101年度研究年報-all(中文版)

.187.

(2 )

圖 1 本研究渠首工程分佈位置一覽

A. 獨立構造 B. 堤防共構 C. 邊坡共構
圖 2 渠首工之型式

.188.

圖 3 渠首工程結構安全性分析流程
圖 4 HEC-RAS 河川切割子斷面之通水容量圖

Elevation (m) .189.
圖 5 HEC-RAS 模擬成果-大安溪水系

.190.

280 ( ) 240 -( )
270
260 230
250
240 220
230
220 210

0 200
50 100 150 200 250 300 350 0 100 200 300 400 500 600 700 800 900

240 - ( -30) ) 100 ()

230 95
220

90
210

200 100 200 300 400 500 600 700 85 0 150 300 450 600 750 900
0

70 ( ) 20 ()
150 300 450 600 750 900 1050
65 15

60 10

65 150 300 450 600 750 900 1050 1200 0

50
0

85 ( ) 20 ()
150 300 450 600 750 900 1050
80 15

75 10
70
5
65
0 150 300 450 600 750 0
900 1050 0

Station (m)

圖 6 HEC-RAS 模擬成果-大甲溪、烏溪水系

A. 大甲溪平日之流況 .191.
B. 大甲溪之高流量(610 暴雨事件)

C. 內埔圳新渠首工(平時取水) D. 內埔圳新渠首工(610 暴雨事件)

E. 內埔圳舊渠首工(平時取水) F. 內埔圳舊渠首工(610 暴雨事件)

圖 7 內埔圳流量模擬結果之驗證(610 豪大雨事件前後)

.192.

表 1 渠首工基本資料一覽

水系 站代碼 圳路 二度分帶(TM97) 導水路 退水路 結構型態
泰安站 代碼 XY 臨時 永久
M144 無 臨時 永久 獨立 邊坡 堤防

225709.79 2690816.44 ○ ○○

山腳站 M169 221161.39 2694915.66 ○ ○○

大 M174 218764.21 2695014.67 ○ ○ ○
安 日南站 M179 216223.09 2695697.62 ○ ○○
溪 L6-1 211721.74 2699018.34 ○ ○ ○
L6-2 210784.47 2699606.52 ○ ○ ○

M184 214298.07 2695561.06 ○ ○ ○ ○
大甲站 214592.48 2695432.62 ○ ○ ○

M184-1

豐原站 M249 224080.32 2685941.26 ○ ○ ○

屯子腳站 M254 223127.84 2686473.89 ○ ○ ○○
大 M264 213050.35 2689500.91 ○ ○ ○
甲 大安站 M269 210202.86 2690989.74
溪 M259 211874.84 2688976.35 ○ ○ ○
M274 211292.32 2689474.74 ○ ○ ○
清水站 ○ ○

烏溪 大肚站 M379 204305.26 2668368.14 ○ ○ ○

註：圳路代碼對應之圳路別分別為 M144(后里圳)、M169(苑裡圳)、M174(日南圳)、M179(九張犁圳)、L6(雙寮補給
水路，二處取水口)、M184(頂店圳)、M184-1(頂店圳第一取水口)、M249(葫蘆墩圳)、M254(內埔圳)、M264(虎
眼一圳)、M269(虎眼二圳)、M259(五福圳)、M274(高美圳)、M379(大肚圳)。

表 2 各渠首工可進行之分析項目一覽表

水系 站別 圳路名稱 構造名稱 分析項目

泰安站 后里圳 (M144) 排砂道、制水門 FSs、e、σ、FSo
FSs、e、σ、FSo
山腳站 苑裡圳 (M169) 排砂門 FSs、e、σ、FSo
FSs、e、σ、FSo
大 日南圳 (M174) 排砂門、堤防 FSs、e、σ
安 FSs、e、σ
溪 日南站 九張犁圳 (M179) 制水門* FSs、e、σ、FSo
FSs、e、σ、FSo
雙寮補給水路第一取水口 (L6-1) 堤防、制水門*
FSs、e、σ、FSo
雙寮補給水路第二取水口 (L6-2) 堤防、制水門* FSs、e、σ、FSo
FSs、e、σ
大甲站 頂店圳 (M184) 制水門* FSs、e、σ
頂店圳第一取水口 (M184-1) 制水門* FSs、e、σ、FSo
FSs、e、σ、FSo
豐原站 葫蘆墩圳 (M249) 排砂門 FSs、e、σ

大 屯子腳站 內埔圳 (M254) 渠首工
甲 堤防、制水門
溪 大安站 虎眼一圳 (M264) 堤防、制水門
虎眼二圳 (M269) 溢洪道、攔河堰、堤防、制水門
攔河堰、堤防、制水門*
清水站 五福圳 (M259)
高美圳 (M274)

烏溪 大肚站 大肚圳 (M379) 堤防、制水門*

註：FSs為抗滑動係數、e為偏心距、σ為基礎承載力、FSo為抗傾倒係數。

.193.

表 3 HEC-RAS 模擬基本參數一覽

水系別 平均坡度 河道曼寧 n 值 重現期距(T 年)之洪峰流量

QT=2 QT=5 QT=10 QT=20 QT=50 QT=100 QT=200
15,990
大安溪 0.0111 0.037 3,150 5,620 7,430 9,270 11,820 13,840 11,500
大甲溪 0.0060 26,000
烏溪 0.0007 0.040 2,600 4,500 5,900 7,300 8,900 10,300

0.037 3,800 7,000 9,400 12,000 17,000 21,000

表 4 臺中農田水利會各渠首工程之安全性分析結果一覽表

分析 檢核結果 相關規範係數

水系 站別 圳路名稱 構造物 傾倒 滑動 基底 傾倒係數 滑動係數 土壤

泰安站 M144 名稱 係數 係數 壓應力* FSo>1.5 FSs>1.3 承載力*
排砂道 2.00 23.58 7.47 符合 符合 符合
制水門 2.06 5.25 符合 符合 符合
13.07

山腳站 M169 排砂門 6.22 2.47 11.87 符合 符合 符合

大 M174 堤防 1.55 23.00 2.93 符合 符合 符合
M179 排砂門 3.68 3.80 1.28 符合 符合 符合
安 日南站 L6-1 制水門 2.34 3.61 35.72 符合 符合 符合
溪 3.07 24.21 8.90 符合 符合 符合
堤防 3.24 1.47 16.14 符合 符合 符合
制水門

堤防 3.23 23.07 11.57 符合 符合 符合
L6-2 制水門 1.70 3.94 5.00 符合 符合 符合

大甲站 M184 制水門 3.00 9.90 18.30 符合 符合 符合
M184-1 制水門 3.67 3.04 6.63 符合 符合 符合

豐原站 M249 排砂門 1.68 12.77 11.08 符合 符合 符合

屯子腳站 M254 渠首工 40.56 5.95 11.38 符合 符合 符合

大安站 M264 堤防 3.47 17.18 9.30 符合 符合 符合
大 M269 制水門 4.15 6.10 10.23 符合 符合 符合
3.55 22.17 符合 符合 符合
堤防 2.57 2.80 9.04 符合 符合 符合
制水門 12.68

