Impact of meteorological conditions on water resources in the Upper East Region of Ghana using remotely-sensed and modelled hydrological data

Abstract

Study region
The Upper East Region, Ghana, West Africa, lies within the Volta Basin, floods annually, and contributes substantially to Ghana’s food production.

Study focus
We assessed precipitation (P), evapotranspiration (ET), and total water storage anomalies from GRACE (TWSA) and GLDAS-Noah (TWCA) to study the influence of the UER’s climate on water availability between 2002 and 2017. We analysed (1) the relative uncertainties of the data sets using the triple-cornered hat method, (2) the terrestrial water budget to validate TWSA/TWCA and (3) cross- and multi-correlation analyses to study the relationship between water storage (or availability) and meteorological variables.

New hydrological insights
We found strong correlations between the different P products (r > 0.96), between the different GRACE products (r > 0.95), but not between the different ET products. The hybrid P, TWSA from the Jet Propulsion Laboratory, and ET from ERA-5 had the smallest relative uncertainties. TWSA increased by 9.8 ± 0.8 mm yr⁻¹ while TWCA decreased. P and ET showed no evidence of a trend and were similarly influenced by the other meteorological variables. However, 93 of 183 months had water surplus and mean net P was positive – indicating the UER received more water than it lost. These agree with the increasing TWSA trend. The water budget validation also confirmed that GRACE can be used for water management; GLDAS-Noah underestimates storage in the UER.

Full text

Journal of Hydrology: Regional Studies 42 (2022) 101124
2214-5818/© 2022 Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/).
Impact of meteorological conditions on water resources in the
Upper East Region of Ghana using remotely-sensed and modelled
hydrological data
C.I. Kelly
a
,
1
, C.M. Hancock
b
,
2
, S. Grebby
c
,
3
, S. Marsh
c
,
4
, V.G. Ferreira
d
,
5
,
N.A.S. Hamm
a
,
*
,
6
a
Geospatial and Geohazards Research Group, Faculty of Science and Engineering, University of Nottingham Ningbo China, Ningbo, China
b
School of Architecture, Building and Civil Engineering, Loughborough University, Loughborough, UK
c
Nottingham Geospatial Institute, Faculty of Engineering, University of Nottingham, Nottingham, UK
d
School of Earth Sciences and Engineering, Hohai University, Nanjing, China
ARTICLE INFO
Keywords:
GRACE
Evapotranspiration
Water storage
Precipitation
Ghana’s Upper East Region
Water budget
ABSTRACT
Study region: The Upper East Region, Ghana, West Africa, lies within the Volta Basin, oods
annually, and contributes substantially to Ghana’s food production.
Study focus: We assessed precipitation (P), evapotranspiration (ET), and total water storage
anomalies from GRACE (TWSA) and GLDAS-Noah (TWCA) to study the inuence of the UER’s
climate on water availability between 2002 and 2017. We analysed (1) the relative uncertainties
of the data sets using the triple-cornered hat method, (2) the terrestrial water budget to validate
TWSA/TWCA and (3) cross- and multi-correlation analyses to study the relationship between
water storage (or availability) and meteorological variables.
New hydrological insights: We found strong correlations between the different P products (r >
0.96), between the different GRACE products (r >0.95), but not between the different ET
products. The hybrid P, TWSA from the Jet Propulsion Laboratory, and ET from ERA-5 had the
smallest relative uncertainties. TWSA increased by 9.8 ±0.8 mm yr
−1
while TWCA decreased. P
and ET showed no evidence of a trend and were similarly inuenced by the other meteorological
variables. However, 93 of 183 months had water surplus and mean net P was positive – indicating
the UER received more water than it lost. These agree with the increasing TWSA trend. The water
budget validation also conrmed that GRACE can be used for water management; GLDAS-Noah
underestimates storage in the UER.
* Corresponding author.
E-mail addresses: calebaid2000@gmail.com (C.I. Kelly), nicholas.hamm@nottingham.edu.cn (N.A.S. Hamm).
1
https://orcid.org/0000-0002-3292-8271.
2
https://orcid.org/0000-0002-9692-0439.
3
https://orcid.org/0000-0001-9768-2682.
4
https://orcid.org/0000-0002-1168-6760.
5
https://orcid.org/0000-0003-2209-9921.
6
https://orcid.org/0000-0002-5105-7846.
Contents lists available at ScienceDirect
Journal of Hydrology: Regional Studies
journal homepage: www.elsevier.com/locate/ejrh
https://doi.org/10.1016/j.ejrh.2022.101124
Received 28 January 2022; Received in revised form 26 May 2022; Accepted 27 May 2022

