FormalPara Overview

The following tutorial details how to use observations from the Gravity Recovery and Climate Experiment (GRACE) to evaluate changes in groundwater storage for a large river basin. Here, you will learn how to apply remote sensing estimates of total water storage anomalies, land surface model output, and in situ observations to resolve groundwater storage changes in California’s Central Valley. The following method has been applied to study water storage changes around the world, and can be ported to quantify groundwater storage change for major river basins.

FormalPara Learning Outcomes

  • Plotting changes in total water storage using GRACE.

  • Mapping trends in water storage.

  • Resolving changes in groundwater storage for a river basin.

  • Import image collections and create image collections from assets.

  • Create charts by reducing an ImageCollection with a feature geometry.

FormalPara Helps if you know how to

  • Use expressions to perform calculations on image bands (Chap. 9).

  • Write a function and map it over an ImageCollection (Chap. 12).

  • Fit linear and nonlinear functions with regression in an ImageCollection time series (Chap. 18).

  • Use ee.Join to join one ImageCollection to another to compute differences (Chap. 21).

  • Filter a FeatureCollection to obtain a subset (Chaps. 22 and 23).

1 Introduction to Theory

Since 2002, GRACE and the follow-on mission, GRACE-FO, have provided a new vantage to track changes in water resources (Tapley et al. 2004). GRACE holds the unique ability to directly track changes in total water storage anomalies (TWSa), according to the following equation:

$$ {\text{TWSa }} = {\text{ CANa }} + {\text{ SWa }} + {\text{ SMa }} + {\text{ SWEa }} + {\text{ GWa}} $$
(40.1)

where CANa is canopy water storage anomaly, SWa is the surface water anomaly, SMa is the soil moisture anomaly, SWEa is the snow water equivalent anomaly, and GWa is the groundwater storage anomaly.

By utilizing supplemental observations from other remote sensing platforms and land surface models and rearranging Eq. 40.1, scientists have been able to resolve changes in groundwater storage within major river basins around the planet (Famiglietti 2014). From Bangladesh (Purdy et al. 2019) and India (Rodell et al. 2009) to the Middle East (Voss et al. 2013) and the American Southwest (Castle et al. 2014), the problem of declining groundwater storage has emerged with varying levels of severity (Richey et al. 2015). Along with many other regions around the world, California shares an overreliance on groundwater (Famiglietti et al. 2011). This tutorial demonstrates the analytical steps to resolve groundwater storage changes using GRACE for California’s Central Valley.

2 Practicum

2.1 Section 1: Exploring the Study Area

Evaluating changes in hydrologic storage requires examining change within a hydrologically connected system. Watersheds and basins represent areas of land where precipitation drains to a common point. We will use already-generated basins from the Watershed Boundary Dataset (WBD) to delineate the drainage area for California’s Central Valley. The WBD includes hydrologic unit codes (HUCs) to identify connected basins within the United States.

In the following sections of code, we will load three basins by their unique four-digit HUCs and merge the basins together. To accomplish this task, we will use the ee.Filter.inList function to filter the basins variable by the ‘huc4’ property, extracting three to a variable basin.

A code to import basins, extract the 3 H U C 04 basins for the central valley, and add the basin to the map to show the extent of our analysis uses the functions e e dot feature collection, dot filter, map dot center object, and map dot add layer.

2.1.1 Section 1.1: Map the Extent of Agriculture in the Region

To get a sense for the extent of agriculture in California, we can visualize all cultivated land in the Central Valley. This will map where the greatest need for water occurs.

A code uses the functions var, e e dot image collection, dot filter, dot select, map dot add layer, dot first, and dot clip.

The extent of cultivated lands shows up as a translucent purple (Fig. 40.1).

Fig. 40.1
An enlarged Google map of the United States of America highlights the agricultural patches of land passing through San Francisco, San Jose, and Sacramento.

