Estimating areal rainfall over Lake Victoria and its basin using ground-based and satellite data

Journal of Hydrology 464–465 (2012) 401–411

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Estimating areal rainfall over Lake Victoria and its basin using ground-based and satellite data Michael Kizza a,b,⇑, Ida Westerberg b,c, Allan Rodhe b, Henry K. Ntale a a

School of Engineering, Makerere University, PO Box 7062, Kampala, Uganda Department of Earth Sciences, Uppsala University, Villavägen 16, SE-752 36 Uppsala, Sweden c IVL Swedish Environmental Research Institute, PO Box 21060, SE-100 31 Stockholm, Sweden b

a r t i c l e

i n f o

Article history: Received 24 November 2010 Received in revised form 31 May 2012 Accepted 16 July 2012 Available online 26 July 2012 This manuscript was handled by Andreas Bardossy, Editor-in-Chief, with the assistance of Harald Kunstmann, Associate Editor Keywords: Lake Victoria Precipitation Spatial interpolation Inverse distance weighting Universal kriging TRMM 3B43

a b s t r a c t A gridded monthly rainfall dataset having a spatial resolution of 2 km and covering the period 1960–2004 was derived for the Lake Victoria basin. The lake and its basin support more than 30 million people and also contribute substantially to the River Nile flow. The major challenge in the estimation of the Lake Victoria water balance is the estimation of the rainfall over the lake, which is further complicated by the varying quality and spatial coverage of rain-gauge data in the basin. In this study, these problems were addressed by using rain-gauge data for 315 stations around the basin and satellite-derived precipitation data from two products to derive a monthly precipitation dataset for the entire basin, including the lake. First, the rain-gauge data were quality controlled. Thereafter short gaps were filled in the daily data series which resulted in 9429 additional months of data. Two spatial interpolation methods were used for generating the gridded rainfall dataset and the universal kriging method performed slightly better than the inverse distance weighting method. The enhancement of rainfall over the lake surface was addressed by estimating a relationship between rain-gauge and satellite data. Two satellite rainfall products, TRMM 3B43 and PERSIANN were compared to the interpolated monthly rain-gauge data for the land part of the basin. The bias in the TRMM 3B43 rainfall estimates was higher than the bias for PERSIANN but its correlation was higher with a better representation of the intra-annual variability. The TRMM 3B43 product showed an enhancement of lake rainfall over basin rainfall of 33% while the PERSIANN product gave a much higher enhancement of up to 85%. Ó 2012 Elsevier B.V. All rights reserved.

1. Introduction With a surface area of 68,800 km2, Lake Victoria is the largest freshwater lake in the tropics and the second largest in the world. The lake and its basin support over 30 million people, who directly or indirectly depend on it for their livelihoods, drawing on services like fishing, transport, agriculture, water supply, tourism and hydropower (Ntiba et al., 2001). The lake system, including the wetland and the rivers that flow into it, is the largest inland water sanctuary in East Africa. Being one of the sources of the Nile, the lake is a major supplier for the water needs of Sudan and Egypt (Sutcliffe and Parks, 1999). About 80% of the input into the lake is rainfall over its surface, leading some researchers to describe it as ‘atmosphere controlled’ (Flohn and Burkhardt, 1985; Tate et al., 2004; Yin and Nicholson, 2002). This essentially means that the variability of rainfall over the lake plays a key role ⇑ Corresponding author at: School of Engineering, Makerere University, PO Box 7062, Kampala, Uganda. Tel.: +256 77 2614580; fax: +256 41 4530686. E-mail addresses: [email protected], [email protected] (M. Kizza). URL: http://www.geo.uu.se/michael/lake_victoria_dataset (M. Kizza). 0022-1694/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jhydrol.2012.07.024

in the fluctuation of the lake levels. Evaporation, which is the largest output, is considered to have less inter-annual variation and, therefore, a smaller effect on lake level fluctuations (Sutcliffe and Parks, 1999). In addition, evaporation is difficult to estimate as available data are usually fragmented and unreliable. Historically, the lake levels have exhibited large and rapid changes in response to rainfall anomalies over the last century (Conway, 2002; Fraedrich, 1972; Mistry and Conway, 2003; Yin and Nicholson, 2002). There are three major problems related to the assessment of spatial variability of rainfall in the Lake Victoria basin. The first is the differences in the spatial distribution of rainfall stations around the lake (Fig. 1). The second is that the data quality varies considerably depending on data source and period analysed, with frequent gaps in the series varying from days to several years. The third problem is that there are hardly any long-term rainfall stations on the lake surface which makes the estimation of the lake areal rainfall based only on rain-gauges impossible. The earliest data collection expeditions in the basin were carried out at the turn of the 20th century, but more regular collection