甲 溢洪道 2.77 26.75 2.75 符合 符合 符合

溪 堤防 2.28 3.49 4.69 符合 符合 符合
M259 制水門 2.34
1.40 10.85 符合 符合 符合

清水站 攔河堰 1.83 8.28 5.62 符合 符合 符合

堤防 4.27 5.90 11.31 符合 符合 符合

M274 制水門 2.55 1.30 7.89 符合 符合 符合

攔河堰 1.86 4.61 5.51 符合 符合 符合

烏溪 大肚站 堤防 3.50 48.67 9.77 符合 符合 符合
M379 制水門 1.55 1.85 10.18 符合 符合 符合

註 1：土壤安全承載力均以礫石(50 ton/m2)計算，基底壓應力須小於土壤安全承載力。
註 2：土壤安全承載力與基底壓應力單位均為 ton/m2。

註 3：圳路代碼對應之圳路別分別為 M144(后里圳)、M169(苑裡圳)、M174(日南圳)、M179(九張犁圳)、L6(雙寮補給

水路，二處取水口)、M184(頂店圳)、M184-1(頂店圳第一取水口)、M249(葫蘆墩圳)、M254(內埔圳)、M264(虎

眼一圳)、M269(虎眼二圳)、M259(五福圳)、M274(高美圳)、M379(大肚圳)。

.194.

表 5 HAC-RAS 水理模擬使用斷面一覽

大安溪水系 大甲溪水系 烏溪水系

No. 樁號 樁距 No. 樁號 樁距 No. 樁號 樁距

1 安斷-00 0k+000 1 甲斷-03 0k+000 1 烏斷-15 0k+000

2 安斷-01 0k+479 2 甲斷-04 0k+646 2 烏斷-16 0k+517

3 安斷-01-1 0k+732 3 甲斷-05 1k+339 3 烏斷-17 1k+039

4 L6-1 0k+986 4 甲斷-06 2k+001 4 烏斷-18 1k+594

5 安斷-02 1k+204 5 甲斷-07 2k+575 5 烏斷-19 2k+110

6 安斷-03 1k+797 6 M269 2k+599 6 M379 2k+444
7 L6-2 2k+101 7 甲斷-08 2k+698 7 烏斷-20 2k+610

8 安斷-04 2k+415 8 甲斷-09 3k+264 8 烏斷-21 3k+194

9 安斷-05 2k+998 9 甲斷-10 3k+775 9 烏斷-22 3k+767

10 安斷-06 3k+683 10 M274 3k+885 10 烏斷-23 4k+396
11 安斷-07 4k+277 11 甲斷-11 4k+256 11 烏斷-24 5k+021

12 安斷-08 4k+874 12 M259 4k+713
13 安斷-09 5k+609 13 甲斷-12 4k+815

14 安斷-09-1 5k+910 14 M264 5k+412

15 M184 6k+228 15 甲斷-13 5k+609
16 安斷-10 6k+431 16 甲斷-14 6k+135

17 M184-1 6k+500 17 甲斷-15 6k+692

18 安斷-10-1 6k+782 18 甲斷-17 7k+777

19 安斷-11 7k+159 19 甲斷-18 8k+424

20 安斷-11-1 7k+579 20 甲斷-26 13k+843

21 M179 7k+868 21 甲斷-27 14k+386
22 安斷-12 7k+998 22 甲斷-28 14k+876

23 安斷-13 8k+576 23 甲斷-28-1D 15k+263

24 安斷-13-1 9k+031 24 甲斷-29 15k+539

25 安斷-14 9k+289 25 甲斷-30 16k+304

26 安斷-14-1 9k+782 26 M254 16k+672

27 安斷-15 10k+153 27 M249 17k+571
28 M174 10k+506 28 甲斷-33 17k+915

29 安斷-16 10k+847 29 甲斷-34 18k+560

30 安斷-17 11k+505 30 甲斷-35D 19k+223

31 安斷-18 11k+994 31 甲斷-35-1 19k+343

32 安斷-19 12k+532 32 甲斷-36D 20k+200

33 安斷-19-1 12k+912

34 M169 13k+035
35 安斷-20 13k+419

36 安斷-21 13k+904

37 安斷-21-1 14k+495

38 安斷-23 15k+092

39 安斷-24 15k+456

40 安斷-26 16k+635

41 安斷-27 17k+203

42 安斷-28 17k+922

43 安斷-29 18k+330 註1：安斷-00為河口；甲斷-03距河口約2.3 km，甲斷-36D

.195.

44 安斷-30 18k+929
19k+060
45 M144 19k+606
46 安斷-31 20k+351
47 安斷-32 21k+049
48 安斷-33 21k+467
49 安斷-34 22k+107
50 安斷-35

表 6 大安溪渠首工程耐淹程度水理模擬結果

水 渠首工 分析對象 高程 HEC-RAS 重現期距(T，年)之洪峰流量
系 代碼 (m) 模擬結果
QT = 2 QT = 5 QT = 10 QT = 20 QT = 50 QT = 100 QT = 200
L6-2 河川渠底 11.00 水面高程 14.84 15.63 16.08 16.49 16.99 17.34 17.69
吊門機座 15.80 淹沒深度 -0.96
21.28 -0.17 0.28 0.69 1.19 1.54 1.89
-2.04
L6-1 河川渠底 17.00 水面高程 65.14 22.25 22.79 23.45 24 24.4 24.82
吊門機座 23.32 淹沒深度 -4.07
-1.56 -1.07 -0.53 0.13 0.68 1.08 1.50
-3.56
河川渠底 62.00 水面高程 65.69 66.15 66.49 66.95 67.32 67.64
1.14
吊門機座 69.21 69.43 -3.52 -3.06 -2.72 -2.26 -1.89 -1.57
-4.70
M184 清污平台 66.70 淹沒深度 84.56 -1.01 -0.55 -0.21 0.25 0.62 0.94
攔汙閘門機座 68.70 -7.33
-5.63 -3.01 -2.55 -2.21 -1.75 -1.38 -1.06
120.09
作業橋 64.00 -7.07 1.69 2.15 2.49 2.95 3.32 3.64
-2.84
M184-1 河川渠底 66.00 水面高程 148.09 70.13 70.54 70.93 71.44 71.80 72.17
大 吊門機座 74.13 淹沒深度 -13.91
河川渠底 82.00 水面高程 -4.00 -3.59 -3.20 -2.69 -2.33 -1.96
安 吊門機座 91.89 -9.71
溪 M179 90.19 淹沒深度 85.43 85.68 85.91 86.29 86.55 86.90
地表
-6.46 -6.21 -5.98 -5.60 -5.34 -4.99

-4.76 -4.51 -4.28 -3.90 -3.64 -3.29

河川渠底 117.00 水面高程 120.23 120.65 121.14 121.56 121.89 122.26

M174 吊門機座 127.16 淹沒深度 -6.93 -6.51 -6.02 -5.60 -5.27 -4.90
作業橋 122.93
-2.70 -2.28 -1.79 -1.37 -1.04 -0.67