California’s Central Valley Basin, including agricultural lands

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2.1.2 Section 1.2: Load Reservoir Locations

California has over 150 reservoirs distributed across the state. These reservoirs vary in size and capacity, and the regions of the state that they support. For the Central Valley, water conveyance infrastructure allows the transport of water from north to south. We will use our basin boundary to select the reservoirs within our basin to quantify changes in surface water storage. The list of reservoirs was gathered from the California Department of Water Resources’ Data Exchange Center (CDEC). For an application in another study region, acquiring in situ surface water storage would be required to resolve that region’s groundwater storage changes.

A code with the comments, this table was generated using the index from the C D E C website and filter reservoir locations by the Central Valley geometry uses the functions like var, e e dot feature collection, dot filter bounds, and map dot add layer.

The blue dots that now appear on the map represent the distribution of water storage across the Central Valley. Water conveyance infrastructure and natural rivers deliver water to farms across the valley. Despite all these reservoirs, many water users continue to rely on groundwater to meet their needs. A 2011 study detailed the magnitude of this reliance using gravity-sensing satellites (Famiglietti et al. 2011). The next sections of this chapter reveal how to resolve groundwater storage changes using these methods.

Code Checkpoint A21a. The book’s repository contains a script that shows what your code should look like at this point.

2.2 Section 2: Tracking Total Water Storage Changes in California with GRACE

GRACE can directly track changes in TWSa. Changes in TWSa indicate which regions are gaining or losing water.

2.2.1 Section 2.1: Import GRACE Data and Plot Changes in Total Water Storage in California

First, we will import the image collection and select the proper band to chart.

A code with the comment subset GRACE for liquid water equivalent dataset uses the functions like var, e e dot image collection, and dot select.

The GRACE data imported here have already been processed to provide units of TWSa. The data contained in this dataset are units of “equivalent water thickness” anomalies. GRACE hydrologic data are presented as anomalies because GRACE does not directly observe the gravitational pull of only water. The gravity observed also includes Earth’s surface (e.g., mountains). To disentangle the signal of water, we can look at changes relative to a longer term mean gravity signal. The anomalies represent the difference between a given month’s observation and a multi-year mean. We will now plot TWSa for basins in a large part of California (Fig. 40.2).

Fig. 40.2
A graph of T W S a versus the years plots a curve for l w e underscore thickness. Values are estimated. (0 1, 2004, 17), (0 1, 2008, 16), and (0 1, 2016, negative 5).

TWSa for the Sacramento-San Joaquin Basin

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A code to make plot of T W S a for basin boundary uses the functions u i dot chart dot image dot series, dot filter, e e dot reducer dot mean, dot set options, and print.

In the Console, you will see a plot of TWSa. Notice the seasonality and interannual variations in TWSa. Winter months reveal periods of maximum water storage due to snowpack, full reservoirs, and wet soil. Summer and early fall reveal less TWSa, as the snow has melted, reservoir water has been used, and soil is drying out. Additionally, summer months are periods when groundwater is extracted and used to supplement a limited surface water supply. Evidence of drought emerged through declining TWSa between 2006–2009 and 2012–2017.

Next, we will look at the trend in TWSa for the entire period of record.

2.2.2 Section 2.2: Estimate the Linear Trend in TWSa Over Time

As presented in Chap. 18, Earth Engine can fit linear models to time series data, with unique linear fits for each pixel based on the values through time. Consider the following linear model, where et is a random error:

$$ {{pt}} = \beta 0 + \beta {{1t}} + {{et}}\left( {1} \right) $$
(40.2)

This is the model behind the trendline added to the chart we just created. This model is useful for detrending data and reducing non-stationarity in the time series. The goal of the regression is to discover the values of the β’s in each pixel.

To fit this trend model to the GRACE-based TWSa series using ordinary least squares, we can use the linearRegression reducer.

A code to compute the trend for each pixel to map regions of most change, compute time in fractional years since the epoch, return the image with the added bands, add a time band, add a constant band, list of the independent variable names, name of the dependent variable, compute a linear trend, and a 2 by 1 band called coefficients.