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of rainfall and other hydro-meteorological data started in the mid-1920s as part of the preparations for the construction of the Owen Falls dam. Following the sudden rise in water level between 1961 and 1964, the hydrometerological survey project was set up under WMO and intensified the collection of data in the lake and its basin (de Baulny and Baker, 1970; WMO, 1982). This monitoring network was later handed over to the respective countries to manage. As a result there have been more than 1000 documented rainfall gauging stations in the Lake Victoria basin over time. While the distribution of the stations is not uniform in time and space around the basin, they, nonetheless, provide a sample that is representative for analysing the spatial rainfall variability within most parts of the basin. Estimation of rainfall over Lake Victoria has been a subject of intense investigation due to the lake’s abrupt water-level variations and anomalous hydrologic fluctuations (de Baulny and Baker, 1970; Fraedrich, 1972; Mistry and Conway, 2003; Tate et al., 2004; WMO, 1982; Yin and Nicholson, 2002). A standard scheme was proposed by the WMO (1982) hydro-meterological survey project that relied on eight stations around the lake. These stations were used by de Baulny and Baker (1970) to derive a monthly rainfall series for the period 1925–1969. Kite (1981) pointed out that neither the lake’s water balance for the 1950s, nor the lake’s abrupt rise in the early 1960s could be adequately simulated using a simple water-balance model or a lake-routing model. The discrepancy was particularly large for the 1961–1964 period, when the simulated lake water level rise of 151 mm/year was far smaller than the observed rise of 505 mm/year over the 4-year period. When Kite (1981) increased the lake rainfall values of de Baulny and Baker (1970) by 25–30%, he could accurately reconstruct Lake Victoria’s fluctuations prior to the 1970s using a routing model. By increasing the lake rainfall data by 25% in 1977 and 1978 and by 30% in 1979, he could also reproduce the lake’s rise during these years. While the selection of the multiplication factors is subjective, later studies also support this idea of an enhancement of rainfall over the lake compared to the surrounding land (Ba and Nicholson, 1998; Datta, 1981; Flohn, 1987; Fraedrich, 1972; Piper et al., 1986). Rainfall enhancement is produced by a nocturnal lake-breeze circulation that produces convergence over the center of the lake (Ba and Nicholson, 1998). The convergence effect is further enhanced by the thermal instability of the boundary layer over the lake, which is a result of air temperatures above the lake being approximately 3 °C lower than the lake surface itself. Consequently, large and intense cumulonimbus clusters develop over the lake at night. The nocturnal circulation produces about 50% of the rainfall over the land and enhances rainfall over the lake considerably, compared to that over its catchment (Fraedrich, 1972). Observations on islands in the lake showed that rainfall amounts can be in excess of 2000 mm/year compared to an average of about 1200 mm/year over the land. There is therefore no doubt that land-based rain gauges are inadequate for direct estimation of lake rainfall. Therefore, to produce reliable areal rainfall estimates over the lake as an input to water-balance studies, it is necessary to account for the rainfall enhancement over the lake. Remotely sensed precipitation data provide a direct means to assess the lake rainfall. The aim of this study was to derive a spatially detailed gridded monthly rainfall dataset for the lake basin with an improved estimate of the lake surface rainfall through the use of satellite-derived precipitation data. A systematic three-step approach was used to address the three problems identified above; (1) data quality control of rainfall from land gauging stations, (2) spatial interpolation, and (3) estimation of lake rainfall using two remotely sensed precipitation datasets. This dataset is intended as an input to future hydrological studies aimed at water resources management in the basin.

2. Study area and data 2.1. The Lake Victoria basin Lake Victoria is located between latitudes 0°200 N–3°S and longitudes 31°400 E–34°530 E (Fig. 1). The lake basin area is 194,000 km2 and the lake surface area is about 68,800 km2 or 35% of the basin. The lake surface is shared between Kenya (6%), Uganda (43%) and Tanzania (51%) while its basin also includes parts of Burundi and Rwanda. The altitude of the lake surface is about 1,135 m above mean sea level (a.s.l.). The basin consists of a series of stepped plateaus with an average elevation of 2,700 m a.s.l. but rising to 4,000 m a.s.l. or more in the highland areas. The lake is relatively shallow with an average depth of 45 m and maximum depth of 92 m. The main river flowing into the lake is the Kagera which, together with four other tributaries (Nzoia, Yala, and Sondu and Awach-Kaboun) contribute about 50% of the inflow (about 11.5 km3/year) though there are more than 20 rivers that drain into the lake.

2.2. Rainfall regime The general climate of the Lake Victoria basin ranges from a modified equatorial type with substantial rainfall occurring throughout the year, particularly over the lake and its vicinity, to a semiarid type characterised by intermittent droughts over some areas located even within short distances from the lake shore (Anyah et al., 2006; Nicholson, 1996). The diurnal, seasonal and interannual variability of the basin climate (and East Africa generally) results from a complex interaction between the Inter-Tropical Convergence Zone (ITCZ), El Nino/Southern Oscillation (ENSO), Quasi-Biennial Oscillation (QBO), large-scale monsoonal winds, meso-scale circulations and extra-tropical weather systems (Mutai et al., 1998; Nicholson and Yin, 2002; Ogallo et al., 1988). The wind and pressure patterns that govern the region’s climate include three principal air streams namely; the Congo airstream with westerly and south-westerly winds, the southeast monsoon and the northeast monsoon (Nicholson, 1996; Trewartha, 1981). The Congo air mass is humid, thermally unstable and, therefore associated with rainfall. The monsoons are thermally stable, and associated with subsiding air, and are therefore relatively dry, which partly accounts for the relatively arid conditions in much of East Africa. The three airstreams are separated by two convergence zones; the ITCZ which separates the monsoons and the Congo air boundary which separates the Indian Ocean easterlies and Atlantic Ocean westerlies (Trewartha, 1981). A third convergence zone aloft separates the dry, stable northerly flow from Sahara and the moister southerly flow (Nicholson, 1996). The seasonal climate patterns follow the seasonal north–south movement of the ITCZ which lags the seasonal migration of the sun by about 1.5 months and results in a bimodal rainfall distribution; the March–May rainfall period (long rains) and the October– December rainfall period (short rains). The northeast (NE) and southeast (SE) monsoon winds also modify the seasonal climate of East Africa (Mukabana and Pielke, 1996). The NE monsoon air stream occurs when the sun is south of the equator (October– March) and, after traversing over Egypt and Sudan, is warm and dry. On the other hand, the SE monsoon air stream occurs when the sun is north of the equator (April–October). It is cool and moist after picking up maritime moisture from the Indian Ocean and is responsible for large-scale precipitation over most of East Africa. The QBO is a quasi-periodic oscillation of the equatorial zonal wind between easterlies and westerlies in the tropical stratosphere with a mean period of 28 months (Indeje and Semazzi, 2000). A strong relationship has been demonstrated between QBO and seasonal

