Satellite rainfall estimates (SREs) are prone to bias as they are indirect
derivatives of the visible, infrared, and/or microwave cloud properties,
and hence SREs need correction. We evaluate the influence of elevation and
distance from large-scale open water bodies on bias for Climate Prediction
Center-MORPHing (CMORPH) rainfall estimates in the Zambezi basin. The
effectiveness of five linear/non-linear and time–space-variant/-invariant
bias-correction schemes was evaluated for daily rainfall estimates and
climatic seasonality. The schemes used are spatio-temporal bias (STB),
elevation zone bias (EZ), power transform (PT), distribution transformation
(DT), and quantile mapping based on an empirical distribution (QME). We
used daily time series (1998–2013) from 60 gauge stations and CMORPH SREs
for the Zambezi basin. To evaluate the effectiveness of the bias-correction
schemes spatial and temporal cross-validation was applied based on eight
stations and on the 1998–1999 CMORPH time series, respectively. For
correction, STB and EZ schemes proved to be more effective in removing bias.
STB improved the correlation coefficient and Nash–Sutcliffe efficiency by 50 % and 53 %, respectively, and reduced the root mean squared difference
and relative bias by 25 % and 33 %, respectively. Paired t tests showed
that there is no significant difference (p<0.05) in the daily
means of CMORPH against gauge rainfall after bias correction. ANOVA post hoc
tests revealed that the STB and EZ bias-correction schemes are preferable.
Bias is highest for very light rainfall (<2.5 mm d-1), for
which most effective bias reduction is shown, in particular for the wet
season. Similar findings are shown through quantile–quantile (q–q) plots.
The spatial cross-validation approach revealed that most bias-correction schemes removed bias by >28 %. The temporal
cross-validation approach showed effectiveness of the bias-correction
schemes. Taylor diagrams show that station elevation has an influence on
CMORPH performance. Effects of distance >10 km from large-scale
open water bodies are minimal, whereas effects at shorter distances are
indicated but are not conclusive for a lack of rain gauges. Findings of this study
show the importance of applying bias correction to SREs.
Introduction
Correction schemes for rainfall estimates are developed for climate models
(Maraun, 2016; Grillakis et al., 2017; Switanek et al., 2017), for radar
approaches (Cecinati et al., 2017; Yoo et al., 2014), and for satellite-based,
multi-sensor approaches (Najmaddin et al., 2017; Valdés-Pineda et al.,
2016). In this study the focus is on satellite rainfall estimates (SREs) to
improve reliability in spatio-temporal rainfall representation.
Studies in satellite-based rainfall estimation show that estimates are prone
to systematic and random errors (Gebregiorgis et al., 2012; Habib et al.,
2014; Shrestha, 2011; Tesfagiorgis et al., 2011; Vernimmen et al., 2012; Woody
et al., 2014). Errors result primarily from the indirect estimation of
rainfall from visible (VIS)-, infrared (IR)-, and/or microwave (MW)-based
satellite remote sensing of cloud properties (Pereira Filho et al., 2010;
Romano et al., 2017). Systematic errors in SREs commonly are referred to as
bias, which is a measure that indicates the accumulated difference between
rain-gauge observations and SREs. Bias in SREs is expressed for rainfall
depth (Habib et al., 2012b), rain rate (Haile et al., 2013), and frequency at
which rain rates occur (Khan et al., 2014). Bias may be negative or positive,
where negative bias indicates underestimation, whereas positive bias
indicates overestimation (Liu, 2015; Moazami et al., 2013).
Recent studies on the National Oceanic and Atmospheric Administration (NOAA)
Climate Prediction Center-MORPHing (CMORPH) (Wehbe et al., 2017; Jiang et
al., 2016; Liu et al., 2015; Haile et al., 2015) reveal that the accuracy of
this satellite rainfall product varies across regions (Gumindoga
et al., 2019), but causes are not directly identifiable. As such correction
schemes serve to reduce systematic errors and to improve applicability of
SREs. Correction schemes rely on assumptions that adjust errors in space
and/or time (Habib et al., 2014). Some correction schemes consider
correction only for spatially distributed patterns in bias, commonly known as
space-variant/-invariant. Approaches that correct for spatially averaged bias
have roots in radar rainfall estimation (Seo et al., 1999), but are
unsuitable for large-scale basins (> 5000 km2) where
rainfall may substantially vary in space (Habib et al., 2014). Studies by
Müller and Thompson (2013) in Nepal concluded that space-variant correction schemes are more
effective in reducing bias for CMORPH and TRMM than space-invariant correction
schemes. In a study conducted in the Upper Blue Nile basin in Ethiopia,
Bhatti et al. (2016) show that CMORPH bias correction is most effective when
bias factors are calculated for 7 d sequential windows.
Bias-correction schemes based on regression techniques have reported
distortion of frequency of rainfall rates (Ines and Hansen, 2006; Marcos et
al., 2018). Multiplicative shift procedures tend to adjust SRE rainfall
rates, but Ines and Hansen (2006) reported that they do not correct
systematic errors in rainfall frequency of climate models.
Non-multiplicative bias-correction schemes preserve the timing of rainfall
within a season (Fang et al., 2015; Hempel et al., 2013). Studies that have
applied non-linear bias-correction schemes such as power functions report
correction of extreme values (depth, rate, and frequency), thus mitigating the
underestimation and overestimation of CMORPH rainfall (Vernimmen et al.,
2012). The study by Tian (2010) in the United States noted that the Bayesian
(likelihood) analysis techniques are found to over-adjust both light and
heavy CMORPH rainfall.
Bias often exhibits a topographic and latitudinal dependency as, for
instance, shown for the CMORPH product in the Nile basin (Bitew et al., 2011;
Habib et al., 2012a; Haile et al., 2013). For southern Africa, Thorne et al. (2001), Dinku et al. (2008), and Meyer et al. (2017) show that bias in
rainfall rate and frequency can be related to location, topography, local
climate, and season. The first studies in the Zambezi basin (southern Africa) on
SREs show evidence that necessitates correction of SREs. For example, Cohen
Liechti (2012) show bias in CMORPH SREs for daily rainfall and for
accumulated rainfall at a monthly scale. Matos et al. (2013), Thiemig et al. (2012), and Toté et al. (2015) show that bias in rainfall depth at time
intervals ranging from daily to monthly varies across geographical domains
in the Zambezi basin and may be as large as ±50 %. Besides
elevation, there are indications that the presence of a large-scale open water body affects rainfall at short distances (<10 km)
(Haile et al., 2009).
For less developed areas such as in the Zambezi basin that is selected for
this study, studies on SREs are limited. This is despite the strategic
importance of the basin in providing water to over 30 million people (World
Bank, 2010a). An exception is the study by Beyer et al. (2014) on correction
of the TRMM-3B42 product for agricultural purposes in the Upper Zambezi
basin. Studies (Cohen Liechti et al., 2012; Meier et al., 2011) on use of
SREs in the Zambezi River basin mainly focused on accuracy assessment of the
SREs using standard statistical indicators, with little or no effort to
perform bias correction despite the evidence of errors in these products.
The use of uncorrected SREs is reported for hydrological modelling in the
Nile basin (Bitew and Gebremichael, 2011) and Zambezi basin (Cohen Liechti
et al., 2012), respectively, and for drought monitoring in Mozambique
(Toté et al., 2015). The poor performance of SREs in the above studies urges
bias correction to result in more accurate rainfall representation. The
selection of CMORPH satellite rainfall for this study is based on successful
applications of bias-corrected CMORPH estimates in African basins for
hydrological modelling (Habib et al., 2014) and flood predictions in western
Africa (Thiemig et al., 2013). In the first publications on CMORPH, Joyce et al. (2004) describe CMORPH as a gridded precipitation product that estimates
rainfall with information derived from IR data and MW data. CMORPH combines
the retrieval accuracy of passive MW estimates with IR measurements which
are available at high temporal resolution but with low accuracy. The
important distinction between CMORPH and other merging methods is that the
IR data are not used for rainfall estimation, but are used only to propagate
rainfall features that have been derived from microwave data. The flexible
“morphing” technique is applied to modify the shape and rate of rainfall
patterns. CMORPH has been operational since 2002, for which data are available at
the CPC of the National Centers for Environmental Prediction (NCEP) (after
http://www.ncep.noaa.gov/, last access: 4 July 2019). Recent publications on CMORPH in African basins
exist (Wehbe et al., 2017; Koutsouris et al., 2016; Jiang et al., 2016;
Haile et al., 2015). However, studies on bias correction of CMORPH in the
semi-arid Zambezi basin are limited.
