a. Conventional approaches

Satellite imagery has been used for rainfall monitoring for more than 30 yr (Barrett 1970). Much of the interest in that time has focused on generating global datasets for climatological purposes (Kidd 2001). Initial methodologies used data from the thermal infrared (TIR) and visible sensors on geostationary satellites to identify convective cumulonimbus clouds (Barrett and Martin 1981). Geostationary satellites have the advantage of good spatial (∼5 km for TIR imagery in the Tropics) and temporal (30 min) resolution, but these methods tend to perform poorly at high latitudes because of the preponderance of nonconvective rain.

The most widely used of these algorithms is the Geostationary Operational Environmental Satellite (GOES) Precipitation Index (GPI, Arkin 1979) in which a rainfall amount of 3 mm is associated with each hour of CCD [a₀ = 0 mm, a₁ = 3 mm h⁻¹ in Eq. (1)]. For the GPI, the temperature threshold is normally taken as −38°C. Although the GPI gives good results over the tropical oceans, it is known to overestimate rainfall amounts over land (Arkin et al. 1994).

Since the late 1970s, methodologies based on passive microwave data (between 10 and 100 GHz) from instruments such as Special Sensor Microwave Imager (SMM/I) on polar-orbiting satellites have been used (Kidd 2001). Over the oceans at frequencies less than 40 GHz, microwave emission from raindrops gives a more reliable indication of rainfall than inference from TIR images. However over land surfaces at these frequencies, the information is degraded by the high and variable emissivity, which depends on vegetation and soil moisture (Morland et al. 2001). At higher frequencies (>60 GHz) the signal is dominated by scattering from ice particles within clouds and is therefore less sensitive to surface characteristics, but is conversely less directly related to raindrop density. An alternative approach is to make use of differences in the signal at different polarizations to correct for variations in surface emissivity (Kidd 1998).

An additional problem with sensors on polar-orbiting satellites is the poor temporal resolution (one or two overpasses per day), which is inadequate for monitoring rainfall on a daily timescale. Some workers have attempted to combine the advantages of geostationary TIR and microwave data, for example, by using the microwave data to recalibrate the TIR algorithm whenever it is available (Todd et al. 2001).

An important technological advance was made in 1997 with the launch of the Tropical Rainfall Measuring Mission (TRMM) satellite. This is the first satellite to have an onboard precipitation radar. Rainfall estimates using the precipitation radar are promising and this may be the method of choice in the long term but the current TRMM satellite does not provide data at appropriate temporal resolutions to be usable for the operational purposes of interest here.

b. Methods based on artificial neural networks

An artificial neural network (ANN) provides a computationally efficient way of determining an empirical, possibly nonlinear relationship between a number of “inputs” and one or more “outputs.” In addition, the ANN has been shown to be effective in extracting significant features from noisy data (Davolo and Naim 1991) and for this reason the most common applications have been in the field of pattern recognition. A more detailed description of neural networks is given in section 4b; here, we briefly indicate studies relevant to rainfall estimation.

Many studies have been performed using an ANN approach in atmospheric science (Hsieh and Tang 1998). In the field of remote sensing, an ANN approach has also been used by Aires et al. (2001) for retrieval of surface temperature and atmospheric water vapor from satellite data. Recently ANN algorithms for rainfall monitoring have been successfully applied by Hsu et al. (1997), Tsintikidis et al. (1997), and Bellerby et al. (2000).

In the case of the Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks (PERSIANN) system described by Hsu et al. (1997), the inputs are satellite TIR temperatures and their spatial derivatives plus a parameter that classifies the underlying surface as land, sea, or coast. The neural network is used to discriminate between rain rates of different cloud patterns via a “self-organizing feature map.” A big improvement was noticed if the network was continually updated by calibration against available real-time data. In a further paper (Sorooshian et al. 2000) good results could be achieved by real-time updating with TRMM precipitation radar.

Tsintikidis et al. (1997) compared an ANN approach with linear regression for rainfall estimation over the ocean from SSM/I passive microwave data and found that the ANN performed better than the regression for the same input.