河川渠底 142.79 水面高程 150.32 151.62 152.8 154.24 155.29 156.30

M169 吊門機座 162.00 -11.68 -10.38 -9.19 -7.76 -6.71 -5.69
取水門 淹沒深度
作業橋 -7.48 -6.18 -5.00 -3.56 -2.51 -1.50
157.80

M144 河川渠底 230.05 水面高程 231.87 232.64 233.11 233.57 234.14 234.6 235.02
大 吊門機座 240.00 淹沒深度 -8.13 -7.36 -6.89 -6.43 -5.86 -5.40 -4.98
甲 M269 排砂道 2 232.00 水面高程 -0.13 0.64 1.11 1.57 2.14 2.60 3.02
溪 河川渠底 52.00 淹沒深度 53.89 54.26 54.44 54.6 54.86 55.06 55.21
吊門機座 63.17 水面高程 -9.28 -8.91 -8.73 -8.57 -8.31 -8.11 -7.96
M274 59.12 淹沒深度 -5.23 -4.86 -4.68 -4.52 -4.26 -4.06 -3.91
作業橋 70.00 水面高程 72.78 73.31 73.69 73.91 74.16 74.34 74.49
M259 河川渠底 80.10 淹沒深度 -7.32 -6.79 -6.41 -6.19 -5.94 -5.76 -5.61
吊門機座 75.70 水面高程 -2.92 -2.39 -2.01 -1.79 -1.54 -1.36 -1.21
M264 攔河堰頂 74.00 淹沒深度 78.65 79.5 79.97 80.42 80.80 81.15 81.39
河川渠底 87.95 -9.30 -8.45 -7.98 -7.53 -7.15 -6.80 -6.56
吊門機座 82.90 -4.25 -3.40 -2.93 -2.48 -2.10 -1.75 -1.51
攔河堰頂 89.00 91.08 91.48 91.72 91.94 92.26 92.44 92.59
河川渠底 96.24 -5.16 -4.76 -4.52 -4.30 -3.98 -3.80 -3.65
吊門機座 93.69 -2.61 -2.21 -1.97 -1.75 -1.43 -1.25 -1.10

作業橋

.196.

甲斷 河川渠底 208.34 水面高程 214.98 215.84 216.29 217.09 217.61 217.83 218.02
-303 吊門機座 227.13 淹沒深度 -12.15 -11.29 -10.84 -10.04 -9.52 -9.30 -9.11
216.93 0.68 0.90 1.09
作業橋 -1.95 -1.09 -0.64 0.16

河川渠底 209.62 水面高程 215.61 216.71 217.34 218.16 218.72 219.03 219.28

M254 吊門機座 217.90 淹沒深度 -2.29 -1.19 -0.56 0.26 0.82 1.13 1.38
地表 216.90 -1.29 -0.19 0.44 1.26 1.82 2.13 2.38

河川渠底 229.00 水面高程 231.78 232.88 233.46 234.06 234.66 235.27 235.56

M249 吊門機座 236.58 淹沒深度 -4.80 -3.70 -3.12 -2.52 -1.92 -1.31 -1.02
地表(工作橋) 232.68 -0.90 0.20 0.78 1.38 1.98 2.59 2.88

河川渠底 0.04 水面高程 7.12 8.87 9.88 10.85 12.15 12.96 13.86

烏 吊門機座 16.33 -9.21 -7.46 -6.45 -5.48 -4.18 -3.37 -2.47
溪 M379 堤頂高程 16.32 淹沒深度 -9.20 -7.45 -6.44 -5.47 -4.17 -3.36 -2.46

清污平台 12.19 -5.07 -3.32 -2.31 -1.34 -0.04 0.77 1.67

註 1：淹沒深度為水面高程減分析目標高程之差值，灰底粗體表被水淹沒之深度。

註 2：后里圳之排砂道無機械設備，且構造物均位於地表下方，不受洪水淹沒影響。

註 3：大甲溪斷面編號「甲斷-30」處為內埔圳(M254)渠首工舊址；該處僅存輸水功能但位處洪泛區內，故列入耐淹評估中。

註 4：圳路代碼對應之圳路別分別為 M144(后里圳)、M169(苑裡圳)、M174(日南圳)、M179(九張犁圳)、L6(雙寮補給水路，

二處取水口)、M184(頂店圳)、M184-1(頂店圳第一取水口)、M249(葫蘆墩圳)、M254(內埔圳)、M264(虎眼一圳)、M269(虎

眼二圳)、M259(五福圳)、M274(高美圳)、M379(大肚圳)。

Estimation of the spatial rainfall distribution using inverse distance weighting (IDW)…. .197.

Estimation of the spatial rainfall distribution using
inverse distance weighting (IDW) in the middle of

Taiwan

Agricultural Engineering Research Center Department of Bioenvironmemt System
Feng-Wen Chen Engineering, National Taiwan University

Chen-Wuing Liu

ABSTRACT

In this article, we used the inverse distance weighting (IDW) method to estimate the rainfall
distribution in the middle of Taiwan. We evaluated the relationship between interpolation accuracy and
two critical parameters of IDW: power (a value), and a radius of influence (search radius). A total of
46 rainfall stations and rainfall data between 1981 and 2010 were used in this study, of which the 12
rainfall stations belonging to the Taichung Irrigation Association (TIA) were used for cross-validation.
To obtain optimal interpolation data of rainfall, the value of the radius of influence, and the control
parameter-a were determined by root mean squared error. The results show that the optimal parameters
for IDW in interpolating rainfall data have a radius of influence up to 10¡V30 km in most cases.
However, the optimal a values varied between zero and five. Rainfall data of interpolation using IDW
can obtain more accurate results during the dry season than in the flood season. High correlation
coefficient values of over 0.95 confirmed IDW as a suitable method of spatial interpolation to predict
the probable rainfall data in the middle of Taiwan.

Keywords Inverse distance weighting (IDW)、 Spatial interpolation Rainfall data 、 Omission

INTRODUCTION

Rainfall is a highly significant piece of hydrologic data. Such data are recorded as observational
data through comprehensively designed rainfall station networks. However, rainfall records are often
incomplete because of missing rainfall data in the measured period, or insufficient rainfall stations in
the study region. To resolve the problems of such partial rainfall data, probable rainfall data can be
estimated through spatial interpolation techniques.

Various spatial interpolation techniques have already been employed in related fields. Such

本篇論文原刊載於「Paddy and Water Environment，Vol. 10(3), P.209-222」，2012，9 月。

.198. 一○一年度研究年報

techniques can be divided into geographical statistics and non-geographical statistics. Examples
include nearest neighbor (NN), Thiessen polygons, splines and local trend surfaces, global polynomial
(GP), local polynomial (LP), trend surface analysis (TSA), radial basic function (RBF), inverse
distance weighting (IDW), and geographically weighted

ARTICL E Estimation of the spatial rainfall distribution using inverse distance weighting (IDW)
and geographically weighted regression proposed by Fotheringham et al. (2002), which are all
classified as non-geographical statistics. On the other hand, various forms of Kriging method are
classified as geographical statistics (Lam 1983; Jeffrey et al. 2001; Price et al. 2000; Li and Heap 2008;
Yeh et al. 2011).

