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International Journal of Applied Earth Observation and Geoinformation 11 (2009) 15–26

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International Journal of Applied Earth Observation and Geoinformation journal homepage: www.elsevier.com/locate/jag

A comparison of rainfall estimation techniques for sub-Saharan Africa Elias Symeonakis a,*, Rogerio Bonifaçio b, Nick Drake c a

Department of Geography, University of the Aegean, University Hill, Mytilene 81100, Greece Vulnerability Analysis and Mapping Unit, United Nations WFP, PO Box 913, Khartoum, Sudan c Department of Geography, King’s College, Strand, London WC2R 2LS, UK b

A R T I C L E I N F O

A B S T R A C T

Article history: Received 29 September 2006 Accepted 22 April 2008

Interpolated rain-gauge data were compared to Meteosat-based precipitation estimates for sub-Saharan Africa. Validation was carried out using a dataset from a very dense gauge network in South Africa, on a point-to-pixel (PO–PI) as well as on a pixel-to-pixel (PI–PI) basis. Error criteria computed at the gauged pixels indicate that overall the interpolated estimates perform similarly to the satellite-based data: they provide good estimates of lower but underestimate larger precipitation amounts. It is concluded that the satellite estimates are more fitted for the operational modelling of processes such as surface runoff and soil erosion, especially in the developing areas where resources are scarce. ß 2008 Elsevier B.V. All rights reserved.

Keywords: Precipitation Sub-Saharan Africa Block kriging Indicator kriging Meteosat FEWS

1. Introduction Precipitation, the primary input to hydrological models, shows a considerable spatial variation. This is brought about by differences in the type and scale of development of precipitation producing processes, and strongly influenced by local or regional factors, such as topography and wind direction at the time of precipitation (Sumner, 1988). The problem is to try to describe the spatial variation and to make estimates of precipitation in areas where there are no monitoring stations. Resources for collecting such basic information are limited particularly in the developing world. Two main approaches have emerged for estimating precipitation amounts: interpolation of point measurements and satellitebased estimation techniques. Methods for precipitation interpolation from ground-based point data have ranged from techniques based on Thiessen polygons (Thiessen, 1911) and simple trend surface analysis (Gittins, 1968), inverse distance weighting (Weber and Englund, 1994), multiquadratic surface fitting (Borga and Vizzaccaro, 1997) and Delauney triangulations (Cohen and Randall, 1998) through to more sophisticated statistical methods such as kriging, and its various extensions, also known as geostatistical methods (Tabios and Salas, 1985). A number of

* Corresponding author. Tel.: +30 22510 36443; fax: +30 22510 36409. E-mail addresses: [email protected], [email protected] (E. Symeonakis), [email protected] (R. Bonifaçio), [email protected] (N. Drake). 0303-2434/$ – see front matter ß 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jag.2008.04.002

studies exist that draw comparisons between the various methods, most of which argue that geostatistical methods provide the most accurate estimates (Borga and Vizzaccaro, 1997; Creutin and Obled, 1982; Lebel et al., 1987; Nalder and Wein, 1998; PardoIgusquiza, 1998; Tabios and Salas, 1985). The majority of these studies focus on interpolating precipitation for small to regional scale applications emphasising the need for similar research over larger areas to support the respective work on hydrological processes, such as surface runoff and soil erosion, on the continental and global scales. Areal averages derived from rain-gauge observations suffer from limitations due to sampling but also because gauges are usually distributed with a spatial bias toward populated areas and against areas with high elevation and/or slope (Xie and Arkin, 1997). An alternative ground-based estimation method is the use of precipitation radar but this is usually not feasible in terms of cost and the lack of infrastructures (Grimes, 2003). An answer to these limitations is likely to come from satellite remote sensing, whose potential for estimating rainfall has been evident since its early days: the data are inexpensive, provide a complete area coverage and are available in real-time (Grimes, 2003). For a review of indirect, passive microwave and radar precipitation estimation techniques see Kidd (2001), Kidder and Vonder Haar (1995) and Petty (1995). Methods that are appropriate for operational use for sub-Saharan Africa usually rely on empirical relationships of Meteosat thermal infra-red (TIR) and passive microwave imagery and rain-gauge Global Telecommunications System (GTS) data (Carn et al., 1989; Dugdale et al., 1990; Grimes et al., 1999; Todd et al., 1995; Xie and Arkin, 1997). However, the success of the

