An Artificial Neural Network Approach to Multispectral ... - AMS Journals

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An Artificial Neural Network Approach to Multispectral Rainfall Estimation over Africa ROBIN CHADWICK Met Office Hadley Centre, Exeter, United Kingdom

DAVID GRIMES* Department of Meteorology, University of Reading, United Kingdom (Manuscript received 22 June 2011, in final form 8 December 2011) ABSTRACT Multispectral Spinning Enhanced Visible and IR Interferometer (SEVIRI) data, calibrated with daily rain gauge estimates, were used to produce daily high-resolution rainfall estimates over Africa. An artificial neural network (ANN) approach was used, producing an output of satellite pixel–scale daily rainfall totals. This product, known as the Rainfall Intensity Artificial Neural Network African Algorithm (RIANNAA), was calibrated and validated using gauge data from the highland Oromiya region of Ethiopia. Validation was performed at a variety of spatial and temporal scales, and results were also compared against Tropical Applications of Meteorology Using Satellite Data (TAMSAT) single-channel IR-based rainfall estimates. Several versions of RIANNAA, with different combinations of SEVIRI channels as inputs, were developed. RIANNAA was an improvement over TAMSAT at all validation scales, for all versions of RIANNAA. However, the addition of multispectral data to RIANNAA only provided a statistically significant improvement over the single-channel RIANNAA at the highest spatial and temporal-resolution validation scale. It appears that multispectral data add more value to rainfall estimates at high-resolution scales than at averaged time scales, where the cloud microphysical information that they provide may be less important for determining rainfall totals than larger-scale processes such as total moisture advection aloft.

1. Introduction The African continent spans a vast array of different landscapes and climates, but factors common to the whole region are the huge importance and frequent unreliability of rainfall. Because of the scarcity of rain gauge data available in real time over Africa, rainfall estimates are usually taken from satellite-based algorithms or from a combination of gauge and satellite estimates (e.g., Grimes et al. 1999). For drought monitoring, 10-day (dekadal) rainfall accumulations have traditionally been used. This is because satellite rainfall estimates (RFEs) are more accurate when averaged over longer time scales, and because it was considered that 10-day rainfall estimates

* Deceased.

Corresponding author address: Robin Chadwick, Met Office Hadley Centre, Fitzroy Rd., Devon EX1 3PB, United Kingdom. E-mail: [email protected] DOI: 10.1175/JHM-D-11-081.1

provided a high enough temporal resolution to monitor the availability of water for crops during the growing season. Recently there has been interest in providing daily rainfall estimates, as it is not only the total dekadal rainfall that affects crop growth, but also the daily distribution of rainfall within a dekad (Teo and Grimes 2007). However, this requires satellite RFEs to be accurate at a daily scale. As well as being used for famine early warning systems, rainfall estimates have more general potential applications in agriculture in the region. Numerical crop-yield models such as the General Large-Area Model (GLAM; Challinor et al. 2004) require rainfall inputs at a daily scale over a growing season. In this case a seasonal rainfall forecast updated throughout the season with daily satellite rainfall observations would seem to provide one possible method of producing accurate crop-yield forecasts. Short-term river flow and flood forecasting is another potential application of rainfall estimates (Grimes and Diop 2003). The requirement here is for short timescale (daily or shorter) rainfall estimates over a river basin,

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which can then be combined with a hydrological model. This technique has so far proved impractical for operational purposes because of the limited accuracy of available rainfall estimates at short time scales over Africa. Various satellite RFE products are commonly used to provide rainfall estimates over Africa, and these normally use infrared (IR) and/or microwave data from a variety of satellite platforms, often combined with available gauge data (see Kidd et al. 2009 or Kidd 2001 for a review of satellite RFE methods). However, estimates from the current generation of satellite RFEs show relatively low accuracy when validated at a daily time scale over Africa (Dinku et al. 2008; Laws et al. 2004). This paper investigates whether the use of multispectral visible and IR data from the Spinning Enhanced Visible and IR Interferometer (SEVIRI) instrument can lead to improved satellite rainfall estimates over Africa compared to a single-channel IR product, particularly at daily time scales. No current operational satellite RFE uses geostationary multispectral data to produce rainfall estimates over Africa for use in food-security applications. The advantage of using only SEVIRI data, as opposed to a multisatellite product, is that many African Met services are equipped to receive SEVIRI data, and could therefore apply and adapt rainfall estimates produced from SEVIRI themselves. Estimates were produced and validated at several spatial and temporal scales, as applications of RFEs over Africa require products at a variety of different scales. The Tropical Applications of Meteorology Using Satellite Data (TAMSAT) Met Office Rainfall for Africa (TAMORA) algorithm (Chadwick et al. 2010) used data from a mobile precipitation radar to calibrate SEVIRI data and produce precipitation estimates over West Africa. A validation against gridded dekadal gauge data showed that TAMORA produced accurate estimates in the region close to the calibration radar, but that this accuracy was reduced for other areas of West Africa. This suggests the need for local calibration of multispectral satellite rainfall products, which is a result also found by Ba and Gruber (2001) when using a multispectral satellite RFE over North America. Because of the lack of precipitation radar networks over most of Africa, regional calibration of satellite RFEs by radar is currently impractical. One alternative is to use rain gauge data for calibration of a satellite RFE algorithm. Although gauges are comparatively sparse in Africa compared with other continents, there is far greater gauge coverage than radar coverage. This is particularly true if real-time gauge data are not needed, as relatively dense rain gauge data are often collected by African Met agencies but not distributed internationally in real time. Therefore an algorithm that is calibrated

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with historical gauge data has the potential to be used over much more of Africa (with regional calibration) than one calibrated with radar. The relationship between multispectral SEVIRI data and surface rainfall is complex, nonlinear, and not well understood. Therefore, any algorithm relating the two must currently be largely empirical in nature. TAMORA uses a contingency table method to establish a probabilistic relationship between the SEVIRI data and rainfall rain rate. The alternative method chosen here is to employ an artificial neural network (ANN) to find the pattern between satellite data and rainfall. Neural networks have previously been used on many occasions in the field of satellite rainfall estimation (Sorooshian et al. 2000; Bellerby et al. 2000; Hong et al. 2004) with the Estimation of Precipitation by Satellites-Second Generation (EPSAT-SG) method of Berge`s et al. (2010) using an ANN to produce rainfall estimates over Africa from multispectral SEVIRI data. However, rain gauges have rarely been used for calibration (the exception being the TAMANN algorithm of Coppola et al. 2006), and as far as the authors are aware this paper describes the first instance of gauge calibration combined with multispectral input data. The ANN used here will be referred to as the Rainfall Intensity Artificial Neural Network African Algorithm (RIANNAA).

