J. Hydrol. Hydromech., 66, 2018, 2, 143–152
DOI: 10.1515/johh-2017-0051

Effect of temporal averaging of meteorological data on predictionsof groundwater recharge
Marcia S. Batalha1, Maria C. Barbosa1, Boris Faybishenko2, Martinus Th. van Genuchten3,4*1

Department of Civil Engineering, Federal University of Rio de Janeiro, UFRJ, Rio de Janeiro, RJ, Brazil.
Lawrence Berkeley National Laboratory, Berkeley, California, CA, USA.
3
Center for Environmental Studies, CEA, São Paulo State University, UNESP, Rio Claro, SP, Brazil.
4
Department of Earth Sciences, Utrecht University, Utrecht, Netherlands.
*
Corresponding author. E-mail: rvangenuchten@hotmail.com
2

Abstract: Accurate estimates of infiltration and groundwater recharge are critical for many hydrologic, agricultural andenvironmental applications. Anticipated climate change in many regions of the world, especially in tropical areas, is expected to increase the frequency of high-intensity, short-duration precipitation events, which in turn will affect the
groundwater recharge rate. Estimates of recharge are often obtained using monthly or even annually averaged meteorological time series data. In this study we employed the HYDRUS-1D software package to assess the sensitivity ofgroundwater recharge calculations to using meteorological time series of different temporal resolutions (i.e., hourly, daily, weekly, monthly and yearly averaged precipitation and potential evaporation rates). Calculations were applied tothree sites in Brazil having different climatological conditions: a tropical savanna (the Cerrado), a humid subtropical area(the temperate southern part of Brazil), and a very wet tropical area (Amazonia). To simplify our current analysis, we did
not consider any land use effects by ignoring root water uptake. Temporal averaging of meteorological data was found tolead to significant bias in predictions of groundwater recharge, with much greater estimated recharge rates in case of very
uneven temporal rainfall distributions during the year involving distinct wet and dry seasons. For example, at the Cerrado
site, using daily averaged data produced recharge rates of up to 9 times greater than using yearly averaged data. In allcases, an increase in the time of averaging of meteorological data led to lower estimates of groundwater recharge, especially at sites having coarse-textured soils. Our results show that temporal averaging limits the ability of simulations topredict deep penetration of moisture in response to precipitation, so that water remains in the upper part of the vadosezone subject to upward flow and evaporation.
Keywords: Groundwater recharge; Meteorological data; Temporal averaging; HYDRUS-1D; Infiltration; Evaporation.
INTRODUCTION
Having accurate estimates of water flow rates into andthrough the vadose zone, and related groundwater recharge
rates, is critical in many hydrologic, environmental agricultural
applications such as surface- and ground-water management,
management and remediation of contaminated soils andgroundwater, and irrigation and drainage operations in agriculture. As groundwater is increasingly being used, and available
resources are slowly diminishing in many parts of the world, a
critical need exists to develop sustainable groundwater use andmanagement practices (Gleeson et al., 2015; Shah et al., 2000;
Shiklomanov, 1997; Vörösmarty et al., 2000). This in turnrequires an accurate quantitative understanding of the fundamental meteorological controls on groundwater recharge underconditions of climate change (Gorelick and Zheng, 2015;
Maxwell and Kollet, 2008; Veldkamp et al., 2016). Groundwater depletion currently occurs in many arid and semi-arid areas
due to excessive extraction, especially for irrigation (Aeschbach-Hertig and Gleeson, 2012), with global change exacerbating this problem in various parts of the world.
The expected intensification of precipitation due to global
climate change, with a shift toward more heavy precipitation
events of often short duration, may lead to an increase in
groundwater recharge in tropical and other areas (Allan et al.,2010; Jasechko and Taylor, 2015; Owor et al., 2009). Failure toconsider realistic changes in precipitation intensity can influence predictions of both climate change and groundwater recharge (Gee and Hillel, 1988; Mileham et al. 2009; Owor et al.,2009). Intense rainfall events may lead to episodic recharge
events (Taylor et al., 2013), which are not accounted for in
calculations of groundwater recharge when using monthly or
especially annually averaged (aggregated) meteorological timeseries data, such as is the case with large-scale and long-time
averaged water balance equations (Shiklomanov and Rodda,
2003) or using other methods (Kim and Jackson, 2012; Phillips,
1994; Scanlon et al., 2002).
Predictions of water flow into and through the vadose zone
contributing to groundwater recharge are dependent upon theavailability of meteorological data sets. Data of this type areoften obtained from weather stations on daily, weekly, monthly
or even yearly averaged time scales. Unfortunately, climate
simulations using monthly or annually averaged (aggregated)
simulations fail to consider high-intensity precipitation eventsof relatively short duration (Allan and Soden, 2008), and assuch may severely underestimate groundwater recharge rates(Portmann et al., 2013; Wada et al., 2014).
While many methods exist for calculating recharge (e.g.,
Ngatcha et al., 2007; Scanlon et al., 2002), one common
approach is to model variably saturated flow processes in thenear-surface to partition precipitation into runoff, evaporation,root water uptake and deep drainage, and hence recharge (Assefa and Woodbury, 2013; Jiménez-Martinez et al., 2009;
Leterme et al., 2012). Accurate modeling of vadose zone flow
processes and recharge very much depends on having reliable
weather data, including their temporal resolution such as daily
versus monthly averaged data. Using high-resolution meteorological data is important for transient simulations, especially for143Marcia S. Batalha, Maria C. Barbosa, Boris Faybishenko, Martinus Th. van Genuchten

