Journal of Natural Disaster Science, Volume 23, Number 1, 2001, pp23-33

Prediction of Precipitation by Aneural Network Method
Naoya MAEDA*, Shun'ichi KOBAYASHI**, Kaoru IZUMI**, Shigekazu KOUNO***,and Michihiro AMENOMORI*****Graduate School of Science and Technology, Niigata University, Japan(Present affiliation: Digital Weather Platform Co., Ltd, Japan)** Research Institute for Hazards in Snowy Areas, Niigata University, Japan*** Japan Weather Association Tohoku Branch, Japan**** Faculty of Science and Technology, Hirosaki University, Japan(Received for 8 Nov., 2000 and in revised from 10 Jul., 2001)

ABSTRACT
A neural network method to reduce natural disasters (particularly, avalanches, slush flow, and melting snow insnow hazards) was used to predict precipitation on the ground. Based on computation cost and similar pattern
two types of simulations were made. Two methods were used to evaluate precipitation, mean square error which
is superior for evaluating the strength of precipitation over the prediction range and Critical Success Index (CSI)
evaluation used to judge the existence of precipitation. Results were compared with prediction results from theshort time precipitation forecast method used by the Japan Meteorological Agency. Mean square error was about
0.1 to 0.2 mm/h toward the term when there was much precipitation whether rain or snow. In the CSI evaluation,
the neural network method gave high values as compared with the short time precipitation forecast method for thestrong winter characteristics. Results of these two evaluations show that our method can adequately predict forthe subsequent hour and is a practical tool for reducing snow hazards.

1. INTRODUCTION
Changes in precipitation distribution are complicated, being
affected by meteorological and geographical factors. The methodof predicting precipitation distribution for several hours is called
short-time rainfall prediction, consisting of topographical methods,
the rainfall conception model and the meso-scale model (Nakakita
et al; 1996, 1999). The most typical prediction method has been
the short time precipitation forecast used by the Japan
Meteorological Agency. It consists of complicated equations
involving various factors. One of the main problems with thismethod is that error is produced when the strength and movementof precipitation change nonlinearly with time. Private weather
companies have started predicting weather, by nonlinear methods(e.g. neural networks) (Shinozawa et al; 1995, Ochiai et al; 1998).
There have been two methods for predicting rainfall andsnowfall with a neural network. One is the prediction of daily
fresh snowfall at a specific point after determining the snowfall
pattern from past history (Amenomori and Hashiyama, 1993;
Yamada et al., 1997). The other, local short-range prediction ofcloud movement that brings snowfall, uses mesh data for a radiusof a few kilometers (Asuma et al., 1984; Maeda and Amenomori,1999). The latter can deal with complicated movement (development, decline, and appearance) because of being a nonlinear
method. In reality, the prediction of rainfall and snowfall on the
ground is more useful for the reduction, prediction, and investigation of natural disasters (in particular, the avalanches, slush flow,

and melting snow seen in snow hazards), because conditions in thesky differ from those on the ground. Moreover, because it uses alarge number of learning patterns (precipitation patterns), it
requires a large amount of calculation time to sufficiently reduce
error. Based on past examples, only 5 to 25 input neurons wereobtained. Therefore, we have attempted to increase the number of
input neurons to reduce prediction error by classifying a few snowfall patterns during the snowy season, ignoring the computation
cost and to predict snowfall on the ground by use of function produced through the learning process. We then compared our results
those predicted results as calculated by the Japan Meteorological
Agency.
2.

DATA USED

Mesh data for the Kanto and Chubu areas of eastern Japan
were used (see Fig.1-a). Precipitation data was obtained from theJapan Weather Association. Data, recorded hourly consisted of
14400 (120x120) pixcels, with a 5km x 5km range for each pixcel.
Based on the actual precipitation, we chose a classification rangeof 1 to 15 strength levels (0 to 13 mm/h) of precipitation. Morethan 16 strength levels were combined to make the 15th level(Table 1). The prediction and learning ranges of these simulations
by neural network methods were based on an area of 21x39 pixcels(about 105 x 195 km) in the Jouetsu and Chuetsu areas, Niigata
Prefecture, Japan (Fig.1-b). This data collected by the Japan
Meteorological Agency, is generally available to the public for

KEY WORDS: neural network, precipitation, maximum cross correlation, mean square error, CSI evaluation, short time precipitation forecast

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N. MAEDA, S. KOBAYASHI, K. IZUMI, S. KOUNO AND M. AMENOMORI

prediction. It consists of synthetic radar data made up of the precipitation at AMeDAS observation points and the estimated precipitation on the ground in order to supplement echo strength in theFig. 1sky at points not covered by the observations. Full details are
given in section 3.1.