Journal of Hydrology: Regional Studies 42 (2022) 101124
2
1. Introduction
The 2020 World Meteorological Organization’s report on the state of the global climate showed that temporal variations in climate
indicators and extreme weather events, e.g., droughts and oods, increased in 2020 in comparison to previous years (World Meteo-
rological Organization, 2020). A consequence is the continual rise in temperatures, the effect of which is pronounced over vulnerable
regions such as West Africa, where increasing temperatures are linked to the large climatic variability, particularly in terms of rainfall
(Christensen et al., 2013). Since the region depends heavily on agriculture, it is critical to understand the impact of climate variability
on water resources.
In situ data for water resources monitoring are typically unavailable or scanty over areas such as Ghana’s Upper East Region (UER).
The UER (1) contributes substantially to Ghana’s food production (Owusu et al., 2013), (2) has a long dry season and (3) gets ooded
annually – a result of rainfall and the opening of the Bagre dam in Burkina Faso (e.g., Bempah and Oyhus, 2017). The region’s strategic
location explains the decision of the Government of Ghana to construct a multi-purpose dam to (1) mitigate the effects of ooding, (2)
aid irrigation and, (3) provide electricity (Ghana Web, 2021). These necessitate the study of water resources in the region for sus-
tainable crop production. Yet, according to the Ghana Meteorological Agency, there are only six weather stations distributed across the
UER. Hydrological data are either unavailable or not easily accessible. Although the UER falls entirely within the Volta Basin, which
has been the subject of some hydrological studies (Andam-Akorful et al., 2015; Ni et al., 2017), the basin spans several jurisdictions
with varying climates. Consequently, basin-wide analysis of hydro-meteorological data may not represent processes in the UER.
However, the sparseness or unavailability of in situ components of total water storage (TWS) presents a huge limitation to water
resources analysis in the UER.
Satellite and global hydro-meteorological data provide an alternative to monitor water resources. Examples include satellite-only,
gauge-only and hybrid precipitation (P) products and evapotranspiration (ET) products. For hydrological studies, modelled data such
as those from the Global Land Data Assimilation System (GLDAS) (Rodell et al., 2004b) may provide adequate hydrological infor-
mation over an area (Syed et al., 2008). Also, the advent of the Gravity Recovery and Climate Experiment (GRACE) mission has
enabled the measurement of TWS anomalies (TWSA) by recovering temporal variations in the Earth’s gravity eld at monthly scales
(Wahr et al., 1998, 2004). Thus, GRACE data are applicable to studying the temporal evolution of the different drivers of the water
cycle – P, ET, etc. (Chen et al., 2010; Landerer et al., 2020; Ramillien et al., 2006). In this study, we assessed various freely available
hydro-meteorological and GRACE products to study water resources in the data-poor UER. We used methods including the
three-cornered hat (TCH) for a relative uncertainty estimation of the respective data sets to enable the selection of the most appropriate
of the analysed data. While such methods yield relative rather than absolute uncertainties, they are widely used as proxies to absolute
error analysis and provide sufcient information to support data selection in data-poor regions/situations (Ferreira et al., 2016;
Galindo and Palacio, 2003; Gray and Allan, 1974; McColl et al., 2014; Yakubu et al., 2019).
A potential limitation to our study is the resolution of GRACE. The robustness of GRACE measurements cannot be assured because
the area of the UER (~ 8600 km
2
) is substantially smaller than 150,000 km
2
(Longuevergne et al., 2013; Rowlands et al., 2005). This
leads to the mixing of GRACE signals in the UER with the surrounding signals, which can cause biases if the surrounding signals have
different signs (e.g., Vishwakarma et al., 2018). However, if storage variations in the UER are >8 km
3
, this will improve the
signal-to-noise ratio (SNR) of the recovered signals (Tourian et al., 2015). Thus, GRACE may provide accurate TWSA in the UER.
GRACE studies have been conducted over similarly smaller regions (Biancamaria et al., 2019; Guo et al., 2016; Ni et al., 2017; Tourian
et al., 2015) including one as small as 38 km
2
(Zheng et al., 2018). Even so, validating GRACE over a small region, especially one with
no prior GRACE studies, is necessary to inspire condence in the results. Where available and sufcient, in situ data may be used to
validate GRACE. Here, we used the water budget equation to evaluate whether GRACE is suitable for the UER. GRACE can provide
TWS change (TWSC). Hence, we expect that the difference of net precipitation and GRACE TWSC will provide insight into the validity
of GRACE results over the UER. This assertion is supported, for instance, by Riegger et al. (2012) who mentioned that the water budget
equation can be used to estimate errors in GRACE. Furthermore, the combination of GRACE and uxes in the water budget equation is
well-established in the literature (Abolaa-Rosenzweig et al., 2021; Andam-Akorful et al., 2015; Rodell et al., 2004a).
Previous studies over the UER focused on the spatial-temporal variations of only a single aspect of the region’s climate such as
rainfall or temperature. For instance, rainfall reportedly decreased between 1954 and 2014, while temperatures increased (Issahaku
et al., 2016). Quaye-Ballard et al. (2020a) also showed that more than 50 % of the UER was characterised by a decrease in rainfall
between 1981 and 2016. Owusu et al. (2013) reported severe desertication, a drought indicator, in the UER. Yet, how these and other
hydro-meteorological conditions impact water availability in the UER has yet to be studied. Given the agroecological importance of the
UER to Ghana (Owusu et al., 2013), understanding the relationship between hydro-meteorological processes and water availability is
necessary to implement policies for water resources management. Hence, our study extended the scope of previous studies by ana-
lysing multiple hydro-meteorological variables in relation to water resources. Our objectives were: (1) to assess freely available space
geodetic, hydro-meteorological, and modelled hydrological data in the UER, (2) to assess the use of GRACE over the UER and (3)
extend the scope of previous UER studies to characterise the impact of multiple hydrological and meteorological variables on water
resources. Our study is important because it provides pertinent information that can be used by stakeholders such as the Hydrological
Services Department, the Ghana Water Company Limited, and the Ghanaian Ministry of Food and Agriculture. The ndings of this
study will also provide important information to the authorities of the yet-to-be-constructed Pwalugu Dam on its operations (e.g., on
irrigation).
C.I. Kelly et al.

Journal of Hydrology: Regional Studies 42 (2022) 101124
3
2. Regional setting
2.1. Geography
The UER shares boundaries with two of Ghana’s neighbouring countries: Togo to the east and Burkina Faso to the north. It is located
at 10.2–11.2
∘
N, 1.6
∘
W to 0.03
∘
E in the northeast of Ghana (Fig. 1). The area is approximately 8600 km
2
, making up about 4 % of
Ghana and 2 % of the Volta Basin. It is characterised by a fairly undulating topography with moderate variations (Kelly et al., 2021).
Slopes range between 1 % and 5 %, but with a few outcrops and highlands (Ghana Statistical Service, 2014). The maximum elevation is
455 m and the minimum is 119 m, with the majority lying around 200 m. The major occupation of the region is agriculture (Ministry of
Food and Agriculture, 2019) and farmers typically rely on ponds and dugouts for irrigated farming during the dry season (Quaye--
Ballard et al., 2020b). The region is drained by the Sisili River and the Red and White Volta Rivers. Furthermore, the region’s valleys
are characterised by heavy textured soils, making them suitable for rice farming. However, some of the soils are composed of coarse
material, e.g., gravel, stones, and concretion, thus reducing their water retention capabilities (Ministry of Food and Agriculture, 2019).
The vegetation of the UER is Savannah, mainly Guinea-Savannah, but also Sudan-Savannah (Ministry of Food and Agriculture, 2019).
2.2. Climatology
The UER is characterised by two meteorological regimes: the rainy (April to October) and the dry (November to March) seasons.
The dry season lasts relatively longer than the rainy season (6–7 months vs 5–6 months) and is characterised by low humidity and dry
winds (harmattan). Dry season average temperatures range between 15 ◦C (December–February) and 45 ◦C (March–April), with
relatively lower nighttime temperatures. The mean annual rainfall in the region is 921 mm, but exceeded 1200 mm in 2002 and 2007
(Ministry of Food and Agriculture, 2019). Although rainfall in the region is decreasing (Quaye-Ballard et al., 2020a; Yiran and Stringer,
2016), the region is inundated annually. These oods occur in response to contributions from the Bagre Dam in Burkina Faso, rainfall,
and the Volta river.
Fig. 1. Topography of the UER. The area is about 8600 km
2
, making up approximately 4 % of the total area of Ghana and 2 % of the Volta Basin.
The inset map shows the location of UER (red) in Ghana and the locations of Ghana (yellow) and the Volta Basin (purple) in West Africa.
C.I. Kelly et al.