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Fig. 1. Lake Victoria basin and the location of the rainfall stations used in this study. The numbers 1–20 are the sub-basins whose mean areal rainfall are reported in Table 4.

rainfall in East Africa during the boreal summer (June–August). The humid Congo air mass also significantly boosts convection and overall rainfall amounts received over the western and north-western parts of the lake (Nicholson, 1996). Inter-annual variability corresponds to the ENSO variability. El Niño years are usually associated with above normal rainfall amounts in the short rainfall season in most of the region (Indeje et al., 2000). However arguments remain with regard to the relative importance of Indian Ocean versus Pacific Ocean forcing of East African rainfall. 2.3. Data 2.3.1. Ground-based precipitation data Rainfall in the lake basin has been recorded since the begining of the twentieth century using manual rain gauges and, more recently, some automatic recording gauges. The rain gauge data used in this study were collected as daily or monthly aggregations from various sources including the hydro-meteorological database of the World Meteorological Organisation (WMO, 1982), meteorological departments in Kenya, Tanzania and Uganda as well as from our correspondence with other researchers in the region. From these sources, a dataset of over 1000 daily rainfall stations was created. Out of these, 362 stations having at least 2 years of record were selected for further analysis. The evolution of the number of stations in the basin with time shows that from just a few stations at the turn of the twentieth century, the number grew to over 400 at the peak in the mid 1970s and was followed by a general decline since then (Kizza et al., 2009). As noted by Sene and Farquharson (1998), this downward trend in rainfall station numbers is a familiar pattern, especially in developing countries, caused by a combination of factors like insufficient funding, inadequate institutional frameworks, lack of appreciation of the worth of long-term data and, sometimes, political turmoil. Because of changes in rain-gauge network density over time, the analysis in this study was carried out for two periods in order to identify effects of a limited network density on the results: (i) 1960–1984 for which the

network density was high and (ii) 1985–2004 for which the network density was much lower. The results for the two periods were then combined into a single continuous gridded dataset covering the period 1960–2004. 2.3.2. Satellite precipitation data Two basic types of satellites are used for estimation of rainfall fields. Geostationary satellites use infrared (IR) channels to infer rainfall rates from temperature measurements made on top of clouds. They can provide high-resolution data, with continuous temporal coverage for the observed region. Polar-orbiting satellites use microwave channels which can provide better estimates of rainfall by monitoring the scattering of naturally emitted passive microwaves (PMWs) within clouds. However, since the satellites only pass over a given location once or, at most, twice a day, gaps in the resultant data time series can exist over the study area. Several algorithms are used to combine the high temporal resolution of infrared data with the higher quality of microwave estimates. In some cases, additional calibration of the satellite data is carried out using ground-based rain gauges. There is a variety of products including TRMM 3B42 and 3B43, CMORPH, PERSIANN, TAMSAT, RFE 2.0, CMAP and others (Dinku et al., 2007). We chose two such products, namely TRMM 3B43 and PERSIANN for estimating lake rainfall in the current study on the basis of their prior good performance for the region (Asadullah et al., 2008; Dinku et al., 2007). TRMM 3B43 is a monthly satellite rainfall data product of the NASA Goddard Space Flight Centre with a spatial resolution of 0.25°  0.25° (Huffman et al., 2007). The approach used in building the product is to use all available PMW estimates and fill any cells without a PMW estimate for a given time step using IR estimates that have been calibrated using the PMW and space-born precipitation radar data. The product is further calibrated against monthly gauge data to scale the estimates. The TRMM algorithm ensures that every grid box has the best possible estimate, but it also can result in a statistically heterogeneous dataset. TRMM 3B43 data used for the current study covers the period from January 1998