E. Symeonakis et al. / International Journal of Applied Earth Observation and Geoinformation 11 (2009) 15–26

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techniques is limited by the indirect nature of the relationship between the remote sensing data and precipitation and the fact that they require calibration using gauge data. The aim of the present study was twofold: to produce daily and dekadal (i.e. 10-daily) precipitation estimates over sub-Saharan Africa by interpolating rain-gauge (GTS) data using two variations of kriging; to compare these to freely-available dekadal METEOSAT-based satellite estimates of the area by validating on data from a very dense rain-gauge network in South Africa. 2. Datasets and methods 2.1. Area of study The area of study is the African continent south of the 208N parallel or sub-Saharan Africa. For an extensive physiographic description of the area see Stock (1995). The area was chosen for its continental size and scarcity of rain gauges which makes precipitation estimation an exigent task. The region of Northern Africa along the Mediterranean Sea was left out of the scope of the present study due to its pronounced climatological dissimilarity to the rest of the continent. The period of study was the 36 dekads of 1996 to include the period of the validation data. 2.2. Datasets 2.2.1. The gauge data The only readily available daily rainfall data for the African continent are the World Meteorological Organisation (WMO) records from about 760 GTS stations. Around 580 of these are within sub-Saharan Africa. The GTS data were used for the estimation of interpolated areal rainfall as daily and as dekadal sums, produced by summing the daily sets on a 10-daily basis to match the temporal resolution of the satellite estimates. The total number of rain-gauge reports received daily varied, so that the number of stations reporting observations for each estimation period (i.e. dekad) was approximately 550. 2.2.2. The satellite data Freely available1 Meteosat-based precipitation estimates, developed by the Climate Prediction Centre/Famine Early Warning System (CPC/FEWS), are used in this study. The production of these estimates, hereafter referred to as the ‘FEWS’ estimates, is based on Meteosat 5 satellite data, GTS rain-gauge reports, model analyses of wind and relative humidity, and orography for the computation of accumulated rainfall. Meteosat-5 TIR data at 5 km pixel resolution is accessed every 30 min and then reformatted and converted to a geographical grid with a 0.18 spatial resolution. A preliminary estimate of accumulated precipitation is made based on the GOES Precipitation Index (GPI), an algorithm developed by Arkin and Meisner (1987). The GPI estimate is corrected using a bias field that is calculated by incorporating the GTS observational data and fitting the biases to a grid using optimal interpolation, thus producing an estimate of convective precipitation (Herman et al., 1997). The final precipitation estimates have a maximum error of approximately 40% of the measured precipitation value with a 68.3% assurance (Herman et al., 1997). It is important to note here that the FEWS estimates also utilise the GTS gauge data to correct for biases in the preliminary 1

http://www.cpc.ncep.noaa.gov/products/fews/data.html.

estimates. The technique can therefore be seen as an alternate way, other than geostatistics, to interpolate rain-gauge data using additional knowledge (i.e. remote sensing and model output data). 2.2.3. The validation data The validation rainfall data consisted of 31 daily records for March 1996 from a network of 1800 stations in South Africa. They were the only daily records available for the year of the present study, i.e. 1996. 2.3. Methodology The methodology involved two main steps: (i) the interpolation of the GTS rain-gauge data on daily and dekadal time-steps and (ii) the validation of the interpolated and FEWS satellite estimates against the South African validation data, using a point-to-pixel and a pixel-to-pixel approach. 2.3.1. Interpolation of gauge data Two different interpolation schemes were applied and compared: ordinary block kriging (BK) (Isaaks and Shrivastava, 1989), and a combination of BK and indicator kriging (IK) (Barancourt et al., 1992), which we will refer to as the ‘combined kriging’ (CK) technique. Both interpolation schemes were applied to the 31 daily and the 3-dekadal datasets. 2.3.1.1. Experimental semi-variograms and theoretical models. Daily and dekadal experimental variograms were plotted and two theoretical models were fitted to them: spherical and exponential (Burrough and McDonnell, 1998). A programme that uses the method of generalised least squares (GLSs) was developed to assign weights according to the number of pairs of stations that fall within each distance class of the semi-variogram. Leave-one-out cross-validation was then applied for selecting the most closely fitted model. Cross-validation works by leaving each sample point in turn out of the dataset and predicting its value from the rest of the data, using a particular variogram model (Burrough and McDonnell, 1998). This results in a set of predicted values and true values at each sample site. A cross-validation programme was also developed in this study which requires the user to specify the model type (spherical or exponential), total sill (i.e. sum of the sill and the nugget), range and maximum number of neighbouring points to be included in the estimation of the value at the dropped point. Finally, for the chosen combination of model type, range, sill and nugget, a number of statistical indicators were used to select the best model. 2.3.1.2. Combined kriging. Ordinary BK was applied to both dekadal and daily sets using the model parameters identified as optimal by cross-validation. A search radius of 1000 km was chosen, as this should be able to cover a typical size of convective events. Also, a minimum number of eight participating neighbouring stations were used. A problem with BK is that it assigns zero values only by rounding or if the entire set of neighbouring data points is also zero. This way it spreads low rainfall values over dry areas. To overcome this problem BK was applied to the GTS data in conjunction with IK which has been proven to be a good estimator of the occurrence of precipitation (Barancourt et al., 1992; Sun et al., 2003). In IK, a non-linear form of ordinary kriging, the original data are transformed from continuous to binary, with ones representing rain occurrence and zeros the absence (I(p) = 0 for p = 0 and I(p) = 1 for p > 0). The CK scheme consisted of three additional individual stages, other than BK, namely: (i) the calculation of the indicator field; (ii) the thresholding of the IK