climates having high precipitation rates but also long periods
without much rain. In an earlier study (Batalha et al., 2012) we
showed that using monthly averaged daily precipitation andevapotranspiration data can produce very different results forrecharge as compared to using data having a daily resolution.
This occurs since net infiltration, and hence recharge, is verymuch dependent upon the intensity of short-term rainfall
events, as well as the local soil hydraulic properties. On theother hand, the more regular availability of water near the soil
surface when precipitation and evaporation or evapotranspiration rates are averaged over relatively long time periods, willlead to less deep penetration of moisture and higher calculated
evaporation rates, as compared to transient simulations involving precipitation and evapotranspiration patterns recorded overtime periods of days, hours, or even minutes.
Several previous studies have shown the effects of temporal
averaging on near-surface flow water flow and contaminanttransport processes. For example, Wang et al. (2009) conducteda series of flow and transport simulations with daily data of atypical semi-arid region subject to considerable temporal variability in precipitation. They concluded that reliance on annual
meteorological data, as done routinely for contaminanttransport simulations, can significantly underestimate thedownward migration of contaminants. Predictive errors stemming from the use of annual data increased considerably withtime and were more pronounced for very permeable soils thatallow water to penetrate much deeper during single rainfall
events. Saifadeen and Gladnyeva (2012) similarly inferred that
averaging moisture input over larger time periods will lead tounderestimates of the center of mass migration, especially formore permeable (coarse-textured) soils. Related contaminanttransport examples for different water inflow conditions, withsome including steady-state flow conditions, are provided by
Marshall et al. (2000), Kuntz and Grathwohl (2009), Harman etal. (2011), Vero et al. (2014) and Yin et al. (2015). In anotherstudy relating precipitation and recharge based on monthly andannual averages for groundwater modeling, Jyrkama et al.
(2002) concluded that on a monthly basis, precipitation andrecharge rates exhibited little correlation due to the delaycaused by water percolating through the unsaturated zone.
The various studies above indicate that calculations of waterflow into and through the vadose zone may depend very muchupon temporal averaging of available meteorological data.
Unfortunately, hourly or even daily data are often unavailable
from weather stations, while only monthly- or yearly-averagedata may be present. The overall goal of our study was to findout how different ways of temporally averaging meteorological
data would affect infiltration and groundwater recharge processes. Specific objectives were to investigate differences in
predicted recharge rates resulting from hourly, daily, weekly,monthly and yearly averaged meteorological data from threesites in Brazil having different climatological conditions: atropical savanna (the Cerrado), a humid subtropical area (thetemperate southern part of Brazil), and a very wet tropical area
(Amazonia). In our current analysis we did not consider any
land use effects by ignoring root water uptake. The analysis
hence is limited to evaporation processes from bare soils.
SIMULATION METHODOLOGY
Various numerical approaches may be used to estimate
groundwater recharge (Assefa and Woodbury, 2013; Jyrkama
and Sykes, 2007). In this study we evaluated the different
temporal scaling effects on groundwater recharge using the
HYDRUS 1-D software package of Šimůnek et al. (2013,1442016), which has been previously used in several other recharge
studies (e.g., Assefa and Woodbury, 2013; Jiménez-Martinez etal., 2009; Leterme et al., 2012; Neto et al., 2016). Simulations
were carried out for a 2-m deep unsaturated soil profile subject
to transient meteorological conditions involving precipitation,
evaporation and possible runoff. Preliminary calculations, notfurther shown here, indicated that a soil profile of 2 m was
sufficient to estimate deep drainage, and hence recharge. Simulations of mean annual recharge using a 4-m deep profile differed by at most 5% for the most extreme situation when arelatively fine-texture soil was considered.
One-dimensional water flow in the soil profile can be represented using the classical Richards equation as follows
 ∂h  ∂θ (h) ∂ =  K ( h )  − 1 
∂t
∂x 
 ∂x
 

(1)

where h is the soil water pressure head [L], θ is the volumetricwater content [L3L–3], t is time [T], x is the spatial coordinate(positive downwards) [L], and K is the unsaturated hydraulicconductivity [LT–1]. The soil hydraulic relationships θ(h) andK(h) in Eq. (1) were described using the constitutive relationships of van Genuchten (1980):n −mθ (h) − θ r = 1 + α h 
Se ( h ) =θ s − θ r 





(

1

K ( h ) = K s Sel 1 − 1 − Se1/ m


m 2

) 

h<0

(2)

h≥0
(3)

where Se is effective saturation [–], θr and θs are the residual
and saturated volumetric water contents, respectively [L3L–3],
Ks is the saturated hydraulic conductivity [LT–1], α [L–1], n>1[–] and l [–] are shape factors, and m = 1–1/n [–]. Following
van Genuchten (1980), the pore-connectivity parameter l was
fixed at a value of 0.5.
The 2-m deep soil profile was discretized into a 201-node finite element mesh with variably-sized elements (smaller values
near the soil surface) to facilitate numerical convergence during
the calculations. Atmospheric boundary conditions were considered at the soil surface to enable prescribed flux or pressure
head conditions depending upon prevailing meteorologicalconditions (Šimůnek et al., 2013). The boundary fluxes andheads were limited by given precipitation and potential evaporation fluxes in combination with specific parameters to restrict
boundary pressure heads to remain above prescribed minima (inour study –100,000 cm) during evaporation, and below certain
maximum values (e.g., 0 cm) during precipitation events(surface runoff may then occur). Several simulations also considered the situation where ponding of up to 2.5 cm could occur. This situation may be more realistic for relative flat terrains
with a low-permeability surface horizon. The lower boundary
condition of the flow domain was set as free drainage(∂h/∂x = 0). We note that HYDRUS-1D uses a self-adjustingtime-stepping scheme for numerical solution of the Richards
equation (Šimůnek et al., 2013). This is important since numerical time steps will be reduced automatically to sometimes
seconds or less to correctly simulate high-intensity infiltration
rates in relatively dry soils, while remaining consistent with thehourly or daily input data.