2. Data a. Ethiopian rain gauge dataset A relatively dense rain gauge dataset for the Oromiya region of Ethiopia was provided by the National Meteorological Agency of Ethiopia, comprising 278 stations with daily data from 2002 to 2006. After quality control procedures, this number was reduced to 215 as a number of stations containing large amounts of missing, duplicated, or questionable data were excluded. Oromiya gauge locations are shown in Fig. 1. To calibrate and assess satellite rainfall estimates over Africa, it is usually necessary to compare them with rain gauge data. Satellite rainfall products produce pixel rainfall estimates with a resolution of 3 km at the equator for SEVIRI-based algorithms (Schmetz et al. 2002). However, rain gauge data by their nature consist of point estimates, which in Africa are often sparse and unevenly distributed. A comparison of SEVIRI pixelscale radiances with gauge point rainfall estimates would not be comparing like with like. Therefore, it is necessary to interpolate the gauge data to satellite pixel scale. The interpolation method used here is kriging, which has been shown to perform better than other interpolation methods (e.g., Thiessen polygons and spline surface fitting) for medium- and low-density gauge

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FIG. 1. (a) Elevation of Oromiya region of Ethiopia. Gauges used for RIANNAA training, testing, and validation are shown as black crosses; country boundary is in white. Elevation data used is U.S. National Imaging and Mapping Agency (NIMA) Digital Terrain and Elevation Data (DTED). (b) Location of gauge data used for training, testing, and validation of RIANNAA, and missing data for 1 Jul 2006. Black line shows country border.

networks such as the ones generally found in Africa (Creutin and Obled 1982; Lebel et al. 1987; Grimes and Pardo-Iguzquiza 2010). Separate variograms for July, August, and September (JAS) were computed, and the daily time series for JAS 2004–06 was then interpolated to SEVIRI pixel scale using ordinary kriging. The variogram for August is shown in Fig. 2, and the exponential model fitted to the experimental variogram appears to reproduce well the spatial correlation of the data. Detailed investigation of any anisotropy of the variogram in this dataset was beyond the scope of this study. To minimize the error in the comparison of satellite data to kriged gauge estimates, only satellite pixels containing at least one gauge were used in this study (these are referred to as gauge pixels). As for the purposes of satellite RFE calibration and validation, we are only interested in these gauge pixels; it was considered a reasonable assumption that if a gauge registered zero rainfall for a day, the gauge-pixel estimate could also be taken to be zero. Following Grimes et al. (2003), all gauge-pixel kriged estimates where the corresponding gauge recorded zero rainfall were set to zero. When using this method, the variogram for nonzero rainfall is computed using only nonzero rainfall values. Figure 3 shows the distribution of daily 2006 JAS gauge data with and without interpolation to 4-km scale by kriging. It can be seen from Fig. 3d that the kriging procedure has the effect of increasing low gauge rainfall values and reducing high ones. This transformation is consistent with the findings of Balme et al. (2006) with regard to the distribution of point and areal rainfall time series in the Sahel.

b. Multispectral SEVIRI data SEVIRI measures radiance values in a number of different spectral bands. Each spectral channel can be used to give different information about the atmosphere and in particular about clouds and indirectly about rainfall. The infrared window channels (10.8 and 12.0 mm) can be used to infer the temperature, and therefore height of the emitting cloud top, and this has been the basis of single-channel rainfall estimation techniques such as the Geostationary Operational Environmental Satellite (GOES) precipitation index (GPI; Arkin 1979) and TAMSAT (Grimes et al. 1999). Radiance in the visible channels (0.6 and 0.8 mm) is mainly a function of the physical thickness and geometry

FIG. 2. Climatological variogram of Ethiopian daily rainfall (excluding zero rainfall values) in August, fitted with the exponential model. The y axis shows the variogram value. Experimental variogram is shown by line interspersed by dots and model variogram by smooth line.

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FIG. 3. Histograms of daily Oromiya rain gauge data for 2006 JAS: (a) raw gauge data, (b) gauge data kriged to 4km Meteosat Second Generation (MSG) pixel scale, (c) gauge data kriged to 4-km and standardized by ECDF method, and (d) kriged data plotted against raw gauge estimates (excluding zero estimates), with least squares fit line.

of a cloud together with the incident angle of the solar beam, with effective particle size re of only secondary importance and cloud phase seemingly unimportant (Barrett and Martin 1981; King et al. 1995). As cloud thickness is an important constraint upon rainfall, with rain formation processes much more likely to occur for thicker clouds, visible data can give useful information about rainfall probability. This is particularly true when combined with IR information about cloud-top temperature. As well as visible wavelengths, measurements of reflectance in the near-IR (NIR) part of the spectrum are available during the day in the 1.6- and 3.9-mm channels. These channels are useful for the determination of cloudtop properties, as the reflectance in these channels is determined by optical depth (t), re, and particle phase. The 1.6-mm channel can be considered a purely solar channel, whereas the 3.9-mm channel has components from both solar reflectance and thermal emission. Therefore, the thermal component of the received 3.9-mm radiance must be removed before the reflectance can be used. This is done following the method of Lindsey et al. (2006) by assuming that the emitting temperature at 8.7 mm is the

same as the 3.9-mm emitting temperature and subtracting this from the total 3.9-mm radiance. The NIR channels are often used in combination with a visible channel to provide information on both cloud depth and particle phase/size. During the night, when visible and NIR channels are unavailable, a combination of IR channels can be used to provide information about cloud properties. The split-window technique of Inoue (1987) uses the 10.8– 12.0-mm brightness temperature difference (BTD) to distinguish thin high-level cirrus cloud from thicker clouds. The 3.9–10.8-mm or 8.7–10.8-mm BTD can be used for discrimination of deep clouds with large cloud particles from thin clouds and clouds composed of small particles (Lensky and Rosenfeld 2003; Thies et al. 2008). The 8.7–10.8-mm BTD is more useful for ice clouds than water clouds (Lutz et al. 2003).