output to produce the rainfall occurrence field; (iii) the multiplicative combination of the binary rain/no-rain masks with the interpolated rainfall images created by BK (Fig. 1). The first step of IK was to transform the original daily and dekadal GTS data from continuous to binary, with ones representing rain occurrence and zeros the absence. Indicator experimental variograms for the binary data were then computed and theoretical models were fitted to them, as in the case of the BK interpolation. The output of IK, a field valued between 0 and 1, can be interpreted as the probability of an (x, y) location being wet. The IK

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outputs were transformed into binary by selecting for each image an appropriate threshold, such that Occ(x) = 1 for IK(x) > t and Occ(x) = 0 for IK(x) t, where Occ(x) is the occurrence value at pixel x, IK(x) is the IK output value at pixel x and, t is the threshold for the transformation. For every binary rain-occurrence image, a contingency table was constructed showing the proportion of correct and incorrect estimates of occurrence of precipitation at the GTS (x, y) locations (Table 1). The estimated indicator values at the GTS locations were then extracted and paired with the observed values at the same locations. For each image and for all probability levels (i.e.

Fig. 1. Flowchart of the combined kriging (CK) scheme, first dekad March 1996.


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Table 1 Contingency table for estimated and observed binary event (Stanski et al., 1989)

Table 2 Scores for different probability threshold levels for the 2nd dekad March 1996

Observed

Estimated

No Yes

Probability level

No

Yes

a c a+c

b d b+d

a+b c+d

threshold values) from 0.0 to 1.0 separated by 0.1, a number of statistical scores were estimated: bias ¼

cþd ; bþd

(1)

which measures the relative frequency of predicted and observed occurrence, without considering forecast accuracy; the hit rate for wet occurrences, HRwet ¼

d ; bþd

(2)

which is defined as the proportion of wet occurrences which were correctly estimated; the false alarm rate, FAR ¼

c ; aþc

(3)

which is the proportion of non-occurrences for which the event was incorrectly estimated; the hit rate for dry occurrences, HRdry ¼

a ; aþc

(4)

which is defined as the proportion of dry occurrences which were correctly estimated; the accuracy of the predictions or percent correct, ACC ¼

aþd ; aþbþcþd

(5)

which is the summation of the correct predictions divided by the sum of all cases; and the skill of estimates, measured using Kuipers skill score (Stanski et al., 1989), also known as the ‘true skill score’, ad bc KS ¼ : ða þ bÞðb þ dÞ

(6)

ACC HRdry FAR HRwet KS

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.74 0.26 0.74 1.00 0.26

0.79 0.41 0.59 1.00 0.41

0.85 0.57 0.43 1.00 0.57

0.87 0.66 0.34 0.99 0.65

0.90 0.75 0.25 0.98 0.73

0.90 0.81 0.19 0.95 0.76

0.91 0.88 0.12 0.93 0.80

0.90 0.96 0.04 0.87 0.83

0.81 0.99 0.01 0.72 0.70

0.71 1.00 0.00 0.55 0.55

0.35 1.00 0.00 0.00 0.00

Highest ACC and KS values in bold and optimal probability level underlined.

The KS has the desirable characteristics that random or constant estimates will score zero; perfect estimates will have a score of 1. Ideally, for a perfect match between estimated and observed occurrence/absence of rainfall, ACC, HRwet, HRdry, KS, and bias should be 1 and the FAR zero. According to Stanski et al. (1989) it is not always possible for all scores to be optimised for the same probability level, and therefore it is best to choose the level which optimises KS. Table 2 is an example of ACC, HRwet, HRdry, FAR and KS values for different probability levels for the second dekad of March 1996. Fig. 2a, which contains the plots of the statistical scores of Table 2 (ACC, KS, HRdry and HRwet), demonstrates that 0.7 was the probability level chosen for the thresholding of the IK output of the second dekad March 1996. Another way of analysing the results in Table 2, is with the Relative Operating Characteristic (ROC) diagram (Manzato, 2005; Pontius and Schneider, 2001; Stanski et al., 1989). In Fig. 2b, the ROC diagram for the second dekad of March 1996 is shown, where FAR is plotted against HRwet. An ideal estimation system would produce 100% HRwet for 0% FAR and therefore the ROC diagram would look like the dashed line in Fig. 2b. In the real case (continuous line in Fig. 2b), the point on the ‘‘HRwet vs. FAR’’ curve which is closer to the (0, 1) top left vertex, is the one which maximises the HRwet and minimises the FAR. The probability level that corresponds to that point, in this case 0.7, is the optimal threshold selected for the transformation of the indicator field to a rainfall occurrence field. To produce the final CK estimate (Fig. 1e), the interpolated rainfall outputs of BK (Fig. 1a) were multiplied by the binary rain/norain masks (Fig. 1d) using a Geographical Information System (GIS). 2.3.2. Validation of precipitation estimates The interpolated and satellite-based estimates were validated against the dense reference data in the area of South Africa. The