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to December 2009. The dataset has shown good performance in different regions around the world including Australia (Huffman et al., 2007), Ethiopia (Dinku et al., 2007) and Uganda (Asadullah et al., 2008). The PERSIANN product, from University of California, Irvine, uses an artificial neural network algorithm to combine the IR and PMW data. The approach is to calibrate the IR data to PMW estimates by continually updating the parameters whenever a new PMW estimate becomes available. By using this approach, the product is able to recursively adapt the calibration in different regions (Hsu and Sorooshian, 2008). Therefore, the PERSIANN system involves no local calibration in producing its rainfall estimates. PERSIANN product estimates are available at a spatial resolution of 0.25°  0.25° and a temporal resolution of 6 h. The monthly estimates used in the current study, where obtained by grid by grid summation over the entire month. The data used for this study covers the period from March 2000 to December 2009. 3. Methods The study was divided into three parts; (i) data quality control and filling of missing data, (ii) spatial interpolation of gauge data, and (iii) regression analysis with satellite data to estimate lake rainfall. 3.1. Data quality control Many different approaches to quality control of precipitation data have been used (Eischeid et al., 1995; Feng et al., 2004; Gonzalez-Rouco et al., 2001; Westerberg et al., 2010; You et al., 2007). Here, quality control was performed at both daily and monthly time scales and potentially erroneous data were flagged using automatic routines and visual inspection. Flagged data were further investigated and removed if deemed erroneous. Automatic routines similar to the ones developed by Westerberg et al. (2010) for a Honduran basin were used to check for; (1) too-frequently occurring data that may be due to rounding off errors or data falsification by gauge readers. These were handled by treating any sequence of 5 or more days with the same rainfall amount greater than zero as suspicious and requiring further investigation, (2) sequences of too-low or too-high data, which were crosschecked for consistency using double mass curve plots, (3) unusually dry or wet months, which were checked by visual inspection of monthly rainfall plots, and (4) outliers which were defined as rainfall values higher than three standard deviations above the mean. These values were then scrutinised (e.g. very high rainfall values during the dry season were deemed to be suspicious), and compared to values recorded at nearby stations. In all the above checks, three types of decisions had to be made depending on the evidence gathered; (1) retain the data and station, (2) remove the erroneous data from the station data series or (3) remove the entire station from the database. The decision to remove data was subjective but the previous analysis provided a sound basis for this decision. 3.2. Estimation of missing values The gauged rainfall data had varying periods of missing values ranging from 1 day to several years which limit their usefulness in hydrological analysis. Gaps shorter than 1 month were filled to obtain more complete monthly data. The missing data were estimated at a daily time step if there was at least 1 day with data during a given month. The coefficient-of-correlation-weighting method (CCW) which was shown to work well by Teegavarapu and Chandramouli (2005) was chosen here. CCW is similar to the

inverse distance weighting method (IDW) but uses the correlation coefficient instead of inverse squared distance to compute the weighting factor:

Pn hi Rmi hm ¼ Pi¼1 n i¼1 Rmi

ð1Þ

where hm is the missing rainfall value to be interpolated, Rmi is the correlation coefficient between the data at station m with the missing value and the ith surrounding station, hi is the rainfall value at station i and n is the number of surrounding stations. 3.3. Spatial interpolation Spatial interpolation was carried out at a monthly time step for 1960–2004 and the results were then analysed separately for the periods 1960–1984 and 1985–2004. A monthly time step was used partly because of the intended use of the interpolated data in planned future water-balance studies but also to take advantage of the higher correlations for monthly data compared to daily data. Spatial interpolation methods are based on the concept of spatial continuity, i.e. positive spatial autocorrelation – that data located closer to each other are more similar than data located further apart (Isaaks and Srivastava, 1989). Many different interpolation methods exist and the selection of which methods to use depends on the nature of the dataset and the purpose of the analysis. Initial assessments showed that there were no significant correlations between rain-gauge elevation and climatological mean rainfall. Checks on the relationship between climatological mean rainfall and distance from the lake also did not give significant results. Therefore, two methods that are based on weighted linear combinations of the point rainfall data were selected; inverse-distance weighting (IDW) and universal kriging (UK) with coordinate base functions. For UK interpolation, an exponential variogram model with a nugget effect performed best in an initial analysis. The variogram was omni-directional owing to the relatively low density of stations for the large basin area. In UK a trend (estimated as a function of the coordinates) is first subtracted from the data, where after the semi-variogram is calculated on the residuals. A normalised kriging variance map for each month was calculated by dividing the variance map by the maximum variance. The mean of the normalised variance maps for all months was then used to assess the spatio-temporal coverage of data in the basin in the same way as Westerberg et al. (2010). Both UK and ID were performed as block estimation (Isaaks and Srivastava, 1989) with a grid size of 2000 m and a discretisation of 100 points per block. 3.4. Estimation of lake rainfall To estimate areal rainfall over Lake Victoria, three key assumptions were made. Firstly, it was assumed that, owing to the relatively good rain-gauge network distribution over the land part of the basin, the interpolated rainfall estimates for the land part were accurate and represented a realistic rainfall distribution. This could be considered a realistic assumption owing to the strongly coherent rainfall patterns in the region (Ba and Nicholson, 1998). Secondly, it was assumed that the satellite rainfall products (TRMM 3B43 and PERSIANN) were capable of capturing the enhancement of rainfall over the lake compared to the land part of the basin to an acceptable level of accuracy. The third assumption was that there had been no significant changes in rainfall dynamics, and the regression equations derived for the periods of satellite data availability (1998–2009 for TRMM 3B43 and 2000–2009 for PERSIANN) were applicable over the study period (1960–2004). A threestep approach was used to estimate the lake rainfall.

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3.4.1. Quality of satellite estimates over the land part of the basin An assessment was made of how well the two satellite products reproduced mean areal rainfall over the land part of the basin as estimated using the interpolated rain-gauge data. The comparison was made by analysing the bias and correlation between the interpolated and satellite data as well as comparing their basic statistics and plotting the cumulative distribution functions and the intraannual variability (mean monthly data). 3.4.2. Derivation of linear regression coefficients for land and lake rainfall Linear regression equations for the satellite products were derived to relate the areal rainfall over the Lake Victoria surface to areal rainfall over the land part of the basin. Two approaches were used: Case 1 – a single regression equation was derived for all the monthly values and Case 2 – regression equations were derived for each calendar month. Regression performance was compared using the coefficient of determination (R2) and the root-mean square error. 3.4.3. Estimation of lake rainfall from interpolated land rainfall Lake rainfall estimates for the period 1960–2004 were then derived by applying the regression coefficients to interpolated areal rainfall over the land and the results were compared with previously published values.