3. TAMSAT TAMSAT is similar in approach to the GPI, but with the adaptation that both the threshold temperature at which rain is assigned and the assigned rain rate vary

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regionally and seasonally in the algorithm. This corresponds to the empirical relationship between IR cloudtop temperature and rainfall varying in both space and time, particularly over the diverse terrain and climate of Africa. TAMSAT is calibrated with historical rain gauge data in a two-stage process. The first stage is to determine a cloud-top threshold temperature, below which a satellite pixel is assigned as raining. This is done by comparing gauge observations against several different satellite IR brightness temperature (BT) thresholds. Once a threshold temperature has been established, rainfall estimates are produced using a linear fit between cold-cloud duration (CCD) and historical gauge values. For a more detailed description of TAMSAT methodology, see Grimes et al. (1999). While this simple approach has been shown to perform well in many regions of Africa (Jobard et al. 2011; Dinku et al. 2007), it has obvious limitations. High cirrus clouds with tops colder than the threshold temperature will be identified as raining, while warm-cloud rainfall events will not be captured.

4. ANN methodology ANNs are a pattern recognition tool used to find empirical relationships between a set of ‘‘input’’ variables and some corresponding ‘‘output’’ variables. ANNs consist of a number of ‘‘nodes’’ able to pass information between one another in a similar way to neurons in the brain (see Fig. 4 for a schematic of an ANN). For a full description of ANN theory, see Bishop (2000) or Picton (2000). Grimes et al. (2003) gives a description of the particular type of ANN (a multilayer perceptron) used for RIANNAA. The ANN back-propagation code used here was based on a modified version of that developed by Lo¨nnblad et al. (1991) for pattern recognition problems in particle physics. A calibration, or ‘‘training,’’ process is used to prepare an ANN for a particular purpose. A large number of training patterns are used where both the inputs and the corresponding output(s) are known. Each pattern consists of a set of input variables and the corresponding ‘‘target’’ output variable(s). To be useful, ANNs must be capable of generalization. This means that after training they can process a set of inputs not used in the training process (and hence not previously ‘‘seen’’ by the network) into a reasonable output value. If training continues for too long, an ANN can become ‘‘overtrained’’ to its training dataset and loses the ability to generalize. To avoid overtraining, the available input/output patterns can be separated into a training dataset, a smaller

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FIG. 4. Schematic of the feed-forward multilayer perceptron with seven inputs and four layers used in RIANNAA IR108, showing nodes and weighted connections between them. The final output layer gives a rainfall estimate.

‘‘test’’ dataset, and a third ‘‘validation’’ dataset. During training, an error value E is periodically calculated for both the training and test datasets. If E continues to fall or stabilizes for the training dataset but begins to rise for the test dataset, then overtraining is diagnosed and the training process is stopped. The validation dataset is reserved for independent validation of ANN output. A multilayer perceptron with at least three layers should be able to reproduce any mapping between input and output variables (Hornick et al. 1989), but four layers are used here, as it has been found previously that an extra layer leads to more efficient ANN training for the kind of process modeled here (Grimes et al. 2003; Coppola et al. 2006; Bellerby et al. 2000). The choice of number of nodes in the hidden layers is more arbitrary, but was based here on configurations of ANNs used for similar purposes in the literature (Grimes et al. 2003; Coppola et al. 2006; Bellerby et al. 2000). The shape of the architecture used for each ANN here can be seen from Table 1.

5. ANN inputs For RIANNAA, the input data were various combinations of SEVIRI radiances and the output data were daily rainfall estimates, with kriged daily rain gauge totals used for training. The main challenge when designing this ANN was the mismatch in time scale between SEVIRI radiance data (available for this project at 30-min intervals) and the daily rain gauge training data. As it was not possible to accurately downscale the gauge data to a smaller time scale, the SEVIRI data had to be upscaled in some way to daily scale. One option would be to take the mean and variance of each SEVIRI channel over each day. However, as

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TABLE 1. Channel combinations included, total number of inputs and number of nodes in each hidden layer for each version of RIANNAA. ANN name

Nighttime channels (mm)

Daytime channels (mm)

No. inputs

Second layer

Third layer

IR108 IR120 IR087 IRMS Vis008 Vis016 Vis039 VisMS

10.8 10.8, 10.8–12.0 10.8, 8.7–10.8 10.8, 10.8–12.0, 8.7–10.8 10.8, 10.8–12.0, 8.7–10.8 10.8, 10.8–12.0, 8.7–10.8 10.8, 10.8–12.0, 8.7–10.8 10.8, 10.8–12.0, 8.7–10.8

10.8 10.8, 10.8–12.0 10.8, 8.7–10.8 10.8, 10.8–12.0, 8.7–10.8 10.8, 0.8 10.8, 0.8, 1.6/0.8 10.8, 0.8, 3.9/0.8 10.8, 0.8, 1.6/0.8, 3.9/0.8

7 10 10 28 37 55 55 82

5 5 5 16 20 24 24 32

2 2 2 6 4 6 6 6

convective rain events typically last only a few hours or less, this method would probably not be effective at capturing and distinguishing between different types of cloud and rainfall amounts. A second option is to separate each channel into radiance bins, and then to record the number of half hours that the channel falls within each bin during a particular day. This method seems more likely to be able to distinguish between different cloud types than simply taking the mean radiance over the day. An additional complexity is that it would be preferable to retain the synchronicity of the information from different channels. For example, if the channels are binned and recorded independently for each day, it may be found that on a particular day the 10.8-mm channel showed cold brightness temperature for 6 h and the 0.8-mm channel showed high optical depth for 4 h. However, to identify better the cloud types present (and estimate rainfall), it is also preferable to know for how long these two time periods overlapped. Therefore, the method chosen to upscale SEVIRI radiances to daily scale was to bin combinations of radiances together. A 2D example of this, for the case where only the 10.8-mm and 10.8–12.0-mm channels are used, is shown in Table 2. In this case, each channel BT (or BTD difference) is divided into three bins, producing nine ANN inputs (plus one for elevation, which will be explained later in this section). The actual value of each of the nine ANN inputs for a particular day is the number of half hours for which the input channel–bin combination is recorded. So, for example, Input 1 5 Number of ½ hours for which simultaneously: (IR 10. 8-mm BT is in bin 1) and (IR 12. 0-mm BT is in bin 1), Input 2 5 Number of ½ hours for which simultaneously: (IR 10. 8-mm BT is in bin 1) and (IR 12. 0-mm BT is in bin 2), and so on. For ANNs with more than two channels the same method is used, with an extra column being added

