DECEMBER 2003
GRIMES ET AL.
1119
A Neural Network Approach to Real-Time Rainfall Estimation for Africa
Using Satellite Data
D. I. F. GRIMES
TAMSAT, Department of Meteorology, University of Reading, Reading, Berkshire, United Kingdom
E. COPPOLA
TAMSAT, Department of Meteorology, University of Reading, Reading, Berkshire, United Kingdom, and Physics Department,
University of L’Aquila, CETEMPS Coppito I’Aquila, Italy
M. VERDECCHIA
AND
G. VISCONTI
Physics Department, University of L’Aquila, CETEMPS, Coppito l’Aquila, Italy
(Manuscript received 29 October 2002, in final form 10 April 2003)
ABSTRACT
Operational, real-time rainfall estimation on a daily timescale is potentially of great benefit for hydrological
forecasting in African river basins. Sparseness of ground-based observations often means that only methodologies
based predominantly on satellite data are feasible. An approach is presented here in which Cold Cloud Duration
(CCD) imagery derived from Meteosat thermal infrared imagery is used in conjunction with numerical weather
model analysis data as the input to an artificial neural network. Novel features of this approach are the use of
principal component analysis to reduce the data requirements for the weather model analyses and the use of a
pruning technique to identify redundant input data. The methodology has been tested using 4 yr of daily rain
gauge data from Zambia in central Africa. Calibration and validation were carried out using pixel area rainfall
estimates derived from daily rain gauge data. When compared with a standard CCD approach using the same
dataset, the neural network shows a small but consistent improvement over the standard method. The improvement
is greatest for higher rainfalls, which is important for hydological applications.
1. Introduction
In many parts of Africa, rainfall is the single most
important meteorological parameter. Too little rainfall
can mean crop failure and famine while too much can
lead to devastating floods as in Mozambique in 1999.
Real-time monitoring of rainfall is vital to allow timely
responses to potential disasters. For crop monitoring and
famine early warning, real-time monitoring at 10-day
intervals (10 days 5 one dekad) has in the past been
regarded as an appropriate temporal resolution for rainfall amounts. However for hydrological forecasting, the
time step needed even for large (.10 000 km 2 ) catchments is of the order of 1 day and for smaller catchments
is correspondingly shorter. Daily estimates are also useful for some agricultural applications such as monitoring
gaps in the growing season.
Although a conventional rain gauge network gives
Corresponding author address: Dr. D. I. F. Grimes, Department of
Meteorology, University of Reading, Earley Gate, Reading, Berkshire, RG6 6BB, United Kingdom.
E-mail: [email protected]
q 2003 American Meteorological Society
rainfall observations at a daily time step, throughout
much of the African continent the network is inadequate
both in terms of spatial coverage and timeliness of data
collection, while radar is generally not a feasible proposition on cost and infrastructure grounds. Monitoring
rainfall from satellite imagery is an attractive alternative
as it has the potential for good spatial coverage, is available in real time and is relatively inexpensive to access.
Many algorithms for satellite-based rainfall monitoring exist but most are not appropriate to the specific
requirements of real-time, daily, operational rainfall
monitoring in Africa. Of those that have been designed
for the purpose, most rely on simple empirical algorithms making use of Meteosat thermal infrared data,
sometimes in combination with passive microwave imagery or rain gauge data available via the Global Telecommunications System (GTS). In this paper we describe a new approach based on the application of an
artificial neural network (ANN) to a combination of
satellite imagery and data from numerical weather prediction (NWP) model analyses. The method described
could in principle be used for time periods shorter than
1 day but because the most readily available data for
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calibration and validation are daily rain gauge observations, we have focused on a daily timescale. As a case
study we have applied the approach to 4 yr of data from
Zambia in central Africa.
Section 2 reviews current rainfall estimation techniques. The case study area and data used are described
in section 3. Section 4 gives a brief introduction to
neural networks and describes the rainfall estimation
algorithms while section 5 outlines the validation methodology. Results for the Zambian case study are presented in section 6.
2. Satellite-based rainfall estimation
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.