Journal of Hydrology: Regional Studies 42 (2022) 101124
4
3. Material and methods
Fig. 2 summarises the main data and processing workow adopted in our study. We used water storage, rainfall (P), evapo-
transpiration (ET), and meteorological data. Methods include (1) areal averaging for time series extraction, (2) multi-linear regression
for time series decomposition and, (3) cross-correlation and, (4) multiple correlation analyses, both, to examine the relationship
between different variables.
3.1. Data sets
The data sets are summarised in Table 1 and are described in detail as follows.
3.1.1. GRACE TWSA products
We used the mass concentration (mascon) solutions release 6 version 2 from the Jet Propulsion Laboratory (JPL) and the Center for
Space Research (CSR) at the University of Texas (Save et al., 2016; Save, 2020; Wiese et al., 2019). For comparison with the mascon
grids, we also used GRACE TELLUS land mass grids that were calculated from CSR RL05 (CSR-T) spherical harmonic coefcients
(SHCs) (Landerer, 2020). We applied the gain factors that were provided with the JPL mascon (JPL-M) and CSR-T solutions to restore
the attenuated signals and reduce leakage effect. GRACE signal attenuation and leakage occur during JPL mascon processing and
post-processing of SHCs (CSR-T). Restoring signals and reducing the leakage effect improves the signal-to-noise ratio (SNR) of
GRACE-derived TWSA (Landerer and Swenson, 2012; Wiese et al., 2016). CSR-M is distributed on a 0.25◦grid, JPL-M on a 0.5◦grid,
and CSR-T is distributed on a 1◦grid. TWSA represents total water storage as anomalies from the 2004 to 2009 mean. The long-term
mean is subtracted to account for the static gravity eld.
The study period was limited to April 2002–June 2017 mainly because of the almost 1-year gap between the two GRACE missions.
There is also the possibility of a bias between the two missions, which requires further investigation (not addressed here). Apart from
Section 4.4, we used cubic spline interpolation to ll in missing GRACE months (cf. Andam-Akorful et al., 2015; Ramillien et al., 2006).
This was necessary for the implementation of Eq. (3), which describes storage change from month to month (Ramillien et al., 2006).
3.1.2. The Global Land Data Assimilation System (GLDAS)
GLDAS uses satellite and terrestrial data as constraints to land surface states to provide an array of (near) global, high-resolution,
and accurate land surface models (Rodell et al., 2004b). We calculated total water content (TWC) from GLDAS-Noah (Rui et al., 2018)
as the sum of canopy water storage (CWS) and soil moisture storage (SMS). Then we converted TWC into anomalies (TWCA) by
estimating and subtracting the mean for the period 2004–2009, consistent with the GRACE solutions. We chose GLDAS-Noah to
evaluate the inuence of unmodelled storage compartments in GLDAS for storage analysis in the UER.
Fig. 2. Flow chart summarising the main methods in this study. TCH is the three-cornered hat (TCH) method. “Met" is used to describe meteo-
rological data sets described in Section 3.1.6. “Data" represents the three solutions of water storage, ET, and P. s(t) is the area-weighted average of
the data sets (Eq. (4)).
C.I. Kelly et al.

Journal of Hydrology: Regional Studies 42 (2022) 101124
5
3.1.3. Precipitation
We did not have access to ground-based precipitation data. Thus, we compared three freely available precipitation (P) products: the
Global Precipitation Measurement (GPM), the Climate Prediction Centre (CPC), and the Climate Hazards group Infra-red Precipitation
with Stations (CHIRPS). These products represent satellite-only, gauge-only, and hybrid (satellite and gauge) solutions and are
described as follows.
The GPM mission is a collaboration between NASA and the Japan Aerospace Exploration Agency and comprises a constellation of
satellites providing continuity to global precipitation measurement from the Tropical Rainfall Measurement Mission (TRMM) (Hou
et al., 2014). We used the satellite-only IMERG Final Precipitation L3 version 6 product, which has spatial and temporal resolutions of
0.1◦and 1 month.
The CPC solution is a purely gauge-based global rainfall solution using data from more than 30,000 stations 0.125◦grid (Xie et al.,
2007, 2010). It is managed by the Physical Sciences Laboratory of the US’s National Oceanic and Atmospheric Administration
distributed at spatial and temporal resolutions of 0.5◦and 1 day.
The CHIRPS product is managed by the Climate Hazards Centre of the University of California and is based on a combination of rain
gauge and satellite data. We used the monthly CHIRPS version 2 (v2.0) product distributed on 0.05◦grid (Funk et al., 2015).
3.1.4. Evapotranspiration
Evapotranspiration (ET) uxes were extracted from three hydrological models: GLDAS-Noah, the Moderate Resolution Imaging
Spectroradiometer (MODIS), and the fth generation reanalysis for the global climate and weather (ERA-5) from the European Center
for Medium-Range Weather Forecasts.
The MODIS ET algorithm (MOD16) combines a surface energy partitioning process and environmental factors that impact ET to
calculate a global 8-day ET product using data from MODIS, onboard the Aqua and Terra satellite, and station-based meteorological
observations (Mu et al., 2007, 2011). We downloaded the 500-m, 8-day resolution MOD16A2 product and aggregated to monthly ET.
The data is provided in the Sinusoidal map projection. Hence, we dumped the latitude and longitude using the eosdump software
(http://hdfeos.org/software/eosdump.php; last accessed: January 20, 2021).
ERA-5 is the replacement of the third generation ERA-Interim reanalysis and leverages developments in the Integrated Forecasting
System Cycle version 41r2 (Hersbach et al., 2018). We downloaded the ERA5-Land monthly averaged reanalysis data and calculated
ET as the sum of evaporation and vegetation transpiration. The data is provided on a 0.1◦grid. Quantities in ERA-5 are provided
relative to the rst day of the month. Thus, we calculated monthly estimates by multiplying these quantities by the number of days in
each month.
3.1.5. Aridity
Aridity describes the unavailability of water within a region. This dryness is described by the aridity index (AI) given by Cherlet
Table 1
Summary of data sets used in this study.
Data Quantity Resolution Website
Last
accessed
CSR Mascon
RL06v02 TWSA Monthly 0.25◦http://www2.csr.utexas.edu/grace 2021-08-06
CSR TELLUS land
grid TWSA Monthly 1◦https://podaac.jpl.nasa.gov/GRACE 2021-08-06
JPL Mascon
RL06v02 TWSA Monthly 1◦https://podaac.jpl.nasa.gov/GRACE 2021-08-06
GLDAS-Noah v2.1
TWCA, temperature, humidity, wind speed,
pressure, SWR, ET Monthly 0.25◦https://disc.gsfc.nasa.gov/ 2021-01-01
CRU TS v4.04 PET Monthly 0.5◦https://crudata.uea.ac.uk/cru/data/hrg/ 2021-04-16
ERA-5 ET Monthly 0.1◦
https://cds.climate.copernicus.eu/cdsapp#!/dataset/reanalysis-
era5-land-monthly-means?tab=form 2021-01-29
MODIS
(MOD16A2) ET 8 days 500 m https://modis.gsfc.nasa.gov/data/dataprod/mod16.php 2021-01-18
CHIRPS P Monthly 0.05◦https://data.chc.ucsb.edu 2020-12-10
GPM P Monthly 0.1◦https://disc.gsfc.nasa.gov 2021-01-01
CPC P Daily 0.125◦https://psl.noaa.gov 2020-07-06
Table 2
Aridity index and classication (Cherlet et al., 2018).
Classication AI
Hyperarid AI <0.05
Arid 0.05 <AI <0.20
Semi-arid 0.20 <AI <0.50
Dry sub-humid 0.50 <AI <0.65
Humid AI ≥0.65
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Journal of Hydrology: Regional Studies 42 (2022) 101124
6
et al. (2018):
AI =P
PET,(1)
where P is the annual average of precipitation and PET is the annual average of potential evapotranspiration. AI classications are
summarised in Table 2 (Cherlet et al., 2018).
To avoid the possible biasing of AI analysis because of the incomplete years in our study (start and end years respectively April 2002
and June 2017), we recalculated AI from 2003 to 2016. For PET, we used monthly CRU Time Series version 4.04 (CRU TS v4.04)
(Harris et al., 2020). CRU TS v4.04 is managed by the Climate Research Unit (CRU) of the University of East Anglia.
3.1.6. Other meteorological data
In addition to P and ET, we used temperature, wind speed, humidity, and net short wave radiation (SWR) ux, all extracted from
GLDAS-Noah. We refer to these collectively as predictor variables and analysed their impact on TWSA, rainfall, ET, and available
water.
3.2. Methods
3.2.1. The UER water budget
The terrestrial water budget equation relates water storage in an area to P, runoff (Q) and ET, and is expressed as (Brutsaert, 2005;
Ramillien et al., 2006):
P−ET −Q−ds
dt =0,(2)
where Δs=ds∕dt is TWS change (TWSC) or TWC change (TWCC), and describes storage change from month to month.
The terrestrial water budget equation balances if there are no errors in the individual data sets, presenting a means of a mutual
validation of the data. Thus, we used Eq. (2) to validate GRACE and GLDAS-Noah estimates of Δs. We approximated Δs by numerically
differentiating GRACE/GLDAS-Noah storage anomalies using the central difference formula:
Δs(t) ≈ s(t+1) − s(t−1)
2,2≤t≤tmax −1,(3)
where t is time (mth).
We also ltered P and ET using a 300-km half-width Gaussian lter (Wahr et al., 1998) to account for the spectral inconsistencies
between GRACE and P and ET (Ferreira and Zibrila, 2015).
3.2.2. Time series analysis
For time series, we extracted grid points (x) falling within the UER and calculated their area-weighted average, s(t):
s(t) = 
n
i=1
aixi(t)