As this article aims to discuss the spatial interpolation of rainfall, the research literature carried
out by Naoum and Tsanis (2004) on the interpolation of rainfall in the island of Crete, Greece was
reviewed. The research had developed a new Geographical Information System (GIS)-based spatial
interpolation module that adopts a multiple linear regression (MLR) technique. This technique can be
compared with other methods, such as splin_regularized, spline_tension, IDW, kriging, and
second-order polynomial. When estimating precipitation at ungauged locations, the MLR models
provided better estimations than the other spatial interpolation techniques. Li et al. (2006) used the
annual precipitation over a span of 30 years between 1961 and 1990 from 2114 meteorological stations
in China. The data were compared with its respective nearby regions and analyzed through spline,
ordinary kriging (OK), and IDW. The result in cross-validation tests shows that the precision of
interpolated results are very high. The relative mean errors of three methods were 8.31, 8.76 and
8.76%, respectively ranking as OK > IDW = spline. Similar results of OK > Spline > IDW (the mean
absolute error, MAE are 42.94, 44.79, and 49.86) The study carried out by Chu et al. (2008) reported a
similar trend.

Segond et al. (2007) indicated that high spatial and temporal rainfall resolutions are required for
urban drain-age and urban flood modeling applications. Through IDW, the spatial rainfall field can be
obtained when data over a whole catchment are interpolated. When using such method, the results
were proven satisfactory as the stimu-lated data at individual sites preserved properties which
mimicked the observed statistics at an acceptable level for practical purposes. Garcia et al. (2008)
reported that Mul-tiquadric¡Vbiharmonic (MQB) methods surpass IDW methods in terms of
interpolation accuracy for both con-vective and mixed/stratiform events in the study regarding the
North American monsoon season over a dense gauge network in the southwestern United States.
However, it is found that the order in the IDW method is more important as under certain conditions,
results obtained are just as accurate as the MQB method. Dong et al. (2009) used OK, co-kriging (CK),
and IDW to interpolate daily precipitation in Qingjiang river basin of China. Daily precipitation data
from 36 rainfall stations in June 2006 were analyzed, and the result demonstrated that CK was

Estimation of the spatial rainfall distribution using inverse distance weighting (IDW)…. .199.

superior to OK and IDW. The author explained that IDW was unable to take the spatial dependencies
of adjacent rain gauges in the basin into account. A similar conclusion was also reached in another
case study in Xinjiang, China. The study sug-gested that the CK method is the most superior compared
with RBF, IDW, Kriging methods based on the results of annual precipitation in 75 weather stations
from 1995 to 2008 (Zhong 2010). A model composed of OK and entropy with probability distribution
function is proposed to relo-cate the rainfall network and to obtain the optimal design with the
minimum number of rain gauges by Yeh et al. (2011).

Nevertheless, several researchers have contrasting views in this area of study. Dirks et al. (1998)
compared four spatial interpolation methods using rainfall data from a network of 13 rain gauges on
Norfolk Island. The more computationally demanding method of Kriging provided no significant
advantage over any of the much simpler IDW, Thiessen, or areal-mean methods. This further indicates
that in order to assimilate some characteristics of spatially varying rainfall, the inverse distance
method is the most advantageous for interpolations using spatially dense networks.

In another case study, the daily precipitation data from 72 meteorological stations between 1961
and 2000 in Northeast China were analyzed using OK and IDW methods with the weighting of
longitude and latitude, and gradient of height plus IDW (GIDW). For daily precipita-tion, the results
showed that the precision of the evaluated value with IDW is greater than OK and GIDW (Zhuang and
Wang 2003). Hsieh et al. (2006) used daily summer rainfall records from 20 rain gauges stations
between 1990 and 2000 to predict the spatial rainfall distribution in the Shih-Men Watershed in
Taiwan using two schemes as OK and IDW. The results indicated that IDW (mean error = 0.04)
produced more accurate representations of spatial distribution of rainfall than OK (mean error = 0.54).
Kurtzman et al. (2009) aimed at improving the spatial interpolation of daily precipitation for
hydrologic models. Different parameterizations of IDW and a local weighted regression (LWR)
method were tested in a mountainous terrain in the eastern Mediterranean using 16 years of daily data.
The LWR took into account of the weighting factors of elevation which are the explanatory variable
and distance, elevation factors, and aspect difference. The IDW interpolation was preferred over the
LWR scheme in 27 out of 31 validation gauges. Wu et al. (2010) analyzed and compared five typical
interpolation models: IDW, OK, GP, LP, and RBF. The results show that OK and IDW are suitable
methods for maximum and minimum precipita-tions respectively; the results were consistent with the
30 years worth of data in 599 climate stations situated in Texas, US as analyzed by Kong and Tong
(2008). A sim-ilar research was carried out by Li et al. (2010) utilizing the mean yearly precipitation of
72 meteorological stations from 1971 to 2008 in Zhejiang, China. Different interpo-lation methods
such as the combining stepwise regression and IDW, kriging, spline, and trend were tested. The result
demonstrated that the combination of stepwise regression and IDW showed the highest accuracy in

.200. 一○一年度研究年報

prediction, and was better than other methods.
From the above review and comparison of the related researches on spatial interpolation

techniques of rainfall, a conclusion can be drawn. According to the comparisons, each method has its
advantages and disadvantages based on its objectives, and hence the optimal interpolation method to
be adopted varies for different proposals. In general, OK is only suitable for normal distributions; the
advantage the IDW method is its usefulness when the distribution of the estimated parameters is not a
normal distribution.

In this article, the IDW method is used to interpolate the spatial rainfall distribution in the middle
of Taiwan. The choice of the IDW exponent was found to be more signif-icant than the choice of
whether or not to use elevation as explanatory data (Kurtzman et al. 2009). In most cases, the critical
influence parameter of IDW is the distance. For this reason, elevation of rainfall stations is not
considered in this study. The study aims at improving interpolation accuracy of rainfall using IDW,
which is concerned with parameters adjustment including the power (a value) and search radius.

MATERIALS AND METHODS

Study area and data

In this study, the region of the middle of Taiwan was chosen as the main research area. There are
46 rainfall stations distributed in this region. Figure 1 shows the schematic diagram of the rainfall
stations spatial distribu-tion in the middle of Taiwan. The rainfall stations are managed by two
organizations. The 33 rainfall stations, which are shown as blue points in Fig. 1, are managed by Water
Resources Agency (WRA), Ministry of Economic Affairs, while the remaining 13 rainfall stations,
which are shown as red points in Fig. 1, are managed by TIA.

For the purpose of using IDW to interpolate spatial rainfall, long-term observed rainfall data were
necessary for analysis in the process. Therefore, the daily rainfall data of 30 years from 1981 to 2010
were adopted in this study.
IDW

IDW is based on the concept of Tobler¡¦s first law (the first law of geography) from 1970. It was
defined as everything is related to everything else, but near things are more related than distant things.
The IDW was developed by the U.S. National Weather Service in 1972 and is classified as a
deterministic method. This is due to the lack of requirement in the calculation to meet specific
statistical assumptions, thus IDW is different from stochastic meth-ods (e.g., Kriging and TRA).

