Daisuke Hirayama, Mutsuhiro Fujita
and Makoto Nakatsugawa

Introduction

Purpose Of This Study

The Japanese Ministry of Construction has already established a nationwide radar network system. Twenty-two radar raingages have been installed, covering the whole area of the Japanese Archipelago. Four radar raingages are in operation in Hokkaido Prefecture. The first stage to build the radar network system has been accomplished. For the second stage, we have to establish how to effectively use the information obtained from the weather radar. It is well known that the rainfall rate is estimated through the Z-Rr relation and that rainfall estimation based on Eq.(1) (the authors call it radar rainfall intensity here.) will lead to errors.

Given below is a short list of factors affecting the accuracy of rainfall measurement derived from radar measurements (Zawadzki,1984).

(1) High variation in raindrop size distribution which makes the problem of optimum selection of a Z-Rr relationship difficult.

(2) Reflectivity gradients across a sampling volume and partial beam filling violate the assumption leading to Eq.(2).

(2)
where Pr is the power transmitted, C is a constant depending on the parameters of the radar system, K is the attenuation constant and L is the range from the antenna to the target.

(3) Bright band caused by the scattering of radar waves due to ice particles present in the higher levels of some clouds.

(4) False echo caused by anomalous propagation of radar waves. If it remains undetected, it causes severe errors in rainfall estimates.

(5) Miscalibration of radar electronic instruments can cause biased measurements of the reflectivity factor.

Figure 1 shows the relationship between radar reflectivity factor Z and observed ground rainfall Rg at the central radar operated by the Hokkaido Development Bureau. The solid line in the figure shows the Z-Rr relation identified by the Hokkaido Development Bureau. The general sources of error between radar rainfall intensity and observed ground rainfall are listed above. Another source of error is a scale problem. The central radar in Hokkaido provides an average reflectivity factor over a 1 mesh.

Fig. 1- Relationship between Z-Rr

On the other hand, the standard precipitation gage is 20cm in diameter. To avoid such scale gaps between the radar raingage and precipitation gage, Hashimoto(1994) proposed the application of areal rainfall instead of rainfall intensity from the precipitation gage. This paper also focuses on the above scale gap. The authors propose a new method to identify the parameters included in the Z-Rr relation based on runoff data. This proposed method has the following advantages:

(1) Runoff is a response from a basin, that is, a basin is considered to be a big rainfall gage. It is possible to narrow the above scale gaps.

(2)The basin acts as a filter. Basin characteristics get rid of the high frequency components of rainfall input. It is possible to obtain average radar constants.

Fig. 2 - Map of the Central Radar

The authors used data obtained from the central radar operated by the Hokkaido Development Bureau to identify two radar constants. The radar site is located on the top of Mt.Pinneshiri in Hokkaido, Japan. It is possible to obtain quantitative information for the area within a radius of 120 km from the radar site at intervals of 5 minutes. The quantitative domain of this radar is divided into 128 sections along the circumference and 40 sections along the radial direction. The size of each section is about 2. The beam angle is 0.4 degrees.

Kanayama Dam, Katsurazawa Dam and Jouzankei Dam were chosen as the subject of this study. These dams are located within the quantitative domain shown in Figure 2. Table 1 shows the details of these dams. Hourly rainfall and discharge data are available at these dam basins.

Table 1. Details of dam basins

IDENTIFICATION PROCESS OF RADAR CONSTANTS

Authors adopt the well-known tank model to identify the radar constants because this runoff model can yield both surface and base runoff. Consequently, it is unnecessary to separate total precipitation into effective and lost one. Figure 3 illustrates a typical tank model widely used in Japan. This tank model is one of the concentrated parameter models and includes only one independent variable, time. On the other hand, radar reflectivity factor Z changes spatially and temporally. It is inevitable to use the average of Z over space. It is possible to use two kinds of method to average the radar rainfall intensity.

Averaging Method 1 :

Average the radar reflectivity factor of all meshes which cover a dam basin. The radar rainfall intensity is calculated from the averaged radar reflectivity factor.

where : Average radar reflectivity factor of the basin

Z(i,t) : Radar reflectivity factor of i-th radar mesh

n : Total number of radar meshes

4 : Average radar rainfall at the dam basin

Calculate the radar rainfall from the radar reflection factor for each radar mesh. The average radar rainfall is obtained by its mean.

