**4. Continental hydrology assessment by GRACE observations**

The GRACE mission has been observing mass changes in the Earth's body during 15 years, and since 2018 the new mission GRACE-FO continues this task. These satellite gravimetric missions have many applications as: to better understanding earthquake mechanism [57–60]; to quantify sea level rise [61, 62] and; to observe hydrological cycles [6, 63].

Analysis of the GRACE solutions consists of finding a set of time coefficients from SH or gridded solutions, so that the TWS anomalies for a given period can be decomposed into geographical coefficients:

$$\begin{array}{c} \Delta\sigma \Big(\dot{\lambda}, \theta, t\big) = A \big(\dot{\lambda}, \theta\big) + B \big(\dot{\lambda}, \theta\big)t + C\_1 \big(\dot{\lambda}, \theta\big)\sin\big(\alpha\mathfrak{t}\big) + C\_2 \big(\dot{\lambda}, \theta\big)\cos\big(\alpha\mathfrak{t}\big) \\ + D\_1 \big(\dot{\lambda}, \theta\big)\sin\big(\alpha\mathfrak{t}\big) + D\_2 \big(\dot{\lambda}, \theta\big)\cos\big(\alpha\mathfrak{t}\big) \end{array} \tag{3}$$

With *ω = 2π/T* and *ω' = 2π/T'*, considering *T = 1* year and *T' = 1/2* year, so that annual and semi-annual amplitudes *C* and *D* and phases *φ* and *φ'* are:

$$C = \sqrt{C\_1^2 + C\_2^2} \text{ and } D = \sqrt{D\_1^2 + D\_2^2} \tag{4}$$

**65**

**Figure 3.**

*Continental Water Storage Changes Sensed by GRACE Satellite Gravimetry*

ϕ

mass balance on the considered multi-year period.

regions like in the endoheric Okavango delta in Africa [63].

*Global map of the TWS trends and their climatic causes sorted by colors according to [64].*

rise of about 0.3 mm/y.

melting.

1 1 1 1 2 2

− − = ′ = (5)

tan and tan *C D C D*

In particular, the linear trend, or equivalently the *B(λ,θ)* term, that is expressed in mm of EWH per year, corresponds to the increase if positive (or decrease when negative) of the water mass storage, and it can be interpreted in terms of long-term

A relatively complete synthesis of works on the evolution of the water storage in several parts of the world for 2002–2017 have recently presented [64] (**Figure 3**). The most important losses of mass are located on the ice shelves of Greenland and Antarctica, where ice storage is drastically melting at the highest rates (more than 200 Gt/y) due to the global warming and this can contribute to half of the sea level

In earlier studies based on SH and recently mascons solutions [47], analyzing these GRACE data has shown a continuous acceleration of the Greenland ice shelf

Regions of important loss of water are revealed by GRACE such as the drought lasting up to 2007 in the southeast of Australia [48], in the North of India [62] as well as California [65]. Besides, continental waters are accumulating in other

These model coefficients A, B, C1, C2, D1 and D2 for GRACE variations are usually adjusted following the least square minimum criteria and then represented regionally or globally. The residuals from this relatively simple Eq. 3 of water mass variations represent intermediate wavelengths, short-term variations of unmodeled phenomena and possibly errors of the a priori correcting models (see Section 3.1).

**4.1 Long term water mass variations, climate changes and irrigation**

 ϕ

*DOI: http://dx.doi.org/10.5772/intechopen.96109*

*Continental Water Storage Changes Sensed by GRACE Satellite Gravimetry DOI: http://dx.doi.org/10.5772/intechopen.96109*

*Geodetic Sciences - Theory, Applications and Recent Developments*

the SH or mascons representation [51–53].

grids of mascons solutions can be easily downloaded from [48, 49] for CSR and JPL Releases 06, respectively. Note that these latter solutions need to be scaled by a gain factor that varies geographically. A sequential Kalman Filtering (KF) approach for estimating regional maps of water mass changes by progressive integration of daily along-track GRACE geopotential anomalies has been recently proposed by [1, 50]. This iterative Kalman filter procedure has been successfully applied to determine 2° x 2° surface water mass density solutions over continental regions instead of using

The GRACE products contribute in continental hydrology research witn a novel information: the terrestrial water storage or integrated water content, i.e. the sum of the water contained in the column from the different hydrological reservoirs: surface water, soil water, groundwater and snow cover. An early study showed an expected measurement accuracy of a few millimeters of EWH in terms of

by 400 km, this work was based on Land Surface Models (LSM) outputs as soil moisture, evapotranspiration and run-off. It is expected that the presence of noise in the shorter wavelengths affects the TWS retrieval [34]. In addition, errors due to the spectra truncation increase as the area of the studied basin decrease. Based on LSM outputs and the expected accuracy of the GRACE land water solutions, it was proved that the changes in TWS could be detected by the GRACE system if