n
i=1
ai
,(4)
where n is the number of pixels and a represents the area per pixel. We resampled all data sets on a 0.25◦grid to match that of CSR-M.
For GRACE, we calculated equivalent water volume (EWV, km
3
) by multiplying equivalent water height (EWH, mm) by a
i
.
We adopted a time-variable regression model to analyse s(t). We tted the harmonic function characterised by an offset, a linear
trend, annual and semi-annual amplitudes and phases (Ogawa et al., 2011):
s(t) = β0+β1Δt+
2
k=1
Akcos(
ω
kt −ϕk) + ϵ,(5)
to s(t). The regression coefcients, β
0
and β
1
denote the constant term and the linear trend, respectively, and A and ϕ are respectively
the amplitude and phase. Δt is the time difference between each data point (in years) and the median time of the study (2009.5) and
ω
=2
π
∕T is the angular frequency, with the period T=1 yr =365.25 days. k has a value of 1 or 2 respectively corresponding to the
annual and semi-annual terms. To solve for the parameters and their standard errors, we expanded the last term into two pairs of sine
and cosine functions; a pair for each value of k. The expansion uses the trigonometric identity that cos(
ω
kt −ϕk) = Bkcos(
ω
kt) +
Cksin(
ω
kt). We then estimated the parameters, β
0
, β
1
, B
k
, and C
k
and their standard errors via a least squares inversion. Then, Ak =

B2
k+C2
k
and ϕk=tan−1Ck
Bk.
We evaluated the estimated parameters by testing the null hypothesis that the parameter was equal to zero against the alternative
that it was not equal to zero using the t-test. We calculated t as the ratio of the parameter estimates to their respective standard errors
C.I. Kelly et al.

Journal of Hydrology: Regional Studies 42 (2022) 101124
7
(Kutner et al., 2005), from which the associated p-values were calculated using the tcdf function in MATLAB R2021a.
3.2.3. Uncertainty analysis
Since we did not have in situ data, for the different groups of data sets (i.e., TWSA, P, and ET), we calculated the relative un-
certainties (
σ
TCH
) of the three solutions in each group using the generalised three-cornered hat (TCH) method (Galindo and Palacio,
2003; Gray and Allan, 1974; Premoli and Tavella, 1993; Tavella and Premoli, 1994). The TCH method allowed us to estimate the
relative error variances of the three time series, with the underlying assumption of a normal distribution of their errors. Like the
extended triple collocation (ETC) method (McColl et al., 2014), TCH does not require a reference data set (Gray and Allan, 1974).
However, we chose TCH because ETC has the strict requirement that the error variances of the systems must be uncorrelated. The error
variances of our data sets are likely correlated (cf. Yakubu et al., 2019), thus excluding the use of ETC in our study. We refer the
interested reader to Ferreira et al. (2016) and the references therein for further details on the TCH technique.
We used
σ
TCH
to calculate the ensemble averages of the different groups using a weighted averaging method similar to Eq. (4) by
replacing a
i
with 1∕
σ
TCH
and x
i
(t) with s(t). We then used the ensemble average to estimate the relative biases of the solutions. We
calculated the bias as the difference of the individual products and the ensemble average. All results based on TCH should be inter-
preted relative to the input solutions. For instance, if solution A has the smallest
σ
TCH
of the solutions A, B, and C, we will refer to it as
the best of the three. However, this conclusion is true only in the context of the three solutions. We also expect that solutions with
smaller
σ
TCH
will have the least deviation (bias) from their ensemble average. This is because solutions with larger
σ
TCH
will be down
weighted in the ensemble average. In some cases, we also calculated the SNR of the different solutions as the ratio of the mean of the
time series and
σ
TCH
. For decomposed time series components (Eq. (5)), we used the estimated standard errors from the least squares
inversion (Section 3.2.2).
3.2.4. Cross-correlation analysis
Given two random, equal-length (L) time series X and Y acquired at times t=1, 2, …L, cross-correlation analysis examines the
relationship between X and Y at different times. If the variables are detrended, then this is given by the cross-covariance of X and Y
(Chateld and Xing, 2019):
cov(Xt,Yt+l) = E[(Xt−
μ
X)(Yt+l−
μ
Y) ] =
σ
XY (l),(6)
where l=lag (in mth). The cross-covariance is related to the cross-correlation, r
XY
, by:
rXY (l) =
σ
XY (l)
σ
X
σ
Y
,(7)
where
σ
X
and
σ
Y
are the standard deviations of X and Y. We estimated r
XY
(l) by shifting Y to the right and left of X and each time
calculating the Pearson’s correlation coefcient. We determined the lag at which r
XY
was maximum. This represents the lag (time) of
maximum dependence between X and Y. If maximum r
XY
occurs anywhere else but lag 0, then there is a time delay (phase shift)
between X and Y. If r
XY
>0 or r
XY
<0, then X leads or lags Y at the given lag. We also calculated the square of Eq. (7), i.e., the co-
efcient of determination, R
2
, to determine the percentage of variations in the response variable that are accounted for by the predictor
variable.
3.2.5. Multiple correlation coefcient
We used multiple correlation analysis to inspect the relationship between the predictor variables (Section 3.1.6) and the other
quantities. For this, we formed two matrices – the N×1 vector b representing the response variable and the N×(J+1) matrix A of the
predictor variables. We set the rst column of A to 1 (Abdi, 2007) and solved for the J unknowns, 
b, via a least squares inversion.
The multiple R2
Y.1,..,J, which describes the percentage of variations in the response variable that can be explained by the predictor
variables, was then calculated as:
R2
Y.1,..,J=SSR
SST,(8)
where SSR is the regression sum of squares and is given by:
SSR =
bTATb−1
N1Tb2(9)
and SST is the total sum of squares, given by:
SST =bTb−1
N1Tb2
,(10)
where 1 is a column vector of ones and represents the rst column of A and (⋅)
T
denotes the transpose operator.
C.I. Kelly et al.