The image of coefficients, computed below, is a two-band image in which each pixel contains values for β0 and β1. The β1 value will represent the temporal slope for the GRACE mascon.

A code to flatten the coefficients into a 2-band image uses the functions var, dot select, dot array project, and dot array flatten.

Next, we can visualize the GRACE trends to capture the spatial scales on which GRACE can resolve TWSa. GRACE is adept at capturing these changes only for larger basins.

A code to create a layer of the T W S a slope to add to the map, set visualization parameters to represent positive and negative trends uses the functions map dot add layer, dot clip, and dot select.

The slope layer reveals that the Tulare Basin (the southernmost basin in the Central Valley) experienced the largest negative changes in TWSa over the time period (Fig. 40.3). Darker reds indicate greater negative change, and blue represents positive change. This is a result of the region not receiving winter rain or snow and having the most junior surface water rights in the Central Valley.

Fig. 40.3
An enlarged Google map of the United States of America highlights in two colors the patches of land passing through San Francisco, San Jose, and Sacramento.

Slope in TWSa for California. Darker reds indicate greater declines in total water storage. Blue represents increases in water storage. White represents no change in water storage

Full size image

The next steps in this chapter will review how to unpack the TWSa signal to resolve changes in groundwater storage anomalies for the basin.

Code Checkpoint A21b. The book’s repository contains a script that shows what your code should look like at this point.

2.3 Section 3: Tracking Changes in Soil Water Storage and Snow Water Equivalent in California

The Global Land Data Assimilation System (GLDAS) utilizes multiple land surface models to globally resolve fluxes in storage of water (like soil moisture and snow) and energy at a three-hour frequency (Rodell et al. 2004). An example of how to convert three-hourly GLDAS snow water equivalent to annual SWEa for 2003 can be found in script A21s1 in the book’s repository. Running the supplemental script is an optional part of this lab: it is added to provide clarity on how the image assets were created for each GLDAS variable in this chapter.

For the next analysis, you will be starting with a script that imports the GLDAS SMa and SWEa processed by the methods above. GLDAS estimates of soil moisture and snow water equivalent are resolved at a three-hour temporal frequency. Therefore, we have taken the time to reduce the GLDAS data to annual means from the three-hour estimates.

Additionally, we aggregated monthly GRACE observations to annual average estimates to improve the efficiency of running this analysis. More experienced users can adapt these methods to resolve monthly changes. However, it should be noted that to replicate the same methods at a monthly cadence would require the interpolation of missing months of GRACE observations. Please use the code starting point below, as the script imports the necessary assets to complete the final analysis.

2.3.1 Section 3.1: Load GLDAS Soil Moisture Images from an Asset to an Image Collection

Code Checkpoint A21c. The book’s repository contains a script to use to begin this section. You will need to start with that script and paste code below into it.

When you run the script, you will see a number of assets being imported and an annual time series of GRACE. Additionally, the script is set to convert the list of annual mean soil moisture images to an ImageCollection.

A code uses the functions e e dot list and e e dot image collection dot from images with the details as s m 2003, s m 2004, s m 2005, s m 2006, s m 2007, s m 2008, s m 2009, s m 2010, s m 2011, s m 2012, s m 2013, s m 2014, s m 2015, s m 2016.

Before we compute groundwater storage anomalies from GRACE and GLDAS data following Eq. 40.1, we should inspect the units to ensure that our math is sound. In the search bar of Earth Engine, search for “GLDAS” and click on GLDAS-2.1: Global Land Data Assimilation System, then navigate to Bands to see what the units are for ‘RootMoist_inst’ and ‘SWE_inst’.

The units for GLDAS are currently showing as kg/m2. We need to convert the soil moisture and snow values to equivalent water depth units of centimeters. Define the following conversion variable and map this over the ImageCollection. As described in Chaps. 12 and 13, mapping over an ImageCollection is similar to running a loop: You apply the same function to each image and return the value back to the ImageCollection.