Effect of temporal averaging of meteorological data on predictions of groundwater recharge

METEOROLOGICAL DATA
Data from three sites in Brazil (Fig. 1) representing different
climatic regions were used for the groundwater recharge calculations. The sites represented the following regions (from driest
to wettest site): a tropical savanna (the Cerrado region), a humid subtropical area (the temperate South of Brazil), and atropical area (Amazonia). Average annual rainfall rates for thethree sites were about 1500, 1600 and 2500 mm, respectively.
Figure 2 shows daily rainfall data for the three weather stations.
While annual rainfall in the Cerrado is still relatively high(about 1500 mm/yr), rainfall is not distributed evenly over theyear. The Cerrado is characterized by summers (December–March) with intense rainfall, and very dry winters. The averagemonthly temperature variation is only about 4.4°C (even thoughdaily temperatures vary about 12°C). Meteorological data fromthe Cerrado were taken from Paracatu Station located at
17.25S, 46.88W, and having an altitude of 625 m above meansea level (a.s.l.).
The subtropical site in southern Brazil (further referred to as
the Temperate site) has a warm but relatively temperate climate. As compared to the Cerrado, precipitation at this site is
not much higher (about 1600 mm/y) but distributed far more
evenly over the year. Even the driest month (July) shows considerable precipitation. Mean temperature varies by 8.8°C
throughout the year, with daily variations being about 10°C.
Meteorological data for this area were taken from the Urussanga weather station (28.51S, 49.17W) at an altitude of 48.2 m
a.s.l. The third site, located in the Amazonia, is characterizedby significant rainfall (about 2500 mm/y), and a very short“dry” period in August. Temperatures do not vary much along
the year (only about 1.3°C), while daily variations are relatively
small also (about 8°C).
Meteorological data for the three sites for a five-year period(2008 through 2012) were downloaded from the Brazilian
National Meteorological Institute website (INMET, 2015). The
data included daily precipitation (mm), maximum andminimum temperatures (°C), wind speed (km d–1) at 200 cm
above the land surface, air humidity (%) and daily sunshine
hours. The data were used to calculate daily potential evaporation rates using the Penman-Monteith combination equation(Allen et al., 1998):

Ep =

900
U 2 ( ea − ed )T + 273
Δ + γ (1 + 0.34U 2 )0.408Δ ( Rn − G ) + γ(4)in which Δ is the slope of the saturation vapor pressure temperature curve (kPa °C–1), and γ the psychrometric constant (kPa°C–1) as follows:Δ=γ=

4098ea(T + 237.3)
Pc p

ελ

(5)

2

*10−3 = 0.00163

P

λ

(6)

In the equations above, Ep is the potential evaporation rate
[mm d–1], Rn is net radiation at the soil surface [MJ m–2d–1], G is
the soil heat flux density [MJ m–2 d–1], T is the average daily air
temperature [°C]; U2 is the wind speed at 2 m height [m s–1], ea
is the saturation vapor pressure at temperature T [kPa], ed is
actual vapor pressure [kPa], P is atmospheric pressure [kPa], cp
is the specific heat of moist air (assumed to be 1.013 kJ
kg–1 °C–1), ε is the ratio of the molecular weights of water vaporand dry air (0.622), and λ is the latent heat of vaporization [MJ
kg–1]. We emphasize that Eqs. (4)–(6) were used to calculatepotential evaporation rates. Actual evaporation (and infiltration)
rates are limited by the soil to produce (or accept) the potential
surface fluxes as modeled using the atmospheric boundary
conditions of HYDRUS-1D (Šimůnek et al., 2013).

Fig. 1. Location of the three meteorological sites in Brazil (adapted from an image mask from the IBGE site (ftp://geoftp.ibge.gov.br/mapas_interativos/)using Google Earth Software).

145

Marcia S. Batalha, Maria C. Barbosa, Boris Faybishenko, Martinus Th. van Genuchten

Precipitation

Potential Evaporation

Figure 2. Observed daily precipitation and calculated daily potential evaporation rates for the Cerrado, Temperate and Amazonia sites.

Figure 2 shows daily precipitation and calculated potential
evaporation rates for the Cerrado, Temperate and Amazonia
sites. The plots show that the Cerrado has well-defined seasons
with precipitation concentrated mostly in the Brazilian summer
months, while precipitation at the Amazonia site and especially
the Temperate site are distributed much more evenly over theyear. By comparison, potential evaporation is least variable
during the year at the Amazonia site, ranging from 2 to about 6
mm/day, and most variable in the Temperate region (ranging
between 2.5 and 6 mm/d in the summer and between 1 and 1.5mm/d in the winter months). The precipitation data in Figure 2
represent daily rates (daily totals) during the 5-year study period. We also carried out recharge calculations using hourly input
values of precipitation and evaporation. Unfortunately, hourly
data are generally not collected at meteorological stations. For
our hourly recharge calculations we used precipitation datafrom Criciuma, which is located about 30 km from the Temperate (South) weather station in Urussanga and has very similar
climatological conditions as those in Criciuma. The hourly data
were obtained in 2008 by Soares et al. (2012) for an acid minedrainage project in the area. Since only one year of hourly
precipitation data were available, the 2008 data were scaled up
or down in such a way that the daily values for the years 2009–2012 were respected. For the 5-year study we obtained in thisway close to 44,000 hourly precipitation data entries.