(5)

(6)

where : Radar rainfall of i-th radar mesh

The authors group the flood data at each dam basin into identification and checking data. The identification process of the radar constants consists of the following three steps.

1) Assumption of the radar constants and calculation of the average radar rainfall intensity by Eq.(4) or Eq.(6).

2) Estimate of two radar constants and model parameters using identification data. The practical computation is carried out by Kalman filter theory.

3) Determination of the optimum radar constant using the checking data.

Table 2 and Table 3, show the identified radar constants. Eq(4) and Eq(6) yield almost the same radar constants at Jouzankei Dam Basin and Katsurasawa Dam Basin.

Figures 4, 5 and 6 indicate examples of comparison of observed discharge with an estimated one using radar rainfall input at each dam basin.

Figures 7, 8 and 9 show three kinds of hyetograph. The left hyetographs(Rg) are precipitation results obtained by observed ground precipitation. The middle ones(Rr) are results from the proposed method by using Eq.(4). The right ones(Ra) show hyetographs using radar constants authorized by the Hokkaido Development Bureau.

Figure 10. shows the hyetograph of radar rainfall using Eq.(6).

Table 2. Results of identification using Eq.(4)

Fig. 3. Tank Model

Fig. 4. Calculated discharge at Jouzankei Dam

Fig. 5. Calculated discharge at Katsurasawa Dam

Fig. 6. Calculated discharge at Kanayama Dam

Fig. 7. Hyetograph of Jouzankei Dam using Eq.(4)

Fig. 8. Hyetograph of Katsurasawa Dam using Eq.(4)

Fig. 9. Heyeotgraph of Kanayama Dam using Eq.(4)

Fig. 10. Hyetograph of Dam basins using Eq.(6)

CONCLUSIONS

Figures 7, 8, 9 and 10 show that the radar rainfall intensity obtained by this method corresponds very well to the observed rainfall. On the other hand, the authorized radar constants overestimate the radar rainfall. It is possible to estimate radar constants using runoff data. However, the authors think that the proposed method has room for improvement. The authors pointed out the scale gap between the radar mesh size and precipitation gage at the introduction of this paper, and considered the basin to be a kind of precipitation gage. The drainage area of the selected dam basins ranges from 100 km² to 500 km². Consequently, another scale gap may exist. The authors set up four experimental basins whose catchment areas range form 3 km² to 10 km² in the Jouzankei Dam basin, and these have been under observation.

REFERENCES

Hashimoto Norihide, Tetsuo Horita,Yasuharu Sato And Kiyoshi Hoshi,1994,In "Application Of Kriging Method To Calibration Of Radar Data",Journal Of Japan Society Of Hydrology And Water Resources Vol.7, pp411-419

Hirayama Daisuke, Mutsuhiro Fujita And Makoto Nakatsugawa,1994,In "The Identification Method Of Optimum B, 15 By Using Discharge Information In Jouzankei Dam Basin", Proceedings Of Hokkaido Branch Of Jsce, Vol.51, pp36-39

Hokkaido Development Beureau,1989, In "Operation Manual Of Central Radar"

Saga Hiroshi, Tetsuji Nishimura,Kyaku Sakamoto And Mutsuhiro Fujita,1992,In "Runoff Analysis By The Quasi Channel Network Model In Mountainous Basin", Proceedings Of Hokkaido Branch Of Jsce,Vol.49,pp511-514

Takasao Takuma, Kaoru Takara,Yujiro Mitani And Shunji Hukita,1988,In"Calibration Of The Radar Rainfall Using Kriging Method",Disaster Prevention Research Institute Annuals, Kyoto University Vol.31 B-2, pp241-254

Yoshino Fumio, Masamitsu Mizuno And Shouji Tamamoto,1988,In "Comparison Of The Radar Rainfall Using Kriging Method",Proceedings Of 1988 Annual Conference, Japan Society Of Hydrology And Water Resources, pp.194-197