to Table 2 for each additional channel, resulting in a correspondingly larger number of ANN inputs. The physical reasoning behind creating the inputs in this way is to produce an implicit cloud-classification system. Each input corresponds to a specific combination of SEVIRI radiances, which is the signature of a particular cloud type. Certain cloud types (and therefore ANN inputs) are more likely to produce rain than others, and some are more likely to produce heavy or light rain. Therefore, if input 1 is equal to nine half hours over a day, this is on average likely to correspond to a different amount of rainfall from the case where input 5 is equal to nine half hours over a day. The advantage of using a nonlinear calibration such as an ANN is that any nonlinear relationships between cloud types and rainfall should also be recognized by the algorithm. For example, a squall line with deep convective cloud followed by a stratiform layer and a cirrus anvil might produce more rain than a local convective event. It can be seen that a three- or four-channel ANN would have a large number of inputs, even for a small number of radiance bins per channel. As the maximum number of inputs that an ANN can support is constrained by the TABLE 2. Composition of ANN inputs for a two-channel ANN (referred to later as IR120), with both channels divided into three radiance bins. The actual value of each input is the number of half hours during a day for which both channels are simultaneously in the required radiance bins for that particular input. The last input for all ANNs used in this study is elevation above sea level. ANN input number

10.8-mm bin

10.8–12.0-mm bin

1 2 3 4 5 6 7 8 9 10

1 1 1 2 2 2 3 3 3 Elevation

1 2 3 1 2 3 1 2 3 Elevation

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number of training patterns available (in this case the number of gauge days in the training dataset), it was desirable to minimize the number of radiance bins for each channel while still retaining as much information as possible. Another issue raised by upscaling the SEVIRI radiances to a daily time scale is the unavailability of solar channels at nighttime and the unavailability of the 3.9-mm BT channel during the day (because of the solar component of the 3.9-mm channel). To try to understand the importance of each of the channels with regard to rainfall estimation, several versions of RIANNAA were created, each with different combinations of inputs. These are shown in Table 1. These channels were chosen based on the analysis of Capacci and Conway (2005), who used an ANN approach to identify the combination of channels that produced the most skillful rainfall estimates. Ideally, it would also have been possible to assess the potential of the water vapor channels to improve rainfall estimates, but unfortunately the SEVIRI data available was that which had been acquired for TAMORA (Chadwick et al. 2010) and did not include the water vapor (WV) channels. The 8.7-, 10.8-, and 12.0-mm channels were each available for the full 24-h period, so day–night separation was unnecessary for the ANNs that used only combinations of these channels. For the versions of RIANNAA that used any of the 0.8-, 1.6-, or 3.9-mm channels, it was necessary to have inputs for day and night separated but together in the same ANN. The value of each of the nighttime inputs is equal to the number of half hours during the night for which the channel-bin combination of that input is met, and similarly for the daytime inputs during the day. So for example, for the Vis008 RIANNAA there were three channels at night, each divided into three radiance bins, leading to 27 inputs. During the day there were two channels, again divided into three radiance bins each, leading to 9 inputs. Including elevation (see later), the total number of Vis008 inputs is 37. For the purposes of this algorithm, ‘‘day’’ was defined as 0400–1400 UTC, as this was the time period for which solar zenith angle (SZA) was below 808 for the whole Ethiopian Oromiya region throughout the period JAS, and so the solar channels could be considered reliable. Time slots outside this period were defined as ‘‘night.’’ Although the actual period of daylight for this region varies continuously over the 3 months, it was necessary to define a fixed day/night boundary so that the ANN inputs could be standardized in a consistent way (see section 6). For satellite RFEs that use visible channels to produce estimates at subdaily time scales, one problem is an inconsistency between daytime and nighttime estimates due to different channel combinations being used for the

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two periods. However, the same problem does not arise for RIANNA where daily total rainfall is estimated as a single value. RIANNAA does not use nighttime and daytime channels separately to produce nighttime and daytime rainfall estimates that are then aggregated to produce a daily total. Instead, both daytime and nighttime channels are used together to produce a single daily estimate. The ANN will learn to recognize and replicate the pattern that best fits the combination of inputs (including both daytime and nighttime channels) to the daily kriged gauge totals. For RIANNAA, it was necessary to choose the radiance bins into which the channels were partitioned into carefully and sparingly because of the restriction on the number of inputs caused by limited training data. This choice of bins was made by analyzing the probability of rainfall [P(R)] resulting from combinations of different channel radiances examined for the TAMORA algorithm (Chadwick et al. 2010). For the IR channels, more useful information about cloud properties can be obtained from the 10.8–12.0-mm and 8.7–10.8-mm BTDs than from the 12.0- and 8.7-mm channels alone; therefore, these BTDs were used as inputs in conjunction with the 10.8-mm BT. For the daytime 1.6- and 3.9-mm channels, the channel ratios 1.6/0.8 and 3.9/0.8 were used in order to try to reduce the dependence of these channels on optical depth and produce variables that are mainly dependent on cloud microphysical properties. The SEVIRI channel binnings used in RIANNAA are shown in Table 3. For the IR108 version of Riannaa, the 10.8-mm channel was separated into six bins, with one bin every 108C from 2208 to 2708C. A sensitivity test of the IR108 ANN showed that using three or six 10.8-mm bins did not significantly affect the ANN output. Therefore only three 10.8-mm bins were used for the multispectral ANNs in order to reduce the number of ANN inputs needed. Similarly, the 3.9/0.8 ratio input was binned into fewer segments for the Visible Multispectral (VisMS) ANN than for Vis039 to limit the already large number of degrees of freedom in VisMS. Here, 10.8-mm data warmer than 2208C were not included in the ANN inputs, as clouds with tops warmer than this were considered unlikely to be raining in this region. As will be described later in this section, a 10.8-mm thresholding approach was used to separate RIANNAA rain/no-rain estimates, so warmer 10.8-mm data would not have given extra information to the final estimates in any case. As well as the multispectral SEVIRI inputs, pixel terrain elevation was also included as one of the RIANNAA inputs (for all versions of RIANNAA). The Oromiya region is mountainous (see Fig. 1), and orographic effects

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TABLE 3. SEVIRI channel bins used in RIANNAA. All BT and BTD values are in 8C; 10.8-mm BT V1 binning is used for the IR108 RIANNAA; V2 is used for all others. Here 3.9/0.8 ratio V1 binning is used for Vis039 RIANNAA; V2 is used for VisMS. Channel

Bin 1

Bin 2

Bin 3

Bin 4

Bin 5

Bin 6

10.8-mm BT V1 10.8-mm BT V2 10.8212.0-mm BTD 8.7–10.8-mm BTD 0.8-mm 1.6/0.8 ratio 3.9/0.8 ratio V1 3.9/0.8 ratio V2

220 to 230 220 to 230 #1 #0 #0.8 #0.3 #0.04 #0.06

230 to 240 230 to 250 1 to 3 0 to 2 0.8 to 0.9 0.3 to 0.5 0.04 to 0.08 .0.06

240 to 250 #250 .3 2 .0.9 .0.5 .0.08 NA

250 to 260 NA NA NA NA NA NA NA

260 to 270 NA NA NA NA NA NA NA

#270 NA NA NA NA NA NA NA

would be expected to play a large part in rainfall formation processes; therefore, including elevation in the inputs might allow the ANN to produce more accurate estimates. Some weight is lent to this argument by the fact that the original version of the Climate Prediction Center (CPC) RFE satellite rainfall product performs better over Ethiopia than the updated version (Dinku et al. 2007). The most likely reason for this is that the original version includes an orographic enhancement correction that was not included in the updated version.