Fig. 2. (a) Plots of the statistical scores of Table 2 (ACC, KS, HRdry and HRwet), for the 2nd dekad March 1996. (b) Relative Operating Characteristic (ROC) diagram for the same dekad (continuous line) and an ideal estimation system (dashed line).


first validation approach adopted here was the most commonly used comparison between validation point measurements and estimated pixels (point–to–pixel or PO–PI). The problem arising from this approach is that, if the validation gauge network is dense, a number of points might fall within the same pixel. Sub-sampling the validation point data in order to obtain a maximum of one gauge per pixel does not solve the problem. For example, randomly selecting one rain-gauge that falls within the 0.18 0.18 pixel of Fig. 3 (which occupies an area of around 170 km2 in these longitudes and latitudes), with an interpolated value of 11 mm/ dekad, can result in choosing a station from a group of nine raingauges with measured precipitation values ranging from 0 to 33 mm/dekad. Therefore, for that specific pixel, the difference from the ‘‘ground truth’’ could take a number of values, ranging from 11 mm to 22 mm. To overcome this situation Lebel and Amani (1999) suggested the calculation of areal estimates from the point measurements and thus a comparison of pixel-to-pixel (or PI–PI) precipitation. They pointed out that researchers interested in the validation of rainfall estimates have to rely on very dense rain-gauge networks to compute reference areal depths supposedly equal to the true rainfall. This approach was adopted here and applied to the dense South African network that allowed for the calculation of accurate reference areal rainfall against which the FEWS and the GTS estimates, based on a much lower density network, could be compared. The methodology undertaken to analyse and interpolate the South African data using CK, was the same with that described in Section 2.3 for the GTS data. Both daily and dekadal South African data were interpolated in order to compare them with the respective interpolated daily and dekadal GTS data. The experimental variograms were produced using a lag distance of 5 km. Spherical and exponential theoretical models were considered as possible suitable models to be fitted to the experimental semivariograms by GLSs. Model types, sills, ranges and nuggets, estimated using the GLS technique, were cross-validated and selected for the interpolation of the dekadal and the daily datasets, respectively. BK was applied using a minimum number of 20 neighbouring stations and a radius of 100 km. IK was then applied to the dekadal and the daily datasets and rainfall occurrence masks

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were calculated and combined with the BK outputs to produce the CK final interpolated validation images. From the validation images, only the pixels that contained validation gauges were selected for the comparison of the interpolated GTS and the FEWS data. These were 1624 pixels in total. For both PO–PI and PI–PI validation methods a number of criteria were used to measure the strength of the statistical relationship between the estimated and measured values: PN ðP pi Þ biasd ¼ i¼1 i ; (7) N the absolute root mean square error, sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi PN 2 i¼1 ðP i pi Þ RMSEabs ¼ ; N

(8)

where Pi (i = 1, . . ., N) is the set of N reference values, pi (i = 1, . . ., N) the set of estimates. Ideally, for a perfect estimate, biasd = 0 and RMSEabs is minimised. The linear correlation coefficient, PN ¯ pi pÞ ðP PÞð ¯ ; (9) r ¼ i¼1 i Ns P s p where P¯ and p¯ are the mean values of the observed and estimated precipitation values at a location i, and sP and sp the standard deviations of P and p, respectively. r measures the co-fluctuation between estimated and measured value, and therefore is not sensitive to a bias. The Nash Index or non-dimensional skill score (Murphy, 1995; Obled et al., 1994): I ¼ 1

RMSE2

s 2P

(10)

;

where I is equal to 1 for a perfect estimate (i.e. pi = Pi), and equal to ¯ This non-dimensional 0 for the best constant estimate (i.e. pi ¼ P). index is useful for comparing results obtained with different datasets since it can be interpreted as a relative measure of the deviation between estimate and observation (Laurent et al., 1998). The scaled-RMSE or, s-RMSE2 ¼

N 1X pi P i 2 N i¼1 Pi

for P i > 10 mm;

(11)

where s-RMSE is another measure of the relative deviation between estimate and observation, but with a different meaning to the Nash index I, since I depends on the standard deviation of the observed set while s-RMSE, with respect to the observed values, depends on their mean. For small-observed precipitation values the contribution of Pi to s-RMSE would be very large and therefore s-RMSE was computed only for Pi larger than a threshold. The value of 10 mm was chosen as that threshold so that a sufficient number of observed values could be used for the calculation of s-RMSE. 3. Results and discussion 3.1. Visual comparison of precipitation estimates

Fig. 3. A pixel-size window for which data from nine South African validation stations exist (1st dekad March 1996). Numbers represent precipitation (mm). Diamond-shaped stations are from the entire validation dataset. The square-shaped station is the one randomly selected from the reference data using the condition that only one station per 0.18 pixel is to be used.