Table 1 Number of stations for which data were removed. Number of days removed

Number of stations affected

Percentage

1 Day 2 Days–1 month 1 Month–1 year >1 Year Total

20 12 4 7 43

47 28 9 16 100

4. Results and discussion 4.1. Data quality control A total of 47 stations (13%) of the 362 stations were dropped during the quality control. The 315 remaining stations represent an average network density of 620 km2/gauge over the land part of the basin and 830 km2/gauge if the lake area was included. Furthermore, a total of 43 stations (12%) had their time series edited by removing some data that were deemed unreliable. Of these, 32 stations were edited because of outliers at a daily time step, six stations because of repeated values and five stations because of having sequences of abnormally high or low values as reflected by outliers in the monthly and annual time scale but not at the daily time scale. The number of data removed from the affected stations ranged between 1 day and 2920 days (8 years, Table 1).

4.2. Estimation of missing data Data gap filling using the CCW method resulted in an additional 6724 months which added 1514 years with complete records for the period 1960–1984. For 1985–2004 the additional number of months was 2705 giving 566 more years with complete records. Gap filling also resulted in an increase in the mean data length from 14 to 19 years for the period 1960–1984 and from 7 to 10 years for the period 1985–2004. It can be concluded that the gap filling process was robust and preserved most of the key statistics of the dataset (Table 2). The variability in the gap-filled dataset was higher than in the raw dataset as more data were included. In addition, there were no significant changes in the annual statistics of the dataset for the period 1960–1984 and the period 1985–2004 despite a drop in stations density over the later period. The changes in the station distribution pattern over the two periods were also minimal and were not expected to significantly change the rainfall estimates.

Table 2 Summary statistics of the dataset before and after gap filling. The number of stations was as the number of stations having at least 50% of the years with a data value for each month. Variable

Before gap filling

Number of stations Mean data length (years) Mean annual rainfall (mm) Median annual rainfall (mm) Coefficient of variation (–) Minimum annual rainfall (mm) Maximum annual rainfall (mm)

After gap filling

1960–1984

1985–2004

1960–1984

1985–2004

223 14 1256 1242 0.18 903 1672

63 7 1280 1244 0.20 969 1622

280 19 1259 1244 0.19 862 1743

134 10 1265 1239 0.20 917 1670

Fig. 2. Estimated residual semi-variograms for long-term mean annual rainfall for the two study periods: (a) 1960–1984 and (b) 1985–2004.

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Table 3 Statistics of results based on interpolation of monthly rainfall totals using the two methods for different time periods. Interpolation method

IDW

UK

Time period

1960–1984

1985–2004

1960–2004

1960–1984

1985–2004

1960–2004

Coefficient of correlation Mean error (mm) Maximum positive error (mm) Maximum negative error (mm) Mean absolute error (mm) Mean relative error (%) Root mean square error (mm)

0.61 1.50 235.4 138.9 32.5 0.93 46.2

0.40 0.44 200.3 110.7 33.3 0.85 48.3

0.52 0.64 219.8 126.3 32.8 0.90 47.1

0.61 0.17 234.4 130.8 32.4 0.85 45.7

0.41 0.10 197.2 104.7 32.4 0.81 47.0

0.52 0.14 217.9 119.2 32.4 0.83 46.3

Fig. 3. Spatial variations of the climatological mean rainfall (mm/year) interpolated by (a) IDW and (b) UK methods for the period 1960–2004. Note: since there were no rainfall stations on the lake, the resulting rainfall field over the lake is far from accurate (see discussions in the sections below).

4.3. Spatial interpolation 4.3.1. Estimated semi-variograms for UK The estimated residual semi-variograms for the climatological mean (long-term mean annual) rainfall showed a different behaviour for 1960–1984 compared to 1985–2004 (Fig. 2). The variogram for 1960–1984 reached a sill while for 1985–2004 the residual semi-variance continued to increase as the lag increased, suggesting a spatial trend in the data that was not represented by the UK method. The range of spatial continuity taken at 95% of the sill for the 1960–1984 semi-variogram was about 65 km. For some months, two additional forms of the semi-variograms were obtained; namely a pure nugget effect and a linear form. A pure nugget occurred, where the range was very small and the semi-variance jumped from zero to maximum value over short distances. In effect this meant that there was no spatial correlation between the station pairs and the interpolated values were then estimated as a simple average (all stations got the same weight) plus the UK coordinate base-function trend. Pure nugget forms accounted for 8% and 29% of all semi-variograms for the 1960–1984 and 1985–2004 analysis periods respectively. The linear form occurred in cases, where the semi-variogram did not reach a sill and was best represented by a straight line. These linear forms accounted for 10% and 17% of all semi-variograms for the 1960–1984 and 1985–2004 analysis periods respectively. The rest of the estimated semi-variograms (82% for 1960–1984 and 54% for 1985– 2004) behaved in a more conventional manner expected from exponential models with a small nugget effect. 4.3.2. Comparison of the interpolated results for UK and IDW IDW and UK gave similar results during cross validation (Table 3). Several of the statistics for 1960–1984, when there were more stations compared to 1985–2004 were better than for the later

Fig. 4. Mean normalised UK variances of monthly precipitation for 1960–2004. Darker areas represent locations with poor temporal coverage in the period and lighter areas locations with good temporal coverage. Note: the mean normalised UK variance was derived by computing the ratio between the UK variance for each month and the maximum variance for that month and then taking the mean for the whole study period.

period (Table 2). The statistical measures for IDW and UK interpolation were of the same order of magnitude, though UK performed slightly better. For months when the estimated semi-variogram resulted in a pure nugget effect (8% for 1960–1984 and 10% for 1985– 2004), UK estimates were expected to be inferior to IDW estimates. In those cases, the spatial pattern of UK estimates was very uniform across the basin, which is not expected for rainfall data. However, areal rainfall estimates were not expected to be much affected.