In the method described by Bellerby et al. (2000), the input parameters are brightness temperatures and their spatial derivatives for three IR and one visible sensor on the GOES geostationary satellite. The output is the instantaneous rain rate. Training of the network was carried out using TRMM precipitation radar data. The method is shown to perform consistently better than a locally calibrated GPI technique.

c. Operational rainfall estimation for Africa

For operational, real-time rainfall monitoring in Africa, appropriate methodologies must not only be sufficiently accurate but must fulfil practical criteria with regard to availability of data, low cost, and low technological specifications for hardware and software.

There are several methods that are currently, or have been recently, in operational use in Africa. Most make use of a 10-day (dekadal) time step and are intended primarily for monitoring crop development on a regional or national scale during the growing season. Examples are listed next.

In West Africa a method devised by the Institut Français pour le Developpement en Coopération (ORSTOM) group [now Institut de Recherches pour le Développement (IRD)] at Lannion in France has been used over a number of years (Carn et al. 1989). As well as Meteosat TIR data, this approach uses surface temperature estimates to identify conditions conducive to strong convection.

The B4 method (Todd et al. 1995) is one of a number of methods devised by the Remote Sensing Unit at Bristol University and has been used operationally in West Africa and in the Nile basin. In this case the rainfall is estimated as a function of CCD and mean rainfall amount per rain day. Both the threshold temperature and the CCD calibration against rainfall amount are determined by comparison with local rain gauge data available in the previous 10-day period.

The Climate Prediction Center (CPC) at the United States National Oceanic and Atmospheric Administration (NOAA) has developed several algorithms, the results of which have been used by U.S. Agency for International Development (USAID) in Africa for famine early warning. Until December 2000 an algorithm was employed (Herman et al. 1997) using the GPI as a baseline estimate, which was then recalibrated in the light of available real-time rain gauge data from the GTS. An additional feature was the incorporation of numerical weather analysis data to represent orographic rainfall. Since January 2001, this has been replaced by an algorithm which incorporates GPI, microwave imagery from SSM/I, and the Advanced Microwave Sounding Unit (AMSU) satellite and GTS rain gauge data combined according to a methodology described by Xie and Arkin (1996). The algorithm is calibrated to give daily rainfall amounts.

The Tropical Applications of Meteorology using Satellite Data (TAMSAT) group at Reading University uses an approach based on Eq. (1) but as with the B4 method, T_t, a₀, and a₁ are determined by calibration against local gauges (Milford and Dugdale 1990). A difference between this method and the operational techniques described so far is that calibration is carried out using historic rain gauge data. The rationale is that, while contemporaneous, high-quality gauge data should give the best calibration; in practice, sufficient data are rarely available in near real time with adequate quality control. Using data from previous years for the same calendar month means that the calibration can be performed with many more observations and greater opportunity for filtering out suspect values. The disadvantage is that the accuracy of the estimates is degraded by the interannual variability in the calibration parameters (Laurent et al. 1998). The TAMSAT algorithm is used as the control for comparison with the ANN approach in this paper and is therefore described in more detail in section 4.

More recently Grimes et al. (1999) have attempted to make best use of both historic and contemporaneous gauge data by basing an initial calibration on historic data and then using a kriging technique to merge this rainfall estimate with any good quality rain gauge data available in real time.

Comparisons between methods used operationally in Africa have been inconclusive. Snijders (1991) compared the TAMSAT approach with the University of Bristol Polar-Orbiter Effective Rainfall Monitoring Integrative Technique (PERMIT) method (similar to B4 described earlier) and several other techniques in the West African Sahel and found that there was little to choose between the methods. Laurent et al. (1998) performed a more detailed comparison of the Lannion and TAMSAT methods at a variety of space and time scales for West Africa and confirmed that the real-time Lannion calibration gave significantly better results provided sufficient gauge data were available. In the absence of real-time calibration, both methods gave similar results. Thorne et al. (2001) compared the TAMSAT method and the earlier (prior to 2001) CPC method in southern Africa and found that the CPC algorithm was superior where there was a high density of GTS gauges, but the TAMSAT approach worked better in other areas.

d. Rainfall monitoring for hydrological purposes in Africa

The methods described in section 2c with the exception of the current CPC algorithm have all been designed to produce dekadal (10 day) rainfall estimates. There has been little investigation of the accuracy and reliability of operational daily estimates in Africa—particularly within a hydrological context. From the ergodic principle, one would expect that daily estimates would be useful provided the reduced averaging in the time domain was compensated for by increased averaging in space. Grimes and Diop (2003) have shown that daily CCD-based estimates (with historic calibration) give useful results as the input to a river catchment with an area of ∼80 000 km². In this case, the results are at least as good as a gauge network with one gauge per 15 000 km², which is relatively dense for this part of Africa. They also show that the river flow model output can be improved if numerical weather prediction model analysis data are used to modulate the rainfall estimation algorithm.

