A study on short-term rainfall prediction by radar raingauge

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1 New Directions for Surface Water Afode/mg(Proceedings of the Baltimore Symposium, May 989) IAHSPubl.no. 8,989. A study on short-term rainfall prediction by radar raingauge K. Ishizaki & F. Yoshino Public Works Research Institute, Ministry of Construction Tsukuba, Ibaraki 05, Japan K. Takeuchi Department of Environmental Engineering, Yamanashi University Kofu, Yamanashi 400, Japan and A. Yoo CTI Engineering Co., Ltd. Chuo-ku, Tokyo 0, Japan ABSTRACT A short-term rainfall prediction model using the echo-tracking method was applied to a number of rainfall cases to determine the accuracy of the model, and the accuracy of one-hour prediction proved to be practical. The echo-tracking method and the advection model method were compared by applying them to the Nagasaki Storm. The results confirmed that a storm rainfall can be predicted one hour before it occurs and that there is little difference in prediction accuracy between these methods. INTRODUCTION Flood runoff prediction is critically important for river management. The dominant input for runoff prediction is a rainfall for several hours from the present time. With the radar raingauge put into practice recently, prompt collection of rainfall data from a wide area at flood has been made possible. Although many short-term rainfall prediction models that use data obtained from a radar raingauge were proposed in Japan, few have been valued for their prediction characteristics and accuracy. This paper discusses the characteristics and accuracy of the short-term rainfall prediction model using the echo-tracking method, which was developed by the Public Works Research Institute, the Ministry of Construction, through its application to a number of rainfall cases. The predictability of a heavy rain was also studied by applying both the echo-tracking method and the advection model to a storm rainfall that arose in and around the Nagasaki Prefecture in 98. SHORT-TERM RAINFALL PREDICTION METHOD The short-term rainfall prediction method can be broadly classified into three methods: (a) Kinematic method (b) Dynamic method (c) Statistical method Among these methods, the dynamic and the statistical methods are seldom used. The dynamic method is not suitable for short-term rainfall prediction that requires timeliness because it is difficult to determine initial and boundary conditions. The statistical method is not applicable because so far no definite correlation has been found between rainfall, and topographical and meteorological data. In Japan, many short-term rainfall prediction techniques based on the kinematic method have been proposed. The simplest one is the advection of a wide-ranging rainfall intensity distribution obtained from the radar raingauge (hereafter referred to as "radar echo") by an observed wind of 700 mb (Tatehira & Makino, 974). However, this method is not being used because the 700 mb wind is only available every six hours, and the direction and speed of the wind and the movement of a rainfall pattern do not necessarily correspond. Asai et al. (977) found a method of obtaining a translation

2 K. Ishizaki et al. 4 vector from two echo charts by the cross-correlation method. This method is still frequently used mainly at the Meteorological Agency, for calculating a translation vector. The Public Works Research Institute has proposed a new method in which a coefficient of cross-correlation is not calculated directly from radar echo charts, but a translation vector is determined from a coefficient of association obtained from radar echo charts that have been binary-coded by a certain threshold (Ohkura et al., 98). This method was developed specifically for tracking medium-scale rainfall, and many applications have been reported (Yoshino et al., 987) to date. The above three methods were developed on the assumption that a rainfall pattern translates in parallel in accordance with a translation vector, while the advection model method proposed by Shiiba et al. (984) employs a linear expression of position coordinates to determine a translation vector, and can incorporate the parallel translation, rotation, and expansion of a rainfall pattern. Another short-term rainfall prediction technique that uses an advection equation incorporating a diffusion term (advectiondiffusion model) is being studied by Moriyama et al. (985), but it is now at a stage of 0-minute prediction and more time seems to be required for practical use. A prediction method that combines the pattern recognition capability of man and the computing capability of a computer is referred to as "man-machine system", which is represented by Takeuchi's (978) deformation tensor method. The method is used to express the deformation of a rainfall-intensity plane between two points of time in terms of the deformation tensor, assuming the deformation is linear. Four or more corresponding hyetal echoes on two radar echo charts of two different points of time are picked up manually, and then a translation vector and a deformation tensor are calculated. The Hino (985) method, which employs a Kalman filter, is another unique technique, where the spatial distribution of rainfall intensity corresponds to the deflection of an imaginary elastic plate, and the change in rainfall distribution is expressed by the change in virtual load. The position of load, moving speed, and virtual load are expressed by a state equation, and their coefficients are determined by the Kalman filter. A prediction by this method is an extrapolation using these coefficients. Of the many prediction techniques mentioned above, this paper focuses on the echo-tracking method and the advection model method, which have left many examples of practical application and have proved their applicability, to establish the characteristics of their predictions. A brief explanation of the two prediction methods follow. Echo-tracking method There is a close correlation between the scale of space where a phenomenon takes place and the duration of the phenomenon: the larger the scale of space is, the longer the duration is. Since the life of an atmospheric phenomenon is in tens of minutes in meso-7 ( to 0 km) (Smith, 976), predicting a phenomenon that will take place several hours later requires a phenomenon that is in meso-( (0 to 00 km). A short-term rainfall prediction model that was developed with this in mind is the echo-tracking method. The procedure of the echo-tracking method is as follows. () Designate every mesh on the radar echo chart as "", which represents a rainfall intensity exceeding a predetermined threshold, or as "0", which represents a rainfall intensity below the predetermined threshold (binary coding). () Find a coefficient of association between the binary-coded data of a radar echo chart at T-At and the data of another radar echo chart at T. Then determine the combination of a direction and a distance which gives the maximum value, and let the combination be a translation vector. () Advect the echo at T-At by using the determined translation vector so that the advected echo may overlap the echo chart at T. Then find E(T)-E'(T-At) and let the value obtained be a growth or a decay during the time of At. (4) Advect the echo at T at intervals of five minutes by using the translation vector obtained in step above, and extrapolate growth/decay from a series of growth/ decay values obtained in step above to predict a radar echo chart at each point