Journal of Hydrology: Regional Studies 42 (2022) 101124
8
4. Results
In line with the aim and objectives of the study, we used the following results to answer the questions (1) what is the relative
performances of ET/P/TWSA solutions from different providers over the UER? (2) Can GRACE provide TWSA over the UER with a high
SNR? (3) How does GLDAS-Noah perform over the UER? and (4) What is the relationship between meteorological conditions and water
availability in the UER?
The results for the time series analysis are shown in Table 3. This shows the parameter estimates (
β0, 
β1, 
A1, 
A2, 
ϕ1 and 
ϕ2) from
Eq. (5) and their associated standard errors. In most cases the standard errors are small compared to the point estimates of the pa-
rameters, indicating that the parameter is clearly signicantly different from zero. This is a particular concern for the estimate of the
trend, 
β1. If this parameter is not signicantly different from zero (p-value <0.05), it indicates that there is no evidence of a trend over
time and this component can be ignored in the model.
4.1. Rainfall
Fig. 3 shows the time series of rainfall (Eq. (4)) from GPM, CPC, CHIRPS, and their ensemble average. Table 4 summarises their
statistics differences, and relative uncertainties. The rainfall peaks usually occur in August and the maximum occurred in August 2007
for all the products (Table 4 and Fig. 3).
Fig. 3 and Table 4 indicate good agreement between the three rainfall products. The products also had high correlation coefcients
(r>0.96, p-value <0.001), and their estimated parameters from Eq. (5) (not shown) were similar. Relative to their ensemble average,
CHIRPS and CPC underestimated rainfall (negative biases, Table 4), while GPM overestimated rainfall. We selected the CHIRPS P
product for the rest of the study because of its relatively low bias (Table 4) and
σ
TCH
. See Table 3 for the estimated parameters of
CHIRPS.
4.2. Aridity
We illustrate the aridity PET time series in Fig. 4a. We used PET to calculate aridity index (AI). The AI (Eq. (1)) for the period April
2002 to June 2017 ranged between 0.4 and 0.75 (Fig. 4b), i.e., between semi-arid and humid (Table 2) (Cherlet et al., 2018). When we
excluded the incomplete years (2002 and 2017) and recalculated AI, the average was 0.64, that is, a dry sub-humid classication
(Table 2). This classication suggests the UER is susceptible to dryness.
4.3. Water loss
The results for runoff (not shown) did not exceed 2 mm mth
−1
and were, therefore, excluded from the analysis of water loss. Fig. 5
shows the ET time series, and Table 5 summarises their differences, biases, and relative uncertainties. Unlike the P products, the ET
solutions were more dissimilar. For instance, MOD16A2 did not exceed 80 mm mth
−1
, but GLDAS-Noah and ERA-5 exceeded 100 mm
mth
−1
. The r ranged between 0.76 (p-value <0.001, MOD16A2 and GLDAS-Noah) and 0.91 (p-value <0.001, ERA-5 and GLDAS-
Noah), indicating a comparatively wider variability in the estimation of ET by these solutions.
We selected ERA-5 as the best of the three solutions. The maximum ET ux from ERA-5 occurred in October 2015 and the minimum
occurred in March 2006. The time series of the ERA-5 ET product showed no evidence of a trend (Table 3).
4.4. Inter-comparison of GRACE solutions
We found good agreement between the three GRACE solutions (Table 6, Fig. 6). The minimum correlation coefcient was greater
than 0.95 (p-value <0.001). Table 6 shows the summary statistics along with their biases and relative uncertainties and Fig. 6 shows
their time series along with the ensemble average. We selected the JPL-M solution for the rest of our analyses.
Table 3
Harmonic analysis of quantities showing the dimensionless constant term, the linear trend (mm yr
−1
), the amplitudes (mm) and phases (
∘
), and their
standard errors. The standard errors are written in parentheses. ()
f
denotes ltered P−ET. ()* represents 0.02 <p-value <0.05, ()
+
represents p-
value >> 0.05, ()
#
represents p-value =0.07, and ()
o
represents p-value =0.04. All other parameters had p-value <0.001.
Quantity 
β0 
β1
Amplitude (mm) Phase (◦)
(mm yr
−1
) 
A1 
A2 
ϕ1 
ϕ2
TWSA 34.3 (3.3) 9.8 (0.8) 117.0 (4.7) 10.2 (2.3) 37.5 (4.7) 13.9 (7.2)
TWCA -6.7 (1.8) -2.2 (0.4) 80.1 (2.6) 15.3 (1.9) 27.3 (2.6) 9.8 (5.5)
P 81.0 (2.4) 0.01 (0.6)
+
108.8 (3.5) 19.9 (1.8) 37.7 (3.4) 3.3 (5.2)
+
ET 59.1 (0.9) 0.3 (0.2)
#
53.0 (1.3) 16.9 (1.4) 13.2 (1.3) 12.2 (5.7)*
P−ET 22.0 (2.6) -0.3 (0.6)
+
66.3 (3.6) 20.7 (3.1) 38.3 (3.6) 4.2 (5.4)
+
TWSC 1.0 (1.6)
+
-0.03 (0.4)
+
58.3 (2.3) 20.0 (2.2) 33.4 (2.3) 3.9 (3.9)
+
TWCC 0.4 (1.1)
+
0.06 (0.3)
+
40.7 (1.6) 23.5 (2.3) 24.2 (1.6) 3.0 (3.8)
+
(P−ET)
f
11.7 (1.0) -0.4 (0.2)
o
70.1 (1.5) 20.3 (1.2) 18.2 (1.5) 12.6 (4.6)
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Journal of Hydrology: Regional Studies 42 (2022) 101124
9
4.5. Terrestrial Water Storage (TWS) anomalies from GRACE
We recalculated monthly areal averages from the JPL-M data from April 2002 to June 2017. Fig. 7 shows the time series of TWSA
expressed in EWH (red) and EWV (green). The minimum anomaly (−161.1 mm, −50.7 km
3
) was recorded in May 2006 and the
maximum (290.4 mm, 91.3 km
3
) was recorded in October 2012. We summarised the time series components of TWSA (EWH) in
Fig. 3. Areal-averaged rainfall time series over the UER estimated from CHIRPS (red curve), CPC (green curve), and GPM (blue curve). The black
curve represents the ensemble average of CHIRPS, CPC, and GPM.
Table 4
Summary statistics of the rainfall solutions and their TCH-based relative uncertainties (
σ
TCH
). We calculated the bias as the mean of the difference
between each solution and the ensemble average. Units: mm/mth; Mean and Bias: mm.
Solution Min Max STD Mean Bias
σ
TCH
GPM 0.03 393.97 87.23 84.12 3.36 12.4
CPC 0 362.87 76.95 71.85 -8.92 20.4
CHIRPS 0.57 396.88 87.14 80.71 -0.06 11.1
Ensemble 0.28 390.96 85.12 80.77
GPM - CPC -44.66 118.74 23.85 12.28
GPM - CHIRPS -47.25 61.46 16.62 3.42
CPC - CHIRPS -98.79 58.15 23.22 -8.86
Fig. 4. Time series of (a) potential evapotranspiration from CRU TS v4.04 and (b) aridity index.
Fig. 5. Evapotranspiration from MOD16A2 (blue), GLDAS-Noah (green), ERA-5 (red), and the ensemble average (black).
C.I. Kelly et al.