Of the algorithms that make use of geostationary TIR
data, many are based around the idea of Cold Cloud
Duration (CCD), which is defined for a pixel as the
number of hours for which the pixel temperature is colder than some specified temperature threshold T t . A linear
relationship is then usually established between the
CCD and the rainfall amount R
R 5 a 0 1 a1CCD,
(1)
where a 0 and a1 are parameters to be determined empirically.
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
[a 0 5 0 mm, a1 5 3 mm h 21 in Eq. (1)]. For the GPI,
the temperature threshold is normally taken as 2388C.
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
VOLUME 4
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
DECEMBER 2003
GRIMES ET AL.
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.
1121
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 , a 0 , 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
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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 km 2 . In this case, the results are at
least as good as a gauge network with one gauge per
15 000 km 2 , 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.
3. Data and data preparation
a. Data for case study area
Zambia is located in central Africa between 88 and
188S and 228 and 348E. It covers an area of 750 000
km 2 . 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 0.58 grid resolution. The
fields selected as being likely to provide information on
VOLUME 4
FIG. 1. Locations of gauges used for calibration and validation
during this study. The inset shows the location of Zambia in Africa.
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 88–218S and 188–348E. 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 3 5 km.
b. Data preparation
1) GAUGE
DATA
A problem with comparing satellite-based rainfall estimates against rain gauge data is that they are concerned
with different spatial scales. The gauge value represents
rainfall at a point, whereas a satellite pixel based on
Meteosat TIR imagery for Zambia is an average over
an area of about 35 km 2 . Flitcroft et al. (1989) analyzed
data from a dense rain gauge network in West Africa
and showed that the standard deviation of individual
point values used to represent a given pixel average
rainfall was ;10 mm and this figure was almost independent of rainfall quantity. They also found a systematic bias in that gauge measurements of high rainfall
amounts were likely to overestimate the pixel average
rain; whereas gauge measurements of low rainfall
amounts tended to underestimate. It is reasonable to
suppose that convective rainfall associated with the
ITCZ elsewhere in Africa would display similar variability.
To address this problem, we have converted the raw
gauge data to areal averages for each pixel by applying
the technique of block kriging (Journel and Huijbregts
1978). Using this approach, the best estimate for a pixel
is a weighted mean of nearby gauges. The weighting is
determined by the distance of the gauges from the target
pixel taking into account the spatial correlation of the
rainfall event as represented by a variogram function
DECEMBER 2003
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GRIMES ET AL.
TABLE 1. Total explained variance for the first five principal
components of the NWP model parameters used in this study.
FIG. 2. Comparison of gauge and kriged pixel rainfall amounts.
The solid line indicates one-to-one correspondence.
Model
parameter
Explained
variance
(%)
R
U
V
W 400
W 700
84
76
65
33
21
mation 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
O a (t)E ,
P
computed from the gauge data. Given the small number
of gauges in this study, a climatological variogram was
computed from all 4 yr of data for each calendar month.
With this approach the rainfall field generated from the
gauge data is directly comparable to the satellite-derived
rainfall image. The block kriging technique is in principle superior to other interpolation procedures; first because the final pixel estimates are informed by the spatial structure of the rainfall and second because it allows
confidence limits to be calculated for each pixel value.
Obviously, the error is lowest for pixels containing
gauges and highest for pixels far away from any gauge.
For the calibration and validation part of this work,
only those pixels containing a rain gauge were used.
From now on these will be referred to as gauge pixels.
In the interests of simplicity, the variogram was computed using only nonzero gauge values and kriged pixel
rainfall estimates were set to zero if the gauge measurement within the pixel was zero.
Figure 2 compares the kriged pixel estimates with the
raw gauge observations for the gauge pixels. As might
be expected, the kriging process tends to move rainfall
amounts towards the mean rain amount per rain day.
Thus pixel estimates corresponding to low gauge values
are raised while those corresponding to high gauge values are lowered. Note this does not imply that for a high
rainfall measurement, the true mean rainfall in the surrounding pixel is necessarily lower; rather it implies that
in the absence of other information the best (i.e., most
likely) estimate of the pixel rainfall will be lower. The
relationship between kriged pixel rainfall and gauge observations is in broad agreement with Flitcroft et al.
(1989).
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 infor-
x i (t) 5
j
ij
(2)
j51
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 5 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.