The IDW method is also for multivariate interpolation. Its general idea is based on the

Estimation of the spatial rainfall distribution using inverse distance weighting (IDW)…. .201.

assumption that the attribute value of an unsampled point is the weighted average of known values
within the neighborhood (Lu and Wong 2008). This involves the process of assigning values to
unknown points by using values from a scattered set of known points. The value at the unknown point
is a weighted sum of the values of N known points. In this study, the IDW method is used to
interpolate spatial data,

Fig. 1 Location of 46 rainfall stations in the middle of Taiwan. Blue and red dots denote the rainfall
stations managed by the WRA and Taichung Irrigation Association, respectively. (Color figure
online)

which is based on a concept of distance weighting. It can be used to estimate the unknown spatial
rainfall data from the known data of sites that are adjacent to the unknown site (Bedient and Huber
1992; Burrough and McDonnell 1998; Goovaerts 2000; Li and Heap 2008). The IDW for-mulas are
given as Eqs. 1 and 2.

(1)

.202. 一○一年度研究年報

(2)

where means the unknown rainfall data (mm); Ri means the rainfall data of known rainfall stations
(mm); Nmeans the amount of rainfall stations;wi means the weighting of each rainfall stations; di
means the distance from each rainfall stations to the unknown site; a means the power, and is also a
control parameter, generally assumed as two as used by Zhu and Jia (2004) and Lin and Yu (2008), or
as six as set by Gemmer et al. (2004). Several researches (e.g., Simanton and Osborn 1980;Tung 1983)
have experimented with variations in a power, examining its effects on the spatial distribution of
information from precipitation observations. For this reason, a value is conducted in the range of zero
to five with an incremental interval value of 0.1 in this article.
Cross-validation

As IDW is the chosen method to interpolate spatial rainfall data for this article, cross-validation is
essential to validate critical parameters that could affect the interpolation accuracy of rainfall data. In
this case, a value and search radius were evaluated for optimal parameters. This insures the overall
utility of the IDW models and enables optimal data prediction that is comparable to the observed data.

Cross-validation, also called rotation estimation, is a technique for assessing how generalized the
results of a statistical analysis are with respect to an independent dataset. Common types of
cross-validation methods include k-fold cross-validation, twofold cross-validation, repeated random
sub-sampling validation, leave-one-out cross-validation (LOOCV), etc. It is mainly used in settings
where the objective is to gain a prediction, and estimating how accurately a predictive model will
perform in practice (Devijver and Kittler 1982; Seaman 1983; Geisser 1993; Kohavi 1995).
Cross-validation has been widely applied in studying the accuracy of prediction methods in
precipita-tion fields. Related research studies include Gyalistras (2003), Feng et al. (2004), Lloyd
(2005), Li et al. (2006), Hsieh et al. (2006), Chu et al. (2008), Wang et al. (2008), and Kong and Tong
(2008).

Cross-validation can be defined as a method for esti-mating the accuracy of an inducer by
dividing the data into k mutually exclusive subsets (the “folds”) of approximately equal size. The
inducer is trained and tested ktimes. Each time it is trained on the data-set minus a fold and tested on
that fold. The accuracy estimate is the average accuracy for the kfolds (Cressie 1993; Kohavi and
Provost

1998). In general, LOOCV involves using a single observation from the original sample as the
validation data, and the remaining observations as the training data. This is repeated such that each

Estimation of the spatial rainfall distribution using inverse distance weighting (IDW)…. .203.

observation in the sample is used once as the validation data. This is the same as a K-fold
cross-validation with K being equal to the number of observations in the original sample. Because of
considering tenfold cross-validation is commonly used (McLachlan et al. 2004). Thus, for the
cross-validation purpose of this study, from the total of 46 rainfall stations, the 12 rainfall stations that
belonged to the Taichung Irrigation Association (TIA), within Taichung irrigation area (Fig. 2) were
adopted for this study.
Performance assessment

In this study, the root mean squared error (RMSE) was adopted to assess the IDW models
performances. The RMSE is also called root-mean-square deviation (RMSD), a measure frequently
used on the differences between values predicted by a model or an estimator and the values actually
observed from the thing being modeled or estimated. RMSE is a robust measure of accuracy. These
individual differences are also called residuals, and the RMSE is served to aggregate them into a single
measure of predictive power. The RMSE is applied widely in various fields as follows: in
hydrogeology, RMSE is used to evaluate the calibration of a groundwater model; in meteorology, to
see how effectively a mathematical model predicts the behavior of the atmosphere; in GIS, the RMSE
is one of the measures used to assess the accuracy of spatial analysis and remote sensing. In this study,
the RMSE was used to evaluate the optimal model of IDW. At the same time, coefficient of correlation
(r) was also used for evaluate whether the estimated data fits observed data. The formulas of RMSE
and r are considered by Phogat et al. (2010) and Traore et al. (2010) and given as Eqs. 3-4:

(3)

(4)

where: means spatial rainfall values interpolated using IDW in the unknown rainfall station (i);

means observed rainfall data in the unknown rainfall station (i); n means numbers of year (t)

adopted, n was equal to 30 in this study.

.204. 一○一年度研究年報

Fig 2 Distribution of 12 rainfall stations for cross vaildation
Analysis procedure

There are 46 rainfall stations used for interpolate rainfall data by IDW models, adopting
cross-validation as an appropriate method to assess the accuracy of spatial interpolated rainfall data.
25% of the 46 rainfall stations were selected for a cross-validation process. The selection of rainfall
stations was based on the conditions of isotropic and maximum search radius to increase the evaluated
groups in a cross-validation process. For this reason, the 12 rainfall stations that are managed by the
TIA were selected to conduct the model testing of validity using cross-vali-dation. These 12 rainfall
stations were selected in following of Taichung, Zhunlan, Taian, Yuemei, Ciyao, Yuanli, Rinan, Dajia,
Danan, Dongshi, Fengyuan and Dadu. Rainfall data required were continuous daily data in the period
of 1981-V2010 (30 years). Table 1 shows the dis-tance between respective rainfall stations, and is used
to calculate the weighting of individual rainfall station to the objective rainfall station. To determine

Estimation of the spatial rainfall distribution using inverse distance weighting (IDW)…. .205.

the optimal search radii (O.S.R.) of IDW of the 12 rainfall stations, 11 search radii (10-V110 km) were
executed (Table 2). The italicized numbers in Table 2 represent the optimal number of rain-fall stations
nearby the objective that were selected for daily rainfall interpolation. Figure 3 shows the schematic
Table 1 Distance (km) between 46 rainfall stations to the 12 objective rainfall stations for calculation

of the individual weighting

.206. 一○一年度研究年報

diagram of different groups in Taichung rainfall station as an example. It illustrates that different
rainfall stations within different selected search radii can used for inter-polate rainfall data. For
example, 19 and 45 rainfall stations falls within the selected search radius of 30 and 70 km for rainfall
data interpolation. We compared and analyzed the data with seven groups, assessing the relationship
between prediction accuracy with search radius (the number of selected rainfall stations). This was
used for further cal-culations in cross validation. Finally, RMSE was used for determining optimal
parameters: a value and search radius of IDW. This is done through data verification testing which
must be conducted subsequent to all procedures of cross-validation. The data verification testing then
com-pared the data interpolated with observed data. To express the applicability of IDW models, the
results of rainfall data interpolation using IDW were all determined by r.
Results and discussions

To interpolate the unknown rainfall data, 12 rainfall stations (Table 2) were assumed as unknowns
and rainfall data estimated using IDW in a common parameter of a = 0-V5.0. As the adopted data
expressed as daily rainfall, all interpolated data results were also expressed as daily rainfall data.
Every different group of each rainfall station was estimated individually using only the observed data
respective to individual rainfall station¡¦s search radius. After interpolation of daily rainfall levels, data
were then compiled accordingly to create data expressed as ten-day rainfall, monthly rainfall and
annual rainfall.