3 5 Short-term rainfall prediction by radar raingauge of time. Note that the calculation method of growth and decay shown above is only an example, and that this method is not necessarily appropriate for accurate rainfall prediction, as described later. When growth and decay are not taken into account, step above is to be omitted. Advection model If a rainfall intensity at the point (x, y) at the time (t) is represented by z (x, y, t), the equation of advection for the change of time-space distribution of z is assumed to be as follows: 9z/9t+u-9z/9x+v9z/9y=w () where w is the amount of growth or decay, and the translation vector (u, v) and the term of growth/decay (w) are assumed to be expressed by the linear expressions of the position coordinate (x, y), as follows: u=cix+c y+c, v=c 4 x+c s y+c 6, w=c 7 x+c s y+c 9 () where c x... c 9 are parameters to be inferred from known quantities. With the expressions u, v, and w, this model can express the rotation, shearing strain, and expansion of a rainfall pattern. The prediction procedure is as follows: () Infer parameters Cj to c 9 by the method of least square from the radar data of the past several points of time. () Advect the rainfall pattern at the present time by using the above parameters to predict rainfall. If the growth and decay are not taken into consideration for prediction, then define c 7 =c 8 =c g =0. PREDICTION ACCURACY OF ECHO-TRACKING METHOD To determine the prediction accuracy of the echo-tracking method, short-term rainfall prediction by the method has been carried out by using the data on eight rainfalls with the total rainfall duration of 6 hours. The data used are those collected by the Radar Raingauge System at Mt. Akagi, Gunma Pref., of the Ministry of Construction. Tables and show the results of the prediction. In the prediction, the echo at the present time was advected by the translation vector without considering its growth or decay. The evaluation criteria of the prediction accuracies shown in Tables and are as follows: (a) The measured values used for comparison with predicted values were those from the radar raingauge, and ground rainfall was not used. (b) The unit area for the evaluation is a square area of 5 km x 5 km = 5 km. (c) The term "one-hour prediction" is defined as an hourly rainfall during the first hour after the point of time of prediction. The terms "two-hour prediction" and "three-hour prediction" are defined as an hourly rainfall during the second and the third hours after the point of time of prediction, respectively. As is obvious from Tables and, the practicability of the echo-tracking method is high in one-hour prediction, judging from the fact that a stable prediction accuracy with a correlation coefficient of 0.6 to 0.9 has been obtained. By comparison, the accuracies of the two-hour and three-hour predictions are extremely low, showing a correlation coefficient of 0. to 0.6. Careful examination of the prediction accuracies of individual steps has revealed a fair stability of the one-hour prediction accuracies, and a wide variation of the two-hour and three-hour prediction accuracies with some extreme examples of negative coefficient of correlation. Tables and show the results that were obtained by using the translation vector