GRACE land water solutions was expected to be about 0.7 cm of EWH for a drain-

**4. Continental hydrology assessment by GRACE observations**

1 2

∆ =+ + +

 λθ

> ω

annual and semi-annual amplitudes *C* and *D* and phases *φ* and *φ'* are:

Current GRACE Products have a spatial resolution of a few hundred kilometers (around 200 km for the mascons and for the regional solutions, and 330 km for the releases 03 and 05 for a typical degree of truncation of n = 60–90). Errors were estimated to be around 4 cm at the Equator, and decreasing to 1.5 cm in Polar regions

The GRACE mission has been observing mass changes in the Earth's body during

15 years, and since 2018 the new mission GRACE-FO continues this task. These satellite gravimetric missions have many applications as: to better understanding earthquake mechanism [57–60]; to quantify sea level rise [61, 62] and; to observe

Analysis of the GRACE solutions consists of finding a set of time coefficients from SH or gridded solutions, so that the TWS anomalies for a given period can be

> ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 2

*t A B tC t C t*

 ω

 ω

1 2 1 2 *C CC D DD* =+ =+ and (4)

 λθ

(3)

 ω

 λθ

2 2 2 2

 λθ

, , , , , sin , cos , sin , cos

With *ω = 2π/T* and *ω' = 2π/T'*, considering *T = 1* year and *T' = 1/2* year, so that

*D tD t*

+ ′ ′ +

and 0.3 cm for a drainage basin of 4 million of km2

, over areas of 400 km

[54]. The accuracy of the

[55].

**3.3 Spatial resolution and accuracy of the GRACE products on lands**

surface density for a reference water density of 1000 kg/m3

they exceed 1.5 cm of EWH over an area of 200 000 km2

due to denser GRACE satellite tracks coverage [56].

age area of 400 000 km2

hydrological cycles [6, 63].

σ λ θ

decomposed into geographical coefficients:

 λθ

λθ

**64**

$$\varphi = \tan^{-1} \frac{C\_1}{C\_2} \text{ and } \varphi' = \tan^{-1} \frac{D\_1}{D\_2} \tag{5}$$

These model coefficients A, B, C1, C2, D1 and D2 for GRACE variations are usually adjusted following the least square minimum criteria and then represented regionally or globally. The residuals from this relatively simple Eq. 3 of water mass variations represent intermediate wavelengths, short-term variations of unmodeled phenomena and possibly errors of the a priori correcting models (see Section 3.1).

### **4.1 Long term water mass variations, climate changes and irrigation**

In particular, the linear trend, or equivalently the *B(λ,θ)* term, that is expressed in mm of EWH per year, corresponds to the increase if positive (or decrease when negative) of the water mass storage, and it can be interpreted in terms of long-term mass balance on the considered multi-year period.

A relatively complete synthesis of works on the evolution of the water storage in several parts of the world for 2002–2017 have recently presented [64] (**Figure 3**). The most important losses of mass are located on the ice shelves of Greenland and Antarctica, where ice storage is drastically melting at the highest rates (more than 200 Gt/y) due to the global warming and this can contribute to half of the sea level rise of about 0.3 mm/y.

In earlier studies based on SH and recently mascons solutions [47], analyzing these GRACE data has shown a continuous acceleration of the Greenland ice shelf melting.

Regions of important loss of water are revealed by GRACE such as the drought lasting up to 2007 in the southeast of Australia [48], in the North of India [62] as well as California [65]. Besides, continental waters are accumulating in other regions like in the endoheric Okavango delta in Africa [63].

#### *Geodetic Sciences - Theory, Applications and Recent Developments*

The same authors have validated the constant decrease of deep water of the North Sahara aquifer sensed by GRACE with in situ water table records from wells. The Level-2 solutions need to be combined with radar altimetry data and/or model outputs in lower thus wetter latitudes, so that GRACE solutions have been used to isolate the long-term evolution of groundwater over the entire Amazon basin [66].

### **4.2 Seasonal cycles in major drainage river basins**

The fluctuations of TWS at annual and semi-annual scales reflect the effects of climatic phenomena varying seasonally as: rainfalls, snow, temperature, evapotranspiration, river runoff, soil moisture, river discharge, groundwater and human activities. The knowledge of these periodical variations that are dominant in the large tropical basins is important to evaluate water resources. The seasonal signals estimated by GRACE are generally adjusted as described by C1, C2, D1 and D2 in Eq.

#### **Figure 4.**

*Times series of in-situ observations of Agência national del Agua (red) and GRACE observations (blue) at the stations of Porto Velho and Santarem in the Amazon basin [28]. We can notice the high correlation of these dominant annual amplitudes.*

**67**

**Figure 5.**

*2003–2012 [70].*

*annual sinusoids at grid cells [ C sin t* (

*Continental Water Storage Changes Sensed by GRACE Satellite Gravimetry*

role in the modeling of soil moisture in the Sahel region [66].