4. Rainfall estimation algorithms
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 Tt ,
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VOLUME 4
FIG. 3. First principal component of surface relative humidity over the study period.
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
n11 1 n22 k n12 1 n21 ,
n12 ø n21 .
(3)
Having established the optimum value for T t , the parameters a 0 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.
TABLE 2. Contingency table to determine optimum rain–no-rain
threshold temperature Tt .
CCD 5 0
CCD . 0
gauge 5 0
gauge . 0
n11
n 21
n12
n 22
b. Artificial neural network algorithms
1) GENERAL
REMARKS ON NEURAL NETWORKS
In the terminology usually used, a neural network
consists of a number of layers of nodes or neurons. The
first layer is the input layer, the final layer is the output
layer and layers between the input and output are referred to as hidden layers. Connections exist between
the nodes that allow a set of values presented at the
input layer to be mapped to the output layer. The exact
form of the connections is specified by the network
‘‘architecture.’’ Any given node (apart from those in the
input layer) will receive inputs from a subset of the other
nodes. The total input to any node is the weighted sum
of the outputs from all nodes with an input connection
to that node. The weights involved are a property of the
individual connections. The output from any node is a
function (usually nonlinear) of the input. An expected
advantage of the ANN in this kind of study is that its
distributed nature makes it more robust to errors or missing values in any individual input parameter.
A network is ‘‘trained’’ to a specific task by presenting it with many examples of inputs and the corresponding desired outputs. After each example, the internodal weights are adjusted so as to improve the match
between desired and actual output. Training continues
until a stable solution is reached or until a desired degree
of accuracy is achieved as judged by the mean-square
difference between desired and actual output. A full
DECEMBER 2003
description of the neural network approach can be found
in a number of texts, for example Hecht-Nielsen (1990)
or Davolo and Naim (1991).
2) INITIAL
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GRIMES ET AL.
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 2 1)th
layer
Ik j 5
O
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 kj 5 [(1 1 exp(22l kj )] 21.
N k21
w(k21)i j o(k21)i ,
(4)
i51
where w(k21)ij is the weight connecting the output of the
node i in the (k 2 1)th layer to node j in the kth layer
and N k21 is the number of nodes in the (k 2 1)th layer.
The output of node j is a specified function of l kj
o kj 5 f (l kj ).
(5)
The eventual output is then a function of the weighted
(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 xmax and minimum xmin we
calculate the normalized value x A as
xA 5
x 2 xmin
.
xmax 2 xmin
(7)
The optimum weights were determined by training
FIG. 4. Schematic diagram of the artificial neural network architecture. (a) Initial network. (b) Final network.
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TABLE 3. Input parameters for the initial and final versions of
the ANN.
Input parameter
No. of inputs
(initial network)
No. of inputs
(final network)
4
0
4
0
4
0
4
0
4
0
5
5
TIR pixel value (0000,
0600, 1200, 1800 UTC)
3 3 3 mean TIR pixel value (0000, 0600, 1200,
1800 UTC)
5 3 5 mean TIR pixel value (0000, 0600, 1200,
1800 UTC)
3 3 3 TIR pixel std dev
(0000, 0600, 1200, 1800
UTC)
5 3 5 TIR pixel std dev
(0000, 0600, 1200, 1800
UTC)
First five PCs of relative
humidity field at 1800
UTC
First five PCs of zonal
wind component at 1800
UTC
First five PCs of meridional
wind component at 1800
UTC
First five PCs of vertical
wind at 400 mb at 1800
UTC
First five PCs of vertical
wind at 700 mb at 1800
UTC
CCD (T t 5 2308C)
CCD (T t 5 2408C)
CCD (T t 5 2508C)
CCD (T t 5 2608C)
Pixel altitude
Pixel latitude
Pixel longitude
Total inputs
1
Nt Np
O O 11 1w w/w /w 2 ,
N1
N2
i51 j51
5
5
5
5
5
5
5
0
0
1
0
1
1
1
49
Np
Nt
A pt
2 rk pt ) 2 ,
(8)
p51 t51
ANN ALGORITHM
2
0
2
1i j
C 5 msd 1 Z.
5
1
1
1
1
1
0
0
30
O O (r
2
1i j
2
0
(9)
where W1ij are the weights connecting the input and
second layers; W 0 is an empirically determined scaling
parameter for the weights; N1 and N 2 are the numbers
of input and second-layer nodes.