4 K. Ishizaki et al. Table Prediction accuracy of echo-tracking method (Coefficient of correlation) No. Date Rainfall May 4, 979 Oct. 8, 979 Oct. 9, 980 Jun. 5, 98 Aug., 98 Jul. 9, 98 Aug., 98 Sep., 98 Cause Cyclone Typhoon Bai-u front Bai-u front Typhoon Bai-u front Typhoon Typhoon One-hour prediction* Two-hour prediction* Three-hour prediction* *Upper line: Coefficient of correlation Lower line: Number of samples Table Results of one-hour rainfall prediction by echo-tracking method (Ranking) Predicted value Measured value mm mm~ Total - mm mm mm mm mm mm mm 50mm 6 Total calculated from the radar echoes at two different points of time with a 5-minute interval. Rainfall was also predicted by advecting the area of storm rainfall and the entire hyetal region with different translation vectors, and by using the average translation vector of the previous 45 minutes. Since a little improvement in accuracy was observed in the one-hour prediction, it was found that substantial accuracy improvement cannot be achieved even if the definition of the translation vector is changed, as pointed out by Bellon & Austin (978). In using the results of rainfall prediction, there is a need for its users to know the reliability of the predicted rainfall. Pig. shows the statistically calculated confidence limit of the predicted rainfall. Note that the two-hour prediction is an accumulated rainfall for two hours from the start of the rainfall prediction. Pig. shows that the two-hour prediction is less accurate than the one-hour prediction, that a predicted rainfall tends to be higher than a measured rainfall, and that the higher the rainfall intensity is, the wider the confidence limits become.

5 7 Short-term rainfall prediction by radar raingauge One-hour prediction % / / ^*: 68 "% /^pglpgft Average ÊÊÊÊÈÈÊÊ& 68.% 0- fêê^ -^ 90% Predicted rainfall (mm) Predicted rainfall (mm) Fig. Confidence limit of rainfall prediction SHORT-TERM RAINFALL PREDICTION OF NAGASAKI STORM The Nagasaki Storm is a record storm that hit Nagasaki Prefecture and neighboring areas in July 98. According to the record of the Nagasaki Marine Observatory, the maximum hourly precipitation, three-hour precipitation, and daily precipitation were.5 mm, mm, and 449 mm, respectively. The disastrous storm caused the death of more than 00 people, mainly in Nagasaki and Kumamoto Prefectures. To examine the predictability of storm rainfall and compare the prediction characteristics of the two models, the echo-tracking method and the advection model have been applied to this Nagasaki Storm. The coefficients of correlation, the hyetographs, and spatial distribution of onehour rainfall, in Table, Fig., and Fig., respectively, show the prediction accuracies of the two methods. The accuracy of the one-hour prediction is consistent, and the storm probably could have been predicted one hour before its occurrence. The Table Accuracy of rainfall prediction for Nagasaki storm (Coefficient of correlation) Time of p rediction July, July 4, Average 6:00 7:00 8:00 9:00 0:00 :00 :00 :00 0:00 :00 :00 :00 4:00 5:00 6:00 7:00 8:00 9:00 0:00 :00 Echo-tracking method One-hour prediction J Two-hour prediction Advection model One-hour prediction Note ) Comparison was made in terms of the average for 8 km ) Rainfall of mm/hr or less is not inlcluded. Two-hour prediction

6 K. Ishizaki et al. Nagasaki city (-hour prediction) 0 Nagasaki city (-hour prediction) 0~ g ' g ' 6 Local time Kumamoto city (-hour prediction) 0 6 Local time Kumamoto city (-hour prediction) 0- c ' g ' té 6 Local time -e- Measured value j Predicted value ; "\ Unpredictable Fig. Hyetograph for comparison of rainfall prediction. 6 Local time coefficient of correlation of the two-hour prediction is much lower, and its quantitative prediction accuracy is low. However, the rainfall prediction of up to two hours seems to be practical as long as accumulated rainfall or the average rainfall of a larger area is employed. To compare the prediction characteristics of the echo-tracking method and the advection model method, translation vectors obtained by these two methods were compared with the observed wind (see Fig. 4). The moving direction of the rainfall pattern is almost stable, and since the directions of translation vectors obtained by the two methods correspond well to each other, the moving direction seems to have been determined with fair accuracy by either method. Fig. 5 shows a comparison of translation vectors between the two methods. Table shows that the prediction accuracy of the advection model at 8:00 on July is more accurate than that of the echo-tracking method. As shown in the spatial distribution chart of a translation vector obtained by the advection model, the movement of the rainfall pattern is not a parallel translation, but an expansion. Therefore, this specific rainfall pattern was judged by the echo-tracking method, which assumes a parallel translation, to be moving at a speed of zero, that is, stationary. The graph at 09:00 on July 4 is an example that shows an advantage of the echo-tracking method in prediction accuracy. The speed identified by the advection model seems to be lower than the actual one. This seems to be because the movement of the echo with a low rainfall intensity or on a scale of meso-7 was captured; hence, the movement of the entire rainfall pattern could not be abstracted. The prediction accuracies may vary in individual steps according to the characteristics of these prediction methods. Statistically, however, the prediction accuracies of these methods are almost at the same level.

