List of Figures

• 1.1 A typical representation of the natural water cycle, published by the US Geological Survey.
• 1.2 Detailed water cycle diagram published by the USGS in 2022, showing human influences.
• 1.3 A simplified water budget showing the main water cycle components P, E, R, and ΔS.
• 1.4 Water budget for part of a watershed.
• 1.5 Earth observation missions developed by the European Space Agency.
• 2.1 Important measurement devices for two fundamental hydrologic variables, which measure the change in depth of liquid water.
• 2.2 Selected stations providing precipitation data from the Global Historical Climatology Network (n = 21,880).
• 2.3 Map of the selected flux towers used in this study for their measurements of evapotranspiration.
• 2.4 Trends in total water storage based on three different GRACE solutions.
• 2.5 Time series of GRACE observations of total water storage anomaly for a random pixel over the Amazon basin in Brazil.
• 2.6 Number and duration of gaps in the GRACE record of TWS between April 2002 and December 2019.
• 2.7 Errors in the begin date (left) and duration (right) of GRACE observations compared to calendar months.
• 2.8 The time coverage of select GRACE observations, showing overlapping observations that were removed.
• 2.9 Timeline of GRACE data availability and gaps.
• 2.10 Map showing the location and data source of the 2,056 river flow gaging stations used in this analysis.
• 2.11 Distribution of data length in years for our 2,056 gages.
• 2.12 Number of gages with observations, by year.
• 2.13 Normal probability plots of the normalized runoff dataset.
• 2.14 Comparison between GRUN estimated runoff and observed monthly average river discharge at 2,056 gaged basins.
• 2.15 Global map of the CGIAR aridity index.
• 2.16 Correlation between NDVI and EVI time series at the pixel scale.
• 2.17 Distribution of average values of Terra/MODIS NDVI and EVI for 2000 to 2019.
• 2.18 Global irrigation in 2005, from Siebert et al. (2015).
• 2.19 Average monthly solar radiation over the period 2000 to 2019, from the ERA5 model.
• 2.20 Maps of EO data for the month of January 2005.
• 2.21 Boxplots showing the distribution of values in the EO datasets.
• 2.22 Trends in total water storage based on GRACE-JPL, (a) calculated by the author; (b) from Rodell et al. (2018).
• 2.23 Pixelwise trends in total water storage and associated p-value calculated with the 3 GRACE solutions.
• 2.24 Trends in total water storage in South American based on the 3 GRACE solutions.
• 3.1 Example of internal gaps or “donut holes” in a delineated watershed.
• 3.2 Geographic coverage of the this study’s 2,056 gaged river basins.
• 3.3 Comparison of reported and calculated watershed areas for the project’s 2056 gaged basins.
• 3.4 Distribution of the basin area of the 2,056 gaged river basins.
• 3.5 Flow direction encoding in the 0.1° resolution GloFAS local drainage direction raster.
• 3.6 Map of the 1,698 synthetic river basins created for training and validating the neural network model.
• 3.7 Grid cells on the earth vary in size due to projection distortions.
• 3.8 Area of grid cells varies by latitude.
• 3.9 Rasterization of basin polygons to create basin masks.
• 3.10 CMORPH precipitation over the Vals River basin in February 2001.
• 3.11 Indexing of grid cells.
• 3.12 Distributions of the water cycle imbalance for each of the 27 possible combinations of EO variables, plus the simple weighted solution.
• 3.13 Monthly average precipitation across all terrestrial land surfaces (excluding Greenland and Antarctica) for the three precipitation datasets used in this study.
• 3.14 Maps of the difference between pixel mean precipitation and the ensemble mean for each dataset.
• 3.15 Time series plots of the four major water cycle components, showing remote sensing observations and the optimal interpolation solution.
• 3.16 Scatter plots of uncorrected EO data vs. the OI solution, over the 2,056 gaged basins.
• 3.17 Distribution of the changes made to EO datasets by the OI algorithm. Represents all months over 2,056 gaged basins.
• 3.18 Map of the mean difference between the OI solution and SW average of observations for each of the four water cycle components.
• 4.1 Overview of the two steps of the integration NN method.
• 4.2 Illustration of the concepts of measurement accuracy and precision in one dimension.
• 4.3 Illustration of the concepts of a predictive model bias and standard error.