Journal of Hydrology: Regional Studies 42 (2022) 101124
10
Table 5
Summary statistics of the ET solutions and their relative uncertainties. We calculated the bias as the mean of the difference between each solution and
the ensemble average. Units: mm/mth; Mean and Bias: mm.
Solution Min Max STD Mean Bias
σ
TCH
ERA-5 4.5 127.63 40.37 58.74 1.01 6.08
MOD16A2 0.49 75.90 17.96 16.95 -40.79 27.25
GLDAS-Noah 5.96 138.05 43.09 65.16 7.43 16.36
Ensemble 4.92 123.95 39.23 57.74
ERA-5 - GLDAS-Noah -71.52 29.90 17.46 -6.42
ERA-5 - MOD16A2 -20.41 109.13 27.92 41.80
GLDAS-Noah - MOD16A2 4.82 120.40 31.78 48.22
Table 6
Summary statistics of the GRACE solutions. We calculated the bias as the mean of the difference between each solution and the ensemble average.
Units: mm/mth; Mean and Bias: mm.
Solution Min Max STD Mean Bias
σ
TCH
JPL-M -161.06 282.56 104.49 27.44 3.85 13.8
CSR-M -150.81 222.34 83.64 16.13 -7.45 28.2
CSR-T -203.43 314.24 121.82 28.09 4.50 34.8
Ensemble -174.32 274.85 103.66 23.59
JPL-M - CSR-M -59.17 93.58 31.38 11.30
JPL-M - CSR-T -81.50 107.24 37.51 -0.65
CSR-M - CSR-T -105.78 74.12 44.84 -11.95
Fig. 6. TWSA expressed in terms of equivalent water height (EWH) for JPL mascon (red), CSR mascon (green), and CSR TELLUS (blue) from April
2002 to January 2017.
Fig. 7. TWSA time series over the UER. Red curve represents TWSA expressed in terms of EWH (mm) and green denotes equivalent water volume of
TWSA (km
3
).
Fig. 8. Plot of TWCA time series. Red curve represents TWCA in EWH (mm) and green is EWV (km
3
).
C.I. Kelly et al.

Journal of Hydrology: Regional Studies 42 (2022) 101124
11
Table 3. Notably, TWSA showed a signicant trend of 
β1=9.8 (s
β1
=0.8) mm yr
−1
.
4.6. Terrestrial Water Content (TWC) from GLDAS
Fig. 8 shows the TWCA time series. The peak TWCA (154.8 mm, 48.7 km
3
) occurred in September 2003 and the lowest
(−90.9 mm, −28.6 km
3
) in March 2012. Contrary to GRACE, TWCA showed a declining trend of 
β1=2.2 (s
β1
=0.4) mm yr
−1
(Table 3).
4.7. The terrestrial water budget
We calculated three Δs time series: (1) P−ET (net precipitation), (2) TWS change (TWSC) from GRACE (Eq. (3)), and (3) TWC
change (TWCC) from GLDAS-Noah (Eq. (3)). Fig. 9 shows these time series and (P−ET)f (ltered net P) – see Section 3.2.1. All but
(P−ET)f showed no evidence of a trend (p-value >0.05; Table 3).
We summarised their statistics in Table 7. All Δs time series were characterised by positive means, indicating that the UER received
more water than it lost. The peak of net precipitation (288.9 mm mth
−1
) occurred in August 2007 around the time of the anomalously
high rainfall in the Volta Basin (see Fig. 3). Its maximum depletion (83.6 mm mth
−1
) occurred around the start of the dry season in
October 2007. TWSC peaked (139.4 mm mth
−1
) in August 2015, with relatively smaller amplitudes than net P (Fig. 9), but the two
time series were highly correlated (r=0.87, p-value <0.001). The minimum TWSC (−91.2 mm mth
−1
) was recorded in November
2015. TWCC had comparatively smaller values.
The residual of ltered net P and TWSC (δΔsf
GRACE) resulted in smaller differences than that of net P and TWSC (Table 7). Dif-
ferences between net P and TWCC were the largest.
4.8. Meteorological conditions and water availability
The following describe the results of the relationships between water availability and the meteorological variables. Fig. 10 shows
the time series of humidity, pressure, SWR ux, temperature, and wind speed. All, except humidity, were characterised by increasing
trends (Table 8).
The multiple r (Section 3.2.5) between P and the predictor variables was 0.88 (p-value <0.0001). When we included ET in the
predictor variables, we found no substantial change in r between P and the predictor variables (ET included). We also found similar
relationships between ET and the predictor variables (with and without P). The percentages of the variations in P and ET that were
explained by the predictor variables were similar, with multiple R
2
=0.76 and 0.77 respectively. Thus, we conclude that our predictor
variables had a similar inuence on both ET and P.
Rainfall and ET had r=0.74 (p-value <0.001) and rainfall accounted for 54.0 % of the variations in ET. Cross-correlating P and ET
showed that ET lagged rainfall by 1 mth, with maximum r=0.9 (p-value <0.001). This is equivalent to an R
2
=0.81, suggesting that P
accounted for 81 % of ET variations a month after rainfall. Hence, rainfall’s maximum contribution to ET variations occurred a month
after rainfall.
We analysed the ratio of ET to P, which is a measure of water surplus or decit (Castellani, 2017). Fig. 11 shows the resulting
decit/surplus graph. Ninety-three of the 183 months were characterised by a ratio <1 (surplus). These surplus months were during
the months of April to September in the years between 2002 and 2016 and April to June 2017. The average P in surplus months was
143.5 mm and average ET was 74.2 mm. Months of decit ET
P>1were between October and March, with average P of 15.8 mm and
average ET of 42.7 mm. Both surplus and decit months were equal in length, except in 2002 and 2017.
The multiple correlation analysis between TWSA and the predictor variables yielded an R
2
=0.3 (p-value <0.001). This value
increased to R
2
=0.32 and R
2
=0.65 when P and ET were respectively added to the predictors (p-value <0.001). The multiple R
2
=0.42 when only P and ET were used as the predictor variables. However, ET and TWSA were more highly correlated (r=0.58) than P
and TWSA (r=0.22). Nonetheless, cross-correlation analysis (Section 3.2.4) estimated a 2-month lag between P and TWSA (r=0.78,
Fig. 9. Available water in the UER calculated as P−ET (green) and calculated from GRACE (red) and GLDAS-Noah (black). The blue curve
represents the time series of ltered net precipitation (P−ET)
f
.
C.I. Kelly et al.