From these considerations and following the discussion in the preceding sections, we have developed an artificial neural network approach to real-time rainfall estimation at a daily time step based on Meteosat TIR data and NWP model analysis information. Both sources of data are readily and reliably available in Africa in real time. Data from passive microwave sensors have not been included in the interests of algorithm simplicity (taking into account problems mentioned earlier) and also because microwave data reception systems are not widely available within Africa. The work focuses on seasonally arid Africa but it is expected that the methodology is applicable to many regions within the Tropics.

a. Data for case study area

Zambia is located in central Africa between 8° and 18°S and 22° and 34°E. It covers an area of 750 000 km². It was chosen for this study mainly because the rainfall climate is uncomplicated and representative of much of Africa. Additionally we were grateful for the excellent cooperation of the Zambian Meteorology Service in providing rain gauge and other data. Zambia has one rainy season running from October to April corresponding to the annual passage of the intertropical convergence zone (ITCZ) with little influence from either orography or coastline. Daily records from 77 gauges were available covering the period October 1995–April 1999. Rigorous quality control was applied. Stations were rejected for gaps in time series and other data irregularities as well as local knowledge of past reliability. This left a total of 35 gauges, the locations of which are shown in Fig. 1.

NWP analysis fields for this area and time period were available from the European Centre for Medium-Range Weather Forecasts (ECMWF) for each day at 0000, 0600, 1200, and 1800 UTC at 0.5° grid resolution. The fields selected as being likely to provide information on rainfall rate were relative humidity and horizontal wind velocity at the surface and vertical velocity at 400 and 700 mb. In order to reduce data requirements, only the 1800 UTC data were used and the data were extracted for a window 8°–21°S and 18°–34°E. Meteosat TIR images corresponding to the ECMWF analysis time and daily CCD images were extracted from the TAMSAT archive. The pixel size of the Meteosat images for Zambia is roughly 7 km × 5 km.

b. Data preparation

2) NWP model analysis fields

The NWP model analysis fields are expected to contribute information about the large-scale weather pattern to the neural network. In order to represent this information with minimum data requirements, a principal component analysis was first performed on the windowed data (Wilks 1995). The model field at grid point i and time t [written x_i(t)] can then be expressed as a linear combination of p principal components or empirical orthogonal functions

View Expanded

where a_j are the amplitudes required to build the field x_i(t) from the principal components E_ij.

In this way, we can represent of the whole field within the windowed area at time t by the p amplitudes a_j. The process is efficient if most of the variance in the dataset can be represented by a small number of principal components—in other words, p can be set to a small value.

In our case, most of the variance for relative humidity and horizontal velocity is explained by the first five principal components (see Table 1). Although the proportion explained for the vertical wind components is relatively small, p was set to 5 for all variables for the sake of consistency. Thus the 1800 UTC field pattern for each day is described by just five numbers (the amplitudes a_j, j = 1–5) for each parameter. As an example, the first principal component of the humidity field is shown in Fig. 3. The dominant feature is a strong maximum of humidity over southern Zambia roughly reflecting the position of the ITCZ at the height of the rainy season. The other components are not shown as a direct physical interpretation is less obvious.

a. The TAMSAT algorithm (TAMCCD)

The TAMSAT rainfall estimation technique was used in this study as an example of a simple TIR-only technique against which to compare the ANN approach, therefore it is worth describing in some detail.

For daily rainfall estimates, a separate calibration was carried out for each month for the whole of Zambia. Detailed examination of the gauge data did not indicate that subdivision into smaller calibration zones was necessary. The calibration is a two-stage process. In the first stage rain gauge observations are compared with CCD values for the gauge pixels at a number of different temperature thresholds in order to determine the value of T_t, which best discriminates between rain and no rain. This is done using a contingency table as shown in Table 2.