3. These amplitudes and phases determined from GRACE solutions (Eqs. 4 and 5)

In the African continent, GRACE solutions show that the stronger seasonal amplitudes are located in the Sahel latitudinal band and in the tropical Congo basin (**Figure 5**). An extended study based on Principal Analysis Components reveals a biannual or quadrennial water mass variations related to the West African monsoon [63]. The use of GRACE products also helps to conclude that dry season processes, in particular, evapotranspiration and the presence of vegetation, have an important

GRACE solutions have also been useful to observe snow cover variations in high latitude regions [68]. For Antarctica, seasonal analysis shows very variable TWS amplitudes in coastal areas with important snow accumulation rates because of

In the tropical and equatorial regions, GRACE products reveal that seasonal precipitations precede land water storage with a temporal lag of 2 months, however, seasonal cycle of surface temperature is out of phase with respect to TWS, whereas in cold and temperate regions seasonal phenomena are due to more complex

*Map of the seasonal amplitudes of the water mass changes adjusted by least squares adjustment of pure* 

+ ) *] using the 10-day regional solutions over Africa for the period* 

ω ϕ

For example, GRACE-based annual signals over the Amazon basin show a predominant annual amplitude in fall and in spring of hundreds of EWH at the basin scale [3] driven essentially by the rainfall seasonality [67]. A comparison of GRACE observed signals and in-situ measured are shown in **Figure 4**. A detailed study of the major tributaries in the Amazon river basin demonstrates that the rainfall variations generated surface water fluxes delayed by two months due to transfer

*DOI: http://dx.doi.org/10.5772/intechopen.96109*

processes [53].

oceanic humidity [69].

allow to improve the understanding of water cycle.

## *Continental Water Storage Changes Sensed by GRACE Satellite Gravimetry DOI: http://dx.doi.org/10.5772/intechopen.96109*

*Geodetic Sciences - Theory, Applications and Recent Developments*

**4.2 Seasonal cycles in major drainage river basins**

basin [66].

The same authors have validated the constant decrease of deep water of the North Sahara aquifer sensed by GRACE with in situ water table records from wells. The Level-2 solutions need to be combined with radar altimetry data and/or model outputs in lower thus wetter latitudes, so that GRACE solutions have been used to isolate the long-term evolution of groundwater over the entire Amazon

The fluctuations of TWS at annual and semi-annual scales reflect the effects of climatic phenomena varying seasonally as: rainfalls, snow, temperature, evapotranspiration, river runoff, soil moisture, river discharge, groundwater and human activities. The knowledge of these periodical variations that are dominant in the large tropical basins is important to evaluate water resources. The seasonal signals estimated by GRACE are generally adjusted as described by C1, C2, D1 and D2 in Eq.

*Times series of in-situ observations of Agência national del Agua (red) and GRACE observations (blue) at the stations of Porto Velho and Santarem in the Amazon basin [28]. We can notice the high correlation of these* 

**66**

**Figure 4.**

*dominant annual amplitudes.*

3. These amplitudes and phases determined from GRACE solutions (Eqs. 4 and 5) allow to improve the understanding of water cycle.

For example, GRACE-based annual signals over the Amazon basin show a predominant annual amplitude in fall and in spring of hundreds of EWH at the basin scale [3] driven essentially by the rainfall seasonality [67]. A comparison of GRACE observed signals and in-situ measured are shown in **Figure 4**. A detailed study of the major tributaries in the Amazon river basin demonstrates that the rainfall variations generated surface water fluxes delayed by two months due to transfer processes [53].

In the African continent, GRACE solutions show that the stronger seasonal amplitudes are located in the Sahel latitudinal band and in the tropical Congo basin (**Figure 5**). An extended study based on Principal Analysis Components reveals a biannual or quadrennial water mass variations related to the West African monsoon [63]. The use of GRACE products also helps to conclude that dry season processes, in particular, evapotranspiration and the presence of vegetation, have an important role in the modeling of soil moisture in the Sahel region [66].

GRACE solutions have also been useful to observe snow cover variations in high latitude regions [68]. For Antarctica, seasonal analysis shows very variable TWS amplitudes in coastal areas with important snow accumulation rates because of oceanic humidity [69].

In the tropical and equatorial regions, GRACE products reveal that seasonal precipitations precede land water storage with a temporal lag of 2 months, however, seasonal cycle of surface temperature is out of phase with respect to TWS, whereas in cold and temperate regions seasonal phenomena are due to more complex

#### **Figure 5.**

*Map of the seasonal amplitudes of the water mass changes adjusted by least squares adjustment of pure annual sinusoids at grid cells [ C sin t* (ω ϕ+ ) *] using the 10-day regional solutions over Africa for the period 2003–2012 [70].*

interactions [69]. There is also a significant contribution of river discharge in the spatial distribution of seasonal water storage with a dependency of climate [70].