The interpolated and the FEWS precipitation estimates are shown in Fig. 4 for March 1996. The two methods appear to have some qualitative similarities as well as differences. More specifically, they seem to agree in both amount and spatial distribution of rainfall over areas, such as Madagascar, western and southern Africa, where the GTS gauge network is dense enough for kriging to produce reasonable results. In other areas, the FEWS

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Fig. 4. Precipitation estimates for the three dekads of March 1996, produced by the combined kriging technique (a, c and e) and FEWS (b, d and f).

estimates are generally higher. In central Africa over parts of the Democratic Republic of Congo and Angola, for example, rainfall estimated by FEWS is very high (i.e. around 200 mm/dekad) in contrast to that estimated by kriging. This can be attributed to the fact that those areas suffer most from the rain-gauge insufficiency problem. Finally, the interpolation technique produced rainfall amounts in areas such as the Sudan where FEWS generally estimated zero rainfall. Since there are no GTS stations in that area this is probably due to the spill-over effect of kriging, which the combined technique could not rectify properly.

In general, the fact that ten of forty-two countries of the subSaharan mainland (namely the Democratic Republic of Congo, Gabon, Equatorial Guinea and Angola in central Africa, the Sudan, Somalia, Djibouti and Eritrea in the East, and Liberia and Sierra Leone in the West), covering 30% of the total area, is not covered by the GTS network, is a drawback for the interpolation technique. On the contrary, the FEWS data are uniformly distributed and can therefore be used to alleviate the gauge insufficiency problem. However, since the GTS data are also used for calibrating the FEWS preliminary estimates, the lack of


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Table 3 Error criteria estimated from the point-to-pixel (PO–PI) comparison for the three dekads of March 1996 Dekad 1

2

3

Mean values (mm)

Biases (mm)

Nash index

Linear corr. coef. (r)

RMSEs (mm)

Scaled RMSEs

Validation SAF CK dekadal GTS CK daily GTS FEWS

30.31 29.9 40.6 33.8

0.01 0.34 0.16

0.75 0.58 0.68

0.69 0.69 0.65

14.75 19.11 16.80

0.60 0.77 0.71


15.19 12.43 14.09 14.24

0.18 0.07 0.06

0.76 0.74 0.73

0.58 0.58 0.56

9.90 10.15 10.47

0.63 0.54 0.71


7.97 8.46 8.01 7.93

0.06 0.006 0.005

0.61 0.62 0.64

0.34 0.40 0.41

7.43 7.32 7.15

0.57 0.53 0.63

SAF, South Africa; CK, combined kriging; GTS, Global Telecommunication System rain-gauge interpolated estimates; FEWS, Famine Early Warning System Meteosat-based estimates. Best scores are highlighted in bold.

gauges also affects the accuracy of the FEWS data in those poorly gauged areas. 3.2. Precipitation estimates validation results The most significant dekad with respect to precipitation totals is the first (1–10 March) with a measured mean of the South African rain-gauge data of 30.31 mm. In this dekad, according to the PO–PI validation method (Table 3), CK of the dekadal GTS data scored better in all of the five criteria (bold numbers). In the second dekad, all techniques performed similarly according to the correlation coefficient and the Nash index. The dekadal GTS data scored the highest Nash index and the lowest RMSE and CK of the daily GTS yielded the lowest s-RMSE. In the third and driest dekad, FEWS produced the lowest RMSE and bias and the highest Nash index and correlation coefficient. CK of the daily data yielded the lowest s-RMSE. In Fig. 5 measured precipitation is plotted against the estimated amounts for the three dekads of March 1996. In all dekads the estimation methods severely underestimated the higher amounts of precipitation, especially in the drier second and third dekads. They all produced a large number of ‘false alarms’ plotted on the yaxis (i.e. pixels with wrongly estimated amounts of precipitation greater than zero). They also produced a number of ‘misses’ plotted on the x-axis (i.e. estimated amounts of zero for locations with measured precipitation greater than zero), with the exception of

FEWS in the first dekad (Fig. 5c). r for all methods was highest in the first and rainiest dekad. Dekadal GTS provided the best estimate for low rainfall amounts up to 20 mm in the first dekad (Fig. 5a). The daily GTS data severely overestimated the lower amounts of rainfall (up to 60 mm) but provided the best estimate for the higher amounts. In the second dekad (Fig. 5d–f), all methods yielded similar results. Dekadal GTS was slightly better in the lowest amounts of rainfall and FEWS in the highest (over 30 mm). In the third dekad all methods performed poorly. The daily GTS data (Fig. 5 h) provided an almost invariant estimate. This can be attributed to the very low rainfall amounts and the smoothing effect of kriging. For this dekad, the lower precipitation values (i.e. as high as the mean of 8 mm) were estimated most closely by the dekadal GTS. For any higher amounts (up to 35 mm) FEWS produced the closest estimate. In general, the PI–PI validation method (Table 4) yielded better results than the PO–PI with higher correlation coefficients and Nash indices and lower RMSEs. Daily GTS data perform better in the PI–PI validation with lower RMSEs than the RMSEs of the other two techniques in all dekads. The slightly higher Nash index in the PI–PI results also shows that the daily GTS data yield more accurate estimates in all dekads which contradicts the findings of the PO–PI validation, which showed that dekadal GTS was better in the first two dekads and FEWS in the third. In Fig. 6 the interpolated South African precipitation is plotted against the estimated GTS and FEWS. Although the PI-PI