The total cost function C to be minimized for the
optimized network is then
where rApt and rkpt 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
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
Z5
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)
msd 5
VOLUME 4
(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
(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
1127
0.13
0.82
0.57
0.54
0.32
0.44
0.66
1998/99
1997/98
1996/97
0.15
0.86
0.42
0.34
0.27
0.43
0.96
0.04
0.90
0.49
0.46
0.39
0.41
1.06
1995/96
1998/99
0.26
20.55
20.18
20.66
2.38
0.72
20.97
20.04
20.71
0.08
1.16
3.10
0.82
22.10
1997/98
1996/97
1998/99
1995/96
a 0 mm
TABLE 4. Calibration parameters for TAMSAT rainfall estimation.
Estimates of rainfall from the TAMCCD and TAMANN algorithms described in section 4 were compared against the block-kriged gauge pixel values described in section 3b. Both algorithms were calibrated
using the same 25 gauge pixels shown in Fig. 1. The
remaining 10 gauge pixels from the full set of 35 (also
shown in Fig. 1) were used as an independent validation
set. In order to make the best possible use of the 4 yr
of available data, a cross-validation approach was adopted in which each permutation of 3 yr from 4 was used
for calibration and the remaining year was used for validation. In this way we have four separate years for
which the validation data are independent of the calibration both in space (different gauges) and in time
(different year). To simplify computation the principal
components for the NWP analysis and the variograms
for the kriging were calculated only once using all 4 yr
of data.
It has been suggested that the kriged pixel values for
the validation gauge locations are not truly independent
as they contain information from nearby calibration
gauges. However, this merely reflects the physical reality of the spatial coherence of the rainfall field. The
important point is that the calibration gauge pixels are
not included and the validation year is outside the calibration period.
20.13
20.81
0.30
2.36
3.91
1.04
0.37
a1 (mm h21 )
5. Validation methodology
0.36
21.17
20.23
0.12
3.81
0.80
0.18
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 5 0 for T t 5 2308C.
This final algorithm as described in the preceding
paragraphs will be referred to as TAMANN2 in the rest
of this paper.
0.13
0.83
0.46
0.50
0.56
0.42
0.82
GRIMES ET AL.
240
250
230
230
240
230
240
DECEMBER 2003
The ANN algorithms were trained using the same 3yr calibration periods as for TAMCCD. As an example,
1996/97
230
250
230
230
230
230
250
1995/96
230
250
230
230
240
230
250
Validation year
b. Calibration of ANN algorithms
Oct
Nov
Dec
Jan
Feb
Mar
Apr
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 2308 (October, March) and
2508C (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 208C.
T t 8C
a. Calibration of TAMCCD
230
250
240
240
230
230
230
1997/98
6. Results
1128
JOURNAL OF HYDROMETEOROLOGY
FIG. 5. Mean input weights for optimized TAMANN algorithm.
Weights are shown for five principal components of relative humidity
(RH), horizontal velocity (U, V ) and vertical velocity (W 400 , W 700 );
altitude (h) and CCD at temperature thresholds of 2308, 2408, 2508,
2608C. Note that vertical lines are plotted between points to aid
identification of the various years; they have no physical significance.
The year indicated in each case is the validation year for which the
weights were applied.
the mean input weights for TAMANN2 as represented
2
by S Nj51
N ij /N 2 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 2308 and 2608C 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.
VOLUME 4
FIG. 6. Time series of observed rainfall and amplitude of the first
EOF of relative humidity averaged over validation pixels for one
season.
• average rainfall over 10-day period and all 10 validation pixels (scale 5 100 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 R 2 and skill. Their definitions follow:
O (r 2 r )
1
rmsd 5
O (r 2 r )
N!
O (r 2 r )
nrmsd 5
O«
O (r 2 r )(r 2 r )]
[
R 5
O (r 2 r ) O (r 2 r )
O (r 2 r )
skill 5 1 2
.