Regional time variations of evapotranspiration rate - expressed in mm/yr. - can be also derived by integrating and solving the water mass balance equation, which relates TWS on land provided by GRACE, precipitation data from the Global Precipitation Climatology Centre, runoff given by a global land surface model and the unknown evapotranspiration to be determined [71].

### **4.3 Detection of extremes events**

Gravimetric satellites missions also image the extreme climate events in the whole Earth system. Floods and droughts have been largely studied in different continents using the GRACE Level-2 products.

In the case of the Amazon basin, GRACE has revealed periods of extreme droughts and floods. During the 2005 drought, the TWS in the river and floodplains of the Amazon basin was 70% below its average for the 2003–2007 period [71]. However, in 2009 gravity measurements display an exceptional flood associated to La Niña event [26]. The maximum value of TWS in the entire Amazon basin was estimated at ∼624 ± 32 Gt with respect to the mean value.

New detection approaches based on GRACE data are developed to identify drought episodes and their severity [72]. Advances in GRACE data treatment

#### **Figure 6.**

*Differences of weekly-averaged of GRACE solutions derived by the Kalman filter approach as proposed by [73], before and during the Katrina and Rita episodes (top); and comparison with the anomalies of TRMM precipitation for the same periods (bottom).*

**69**

**Acknowledgements**

improving the quality of this chapter.

*Continental Water Storage Changes Sensed by GRACE Satellite Gravimetry*

have allowed to improve spatial and temporal resolution, then rapid extremes events of several days has been observed [73]. One example is the most powerful depressions in late summer 2005 during the cyclonic season in the Gulf of Mexico and Louisiana, better known under the name of "Katrina" (23–31/08/2005), and followed by "Rita" (17–26/09/2005). The direct consequences of the passage of these hurricanes caused important rainfalls along their tracks, thus the significant storage and accumulation of water falling on land could be observed as water mass variations in the range of a few days. As shown in **Figure 6** the important rainfalls of Katrina located in the south of the Great Plains have produced river floods, and thus an important water accumulation is revealed by GRACE in the coastal region

During its sixteen years of operation, the GRACE mission provided a novel source of information on variations of water mass on lands at unprecedented spatial and temporal resolutions. This mission offered an exceptional dataset for studying large-scale water mass redistributions, and for the very first time, the opportunity to monitor water changes in all the hydrological compartments and from regional to global scales. While spherical harmonics solutions were firstly used, regional and local approaches have already demonstrated the possible access to spatial (better localization of structures by construction) and temporal (through daily updates using Kalman filter strategies, e.g. see [73]) scales that were higher than those that were offered by global SH solutions. Additional bibliographic resources and useful information about GRACE can be found on the GRACE Tellus web site [74]. The GRACE mission ended in 2017, and later on a partnership between NASA and the German Research Centre for Geosciences (GFZ) decided to schedule GRACE Follow-On (GRACE-FO) mission to launch in 2018 in order to ensure the continuity of GRACE-type space gravimetry. By using a similar twin satellite configuration of the low-Earth and nearly polar orbit at 300–500 km altitude, the GRACE-FO mission is following its successful predecessor [75]. Additionally, it carries a demonstrator of laser system to measure the inter-satellite distance and velocity, and hence for an improved precision. It is promising for providing new perspectives in hydrology studies, such as refined long-term mass balance estimates of surface water storage and ice sheets. These new data that offer continuity with the previous GRACE observations will be of first interest for hydrology of global hydrological model calibration to constrain their operations through assimilation techniques.

We would like to thank the anonymous reviewer for his helpful contribution for

*DOI: http://dx.doi.org/10.5772/intechopen.96109*

of New Orleans (up to 300 mm of EWH).

**5. Conclusion**

## *Continental Water Storage Changes Sensed by GRACE Satellite Gravimetry DOI: http://dx.doi.org/10.5772/intechopen.96109*

have allowed to improve spatial and temporal resolution, then rapid extremes events of several days has been observed [73]. One example is the most powerful depressions in late summer 2005 during the cyclonic season in the Gulf of Mexico and Louisiana, better known under the name of "Katrina" (23–31/08/2005), and followed by "Rita" (17–26/09/2005). The direct consequences of the passage of these hurricanes caused important rainfalls along their tracks, thus the significant storage and accumulation of water falling on land could be observed as water mass variations in the range of a few days. As shown in **Figure 6** the important rainfalls of Katrina located in the south of the Great Plains have produced river floods, and thus an important water accumulation is revealed by GRACE in the coastal region of New Orleans (up to 300 mm of EWH).