6. Standardization of input and training data To improve the efficiency of ANN training by giving all inputs equal weight in the ANN input layer, inputs should be standardized to values in the range [0, 1]. The simplest way to achieve this is to use the function xfinal 5

x 2 xmin , xmax 2 xmin

(1)

where xmax and xmin are the mininum/maximum values for a particular input and xfinal is the final standardized input for use in the ANN. The final values of the inputs to RIANNAA were standardized in this way. The training data should also be standardized to the same range, but in this case the method described above was considered inappropriate for standardization of daily rainfall values. Daily rainfall values, even after interpolation to satellite pixel scale by kriging, have a highly nonnormal distribution. This can be seen from Fig. 3a, which shows the histogram of daily kriged rainfall for the Oromiya gauge dataset for JAS 2006. As well as the obvious bimodal zero/nonzero distribution, the nonzero rainfall distribution itself is highly skewed. Coppola et al. (2006) found that standardizing daily rainfall values using an empirical cumulative distribution function (ECDF) approach (Wilks 1995) gave improvements to ANN rainfall estimation over using the maximum/minimum standardization of Eq. (1).

Zero rainfall values were dealt with separately to nonzero values throughout the ANN process, so only nonzero values were standardized using an ECDF: ðR f (R) dR R

R9 5 ð Rmin

max

, f (R) dR

(2)

Rmin

where R is the kriged gauge value, f(R) is the kriged rainfall frequency distribution, R9 is the standardized rainfall value, and Rmin and Rmax are the minimum and maximum values of R in the dataset. Here, R9 is a value between [0, 1]. Figure 3c shows the distribution of JAS 2006 daily Oromiya kriged rainfall standardized in this way, and it can be seen that the nonzero rainfall distribution is approximately uniform. As the rainfall training data for RIANNAA is standardized in this way, the RIANNAA output will have the same form. Output values have to be destandardized by inverting Eq. (2) to produce actual rainfall estimates. One side effect of using an ECDF standardization is that RIANNAA rainfall outputs can never be higher than the maximum rainfall value in the training dataset. Figure 3 shows that there is a large number of zeros present in the daily rainfall dataset. Coppola et al. (2006) found that using all zeros during the training process reduced the ability of an ANN to correctly discriminate low rain rates. They found that removing 90% of zero rainfall values from ANN training gave a more stable calibration, and this same procedure was followed for RIANNAA.

7. Training and validation procedure Kriged gauge data from the Oromiya gauge dataset described in section 2a were used to train, test, and validate RIANNAA. Data were available for three rainy seasons of JAS for 2004–06, and the corresponding SEVIRI multispectral data were also obtained for this time period. Only SEVIRI pixels that contained at least

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one rain gauge were used in order to minimize error due to gauge uncertainty. The gauge data (215 gauges) were randomly separated into 70% training, 10% test, and 20% validation datasets. These are shown in Fig. 1. A cross-validation procedure was then performed, using two of the three years for training and the third for validation in all three possible permutations of years. The validation was therefore independent of the ANN training in both time and space, making it a stringent test of an operational rainfall estimation scenario. Days where more than three half hours of SEVIRI data were missing were excluded from the process, as were gauge days where the gauge data was missing. Training was carried out separately for each month, giving approximately 7000 training patterns for each calibration. Grimes et al. (2003) used an ANN approach to produce daily rainfall estimates over Africa and found that it was difficult to generate zero rainfall values, instead producing estimates of very low rainfall (less than 1 mm) over large areas. To resolve this, they used a non-ANN approach to separate estimates into rain/no-rain, then used an ANN to produce rainfall estimates only for the areas assigned as rainy. The chosen rain/no-rain discrimination technique was to use a CCD threshold, as in the TAMSAT algorithm (see section 3). Pixel days without any cloud colder than a certain threshold (2308C in the case of Grimes et al. 2003) were taken to have zero rainfall. The same approach was used for RIANNAA, with the CCD threshold determined during the TAMSAT calibration described below.

8. Daily calibration of TAMSAT over Ethiopia In order that RIANNAA estimates could be compared with an operational rainfall estimation method, TAMSAT daily estimates were produced for the Oromiya region. To make the comparison as fair as possible, TAMSAT was calibrated and validated with exactly the same gauge data as RIANNAA, using the crossvalidation approach described above for 2004206. The TAMSAT calibration method is described in detail in section 3. Here, a separate calibration was determined for each combination of calibration years and month, then applied to the validation year and month. The best CCD threshold for rain/no-rain discrimination was found to be 2308C, and this was also used for rain/no-rain discrimination for the RIANNAA algorithm. As the two methods use the same technique for this, any difference in skill between them (and between different versions of RIANNAA) can only be due to the ability to correctly estimate rainfall amount, not occurrence.

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FIG. 5. Boxplots of daily kriged gauge rainfall for each value of CCD (with a threshold of 2308C) for Oromiya calibration gauges, July 2004 and 2005. The least squares fit line is computed by using the median of each distribution (excluding zero CCD), weighted by the amount of data in that distribution. This line provides the TAMSAT calibration parameters used to compute estimates for July 2006.

An example of a TAMSAT calibration plot using data from July 2004 and 2005 is shown in Fig. 5. It can be seen from the spread of the rainfall distribution for each value of CCD that the TAMSAT approach will clearly not be able to accurately estimate all high values of rainfall.

