Multistep Ahead Groundwater Level Time-Series Forecasting Using Gaussian Process Regression and ANFIS

2015 ◽  
pp. 289-302 ◽  
Author(s):  
N. Sujay Raghavendra ◽  
Paresh Chandra Deka
Keyword(s):  
Time Series ◽  
Gaussian Process ◽  
Groundwater Level ◽  
Gaussian Process Regression ◽  
Time Series Forecasting

Industrial time series forecasting based on improved Gaussian process regression

2020 ◽  
Vol 24 (20) ◽  
pp. 15853-15869 ◽  
Author(s):  
Tianhong Liu ◽  
Haikun Wei ◽  
Sixing Liu ◽  
Kanjian Zhang
Keyword(s):  
Time Series ◽  
Gaussian Process ◽  
Gaussian Process Regression ◽  
Time Series Forecasting

scholarly journals Groundwater level prediction in arid areas using wavelet analysis and Gaussian process regression

2021 ◽  
Vol 15 (1) ◽  
pp. 1147-1158
Author(s):  
Shahab S. Band ◽  
Essam Heggy ◽  
Sayed M. Bateni ◽  
Hojat Karami ◽  
Mobina Rabiee ◽  
...  
Keyword(s):  
Wavelet Analysis ◽  
Gaussian Process ◽  
Groundwater Level ◽  
Gaussian Process Regression ◽  
Arid Areas ◽  
Groundwater Level Prediction

Conditioned Simulation of Ground-Motion Time Series at Uninstrumented Sites Using Gaussian Process Regression

2021 ◽  
Author(s):  
Aidin Tamhidi ◽  
Nicolas Kuehn ◽  
S. Farid Ghahari ◽  
Arthur J. Rodgers ◽  
Monica D. Kohler ◽  
...  
Keyword(s):  
Time Series ◽  
Gaussian Process ◽  
Ground Motion ◽  
San Francisco ◽  
Earthquake Engineering ◽  
Seismic Analysis ◽  
Ground Motions ◽  
Free Field ◽  
Gaussian Process Regression ◽  
Motion Time

ABSTRACT Ground-motion time series are essential input data in seismic analysis and performance assessment of the built environment. Because instruments to record free-field ground motions are generally sparse, methods are needed to estimate motions at locations with no available ground-motion recording instrumentation. In this study, given a set of observed motions, ground-motion time series at target sites are constructed using a Gaussian process regression (GPR) approach, which treats the real and imaginary parts of the Fourier spectrum as random Gaussian variables. Model training, verification, and applicability studies are carried out using the physics-based simulated ground motions of the 1906 Mw 7.9 San Francisco earthquake and Mw 7.0 Hayward fault scenario earthquake in northern California. The method’s performance is further evaluated using the 2019 Mw 7.1 Ridgecrest earthquake ground motions recorded by the Community Seismic Network stations located in southern California. These evaluations indicate that the trained GPR model is able to adequately estimate the ground-motion time series for frequency ranges that are pertinent for most earthquake engineering applications. The trained GPR model exhibits proper performance in predicting the long-period content of the ground motions as well as directivity pulses.

scholarly journals Monitoring Cropland Phenology on Google Earth Engine Using Gaussian Process Regression

2021 ◽  
Vol 14 (1) ◽  
pp. 146
Author(s):  
Matías Salinero-Delgado ◽  
José Estévez ◽  
Luca Pipia ◽  
Santiago Belda ◽  
Katja Berger ◽  
...  
Keyword(s):  
Time Series ◽  
Gaussian Process ◽  
Satellite Data ◽  
Gaussian Process Regression ◽  
Google Earth ◽  
Gap Filling ◽  
Area Index ◽  
Filling Time ◽  
Google Earth Engine ◽  
Mean Square Errors