Table 4 Error criteria estimated from the pixel-to-pixel (PI–PI) comparison for the three dekads of March 1996 Dekad 1

2

3

Mean values (mm) Validation dekadal SAF CK Dekadal GTS FEWS Validation daily SAF CK daily GTS

28.94 29.41 33.27 28.49 31.09

Validation dekadal SAF CK dekadal GTS FEWS Validation daily SAF CK Daily GTS

13.92 11.74 13.48 14.11 11.10

Validation dekadal SAF CK dekadal GTS FEWS Validation daily SAF CK daily GTS

7. 07 8.49 7.79 8.68 5.58

Biases (mm)

Nash index

Linear corr. coefs. (r)

RMSEs (mm)

Scaled RMSEs

0.02 0.15

0.63 0.54

0.79 0.75

16.15 18.02

0.50 0.67

0.09

0.66

0.82

15.31

0.59

0.16 0.03

0.58 0.51

0.77 0.74

10.06 10.86

0.51 0.63

0.21

0.59

0.71

9.16

0.61

0.20 0.10

0.42 0.46

0.46 0.55

8.08 7.12

0.50 0.49

0.36

0.48

0.56

7.03

0.53

SAF, South Africa; CK, combined kriging; GTS, Global Telecommunication System rain-gauge interpolated estimates; FEWS, Famine Early Warning System Meteosat-based estimates. Best scores are highlighted in bold.

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Fig. 5. Measured precipitation in South Africa against estimated GTS and FEWS for 1st (a, b and c), 2nd (d, e and f) and 3rd (g, h and i) dekads, March 1996 (SAF, South Africa; CK, combined kriging; GTS, Global Telecommunication System rain-gauge interpolated estimates; FEWS, Famine Early Warning System Meteosat-based estimates).

comparison yielded better results and higher r values than the PO– PI comparison, it still proved that all methods underestimate the higher amounts of precipitation and overestimate the lower, especially in the drier second and third dekads. In the first (wettest) dekad (Fig. 6a–c), daily GTS provided the best estimate for low rainfall amounts up to almost 20 mm with fewer ‘false alarms’ and ‘misses’ than the other two methods. It also produced the overall closest estimate. In the second dekad (Fig. 6d–f), dekadal GTS gave the highest r. All methods underestimated values greater than 20 mm/dekad but not as severely as the PO–PI comparison suggested. In the third and driest dekad, daily GTS was overall the closest estimate with the highest r and fewer ‘false alarms’, followed by FEWS and dekadal GTS, respectively (Fig. 6g–i). In order to get an impression of the spatial distribution of the differences between the GTS and the FEWS estimates and the interpolated South African data, in the entire area and not only at the gauged pixels, the different estimates were subtracted from the validation images on a pixel-by-pixel basis. Table 5 provides the percentages of overestimated and underestimated pixels for all three dekads. The daily GTS estimates seem to be overestimating the amount of precipitation in more areas and by larger amounts than dekadal GTS and FEWS. On the contrary, dekadal GTS and FEWS are underestimating the rainfall amounts more than daily

GTS but the magnitude of underestimation seems to be smaller than the magnitude of the overestimation in the daily GTS images. More specifically, in the first dekad the most correct pixels, i.e. those that fall within 2 mm from the validation values (Table 5) represent 22% of the daily GTS total, 34% of the dekadal GTS and 17% of the FEWS. In the second dekad, these values are GTSdaily = 41%, GTSdek = 48% and FEWS = 40% and in the third dekad GTSdaily = 34%, GTSdek = 40% and FEWS = 43%. Fig. 7 is a graphic example for the first dekad. 3.3. Comparison of results to other precipitation estimation studies Similar studies on the accuracy of interpolated rainfall data and satellite estimates have been carried out for various areas in Africa. A number of these are presented here and an attempt is made to draw some rough comparisons. Hulme et al. (1996) carried out a 1961–1990 mean monthly climatology for Africa south of the Equator project at a resolution of 0.58 latitude/longitude for a suite of eight surface climate variables, including rainfall. They present accuracy figures for interpolated rainfall of 17% for the month of January and 106% for July. In similar percentage units, according to the PI–PI validation, the monthly accuracy for interpolation implemented in this study is 67% for the dekadal GTS data and 48% for the daily.