Table 2 Optimal numbers of rainfall stations evaluated by different search radii (10-V110 km) of 12
objective rainfall stations Group search radius Rainfall stations

Estimation of the spatial rainfall distribution using inverse distance weighting (IDW)…. .207.

Fig.3 Schematic diagram of rainfall station groups of different search radius – use Taichung rainfall
station for example

To identify the optimal parameters of IDW, a value and research radius, and the minimum RMSE
were calculated. Table 3 shows the minimum RMSE in the forms of both monthly rainfall and
annually rainfall. At the same time, the O.S.R. and a value were recorded in the condition of the
minimum RMSE. Comparing the annual O.S.R. and monthly a values, the results showed two
phenomena. Firstly, in a viewpoint of annual O.S.R., 75% O.S.R. were within 10¡V20 km, there was
only one anomaly (80 km) which occurred in Fengyuan rainfall station; it deemed the use of numerous
rainfall stations unnecessary for data interpolation under most conditions. Nevertheless, the greater
result accuracy occurred when only four to five rainfall stations were considered such as Zhunlan,
Ciyao, Rinan, and Dongshi rainfall stations as opposed to incorporating data from all 45 rainfall
stations. A similar trend also occurred with monthly rainfall levels. The results revealed that the
interpolation accuracy of rainfall was greater with increasing rainfall stations and to an optimal
up-limit. However, the interpolation accuracy can become inferior when the number of rainfall stations
considered exceeds the optimal value. In all cases of this article, when considering all 45 stations, less
than 20 stations, and less than 10 stations, the optimal number of rainfall stations 8, 83 and 58%,
respectively. Excessive number of rainfall stations considered for interpolate rainfall could cause the
data to become meaningless. Such results are similar to previous researches such as those conducted
by Li et al. (2006), Lin and Yu (2008), and Chu et al. (2008) which the optimal number of rainfall

.208. 一○一年度研究年報
stations were 10, 13 and 15 respectively.

Table 3 Optimal parameters of IDW for interpolation of spatial rainfall data

The second phenomenon was that the optimal a value varied greatly from zero to five. There was
only a 1.92% probability met and that the optimal a was equal to 2.0. It revealed that the prediction
accuracy of rainfall could not the optimal when using a value at 2.0. Even at a 2.0 a value, it is only a
general consent but cannot be considered scientific. The result in this article have identical views with
several researches including one by Chu et al. (2008) reported the optimal a value was equal to 3.31
when 15 rainfall stations were considered to measure a case of Gansu, China. Wang et al. (2008) also

Estimation of the spatial rainfall distribution using inverse distance weighting (IDW)…. .209.
reported a case in China where the prediction accuracy of annual rainfall had the highest significance
when the a value was considered in the range of three to five. However, Dirks et al. (1998)

Fig. 4 RMSE variation of different search radii (10-V110 km) and a value (0-V5) of 12 rainfall
stations

.210. 一○一年度研究年報

showed that the exact choice of the numerical value of the power has minimal effect on the resulting
errors providing data using the a values within the range of 1.5-V4. It was an inconsistent argument
with this article, because several optimal a values of this article occurred in the range 0-V1.5 and even
at 4-V5. Table 2 also showed that the annual RMSE existed in the range of 29.5-V44.9. Figure 4
displays a series of 12 sub-diagrams on the RMSE variation at different search radii (10¡V110 km) and
a value (from zero to five with an increment interval of 0.1). The finding was a large RMSE variation
of different groups (search radius) occurred when a approach zero, the RMSE variation also reduced
with the increase in a. This showed that the minimum variation occurred at the largest a value,
regardless of the number of rainfall stations used for interpolation. However, the minimum variation of
RMSE remains uncertain on based of the optimal a and search radius. Therefore the optimal a and
search radius must be further measured.

Figure 5 diagrams the RMSE variation of different groups using annual optimal a value in each
month. These results show that all 12 rainfall stations follows the same trend: the RMSE value was
relatively lower in dry seasons (from October to April) than in flood seasons (from May to September),
it denoted that the data obtained during dry seasons are more accurate than in flood seasons. This point
of view in this study is consistent with the study done by Kong and Tong (2008). It would therefore
consider that spatial rainfall interpolated in flood season is inferior to the data interpolated during dry
seasons due to extreme rainfall events. However, another research had indicated that IDW was better
than kriging and suggested for spatial rainfall prediction in summer (Hsieh et al. 2006). The
relationship between the interpolated rainfall values and the true observed data was also evaluated.
Figure 6 showed a significant accuracy of the predicted data during low rainfall value, and the
deviation increased gradually with increased rainfall. The trend could explain the cause of high RMSE
values occurring during flood seasons (Fig. 5). The phenomenon implied large deviations were caused
from extreme rainfall events in the flood season.

Estimation of the spatial rainfall distribution using inverse distance weighting (IDW)…. .211.

Fig. 5 RMSE variation of different search radii (10-V110 km) using annual optimal a value in each
month of 12 rainfall stations

.212. 一○一年度研究年報

Fig. 6 Scatter plots of monthly interpolation of spatial rainfall data
Finally, for the purpose of evaluating the suitability of using IDW for interpolated data, daily
rainfall data interpolated were accumulated into 36 ten-day rainfall values from 1 year, and was
compared with the observed data.
The coefficient of correlation (r) was utilized as an indicator to evaluate the fittingness of IDW.
Cross-validation methods were applied to 12 optimal monthly a values and a single annual one on an
individual basis. The r can be expressed as rm and ra. 30-years worth of average data (1981-V2010)
presented in the form of 10-day interpolated rainfall were compared with observed data in Fig. 7. The
result showed that rm and ra were all higher than 0.95 in 12 rainfall stations. It was evident that,

Estimation of the spatial rainfall distribution using inverse distance weighting (IDW)…. .213.
rainfall interpolations using IDW showed significant similarities with the observed data, either using
optimal monthly a values or as independent annual values. Therefore an argument can be drawn from
this study: that IDW is a suitable method for rainfall interpolation under the conditions that optimal α
and search radius must be measured.