146

We also generated hourly potential evaporation data corresponding to the hourly precipitation data. One possible approach to generate these is to use hourly time steps in a Penman-Monteith type procedure as advocated by ASCE (2005).
Since our study already used daily potential evaporation rates,
we downscaled the daily rates to hourly values in a mannerconsistent with the daily total values. The conversion was donein accordance with previous experimental studies of hourly
evaporation and evapotranspiration rates by van Bavel (1966),
van Bavel and Hillel (1976), and Katul and Parlange (1992), as
well as with similar studies of diurnal patterns of other meteorological variables such as temperature (Ephrath et al., 1996;
Kimball and Bellamy, 1986; Wann et al., 1985). The approach,as also programmed in the HYDRUS-1D code, assumes that thedaily evaporation rate (the daily total) can be distributed sinusoidally over the day into hourly rates such that they represent
about 12% of the daily total between 0–6 am and between 18–
24 pm, and 88% during the remainder of the day (Šimůnek etal., 2013). Mathematically, the distribution over the day (24 h)
for the potential evaporation rate is then described by0.24 E p
(t < 0.264d or t > 0.736d )Ep (t ) =  2πt π 
− 0.264d ≤ t ≤ 0.736d ) 2.75 E p sin  24 2 (7)Effect of temporal averaging of meteorological data on predictions of groundwater recharge

where E p is the daily value of the potential evaporation rate.
The procedures above allowed us to define daily and hourly
meteorological data for the 5-year recharge calculations. Our
temporal averaging procedure considered at first daily precipitation and temperatures as well as later also all parameters
needed for the Penman-Monteith equation yielding daily evaporation rates. Once daily evaporation and precipitation data wereavailable for the different sites, the data were averaged overtime using the expression: n = 7 for weekly approach n = 30 (28, 29 or 31) for monthly n = 365 (366) for yearly

1 nMP =  mpi
n i =1(8)

where mpi represents the available daily meteorological data
(i.e., precipitation or evaporation), n is the period of temporal
averaging, and MP is the average daily rate of the meteorological parameter over the time period being considered.
To assess the effect of soil texture on recharge as calculatedusing the temporally average data, we decided to carry out thesimulations for three different soil types covering relatively
coarse- to fine-textured soils: a loamy sand, a loam and a clay
loam. Soil hydraulic parameters for these soils were definedusing pedotransfer functions derived by Carsel and Parrish(1988). The parameters used are presented in Table 1. We used
these parameters to define initial pressure head conditions foreach simulation that were consistent with the long-term average
recharge rates obtained for the particular meteorological conditions.

Fig. 3. Time series of groundwater recharge rates obtained using
daily, monthly, and yearly averaged meteorological data from the
Cerrado site. Please note the different scales for the daily andmonthly data (left side) and the yearly data (right side).

Table 1. Soil hydraulic parameters in Eqs. (1) and (2) for the threesoils used in the simulations.
Soil
TextureLoamy sand
Loam
Clay loam

θr
(–)
0.057
0.078
0.095

θs
(–)
0.410
0.430
0.410

α
(cm–1)
0.124
0.036
0.019

n
(–)
2.28
1.56
1.31

Ks
(cm d–1)
350.
25.0
6.24

RESULTS AND DISCUSSION
In this section we compare results of the recharge calculations for the temporal averaging schemes involving daily,
weekly, monthly and yearly averaged meteorological data.
Figure 3 shows that rapid temporal changes in the recharge rate
at the Cerrado site occur when daily averaged meteorological
data are used as compared to monthly averaged values, while
the overall patterns are generally identical (values of the daily
and monthly recharge rates are shown on the left-hand side yaxis). However, the pattern of daily recharge rates when using
yearly averaged data (values shown on the right-hand side axis)
is significantly different from those for the daily and monthly
averaged meteorological data.
Figure 4 shows box-and-whisker diagrams (Chambers et al.,1983) of the daily recharge rates obtained for the Cerrado siteusing daily, monthly, and yearly averaged meteorological data.
The plots include the minimum, first quartile (25th percentile),
median, third quartile (75th percentile), and maximum quartiles,
as well as the upper and lower whiskers representing the+/– 1.5 interquartile ranges between the first and third quartilesof the corresponding upper and lower quartiles. The statisticalparameters are also summarized in Table 2. The data show that,
notwithstanding the differences between the minimum andmaximum recharge values obtained with the daily and monthly

Fig. 4. Box-and-whisker plots and statistical parameters ofgroundwater recharge rates obtained using daily, monthly, andyearly averaged meteorological data from the Cerrado site, ascalculated using the time series shown in Figure 3.
Table 2. Statistical parameters of recharge rates at the Cerrado site
as obtained with daily, monthly, and yearly averaged meteorological data.
Lower hinge
25%
Median75%
Upper hinge

Daily–0.2880.0268
0.148
0.414
0.994

Monthly
0.01080.0350
0.148
0.280
0.646

Yearly0.005880.01200.02110.04960.104

averaged input data, the median values are the same (0.148cm/d) and much larger than the median of the recharge rate
obtained with yearly averaged data (0.021 cm/d). Note that thevertical axis in Figure 4 is given on a log scale to demonstrate
to more clearly visualize the range of variations in recharge forthe three types of input data.
To quantitatively assess differences in the calculated recharge rates using daily, monthly, and yearly averaging of theweather data, we also applied a Kolmogorov-Smirnov (KS)goodness-of-fit test. The nonparametric KS test is used to147

Marcia S. Batalha, Maria C. Barbosa, Boris Faybishenko, Martinus Th. van Genuchten

Fig. 5. Cumulative distributions of groundwater recharge rates
obtained using daily, monthly, and yearly averaged meteorological
data from the Cerrado site (the table shows results of the Kolmogorov-Smirnov test).