In this study we use daily CMORPH and rain-gauge data for the Upper, Middle, and
Lower Zambezi basins to (1) evaluate whether performance of CMORPH rainfall is
affected by elevation and distance from large-scale open water bodies, (2) evaluate the effectiveness of linear/non-linear and time–space-variant/-invariant bias-correction schemes, and (3) assess the performance of
bias-correction schemes to represent different rainfall rates and climate
seasonality. Analysis serves to improve reliability of SREs applications in
water resource applications in the Zambezi basin such as for rainfall–runoff
modelling.
Study area
The Zambezi River is the fourth-longest river (∼2574 km) in
Africa, with a basin area of ∼1390000 km2 (∼4 % of the African continent). The river drains into
the Indian Ocean and has a mean annual discharge of 4134 m3 s-1 (World
Bank, 2010a). The river has its source in Zambia with basin boundaries in
Angola, Namibia, Botswana, Zambia, Zimbabwe, and Mozambique (Fig. 1). The
basin is characterised by considerable differences in elevation and
topography, distinct climatic seasons, and the presence of large-scale open water
bodies and, as such, makes the basin well suited for this study. The basin
is divided into three sub-basins, i.e. the Lower Zambezi comprising the
Tete, Lake Malawi/Shire, and Zambezi Delta basins, the Middle Zambezi
comprising the Kariba, Mupata, Kafue, and Luangwa basins, and the Upper
Zambezi comprising the Kabompo, Lungwebungo, Luanginga, Barotse, and
Cuando/Chobe basins (Beilfuss, 2012).
Zambezi River basin from Africa with sub-basins, major lakes,
elevation, and locations and names of the 60 rain-gauging stations (in each
respective elevation zone) used in this study.
The elevation of the Zambezi basin ranges from <200 m (for some
parts of Mozambique) to >1500 m above sea level (for some parts
of Zambia). Large-scale open water bodies in and around the basin are
Kariba, Cabora Bassa, Bangweulu, Chilwa, and Nyasa. The Indian Ocean lies to
the east of Mozambique. Typical land-cover types are woodland, grassland,
water surfaces, and cropland (Beilfuss et al., 2000). The basin lies in the
tropics between 10 and 20∘ S, encompassing humid, semi-arid, and
arid regions dominated by seasonal rainfall patterns associated with the
Inter-Tropical Convergence Zone (ITCZ), a convective front oscillating along
the Equator (Cohen Liechti et al., 2012). The movement of the ITCZ in
the Southern Hemisphere results in the peak rainy season that occurs during the
summer (October to April) and the dry winter months (May to September), and is a result
of the shifting back of the ITCZ towards the Equator (Schlosser and Strzepek,
2015). The weather system in south-eastern parts such as Mozambique is
dominated by Antarctic polar front (APF) and tropical temperate trough
(TTT) occurrence which is positively related to La Niña and Southern
Hemisphere planetary waves, whereas El Niño–Southern Oscillation (ENSO)
appears to play a significant role in causing dry conditions in the basin
(Beilfuss, 2012).
The basin is characterised by high annual rainfall (>1400 mm yr-1) in the northern and north-eastern areas and by low annual
rainfall (<500 mm yr-1) in the southern and western parts
(World Bank, 2010b). Due to this rainfall distribution, northern tributaries
in the Upper Zambezi sub-basin contribute 60 % of the mean annual
discharge (Tumbare, 2000). The river and its tributaries are subject to
seasonal floods and droughts that have devastating effects on the people and
economies of the region, especially the poorest members of the population
(Tumbare, 2005). It is not uncommon to experience both floods and droughts
within the same hydrological year.
Materials and methodologyRainfall dataCMORPH
For this study, time series of CMORPH rainfall images (1998–2013) at 8 km ×8 km, 30 min resolution were selected and downloaded from the
NOAA repository (ftp://ftp.cpc.ncep.noaa.gov/precip/global_CMORPH/, last access: 4 July 2019). Images are downloaded by means of the GeoNETCAST ISOD
toolbox of the ILWIS GIS software (http://52north.org/downloads/, last access: 4 July 2019). Half-hourly
estimates were aggregated to daily totals to match the observation interval
of gauge-based daily rainfall.
Rain-gauge network
Time series of daily rainfall from 60 stations were obtained from
meteorological departments in Botswana, Malawi, Mozambique, Zambia, and
Zimbabwe for stations that cover the study area. All the stations are
standard-type rain gauges with a measuring cylinder whose unit of
measurement is millimetres (mm).
Some stations are affected by data gaps, but the available time series are of
sufficiently long duration (see Appendix Table A1) to serve the objectives of this
study. Stations are irregularly distributed across the vast basin and are
located at an elevation between 3 and 1575 m (Fig. 1). The minimum, maximum,
and average distances between the rain gauges are 3.5 km (Zumbo in
Mozambique, Kanyemba in Zimbabwe), 1570 km (Mwinilunga in Zambia, Marromeu in
Mozambique), and 565 km, respectively. Distances to large-scale open water
bodies range between 5 and 615 km. This allows us to evaluate whether
elevation and distance to large-scale open water bodies affect CMORPH
performance.
Comparison of CMORPH and gauge rainfall
In this study, we compare gauge rainfall at point scale to CMORPH satellite-derived rainfall estimates at pixel scale (point-to-pixel). Comparison is at
a daily time interval covering the period 1998–2013, following Cohen Liechti
et al. (2012), Dinku et al. (2008), Haile et al. (2014), Hughes (2006),
Tsidu (2012), and Worqlul et al. (2014), who report on point-to-pixel
comparisons in African basins. We apply point-to-pixel comparison to rule
out any aspect of interpolation error as a consequence of the low-density
network with unevenly distributed stations. We refer to Heidinger et al. (2012), Li and Heap (2011), Tobin and Bennett (2010), and Yin et al. (2008),
who report that interpolation introduces unreliability and uncertainty to
pixel-based rainfall estimates. Also, Worqlul et al. (2014) describe that
for pixel-to-pixel comparison, there is demand for a well-distributed rain-gauge network that would not hamper accurate interpolation.
Elevation and distance from large-scale open water bodies
Habib et al. (2012a) and Haile et al. (2009) for the Nile basin reveal that
elevation affects the performance of SREs. Findings in the latter two studies
signal that performance may possibly also be affected by the presence of Lake
Tana. To assess both influences, we classified the Zambezi basin into three
elevation zones for which the hierarchical cluster “within-groups linkage”
method in the Statistical Product and Service Solutions (SPSS) software was
used (Table 1). Based on Euclidian distance to large-scale open water
bodies, four arbitrary distance zones are defined to group stations (Table 1).
A detailed description of the individual stations, their elevation, and
distance to large-scale open water bodies is provided in Table A1. The
Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER)-based
GDEM of 30 m resolution is a product of METI and NASA obtained from
https://earthexplorer.usgs.gov/ (last access: 4 July 2019) is used to represent elevation
across the Zambezi basin. The Euclidian distance of each rain-gauge location
to large-scale open water bodies is defined in a GIS environment through the
distance calculation algorithm. Large-scale open water bodies are defined as
perennial open water bodies with surface area >700 km2. The
threshold is defined based on knowledge of the water bodies in the Zambezi
basin study area and the detailed fieldwork the authors have conducted over
the years in various other study areas in Africa (such as Lake Tana in
Ethiopia and Lake Naivasha in Kenya). The relationship between lake surface
area and CMORPH bias on 300 water bodies in the study area shows that at a
threshold >700 km2, a signal is induced to warrant the
removal from the analysis of all water bodies with surface area <700 km2.