Journal of Hydrology: Regional Studies 42 (2022) 101124
12
p-value <0.001), with TWSA trailing P. This indicates that the maximum contribution of P to TWSA occurred after 2 months of
rainfall.
TWCA was highly correlated with the predictor variables (r=0.89, p-value <0.001). Adding P to the predictor variables did not
change the multiple r, but replacing P with ET increased the multiple r to 0.94 (p-value <0.001). The multiple r when both ET and P
were added to the predictor variables was around 0.94. The multiple r between P and ET as predictor variables and TWCA was 0.88 (p-
Table 7
Terrestrial water budget calculated from GRACE, GLDAS, and as full resolution and ltered net precipitation. Units: mm mth
−1
; mm for Mean.
Statistics P−ET Δs
GRACE
Δs
Noah
(P−ET)
f
δΔs
GRACE
δΔs
Noah
δΔsf
GRACE
Min -83.6 -91.2 -76.7 -69.5 -62.9 -29.1 -99.6
Max 288.9 139.4 100.4 115.1 162.1 225.7 80.4
Mean 21.8 0.71 0.36 11.8 21.0 21.4 11.1
STD 63.8 52.0 36.8 53.0 31.8 39.1 33.0
Fig. 10. Areal averages of (a) relative humidity, (b) pressure, (c) SWR ux, (d) temperature, and (e) wind speed.
Table 8
Harmonic analysis of the predictor variables showing the dimensionless constant term, the linear trend, the amplitudes and phases (◦), and their
standard errors. The standard errors are written in parentheses. Units: Humidity (
β1=kg kg
−1
yr
−1
, 
A=kg); Pressure (
β1=kPa yr
−1
, 
A=kPa);
SWR (
β1=W m
−2
yr
−1
, 
A=W m
−2
); Temperature (
β1=◦C yr
−1
, 
A=◦C); Wind speed (
β1=m s
−2
yr
−1
, 
A=m s
−2
). ()* represents p-val-
ue >> 0.05 and ()
+
represents p-value =0.06. All other parameters had p-value <0.001.
Quantity 
β0 
β1
Amplitude Phase (◦)
(mm yr
−1
) 
A1 
A2 
ϕ1 
ϕ2
Humidity 11.7 (0.1) -0.2 (0.03) 6.7 (0.2) 20.3 (1.4) 2.0 (0.2) 14.6 (4.6)
Pressure 98.6 (0.01) 0.003 (0.001) 0.1 (0.01) 15.5 (3.5) 0.1 (0.01) -3.3 (4.4)*
SWR 195.7 (0.7) 0.5 (0.2) 13.9 (1.0) 37.4 (3.9) 7.8 (1.0) -19.7 (7.0)
Temperature 28.8 (0.1) 0.2 (0.02) 2.5 (0.1) 30.8 (2.5) 2.1 (0.1) 18.5 (2.9)
Wind speed 2.3 (0.02) 0.03 (0.004) 0.4 (0.03) 33.1 (3.8) 0.3 (0.03) -8.0 (5.2)
+
Fig. 11. Ratio of evapotranspiration to rainfall showing water decit and surplus.
C.I. Kelly et al.

Journal of Hydrology: Regional Studies 42 (2022) 101124
13
value <0.001).
Net P compared well with the ve predictor variables, yielding an R
2
=0.54 (p-value <0.001). P accounted for more than 90 % of
the variation in net precipitation. Similarly, the R
2
between TWSC and the predictor variables was 0.64 (p-value <0.001) and was
higher when P was included in the predictor variables (R
2
=0.80) than when ET was added (R
2
=0.64). Collectively, ET, P, and the
predictor variables explained a little over 80 % of the variations in TWSC, indicating a strong relationship between water availability
and meteorological conditions. The multiple R
2
between TWCC, P, ET, and the predictor variables was 0.78 (p-value <0.001). The R
2
between TWCC and the predictor variables was 0.48. This increased to 0.56 and 0.67 upon inclusion of ET and P, respectively, to the
predictor variables.
5. Discussion
5.1. Intercomparison of solutions
The satellite- and gauge-based precipitation data sets were similar in their estimation of precipitation. This was evident in the
closeness of their statistics (Table 4) and their high correlation coefcients. This is further supported by the statistics of their differ-
ences – maximum mean difference of around 12 mm (Table 4) – and by their
σ
TCH
. The ordering of the products based on their biases
(Table 4) and
σ
TCH
may be explained by their constituent data. Recall that (1) CHIRPS combines satellite and gauge data (Funk et al.,
2015), (2) GPM uses purely satellite data (Hou et al., 2014) and, (3) CPC uses purely gauge data (Xie et al., 2007, 2010). Combining
gauge and satellite data can improve precipitation estimates. Conversely, the complete reliance on weather stations (CPC) could mean
low data quality over data-poor regions such as the UER.
In contrast, the statistics of the differences between the ET data sets (Table 5) and their
σ
TCH
showed signicant disparities between
MOD16A2 and the other two solutions. MOD16A2 also underestimated ET by a relatively large amount (cf. Andam-Akorful et al.,
2015). This observed behaviour of the MOD16A2 ET may be attributed to its forcing data, including MODIS land cover, leaf area index
and meteorological data, which may be of low quality in regions like the UER (Mu et al., 2007, 2011). For instance, the coarse MODIS
land cover used in MOD16A2 misclassies the heterogeneity in savanna areas (Ramoelo et al., 2014) and could lead to biases (Chang
et al., 2018) – e.g., the observed comparatively lower ET uxes in the UER.
The GRACE solutions compared adequately well. Results of the intercomparison (Table 6) and
σ
TCH
analysis placed the mascon
solutions ahead of the TELLUS land mass solution. This may point to the superiority of mascon regularisation techniques over the
conventional processing techniques applied to GRACE L2 data. Another possibility is the use of newer data in the mascon solutions
relative to the TELLUS grids.
5.2. Meteorology: P, ET and the predictors
The rainfall time series was characterised by no apparent temporal trend. This is in contrast to a related study over the UER that
found a decreasing trend in rainfall (Issahaku et al., 2016). This difference in the ndings between our study and Issahaku et al. (2016)
could be because of the spatial distribution and resolution of the data sets. The latter studied rainfall from 6 gauge stations between
1954 and 2014.
The largest values of rainfall, which occurred in August, are consistent with Quaye-Ballard et al. (2020a). This is true not only for
CHIRPS – Quaye-Ballard et al. (2020a) used CHIRPS in their study – but also for CPC and GPM. The peak P, recorded in August 2007
(Fig. 3), coincided with the anomalously high rainfall event which occurred in the same year in sub-Saharan Africa (Paeth et al., 2011).
This anomaly was attributed to the 2007 La Ni˜
na, anomalies in atmospheric circulation, and the African easterly waves (Paeth et al.,
2011).
The dry sub-humid classication from the aridity analysis indicated that the UER is prone to dryness (cf. Quaye-Ballard et al.,
2020a). The trends of the predictor variables (Table 8) suggested they supported a drier climate and water loss through ET. However,
considering the strong relationship between P and ET in the UER (cf. Rodell et al., 2011; Grippa et al., 2011; Andreini et al., 2000) and
the similar effects of the predictors on P and ET, the trends of the predictor variables also support P.
5.3. Water storage and meteorological conditions
Our results showed contradictory trends between GRACE and GLDAS-Noah estimates of water storage. Possible explanations
include (1) GRACE had a low SNR because of the area of the UER, thus leading to the observed increasing trend, (2) the unmodelled
storage components in GLDAS-Noah contribute signicantly to water storage in the UER, or (3) the water holding capacity of the soil in
the UER. Items (2) and (3) both refer to GLDAS-Noah.
With regards to low GRACE SNR, the GRACE signals recovered over the UER included signals from the surrounding areas. If the
signals had opposite signs or were substantially different, this would lead to a low SNR, making GRACE unusable over the UER.
However, because the UER completely lies within the Volta Basin, we expect that the surrounding signals will not be different from the
target. In the absence of in situ data, we used the water budget equation for validation. We see from Fig. 9 that GRACE TWSC and
P−ET were generally quite similar (cf. Ferreira and Zibrila, 2015) except when P was close to, or exceeded, ~ 300 mm mth
−1
(discussed further in Section 5.4). One also sees that the differences became much smaller when net P was ltered to account for
spectral inconsistencies (Fig. 9, Table 6). Although the UER is prone to dryness, a positive mean P-ET value and ET∕P<1 for 51 % of
the total months indicate that overall, the UER received more water through P than it lost through ET. These two metrics concur with
C.I. Kelly et al.