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Fig. 5. Mean monthly rainfall variation (mm/month) for UK for 1960–2004. Note: since there were no rainfall stations on the lake, the resulting rainfall field over the lake is far from accurate (see discussions in the sections below).

Seasonal rainfall as a percent of annual rainfall

1600

Oct-Dec

1400

50%

1200

40%

1000

30%

800

20%

600

10%

a

0%

b

60%

1600

Jun-Sep

Jan-Feb

400

1400

50%

1200

40%

1000

30%

800

20%

600

10% 0% 1960

d

c 1970

1980

1990

2000

Years

1960

1970

1980

1990

Annual rainfall total (mm)

Mar-May

60%

400

2000

Years

Fig. 6. Percentages of annual rainfall (dashed lines; left hand scale) and total rainfall (continuous lines; right hand scale) over the land part of Lake Victoria basin according to the season. a And b are for the two rainy seasons (March–May and October–December respectively) while c and d are for the dry seasons (January–February and June– September respectively).

4.3.3. Spatial rainfall characteristics From the results of spatial interpolation, the land part of the basin received a climatological mean rainfall of 1204 and 1230 mm/ year, with a maximum monthly rainfall of 180 and 182 mm in April

and a minimum monthly value of 48 and 54 mm in July for the UK and IDW respectively (Fig. 3). The difference in appearance between the two plots in Fig. 3 was due to the greater smoothing effect of UK compared to IDW. The mean normalised UK variance

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Table 4 Estimates of mean areal rainfall (mm/month) for the different sub-basins using Universal Kriging (UK). SE, NE, NW, and SW stand for south-eastern, north-eastern, north-western and south-western shores of the lake basin respectively that are traditionally treated as complete basins. These shores have numerous streams that flow into the lake that are ungauged. Note: the mean normalised UK variance (last column) was derived for each sub-basin by computing the ratio between the UK variance for each month and the maximum variance for that month and then computing the mean for the whole study period. Basin (number in Fig. 1)

January

February

March

April

May

June

July

August

September

October

November

December

Mean annual

Mean normalised UK variance

Sio(1) Nzoia (2) Yala (3) Nyando (4) Sondu (5) Gucha (6) Mara (7) Ruhama– Grumeti (8) Mbalangeti (9) Duma (10) Simiyu (11) Magogo (12) Isanga (13) Kagera (14) Ruizi (15) Katonga (16) SE Streams (17) NE Streams (18) NW Streams (19) SW Streams (20)

62 51 68 75 84 90 90 108

73 58 72 77 85 90 86 101

139 111 126 126 141 147 132 138

226 192 203 203 213 211 194 181

204 176 177 174 170 164 145 122

103 107 103 105 102 84 80 55

90 117 104 109 94 66 73 45

117 137 129 136 116 87 87 51

124 108 107 100 96 91 77 51

145 114 116 106 104 110 90 71

137 111 122 119 127 141 123 125

76 54 71 75 89 108 99 112

1496 1334 1396 1405 1422 1390 1276 1159

0.32 0.35 0.33 0.32 0.35 0.36 0.43 0.49

112

106

142

182

119

49

40

44

47

71

131

119

1160

0.57

113 115 113 126 108 72 63 108

106 108 105 117 108 74 63 100

144 144 141 146 143 124 124 143

180 176 166 168 175 162 159 183

111 102 86 85 96 108 117 111

42 35 23 18 15 34 49 37

34 27 17 10 8 27 43 31

37 29 20 15 29 53 74 37

44 38 35 37 70 88 101 51

74 70 74 75 113 122 137 87

138 138 142 143 150 139 142 146

124 127 129 141 120 94 82 124

1146 1111 1051 1082 1133 1097 1154 1159

0.56 0.60 0.43 0.58 0.43 0.32 0.36 0.40

80

80

138

202

156

73

62

80

85

111

140

96

1301

0.31

83

83

147

203

152

55

42

61

86

126

151

107

1296

0.28

113

108

151

195

122

30

27

44

71

111

150

133

1255

0.42

Fig. 7. Results of spatial distribution analysis of rainfall over the land part of the Lake Victoria basin for the period 2001–2004: (a) Mean areal monthly rainfall and (b) cumulative distribution function of rainfall. UK and IDW: interpolation methods for measured data; TRMM 3B43 and PERSIANN: satellite products.

map revealed that areas in the south and south-western part of the basin had the lowest temporal coverage of rainfall stations (Fig. 4). The northern part of the basin had a general good temporal coverage while the lack of stations on the lake was also apparent. The plots of mean monthly rainfall for the entire analysis period (1960–2004) estimated by the UK method show considerable seasonal variation (Fig. 5). The influence of the seasonal migration of the ITCZ on the rainy seasons is evident in the plots. In January, the ITCZ is situated far south of the basin at about 15oS (Trewartha, 1981). During February and March the ITCZ moves slowly northwards and extends in width with a concurrent increase in rainfall over the basin so that by April, the zone covers most of the basin and coincides with the maximum monthly rainfall. During the following months, the ITCZ moves northwards coinciding with the relatively dry period experienced in June–September. The zone returns to the Lake Victoria basin around October and continues southwards till it reaches the southernmost point in January. However, this rainfall pattern is modified by varying degrees of