Elevation and distance from large-scale open water bodies.
Bias-correction schemes evaluated in this study are the spatio-temporal bias
(STB), elevation zone bias (EZ), power transform (PT), distribution
transformation (DT), and quantile mapping based on an empirical
distribution (QME), this by our aim to correct for bias while daily rainfall
variability is preserved. The five schemes are chosen based on merits
documented in the literature (Bhatti et al., 2016; Habib et al., 2014;
Teutschbein and Seibert, 2013; Themeßl et al., 2012; Vernimmen et al.,
2012). We note that findings on the performance of selected bias-correction
schemes in literature do not allow for generalisation, but findings only
apply to the respective study domains (Wehbe et al., 2017; Jiang et al.,
2016; Liu et al., 2015; Haile et al., 2015).
In the procedure to define a time window for bias correction we follow Habib
et al. (2014) and Bhatti et al. (2016), who in the Lake Tana basin (Ethiopia)
carried out a sensitivity analysis of moving time windows and of sequential
time windows. Window lengths between 3 and 31 d were tested. Findings
indicated that a 7 d sequential time window for bias factors is most
appropriate, but only when a minimum of 5 rainy days were recorded within
the 7 d window with a minimum rainfall accumulation depth of 5 mm d-1; otherwise, no bias is estimated (i.e. a value of 1 applies as a bias-correction factor). Preliminary tests in this study on 5 and 7 d moving
and sequential windows on 20 individual stations distributed over the three
elevation zones indicate that the 7 d sequential approach is well
applicable in the Zambezi basin. As such, the approach was selected.
The bias-correction factors are calculated using only rain days (rainfall
≥1 mm d-1). Otherwise in cases where both the gauge and satellite
have zero values (rain gauge (G) =0 and CMORPH (S) =0), correction is not
applied and the SRE value remains 0 mm d-1.
Following Bhatti et al. (2016), we spatially interpolate the bias-correction
factors of the rain gauges so that SREs at all pixels can be corrected. For
interpolation, the universal kriging was applied. Thus, to systematically
correct all CMORPH estimates, station-based bias factors for each time
window are spatially interpolated to arrive at spatial coverage across the
study area and to allow for comparison with other approaches.
Spatio-temporal bias correction (STB)
This linear bias-correction scheme has its origin in the correction of
radar-based precipitation estimates (Tesfagiorgis et al., 2011) and
downscaled precipitation products from climate models. The CMORPH daily
rainfall estimates (S) are multiplied by the bias-correction factor
for the respective sequential time window for individual stations resulting
in corrected CMORPH estimates (STB) in a temporally and spatially coherent
manner (Eq. 1).
STB=S∑t=dt=d-lGi,t∑t=dt=d-lSi,t,
where
G is gauged rainfall (mm d-1),
i is gauge number,
d is day number,
t is Julian day number, and
l is the length of a time window for bias correction.
The advantages of this bias-correction scheme are that it is straightforward
and easy to implement due to its simplicity and modest data requirements.
However, just like any multiplicative shift procedures of bias correction,
STB has challenges in correcting systematic errors in rainfall frequency,
particularly the wet-day frequencies (Lenderink et al., 2007; Teutschbein
and Seibert, 2013).
Elevation zone bias correction (EZ)
The elevation zone bias-correction scheme is proposed in this study and aims at correcting satellite
rainfall for elevation influences. This method groups rain-gauge stations
into three elevation zones based on station elevation. The grouping in this
study is based on the hierarchical clustering technique and expert knowledge
about the study area, but is also guided by recent past studies in the basin
(e.g. World Bank, 2010b; Beilfuss, 2012). Each zone has the same bias-correction factor but differs across the three zones. In the time domain
bias factors vary following the 7 d sequential window approach. The
corrected CMORPH estimates (EZ) at a daily time interval are obtained by
multiplying the uncorrected CMORPH daily rainfall estimates (S) by the daily
bias-correction factor of each elevation zone.
EZ=S∑t=dt=d-l∑i=1i=nGi,t∑t=dt=d-l∑i=1i=nSi,t
The merit of this bias-correction scheme is that the effects of elevation on
rainfall depth are accounted for. SREs often have difficulties in capturing
rainfall events due to orographic effects and thus require elevation-based
correction.
Power transform (PT)
The non-linear PT bias-correction scheme has its origin in studies of
climate change impact (Lafon et al., 2013). Vernimmen et al. (2012) show
that the scheme could be applied to correct satellite rainfall estimates for
use in hydrological modelling and drought monitoring. The PT method uses an
exponential form to adjust the standard deviation of rainfall series. The
daily bias-corrected CMORPH rainfall (PT) for a pixel that overlays a
station is obtained using the equation
PT=aG(i,t)b,
where
G is gauged rainfall (mm d-1),
a is a prefactor such that the mean of the transformed CMORPH values is equal
to the mean of rain-gauge rainfall,
b is a factor calculated such that for each rain gauge the coefficient of
variation (CV) of CMORPH matches the gauge-based counterparts,
i is the gauge number, and
t is the day number.
Optimised values for a and b are obtained through the generalised reduced
gradient algorithm (Fylstra et al., 1998). Values for a and b vary for the
7 d sequential window since correction is at a daily time base. In the case
of utilising the PT method in a certain area (or for a certain period), the
bias-correction factor is spatially interpolated to result in comparable
estimates with other bias-correction schemes. The advantage of the bias
scheme is that it adjusts extreme precipitation values in CMORPH estimates
(Vernimmen et al., 2012). PT has reported limitations in correcting wet-day
frequencies and intensities (Leander et al., 2008; Teutschbein and Seibert,
2013).
Distribution transformation (DT)
DT is an additive bias-correction approach which has its origin in
statistical downscaling of climate model data (Bouwer et al., 2004). The
method transforms a statistical distribution function of daily CMORPH
rainfall estimates to match the distribution by gauged rainfall. The
procedure to match the CMORPH distribution function to gauge rainfall-based
counterparts is described in Eqs. (4)–(8). The principle to matching is
that the difference in the mean value and differences in the variance are
corrected for in the 7 d sequential window. First, the bias-correction
factor for the mean is determined by Eq. (4):
DTu=GuSu.Gu and Su are mean values of 7 d gauge and CMORPH
rainfall estimates.
Secondly, the correction factor for the variance (DTτ) is determined
by the quotient of the 7 d standard deviations, Gτ and
Sτ, for gauge and CMORPH, respectively.
DTτ=GτSτ
Once the correction factors which vary within a 7 d time sequential window
are established, they are then applied to correct all daily CMORPH estimates
(S) through Eq. (6) to obtain a corrected CMORPH rainfall estimate (DT). The
parameters DT and u are developed within a 7 d sequential window, but
correction is at daily time intervals.
DT=(S(it)-Su)DTτ+DTu⋅Sτ
Uncorrected CMORPH daily values are returned if Eq. (6) results in negative
values. The merit of this bias-correction scheme is that it corrects wet-day
frequencies and intensities. The disadvantage of this bias-correction scheme
is that adding the gauge-based mean deviation to the satellite data destroys
the physical consistency of the data. In addition, the method might result
in the generation of too few rain days in the wet season, and sometimes the
mean of daily intensities might be unrealistically corrected (Johnson and
Sharma, 2011; Teutschbein and Seibert, 2013).
Quantile mapping based on an empirical distribution (QME)
This is a quantile-based empirical–statistical error correction method with
its origin in empirical transformation and bias correction of regional
climate model-simulated precipitation (Themeßl et al., 2012). The method
corrects CMORPH precipitation based on empirical cumulative distribution
functions (ecdfs) which are established for each 7 d time window and for each
station. The bias-corrected rainfall (QME) using quantile mapping is expressed
in terms of the empirical cumulative distribution function (ecdf) and its
inverse (ecdf-1). Parameters apply to a 7 d sequential window, but
correction is then at daily time interval with bias spatially averaged for
the entire domain to allow for comparison with other approaches:
QME=ecdfobs-1(ecdfraw(S(it))),
where
ecdfobs is the empirical cumulative distribution function for the gauge-based
observation and ecdfraw is the empirical cumulative distribution function for the
uncorrected CMORPH.