determine the probability that a given dataset is drawn from thesame parent population as a second dataset (called the twosample KS test; Marsaglia et al., 2003). The KS statistics aremeasures of the supremum, being the greatest distance between
the empirical cumulative distribution functions (CDFs) of thedatasets. The CDFs, along with results of calculations, areshown in Figure 5. Based on the D statistical measure of thediscrepancy between the CDFs, we reject the hypothesis thatthe distributions are similar. This can be seen from the table
entries in Figure 4, which show that the difference between thedaily and monthly recharge rates is far less than the difference
between daily and yearly values, as well as between the monthly and yearly recharge estimates.
Calculated daily recharge rates for the three ways of temporal averaging are shown in Figures 6 and 7. Figure 6 demonstrates differences in the temporal distributions of groundwater
recharge caused by different patterns of precipitation, while
Figure 7 depicts the corresponding box-and-whiskers plots
along with the statistical parameters for recharge at the threesites. As expected from the climatic conditions at the three sites(Fig. 2), the lowest values of recharge are at the Cerrado site(the negative lower value indicates that evaporation actuallyslightly exceeded infiltration), and the highest values are at the
Amazonia site.
Figure 8 compares results for the three soil types at each site.
Each plot shows for the same period of averaging the calculated
annual recharge rates. In all cases, the highest recharge rates
occurred when using daily averaged data, while the yearly
averaged data always produced the lowest values. The plotsshow that differences between the higher and lower values canbe very significant. The most extreme situation occurred for the
Cerrado, where daily averaged data generated up to 9 times
higher annual average recharge rates than when yearly averaged
data were used. The main reason relates to the irregular distribution of the meteorological data, especially precipitation, over
the year (Fig. 2). The more uneven the precipitation distribution, the higher the difference in calculated recharge rates.
When precipitation is confined to only a short period of theyear, more water penetrates below layers near the soil surface
from which upward flow and evaporation is still possible. Thiseffect is clearly shown when comparing results for the Cerrado
with those for the Temperate and Amazonia sites. Even though148

Fig. 6. Comparison of daily groundwater recharge for three sites,
demonstrating different temporal seasonal patterns, depending on
meteorological conditions at the sites.

Fig. 7. Box-and-whisker plots and statistical parameters ofgroundwater recharge rates obtained using daily, monthly, andyearly averaged meteorological data from the Cerrado, Temperateand Amazonia sites, as calculated using the time series shown in
Figure 6.

the annual precipitation rate at the Temperate site (1600 mm)
was only slightly larger than at the Cerrado site (1500 mm), thedifferences in calculated recharge rates between the daily andannually averaged data were much smaller for the Temperate
site. The same occurs for the Amazonia site, even with its muchlarger annual precipitation rates. Using daily averaging, therecharge rates can still be 25 to 82% higher than for yearly
averaging, depending upon soil type.
Figure 8 further shows that the effect of soil texture on thecalculations can be quite important when the temporal averaging period is relatively short (daily or weekly). Coarser soils
tend to produce 30 to 40% more recharge as long as the hydraulic conductivity is relatively high to allow most of the infiltrated
water to move rapidly below the zone of influence for upward
flow. On the other hand, fine-textured soils may act as buffers
by keeping moisture closer to the surface to enable subsequently upward flow and evaporation. This occurs especially when
the hydraulic conductivity of the surface layer is lower than the
precipitation rate, in which case fine-textured soils facilitate
runoff and thus further diminish infiltration and recharge.

Effect of temporal averaging of meteorological data on predictions of groundwater recharge
Table 3. Calculated recharge rates as a percentage of rainfall at theBrazilian Cerrado, Temperate and Amazonia sites.
Averaging
Daily
WeeklyMonthly
YearlyHourlyDaily
WeeklyMonthly
YearlyDaily
WeeklyMonthly
Yearly

Loamy
Loam
sand
--------- Cerrado --------72
56
58
50
44
40
8
8
--------- Temperate ---------76
47 / 51*
72
54
56
48
45
43
39
40
--------- Amazonia ---------73
61
62
58
56
55
46
46

Clay
loam
51
48
39
7
22 / 46*
50
47
42
39
57
57
54
45

*The first value refers to a runoff and the second to a ponding boundary
condition

Fig. 8. Calculated average annual recharge rates at the Cerrado(top), Temperate (middle) and Amazonia (bottom) sites as obtainedusing daily, monthly, and yearly averaged meteorological data.

Calculated groundwater recharge rates as a percentage of
rainfall for the same period (2008 through 2012) at the different
sites are presented in Table 3. Estimated recharge rates calculated in this study using the daily averaged weather data were
surprisingly independent of location, ranging mostly between
50% for the fine-textured clay loam soil, to about 75% for the
more coarse-textured loamy sand. Values for the weekly,monthly and yearly averaged data on average were always
lower, especially when using the yearly data of the Cerrado,
where recharge became less than 8% of annual precipitation,
irrespective of soil type. The Cerrado situation is quite similar
to what was observed in (semi-) arid sites for contaminanttransport by Wang et al. (2009) and Harman et al. (2011).

