Chapter 7

This short final chapter contains two parts. The first summarizes the findings of this research and highlight its implications and significance. Second, in the Perspectives section, I offer several recommendations based on these findings, including directions for future research.

Summary and Significance of Findings

This research explored methods of analyzing the global water cycle with remote sensing datasets. My goal was to reconcile these data to close the water cycle, or to reduce the overall error in estimating the water budget. This work built upon previous research and also contained several innovative aspects.

I applied a closed-form analytical solution, optimal interpolation (OI), that forces the water budget residual to equal zero. This approach has several advantages – it is straightforward to implement and has a basis in information theory, as it allocates errors in observations inversely proportional to their uncertainty. Compared to previous applications of the OI method, I applied it on a much larger scale, using over 1,600 river basins that I delineated based on topography, on every continent other than Greenland and Antarctica. Unlike with prior uses of OI, I used an affine error model that produces more realistic results under a range of hydrologic regimes. Yet, despite its advantages, OI can only be applied at the river basin scale where discharge observations are available.

I explored two methods for extrapolating the results of optimal interpolation to make predictions in ungaged basins and at the pixel scale. The first method involved fitting simple linear regression models over training basins, and then using spatial interpolation methods to evaluate model parameters over all global land surfaces. Second, I trained a nested set of neural network (NN) models to reproduce the results of OI. The NN models are able to ingest a large amount of information, and to find complex and non-linear relationships among variables (i.e.: remote sensing observations and carefully chosen environmental data).

The NN models outperformed simpler methods in terms of both fit to the OI solution and in terms of water budget closure. The model goodness of fit varies by location; it tends to be better over humid regions, and less accurate over the Arctic or over parts of Asia and South America. I also applied the NN model at the pixel scale and showed that the solution results in lower water cycle imbalance errors over most of the earth’s land surfaces.

There are several potential applications for the resulting calibrated earth observation (EO) datasets. For example, I explored the use of water budget-based methods for predicting missing water cycle components. Such methods are especially useful in uninstrumented regions. Using this method, we could predict evapotranspiration on every continent as well as a state-of-the art remote sensing dataset, based on a comparison with flux tower observations.

Using the water budget method, we also made inferred predictions of runoff and river discharge. When we used the NN-calibrated EO datasets, we saw a significant improvement in discharge predictions, compared to using uncorrected EO datasets. However, the results were slightly less accurate than a statistical model calibrated to gage observations. Thus, the methods and results of this study can contribute to the problem of Prediction in Ungaged Basins (PUB), a longstanding challenge in the hydrologic sciences.

I also explored the capability of using the water budget method with calibrated EO data to fill in missing observations of total water storage (TWS) from 1980 to 2002, before GRACE observations are available. I showed that this method can predict month-over-month total water storage change (TWSC) as well as a state-of-the-art global assimilation model. These results are informative, as they reasonably recreate the seasonal runoff signal and interannual variability. However, greater accuracy is needed to predict trends in TWS.

I do not believe that any of the methods described in the literature can reliably recreate TWS from climate data alone. Small bias errors in TWSC are compounded when integrating to calculate trends in TWS. Another reason is that water storage is profoundly impacted by human activities, such as water diversions and groundwater withdrawals, which are not well monitored globally. A better understanding of how these activities affect the water cycle would require detailed modeling that incorporates information on human activities, e.g., population densities, dam construction, reservoir levels and operations, and irrigation intensity.

Overall, the methods presented in this thesis are effective at reconciling remote sensing data and improving water cycle closure. Yet, they do have certain limitations. The results have fairly coarse spatial and temporal resolutions (0.5°, monthly). They provide a near global view that can be applied over large basins but may not be suitable for local applications or for calculating fluxes over small basins.

This analysis is not quite global as it did not include Antarctica, Greenland, or Arctic regions above 73° North. Regions with permanent snow and ice defy conventional hydrologic analysis – alternative techniques and methods are needed for studying cold regions.

