the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Performance of biascorrection schemes for CMORPH rainfall estimates in the Zambezi River basin
Webster Gumindoga
Tom H. M. Rientjes
Alemseged Tamiru Haile
Hodson Makurira
Paolo Reggiani
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 largescale open water bodies on bias for Climate Prediction CenterMORPHing (CMORPH) rainfall estimates in the Zambezi basin. The effectiveness of five linear/nonlinear and time–spacevariant/invariant biascorrection schemes was evaluated for daily rainfall estimates and climatic seasonality. The schemes used are spatiotemporal 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 biascorrection schemes spatial and temporal crossvalidation 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 biascorrection 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 crossvalidation approach revealed that most biascorrection schemes removed bias by > 28 %. The temporal crossvalidation approach showed effectiveness of the biascorrection schemes. Taylor diagrams show that station elevation has an influence on CMORPH performance. Effects of distance > 10 km from largescale 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.
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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 satellitebased, multisensor approaches (Najmaddin et al., 2017; ValdésPineda et al., 2016). In this study the focus is on satellite rainfall estimates (SREs) to improve reliability in spatiotemporal rainfall representation.
Studies in satellitebased 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 raingauge 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 CenterMORPHing (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 spacevariant/invariant. Approaches that correct for spatially averaged bias have roots in radar rainfall estimation (Seo et al., 1999), but are unsuitable for largescale basins (> 5000 km^{2}) where rainfall may substantially vary in space (Habib et al., 2014). Studies by Müller and Thompson (2013) in Nepal concluded that spacevariant correction schemes are more effective in reducing bias for CMORPH and TRMM than spaceinvariant 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.
Biascorrection 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. Nonmultiplicative biascorrection schemes preserve the timing of rainfall within a season (Fang et al., 2015; Hempel et al., 2013). Studies that have applied nonlinear biascorrection 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 overadjust 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 largescale 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 TRMM3B42 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 biascorrected 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 semiarid Zambezi basin are limited.
In this study we use daily CMORPH and raingauge data for the Upper, Middle, and Lower Zambezi basins to (1) evaluate whether performance of CMORPH rainfall is affected by elevation and distance from largescale open water bodies, (2) evaluate the effectiveness of linear/nonlinear and time–spacevariant/invariant biascorrection schemes, and (3) assess the performance of biascorrection 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.
The Zambezi River is the fourthlongest river (∼2574 km) in Africa, with a basin area of ∼1 390 000 km^{2} (∼4 % of the African continent). The river drains into the Indian Ocean and has a mean annual discharge of 4134 m^{3} 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 largescale open water bodies and, as such, makes the basin well suited for this study. The basin is divided into three subbasins, 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).
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). Largescale 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 landcover 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, semiarid, and arid regions dominated by seasonal rainfall patterns associated with the InterTropical 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 southeastern 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 northeastern 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 subbasin 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.
3.1 Rainfall data
3.1.1 CMORPH
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). Halfhourly estimates were aggregated to daily totals to match the observation interval of gaugebased daily rainfall.
3.1.2 Raingauge 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 standardtype 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 largescale open water bodies range between 5 and 615 km. This allows us to evaluate whether elevation and distance to largescale open water bodies affect CMORPH performance.
3.1.3 Comparison of CMORPH and gauge rainfall
In this study, we compare gauge rainfall at point scale to CMORPH satellitederived rainfall estimates at pixel scale (pointtopixel). 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 pointtopixel comparisons in African basins. We apply pointtopixel comparison to rule out any aspect of interpolation error as a consequence of the lowdensity 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 pixelbased rainfall estimates. Also, Worqlul et al. (2014) describe that for pixeltopixel comparison, there is demand for a welldistributed raingauge network that would not hamper accurate interpolation.
3.2 Elevation and distance from largescale 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 “withingroups linkage” method in the Statistical Product and Service Solutions (SPSS) software was used (Table 1). Based on Euclidian distance to largescale 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 largescale 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 raingauge location to largescale open water bodies is defined in a GIS environment through the distance calculation algorithm. Largescale open water bodies are defined as perennial open water bodies with surface area > 700 km^{2}. 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 km^{2}, a signal is induced to warrant the removal from the analysis of all water bodies with surface area < 700 km^{2}.
3.3 Biascorrection schemes
Biascorrection schemes evaluated in this study are the spatiotemporal 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 biascorrection 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 biascorrection 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 biascorrection 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 biascorrection 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, stationbased 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.
3.3.1 Spatiotemporal bias correction (STB)
This linear biascorrection scheme has its origin in the correction of radarbased precipitation estimates (Tesfagiorgis et al., 2011) and downscaled precipitation products from climate models. The CMORPH daily rainfall estimates (S) are multiplied by the biascorrection 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).