O (r 2 r )
bias 5
Ne
1
Ne
e
(11)
ke
e51
Ne
(12)
2
Î
e
e
ke
e
ke
e51
Ne
2
e51
(13)
Ne
2
ke
e51
2
Ne
e
e
ke
ke
e51
(14)
2
Ne
Ne
2
e
e
e51
ke
2
ke
e51
Ne
2
e
c. Comparison of results
ke
e51
Ne
(15)
2
Results from all the algorithms were compared with
the kriged gauge pixel data on three different spacetime scales. These were
• daily rainfall quantities for individual pixels (scale 5
1 pixel-day),
• daily rainfall average over all 10 validation pixels
(scale 5 10 pixel-days), and
ke
ke
e51
In these equations r e is the estimated rainfall for event
e, rke is the corresponding kriged gauge pixel rainfall
and «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.
DECEMBER 2003
1129
GRIMES ET AL.
TABLE 5. Summary statistics for estimation algorithms at various space and time scales: (a) pixel-day, (b) areal mean pixel-day, (c) areal
mean pixel average over 10 days. For all years, the mean pixel rain per rain-day is between 8 and 9 mm.
Year
Method
Ne
Bias
Rmsd
Nrmsd
R2
Skill
1995/96
TAMCCD
TAMANN1
TAMANN2
TAMCCD
TAMANN1
TAMANN2
TAMCCD
TAMANN1
TAMANN2
TAMCCD
TAMANN1
TAMANN2
TAMCCD
TAMANN1
TAMANN2
1444
1329
1444
1572
1376
1572
1612
1556
1612
1732
1517
1732
6369
5778
6360
20.36
1.33
0.07
20.38
0.86
0.34
20.45
2.58
0.10
20.36
2.83
20.57
20.39
1.95
0.03
4.47
4.99
4.33
5.24
5.52
5.17
5.61
6.63
5.44
5.68
6.69
5.41
5.30
6.05
5.13
1.11
1.23
1.08
1.17
1.27
1.15
1.15
1.35
1.12
1.18
1.46
1.13
1.16
1.34
1.12
0.34
0.26
0.38
0.36
0.33
0.40
0.33
0.28
0.37
0.34
0.30
0.40
0.35
0.23
0.39
TAMCCD
TAMANN1
TAMANN2
TAMCCD
TAMANN1
TAMANN2
TAMCCD
TAMANN1
TAMANN2
TAMCCD
TAMANN1
TAMANN2
TAMCCD
TAMANN1
TAMANN2
160
151
160
210
174
210
200
188
200
170
162
170
740
675
740
20.36
1.42
0.11
20.38
0.96
0.30
20.40
2.64
0.12
20.38
2.79
20.61
20.38
1.97
20.00
1.96
2.80
1.85
2.58
3.08
2.49
2.50
4.20
2.40
2.63
4.45
2.31
2.45
3.72
2.30
1.32
1.89
1.24
1.54
1.89
1.49
1.45
2.38
1.39
1.61
2.94
1.41
1.49
2.31
1.40
0.64
0.48
0.70
0.67
0.58
0.70
0.65
0.55
0.67
0.62
0.54
0.72
0.65
0.43
0.69
0.63
0.28
0.67
0.66
0.53
0.68
0.64
20.01
0.67
0.61
20.14
0.70
0.64
0.18
0.69
TAMCCD
TAMANN1
TAMANN2
TAMCCD
TAMANN1
TAMANN2
TAMCCD
TAMANN1
TAMANN2
TAMCCD
TAMANN1
TAMANN2
TAMCCD
TAMANN1
TAMANN2
16
15
16
21
17
21
20
18
20
17
16
17
74
66
74
20.37
1.41
0.10
20.39
0.99
0.29
20.39
2.76
0.15
20.39
2.84
20.62
20.38
2.02
0.00
0.78
1.85
0.74
1.02
1.46
0.92
1.00
3.24
0.75
0.84
3.51
0.83
0.93
2.68
0.82
1.70
3.68
1.60
2.53
2.85
2.30
1.74
5.45
1.31
1.83
8.65
1.81
1.94
5.24
1.71
0.90
0.81
0.94
0.91
0.88
0.95
0.89
0.89
0.93
0.93
0.92
0.96
0.91
0.59
0.92
0.87
0.36
0.89
0.90
0.76
0.92
0.87
20.60
0.92
0.90
20.58
0.90
0.89
0.03
0.91
(a)
1996/97
1997/98
1998/99
All
(b)
1995/96
1996/97
1997/98
1998/99
All
0.33
0.19
0.37
0.36
0.32
0.38
0.32
0.07
0.36
0.33
0.004
0.40
0.34
0.14
0.38
(c)
1995/96
1996/97
1997/98
1998/99
All
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 R 2 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 5 1 is a perfect match
to the observations; skill 5 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
1130
JOURNAL OF HYDROMETEOROLOGY
VOLUME 4
FIG. 7. Scatterplots of rainfall estimation against kriged pixel data for all time scales; (a) pixel-day, (b) daily pixel mean, 10-day pixel
mean; (left) TAMCCD, (right) TAMANN2. The solid lines indicate a one-to-one relationship.