Those studies showed that daily averaged calculations predicted significant contaminant transport, while little transport
occurred when annually averaged precipitation data were considered.
The data in Table 3 indicate recharge always will be underestimated when monthly and, especially, yearly averaged meteorological data are used. The hourly values for the Temperate
site generated much more variation among soil type when runoff was considered. The values in Table 3 (between 40 and
75%, except for the Cerrado) are well within the range of literature values documented by Kim and Jackson (2012) for unvegetated surfaces. They also correspond to or exceed the upper
limits of annual values for vegetated surfaces inventories by
Kim and Jackson (2012) and determined by Santoni et al.
(2010) and Assefa and Woodbury (2013), among others. As
noted by Assefa and Woodbury (2013) and confirmed by our
results, recharge rates can be very variable in time (see also Fig.
6) depending upon transient weather conditions and soil type.
Still, we acknowledge that our values should be higher, in partsince we did not consider any root water uptake in this study.
The plots and data in Figure 8 indicate that cumulative recharge is always lower when considering yearly averaged data.
Similar calculations that include also results for the hourly
averaged precipitation and evaporation data are presented in
Figure 9 for the Temperate site. The simulations show thatrunoff is now becoming also an important term, especially forthe fine-textured (clay loam) soils. In that case the hourly precipitation rates can become larger than the saturated hydraulicconductivity (Ks), leading to runoff when an atmosphericboundary condition with possible runoff is considered (Figure
8, top plots). It is also possible to allow water to pond on thesurface by assuming the presence of a relatively flat soil surface, in which case little or no runoff may occur. The simulations shown in Figure 8 (bottom) were obtained for the intermediate situation where runoff would occur only when reachinga ponding depth of more than 2.5 cm on the soil surface. Results for the hourly data in that case are now very close to thosefor the daily meteorological data. The results in Figure 10 indicate that the runoff component can be important and withstandard numerical calculations will show up mostly whenhourly averaged data are used, and then only for medium- andespecially fine-textured soils. No difference between the hourly

149Marcia S. Batalha, Maria C. Barbosa, Boris Faybishenko, Martinus Th. van Genuchten

Temperate

Temperate

Fig. 10. HYDRUS-1D calculated cumulative recharge rates
obtained with hourly and daily data for the loam (top) and clay
loam (bottom) soils with and without ponding.

Fig. 9. Calculated average annual recharge rates for the Temperate
site as obtained using hourly, daily, weekly and monthly averaged
weather data assuming atmospheric boundary conditions withinstantaneous runoff (top plot) and with runoff occurring only after
reaching a ponding level of 2.5 cm.

and daily calculations occurred for loamy sand since the hourly
averaged precipitation rates never exceeded the saturated hydraulic conductivity of 350 cm/day. On the other hand, when
ponding is considered, the results for the hourly averaged data
tend to closely approximate results for the daily averaged dataalso for the fine-textured soil.
The important effect of possible runoff is further demonstrated in Figure 10, which shows cumulative recharge during 5
years for both the hourly averaged data (dotted lines) and thedaily averaged data (continuous lines) for both the loam andclay loam soils. Results are for the cases with instantaneous
runoff (dotted line) and runoff after ponding to 2.5 cm (dashedline). Calculations show that hourly averaged data lead to far
less infiltration, and hence lower recharge rates, for the clay
loam soil.
CONCLUDING REMARKSIn this study we evaluated the effects of temporal averaging
of meteorological data on calculated groundwater recharge
rates for three sites in Brazil having very different climatological conditions. Calculations showed that the use of temporally
averaged meteorological data can lead to very different resultsin the recharge calculations, decreasing from daily, weekly,

150

monthly, to yearly averaged data, with the yearly average data
always producing the lowest recharge rates. Results were especially sensitive to averaging when applied to the Cerrado Region in Brazil where recharge rates using daily averaged data
were up to 9 times the recharge rate for yearly averaged meteorological data. But the effects were also apparent for the Temperate and Amazonia sites where the differences ranged from25 to 82%. The important effects of averaging at the Cerradosite were related to the highly uneven rainfall distribution over
the year involving distinct wet and dry seasons. Yearly averaging may then even lead to near-zero recharge rates in certain
time periods, with concomitant significant underestimates of
the actual recharge rates.
While rainfall and its temporal distribution in time are important determinants for recharge, another factor is soil type.
When averaging weather data (and hence infiltration) overlonger periods of time, infiltrated water will fail to reach soil
depths below the influence of evaporation, even in coarsetextured soils. The soils then do not dry out very much, thus
causing evaporation rates to be overestimated, and recharge
underestimated, in some cases by up to 50%. By comparison,fine-textured soils can better regulate near-surface soil moisture
conditions during high precipitation events, leading to recharge
rates that are less dependent upon time averaging (daily tomonthly values), except for the yearly averaged data.
Another important effect of temporal averaging of weather
data is its effect on runoff, which relates to the amount of water
not infiltrated into a soil during a rainfall event. Infiltration
rates during a particular precipitation event ultimately dependon the saturated hydraulic conductivity, Ks. Runoff will occur
when the precipitation rate is higher than Ks for an appreciable

Effect of temporal averaging of meteorological data on predictions of groundwater recharge

time period depending on the initial soil moisture conditions.
Long-term averaging will smooth available precipitation data torates that will always be less than Ks, especially for weekly,monthly and yearly averaged data. Even daily averaged data
seldom produce runoff, unless very fine-textured soils are present. Lack of runoff will then actually increase local recharge
rates. This is why in actuality hourly calculations should be
used for fine-textured soils, subject of course to data availability. Differences, however, will become less significant if ponding will occur in relatively flat areas, thus minimizing runoff.
Overall results of this study indicate that daily averaged meteorological data should be used as much as possible, while yearly averaged data should be avoided as much as possible.
We emphasize that the current study is limited to simulationsof vadose zone flow and evaporation, without directly modelingof root water uptake, which would lead to reduced recharge
rates. We plan to document the additional effects of land use ina separate document. We further acknowledge that other processes such as especially preferential flow in a heterogeneous
soil profile may also modify recharge rates, especially duringhigh-precipitation events in conjunction with surface ponding.
Acknowledgements. BF's part of this study was supported by
NGEE-Tropics, funded by the U.S. Department of Energy,
Office of Science, Office of Biological and Environmental
Research, and Office of Advanced Scientific Computing, under
the DOE Contract No. DE-AC02-05CH11231.
REFERENCES