The advantage of this bias scheme is that it corrects quantiles and
preserves the extreme precipitation values (Themeßl et al., 2012).
However, it also has its limitation due to the assumption that both the
observed rainfall and satellite rainfall follow the same proposed distribution, which
may introduce potential new biases.
Rainfall rates and seasons
To assess the performance of SREs for different classes of daily rainfall
rates, five classes are defined which indicate very light (<2.5 mm d-1), light (2.5–5.0 mm d-1), moderate (5.0–10.0 mm d-1),
heavy (10.0–20.0 mm d-1), and very heavy (>20.0 mm d-1) rainfall.
Furthermore, gauged rainfall was divided into wet and dry seasonal periods
to assess the influence of seasonality on performance of bias-correction
schemes. The wet season in the Zambezi basin spans from October to March,
whereas the dry season spans from April to September.
Evaluation of CMORPH estimates
Corrected and uncorrected CMORPH satellite rainfall estimates are evaluated
with reference to rain-gauge rainfall using statistics that measure
systematic differences (i.e. percentage bias and mean absolute error (MAE)),
measures of association (e.g. correlation coefficient and Nash–Sutcliffe
efficiency – NSE), and random differences (e.g. standard deviation of
differences and coefficient of variation) (Haile et al., 2013). Bias is a
measure of how the satellite rainfall estimate deviates from the rain-gauge
rainfall, and the result is normalised by the summation of the gauge values (Rientjes et al., 2013).
A positive value indicates overestimation, whereas a negative value indicates
underestimation. The correlation coefficient (ranging between +1 and -1)
represents the linear dependence of gauge and CMORPH data. MAE is the
arithmetic average of the absolute values of the differences between the
daily gauge and CMORPH satellite rainfall estimates. The MAE is zero if the
rainfall estimates are perfect and increases as discrepancies between the
gauge and satellite become larger. NSE indicates how well the satellite
rainfall matches the rain-gauge observation, and it ranges between -∞ and 1, with NSE =1 meaning a perfect fit (Nash and Sutcliffe, 1970).
Equations (8)–(11) apply.
8bias(%)=∑(S-G)∑G⋅100,9R=∑(G-G‾)(S-S‾)∑(G-G‾)2∑(S-S‾)2,10MAE=1n∑|S-G|,11NSE=∑(G-S)2∑(G-G‾)2,
where
S are satellite rainfall estimates (mm d-1),
S‾ is the mean of the satellite rainfall estimates (mm d-1),
G is rainfall by a rain gauge (mm d-1),
G‾ are mean values of rainfall recorded by a rain gauge (mm d-1), and
n is the number of observations.
Test for differences of mean
To detect significant differences between gauge and satellite rainfall
(corrected and uncorrected) and differences amongst the five bias-correction
methods described in Sect. 3.3, we apply a paired t test and analysis of
variance (ANOVA) tests.
Paired t tests
A paired t test was used to test whether there is a significant difference
between rain-gauge, uncorrected, and bias-corrected CMORPH satellite rainfall
for the 52 rain gauges. Results are summarised for the Upper, Lower, and
Middle Zambezi. The paired t test compares the mean difference of the values
to zero. It depends on the mean difference, the variability of the
differences, and the number of data. The null hypothesis (H0) is that
there is no difference in mean gauge and satellite daily rainfall
(uncorrected and bias corrected). If the p value is less than or equal to 0.05
(5 %), the result is deemed statistically significant, i.e. there is a
significant relationship between the gauge and satellite rainfall (Wilks,
2006).
Analysis of variance (ANOVA) test
The ANOVA test aims to test whether there is a significant difference
amongst the five bias-correction techniques. The null hypothesis (H0) is
that there are no differences amongst the five bias-correction schemes. We
further determined which schemes differ significantly using three post hoc
tests, namely Tukey HSD, Scheffe, and Bonferroni (Brown, 2005; Kucuk et
al., 2018). Results are summarised for the Upper, Lower, and Middle Zambezi.
Taylor diagram
We apply a Taylor diagram to evaluate differences in data sets generated by
respective bias-correction schemes by providing a summary of how well bias-correction results match gauge rainfall in terms of pattern, variability, and
magnitude of the variability. Visual comparison of SRE performance is done
by analysing how well patterns match each other in terms of Pearson's
product-moment correlation coefficient (R), root mean square difference
(E), and the ratio of variances on a 2-D plot (Lo Conti et al., 2014; Taylor,
2001). The reason that each point in the 2-D space of the Taylor
diagram can represent the above three different statistics simultaneously is
that the centered pattern of root mean square difference (Ei) and the
ratio of variances are related by the following:
Ei=σf2+σr2-2σfσrR,
where σf and σr are the standard deviation
of CMORPH and rain-gauge rainfall, respectively.
Development and applications of Taylor diagrams have roots in climate change
studies (Smiatek et al., 2016; Taylor, 2001) but also have frequent
applications in environmental model evaluation studies (Cuvelier et al.,
2007; Dennis et al., 2010; Srivastava et al., 2015). Bhatti et al. (2016)
propose the use of Taylor diagrams for assessing effectiveness of SRE bias-correction schemes. The most effective bias-correction schemes will have
data that lie near a point marked “reference” on the x axis, a relatively high
correlation coefficient, and a low root mean square difference. Bias-correction
schemes matching gauge-based standard deviation have patterns that have the
right amplitude.
Quantile–quantile (q–q) plots
A q–q plot is used to check whether two data sets (in this case gauge vs. CMORPH
rainfall) can fit the same distribution (Wilks, 2006). A q–q plot is a plot
of the quantiles of the first data set against the quantiles of the second
data set. A 45∘ reference line is also plotted. If the satellite
rainfall (corrected and uncorrected) has the same distribution as the rain
gauge, the points should fall approximately along this reference line. The
greater the departure from this reference line, the greater the evidence for
the conclusion that the bias-correction scheme is less effective
(NIST/SEMATECH, 2001).
The main advantage of the q–q plot is that many distributional aspects can
be simultaneously tested. For example, changes in symmetry, and the presence
of outliers, can all be detected from this plot.
Cross-validation of bias correctionSpatial cross-validation
The spatial cross-validation procedure (hold-out sample) applied in this
study involves the withdrawal of 8 in situ stations from the sample of 60
when generating bias-corrected SREs for all pixels across the study area.
Corrected SREs are then compared to the rain-gauge rainfall of the withdrawn
stations to evaluate closeness of match. From the sample of eight we selected two
stations in the <250 m elevation zone, three stations in the 250–950 m
zone, and three stations in the >950 m elevation zone. Stations selected
have elevation close to the average elevation zone value and are centred in
an elevation zone. This left us with 52 stations for applying the bias-correction methods and spatial interpolation. As performance indicators to
evaluate results of cross-validation, we use the percentage bias, MAE,
correlation coefficient, and the estimated ratio which is obtained by
dividing CMORPH rainfall totals and gauge-based rainfall totals for the
1999–2013 period.
Temporal cross-validation
For evaluation of SREs in the time domain we followed Gutjahr and Heinemann (2013) in omitting rainfall (from both gauge and satellite) for the 1998–1999
hydrological year to remain with 14 years for bias correction of SREs. Bias-corrected estimates for the 14 years are then evaluated against estimates
for the 1998–1999 period that served as a reference. For evaluation we use the
percentage bias, MAE, correlation coefficient, and the estimated ratio, which
all are averaged for the Upper, Middle, and Lower Zambezi but also for the
wet and dry seasons.