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Fig. 6. Interpolated South African validation data against estimated GTS and FEWS for 1st (a, b and c), 2nd (d, e and f) and 3rd dekad (g, h and i), March 1996 (SAF, South Africa; CK, combined kriging; GTS, Global Telecommunication System rain-gauge interpolated estimates; FEWS, Famine Early Warning System Meteosat-based estimates).

Fig. 7. (a) Sum of ten interpolated daily SAF validation data (SAFday); (b) SAFday minus interpolated daily GTS (GTSday); (c) interpolated dekadal SAF (SAFdek); (d) SAFdek minus interpolated dekadal GTS (GTSdek); (e) SAFdek minus FEWS. 1st dekad March 1996 (SAF, South Africa; CK, combined kriging; GTS, Global Telecommunication System raingauge interpolated estimates; FEWS, Famine Early Warning System Meteosat-based estimates).

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Table 5 Percentages of overestimated and underestimated pixels for the three dekads of March 1996, derived from subtracting the estimated from the validation images

The class intervals are different for the third dekad due to the smaller amounts or rainfall (GTS, Global Telecommunication System rain-gauge interpolated estimates; FEWS, Famine Early Warning System Meteosat-based estimates).

Xie and Arkin (1997, 1998) have estimated monthly precipitation for the globe (1987–1995) at a 2.58 2.58 spatial resolution using outgoing longwave radiation estimates from the National Oceanic and Atmospheric Administration’s (NOAA) Advanced Very High Resolution Radiometer (AVHRR). They report an RMSE of 54% of the measured precipitation between the latitudes of 208S and 208N. Herman et al. (1997) have also validated the 0.18 0.18 FEWS estimates quoting for the Sahel region and for June to September 1995 an accuracy of 40% of the measured precipitation value. Expressed in similar units the RMSE for the FEWS estimates in this study is 68% over the area of South Africa. Laurent et al. (1998) compared rainfall estimates from five different methods, at various space and time scales. The studied areas were the Sahel and a small region covering Burkina Faso. The rainfall estimates came from three different satellite-based algorithms, namely the GPI (Arkin and Meisner, 1987), the TAMSAT method developed at the University of Reading (Dugdale et al., 1990), the combined infrared-gauge Lannion-ORSTOM method (Carn et al., 1989) and two interpolation methods. They concluded that the satellite-based methods and the ground-based methods yielded similar results, which is one of the conclusions of the current study. The satellite-gauge technique of ORSTOM lead to slightly better scores: the estimation error for the dekadal cumulated rainfall and for a 0.58 0.58 resolution was about 35% of the mean rainfall amount. The GPI method, which FEWS also utilises, produced the highest dekadal errors of 67%, which is similar to the findings of this study for the first dekad of March 1996 (62%). Finally, Flitcroft et al. (1989) used data from a dense network in the Republic of Niger to investigate sampling errors in the measurement of areal mean precipitation. They found that estimates of 10-day rainfall totals over pixels by point measurements had a smaller average percentage error than daily estimates, which is in agreement with the findings of the PO–PI validation of this study—especially for the wetter dekads where the interpolated dekadal sums yielded better results than the respective daily data, but not with the results of the more sophisticated PI–PI validation.

4. Conclusions Two different precipitation estimation techniques for subSaharan Africa were validated using 31 daily records from a very dense rain-gauge network in South Africa. These were the only daily records available to us for the year 1996, which meant that a more extensive accuracy assessment using more dates could not be carried out at this stage. In general, the satellite-based precipitation estimates of FEWS and the ground-based estimates yielded similar results. The two different methods of validation, i.e. the PO– PI and the PI–PI, carried out for the three dekads of March 1996, were not categorical about which method of precipitation estimation performs better. If only the RMSE and the Nash index are considered then according to the more reliable PI–PI validation, the interpolation of the daily GTS gauge data yields better results. According to the rest of the statistical criteria though, different methods perform better in different dekads. An attempt was also made here to compare the results of similar studies in Sub-Saharan Africa with the validation results from this research but this has not been a straightforward task since they were carried out during different periods and regions with different climatic conditions. Moreover, the majority of these studies refer to monthly or annual estimates and larger spatial resolutions than the present study, which, according to Griffith et al. (1978), reduces the errors significantly. In general, it can be concluded that a relatively simple kriging interpolation scheme applied to the entire continent without subdividing it into smaller areas to examine more fully the spatial variability of the precipitation patterns, yields equally good estimates as the FEWS data, which are produced using a combination of satellite and gauge data and numerical model analyses of meteorological parameters. This is true apparently only for the areas with a sufficient GTS gauge density: the validation was carried out only in South Africa where the greatest density of GTS gauges exists. While a validation network such as the one used in this study over South Africa does not exist for any other subSaharan country, future work should focus on including more areas