Aeschbach-Hertig, W., Gleeson, T., 2012. Regional strategies
for the accelerating global problem of groundwater depletion. Nature Geosci., 5, 853–861.
Allan, R.P., Soden. B.J., 2008. Atmospheric warming and theamplification of precipitation extremes. Science, 321, 1481–
1481.
Allan, P., Soden, B.J., John, V.O., Ingram, W., Good, P., 2010.
Current changes in tropical precipitation. Environ. Res.
Lett., 5, 025205, 7 p.
Allen R.G., Pereira, L.S., Raes, D., Smith, M., 1998. Crop
Evapotranspiration; Guidelines for Computing Crop Water
Requirements. FAO Irrigation and Drainage Paper 56. Foodand Agriculture Organization of the United Nations, Rome,
Italy.
ASCE, 2005. The ASCE Standardized Reference Evapotranspiration Equation. Environmental and Water Resources Institute of ASCE, Final Report. American Society of Civil Engineers, Reston, VA, USA.
Assefa, K.A., Woodbury, A.D., 2013. Transient, spatially varied groundwater recharge modeling. Water Resour. Res., 49,
4593–4606.
Batalha, M.S., Bezerra, C.R., Jacques, D., Barbosa, M.C.,
Pontedeiro, E.M., van Genuchten, M.Th., 2012.
Multicomponent transport predictions of 226Ra in soil
following the use of phosphogypsum. In: Proc. 4th Int. Conf.
on Engineering for Waste and Biomass Valorization,
WASTENG, Porto, Portugal, 6 p.
Carsel R.F., Parrish. R.S., 1988. Developing joint probability
distributions of soil water retention characteristics. Water
Resour. Res., 4, 755–769.
Chambers, J.M., Cleveland, W.S., Kleiner, B., Tukey, P.A.,
1983. Graphical Methods for Data Analysis. Wadsworth &Brooks/Cole.
Ephrath, J.E., Goudriaan, J., Marani, A., 1996. Evaluation andcalibration of three models for daily cycle of air temperature,radiation, wind speed and relative humidity by equations
from daily characteristics. Agric. Syst., 51, 4, 377–393.
Gee, G.W., Hillel, D., 1988. Groundwater recharge in arid
regions: Review and critique of estimation methods. Hydrol.
Process., 2, 255–266. DOI: 10.1002/hyp.3360020306.
Gleeson, T., Befus, K.M., Jasechko, S., Luijendijk, E.,
Cardenas, M.B., 2015. The global volume and distributionof modern groundwater. Nature Geosci., 9, 161–167.
Gorelick, S.M., Zheng, C., 2015. Global change and thegroundwater management challenge. Water Resour. Res.,51, 3031–3051, DOI: 10.1002/ 2014WR016825.
Harman, C.J., Rao, P.S.C., Basu, N.B., McGrath, G.S., Kumar,
P., Sivapalan, M., 2011. Climate, soil, and vegetation
controls on the temporal variability of vadose zone transport.
Water Resour. Res., 47, W00J13
INMET, 2015. Instituto Nacional de Meteorologia, MinistériodaAgricultura,
PecuáriaeAbastecimento<http://www.inmet.gov.br/portal/index.php?r=bdmep/bdmep>,
Brazil.
Jasechko, S., Taylor, R.G., 2015. Intensive rainfall recharges
tropical groundwaters Environ. Res. Lett., 10, 124015.
Jimenez-Martinez, J., Skaggs, T.H., van Genuchten, M.Th.,
Candela, L., 2009. A root zone modelling approach toestimating groundwater recharge from irrigated areas. J.
Hydrol., 367, 138–149.
Jyrkama, M.I., Sykes, J.F., 2007. The impact of climate change
on spatially varying groundwater recharge in the grand riverwatershed (Ontario). J. Hydrol., 338, 237–250.
Jyrkama, M.I., Sykes, J.F., Normani, S.D., 2002. Recharge
estimation for transient ground water modeling. Ground
Water, 40, 638–648.
Katul, G.G., Parlange, M.B., 1992. A Penman-Brutsaert model
for wet surface evaporation. Water Resour. Res., 28, 121–126.
Kim, J.H., Jackson, R.B., 2012. A global analysis ofgroundwater recharge for vegetation, climate, and soils.
Vadose Zone J., 11, 1.
Kimball, B.A., Bellamy, L.A., 1986. Generation of diurnal
solar radiation, temperature, and humidity patterns. Energy
Agric., 5, 185–197.
Kuntz, D., Grathwohl, P., 2009. Comparison of steady-state andtransient flow conditions on reactive transport ofcontaminants in the vadose zone. J. Hydrol., 369, 225–233.
Leterme, B., Mallants, D., Jacques, D., 2012. Sensitivity ofgroundwater recharge using climatic analogues and
HYDRUS-1D. Hydrol. Earth Syst. Sci., 16, 2485–2497.
Marsaglia, G.W., Tsang, W., Wang, J., 2003. Evaluating
Kolmogorov's distribution. J. Stat. Softw., 8, 18.
Marshall, J.D., Shimada, B.W., Jaffe, P.R., 2000. Effect of
temporal variability in infiltration on contaminant transport
in the unsaturated zone. J. Contam. Hydrol., 46, 151–161.
Maxwell, R.M., Kollet, S.J., 2008. Interdependence ofgroundwater dynamics and land-energy feedbacks underclimate change. Nature Geosci., 1, 665–669.
Mileham, L., Taylor, R.G., Todd, M., Tindimugaya, C.,
Thompson, J., 2009. Climate change impacts on theterrestrial hydrology of a humid, equatorial catchment:sensitivity of projections to rainfall intensity. Hydrol. Sci. J.,
54, 727–738.
Neto, D.C., Chang, H.K., van Genuchten, M.Th., 2016. A
mathematical view of water table fluctuations in a shallow
aquifer in Brazil. Ground Water, 54, 82–91.
Ngatcha, B.N., Mudry, J., Sarrot, R.J., 2007. Groundwater
recharge from rainfall in the southern border of Lake Chadin Cameroon. World Appl. Sci. J., 2, 125–131.