Results and discussionPerformance of uncorrected CMORPH rainfall
The spatially interpolated values of bias (%) across the Zambezi basin
are shown in Fig. 2. Areas in the central and western parts of the basin
have bias relatively close to zero, suggesting good performance of the
uncorrected CMORPH product. However, relatively large negative bias values
(-20 %) are shown in the Upper Zambezi's high-elevation areas such as
Kabompo and the northern Barotse basin, in the south-eastern part of the basin
such as the Shire River basin, and in the Lower Zambezi's downstream areas
where the Zambezi River enters the Indian Ocean. CMORPH overestimates
rainfall locally in the Kariba, Luanginga, and Luangwa basins by positive bias
values. As such CMORPH estimates do not consistently provide results that
match rain-gauge observations. Since CMORPH estimates have pronounced error
(-10> bias (%) >10), bias needs to be removed
before the product can be applied for hydrological analysis and in water
resource applications. Figure 2 also shows contours for rain-gauge mean
annual precipitation (MAP) in the Zambezi basin, with higher values in the
northern parts of the basin (Kabompo and Luangwa) compared to localised
estimates of MAP such as in the Shire River and Kariba sub-basins.
The spatial variation of bias (%) for gauge vs. uncorrected
CMORPH daily rainfall (1998–2013) for the Zambezi basin. The gauge-based
isohyets for mean annual precipitation (MAP) are shown in blue.
Effects of elevation and distance from large-scale open water bodies on CMORPH bias
Figure 3 shows Taylor diagrams with a comparison of basin lumped estimates
of daily uncorrected time series (1999–2013) of CMORPH and gauge-based
rainfall for the three elevation zones (Fig. 3a) and four distance zones from
large-scale open water bodies (Fig. 3b). Here CMORPH performance is
indicated by means of the root mean square difference (E), correlation
coefficient (R), and standard deviation. Figure 3a and b show that standard
deviations in the elevation zones and the distance zones (except for the
<10 km distance zone) are lower than the reference/rain-gauge
standard deviation which is indicated by the black arc (value of 8.45 mm d-1). The stations in the high-elevation zone (> 950 m) and
long-distance zone (>100 km) reveal lower variability than
stations in lower-elevation and shorter-distance zones. With respect to the
reference line, CMORPH estimates that are lumped for respective elevation
zones and distance to a large water body do not match the standard deviations of
rain-gauge-based counterparts. Figure 3a and b also show that CMORPH
standard deviations that are close to gauge-based rainfall apply to lower-elevation and shorter-distance zones. Based on the Taylor diagrams, the
statistics (R and E) for uncorrected CMORPH show increasing performance for
increasing elevation and increasing distance from large-scale water bodies.
Specifically, stations in the lower-elevation zones (<250 m) have
lower R and higher E than the higher-elevation zones (>950 m). For
shorter-distance zones lower R and higher E are shown than for longer-distance
zones (>100 km). These findings suggest that in general effects
of distance to a large-scale water body are minimal except for distances
<10 km.
(a) Elevation zones.
(b) Distance zones. Time series of rain-gauge (reference) vs. CMORPH estimations, period 1999–2013, for elevation zones (a) and distance zones (b) in the Zambezi basin. The correlation coefficients for the radial line denote the relationship between CMORPH and gauge-based observations. Standard deviations on both the x and y axes show the amount of variance between the two time series. The standard deviation of the CMORPH pattern is proportional to the radial distance from the origin. The angle between symbol and abscissa measures the correlation between CMORPH and rain-gauge observations. The root mean square difference (red contours) between the CMORPH and rain-gauge patterns is proportional to the distance to the point on the x axis identified as “reference”. For details, see Taylor (2001).
Evaluation of bias correctionStandard statistics
Figure 4 shows frequency-based statistics (mean and maximum) on the accuracy of
CMORPH rainfall estimates for each bias-correction method. The ratios of
cumulated estimates (1999–2013) from rain-gauge and CMORPH estimates for the
Lower, Middle, and Upper Zambezi sub-basins are shown. Results show that the
bias of CMORPH moderately reduced for each of the five bias-correction
schemes. However, the effectiveness of the schemes varies spatially, with
the best performance in the Lower and Upper Zambezi sub-basin and relatively poor
performance in the Middle Zambezi sub-basin (see Fig. 4).
Frequency-based statistics (mean, max, and estimated ratio of
gauged sum vs. CMORPH sum for 1999–2013) of corrected CMORPH for the Lower,
Middle, and Upper Zambezi basin.
Judging by the three performance indicators (mean, max, and estimated ratio),
results indicate that the STB bias-correction scheme is consistently effective
in removing CMORPH rainfall bias in the Zambezi basin. STB and PT
effectively adjust for the mean of CMORPH rainfall estimates. Statistics in
Fig. 5 confirm these findings especially for the Upper Zambezi sub-basin,
where the mean of corrected estimates improved by >60 % from
the mean of uncorrected estimates. In addition, PT in the Lower Zambezi, QME
in both the Middle and Upper Zambezi, and STB in the Upper Zambezi were also
effective (improvement by 16 %) in correcting for the highest values in
the rainfall estimates. STB performs better than other bias schemes in
reproducing rainfall for the Lower and Upper Zambezi sub-basin, where the
ratio of gauge total to corrected CMORPH total is close to 1.0.
Percentage bias, mean absolute error (left axis), and Nash–Sutcliffe efficiency (NSE) (right axis) of corrected and uncorrected CMORPH (R-CMORPH)
daily rainfall averaged for the Lower Zambezi, Middle Zambezi, and Upper
Zambezi for the 1999–2013 period.
Figure 5 shows the MAE and percentage bias (% bias)
on the left axis and NSE on the right axis as
measures to evaluate performance of bias-correction schemes in the Zambezi
basin. The effectiveness of the bias correction by all schemes varies over
the different parts of the basin, but is higher in the Lower and Upper
Zambezi than in the Middle Zambezi. The STB, PT, and EZ show improved
performance by exhibiting smaller MAEs compared to the uncorrected CMORPH
(R-CMORPH). A greater improvement is shown for the Middle Zambezi, where the
uncorrected MAE of 1.89 mm d-1 is reduced to 0.86 mm d-1 after
bias correction by the elevation zone bias-correction scheme (EZ). The
signal on improved performance for the Lower and Middle Zambezi as compared
to the Upper Zambezi is also evident for the majority of the bias-correction
techniques. However, relatively large error remains in the MAE.
NSE for STB is larger than 0.8 for all three Zambezi sub-basins. This is
followed by EZ with NSE larger than 0.7 for the three sub-basins. The lowest
NSE is for QME, which is close to 0.65 for all three sub-basins. The best results
for reducing bias (% bias) are obtained by EZ in the Lower Zambezi (%
bias of 0.7 % ∼ absolute bias of 0.10 mm d-1) and
Upper Zambezi (0.22 % ∼0.23 mm d-1), PT in the Lower
and Middle Zambezi (-0.84 % ∼0.18 mm d-1), and STB in
all the basins (<3.70 % ∼0.24 mm d-1). Gao
and Liu (2013) over the Tibetan Plateau assert that EZ is valuable in
correcting systematic biases to provide a more accurate precipitation input
for rainfall–runoff modelling. Significant underestimation for the
uncorrected (-21.16 % ∼0.44 mm d-1) and bias-corrected CMORPH is shown for the Upper Zambezi sub-basin.
Significance testing
Table 2 shows results of statistical tests to assess whether there is a
significant difference (p<0.05) between rain-gauge vs. uncorrected
and bias-corrected CMORPH satellite rainfall for each of the 52 rain-gauge
stations. Results are summarised for the Upper, Middle, and Lower Zambezi and
in the Zambezi basin. The null hypothesis is rejected for PT (Lower
Zambezi), DT (Upper Zambezi), and QME (all three sub-basins) since p<0.05. This means that statistically the above-mentioned bias-correction schemes results deviate from the gauge. The null hypothesis is
accepted for STB and EZ (all three sub-basins), DT (Lower and Upper Zambezi),
and PT (Middle and Upper Zambezi), since p>0.05, showing the
effectiveness of these bias-correction schemes. Compared to uncorrected
satellite rainfall (R-MORPH), results also reveal that the bias-corrected
satellite rainfall is closer to the gauge-based rainfall.
Paired t tests for the Upper, Middle, and Lower Zambezi. The mean
difference is significant at the 0.05 level. Bold shows significant values.