Monitoring cropland phenology from optical satellite data remains a challenging task due to the influence of clouds and atmospheric artifacts. Therefore, measures need to be taken to overcome these challenges and gain better knowledge of crop dynamics. The arrival of cloud computing platforms such as Google Earth Engine (GEE) has enabled us to propose a Sentinel-2 (S2) phenology end-to-end processing chain. To achieve this, the following pipeline was implemented: (1) the building of hybrid Gaussian Process Regression (GPR) retrieval models of crop traits optimized with active learning, (2) implementation of these models on GEE (3) generation of spatiotemporally continuous maps and time series of these crop traits with the use of gap-filling through GPR fitting, and finally, (4) calculation of land surface phenology (LSP) metrics such as the start of season (SOS) or end of season (EOS). Overall, from good to high performance was achieved, in particular for the estimation of canopy-level traits such as leaf area index (LAI) and canopy chlorophyll content, with normalized root mean square errors (NRMSE) of 9% and 10%, respectively. By means of the GPR gap-filling time series of S2, entire tiles were reconstructed, and resulting maps were demonstrated over an agricultural area in Castile and Leon, Spain, where crop calendar data were available to assess the validity of LSP metrics derived from crop traits. In addition, phenology derived from the normalized difference vegetation index (NDVI) was used as reference. NDVI not only proved to be a robust indicator for the calculation of LSP metrics, but also served to demonstrate the good phenology quality of the quantitative trait products. Thanks to the GEE framework, the proposed workflow can be realized anywhere in the world and for any time window, thus representing a shift in the satellite data processing paradigm. We anticipate that the produced LSP metrics can provide meaningful insights into crop seasonal patterns in a changing environment that demands adaptive agricultural production.

scholarly journals Improving the mean and uncertainty of ultraviolet multi-filter rotating shadowband radiometer in situ calibration factors: utilizing Gaussian process regression with a new method to estimate dynamic input uncertainty

2019 ◽  
Vol 12 (2) ◽  
pp. 935-953 ◽  
Author(s):  
Maosi Chen ◽  
Zhibin Sun ◽  
John M. Davis ◽  
Yan-An Liu ◽  
Chelsea A. Corr ◽  
...  
Keyword(s):  
Time Series ◽  
Gaussian Process ◽  
Average Method ◽  
Moving Average ◽  
Gaussian Process Regression ◽  
Input Uncertainty ◽  
In Situ Calibration ◽  
The Mean ◽  
Mean Function

Abstract. To recover the actual responsivity for the Ultraviolet Multi-Filter Rotating Shadowband Radiometer (UV-MFRSR), the complex (e.g., unstable, noisy, and with gaps) time series of its in situ calibration factors (V0) need to be smoothed. Many smoothing techniques require accurate input uncertainty of the time series. A new method is proposed to estimate the dynamic input uncertainty by examining overall variation and subgroup means within a moving time window. Using this calculated dynamic input uncertainty within Gaussian process (GP) regression provides the mean and uncertainty functions of the time series. This proposed GP solution was first applied to a synthetic signal and showed significantly smaller RMSEs than a Gaussian process regression performed with constant values of input uncertainty and the mean function. GP was then applied to three UV-MFRSR V0 time series at three ground sites. The method appropriately accounted for variation in slopes, noises, and gaps at all sites. The validation results at the three test sites (i.e., HI02 at Mauna Loa, Hawaii; IL02 at Bondville, Illinois; and OK02 at Billings, Oklahoma) demonstrated that the agreement among aerosol optical depths (AODs) at the 368 nm channel calculated using V0 determined by the GP mean function and the equivalent AERONET AODs were consistently better than those calculated using V0 from standard techniques (e.g., moving average). For example, the average AOD biases of the GP method (0.0036 and 0.0032) are much lower than those of the moving average method (0.0119 and 0.0119) at IL02 and OK02, respectively. The GP method's absolute differences between UV-MFRSR and AERONET AOD values are approximately 4.5 %, 21.6 %, and 16.0 % lower than those of the moving average method at HI02, IL02, and OK02, respectively. The improved accuracy of in situ UVMRP V0 values suggests the GP solution is a robust technique for accurate analysis of complex time series and may be applicable to other fields.

scholarly journals Green LAI Mapping and Cloud Gap-Filling Using Gaussian Process Regression in Google Earth Engine

2021 ◽  
Vol 13 (3) ◽  
pp. 403
Author(s):  
Luca Pipia ◽  
Eatidal Amin ◽  
Santiago Belda ◽  
Matías Salinero-Delgado ◽  
Jochem Verrelst
Keyword(s):  
Machine Learning ◽  
Time Series ◽  
Gaussian Process ◽  
Gaussian Process Regression ◽  
Google Earth ◽  
Machine Learning Techniques ◽  
Gap Filling ◽  
Area Index ◽  
Uncertainty Estimates ◽  
Google Earth Engine