The cells in the contingency table indicate the number of daily events for which the CCD and gauge observations agree or disagree as to the presence or absence of rain. Referring to the cell contents in Table 2, the optimum threshold is the one for which

View Expanded

Having established the optimum value for T_t, the parameters a₀ and a₁ in Eq. (1) are determined by linear regression of the daily average kriged rain gauge estimates for the gauge pixels against the daily average CCD values for the same pixels. The regression is carried out using only nonzero CCD pixels as the estimates are calculated by applying the calibration equation only to nonzero CCD pixels. To avoid confusion with other CCD-based approaches, this technique will be referred to as TAMCCD from now on.

b. Artificial neural network algorithms

2) Initial ann algorithm (TAMANN1)

The kind of neural network used for this study is a feed-forward multiple-layer perceptron (MLP). The MLP has a relatively simple architecture in which each node receives output only from nodes in the preceding layer and provides input only to nodes in the subsequent layer. Thus for the node j in the kth layer the net input l_kj is a weighted average of the outputs of the (k − 1)th layer

View Expanded

where w_(k−1)ij is the weight connecting the output of the node i in the (k − 1)th layer to node j in the kth layer and N_k−1 is the number of nodes in the (k − 1)th layer.

The output of node j is a specified function of l_kj

o_kjfl_kj(5)

The eventual output is then a function of the weighted combination of the final hidden-layer output values (Fig. 4).

Guided by previous studies (Sorooshian et al. 2000; Bellerby et al. 2000) and our own assessment of useful information, the initial list of inputs included TIR pixel values and their spatial variance as well as CCD data, location coordinates and NWP model parameters. The full list is shown in Table 3. The initial network architecture consisted of three layers: input, output, and a single hidden layer. In all there were 49 input units, 10 hidden-layer nodes, and 1 output (the estimated rainfall) as shown in Fig. 3a. This gives a total of 500 weights (w_kij) to be determined. The transfer function relating input to output was a sigmoid function:

O_kjl_kj⁻¹(6)

To ensure that the model has similar sensitivity to changes in the various inputs, all of the inputs were normalized to values between 0 and 1. For an input variable x with maximum x_max and minimum x_min we calculate the normalized value x_A as

View Expanded

The optimum weights were determined by training against the target values (in our case the kriged gauge pixels for all days in a designated training period). Initially random values were assigned to all the w_kij and a standard back-propagation algorithm (Lonbladd et al. 1991) was used to adjust the weights as described earlier. The quality of the network performance is defined by the mean-square difference (msd)

View Expanded

where r_Apt and r_kpt are, respectively, the ANN estimate and the kriged estimate for gauge pixel p on day t; N_t is the number of days and N_p is the number of pixels. The algorithm described earlier is referred to from now on as TAMANN1.

3) Final ann algorithm (TAMANN2)

The performance of TAMANN1 was found to be inferior to TAMCCD (see section 5). One of the likely reasons for this is the relatively small number of training values available to train the 500 input weights. It was therefore necessary to reduce the size of the network. Because of the complexity of the internodal connections in the network and the interdependence of some of the input parameters, it is not necessarily obvious which input parameters are important and which, if any, are redundant. Simple strategies like comparison of runs with different combinations of inputs excluded give results that may be very difficult to interpret. A more robust technique is “network pruning” as described by Weigend et al. (1991). During pruning the network is trained to a set of training data with an additional criterion of minimizing the number of weights. This is achieved by use of an algorithm, which considers both the size and the number of weights through a complexity term Z defined as

View Expanded

where W_1ij are the weights connecting the input and second layers; W₀ is an empirically determined scaling parameter for the weights; N₁ and N₂ are the numbers of input and second-layer nodes.

The total cost function C to be minimized for the optimized network is then

CZ.(10)

The learning rule changes the weights according to the gradient of the entire cost function C, continuously reducing the error under the constraint of a low-complexity network. The effect is to suppress the weights of superfluous nodes. Input parameters associated with small weights may then be eliminated. To verify this pruning technique an extra input was added to the ANN for which only random numbers were used. It was confirmed that weights connected to this input were reduced to negligible values during pruning.