influence from the Atlantic, Indian and Pacific Oceans (Nicholson, 2000) as well as lake-induced variations (Anyah et al., 2006). The effect of the Congo air mass is more pronounced on the western and north-western parts of the lake. The changing pattern is more pronounced in the south-western part of the basin, where it is clear that the rainy season lasts from November to April. The north-eastern part receives substantial rainfall amounts from April to November. As a percentage of the mean annual rainfall over the land part of the Lake Victoria basin, the March–May rainy season contributed the largest portion at about 36% (Fig. 6). This seasonal contribution varied slightly around the basin between 35% and 38% for the north-western and south-western part of the basin. April contributed 42% of the March–May seasonal rainfall. The October–December rainy season contributed about 30% of the annual rainfall but it varied over a wider range from 23% in the northeast to 33% in the south and south-eastern part of the basin. November contributed 40% of the October–December rain though the season sometimes

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M. Kizza et al. / Journal of Hydrology 464–465 (2012) 401–411 Table 5 Statistics of monthly rainfall for the period 2001–2004 over the land part of the Lake Victoria basin for the satellite products and estimates using the two interpolation methods. Statistic

TRMM 3B43

PERSIANN

UK

IDW

Mean (mm) Maximum (mm) Minimum (mm) Standard deviation (mm)

94 194 22 46

100 211 11 53

101 209 23 51

101 210 27 48

started as early as September. Mutai et al. (1998) notes this variability and states that March–May rains are more abundant but the October–December rains tend to be more variable. The variability in October–December rainfall had a greater influence on annual rainfall compared to March–May rainfall (Fig. 6). This was exhibited by the correlation coefficient of 0.71 between October– December rainfall and annual rainfall total compared to only 0.5 for March–May rainfall. Peaks in annual rainfall totals tended to coincide with peaks in October–December rainfall as opposed to March–May rainfall (Fig. 6). The October–December season in East Africa is strongly affected by complex interactions between the Indian and Pacific Oceans and exhibits higher inter-annual variability than the March–May season (Mistry and Conway, 2003; Nicholson, 1996). Periodic circulation dipole events in the Indian Ocean tend to be associated with above-average and sometimes very extreme rainfall in October–December. The Sio sub-basin received the highest amount of rainfall of about 1500 mm/year while the Magogo sub-basin received the lowest amount at 1050 mm/year (Table 4). The north-eastern sub-basins, including Sio, Nzoia, Yala, Nyando, Sondu and Gucha, were the wettest. The driest sub-basins were located in the southern and western part of the Lake Victoria basin. 4.4. Estimation of lake rainfall 4.4.1. Comparison of satellite rainfall estimates with ground data Areal rainfall estimates of TRMM 3B43 and PERSIANN over the land part of the Lake Victoria basin were comparable to the estimates from the two interpolation methods used in this study (Fig. 7a). The mean monthly estimates reproduced the expected bimodal rainfall distribution for the basin with peaks in April and November. The mean monthly values for TRMM 3B43 were generally lower than those of the interpolated rain-gauge data while the values for PERSIANN oscillated between higher and lower values. However, both products under predicted the April rainfall which represents a maximum for the basin. The cumulative distribution

Table 6 Regression slope and performance measures for monthly lake rainfall against monthly land rainfall for the TRMM 3B43 satellite products. The equations are of the form y = bx. The analysis periods are 1998–2009 for TRMM 3B43. The unit of RMSE is mm/month while coefficient b and R2 are dimensionless. Case

2 2 2 2 2 2 2 2 2 2 2 2 1

Month

January February March April May June July August September October November December All months

TRMM 3B43

PERSIANN

b

RA2

RMSE

b

RA2

RMSE

1.25 1.04 1.32 1.45 1.43 1.49 1.13 1.13 1.16 1.29 1.36 1.37 1.33

0.754 0.938 0.844 0.188 0.674 0.875 0.742 0.724 0.920 0.583 0.821 0.907 0.855

31.2 11.8 25.0 51.7 37.9 12.7 9.2 11.7 12.9 29.4 40.7 23.3 29.8

1.44 1.28 1.78 2.23 2.08 2.71 1.89 1.83 1.58 1.85 1.75 1.77 1.76

0.565 0.842 0.839 0.718 0.366 0.956 0.629 0.863 0.688 0.189 0.710 0.905 0.784

43.4 20.5 25.6 40.8 46.5 11.9 17.3 14.5 16.9 38.8 68.3 30.5 45.6

Table 7 Areal mean monthly rainfall estimates over Lake Victoria for 1960–2004. The UK interpolated mean monthly areal rainfall values over the land are also shown. Case 1 rainfall estimates are based on a single regression equation for all data, while Case 2 estimates are based on regression equations for each calendar month. Month

January February March April May June July August September October November December Annual

Land rain (mm/month)

90 90 133 180 124 52 48 65 76 104 135 106 1204

Lake rain (mm/month) TRMM 3B43

PERSIANN

Case 1

Case 2

Case 1

Case 2

120 119 177 239 165 68 63 86 101 139 180 141 1598

113 93 176 261 178 77 54 73 88 134 184 145 1577

160 158 235 317 219 91 84 114 134 184 239 188 2124

130 114 238 400 259 140 90 118 121 193 236 188 2227

of the monthly rainfall for PERSIANN provided a better match for the medium and high but not the low interpolated values than the distribution of the TRMM 3B43 values (Fig. 7b). A good performance would also be shown by relatively low values of bias and high correlation coefficients. The bias was negative in all cases as

Fig. 8. Scatter plot for lake rainfall against land rainfall derived by the two satellite products using Case 1 regression equations, (a) TRMM 3B43 data and (b) PERSIANN data.