The analysis herein covers a longer time period than other recently-published global water cycle studies, but still only covers 2002 (when the GRACE satellites were launched) to 2019. I showed how the methods described herein can extend the calibration of EO datasets to previous time periods, but I also showed that extrapolating this information to estimate trends is risky and unreliable.


In this section, I offer some recommendations based on my research, including potential directions for future investigation.

The availability of river discharge observations is an important limiting factor for large-scale hydrologic analysis. In the near future, data from the SWOT satellites will create exciting opportunities for similar lines of research, providing runoff estimates at many more locations than are currently monitored. After a few years of SWOT data have been acquired, the methods described here could be combined with new data for record extension of SWOT-like discharge back to 2002, the beginning of the GRACE era.

To date, most studies analyzing the water cycle with remote sensing data have been done on a small number or river basins. My early efforts at integration of water cycle data focused on using observed river discharges. The results lacked generalizability, however, due to very little training data over Africa, Asia, and parts of South America. It would be valuable to extend the research performed here with new sources of river discharge data. Continental scale studies could readily be performed over North America or Europe. Regional studies could be performed over countries where there is sufficient data, such as Brazil or Chile. For researchers with privileged access to data, China or India would make interesting case studies.

The relatively simple statistical model I described in Chapters 4 and 5 performed almost as well as a more complex neural network model. More could be done to create more detailed parameter regionalization models. For example, we could explore fitting a seasonal regression model, where we fit a different equation for each month or each quarter.

Subsurface flow is neglected in large-sample and global studies, yet it is known that this is a significant flux in some regions. The methods developed in this thesis could help to better characterize those fluxes. Studies in endorheic basins also offer unique opportunities, as there is no outflow, thus simplifying the water budget to three components. There is an opportunity to perform more detailed analyses over such basins using data from GRACE and other satellites.

In Chapter 6, we saw that the calibrated database leads to better predictions of water cycle variables using simple water budget based methods. It would be interesting to see whether calibrated datasets could improve the predictions of more complex simulation models. This could be tested by using EO the datasets before and after calibration as forcing for a hydrologic model. One could choose either an uncalibrated model or a model that can be calibrated automatically.24 My hypothesis is that the calibrated data will result in lower residuals and better fits, but this would need to be tested.

Additional information could be added in terms of sub-components of the water cycle. For example, a more detailed water cycle model could include soil moisture from the SMOS or SMAP missions (Kolassa et al. 2016), or surface water extent from GIEMS (Prigent et al. 2016) or SWOT.

Ground-based observations are critical to our understanding of the water cycle and will be essential for calibrating and interpreting the data returned by SWOT. Greater cooperation and funding is needed to expand and maintain the in situ discharge observation network. Discharge is an “integrating” variable that is key to understanding the water cycle, the effects of climate change, and for calibrating and validating the next generation of satellite measurements. To maximize the value of these data, better data sharing and quality assurance is essential.

GRACE is unique among remote sensing products used in hydrology, as it is the only mission that directly measures the variable of interest: the mass of water, and how it changes over time. GRACE integrates information about all of the water in a region – groundwater, surface water, soil moisture, etc. As one of the mission scientists has noted, “GRACE cannot feasibly be replicated by ground-based observations” (Rodell et al. 2015). The mission has fostered innovative science, spawned dozens of applications, and resulted in hundreds of publications. It is my hope that governments and space agencies provide continued support for this and similar missions.

The field of artificial intelligence is rapidly evolving, and new developments could be tested for better modeling of the water cycle. Alternative approaches in deep learning such as long short-term memory (LSTM) neural network models may be able to exploit the temporal information in EO time series for better predictions of water cycle variables.

As a final word to this Conclusion, allow to share my sincerest hope that advances in science of hydrology and remote sensing will be used to promote peace, equality, and environmental stewardship.

  1. For example, the parsimonious watershed model described by Limbrunner, Vogel, and Chapra (2010) would do nicely, as it has only 4 tunable parameters.↩︎