9. Validation of ANN output and comparison with TAMSAT estimates Examples of RIANNAA IR108, RIANNAA VisMS, and TAMSAT daily rainfall fields, together with the corresponding kriged gauge estimates, are shown in Fig. 6. It can be seen that the rainfall delineation appears to be reasonably accurate when compared to the gauges. None of the satellite estimates capture the higher gauge values on this day. RIANNAA IR108 produces the highest rainfall values of the three satellite images shown here in the north of the image. However, this area lies outside the Oromiya calibration zone, and it is possible that RIANNAA IR108 is extrapolating its calibration to a region containing a different cloud regime (possibly with generally higher cloud tops). It is not known what the true rainfall is for this day in this northern region. A cross validation of RIANNAA was performed as described in section 7, and the three validation years of data for the validation gauges were then collected together and analyzed at various temporal and spatial scales. This was done for each version of RIANNAA shown in Table 1. The three validation years of TAMSAT data were accumulated in the same way and compared with the RIANNAA estimates. All figures and validation

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FIG. 6. Daily (a) TAMSAT, (b) RIANNAA IR108, (c) RIANNAA VisMS, and (d) kriged gauge estimates for 21 Aug 2006 over Ethiopia. (a)–(c) Circles show validation gauge locations for this day; satellite zero rainfall estimates are shown as white. (d) Kriged gauge rainfall estimates shown as colored circles; gauge zeros shown as empty circles.

statistics in this section show the three years of crossvalidation data collected in this way. Four different spatial and temporal degrees of averaging were used for assessing the estimates. The first was at the basic scale of the RIANNAA and TAMSAT estimates, daily SEVIRI-pixel (around 4 km) scale. The second was at daily time scale but averaged over all validation pixels for each day (around 36 pixels, depending on amount of missing data). The third was at pixel scale but aggregated to dekadal time scale, and the fourth was for dekadal aggregates averaged over all validation pixels for each dekad. It was considered worthwhile to perform the analysis at a range of scales, as different applications of satellite rainfall products require estimates at different spatial and temporal scales. As both RIANNAA and TAMSAT use the same method of rain/no-rain discrimination, the skill for this will be the same for both products. Skill scores used for this are defined as follows:

Bias 5

A1B , A1C

POD 5

A , A1C

FAR 5

B , A1B (3)

where A, B, C, and D are defined in Table 4, and N 5 A 1 B 1 C 1 D. Note that the bias used for rain/no-rain discrimination (and defined above) is different to the standard definition of bias, which is used later for rainfall amount validations of RIANNAA and TAMSAT against gauge data.

TABLE 4. Contingency table used for determination of satellite skill scores.

Satellite

Rain No rain

Gauge rain

No rain

A C

B D

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TABLE 5. Skill scores for rain identification at SEVIRI daily pixel scale over Ethiopia using a 2308C threshold for JAS 2004–06. No. gauge No. gauge Probability of False-alarm days rainy days nonrainy detection (POD) rate (FAR) Bias 6265

2741

0.85

0.22

1.08

Daily pixel rain/no-rain skill scores are shown in Table 5. It can be seen that this threshold produces a minor overestimation of the number of rainy pixels, as shown by the bias.

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Histograms of kriged gauge rainfall, RIANNAA and TAMSAT daily pixel estimates are shown in Fig. 7. The median values of the satellite RFE distributions and kriged gauge distribution are similar, but neither RIANNAA nor TAMSAT are able to correctly replicate the spread of the kriged distribution. In particular, the IR108 RIANNAA and TAMSAT have a very high proportion of their estimates close to the median value, suggesting that the 10.8-mm channel alone is not a good discriminator of daily pixel rainfall amount. The VisMS RIANNAA is able to produce a distribution with tails

FIG. 7. Histograms of daily (a) kriged gauge, (b) TAMSAT, (c) RIANNAA IR108, (d) RIANNAA IRMS, and (e) RIANNAA VisMS estimates at pixel scale.

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FIG. 8. Daily (a) TAMSAT, (b) RIANNAA IR108, (c) RIANNAA IRMS, and (d) RIANNAA VisMS estimates against gauge data at pixel scale.

more similar to the kriged gauge distribution than the other algorithms, suggesting that the inclusion of the extra SEVIRI channels may be improving the estimates at this scale. However, the VisMS RIANNAA is still incapable of estimating extreme high rainfall values. Figure 8 shows daily pixel-scale estimates from RIANNAA and TAMSAT against kriged gauge estimates. To conserve space, only three versions of RIANNAA are shown. It was considered inappropriate to calculate skill scores for the data as shown in this figure, as the correlation coefficient and RMSE would be highly affected by the rain/ no-rain discrimination and the values may not be simple to interpret. As the rain/no-rain method is the same for RIANNAA and TAMSAT, any difference in skill between the two methods will be in the estimation of rainfall amount. To account for this, daily pixel estimates were validated but only for the case where both satellite RFE and gauge are nonzero. Validation statistics for this case are shown in Table 6. For the other validation scales zeros were not removed, as the temporal or spatial averaging had the

effect of eliminating the double distribution seen in the histograms in Fig. 7. Also, as the averaging was meant to recreate situations that might occur in an operational satellite RFE scenario, it was more realistic to include the zero estimates in the validation skill scores. RIANNAA

TABLE 6. Validation statistics of RIANNAA and TAMSAT estimates for daily pixel (excluding zeros) and daily mean (including zeros) over all validation pixels. Best skill scores are shown in bold.

Algorithm

Bias

Daily RMSE

R2

Bias

Daily mean RMSE

R2

IR108 IR120 IR087 IRMS Vis008 Vis016 Vis039 VisMS TAMSAT

21.57 21.56 21.57 21.55 21.47 21.36 21.44 21.30 22.65

5.15 5.11 5.11 5.11 5.02 5.01 5.04 5.10 5.55

0.24 0.26 0.26 0.26 0.30 0.29 0.29 0.25 0.25

20.32 20.32 20.33 20.32 20.27 20.20 20.25 20.17 21.13

2.26 2.18 2.19 2.17 2.12 2.13 2.11 2.15 2.47

0.43 0.47 0.47 0.48 0.51 0.51 0.51 0.50 0.43

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FIG. 9. Daily (a) TAMSAT, (b) RIANNAA IR108, (c) RIANNAA IRMS, and (d) RIANNAA VisMS estimates against gauge data, averaged over all validation pixels for each day, including least squares fit line.