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 biascorrection 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 wetday frequencies (Lenderink et al., 2007; Teutschbein and Seibert, 2013).
3.3.2 Elevation zone bias correction (EZ)
The elevation zone biascorrection scheme is proposed in this study and aims at correcting satellite rainfall for elevation influences. This method groups raingauge 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 biascorrection 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 biascorrection factor of each elevation zone.
The merit of this biascorrection 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 elevationbased correction.
3.3.3 Power transform (PT)
The nonlinear PT biascorrection 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 biascorrected CMORPH rainfall (PT) for a pixel that overlays a station is obtained using the equation
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 raingauge rainfall, b is a factor calculated such that for each rain gauge the coefficient of variation (CV) of CMORPH matches the gaugebased 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 biascorrection factor is spatially interpolated to result in comparable estimates with other biascorrection 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 wetday frequencies and intensities (Leander et al., 2008; Teutschbein and Seibert, 2013).
3.3.4 Distribution transformation (DT)
DT is an additive biascorrection 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 rainfallbased 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 biascorrection factor for the mean is determined by Eq. (4):
G_{u} and S_{u} 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.
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.
Uncorrected CMORPH daily values are returned if Eq. (6) results in negative values. The merit of this biascorrection scheme is that it corrects wetday frequencies and intensities. The disadvantage of this biascorrection scheme is that adding the gaugebased 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).
3.3.5 Quantile mapping based on an empirical distribution (QME)
This is a quantilebased empirical–statistical error correction method with its origin in empirical transformation and bias correction of regional climate modelsimulated 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 biascorrected 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:
where ecdf_{obs} is the empirical cumulative distribution function for the gaugebased observation and ecdf_{raw} 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.
3.4 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 biascorrection schemes. The wet season in the Zambezi basin spans from October to March, whereas the dry season spans from April to September.
3.5 Evaluation of CMORPH estimates
Corrected and uncorrected CMORPH satellite rainfall estimates are evaluated with reference to raingauge 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 raingauge 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 raingauge observation, and it ranges between −∞ and 1, with NSE =1 meaning a perfect fit (Nash and Sutcliffe, 1970).
Equations (8)–(11) apply.
where S are satellite rainfall estimates (mm d^{−1}), $\stackrel{\mathrm{\u203e}}{S}$ is the mean of the satellite rainfall estimates (mm d^{−1}), G is rainfall by a rain gauge (mm d^{−1}), $\stackrel{\mathrm{\u203e}}{G}$ are mean values of rainfall recorded by a rain gauge (mm d^{−1}), and n is the number of observations.
3.6 Test for differences of mean
To detect significant differences between gauge and satellite rainfall (corrected and uncorrected) and differences amongst the five biascorrection methods described in Sect. 3.3, we apply a paired t test and analysis of variance (ANOVA) tests.
3.6.1 Paired t tests
A paired t test was used to test whether there is a significant difference between raingauge, uncorrected, and biascorrected 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 (H_{0}) 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).
3.6.2 Analysis of variance (ANOVA) test
The ANOVA test aims to test whether there is a significant difference amongst the five biascorrection techniques. The null hypothesis (H_{0}) is that there are no differences amongst the five biascorrection 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.
3.7 Taylor diagram
We apply a Taylor diagram to evaluate differences in data sets generated by respective biascorrection schemes by providing a summary of how well biascorrection 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 productmoment correlation coefficient (R), root mean square difference (E), and the ratio of variances on a 2D plot (Lo Conti et al., 2014; Taylor, 2001). The reason that each point in the 2D space of the Taylor diagram can represent the above three different statistics simultaneously is that the centered pattern of root mean square difference (E^{i}) and the ratio of variances are related by the following:
where σ_{f} and σ_{r} are the standard deviation of CMORPH and raingauge 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 biascorrection schemes. The most effective biascorrection 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. Biascorrection schemes matching gaugebased standard deviation have patterns that have the right amplitude.
3.8 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 biascorrection 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.
3.9 Crossvalidation of bias correction
3.9.1 Spatial crossvalidation
The spatial crossvalidation procedure (holdout sample) applied in this study involves the withdrawal of 8 in situ stations from the sample of 60 when generating biascorrected SREs for all pixels across the study area. Corrected SREs are then compared to the raingauge 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 biascorrection methods and spatial interpolation. As performance indicators to evaluate results of crossvalidation, we use the percentage bias, MAE, correlation coefficient, and the estimated ratio which is obtained by dividing CMORPH rainfall totals and gaugebased rainfall totals for the 1999–2013 period.
3.9.2 Temporal crossvalidation
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. Biascorrected 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.