BasinRainfall estimatet valueMean SEp value (0.05)Lower ZambeziR-CMORPH8.950.040.04DT39.860.090.35PT21.080.040.03QME23.990.040.04EZ36.430.030.27STB14.70.040.46Middle ZambeziR-CMORPH3.270.030.001DT41.90.070.24PT26.020.030.14QME18.380.030.00EZ26.600.020.07STB23.60.030.09Upper ZambeziR-CMORPH4.280.080.00DT22.630.140.01PT12.980.070.05QME13.270.070.00EZ13.730.070.14STB13.620.070.08Analysis of variance (ANOVA test)
The ANOVA test is similar to a t test, except that the test was used to
compare mean values from three or more data samples. Results of ANOVA show
that there is a significant (p<0.05) difference in the mean values
of the five bias-correction results across the three sub-basins. This warranted
the running of a post hoc test to determine which schemes differ
significantly. The contingency matrix in Table 3 shows results of the
post hoc test results summarised for the Tukey HSD, Scheffe, and
Bonferroni methods but also for the Upper, Lower, and Middle Zambezi. Table 3
also shows that STB, PT, and EZ are significantly different from
distribution transformation (DT) for the three sub-basins. STB,
the best performing bias-correction scheme identified, is also significantly different from QME and EZ. QME, which has
performed poorly, is significantly different from EZ. Results are important
for further application of the bias-correction schemes for studies such as
flood, drought, and water resource modelling.
ANOVA post hoc tests for the results of the five bias-correction
schemes (p<0.05). The checklist table gives an indication (symbol)
where two bias-correction schemes' results are significantly different from
each other. Where there is no symbol, it means that the schemes' results are
not significantly different. The different symbols represent the Upper,
Middle, and Lower Zambezi basins.
Figure 6 shows the Taylor diagram for time series of rain-gauge (reference)
observations vs. CMORPH bias-correction schemes averaged for the Lower
Zambezi (UZ), Middle Zambezi (MZ), and Upper Zambezi (UZ). Absolute values
used to develop the Taylor diagram are shown in Table A2. The position of
each bias-correction scheme and uncorrected satellite rainfall (R-MORPH) in
Fig. 6 shows how closely the rainfall by uncorrected CMORPH (R-MORPH)
matches rain-gauge observations as well as the effectiveness of each of the bias-correction
schemes. Overall, all bias-correction schemes show intermediate performance
in terms of bias removal. Only the PT and STB for the Lower Zambezi
sub-basin lie on the line of standard deviation (brown dashed arc) and means
the standard deviations of the data for the two bias-correction schemes match
the gauge observations. This also indicates that rainfall variations after
PT and STB bias correction for the Lower Zambezi resemble gauge-based
standard deviation. Note however that STB performs better than EZ, as shown
by the superior correlation coefficient. Compared against the reference line
of the mean standard deviation (8.5 mm d-1), the rainfall standard
deviation for most bias-correction schemes is below this line and as such
exhibits low variability across the Zambezi basin.
Taylor's diagram on rain-gauge (reference) observations and CMORPH
bias-corrected estimates (all five schemes) as averaged for the Lower Zambezi
(LZ), Middle Zambezi (MZ), and Upper Zambezi (UZ) for the period 1999–2013.
The distance of the symbol from point (1, 0) is also a relative measure of
the bias-correction scheme performance. The position of each symbol
appearing on the plot quantifies how closely precipitation estimates by
a respective bias-correction scheme match counterparts by rain gauges. The
dashed blue lines indicate the root mean square difference (mm d-1).
Figure 6 also shows that most of the bias-correction schemes have a standard
deviation range of 6.0 to 8.0 mm d-1. There is a consistent pattern
between the bias-correction schemes that have low R and high RMSE difference,
indicating that these schemes are not effective in bias removal. Overall,
the best-performing bias-correction schemes (STB and EZ) have R>0.6, standard deviation relatively close to the reference point, and RMSE <7 mm d-1. The uncorrected CMORPH (R-MORPH) lies far away from
the marked reference (gauge) point on the x axis, suggesting an intermediate
overall effectiveness of the bias-correction schemes such as STB, EZ, DT, and
PT in removing error as they are relatively closer to the marked reference
point.
The least-performing bias-correction scheme is QME, with relatively large
RSMD (>8 mm d-1) and with low R (<0.49) and
standard deviation (<6.5 mm d-1). Inherent to the methodology
of most of the bias-correction schemes (e.g. QME) is that the spatial pattern of
the SRE does not change, and therefore R for a specific station for daily
precipitation does not necessarily improve. The bias-correction results by
the Taylor diagram in Fig. 6 corroborate findings shown in Figs. 4
and 5 for mean, max, ratio of rainfall totals, and bias as performance
indicators.
q–q plots
Figure 7 shows q–q plots for the Upper, Middle, and Lower Zambezi for gauge
rainfall against uncorrected and bias-corrected CMORPH rainfall. Results
show that STB's q–q plots for bias-corrected CMORPH across the three basins have
the majority of points that fall approximately along the 45∘ reference
line. This means that the STB bias-corrected satellite rainfall has closer
distribution to the rain gauge as compared to the uncorrected CMORPH
counterparts, suggesting the effectiveness of the bias-correction scheme. Other
bias-correction schemes such as QME, EZ, and PT have data points showing a
greater departure from the 45∘ reference line, so performance is less
effective.
q–q plot for gauge vs. satellite rainfall (uncorrected and bias
corrected) for the Upper (top panels), Middle (middle panes), and Lower
(bottom panels) Zambezi.
In some instances, in the Upper, Middle, and Lower Zambezi, bias-corrected values are significantly higher than the corresponding gauge
values, whereas in some instances there is serious underestimation. All the q–q
plots also show that for all the bias-correction schemes, the differences
between gauge and satellite rainfall are smallest for low rainfall rates
(<2.5 mm d-1) and increasing for very heavy rainfall
(>20.0 mm d-1). In more detail, all the bias-correction
schemes show a larger difference for the transition area from low to heavy
rainfall. QME and PT are not in good agreement with the rest of the bias-correction schemes for higher rainfall estimates (40 and 60 mm d-1).
CMORPH rainy days
Occurrence (%) of rainfall rates in the Zambezi basin for each bias-correction scheme is shown in Fig. 8. The highest percentage (80 %–90 %)
is shown for very light rainfall (0.0–2.5 mm d-1). A smaller percentage
is shown for 2.5–5.0 mm d-1, which is the light rainfall class. The smallest
percentage (<5 %) is shown for very heavy rainfall (>20 mm d-1). The CMORPH rainfall corrected with STB, PT, and DT matches
the gauge-based rainfall (%) in the Lower, Middle, and Upper Zambezi,
suggesting good performance. All five bias-correction schemes in the Zambezi
basin generally tend to overestimate very light rainfall (<2.5 mm d-1). There is a small difference for moderate rainy day
classification of 10.0–20.0 mm d-1. For QME in the Middle and Upper
Zambezi, there is overestimation by >80 %. There is
underestimation of rainfall greater than 20 mm d-1.
Percentage occurrence for rainfall rate classes.
Figure 9 gives the bias-correction performance for the different rainy-day
classes. Results of bias removal vary for the Lower, Middle, and Upper
Zambezi. Comparatively, the STB and EZ show effectiveness in bias removal
with average bias corrections of 0.97 % and 3.6 % in the whole basin,
respectively. Results show more effectiveness in reducing the percentage
bias for light (2.5–5.0 mm d-1) and moderate (5.0–10.0 mm d-1)
rainfall compared to the heavy (10.0–20.0 mm d-1) and very heavy
(>20.0 mm d-1) rainfall across the whole basin.
Bias correction (%) for the respective rainfall rate (mm d-1)
classes.
Spatial cross-validation
Table 4 shows the cross-validation results on bias correction for eight rain-gauge stations in the wet and dry seasons. It is evident that CMORPH has a
considerable bias, although this bias is not always consistent for all eight
validation stations. Overall, Mutarara station has the highest positive bias
(overestimation), whereas Makhanga has the highest negative bias
(underestimation) for uncorrected CMORPH. Bias is effectively being removed
by the STB followed by the EZ bias-correction schemes. Bias is more
effectively removed for the wet season than for the dry season. For the dry
season, the STB shows good performance for Mkhanga and Nchalo stations,
whereas good performance is shown for Kabompo and Chichiri stations.