and TAMSAT estimates plotted against kriged gauge estimates at daily averaged, dekadal pixel, and dekadalaveraged scales are shown in Figs. 9–11. Daily skill scores are shown in Table 6 and dekadal skill scores in Table 7. When accumulated to dekadal time scale, the satellite histograms peak at a much higher rainfall value than the gauge histogram (see Fig. 12). This appears to be because the satellite dekadal estimates saturate at a value below the gauge maximum, and the high satellite estimates are concentrated into a much narrower range of values than the corresponding gauge estimates. Dekadal rainfall is determined by the number of rain days combined with the amount of rain on each rain day. As both RIANNAA and TAMSAT use the same daily rain/no-rain delineation method, the fact that the dekadal RIANNAA peaks at a higher rainfall value than TAMSAT must be explained by the greater occurrence of high rainfall values in the RIANNAA daily pixel distribution (see Fig. 7). However, as neither RIANNAA nor TAMSAT are able to capture the range of daily

extremes, they are similarly unable to do so at dekadal scale. The validation statistics show an improvement in skill at all scales for RIANNAA as more input channels are included, particularly in the bias. All versions of RIANNAA also show improvement over TAMSAT at all scales, with TAMSAT having a larger negative bias. The negative bias of all algorithms at daily pixel scale can be largely explained by the failure to correctly estimate high rainfall amounts. The extra SEVIRI channels used in the multispectral versions of RIANNAA appear to help in estimating high rainfall values and hence reduce this bias. As the differences in skill scores between the algorithms were small, statistical hypothesis tests were performed to determine whether these differences were statistically significant. These tests were performed on the residuals r 5 ps 2 pg, where ps is the satellite estimate and pg is the kriged gauge estimate. The tests were performed at each validation scale, with only estimates

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FIG. 10. Dekadal (a) TAMSAT, (b) RIANNAA IR108, (c) RIANNAA IRMS, and (d) RIANNAA VisMS estimates against gauge data, at pixel scale. Solid line shows linear least squares fit.

where both satellite and gauge were nonzero included at daily pixel scale. Hypothesis tests were performed on each possible pair of three algorithms: TAMSAT, RIANNAA IR108, and RIANNAA VisMS. The residuals were tested for equality of mean (Student’s t test), equality of variance (F test), and equality of R2 (Pearson Z test). These tests rely on an assumption of normality of the residuals, which was not generally met. Therefore, nonparametric hypothesis tests, which do not require an assumption of normality, were also performed. These were the Wilcoxon rank sum test (mean) and the Ansari–Bradley test (variance). The tests were performed at the 95% confidence level, and results are shown in Tables 8 and 9. The improvement in bias of both versions of RIANNAA over TAMSAT is shown to be statistically significant at all four validation scales, with the IR108 also showing a significant improvement in the RMSE. VisMS shows a significant improvement in RMSE over TAMSAT for the nonparametric test but not for the parametric one. For the comparison, between RIANNAA IR108 and VisMS, the only statistically significant result is the

improvement in bias of VisMS at daily pixel scale. For other validation scales there is no significant improvement in any validation statistics. The improvement in bias of RIANNAA over TAMSAT is consistent with the result of Coppola et al. (2006) that a nonlinear ANN approach can often provide more accurate satellite rainfall estimates than a linear method. This is probably because the relationship between cloud-top variables and surface rainfall is dependent on many complex interactions within cloud microphysics and is almost certainly nonlinear. Therefore, a nonlinear ANN approach may be better equipped to model this relationship than a linear one such as TAMSAT. The addition of multispectral SEVIRI channels does show some statistically significant improvement in the bias at a daily pixel scale. This provides evidence that the inclusion of multispectral data, and the implicit information about cloud properties contained within, can improve surface rainfall estimates at a daily time scale. However, when averaging is performed there is no longer a statistically significant improvement of the multispectral ANN over the IR108 ANN.

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FIG. 11. Dekadal (a) TAMSAT, (b) RIANNAA IR108, (c) RIANNAA IRMS, and (d) RIANNAA VisMS estimates against gauge data, averaged over all validation pixels for each dekad, including least squares fit line.

This is partly explained by the inclusion of gauge and satellite zero rainfall amounts at averaged scales. As these are determined in the same way for all RIANNAA and TAMSAT methods, their inclusion will serve to reduce the differences between the algorithm outputs. In fact, Fig. 7 shows that the range of output of the satellite algorithms is relatively small, with a large proportion of output values clustered around the output median for all algorithms. Therefore, the assignment of rain/no-rain at daily pixel scale would be expected to represent a large proportion of the variance of the estimates when averaged to coarser scales. The lack of extreme values in the satellite rainfall outputs will also lead to similarities between them when averaging is applied. A physical explanation of the lack of statistical significance in the difference in bias between the multispectral and IR108 versions of RIANNAA at temporally and spatially averaged scales may be found in cloud physics. Chadwick et al. (2010) showed that the TAMORA algorithm did not appear to be an improvement over TAMSAT at dekadal time scales. It was theorized that

this may be due to cloud microphysical information being less important for rainfall estimation than total vertical advection of moisture when averaged over time. The same may also be true of spatial averaging, and this would explain why RIANNAA VisMS with its multispectral

TABLE 7. Validation statistics of RIANNAA and TAMSAT estimates for dekadal pixel and dekadal mean over all validation pixels. Best skill scores are shown in bold.

Algorithm

Bias

Dekadal RMSE

IR108 IR120 IR087 IRMS Vis008 Vis016 Vis039 VisMS TAMSAT

23.61 23.61 23.69 23.58 23.07 22.37 22.90 22.05 211.73

27.22 26.96 27.07 26.91 26.59 26.33 26.46 26.44 29.31

R2 0.69 0.69 0.69 0.69 0.70 0.71 0.70 0.71 0.68

Bias

Dekadal mean RMSE

R2

23.11 23.12 23.22 23.14 22.50 21.89 22.31 21.59 211.81

13.03 12.41 12.52 12.43 12.02 11.49 11.73 11.66 17.40

0.38 0.43 0.43 0.43 0.44 0.48 0.46 0.47 0.34

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FIG. 12. Histograms of dekadal (a) kriged gauge, (b) TAMSAT, (c) RIANNAA IR108, (d) RIANNAA IRMS, and (e) RIANNAA VisMS estimates at pixel scale.

data shows a significant improvement over RIANNAA IR108 at daily pixel scale but not at other scales.