After numerous trials, it was found that the raw TIR data and its spatial variance could be eliminated provided CCD at several different temperature thresholds were included. Similarly, station location as represented by latitude and longitude was found to be unimportant. These results were confirmed by improvements in validation statistics as described in the following section. Inclusion of an additional hidden layer produced further improvement in validation statistics in line with the results of Bellerby et al. (2000). The final configuration, which gave the best results earlier, is that shown in Fig. 4b with 30 input variables (listed in Table 3) and two hidden layers.

Experiments were also carried out to examine the effect of training the network with a different numbers of stations. As might be expected optimum results were achieved from training with the full set of 25 calibration gauge pixels although useful results could still be obtained from as few as 2.

A slight problem with this configuration of the ANN was that it was difficult to generate zero rainfall. This resulted in estimates of very low rainfall (<1 mm) over large areas. While this is not significant at a daily timescale, it is obviously nonphysical and may give rise to problems if daily values are integrated over longer periods. A pragmatic solution was to set all pixel estimates to zero if CCD = 0 for T_t = −30°C.

This final algorithm as described in the preceding paragraphs will be referred to as TAMANN2 in the rest of this paper.

a. Calibration of TAMCCD

The CCD–rainfall calibration parameters for all months and all validation years are shown in Table 4. It can be seen that there is significant interannual and intraseasonal variability. Within a season, the optimum threshold varies between −30° (October, March) and −50°C (April).

The interannual variation seems strongest at the beginning and end of the season. October shows the highest percentage change in the rainfall rate a₁ for a given value of T_t, while April is the only month for which T_t varies by as much as 20°C.

b. Calibration of ANN algorithms

The ANN algorithms were trained using the same 3-yr calibration periods as for TAMCCD. As an example, the mean input weights for TAMANN2 as represented by ΣN2j=1 Nij/N2 for all four of these periods are shown in Fig. 5.

Interpretation of Fig. 5 must be made with caution. The complex and distributed nature of the network connections mean that too much significance should not be attached to the relative sizes of the mean weights. Nevertheless, it can be seen that there is a consistency from year to year with the highest mean weights corresponding to CCD values at −30° and −60°C and the first principal components of relative humidity and vertical velocity. The correspondence with CCD is to be expected. The effect of the first principal component of the humidity and vertical velocity appears to be to allow the network to take account of the gross seasonal pattern. The relationship between the amplitude of the first principal component of relative humidity and rainfall is demonstrated for one season in Fig. 6. The rainfall has been scaled to better show the comparison. The principal component amplitude is positive during the rainy season, negative outside it, and reaches a maximum in midseason. Within the season there is also evidence of a correspondence between individual high-rainfall events and high amplitudes.

c. Comparison of results

Results from all the algorithms were compared with the kriged gauge pixel data on three different space-time scales. These were

• daily rainfall quantities for individual pixels (scale = 1 pixel-day),

• daily rainfall average over all 10 validation pixels (scale = 10 pixel-days), and

• average rainfall over 10-day period and all 10 validation pixels (scale = 100 pixel-days).

Quantitative comparison is based on several statistical parameters. These are bias, root-mean-square difference (rmsd), normalized root-mean-square difference (nrmsd), explained variance R² and skill. Their definitions follow:

View Expanded

In these equations r_e is the estimated rainfall for event e, r_ke is the corresponding kriged gauge pixel rainfall and ɛ_ke is the error on the kriged gauge pixel rainfall for the same event. The value N_e is the number of events over which the statistics are calculated and an overbar indicates an average over all events.

The bias is an indicator of the quality of the mean estimated rainfall and the rmsd shows the likely error in an individual event estimate. The nrmsd is the rmsd normalized with respect to the error on the kriged gauge estimate for the same pixel. Thus an nrmsd < 1 indicates that the estimates lie, on average, within the uncertainty limits of the validation data. The value R² shows the fraction of the variance of the rainfall explained by the estimation algorithm. The skill score shows the success of the algorithm relative to using the mean observed rainfall as the estimate. Here, skill = 1 is a perfect match to the observations; skill = 0 means that the estimates are equivalent to using the mean observed value; skill < 0 implies the estimates are worse than using the mean value.

