Downscaling of Open Coarse Precipitation Data Using a Machine Learning Algorithm

In this chapter, the authors propose a novel statistical model with a residual correction of downscaling coarse precipitation TRMM 3B43 product. The presented study was carried out over Morocco, and the objective is to improve statistical downscaling for TRMM 3B43 products using a machine learning algorithm. Indeed, the statistical model is based on the Transformed Soil Adjusted Vegetation Index (TSAVI), elevation, and distance from the sea. TSAVI was retrieved using the quantile regression method. Stepwise regression was implemented with the minimization of the Akaike information criterion and Mallows' Cp indicator. The model validation is performed using ten in-situ measurements from rain gauge stations (the most available data). The result shows that the model presents the best fit of the TRMM 3B43 product and good accuracy on estimating precipitation at 1km according to 𝑅2, RMSE, bias, and MAE. In addition, TSAVI improved the model accuracy in the humid bioclimatic stage and in the Saharan region to some extent due to its capacity to reduce soil brightness.

A Spatial Downscaling Methodology for GRACE Total Water Storage Anomalies Using GPM IMERG Precipitation Estimates

A downscaling framework for coarse resolution Gravity Recovery and Climate Experiment (GRACE) Total Water Storage Anomaly (TWSA) data is described, exploiting the observations of precipitation from the Global Precipitation Measurement (GPM) mission, using the Integrated Multi-satellite Retrievals for GPM (IMERG). Considering that the major driving force for changes in TWS is precipitation, we tested our hypothesis that coarse resolution, i.e., 1°, GRACE TWSA can be effectively downscaled to 0.1° using GPM IMERG data. The algorithm for the downscaling process comprises the development of a regression equation at the coarse resolution between the GRACE and GPM IMERG data, which is then applied at the finer resolution with a subsequent residual correction procedure. An ensemble of GRACE data from three processing centers, i.e., GFZ, JPL and CSR, was used for the time period from June 2018 until March 2021. To verify our downscaling methodology, we applied it with GRACE data from 2005 to 2015, and we compared it against modeled TWSA from two independent datasets in the Thrace and Thessaly regions in Greece for the same period and found a high performance in all examined metrics. Our research indicates that the downscaled GRACE observations are comparable to the TWSA estimated with hydrological modeling, thus highlighting the potential of GRACE data to contribute to the improvement of hydrological model performance, especially in ungauged basins.

Evaluation of the RF-Based Downscaled SMAP and SMOS Products Using Multi-Source Data over an Alpine Mountains Basin, Northwest China

Passive microwave surface soil moisture (SSM) products tend to have very low resolution, which massively limits their application and validation in regional or local-scale areas. Many climate and hydrological studies are urgently needed to evaluate the suitability of satellite SSM products, especially in alpine mountain areas where soil moisture plays a key role in terrestrial atmospheric exchanges. Aiming to overcome this limitation, a downscaling method based on random forest (RF) was proposed to disaggregate satellite SSM products. We compared the ability of the downscaled soil moisture active passive (SMAP) SSM and soil moisture and ocean salinity satellite (SMOS) SSM products to capture soil moisture information in upstream of the Heihe River Basin by using in situ measurements, the triple collocation (TC) method and temperature vegetation dryness index (TVDI). The results showed that the RF downscaling method has strong applicability in the study area, and the downscaled results of the two products after residual correction have more details, which can better represent the spatial distribution of soil moisture. The validation with the in situ SSM measurements indicates that the correlation between downscaled SMAP and in situ SSM is better than downscaled SMOS at both point and watershed scales in the Babaohe River Basin. From the TC method, the root mean square error (RMSE) of the CLDAS (CMA land data assimilation system), downscaled SMAP and downscaled SMOS were 0.0265, 0.0255 and 0.0317, respectively, indicating that the downscaled SMAP has smaller errors in the study area than others. However, the soil moisture distribution in the study area shown by the SMOS downscaled results is closer than the downscaled SMAP to the degree of drought reflected by TVDI. Overall, this study suggests that the proposed RF-based downscaling method can capture the variation of SSM well, and the downscaled SMAP products perform significantly better than the downscaled SMOS products after the accuracy verification and error analysis of the downscaled results, and it should be helpful to facilitate applications for satellite SSM products at small scales.

Geophysical Investigation of a Fault Zone from Aeromagnetic Data over the Ageva Area of Okene Kogi State, Nigeria

High-resolution aeromagnetic data over a part of Ageva fault zone in Nigeria have been analyzed with a view to estimate sedimentary thicknesses within the studied area. The data set of this study area, was subjected to various corrections and interpretation techniques. Regional residual correction was done and the noise level of the data was reduced via upward continuation to a height of 250 m thereby enhancing the reliability of the results obtained. Qualitative interpretation techniques which include: Second Vertical Derivative, Analytic Signal, Tilt derivative were used to delineate the trending pattern of the anomalies in the study area which are in the E-W, NE-SW, NW-SE, and N-S directions. The result suggests that fault zone within Ageva and Owo may be mineralized and also that the faults within Ageva and Ibilo extend by a quarter of their exposed length. The Werner solutions revealed that inferred faults within Owo and Ibilo may have relatively low susceptibilities as compared with others in the study area and the range of the depth extent of linear features is 401.5 m – 982.5 m.