4.1 Performance 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 highelevation areas such as Kabompo and the northern Barotse basin, in the southeastern 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 raingauge 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 raingauge 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 subbasins.
4.2 Effects of elevation and distance from largescale 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 gaugebased rainfall for the three elevation zones (Fig. 3a) and four distance zones from largescale 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/raingauge standard deviation which is indicated by the black arc (value of 8.45 mm d^{−1}). The stations in the highelevation zone (> 950 m) and longdistance zone (> 100 km) reveal lower variability than stations in lowerelevation and shorterdistance 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 raingaugebased counterparts. Figure 3a and b also show that CMORPH standard deviations that are close to gaugebased rainfall apply to lowerelevation and shorterdistance zones. Based on the Taylor diagrams, the statistics (R and E) for uncorrected CMORPH show increasing performance for increasing elevation and increasing distance from largescale water bodies. Specifically, stations in the lowerelevation zones (< 250 m) have lower R and higher E than the higherelevation zones (> 950 m). For shorterdistance zones lower R and higher E are shown than for longerdistance zones (> 100 km). These findings suggest that in general effects of distance to a largescale water body are minimal except for distances < 10 km.
4.3 Evaluation of bias correction
4.3.1 Standard statistics
Figure 4 shows frequencybased statistics (mean and maximum) on the accuracy of CMORPH rainfall estimates for each biascorrection method. The ratios of cumulated estimates (1999–2013) from raingauge and CMORPH estimates for the Lower, Middle, and Upper Zambezi subbasins are shown. Results show that the bias of CMORPH moderately reduced for each of the five biascorrection schemes. However, the effectiveness of the schemes varies spatially, with the best performance in the Lower and Upper Zambezi subbasin and relatively poor performance in the Middle Zambezi subbasin (see Fig. 4).
Judging by the three performance indicators (mean, max, and estimated ratio), results indicate that the STB biascorrection 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 subbasin, 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 subbasin, where the ratio of gauge total to corrected CMORPH total is close to 1.0.
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 biascorrection 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 (RCMORPH). 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 biascorrection 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 biascorrection techniques. However, relatively large error remains in the MAE.
NSE for STB is larger than 0.8 for all three Zambezi subbasins. This is followed by EZ with NSE larger than 0.7 for the three subbasins. The lowest NSE is for QME, which is close to 0.65 for all three subbasins. 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 biascorrected CMORPH is shown for the Upper Zambezi subbasin.
4.3.2 Significance testing
Table 2 shows results of statistical tests to assess whether there is a significant difference (p < 0.05) between raingauge vs. uncorrected and biascorrected CMORPH satellite rainfall for each of the 52 raingauge 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 subbasins) since p < 0.05. This means that statistically the abovementioned biascorrection schemes results deviate from the gauge. The null hypothesis is accepted for STB and EZ (all three subbasins), DT (Lower and Upper Zambezi), and PT (Middle and Upper Zambezi), since p > 0.05, showing the effectiveness of these biascorrection schemes. Compared to uncorrected satellite rainfall (RMORPH), results also reveal that the biascorrected satellite rainfall is closer to the gaugebased rainfall.
4.3.3 Analysis 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 biascorrection results across the three subbasins. 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 subbasins. STB, the best performing biascorrection 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 biascorrection schemes for studies such as flood, drought, and water resource modelling.
4.3.4 Taylor diagrams
Figure 6 shows the Taylor diagram for time series of raingauge (reference) observations vs. CMORPH biascorrection 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 biascorrection scheme and uncorrected satellite rainfall (RMORPH) in Fig. 6 shows how closely the rainfall by uncorrected CMORPH (RMORPH) matches raingauge observations as well as the effectiveness of each of the biascorrection schemes. Overall, all biascorrection schemes show intermediate performance in terms of bias removal. Only the PT and STB for the Lower Zambezi subbasin lie on the line of standard deviation (brown dashed arc) and means the standard deviations of the data for the two biascorrection schemes match the gauge observations. This also indicates that rainfall variations after PT and STB bias correction for the Lower Zambezi resemble gaugebased 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 biascorrection schemes is below this line and as such exhibits low variability across the Zambezi basin.
Figure 6 also shows that most of the biascorrection schemes have a standard deviation range of 6.0 to 8.0 mm d^{−1}. There is a consistent pattern between the biascorrection schemes that have low R and high RMSE difference, indicating that these schemes are not effective in bias removal. Overall, the bestperforming biascorrection 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 (RMORPH) lies far away from the marked reference (gauge) point on the x axis, suggesting an intermediate overall effectiveness of the biascorrection schemes such as STB, EZ, DT, and PT in removing error as they are relatively closer to the marked reference point.