Fig. 1(a)Fig. 1(b)(a) Range of mesh data for the Kanto and Chubu areas in eastern Japan and (b) the learning and prediction range

PREDICTION OF PRECIPITATION BY ANEURAL NETWORK METHOD

3.

SIMULATION

3.1 Short time precipitation forecast method
Predicted results, based on precipitation data over a wide area,
gathered by the Japan Weather Association, were compared withresults provided by the neural network method.
The mesh prediction data for a wide area are computed by amethod called short time precipitation forecast used by the Japan
Meteorological Agency and are provided the Agency to private
meteorological companies. The prediction equations used in the
short time precipitation forecast method estimate complicated

Table 1.

Fig. 225

movement (development, decline, and appearance) by combining
movement vectors of precipitation areas and adding topographicalterms. This movement vector is not obtained from the entire prediction range, but from various vectors in each subrange by the useof a complicated equation involving the moving precipitation
range.
3.2 Neural Network Method(1) Preparation
Hourly maximum cross correlations between the precipitation
distribution for the present hour and that for the next hour were

Correspondence table of the supplemented strength of precipitation

Hourly distribution map of the maximum cross correlation (November 1, 1998 to March 31, 1999)

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N. MAEDA, S. KOBAYASHI, K. IZUMI, S. KOUNO AND M. AMENOMORI

calculated from November 1, 1998 to March 31, 1999 to determine
the optimal input neuron combination of the network.
Fig.2 shows the maximum cross correlation distribution foreach hour from November 1, 1998 to March 31, 1999. The hourly
maximum cross correlation mean was about 0.6 to 0.8 throughout
this snowy season period, and generally was high.
The movement vector throughout this snowy season period
was calculated based on Fig.2. The equations that produced the
movement vector (Vy,Vx) are
Vy=(Y+m)Δy/ΔT,(1)

Vx=(X+n)Δx/ΔT,(2)

m=2(σ-y-2σ0+σ+y)/(σ-y-σ+y),(3)

Fig. 3n=2(σ-x-2σ0+σ+x)/(σ-x-σ+x).

(4)

where
m and n= interpolation point

σ0= value of maximum crosscorrelation;

σ-y,σ+y,σ-x andσ+x= nearby cross correlation valuesofσ0;Δy and Δx= pixcel size;

ΔTtime interval;

Y and X

coordinate of σ0.

Distribution of the movement vector was widely extended,

Distribution map of the movement vectors of precipitation for maximum cross correlation (November 1, 1998 to March 31, 1999)

Fig. 4Structure of the neural network model used (a) pixcels of the concentrated maximum cross correlations,(b) pixcels of the southern and eastern directions in the case of movement of the precipitation range by low pressure

PREDICTION OF PRECIPITATION BY ANEURAL NETWORK METHOD

about 8x8 = 64 pixcels (Fig.3). Consequently, we made 79 input
layers that were parts of the concentrated maximum cross correlations (a), for the southern and eastern directions in the case of
movement of the precipitation range by low pressure (b), that werebased on the Cross Correlation-Neural Network hybrid method(Maeda and Amenomori, 1999) (see Fig.4). Fifteen hidden layers
also were made from results of several experimental, and lastly one
output layer was predicted for the next hour.
The Jacobs Hybrid Algorithm (Jacobs, 1986), which is 10 to
100 times faster than traditional neural networks, was used toreduce error. This faster convergent algorithm consists of the following steps:
Step1
Set the initial weights w[0], the initial learning rateη[0]), its increment and decrement factors, κ,φφ, and thediag(η
α,; then set coefficient θ used to smooth theMomentum factorα
partial derivative.
Step2 Calculate the forward step. As the output function to eachlayer, use the Sigmoid function (Eq.5).
β*S))
F(S)=1/(1+exp(-β(5)

Step3 Calculate the backward step. Calculate gradient g[t] andδ[t]=(1-θθ)*g[t]+θθ*δδ[t-1]. Modify the learning rate based on
the sign δ1[t-1];
ηi[t]=η
ηi[t-1]+κκif δi[t-1]*g[t]>0(6)

ηi[t]=η
ηi[t-1]*φφif δi[t-1]*g[t]<0(7)

ηi[t]=η
ηi[t-1]otherwise.

(8)

Then calculateη[t])*g[t]+αα*(w[t]-w[t-1])
Δw[t] = -diagη

(A)
Fig. 5(9)27

Step4 Change the weights and return to step2
w[t+1]=w[t]+Δw[t].