Journal of Hydrology: Regional Studies 42 (2022) 101124
14
the observed increasing trend in TWSA. Our analysis has assumed that rainfall is the only input to the water cycle in the UER. However,
given that there is no increasing rainfall trend, the TWSA trend is likely to have another source, such as the Bagre Dam, which oods
the UER annually. We, however, did not have data to analyse its impact on TWSA.
We also found similarities between the annual amplitudes and linear trends of our study and that of Ferreira et al. (2012). Fig. 4 of
Ferreira et al. (2012) shows the linear trend of GRACE in the UER to be between ~ 8 and 16 mm yr
−1
. This is important because
Ferreira et al. (2012) used GRACE level 2 data and their study was over the entire Volta Basin, the area of which is greater than twice
the prescribed effective GRACE resolution (150,000–200,000 km
2
). Thus, based on our results and those of previous studies, we
conclude that GRACE has a high SNR in the UER.
Concerning unmodelled storage components in GLDAS-Noah and the low water retention properties of the soil, TWCA in the UER
comprises water stored in the soil and canopy (Rui et al., 2018). However, the total storage in a region comprises surface water,
groundwater and any other major water storages. Canopy water storage made up only a small portion of TWCA perhaps because the
region’s vegetation is Savanna woodland. If there is substantial storage in the unmodelled components, this could result in
GLDAS-Noah underestimating water storage. GRACE aggregates these distinct components vertically as TWSA, and because our results
have established that GRACE can measure water storage in the UER, we conclude that soil moisture alone is not sufcient to describe
the total water stored in the UER. Furthermore, if one considers the water retention properties of the soil in the UER, it becomes clear
why modelled soil water can underestimate water storage in the UER. According to the Ministry of Food and Agriculture (2019), some
of the soil in the UER has low water retention capacity. This claim is further supported by the global water capacity map (United States
Department of Agriculture, 2003), which classied the UER’s soil water capacity between low (<25 mm) and moderate (25–100 mm).
In light of this, and the statistics of ET∕P and P−ET, we conclude that GLDAS underestimates water storage in the UER probably
because of the unmodelled components and the dependence of TWCA on soil water.
Regarding the impact of meteorological conditions on water storage, the annual amplitude variations in rainfall could not entirely
explain the annual amplitude variation in TWSA (
AP
1∕
ATWSA
1=0.93), implying that other factors (e.g., ET and other water inow
sources) contributed to 
ATWSA
1. This is to be expected because the UER has one season during which it receives water, but rainfall does
not account for all the water in the UER (Section 2.1) or that it receives; and other processes (e.g., ET) in the dry season contribute to
the annual amplitude variations. Conversely, rainfall alone was sufcient to explain 
ATWSA
2 (
AP
2∕
ATWSA
2=1.95) probably because the
impact of ET over the period was smaller than that of P, i.e., the UER received more water than it lost (see Table 7 and Section 4.8).
5.4. Water availability
The positive mean values of all the Δs time series (Table 7) indicated that the UER received more water than it lost. The large
difference between net P and Δs from GLDAS-Noah can be attributed to the lack of surface water in GLDAS-Noah (Rui et al., 2018) and
perhaps the water retention properties of the soil in the UER (Sections 2.1, 5.3; Ministry of Food and Agriculture, 2019).
Two possible reasons for the difference between the GRACE Δs time series and net P are: (1) the 2-month lag between rainfall and
the GRACE twin satellites sensing its maximum impact on the temporal variations of the gravity eld (see Section 4.8 and Rieser et al.,
2010) and, (2) the spectral mismatch between GRACE and net precipitation. Notably, the wide variations between P−ET and TWSC
mainly resulted from their differences in August 2003, 2007, 2011, 2015 (Fig. 9). These periods coincided with rainfall exceeding
300 mm mth
−1
. Given (1) the 2-month time lag between rainfall and GRACE, (2) that conditions (predictor variables) supported a drier
climate and, (3) the strong relationship between ET and rainfall, it is probable that some of the water will have been lost through ET.
Runoff had little to no effect on water loss, since it did not exceed 2 mm mth
−1
. Notwithstanding, the differences between net P and
GRACE TWSC were smaller than the bias of net P and TWCC. Filtering P−ET lowered the differences between ltered net P and TWSC.
Furthermore, similarities between our study and that of Andam-Akorful et al. (2015) provide additional support for the usability of
GRACE over the UER. Most importantly, based on our water budget analysis, one would require a mean of 21.0 mm of TWSC to close
the water budget of the UER using GRACE between 2002 and 2017. This translates roughly into a correction of 0.11 mm mth
−1
to close
the UER’s water budget. Thus, we conclude that the SNR of GRACE in the UER is high, and GRACE can provide information for water
resources monitoring in the region.
5.5. Limitations and recommendations
The main limitation of this study was the unavailability of in situ data. For instance, we did not have the necessary data to analyse
the impact of the Bagre Dam on water resources in the UER. Given that TWSA was increasing while rainfall showed no trend, in-
formation from the Bagre Dam could improve the understanding of TWSA dynamics in the UER, especially the observed 9.8
±0.8 mm yr
−1
trend. This can be important to the authorities of the yet to be constructed Pwalugu Dam. A future study could analyse
the contribution of the Bagre Dam to determine its contribution to the increasing TWSA trend.
6. Conclusions
We assessed globally available hydro-meteorological data to study the impact of the climate of the UER on its water resources. We
validated the GRACE and GLDAS water storage time series using the water budget equation and found large differences between net
precipitation and GLDAS-Noah. The GRACE solution however compared well with net precipitation except when rainfall exceeded
C.I. Kelly et al.

Journal of Hydrology: Regional Studies 42 (2022) 101124
15
300 mm mth
−1
. These results indicated that GRACE can provide support for water resources monitoring in the UER. Our results also
showed that conditions in the UER affect P and ET in a similar way, but that overall, the UER received more water through P than it lost
through ET. All the time series of net P, an indication of water availability, were characterised by positive means. Water storage from
GRACE showed an increasing trend of 9.8 ±0.8 mm yr
−1
, which likely includes the contribution of another source of water (the Bagre
Dam) other than rainfall.
Declaration of Competing Interest
The authors declare that they have no known competing nancial interests or personal relationships that could have appeared to
inuence the work reported in this paper.
Acknowledgement
This research was supported by a Faculty of Science and Engineering Ph.D. scholarship, reference code 19073FOSE, to C.I. Kelly at
the University of Nottingham Ningbo China, Ningbo, China.
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