However, the MAE is higher for the wet season than for the dry season.
The correlation coefficient for bias-corrected satellite rainfall is higher for
the wet season than for the dry season.
Cross-validation results for the bias-correction procedure with eight
gauging stations for the dry and wet seasons. Stations lie in an average
elevation zone and are sort of centred in an elevation zone. R-CMORPH is the
uncorrected R-CMOPRPH estimate. DT, PT, QME, EZ, and STB are the bias-corrected rainfall estimate. Bold values indicate best performance. a Zone 1: elevation of <250 m; b zone 2: elevation range of 250–950 m; and c zone 3: elevation >950 m.
Dry season (April–September) Wet season (October–March) StationRainfall estimateBias (%)MAE mm d-1CorrelationEstimated ratioBias (%)MAE (mm d-1)CorrelationMakhangaaR-CMORPH-28.691.230.420.87-21.178.630.43DT-1.370.530.560.99-1.663.960.65PT-5.620.520.540.95-3.54.670.64QME1.980.540.540.95-0.644.860.65EZ2.100.470.551.03-0.114.080.58STB0.770.610.561.040.55.060.62NchaloaR-CMORPH-33.051.130.420.84-25.188.050.38DT-0.230.730.560.96-2.613.650.50PT-4.280.680.540.93-6.485.050.59QME1.900.720.530.81-0.565.290.53EZ0.350.630.540.990.224.40.60STB-0.430.730.580.96-1.235.540.61RukomichibR-CMORPH-23.050.930.420.86-21.186.690.31DT-0.230.900.560.94-6.23.510.60PT-4.280.730.540.93-2.483.620.59QME1.900.750.531.03-0.563.880.54EZ0.350.710.540.990.223.50.60STB-0.430.760.580.94-1.263.330.61MutararabR-CMORPH20.150.240.491.1020.12.340.50DT11.40.180.601.038.71.230.63PT8.40.120.550.914.31.280.68QME5.70.140.631.18.11.40.65EZ-12.80.090.540.951.91.230.69STB4.50.140.531.12.11.330.73MfuwebR-CMORPH40.20.280.450.8535.46.40.48DT2.90.620.530.964.63.90.62PT3.70.220.550.927.95.250.65QME3.90.300.550.935.45.680.64EZ6.10.240.540.923.85.180.56STB5.40.260.650.931.24.660.65KabombocR-CMORPH25.30.700.440.9524.33.80.48DT7.70.320.510.965.73.50.62PT9.20.130.541.108.73.00.64QME2.70.320.621.102.83.20.63EZ5.60.220.530.913.32.70.54STB190.130.621.019.32.70.64ChichiricR-CMORPH34.51.560.470.8-37.34.70.45DT12.20.600.510.855.53.20.51PT9.40.420.521.04-7.84.10.54QME8.40.920.561.05-13.04.10.64EZ-130.610.600.94-9.94.20.60STB3.20.450.630.98-14.32.10.65ChitedzecR-CMORPH41.50.900.471.0642.35.40.48DT16.70.530.540.98-13.23.30.62PT-16.50.440.550.9922.24.50.65QME18.20.410.571.0418.54.30.64EZ11.70.320.571.028.44.60.55STB3.90.230.600.03-8.23.70.65Temporal cross-validation
The same performance indicators in spatial cross-validation are calculated
for the temporal cross-validation. Results are presented in Table 5. The MAE
is higher for the wet season than for the dry season. The difference in
effectiveness in the error removal between the dry and wet seasons is much
larger. STB outperforms both bias-correction methods but does also have
problems correcting the estimated ratios. After the correction, the
correlation coefficient is much improved. The fact that MAE remains
relatively large indicates that errors remain locally large. These values
are almost in the same range as performance indicators obtained from the main
performance assessment period (1999–2013). The estimated ratio shows
improvement for the Middle Zambezi compared to the Lower and Upper Zambezi.
Temporal cross-validation results for the period 1998–1999 for the
wet and dry seasons.
Dry season (April–September) Wet season (October–March) Rainfall estimateBias (%)MAE (mm d-1)CorrelationEstimated ratioBias (%)MAE (mm d-1)CorrelationLower ZambeziR-CMORPH-28.261.100.420.86-22.517.790.37DT-0.610.720.560.96-3.493.710.58PT-4.730.640.540.94-4.154.450.61QME1.930.670.530.93-0.594.680.57EZ0.930.600.541.000.113.990.59STB-0.030.700.570.98-0.664.640.61Middle ZambeziR-CMORPH28.550.410.460.9726.604.180.49DT7.330.370.550.986.332.880.62PT7.100.160.550.986.973.180.66QME4.100.250.601.045.433.430.64EZ-0.370.180.540.933.003.040.60STB9.630.180.601.014.202.900.67Upper ZambeziR-CMORPH381.230.470.932.55.050.465DT14.450.5650.5250.915-3.853.250.565PT-3.550.430.5351.0157.24.30.595QME13.30.6650.5651.0452.754.20.64EZ-0.650.4650.5850.98-0.754.40.575STB3.550.340.6150.505-11.252.90.65Discussion
We present methods to assess the performance of bias-correction schemes for
CMORPH rainfall estimates in the Zambezi River basin. For correction we
applied sequential windows of 7 d that count 5 rain days with a rainfall
threshold of 5 mm d-1. First, we aimed to evaluate whether performance of
CMORPH rainfall is affected by elevation and distance from large-scale open
water bodies. Results in Taylor diagrams show that effects of distances
> 10 km are minimal in this study. For distance <10 km,
results in the same Taylor diagrams show some effect with increased CMORPH
estimation errors, although this is not clearly identifiable by the limited number of
gauging stations at distance <10 km. The low number of gauge
stations constrains clear identification of bias as affected by the short
distance. The low number of stations also constrains detailed analysis of
dependencies of observation time series. To assess bias effects at distances
<10 km we advocate installation of a well-designed network of rain
gauges with stations located at preselected locations that would allow sound
geostatistical analysis of small-scale rainfall variability and spatial
correlation analysis. We refer to Ciach and
Krajewski (2006), who present such analysis for a dense experimental network
of 53 stations. The inter-station distance of the rain gauges in this study
is too large to capture the effect of distance to large-scale open water
bodies on CMORPH rainfall error. For instance, such distance exceeds 350 km
for most of the Upper Zambezi basin. Findings in this study show that effects of
distance would be captured at distances 10–25 km or shorter. Haile et al. (2009) indicate bias effects at short distances (<10 km) for the
Lake Tana, Ethiopia.
The rainfall-elevation bias correction also shows minimal signal. Contrary
to this finding, Romilly and Gebremichael (2011) showed that the accuracy of
CMORPH at a monthly time base is related to elevation for six river basins in
Ethiopia. A similar finding was reported by Haile et al. (2009),
Katiraie-Boroujerdy et al. (2013), and Wu and Zhai (2012), who found that
the performance of CMORPH is affected by elevation. However, Vernimmen et al. (2012) concluded that TRMM Multi-satellite Precipitation Analysis (TMPA)
3B42RT performance was not affected by elevation (R2=0.0001) for
the Jakarta, Bogor, Bandung, Java, Kalimantan, and Sumatra regions (Indonesia).
The study by Gao and Liu (2013) showed that the bias in CMORPH rainfall over
the Tibetan Plateau is affected by elevation. Whilst distances from large-scale open water bodies and elevation have been assessed separately for this
study, Habib et al. (2012a) revealed that both aspects interact in the Nile
basin to produce unique circulation patterns to affect the performance of
SRE.