(10)η=0.05,ββThe initial parameters of these simulations wereη
α=0.9,κ
κ=0.01,φφ=0.9 and θ=0.7.
=0.01,α(2) Learning Process
We tested two types of simulations; (A) the period of a typicalpressure pattern for winter during heavy snowfall in the mountainous region and (B) the period of a typical pressure pattern for winter during heavy snowfall in the plain region based on data for thesnowy season (November 1998 to March 1999). Both types were
tested because of computation cost and similar patterns based on
the results given in Section-3.2.1. The number of acquired learning patterns (number of precipitation patterns) was 30000 to
50000. As the learning iterations increase, errors in the learning
process decrease, but if the learning iteration is increased too
much, there is high possibility that the produced prediction equation will become fixed on specific precipitation patterns. On thebasis of various experimental results, a learning iteration of 30000
steps therefore was selected.
In simulation (A), precipitation patterns which had winter characteristics during heavy snowfall in the mountainous region for about
one week in early January 1999 were used, and in (B) those whichwere characteristic of winter during heavy snowfall in the plain
region near the end of January and early in February 1999 wereused. For both the (A) and (B) simulations, the learning results
obtained gave high evaluations, even when there was much precipitation (Fig.5). Moreover, the mean square errors were about 0.5 0.6 mm for both simulations.
3.3 Prediction results
Data from November 1998 to March 1999 were used as thelearning patterns, to predict the hourly distribution of precipitationfrom November 1999 to March 2000 based on the function pro-(B)

Learning results of characteristics of winter during heavy snowfall in (A) the mountainous region and(B) the plain region (Numbers in these figures indicate precipitation strength)

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N. MAEDA, S. KOBAYASHI, K. IZUMI, S. KOUNO AND M. AMENOMORI

duce after learning the results.
To assess the prediction, two evaluation methods were used;
the mean square error (MSE) that is excellent for evaluating thestrength of precipitation over the prediction range calculated fromequation (11), and the CSI (Critical Success Index) evaluation thatis used to judge the existence of precipitation calculated fromequation (12). Moreover, the correspondence of symbol N in
Table 2.

Fig. 6

Fig. 7equation (12) is shown in Table 2.
MSE = (Σ(Aij-Bij)2)1/2
Aij is the real value, Bij the predicted one.
(1< i < 39, 1< j <21)(11)

CSI(%) = N11 / (N01+N10+N11)(12)

Correspondence of N symbols in the CSI evaluation

Hourly prediction evaluation from November 1, 1999 to March 31, 2000

Comparison of prediction results of the short time precipitation forecast and neural network method in
simulation-(B) by the mean square error (November 1, 1999 to March 31, 2000)

PREDICTION OF PRECIPITATION BY ANEURAL NETWORK METHOD(1) Mean Square Error
Results of the preceding two simulations and of the short time
precipitation forecast method of the Japan Meteorological Agency
were evaluated by the mean square error. The prediction's precision in the winter season of the following year based on learning
results had a mean square error average of about 0.05, although thevalues at the beginning and end of winter were larger than themidterm value (MSE = 0.1 - 0.2) (Fig.6), evidence of satisfactory

Fig. 8prediction results.
Fig.7 shows the comparison with the mean square error for theneural network method in simulation-(B) and the short time precipitation forecast method. Results were compared with the daily precipitation at Takada, Jouetsu City, Niigata Prefecture (Fig.8),
throughout the winter season. The mean square errors showed that
there was little error in the comparison of the prediction evaluationof the short time precipitation forecast method with that of the

Daily precipitation (mm) at Takada, Jouetsu City, Niigata Prefecture from November 1, 1999 to March 31, 2000

Fig. 929

CSI evaluation during each simulation near the end of February 2000

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N. MAEDA, S. KOBAYASHI, K. IZUMI, S. KOUNO AND M. AMENOMORI

neural network methods on days when there was little or no precipitation at Takada. On days when there was much precipitation,
whether rainfall or snowfall, however, the neural network methods
could sufficiently reduce error, in particular when the error waslarge as in the case of the short time precipitation forecast method.