Fig. 7 Comparison of observation and interpolation of spatial rainfall data using optimal monthly and
annual a values

.214. 一○一年度研究年報

CONCLUSION

In this article, the authors have three findings about using IDW for interpolate spatial rainfall: (i)
The predicted accuracy of rainfall interpolated can be improved through the a value adjustment, and
that the a value usually is not equivalent to two. Therefore, for the purpose of increasing prediction
accuracy, searching an optimal a value as a preparation step is necessary. (ii) The number of known
rainfall station is also another influential parameter; most cases show that the prediction accuracy
increases with the increasing numbers of known rainfall station. However, the accuracy of rainfall data
interpolation could be reduced by the interference from the use of excessive rainfall stations.
Nevertheless, radius of influence is important to effective interpolation of rainfall data. The optimal
result is based on only using rainfall stations within the radius of influence. (iii) Application of IDW
for spatial rainfall data interpolation, results show the prediction accuracy are better during dry
seasons (October to April) than in flood seasons (May-VSeptember). It reveals that IDW has
significant prediction ability in small rainfall events than in extreme rainfall events. In summary,
through analyzing the optimization steps of a value and radius of influence, IDW is deemed as a
suitable spatial interpolation method of rainfall.

REFERENCES

1. Bedient PB, Huber WC (1992) Hydrology and floodplain analysis, 2nd edn. Addison-Wesley,
Reading

2. Burrough PA, McDonnell RA (1998) Principles of geographical information systems. Oxford
University Press, Oxford

3. Chu SL, Zhou ZY, Yuan L, Chen QG (2008) Study on spatial precipitation interpolation methods.
Pratacult Sci 25(6):19-V23

4. Cressie N (1993) Statics for spatial data (revised edition). Wiley, New York
5. Devijver PA, Kittler J (1982) Pattern recognition: a statistical approach. Prentice-hall, London
6. Dirks KN, Hay JE, Stow CD (1998) High resolution studies of rainfall on Norfolk Island Part II:

interpolation of rainfall data. J Hydrol 208:187-V193
7. Dong XH, Bo HJ, Deng X, Su J, Wang X (2009) Rainfall spatial interpolation methods and their

applications to Qingjiang river basin. J China Three Gorges Univ (Nat Sci) 31(6):6-V10
8. Feng ZM, Yang YZ, Ding XQ, Lin ZH (2004) Optimization of the spatial interpolation methods

Estimation of the spatial rainfall distribution using inverse distance weighting (IDW)…. .215.

for climate resources. Geograph Res 23(5):357-V364
9. Fotheringham AS, Brunsdon C, Charlton M (2002) Geographically weighted regression: the

analysis of spatially varying relationship. Wiley, New York
10. Garcia M, Peters-Lidard CD, Goodrich DC (2008) Spatial nterpolation
11. of precipitation in a dense gauge network for monsoon storm events in the southwestern United

States. Water Resour Res 44:W05S13(1-V14)
12. Geisser S (1993) Predictive inference. Chapman and Hall, New York Gemmer M, Becker S,

Jiang T (2004) Observed monthly precipitation trends in China 1951¡V2002. Theor Appl
Climatol 77:39-V45
13. Goovaerts P (2000) Geostatistical approaches for incorporating elevation into the spatial
interpolation of rainfall. J Hydrol 228:113-V129
14. Gyalistras D (2003) Development and validation of a high-resolution monthly gridded
temperature and precipitation data set for Switzerland (1951¡V2000). Clim Res 25(1):55-V83
15. Hsieh HH, Cheng SJ, Liou JY, Chou SC, Siao BR (2006) Characterization of spatially distributed
summer daily rainfall. J Chin Agric Eng 52(1):47-V55
16. Jeffrey SJ, Carter JO, Moodie KB, Beswick AR (2001) Using spatial interpolation to construct a
comprehensive archive of Australian climate data. Environ Model Softw 16(4):309-V330
17. Kohavi R (1995) A study of cross-validation and bootstrap for accuracy estimation and model
selection. In: Proceedings of the fourteenth international joint conference on artificial intelligence,
vol 2, no 12. Morgan Kaufmann, San Mateo, pp 1137-V1143
18. Kohavi R, Provost F (1998) Special issue on applications of machine learning and the knowledge
discovery process. Mach Learn 30(2-V3):271-V274
19. Kong YF, Tong WW (2008) Spatial exploration and interpolation of the surface precipitation data.
Geograph Res 27(5):1097-V1108
20. Kurtzman D, Navon S, Morin E (2009) Improving interpolation of daily precipitation for
hydrologic modeling: spatial patterns of preferred interpolators. Hydrol Process 23:3281-V3291
21. Lam NS-N (1983) Spatial interpolation methods: a review. Am Cartogr 10:129-V140
22. Li J, Heap AD (2008) Spatial interpolation methods: a review for environmental scientists.
Geoscience Australia, Record. Geoscience Australia, Canberra
23. Li JL, Zhang J, Zhang C, Chen QG (2006) Analyze and compare the spatial interpolation
methods for climate factor. Pratacult Sci 23(8):6-V11

.216. 一○一年度研究年報

24. Li B, Huang JF, Jin ZF, Liu ZY (2010) Methods for calculation precipitation spatial distribution
of Zhejiang Province based on GIS. J Zhejiang Univ (Sci Ed) 27(2):239-V244

25. Lin XS, Yu Q (2008) Study on the spatial interpolation of agroclimatic resources in Chongqing. J
Anhui Agric 36(30): 13431-V13463, 13470

26. Lloyd CD (2005) Assessing the effect of integrating elevation data into the estimation of monthly
precipitation in Great Britain. J Hydrol 308:128-V150

27. Lu GY, Wong DW (2008) An adaptive inverse-distance weighting spatial interpolation technique.
Comput Geosci 34(9):1044-V1055

.217.

Applicability Analysis for Measuring the Surface Flow Velocity of Rivers
by Using SRV

Feng-Wen Chen Hsiu-Te Lin Chi-Sheng Chen

臺灣河川的流量觀測目前仍以傳統的旋杯式流速儀為主要的觀測設備，當河川為高流
速之流況時，上述旋杯式流速儀應用上有其困難。因此本研究以手持式雷達波流速儀(SRV)
為流速觀測設備，以觀測河川表面流速為主，取代過去量測縱向流速加權平均之方式，期
能解決高流速流況的流速觀測問題；本研究採用手持式雷達波流速儀(SRV)，SRV 採用雷
達測速原理，屬於非接觸式觀測法；SRV 經渠槽校正及建立表面流速與平均流速關係式後，
2011 年實際應用於後龍溪、中港溪、大安溪、烏溪、濁水溪等五條河川流域之流量水位站，
一系列的觀測結果顯示以 SRV 進行表面流速觀測具可行性，尤其可解決高流速流況的流速
觀測問題，並具有縮短觀測時間，降低人為及水理因素造成之誤差，為一值得推廣的觀測
方法。

關鍵詞：流量觀測，雷達波流速儀，表面流速，非接觸式觀測法

Abstract

Cup-type current meter a traditional meter, and it is still as the main equipment which used to
measure the flow velocity of rivers in Taiwan. Actually, the cup-type current meter is difficult applied
in the condition of high flow velocity in rivers. To solve the above problem, the radar surface velocity
meter (SRV) is suggested to measure the surface flow velocity, to replace the traditional method such
as the weighted average of vertical flow velocity. The SRV is based on the principle of radar, and the
surface flow velocity measured is belonged as a non-contact method. To verify the applicability of

本篇論文原刊載於「農業工程研討會」，2012 10 月

.218.

flow velocity using SRV, it had been calibrated in a standard lab channel and a velocity relationship
between surface and average using field experiments. A series experiments were conducted in 15
water level stations which are managed by the Central Water Resources Bureau, Water Resources
Agency during the period of 2011. These 15 water level stations are distributed in five river basins in
following of Houlong River, Zhonggang River, Daan River, Wu River, and Zhuoshui River.