A six-line code uses the functions dot map, e e dot date dot from Y M D, dot select, dot rename, and dot set.

In addition to converting the units, the code renames the variable and sets properties such as ‘system:time_start’, which is necessary in Earth Engine to plot data and compare it with other image collections. Note that you might print out the variables sm_ic and sm_ic_ts to explore the differences between them. You should notice the new band name and properties (e.g., ‘system:time_start’).

Next, plot the data to evaluate soil moisture anomalies during the study period.

A code to make a plot of S M a for basin boundary uses the functions u i dot chart dot image dot series, e e dot reducer dot mean, dot set chart type, and dot set options.

You may notice that SMa is of a similar magnitude to TWSa but is slightly out of phase with TWSa.

2.3.2 Section 3.2: Load GLDAS Snow Water Equivalent Images from an Asset to an Image Collection

Use similar code to load the snow water equivalent data to Earth Engine.

A code uses the functions e e dot list and e e dot image collection dot from images.

Next, convert the snow values to equivalent water depth units of centimeters.

A five-line code uses the functions dot map, e e dot date dot from Y M D, dot select, dot multiply, and dot set.

Next, we will visualize the new ImageCollection. If you did not do the previous step, your code here will not run.

A code to make a plot of S W E a for basin boundary uses the functions u i dot chart dot image dot series, e e dot reducer dot mean, dot set chart type, dot set options, and print.

You successfully plotted soil moisture and snow water equivalent (Fig. 40.4). You may notice that SWEa is much smaller in magnitude than the other two variables.

Fig. 40.4
Two graphs titled soil moisture anomalies and snow water equivalent anomalies plot S M a versus years and S W E a versus years, respectively, and have fluctuating curves.

Time-series charts of SMa and SWEa in units of equivalent water height (centimeters)

Full size image

Code Checkpoint A21d. The book’s repository contains a script that shows what your code should look like at this point.

2.4 Section 4: Importing a Table of Surface Water Storage

Reservoir storage data from the California Data Exchange Center (CDEC) facilitated computing Surface Water storage anomalies (SWa) for the Sacramento-San Joaquin Basin. Surface water storage, unlike the other components of water storage, is not represented in land surface models. Instead, SWa is sourced from in situ observations. Here, the reservoir storage observations were summed for the Central Valley and then total converted to annual anomalies to directly compare with SWEa and SMa. Prior to reading the table of reservoir storage, we compute the area from the combined HUC8 basins.

Double slash extract geometry to convert time series of anomalies in k m 3 to c m. Var area underscore k m 2 equals basin dot geometry left parenthesis right parenthesis dot area left parenthesis right parenthesis dot divide left parenthesis 1000 asterisk right parenthesis semicolon. Var k m underscore 2 underscore c m equal 10000 semicolon.

Next, the imported table res_table is converted to an ImageCollection of constant values to facilitate combining the data with GRACE and GLDAS-resolved water storage anomalies.

A code to convert c s v to image collection uses the functions var, dot map, e e dot date dot from Y M D, e e dot image collection dot from images, e e dot image dot constant, dot divide, dot rename, and dot set.

Plot SWa in equivalent units of centimeters per year (Fig. 40.5).

Fig. 40.5
A graph of surface water anomalies plots S W a in centimeter versus years. Values are estimated. (01, 2003, 2), (01, 2008, negative 3), (0 1, 2011, 4), and (0 1, 2016, negative 1). It has a decreasing trendline.

Time-series chart of SWa in units of equivalent water height (centimeters)

Full size image
A code to create a time series of surface water anomalies uses the functions u i dot chart dot image dot series, e e dot reducer dot mean, dot set chart type, and dot set options.