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
DECEMBER 2003
GRIMES ET AL.
1131
FIG. 8. Time series of daily average rainfall for 1997/98.
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 R 2 ; 0.9 (Table 5c). These high
correlations are attributable to three factors. First, TIRbased 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 2608C CCD while the overall light-rainfall pattern is closer to the 2308C 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.
7. Conclusions
A methodology for the operational estimation of daily
rainfall using an artificial neural network has been devised making use of Meteosat TIR imagery and NWP
model analysis fields from the ECMWF. Zambia in central Africa has been used as a case study. A novel feature
of this methodology is the use of principal component
analysis for the efficient inclusion of NWP model data.
Following the use of a pruning technique to remove
redundant input parameters, the optimum network configuration was a four-layer perceptron for which the input consists of CCD at four threshold temperatures together with the first five principal components of surface
horizontal wind velocities, surface relative humidity,
and higher-level vertical wind velocities. The output is
an estimate of the mean pixel rainfall. The network has
been trained and validated using 4 yr worth of Zambian
1132
JOURNAL OF HYDROMETEOROLOGY
VOLUME 4
FIG. 9. (top-left) TAMANN2 rainfall estimate (mm) 30 Mar 1997; (top-right) TAMCCD rainfall estimate (mm) 30 Mar
1997; (bottom-left) CCD image (T t 5 2308C); (bottom-right) CCD image (T t 5 2608C). For the rainfall estimates, the
range is from gray 5 2 mm to red 5 30 mm.
rain gauge data interpolated to pixel average values using kriging. A comparison has been carried out with a
standard CCD algorithm at three scales: pixel-day, 10
pixel-day, 10-pixel 3 10-day.
Results show that the ANN method is slightly but
consistently better than the standard approach at all
space and time scales. There is a high degree of scatter
for the individual pixel-day estimates because the resolution is too high for either method and additional
uncertainty is introduced by the collocation errors of the
satellite. The daily average (10 pixel-day) comparison
shows that the neural network gives more accurate estimates for higher rainfall amounts (in excess of 10 mm)
although both methods underestimate in this range. This
is important for hydrological applications, particularly
flood forecasting. At the 10-pixel 3 10-day scale, both
methods perform very well with the ANN having a
lower bias. The nature of the averaging means that the
maximum average rainfall is less than 10 mm, so the
performance of the methods with high rainfall amounts
averaged over 100 pixel-days has not been tested.
An additional advantage of the TAMANN2 approach
is that the calibration is carried out in a single-step training procedure with no necessity to select different
threshold temperatures or vary calibration parameters
for different stages of the season.
Development of the TAMANN2 methodology as an
operational tool is still in its early stages. An important
next step will be to test the algorithm in areas such as
East and northeast Africa where there is a lower correlation between CCD and rainfall amount. A useful
feature of the ANN framework is that the inclusion of
additional or different data streams is relatively straightforward. The pruning technique means that the impor-
DECEMBER 2003
GRIMES ET AL.
tance of additional data can be easily assessed. This
could be of great benefit in tailoring the approach to
different climatic conditions.
Acknowledgments. Thanks are due to the Zambian
Meteorological Service for providing the rain gauge
data for this study. Collaboration between L’Aquila and
Reading Universities was facilitated by funding under
the British–Italian Joint Research Initiative financed by
the British Council and CRUI/MIUR. The contributions
of Rogerio Bonifacio and lain Russell in assistance with
the data analysis are also gratefully acknowledged.
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