(e.g. the Sahel, East Africa, central and south-central Africa) so that different climatological regions are included in the validation. Larger validation periods should also be investigated. Nevertheless, considering the fact that there is a serious problem of lack of representivity of rain-gauge measurements in very large parts of sub-Saharan Africa; the satellite-based estimates have performed similarly and in some cases better in both methods of comparison; satellite estimates might not be precise but offer good spatial coverage and can therefore be used in areas with inadequate rain-gauge networks; free, ready-to-use satellite-based products, involving no preprocessing are all the more available on-line (e.g. FEWS, TAMSAT),

it can be concluded that the satellite data appear to be more attractive to use for the operational monitoring of processes such as runoff and erosion, especially in the developing areas where resources are scarce. So far, the FEWS precipitation estimates presented in this paper have been used along with simple and easily paramiterisable surface runoff (SCS, 1972) and soil erosion (Thornes, 1985, 1990) models, to assist in the study of the sedimentation of lake Tanganyika and its consequences (Drake et al., 2004), the development of a land degradation monitoring system for sub-Saharan Africa (Symeonakis and Drake, 2004), and the optimisation of tsetse fly eradication programmes in Zambia (Symeonakis et al., 2007). Acknowledgements This project was funded by the Greek State Scholarships Foundation (IKY) and the Natural Resources Institute/United Nations Development Programme ‘Lake Tanganyika Biodiversity Project’2. The authors are also grateful to two anonymous reviewers for their constructive comments. References Arkin, A., Meisner, B.N., 1987. The relationship between large-scale convective rainfall and cold cloud over the western hemisphere during 1982–1984. Monthly Weather Review 115, 51–74. Barancourt, C., Creutin, J.D., Rivoirard, J., 1992. A method for delineating and estimating rainfall fields. Water Resources Research 28, 1133–1144. Borga, M., Vizzaccaro, A., 1997. On the interpolation of hydrological variables: formal equivalence of multiquadratic surface fitting and kriging. Journal of Hydrology 195, 160–171. Burrough, A., McDonnell, R.A., 1998. Principles of Geographic Information Systems. University Press, Oxford. Carn, M., Lahuec, J.P., Dagorne, D., Guillot, B., 1989. Rainfall estimation using TIR Meteosat imagery over the western Sahel. In: Proceedings of Fourth Conference on Satellite Meteorology and Oceanography, San Diego, CA, American Meteorological Society, pp. 126–129. Creutin, J.D., Obled, C., 1982. Objective analyses and mapping techniques for rainfall fields: an objective comparison. Water Resources Research 18 (2), 413–431. Drake, N.A., Zhang, X., Symeonakis, E., Wooster, M., Patterson, G., Bryant, R., 2004. Near real-time modelling of regional scale soil erosion using AVHRR and Meteosat data: a tool for monitoring the impact of sediment yield on the biodiversity of Lake Tanganyika. In: Kelly, R., Drake, N., Barr, S. (Eds.), Spatial Modelling of the Terrestrial Environment. John Wiley, Chichester, pp. 175– 196. Dugdale, G., McDouglas, V.D., Milford, J.R., 1990. Potential and limitations of rainfall estimates for Africa derived from cold cloud statistics. In: Proceedings of Eighth Meteosat Scientific Users’ Meeting, Norko¨pping, Sweden, Eumetsat EUM P08, pp. 211–220. Flitcroft, I.D., Milford, J.R., Dugdale, G., 1989. Relating point to average rainfall in semi-arid west-Africa and implications for rainfall estimates derived from satellite data. Journal of Applied Meteorology 28, 252–266. Gittins, R., 1968. Trend-surface analysis of ecological data. Journal of Ecology 56, 845–869. 2

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Further reading Cohen, A.J., Randall, A.D., 1998. Mean annual runoff, precipitation, and evapotranspiration in the glaciated northeastern United States, 1951–1980. USGS OpenFile Technical Report (Reston, USGS) available online at: http://water.usgs.gov/ lookup/getspatial?ofr96395_pre (accessed 20.06.06). Grimes, D.I.F., 2003. Satellite-based rainfall estimation for food security in Africa. Proceedings of International Workshop on Crop and Rangeland

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E. Symeonakis et al. / International Journal of Applied Earth Observation and Geoinformation 11 (2009) 15–26 Monitoring in Eastern Africa for Early Warning and Food Security, 28–30 January 2003, Nairobi, pp. 153–160. Available online at http://mars.jrc.it/ marsfood/Meetings/2003-01_Nairobi/Presentations/fullproceedings.pdf (accessed 21.06.06).

Stanski, H.R., Wilson, L.J., Burrows, W.R., 1989. Survey on Common Verification Methods in Meteorology, Geneva: World Meteorologocal Organisation, p. 114. Available online at: http://www.bom.gov.au/bmrc/wefor/staff/eee/verif/Stanski _et_al/Stanski_et_al.html (accessed 21.06.06).