The chart shows that surface water anomalies are of a similar magnitude to soil moisture anomalies. As expected, SWa decreases during each drought period in California (2006–2008 and 2012–2016). These reservoir storage declines show use is greater than inputs during each period.

Now, we will combine the previous datasets to resolve changes in groundwater during the period of record. Unfortunately, it’s still hard to quantify change without having all the variables on one plot. It might be best to compute the differences via Eq. 40.1 from the introductory paragraph at the top of the document.

Code Checkpoint A21e. The book’s repository contains a script that shows what your code should look like at this point.

2.5 Section 5: Combining Image Collections

Here, you will see how to combine multiple image collections and compute differences via an expression. We will start by joining the GLDAS image collections together. This is accomplished with the ee.Join.inner function.

A code to combine G L D A S and GRACE data to compute change in human-accessible water, create the join, and join G L D A S data uses the functions e e dot filter dot equals, e e dot join dot inner, e e dot image collection, and print.

Next, we join the reservoir data.

A code to repeat to append reservoir data now uses the functions e e dot image collection, dot map, e e dot image dot cat, and dot get.

Lastly, we need to repeat this step by joining GRACE to the output from the last join.

A code to repeat to append GRACE now, uses the functions e e dot image collection, dot map, e e dot image dot cat, and dot get.

Take a moment to print out the ImageCollection GRACE_res_GLDAS.

To resolve groundwater storage changes in the basin, one can rearrange Eq. 40.1 to solve for GWa. Here we assume canopy storage anomalies are very small relative to other storage components and ignore them in the equation below.

$$ {\text{GWa }} = {\text{ TWSa }} - {\text{ SWa }} - {\text{ SMa }} - {\text{ SWEa}} $$
(40.3)

To execute this step, we map an expression across an ImageCollection to produce a new variable named GWa.

A code to compute groundwater storage anomalies uses the functions e e dot image collection, e e dot date dot from Y M D, expressions, dot select, dot rename, dot copy properties, and print.

You can see how the variable img is used to extract bands from the combined ImageCollection and create a new one with just one band.

We’ll plot this to see how groundwater storage is changing (Fig. 40.6).

Fig. 40.6
A line graph of changes in groundwater storage plots G W a in centimeter versus years. Values are estimated. (01, 2003, negative 5), (01, 2008, negative 1), (0 1, 2012, negative 5), and (0 1, 2016, negative 17). It has a decreasing trendline.

Time-series chart of GWa in units of equivalent water height (centimeters)

Full size image
A code for the chart results uses the functions u i dot chart dot image dot series, dot filter, e e dot reducer dot mean, dot set chart type, dot set options, and print.

You can see how reliant California is on groundwater. The chart shows large declines during recent drought periods. Using the chart, you can estimate how much groundwater was used during the 2012–2016 drought period. In the Console, hover your mouse over the chart and jot down the value for GWa in 2012 and in 2016. You will use this information, in addition to the area and unit conversion, to estimate groundwater usage during this period in cubic kilometers.

A code to look at the values from the start of 2012 to the end of 2016 drought uses the functions e e dot number, dot subtract, dot multiply, and print.

Code Checkpoint A21f. The book’s repository contains a script that shows what your code should look like at this point.

3 Synthesis

Assignment 1. This chapter provides a roadmap to monitor changes in groundwater storage at a basin scale using observations of TWSa from the GRACE satellites and hydrologic data from GLDAS. Now you can apply these methods to another river basin anywhere in the world.

4 Conclusion

In this chapter, we reviewed how GRACE observations can be used to estimate changes in water storage for a region of interest like California’s Central Valley. Specifically, this chapter demonstrated how to combine equivalent water thickness observations from GRACE with model simulations of soil moisture, snow water equivalent, and in situ reservoir storage observations to quantify groundwater storage declines. Along the way, some advanced Earth Engine skills were explored, including creating an ImageCollection from a table and joining multiple image collections. Earth Engine users now have the skills and the knowledge of GRACE observations to apply this methodology to other regions around the world.