The Adaptable 4A Inversion (5AI): description and first <i>X</i>_CO₂ retrievals from Orbiting Carbon Observatory-2 (OCO-2) observations

A better understanding of greenhouse gas surface sources and sinks is required in order to address the global challenge of climate change. Space-borne remote estimations of greenhouse gas atmospheric concentrations can offer the global coverage that is necessary to improve the constraint on their fluxes, thus enabling a better monitoring of anthropogenic emissions. In this work, we introduce the Adaptable 4A Inversion (5AI) inverse scheme that aims to retrieve geophysical parameters from any remote sensing observation. The algorithm is based on the Optimal Estimation algorithm, relying on the Operational version of the Automatized Atmospheric Absorption Atlas (4A/OP) radiative transfer forward model along with the Gestion et Étude des Informations Spectroscopiques Atmosphériques: Management and Study of Atmospheric Spectroscopic Information (GEISA) spectroscopic database. Here, the 5AI scheme is applied to retrieve the column-averaged dry air mole fraction of carbon dioxide (XCO2) from a sample of measurements performed by the Orbiting Carbon Observatory-2 (OCO-2) mission. Those have been selected as a compromise between coverage and the lowest aerosol content possible, so that the impact of scattering particles can be neglected, for computational time purposes. For air masses below 3.0, 5AI XCO2 retrievals successfully capture the latitudinal variations of CO2 and its seasonal cycle and long-term increasing trend. Comparison with ground-based observations from the Total Carbon Column Observing Network (TCCON) yields a bias of 1.30±1.32 ppm (parts per million), which is comparable to the standard deviation of the Atmospheric CO2 Observations from Space (ACOS) official products over the same set of soundings. These nonscattering 5AI results, however, exhibit an average difference of about 3 ppm compared to ACOS results. We show that neglecting scattering particles for computational time purposes can explain most of this difference that can be fully corrected by adding to OCO-2 measurements an average calculated–observed spectral residual correction, which encompasses all the inverse setup and forward differences between 5AI and ACOS. These comparisons show the reliability of 5AI as an optimal estimation implementation that is easily adaptable to any instrument designed to retrieve column-averaged dry air mole fractions of greenhouse gases.

An Enhanced Adaptive Bernstein Collocation Method for Solving Systems of ODEs

In this paper, we introduce two new methods to solve systems of ordinary differential equations. The first method is constituted of the generalized Bernstein functions, which are obtained by Bernstein polynomials, and operational matrix of differentiation with collocation method. The second method depends on tau method, the generalized Bernstein functions and operational matrix of differentiation. These methods produce a series which is obtained by non-polynomial functions set. We give the standard Bernstein polynomials to explain the generalizations for both methods. By applying the residual correction procedure to the methods, one can estimate the absolute errors for both methods and may obtain more accurate results. We apply the methods to some test examples including linear system, non-homogeneous linear system, nonlinear stiff systems, non-homogeneous nonlinear system and chaotic Genesio system. The numerical shows that the methods are efficient and work well. Increasing m yields a decrease on the errors for all methods. One can estimate the errors by using the residual correction procedure.

An Efficient Downscaling Scheme for High-Resolution Precipitation Estimates over a High Mountainous Watershed

Satellites are capable of observing precipitation over large areas and are particularly suitable for estimating precipitation in high mountains and poorly gauged regions. However, the coarse resolution and relatively low accuracy of satellites limit their applications. In this study, a downscaling scheme was developed to obtain precipitation estimates with high resolution and high accuracy in the Heihe watershed. Shannon’s entropy, together with a semi-variogram, was applied to establish the optimal precipitation station network. A combination of the random forest (RF) method and the residual correction approach with the established rain gauge network was applied to downscale monthly precipitation products from Integrated Multi-satellitE Retrievals for Global Precipitation Measurement (IMERG). The results indicated that the RF model showed little improvement in the accuracy of IMERG-based precipitation downscaling. Including residual modification could improve the results of the RF model. The mean absolute error (MAE) and root mean square error (RMSE) values decreased by 19% and 21%, respectively, after residual corrections were added to the RF approach. Moreover, we found that enough rain gauge records are necessary for and remain an important component of tuning model performance. The application of more rain gauges improves the performance of the combined RF and residual modification methods, with the MAE and RMSE values reduced by 8% and 9%, respectively. Residual correction, together with enough precipitation stations, can effectively enhance the quality of the precipitation patterns and magnitudes obtained in the RF downscaling process. The proposed downscaling scheme is an effective tool for increasing the accuracy and spatial resolution of precipitation fields in the Heihe watershed.

Fractional Bernstein Series Solution of Fractional Diffusion Equations with Error Estimate

In the present paper, we introduce the fractional Bernstein series solution (FBSS) to solve the fractional diffusion equation, which is a generalization of the classical diffusion equation. The Bernstein polynomial method is a promising one and can be generalized to more complicated problems in fractional partial differential equations. To get the FBSS, we first convert all terms in the problem to matrix forms. Then, the fundamental matrix equation is obtained and thus, the solution is obtained. Two error estimation methods based on a residual correction procedure and the consecutive approximations are incorporated to find the estimate and bound of the absolute error. The perturbation and stability analysis of the method is given. We apply the method to some illustrative examples. The numerical results are compared with the exact solutions and known second-order methods. The outcomes of the numerical examples are very encouraging and show that the FBSS is highly useful in solving fractional partial problems. The results show the accuracy and effectiveness of the method.