural anomalous changes in real scenarios http://isp.uv.es/kacd.html. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the effect of spatial and spectral compression on the performance of statistically based retrieval. Although the quality of the information is not completely preserved during the coding process, experiments reveal that a certain amount of compression may yield a positive impact on the accuracy of retrievals. We unveil two strategies, both with interesting benefits: either to apply a very high compression, which still maintains the same retrieval performance as that obtained for uncompressed data; or to apply a moderate to high compression, which improves the performance. As a second contribution of this paper, we focus on the origins of these benefits. On the one hand, we show that a certain amount of noise is removed during the compression stage, which benefits the retrievals performance. On the other hand, we analyze the effect of compression on spectral/spatial regularization (smoothing). We quantify the amount of information shared among the spatial neighbors for the different methods and compression ratios. We also propose a simple strategy to specifically exploit spectral and spatial relations and find that, when these relations are taken into account beforehand, the benefits of compression are reduced. These experiments suggest that compression can be understood as an indirect way to regularize the data and exploit spatial neighbors information, which improves the performance of pixelwise statistics-based retrieval algorithms. [ABSTRACT FROM AUTHOR]