151

Marcia S. Batalha, Maria C. Barbosa, Boris Faybishenko, Martinus Th. van Genuchten

Owor, M., Taylor, R.G., Tindimugaya, C., Mwesigwa, D.,2009. Rainfall intensity and groundwater recharge: Empirical evidence from the Upper Nile Basin. Environ. Res. Lett.,
4, 035009.
Phillips, F.M., 1994. Environmental tracers for water
movement in desert soils of the American Southwest. Soil
Sci. Soc. Am. J., 58, 15–24.
Portmann, F.T., Döll, P., Eisner, S., Flörke, M., 2013. Impact ofclimate change on renewable groundwater resources:
assessing the benefits of avoided greenhouse gas emissions
using selected CMIP5 climate projections. Environ. Res.
Lett. 8, 024023.
Saifadeen, A., Gladnyeva, R., 2012. Modeling of solutetransport in the unsaturated zone using HYDRUS-1D.
TVVR 12/5020, Water Resources Engineering, Lund
University, Sweden.
Santoni, C.S., Jobbágy, E.G., Contreras, S., 2010. Vadose zonetransport in dry forests of central Argentina: Role of landuse. Water Resour. Res., 46, W10541.
Scanlon, B.R., Healy, R.W., Cook, P.G., 2002. Choosing
appropriate techniques for quantifying groundwater
recharge. Hydrogeol. J., 10, 18–39.
Shah, T., Molden, D., Sakthivadivel, R., Seckler, D., 2000. The
global groundwater situation: Overview of opportunities andchallenges. IWMI Books, Rep. H025885. Int. Water
Manage. Ins., Colombo, Sri Lanka.
Shiklomanov, I.A., 1997. Comprehensive assessment of the
freshwater resources of the world. World Meteor. Org.,
Stockholm, Sweden.
Shiklomanov, I.A., Rodda, J.C., 2003. World Water Resourcesat the Beginning of the Twenty-First Century. Cambridge
University Press, Cambridge, UK.
Šimůnek, J., Šejna, M., Saito, H., Sakai, M., van Genuchten,
M.Th., 2013. The HYDRUS-1D Software Package forSimulating the One-Dimensional Movement of Water, Heat,and Multiple Solutes in Variably-Saturated Media, Version
4.17. Dep. of Environmental Sciences, University ofCalifornia, Riverside, California, USA.
Šimůnek, J., van Genuchten, M.Th., Šejna, M., 2016. Recent
developments and applications of the HYDRUS computer
software packages. Vadose Zone J., 15, DOI:
10.2136/vzj2016.04.0033.
Soares, P.S.M., Souza, V.P., Possa, M.V., Soares. A.B., 2012.
Projeto Cooperativo para Realização de Experimento de
Avaliação de Desempenho de Cobertura Seca para
Mitigação de Drenagem Ácida de Mina em Escala Piloto

152

Centro de Tecnologia Mineral (CETEM). Relatório Final de
Projeto Elaborado Para a Carbonífera Criciúma S.A., Rio deJaneiro, Brazil.
Taylor, R.G., Todd, M.C., Kongola, L., Maurice, L., Nahozya,
E., Sanga, H., MacDonald, A.M., 2013. Evidence of thedependence of groundwater resources on extreme rainfall in
East Africa. Nature Climate Change, 3, 374–378.
van Bavel, C.H.M., 1966. Potential evaporation: The
combination concept and its experimental verification.
Water Resour. Res., 2, 3, 455–467.
van Bavel, C.H.M., Hillel, D.I., 1976. Calculating potential andactual evaporation from a bare soil surface by simulation of
concurrent flow of water and heat. Agric. Meteorol., 17,453–476.
van Genuchten, M.Th., 1980. A closed-form equation forpredicting the hydraulic conductivity of unsaturated soils.
Soil Sci. Soc. Am. J., 44 892–898.
Veldkamp, T.I.E., Wada, Y., Aerts, J.C.J.H., Ward, P.J., 2016.
Towards a global water scarcity risk assessment framework:
Incorporation of probability distributions and hydro-climatic
variability. Environ. Res. Lett., 11, 024006.
Vero, S.E., Ibrahim, T.G., Creamer, R.E., Grandt, J., Healy,
M.G., Henry, T., Kramers, G., Richards, K.G., Fenton, O.,
2014. Consequences of varied soil hydraulic andmeteorological complexity on unsaturated zone time lag
estimates. J. Contam. Hydrol., 170, 53–67.
Vörösmarty, C.J., Green, P., Salisbury, J., Lammers, R.B.,
2000. Global water resources: Vulnerability from climatechange and population growth. Science, 289, 284–288.
Wada, Y., Wisser, D., Bierkens, M.F.P., 2014. Global modelingof withdrawal, allocation and consumptive use of surface
water and groundwater resources. Earth Syst. Dyn., 5, 15–40.
Wang, P., Quinlan, P., Tartakovsky, D.M., 2009. Effects ofspatio-temporal variability of precipitation on contaminantmigration in the vadose zone. Geophys. Res. Lett., 36,
L12404.
Wann, M., Yan, D., Gold, H.J., 1985. Evaluation andcalibration of three models for daily cycle of air temperature.
Agric. Forest Meteorol., 34, 121–128.
Yin, Y., Sykes, J.F., Normani, S.D., 2015. Impacts of spatial
and temporal recharge on field-scale contaminant transportmodel calibration. J. Hydrol., 527, 77–87.
Received 16 August 2017
Accepted 20 November 2017