7 40 km Measured rainfall Predicted rainfall by echo-tracking method Le X gend 0~ ~ 5~ mm/hr Unpredictable Predicted rainfall by advection model Fig. Spatial distribution of one-hour rainfall (7:00 ~ 8:00 on July ). Legend N lom/s UN iu m/s _ _ -^ o Moving speed 0 m/s ' >r -Jr ~v -* ^v ^v ^v --*'. o O o o Advection model Echo-tracking method 700 mb observed value / 900 mb observed value i i i i i i i i i i i i i i i i i i i i /5 8 4/0 6 9 Local time Fig. 4 Observation wind and translation vector. (Translation vectors calculated by the advection model are at cordinate (0, 0))

8 K. Ishizaki et al. in X (km)» 50 km/h X (km)» 50 km/h 8:00, July, 98 09:00, July 4,98 Fig. 5 Distribution of translation vector. Ol^7 " represents a translation vector calculated by the echo-tracking method; the translation vector at 8:00 on July is 0 m/s) GROWTH AND DECAY In the echo-tracking method, the amount of growth or decay represented by the letter w is defined as the difference between the echo E(T-At) at the time (T-At) advected by the translation vector and the echo E(T) at the time T, which is expressed as follows: w=e(t)-e'(t-at) () while in the advected model, it is identified as w in the expression (). In conventional prediction models, the amount of growth or decay calculated like this has been used for prediction in the form of constant-value extrapolation. Fig. 6 shows the change with time of the growth or decay obtained by the echotracking method for three areas sampled at random (one of the areas has an area of 6 km x 6 km). In the observation area of the Mt. Akagi Radar site, a hyetal region often moves from southwest to northeast, where mesh A is an upgrade, mesh B is a downgrade, and mesh C is a flatland. As is seen in Fig. 6, the growth/decay greatly varies both in time and space, and its time series data is completely random. The data of the growth/decay identified by the advection model is also random, as pointed out by Takasao & Shiiba (984). For this reason, improvement of prediction accuracy cannot be expected by the constant-value extrapolation of identified growth/decay. Tsonis et al. (98) identified a function, instead of a constant value, to express growth/decay from the growth/decay of the past several tens of minutes, and tried extrapolation using the function; however, he could find no improvement in accuracy. Thus, it can be concluded that the growth/decay identified from the past radar echo data cannot be used, as it is, for prediction. There is a need, however, to predict growth and decay in some way in order to enhance the accuracy of the short-term rainfall prediction. It is known that topographical features is one factor that affects the growth and decay of rainfall, and there is a report (Tatehira, 976) that a good result could be obtained from the calculation of orographic rainfall based on the paper of Kessler (969). Yet a method that incorporates orographic rainfall into the prediction models dealt with in this paper is to be established.

9 Short-term rainfall prediction by radar raingauge a 5/8 6/0 6 9 Local time Fig. 6 Example of time series change in growth/decay. CONCLUSION From above, we conclude as follows: (a) One-hour rainfall prediction by the echo-tracking method is accurate enough for practical use. (b) The accuracy of the two-hour and three-hour rainfall prediction is much lower than that of the one-hour prediction. (c) A storm rainfall, such as the Nagasaki Storm, which could cause a serious disaster, can be predicted one hour before its occurrence. (d) Similar prediction accuracies can be achieved by the echo-tracking method and the advection model. (e) Extrapolation of growth/decay is purposeless. ACKNOWLEDGEMENT The authors wish to express their sincere thanks to the Tone Reservoir Integrated Control Center and the Chikugo Reservoir Integrated Control Center of the Ministry of Construction for the loan of valuable radar data. REFERENCES Asai, T. Yoshizaki, M. & Ichikawa, K. (977) Some results on an objective analysis for tracking radar echoes of convective clouds. J. Met. Soc. Japan 55, Bellon, A. & Austin, G.L. (978) The evaluation of two years of real-time operation of a short-term precipitation forecasting procedure (SHARP) J. Appl. Meteorol. 7, Hino, M. (985) Short-term rainfall prediction by the "virtual load" method. Proc. 9th Japanese Conf. Hydraul In Japanese. Kessler, E. (969) On the distribution and continuity of water substance in atmospheric circulations. Met. Monographs, -84. Moriyama, S., Hirano, M., Kawarada, H. & Hara, H. (985) Short-term rainfall prediction by use of a translation-diffusion model. Proc. 9th Japanese Conf. Hydraul In Japanese. Ohkura^ H., Ishizaki, K., Nakao, H. & Morimoto, R. (98) Short-term precipitation forecasting by radar raingauge. Proc. 7th Japanese Conf. Hydraul In Japanese. Shiiba, M., Takasao, T. & Nakakita, E. (984) Investigation of short-term rainfall prediction method by translation model. Proc. 8th Japanese Conf. Hydraul In Japanese. Smith, D.L. (976) The application of manually digitized radar data to short-range precipitation forecasting. 6th Radar Met. Conf

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