Secondly, we evaluate the effectiveness of linear/non-linear and time–space-variant/-invariant bias-correction schemes. The bias-correction results by
means of performance indicators such as Taylor diagrams, q–q plots, ANOVA,
and standard statistics such as mean, max, ratio of rainfall totals, and bias
reveal that the STB is the best bias-correction method. This method by its
nature considers correction only for spatially distributed patterns in bias,
commonly known as space-variant/-invariant, and thus forces the estimates to
behave as observations. We did not investigate effects of the applied
sequential windows of 7 d for each bias-correction scheme separately, but
note that other window lengths possibly could yield more favourable results
for bias schemes such as PT, DT, and QME that commonly rely on larger sample
sizes. As alluded to by Habib et al. (2014), correction should improve hydrological
applications by improved rainfall representation. This applies to the Zambezi
basin as well with demands for applications of the product such as for
drought analysis, flood prediction, weather forecasting, and rainfall–runoff
modelling. The study is unique as we assess the importance of space and time
aspects of CMORPH bias for rainfall–runoff modelling in a data-scarce
catchment. Findings in this study on cross-validation and temporal validation
contribute to efforts that aim towards enhancing applications of satellite
rainfall products. The study site is the Zambezi basin, an example of many
world regions that can benefit from satellite-based rainfall products for
resource assessments and monitoring.
Thirdly, an assessment of the performance of bias-correction schemes in
representing different rainfall rates and climate seasonality is presented. Our
findings show that bias is most overestimated for the very light rainfall
(<2.5 mm d-1), which is also the range that shows the best
bias reduction, which in turn is most effective during the wet season.
Results also show that there is underestimation of rainfall larger than 20 mm d-1. The poor performance of correction for the heavy rainfall class
is caused by, sometimes, large mismatch of high rain-gauge values vs. low
CMORPH values. This leads to unrealistically high CMORPH values which remain
poorly corrected by bias schemes. Results are consistent with findings by
Gao and Liu (2013) in the Tibetan Plateau, who found consistent underestimation and
overestimation of occurrence by CMORPH for rainfall rates >10 mm d-1. A study by Zulkafli et al. (2014) in French Guiana and North
Brazil noted that the low sampling frequency and consequently missed
short-duration precipitation events between satellite measurements results
in underestimation, particularly for rainfall >20 mm d-1.
Lastly, spatial and temporal cross-validation reveals the effectiveness of bias-correction schemes. The hold-out sample of eight stations in this work showed
the applicability of different bias-correction methods under different
geographical domains. There is improved performance of satellite rainfall
for the wet season as compared to the dry season based on the correlation coefficient
and MAE. The study by Ines and Hansen (2006) for semi-arid eastern Kenya
showed that multiplicative bias-correction schemes such as STB were
effective in correcting the total of the daily rainfall grouped into
seasons. Our results show that effectiveness in bias removal in the wet
season is higher than in the dry season. This is contrary to Vernimmen et al. (2012), who showed that for the dry season, bias for PT decreased in
the Jakarta, Bogor, Bandung, East Java, and Lampung regions after bias correction
of monthly TMPA 3B42RT precipitation estimates over the period 2003–2008.
Habib (2014) evaluated the sensitivity of STB for the dry and wet seasons and
concluded that the bias-correction factor for CMOPRH shows lower sensitivity
for the wet season as compared to the dry season. Our findings also reveal
that bias factors for all the schemes are more variable in the dry season
than in the wet season and lead to poor performance of the bias-correction
schemes in the dry season.
Conclusions
In this study four conclusions are drawn.
Analysis of gauge and CMORPH rainfall estimates shows that CMORPH performance increases for higher elevation (>950 m) in the Zambezi basin and that CMORPH has the largest mismatch at low elevation. Such analysis was established for rain gauges within elevation zone classes of <250, 250–950, and >950 m. The match between gauge and CMORPH estimates improved at increasing distance to large-scale open water bodies. This was established for rain gauges located within specified distances of 10–50, 50–100, and >100 km to a large-scale open water body. For distances <10 km errors by CMORPH increased, but the small sample size of stations and the weak signal require further study. To assess how bias is affected at short distances to a large-scale water body, a specifically designed and dense gauging network is advocated (see Ciach and Krajewski, 2006) that allows evaluation of small-scale rainfall variability. A detailed analysis of small spatial variability and spatial correlation analysis of rain-gauged observations presumably is a prerequisite before satellite rainfall effects at short distances to a large-scale water body can be assessed.
For each of the five bias-correction methods applied, accuracy of the CMORPH satellite rainfall estimates improved. Assessment through standard statistics, Taylor diagrams, t tests, ANOVA, and q–q plots shows that STB that accounts for space and time variation of bias is found to be more effective in reducing satellite rainfall bias in the Zambezi basin than the rest of the bias-correction schemes. This indicates that the temporal aspect of CMORPH bias is more important than the spatial aspect in the Zambezi basin. Quantile–quantile (q–q) plots for all the bias-correction schemes in general show that bias-corrected rainfall is in good agreement with gauge-based rainfall for low rainfall rates but that high rainfall rates are largely overestimated.
Differences in the mechanisms that drive precipitation throughout the year could result in different biases for each of the seasons, which motivated us to calculate the bias-correction factors for dry and wet seasons separately. As such, CMORPH rainfall time series were divided to assess the influence of seasonality on the performance of bias-correction schemes. Overall, the bias-correction schemes reveal that bias removal is more effective in the wet season than in the dry season.
We assessed whether bias correction varies for different rainfall rates of daily rainfall in the Zambezi basin. There is overestimation of very light rainfall (<2.5 mm d-1) and underestimation of very heavy rainfall (>20 mm d-1) after application of the bias-correction schemes. Bias was more effectively reduced for the very light (<2.5 mm d-1) to moderate (5.0–10.0 mm d-1) rainfall compared to the heavy (10.0–20.0 mm d-1) and very heavy (>20 mm d-1) rainfall. Overall, the STB and EZ more consistently removed bias in all the rainy days' classification compared to the three other bias-correction schemes. Effects of length of sequential window sizes for selected bias-correction schemes are not investigated, but different lengths possibly could yield more favourable results for PT, QME, and DT bias-correction schemes.
Analysis serves to improve the reliability of SRE applications in hydrological
analysis and water resource applications in the Zambezi basin such as in
drought analysis, flood prediction, weather forecasting, and rainfall–runoff
modelling. In follow-up studies, we aim at hydrologic evaluation of bias-corrected CMORPH rainfall estimates at the headwater catchment of the
Zambezi River.
Data availability
Supplementary data consist of shapefiles of the Zambezi study area
boundary, sub-basin boundaries, location of the 60 rain gauges, and lakes
(Fig. 1). Additional material provided is the raster files of uncorrected
CMORPH bias (%) making up Fig. 2. Raster files of daily and yearly
uncorrected CMORPH and gauge rainfall from 1998 to 2013 are also provided.
Rain-gauge stations in the Zambezi sub-basins showing x
and y locations, sub-basin they belong to, year of data availability, % of
missing gaps, station elevation, and distance from large-scale water bodies.
Bias-correction scheme-based Taylor diagram performance
indicators (correlation coefficients, standard deviations, and RMSE) of rain-gauge (reference) vs. CMORPH estimations (corrected and uncorrected), period
1998–2013, for the Lower, Middle, and Upper Zambezi basin.
The supplement related to this article is available online at: https://doi.org/10.5194/hess-23-2915-2019-supplement.
Author contributions
WG was responsible for the development of bias-correction
schemes in the Zambezi basin and the research approach. THMR and
ATH were responsible for synthesising the methodology and made
large contributions to the manuscript write-up. HM provided
some of the rain-gauge data and related findings of this study to previous
work in the Zambezi basin. RP assisted in interpretation of bias-correction results.
Competing interests
The authors declare that they have no conflict of interest.
Acknowledgements
The study was supported by WaterNet and the University of Twente's ITC Faculty.
The authors acknowledge the University of Zimbabwe's Civil Engineering
Department for the platform to carry out this research.
Financial support
This research has been supported by WaterNet (DANIDA Transboundary PhD Research in the Zambezi basin).
Review statement
This paper was edited by Alberto Guadagnini and reviewed by Rodolfo Nóbrega and two anonymous referees.