• 4.4 Possible cases in regression between calculated and observed values.
• 4.5 Comparison of the standard Nash-Sutcliffe model efficiency with its bounded version.
• 4.6 Illustration of the bias-variance tradeoff with increasing model flexibility.
• 4.7 Illustration of the competing definitions of “bias” in the domains of statistics and machine learning.
• 4.8 Illustration of the variance among models of varying flexibility.
• 4.9 Illustration of the bias-variance tradeoff with a simple neural network model.
• 4.10 Example learning curve created with Matlab’s Deep Learning Toolbox.
• 4.11 Overview of a single neuron with multiple inputs.
• 4.12 A sampling of the neural network activation functions available in Matlab.
• 4.13 Example neural network layer with multiple neurons.
• 4.14 Example of a neural network with multiple output variables.
• 4.15 Empirical probability distribution of EO variables before and after normalization.
• 4.16 Neural network model architecture for calibration then mixture of EO datasets.
• 4.17 Distribution of EO variable values over training basins and over global land pixels.
• 4.18 Distribution of ancillary variable values over training basins and over global land pixels.
• 5.1 Regressions of OI precipitation against observed precipitation from MSWEP over three river basin.
• 5.2 Regression analysis before and after removing outliers.
• 5.3 Distributions for the number of outliers in the 1,358 training basins for each of the 10 EO variables.
• 5.4 Example fits between the EO variable and the OI solution for 3 regression-type models.
• 5.5 Distribution of values of the scale parameter, c, in the alternative 3-parameter regression.
• 5.6 Distribution of fitted regression parameters for the precipitation variable GPCP over the test basins for four regression methods.
• 5.7 Examples of different surface fitting algorithms.
• 5.8 Demonstration of the EO calibration with the regression-based method for Gleam-A evapotranspiration.
• 5.9 Validation set error vs. the number of neurons.
• 5.10 Residual plots for ERA5 Evapotranspiration and 12 ancillary environmental variables.
• 5.11 Results of computational experiment to determine the significance of ancillary variables in improving the calibration of EO variables using an NN model.
• 5.12 Impact of adding 8, 10, or 12 ancillary variables to the neural network calibration models.
• 5.13 Pixel scale calibrated evapotranspiration for July 2004 calculated by (a) regression model, (b) NN calibration model, and (c) NN mixture model.
• 5.14 Time series plots of hydrologic fluxes over a single basin, showing OI and NN solutions.
• 5.15 Scatter plots showing changes made to EO data by the NN mixture model.
• 5.16 Goodness of fit between model output and the OI solution over the set of 340 validation basins.
• 5.17 Water cycle imbalances over the 340 validation basins, shown as empirical probability distributions (kernel density plots) for (top) Regression-based model, (bottom) neural network model.
• 5.18 Comparison of the water cycle imbalance over validation basins for the two modeling methods, over 340 validation basins.
• 5.19 Map of the average water cycle imbalance at the pixel scale.
• 5.20 Improvement in the water cycle closure at the pixel scale for the two modeling methods.
• 5.21 Boxplots summarizing the fits root mean square error between EO datasets and precipitation observations at 21,880 GHCN stations.
• 5.22 Effect of NN model calibration on the goodness of fit between EO precipitation and the CPC gridded precipitation data product.
• 6.1 Empirical probability distribution plots of the fit between EO and in situ observed evapotranspiration.
• 6.2 Goodness of fit between GRACE observed and modeled monthly TWSC.
• 6.3 Maps of the correlation and root mean square error for predictions of TWSC from two sources: inferred by my NN predictions, and Zhang et al. (2018).
• 6.4 Fit to observations of reconstructed ΔS.
• 6.5 Correlation between NN calibrated ΔS and the ENSO index MEIv2, for 1980 - 2019, at the pixel scale over South America.
• 6.6 Empirical probability distribution plots of the correlation (left) and RMS error (right) between in situ observations and EO-based estimates of basinrunoff.
• 6.7 Distribution of the percent bias error in predicted runoff over 1,781 river basins.
• 6.8 Time series plot and seasonality for monthly runoff for the Mississippi River at Vicksburg calculated from EO datasets, pre- and post-calibration by the NN model.
• A.1 Issue with CMORPH precipitation data between 59.25° and 60° North.

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