The leastperforming biascorrection 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 biascorrection 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 biascorrection 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.
4.3.5 q–q plots
Figure 7 shows q–q plots for the Upper, Middle, and Lower Zambezi for gauge rainfall against uncorrected and biascorrected CMORPH rainfall. Results show that STB's q–q plots for biascorrected CMORPH across the three basins have the majority of points that fall approximately along the 45^{∘} reference line. This means that the STB biascorrected satellite rainfall has closer distribution to the rain gauge as compared to the uncorrected CMORPH counterparts, suggesting the effectiveness of the biascorrection scheme. Other biascorrection schemes such as QME, EZ, and PT have data points showing a greater departure from the 45^{∘} reference line, so performance is less effective.
In some instances, in the Upper, Middle, and Lower Zambezi, biascorrected 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 biascorrection 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 biascorrection 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 biascorrection schemes for higher rainfall estimates (40 and 60 mm d^{−1}).
4.3.6 CMORPH rainy days
Occurrence (%) of rainfall rates in the Zambezi basin for each biascorrection 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 gaugebased rainfall (%) in the Lower, Middle, and Upper Zambezi, suggesting good performance. All five biascorrection 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}.
Figure 9 gives the biascorrection performance for the different rainyday 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.
4.4 Spatial crossvalidation
Table 4 shows the crossvalidation results on bias correction for eight raingauge 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 biascorrection 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 biascorrected satellite rainfall is higher for the wet season than for the dry season.
4.5 Temporal crossvalidation
The same performance indicators in spatial crossvalidation are calculated for the temporal crossvalidation. 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 biascorrection 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.
We present methods to assess the performance of biascorrection 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 largescale 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 welldesigned network of rain gauges with stations located at preselected locations that would allow sound geostatistical analysis of smallscale 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 interstation distance of the rain gauges in this study is too large to capture the effect of distance to largescale 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 rainfallelevation 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), KatiraieBoroujerdy 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 Multisatellite Precipitation Analysis (TMPA) 3B42RT performance was not affected by elevation (R^{2}=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 largescale 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/nonlinear and time–spacevariant/invariant biascorrection schemes. The biascorrection 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 biascorrection method. This method by its nature considers correction only for spatially distributed patterns in bias, commonly known as spacevariant/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 biascorrection 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 datascarce catchment. Findings in this study on crossvalidation 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 satellitebased rainfall products for resource assessments and monitoring.
Thirdly, an assessment of the performance of biascorrection 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 raingauge 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 shortduration precipitation events between satellite measurements results in underestimation, particularly for rainfall > 20 mm d^{−1}.
Lastly, spatial and temporal crossvalidation reveals the effectiveness of biascorrection schemes. The holdout sample of eight stations in this work showed the applicability of different biascorrection 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 semiarid eastern Kenya showed that multiplicative biascorrection 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 biascorrection 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 biascorrection schemes in the dry season.
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 largescale open water bodies. This was established for rain gauges located within specified distances of 10–50, 50–100, and > 100 km to a largescale 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 largescale water body, a specifically designed and dense gauging network is advocated (see Ciach and Krajewski, 2006) that allows evaluation of smallscale rainfall variability. A detailed analysis of small spatial variability and spatial correlation analysis of raingauged observations presumably is a prerequisite before satellite rainfall effects at short distances to a largescale water body can be assessed.

For each of the five biascorrection 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 biascorrection 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 biascorrection schemes in general show that biascorrected rainfall is in good agreement with gaugebased 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 biascorrection 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 biascorrection schemes. Overall, the biascorrection 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 biascorrection 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 biascorrection schemes. Effects of length of sequential window sizes for selected biascorrection schemes are not investigated, but different lengths possibly could yield more favourable results for PT, QME, and DT biascorrection 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 followup studies, we aim at hydrologic evaluation of biascorrected CMORPH rainfall estimates at the headwater catchment of the Zambezi River.
Supplementary data consist of shapefiles of the Zambezi study area boundary, subbasin 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.
The supplement related to this article is available online at: https://doi.org/10.5194/hess2329152019supplement.
WG was responsible for the development of biascorrection 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 writeup. HM provided some of the raingauge data and related findings of this study to previous work in the Zambezi basin. RP assisted in interpretation of biascorrection results.
The authors declare that they have no conflict of interest.
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.
This research has been supported by WaterNet (DANIDA Transboundary PhD Research in the Zambezi basin).
This paper was edited by Alberto Guadagnini and reviewed by Rodolfo Nóbrega and two anonymous referees.
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spatiotemporaland newly developed
elevation zonebias schemes proved more effective in removing CMORPH bias.