The statistics for the TAMCCD, TAMANN1, and TAMANN2 estimation methods for each individual year and for all years combined are summarized in Table 5. Figures in bold indicate the best result for each time period. It can be seen that at all space and time scales and for all statistical parameters TAMANN1 performs least well and TAMANN2 is slightly but consistently better than TAMSAT with the exception of the bias in 1988/89. The small differences in number of events for TAMANN1 is due to days missing from the TIR record. The improvement of TAMANN2 over TAMANN1 is ascribable to the changes in network architecture, inclusion of additional CCD thresholds, and pruning as described in section 4b(3). The remainder of this discussion will concentrate on comparison of TAMANN2 and TAMCCD.

Inspection of scatterplots (Fig. 7) indicates more clearly the nature of the differences. Figure 7a shows the scatterplot for individual pixel-days. A large spread is to be expected here because neither the CCD nor the model data can resolve rainfall quantities accurately at this resolution, while error on the kriged pixel estimates and satellite collocation error will also contribute to the scatter. Nevertheless, differences in the quality of the performance of the two methods are still apparent. Both methods tend to underestimate rainfall above 10 mm but TAMANN2 does somewhat better and there is also a slightly tighter spread around the one-to-one line for lower rainfall.

For the daily pixel average (Fig. 7b), the spread of data points is reduced because of the spatial averaging and the improvement of TAMANN2 for rainfalls above 10 mm is more clearly discernable. Although there is a tendency for both methods to underestimate, it is less pronounced for TAMANN2. Unfortunately, the wide geographical distribution of the validation pixels means that average rainfall amounts do not exceed 25 mm, so it is not possible to see whether TAMANN2 does much better in estimating extreme rainfall over an extended area.

The better estimation of high rainfall amounts can be also seen in a typical time series of daily average data for 1997/98 shown in Fig. 8. The high peaks (>10 mm) in the kriged rainfall are all more closely approached by the TAMANN2 estimate with the exception of day 96 (overestimated by TAMANN2). This is a useful result as better estimates of high daily rainfalls are of obvious importance for river flow forecasting. It is also worth commenting that the pixels averaged here are noncontiguous and that results may well be better when averaged over a similar number of contiguous pixels (such as a river catchment) as errors associated with collocation will become less important.

For the 10-day pixel average in Fig. 7c both methods do extremely well with R² ∼ 0.9 (Table 5c). These high correlations are attributable to three factors. First, TIR-based methods work well in convective rainfall regimes as in Zambia. Second, the use of noncontiguous validation pixels reduces the daily mean rainfall, which again favors TIR-based methods. More contiguous data are needed to see how well higher rainfall amounts with the same degree of averaging are represented. Third, the use of kriged gauge data provides calibration and validation at an appropriate spatial scale and reduces the scatter in the validation plots. Of the two methods TAMANN2 is again slightly better with a more even distribution of points about the one-to-one line as evidenced by the negligible bias in Table 5c.

While the statistics and graphs described so far focus on the 10 validation pixels shown in Fig. 1, it is also informative to look at the area rainfall map produced by the two methodologies. An example is shown in Fig. 9 for 30 March 1997. It is apparent that the overall rainfall pattern is similar for both methods, emphasizing the importance of the CCD in the TAMANN2 algorithm. However TAMANN2 produces higher rainfall values overall and the areas of highest rainfall (shown red in Fig. 9) correspond to regions of very cold cloud. Comparison with CCD images (also shown in Fig. 9) indicate that the shape of the high-rainfall area is largely determined by the −60°C CCD while the overall light-rainfall pattern is closer to the −30°C picture.

A question arises as to whether the better results of the network are due to the additional input data or the greater complexity of the network structure. We have found that a network trained on the CCD data alone does not do as well as the standard regression algorithm. On the other hand, preliminary results of ongoing work indicate that a multiple regression using the same inputs as TAMANN2 performs less well than the neural network. The implication is that both the additional NWP information and the nonlinear network characteristics are important. These results will be reported in full elsewhere.

Although in general the improvements afforded by the TAMANN2 algorithm are small, the reduction in bias for high-rainfall amounts is significant for hydrology. It is also worth pointing out the neural network training process is a one-step calibration process, which does not require separate monthly calibrations or separate specification of a temperature threshold. Furthermore, the neural network framework allows easy incorporation and testing of other data streams, which are likely candidates for improving the rainfall estimates.