Fig. 10(2) CSI Evaluation
In the CSI evaluation, the results of precipitation predictions
by the short time precipitation forecast method were a little higher
than those by the neural network methods throughout the winterseason but particularly during the periods of early and end of winter. Fig.9 shows a comparison of the CSI evaluations for the

Daily snowfall (cm) at Takada, Matsudai Town, and Oyu. Daily precipitation at Takada, Niigata Prefecture

Fig. 11(a)PREDICTION OF PRECIPITATION BY ANEURAL NETWORK METHOD

Fig. 11

Fig. 11(b)

Fig. 11(c)

Prediction images of simulations by neural network methods(a) characteristic of heavy snowfall in the plain region(b) characteristic of heavy snowfall in the mountainous region
upper left: real image at the present time
upper right: real image after an hour
lower left: prediction image after an hour made with the function produced after learning
the characteristics of heavy snowfall in the mountainous region
lower right : prediction image after an hour made with the function produced after learning
the characteristics of heavy snowfall in the plain region(c) precipitation strength

31

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N. MAEDA, S. KOBAYASHI, K. IZUMI, S. KOUNO AND M. AMENOMORI(A),(B) neural network and short time precipitation forecast methods near the end of February, 2000 when both types of winter characteristics were present.
Fig.10 shows predictions for February 21 to 23 when there
were weak winter characteristics during heavy snowfall in themountainous region; for February 24 and 28 when there were winter characteristics during heavy snowfall in the plain region (40 to
55cm deep at Takada.); and for February 29 when there werestrong winter characteristics during heavy snowfall in the mountainous regions (about 50cm deep at Oyu and Matsudai Town,
Niigata Prefecture.), evidence that the two neural network methods
have high prediction precision as compared to the short time precipitation forecast method.
Except for the typical pressure pattern characteristics of winter, there was close similarity to the winter term characteristics
including the results of the CSI evaluation. The evaluation for the
short time precipitation forecast method generally was better thanfor the neural network methods, but when there was much snowfall, the neural network methods also were useful for prediction.
The mean values of the CSI evaluation when there was precipitation frequently were more than 0.6 for all the methods. This prediction method therefore is concluded to have high precision
except when there is almost no precipitation (CSI evaluation values were 0.).
Furthermore, Fig.11 shows prediction images for (a) when
there was heavy snowfall in the plain region (0:00, February 24,2000) and (b) when there was heavy snowfall in the mountainous
regions (0:00, February 29, 2000), and for the following hour when
the function obtained from the learning process in the 1998 to 1999
winter season was used. The prediction images were comparedwith the real images for the following hour. For both (a) and (b)there was little difference in the distribution of the precipitation
range in regard to the prediction images when a different simulation type function was used. When prediction images used thesame simulation type function, (a) was superior for predicting the
distribution and strength of precipitation, whereas (b) was superior
for the output of a narrow precipitation range. Consequently, theprecipitation for the actual following hour can be predicted.
4. CONCLUSION
Prediction of precipitation on the ground was predicted by aneural network method, because this type of prediction is very useful for reducing the chances of a natural disaster in the winter. To
determine the input layers, the maximum cross correlation between
present time and following hour first were calculated. The values
were high, the mean being about 0.6 to 0.8 throughout the winter.
Because, however, the movement vector of the precipitation
ranges of the total radar images produced the maximum cross correlation, which showed a wide distribution, many input neurons
and further calculations were needed.
The precision of this neural network method's learning
process could reduce error sufficiently, producing good results,
even for strong precipitation strength values in both the (A) and(B) simulations.
On the prediction evaluations, the neural network methods
and the short time precipitation forecast method used by the Japan
Meteorological Agency were compared. In some cases the meansquare error is more useful for judging the evaluation of precipitation strength. In early winter and at the end all the methods compared have few high errors in comparison with the coldest period,
but about 0.1 to 0.2 mm/h toward the term there was much precipitation whether rain or snow. Although the CSI evaluation is more
useful for determining the existence of precipitation, the neuralnetwork methods gave high values in comparison with the shorttime precipitation forecast method during the strong winter characteristics. These two evaluations gave results that can sufficiently
cope with prediction for the following hour. As for the output ofprediction image, in cases that used the same type function, thedistribution and strength of precipitation could be predicted almost
exactly, and the output for prediction of the narrow precipitation
range also was almost exact. Furthermore, only after the learning
process, Can the function produced be used to reduce the prediction value immediately. This method therefore is practical for
reducing snow hazards.
In the further, a method for the automatic separation of the(A) and (B) simulations needed to be developed and the errors inall the methods must be evaluated.
ACKNOWLEDGMENTS
We thank Mr. Seiji Kondo of the Japan Weather Association,
Niigata who provided the precipitation data and gave usefuladvice. We also thank Dr. Nicholas Sallah and Miss Stephanie
Libonati of Britanica English Village Co. Ltd., Yasuyoshi
Inushima and Hiroaki Kuriyama of Digital Weather Platform Co.
Ltd. who checked the grammar in this paper.
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