10. Discussion and conclusions An artificial neural network (RIANNAA) was used to produce daily rainfall estimates from SEVIRI input data. Various different combinations of channel inputs were used, and these were also compared with daily TAMSAT estimates. Both RIANNAA and TAMSAT

used the same calibration and validation data from Ethiopia, and the same IR thresholding method of rain/ no-rain delineation. Validation was performed at four different levels of spatial and temporal averaging. RIANNAA was found to have a statistically significant improvement in bias over TAMSAT at all 4 scales, and this may be because of the nonlinear nature of ANNs. Previous work (Grimes et al. 2003; Coppola et al. 2006) has shown that an ANN approach can provide rainfall estimates superior to those

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TABLE 8. Standard and nonparametric hypothesis tests for comparison of daily validation statistics between algorithms; Y indicates difference is significant at the 95% confidence level; N indicates it is not. No nonparametric test for R2 was performed. Algorithms

Bias

Daily RMSE

IR108, VisMS IR108, TAMSAT VisMS, TAMSAT

Y Y Y

N Y N


Y Y Y

N Y Y

R2 Standard N N N Nonparametric NA NA NA

from a linear method using the same inputs. However, it was not the aim of this paper to show this specifically, and as TAMSAT does not have exactly the same input data as any version of RIANNAA then it cannot be stated categorically that the improvement of RIANNAA over TAMSAT is because of the use of an ANN. The aim here was to compare RIANNAA against an operational satellite RFE, and it has been shown that RIANNAA offers a small but statistically significant improvement. One caveat here is that for operational 10-day estimates TAMSAT would normally be calibrated on a 10-day scale, whereas here it has been calibrated at a daily scale and accumulated. A 10-day TAMSAT calibration might be expected to reduce the bias of dekadal estimates (as might a version of RIANNAA calibrated at a 10-day scale). The inclusion of multispectral data in RIANNAA leads to an improvement at the highest resolution here, suggesting that multispectral data do have the capacity to enhance high-resolution rainfall estimates. However, there was no statistically significant improvement seen from including the multispectral data at averaged scales. This is consistent with the results from the validation of TAMORA (Chadwick et al. 2010), which showed an improvement in accuracy for high-resolution estimates, but not averaged ones. The explanation for this could be methodological, physical, or a combination of both. All versions of RIANNAA use the same threshold method of rain/ no-rain identification, so when estimates are averaged in

Bias

Daily mean RMSE

R2

N Y Y

N N N

N N N

N Y Y

N N N

NA NA NA

time and space the results necessarily become more similar to each other as zeros are included. As no version of RIANNAA has the capability of correctly estimating high rainfall values, the different RIANNAA estimates are likely to become smoothed and similar as averaging is applied. From a physical perspective, the lack of improvement of RIANNAA at averaged scales may be simply due to the effect of averaging. The cloud microphysical and optical depth properties of clouds appear to be important in determining rain rates at high temporal and spatial resolutions, as shown by the improvement of RIANNAA VisMS over RIANNAA IR108 at daily pixel scale. However, these properties but may not be so influential on determining accumulated rainfall at more spatially or temporally averaged scales. For these larger scales, the effects of cloud microphysics on rainfall may be averaged out, with large-scale processes such as the total vertical advection of moisture becoming more important. As this large-scale vertical moisture transport is the principle on which IR-only area–time integral methods such as TAMSAT are based, the extra cloud microphysical information provided by multispectral data may not provide enhanced rainfall estimates at averaged scales. There is some evidence of this from the work of Mathon et al. (2002), who found that the total rain yield of organized convective systems in the Sahel is primarily linked to their duration, not mean rain rate.

TABLE 9. Standard and nonparametric hypothesis tests for comparison of dekadal validation statistics between algorithms; Y indicates that the difference is significant at the 95% confidence level; N indicates it is not. No nonparametric test for R2 was performed. Algorithms

Bias

Dekadal RMSE


N Y Y

N N N


N Y Y

N N N

R2 Standard N N N Nonparametric NA NA NA

Bias

Dekadal mean RMSE

R2

N Y Y

N N N

N N N

N Y Y

N N N

NA NA NA

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The failure to capture daily extremes may be a problem with the ANN method, or else it may be due to the limitations of using multispectral cloud-top data to estimate daily surface rainfall. Even for RIANNAA VisMS, the solar channel inputs are used for less than half of the day, so RIANNAA is highly dependent on the ability of a combination of IR channels to provide rainfall amount information. Future improvements to RIANNAA could include the use of a second ANN as a rain/no-rain classifier instead of the current temperature threshold method. It is possible that a combination of two multispectral ANNs, one for rainfall delineation and one for estimating rainfall amount, could provide an improvement over single-channel estimates for averaged estimates. To be applied outside of the Oromiya region and in seasons other than JAS, the calibration of RIANNAA would need to be extended, and it would be interesting to see whether the results shown here apply in other regions of the world. Acknowledgments. The authors thank the National Meteorological Agency of Ethiopia for providing the rain gauge data used in this study, and EUMETSAT and the Met Office for providing the SEVIRI data. RC would also like to thank Erika Coppola for useful discussions about the application of ANNs to satellite rainfall estimation and Helen Greatrex for developing the kriging software used here. David Grimes passed away on 22 December 2011 at the age of 60. REFERENCES Arkin, P., 1979: The relationship between fractional coverage of high cloud and rainfall accumulations during GATE over the B-scale array. Mon. Wea. Rev., 107, 1382–1387. Ba, M., and A. Gruber, 2001: GOES Multispectral Rainfall Algorithm (GMSRA). J. Appl. Meteor., 40, 1500–1514. Balme, M., T. Vischel, T. Lebel, C. Peugeot, and S. Galle, 2006: Assessing the water balance in the Sahel: Impact of small scale variability on runoff, Part 1: Rainfall variability analysis. J. Hydrol., 331, 336–348. Barrett, E., and D. Martin, 1981: The Use of Satellite Data in Rainfall Monitoring. Academic Press, 340 pp. Bellerby, T., M. Todd, D. Kniveton, and C. Kidd, 2000: Rainfall estimation from a combination of TRMM precipitation radar and GOES multispectral satellite imagery through the use of an artificial neural network. J. Appl. Meteor., 39, 2115–2128. Berge`s, J., I. Jobard, F. Chopin, and R. Roca, 2010: EPSAT-SG: A satellite method for precipitation estimation; its concepts and implementation for the AMMA experiment. Ann. Geophys., 28, 289–308. Bishop, C., 2000: Neural Networks for Pattern Recognition. Clarendon Press, 504 pp. Capacci, D., and B. Conway, 2005: Delineation of precipitation areas from MODIS visible and infrared imagery with artificial neural networks. Meteor. Appl., 12, 291–305.

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