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M. Kizza et al. / Journal of Hydrology 464–465 (2012) 401–411

Fig. 9. Annual areal rainfall (a) and mean monthly areal rainfall (b) for Lake Victoria basin. Areal rainfall values over land are based on UK interpolation while lake areal rainfall values are based on a regression relationship derived for the TRMM 3B43 satellite product using the Case 1 option (regression for all months).

expected from Fig. 7a. The values for TRMM 3B43 (7.0% for UK and 6.4% for IDW) were higher than the values for PERSIANN (1.8% for UK and 1.2% for IDW). The bias in TRMM 3B43 estimates is consistent with those quoted for Australia of about 6% (Huffman et al., 2007). The bias in PERSIANN estimates was consistent with values quoted for the region by Asadullah et al. (2008). The correlation coefficients for TRMM 3B43 (0.90 for UK and 0.88 for IDW) were higher than those for PERSIANN (0.75 for UK and 0.71 for IDW). The basic statistics of mean, maximum, minimum and standard deviation were also similar (Table 5). 4.4.2. Regression of lake rainfall For Case 1 (where a single regression equation for all monthly values was used), the fits of the linear regression equations were reasonably good with R2 = 0.9 and RMSE = 29.8 mm/month for TRMM 3B43 which was slightly better than the fit for PERSIANN with R2 = 0.8 and RMSE = 45.6 mm/month (Fig. 8). For Case 2 (where regression equations were derived for each calendar month), the performances were still high (Table 6) for most months. For the TRMM 3B43 product, the R2 values were higher than 0.8 for 7 months and it was only in April when the R2 values fell below 0.6. The maximum RMSE was 51.7 mm/month and occurred in April, the wettest month. The average enhancement of lake monthly rainfall over land rainfall for the TRMM 3B43 product varied between 4% for February and 49% for June. For the PERSIANN product, the R2 values for 5 of the months were higher than 0.8 while values less than 0.6 occurred in 3 months. The average enhancement of monthly lake rainfall for the PERSIANN product over land rainfall varied between 28% for February to more than 171% in June. Using separate regression equations for each calendar month (Case 2) resulted in a 1.3% reduction in mean annual lake rainfall for TRMM 3B43 and a 4.9% increase for PERSIANN when compared to estimates with one regression equation for all months (Case 1). Additionally, there were differences in the distribution of the monthly estimates because of the use of time-varying regression coefficients in Case 2. On average, the enhancement of lake rainfall over land rainfall was 33% for TRMM 3B43 and 76% for PERSIANN using the Case 1 regression equations (Table 7). For Case 2 regression equations, the enhancement was 28% and 85% for the TRMM 3B43 and PERSIANN products respectively. TRMM 3B43 results were more consistent with other results quoted in the literature. Fraedrich (1972) used a simple climatological model to estimate an annual rainfall of 1585 mm over the lake compared to about 1000 mm over the land part of the catchment, or an enhancement of 59%. Hastenrath and Kutzbach (1983) computed an enhancement of lake rainfall of 20–34% compared to the rainfall in the surrounding catchment. Ba and Nicholson (1998) computed a relationship between satellite-

derived cold-cloud indices and rainfall measurements to show an enhancement of 27% of lake rainfall over land rainfall. The annual mean areal rainfall estimates for the land, lake and the entire basin are shown in Fig. 9. 5. Conclusions A spatially detailed gridded monthly rainfall dataset for the Lake Victoria basin with an improved estimate of the lake surface rainfall through the use of satellite-derived precipitation data was produced in this study. The analysis showed that:  A careful data quality assessment and gap filling was needed in order to produce a coherent and comprehensive rainfall dataset from the ground-based rainfall records. The dataset proved useful for analysing the spatial rainfall variability over the land part of the Lake Victoria basin in that it reproduced the rainfall variability expected from the knowledge of the regional climate variability.  While the two interpolation methods (IDW and UK) used were conceptually different, they provided comparable results for the Lake Victoria basin. The interpolated results are expected to be most uncertain for the south-eastern parts of the basin and for parts of the Kagera sub-basin, where the station density was low.  Both satellite products (TRMM 3B43 and PERSIANN) captured the enhancement of lake rainfall compared to land rainfall but the magnitude of the enhancement was different for the two products. Application of this kind of analysis to other satellite rainfall products could contribute further to the understanding of the magnitude of the enhancement. Acknowledgements This work is part of the PhD programme of the first author with sponsorship of the Swedish International Development Cooperation Agency (Sida) through the Department for Research Cooperation (SAREC). We also thank Prof. Chong-Yu Xu from University of Oslo for his valuable advice and comments throughout the research process. References Anyah, R.O., Semazzi, F.H.M., Xie, L., 2006. Simulated physical mechanisms associated with climate variability over Lake Victoria in East Africa. Mon. Wea. Rev. 134, 3588–3609. Asadullah, A., McIntyre, N., Kigobe, M., 2008. Evaluation of five satellite products for estimation of rainfall over Uganda. Hydrol. Sci. J. 53 (6), 1137–1150. Ba, M.B., Nicholson, S.E., 1998. Analysis of convective activity and its relationship to the rainfall over the Rift Valley Lakes of East Africa during 1983–1990 using the meteosat infrared channel. J. Appl. Meteorol. 37, 1250–1264.

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