For the last decade, Gaussian process regression (GPR) proved to be a competitive machine learning regression algorithm for Earth observation applications, with attractive unique properties such as band relevance ranking and uncertainty estimates. More recently, GPR also proved to be a proficient time series processor to fill up gaps in optical imagery, typically due to cloud cover. This makes GPR perfectly suited for large-scale spatiotemporal processing of satellite imageries into cloud-free products of biophysical variables. With the advent of the Google Earth Engine (GEE) cloud platform, new opportunities emerged to process local-to-planetary scale satellite data using advanced machine learning techniques and convert them into gap-filled vegetation properties products. However, GPR is not yet part of the GEE ecosystem. To circumvent this limitation, this work proposes a general adaptation of GPR formulation to parallel processing framework and its integration into GEE. To demonstrate the functioning and utility of the developed workflow, a GPR model predicting green leaf area index (LAIG) from Sentinel-2 imagery was imported. Although by running this GPR model into GEE any corner of the world can be mapped into LAIG at a resolution of 20 m, here we show some demonstration cases over western Europe with zoom-ins over Spain. Thanks to the computational power of GEE, the mapping takes place on-the-fly. Additionally, a GPR-based gap filling strategy based on pre-optimized kernel hyperparameters is also put forward for the generation of multi-orbit cloud-free LAIG maps with an unprecedented level of detail, and the extraction of regularly-sampled LAIG time series at a pixel level. The ability to plugin a locally-trained GPR model into the GEE framework and its instant processing opens up a new paradigm of remote sensing image processing.

Gaussian Process Regression hyperparameter optimization for image time series gap-filling of Earth observation data and crop monitoring

2021 ◽  
Author(s):  
Santiago Belda ◽  
Matías Salinero ◽  
Eatidal Amin ◽  
Luca Pipia ◽  
Pablo Morcillo-Pallarés ◽  
...  
Keyword(s):  
Time Series ◽  
Gaussian Process ◽  
Computational Cost ◽  
Gaussian Process Regression ◽  
Superior Performance ◽  
Observation Data ◽  
Gap Filling ◽  
Crop Monitoring ◽  
Exponential Kernel ◽  
Uncertainty Estimates

<p>In general, modeling phenological evolution represents a challenging task mainly because of time series gaps and noisy data, coming from different viewing and illumination geometries, cloud cover, seasonal snow and the interval needed to revisit and acquire data for the exact same location. For that reason, the use of reliable gap-filling fitting functions and smoothing filters is frequently required for retrievals at the highest feasible accuracy. Of specific interest to filling gaps in time series is the emergence of machine learning regression algorithms (MLRAs) which can serve as fitting functions. Among the multiple MLRA approaches currently available, the kernel-based methods developed in a Bayesian framework deserve special attention because of both being adaptive and providing associated uncertainty estimates, such as Gaussian Process Regression (GPR).</p><p>Recent studies demonstrated the effectiveness of GPR for gap-filling of biophysical parameter time series because the hyperparameters can be optimally set for each time series (one for each pixel in the area) with a single optimization procedure. The entire procedure of learning a GPR model only relies on appropriate selection of the type of kernel and the hyperparameters involved in the estimation of input data covariance. Despite its clear strategic advantage, the most important shortcomings of this technique are the (1) high computational cost and (2) memory requirements of their training, which grows cubically and quadratically with the number of model’s samples, respectively. This can become problematic in view of processing a large amount of data, such as in Sentinel-2 (S2) time series tiles. Hence, optimization strategies need to be developed on how to speed up the GPR processing while maintaining the superior performance in terms of accuracy.</p><p>To mitigate its computational burden and to address such shortcoming and repetitive procedure, we evaluated whether the GPR hyperparameters can be preoptimized over a reduced set of representative pixels and kept fixed over a more extended crop area. We used S2 LAI time series over an agricultural region in Castile and Leon (North-West Spain) and testing different functions for Covariance estimation such as exponential Kernel, Squared exponential kernel and matern kernel with parameter 3/2 or 5/2. The performance of image reconstructions was compared against the standard per-pixel GPR time series training process. Results showed that accuracies were on the same order (12% RMSE degradation) whereas processing time accelerated up to 90 times. Crop phenology indicators were also calculated and compared, revealing similar temporal patterns with differences in start and end of growing season of no more than five days. To the benefit of crop monitoring applications, all the gap-filling and phenology indicators retrieval techniques have been implemented into the <strong>freely downloadable GUI toolbox DATimeS</strong> (Decomposition and Analysis of Time Series Software - https://artmotoolbox.com/).</p>

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