The result show that the method of surface velocity measurement using SRV have some
advantages such as shorten the time of observation, and decrease errors of artificial and hydrological
factors. These findings of experiment have proved that measuring the flow velocity using SRV is
feasible, especially in the condition of high-velocity flow. Finally, the study suggests using the SRV
with surface velocity measured as an observation approach.

Keywords: Flow observation, Radar surface velocity meter, Surface velocity, Non-contact
observation method

流速觀測為流量測定過程之重要一環，流速資料取得的準確性影響流量的測定成果，
隨著流速觀測技術的進步，許多流速觀測方法均被提出及應用，多數為接觸式的觀測方法，
亦即需與水體接觸，觀測過程易受漂流物的干擾或受高流速的牽引而降低觀測準度及歷經
過長的觀測時間，若發生於洪峰流量急速上升段或退水段時，過長的觀測時間間接提高流
量代表值的不確定性，為縮短觀測時間同時兼顧觀測數據的品質，非接觸式的流速觀測方
法即具有解決上述問題之潛力，因此本研究採用非接觸式的流速觀測方法，應用雷達波流
速儀觀測表面流速，透過表面流速與平均流速關係式的建立，將表面流速實測值可於後續
修正步驟，推估準確之平均流速及流量。

2.1
流速觀測已具百年以上歷史，隨著科技的發展，流速觀測的技術日新月異，許多流速

觀測儀器及其觀測方法已被提出及應用。本研究蒐集機械式流速儀、電磁式流速儀、聲波
式流速儀、微波雷達流速儀…等目前常見之流速觀測儀器並簡述其量測原理，茲說明如下。
1.浮標法

本法為最傳統之流速測定方法，迄今仍適用於洪水侵襲期間流況湍急且天候惡劣，流

.219.

速計難以施測之環境。依據達文西(1452-1519)的手稿記載，他曾使用一簡易之木製浮標及
測距推車量測河川之流速，而達文西所使用之浮標測速法迄今仍未有太大之改變，達文西
使用之方法如下：(1).於河川斷面設置一垂直於河川之基準線，將測距推車之數值設定為 0；
(2).助手於上游拋出浮標並於浮標通過基準線時開始推著測距推車往下游移動，並哼唱一首
曲子或計算脈搏數(達文西用此方法確定時間)；(3).於曲子結束或達一定脈搏數時，紀錄測
距推車之數值；4.浮標投於不同斷面位置，並重複上述步驟(Crazier, 1974)；浮標法可區分
為水面浮標及桿浮標等，野外應用浮標法仍有觀測上的困難，如浮標法易受風速影響，於
一定的距離內通常無法保持直線運動而影響準確性(李寶根，1966；Rantz, 1982)；李明靜
(2003)引述 Kinoshita (1992)的研究顯示浮標法之量測速度與真實流速仍有 10~15%之誤
差；但浮標法仍是早期用來觀測洪水流量常用的方法(蕭溪盛，1967)，時至今日，浮標法
仍為手邊無任何流速測量設備時之快速測定流速的方法，現代浮標法的施測與當年之差別
為：(1).設置基準線之位置多位於橋梁上；(2).量測速度之基準較為多元，可依浮標通過固
定距離之二河川斷面時間(碼表計時觀測)，或浮標於固定時間所移動之距離(GPS 浮標)進行
流速之判別；(3).距離、時間之測量方式更為精準。惟本法因浮標流路之不確定及水位、流
況之改變均會影響觀測之準確性。

2.機械式流速儀

機械式流速儀依其旋轉軸運行方向可分為豎軸式流速儀(Horizontal-axis current meter)
與水平軸式流速儀(Vertical-axis current meter)；應用最為廣泛的豎軸式流速儀為普萊氏
(Price Type AA meter)流速儀(USBR, 2001)，其流速觀測以低流速為佳，適用於流速 3 或 4
(m/s)以下之流況，過快的流速將導致誤差擴大及不易施放儀器觀測之問題；賴建信等(2004)
使用六具不同之普萊氏流速儀，依據 ISO3455 之規範進行校正試驗，結果顯示普萊氏流速
儀之轉速與台車速度線性關係良好；惟豎軸式流速儀於流速過小(<0.025 m/s)及水深過淺
時，無法使用本類流速儀進行觀測為其缺點(陳彥璋等，2008)。旋槳式流速儀則屬於水平
軸式流速儀，精密度較高，適用於較高流速的觀測(0.025-10 m/s)。機械式流速儀之量測原
理係為測量時，旋杯(槳)受流水衝擊而轉動，其旋轉數經由發音器的聲響計出，配合所經
時間之量測，最後根據流速與轉速公式求得，公式一般表示如下：

V = aN + b ........................................................................................................................... (1)
式中：V=流速(m/sec)、N=旋杯或旋葉旋轉次數(rev/sec)、a 及 b 為率定常數。

3.電磁式流速儀

電磁式流速儀係利用導電器、磁場及感應電流之原理來量測流速大小(黃偉哲，2002)，

.220.

可量測縱向及橫向之二維流速，惟量測時流速儀不可過於接近渠底，否則將產生干擾現象
為其缺點(呂珍謀等，2006)；陳豐文等(2010)使用電磁式流速儀建立流量及水位關係，校正
臺中中央支線、浮圳支線及下埤幹線等灌溉渠道之大型巴歇爾水槽因施設不良導致流量判
讀的誤差；惟電磁式流速儀不適用於高含砂量水流之觀測。

4.聲波式流速儀

各類型的聲波式流速儀中，以超音波之應用最廣，其運作原理均為都卜勒效應的運用，
量 測 數 據 可 依 聲 納掃描 之 範 圍 區 分 為 聲波都 卜 勒 流 速 儀 (Acoustic Doppler Velocimeter,
ADV)、聲波都卜勒剖面流速儀(Acoustic Doppler Profiler, ADP)；上述二者之差異為 ADV
僅能量測單點之流速，ADP 則可量測一垂直線上之多點流速，可直接量測流速剖面。陳彥
璋等(2008)於南勢溪流域使用 ADV 進行低流量之觀測，其結果顯示在低水深、低流速(0.01
m/s)之條件下 ADV 仍可測得流速，即可淹沒儀器測量探頭之水深便可量測流速，此為 ADV
之優點；王傳益等(1998)於濁水溪流域及烏溪流域使用 ADP 進行流量觀測，其結果顯示
ADP 之穩定性與精度均十分優越，與傳統之機械式流速儀進行比較，其誤差範圍均在 10%
以內；ADP 亦廣泛應用於定型渠道流量觀測之用，並獲得極佳的成果(陳豐文等 a，2008；
陳豐文等 b，2008；陳豐文等 c，2008)。

5.光波式流速儀

光波式流速儀主要以雷射都卜勒測速儀(Laser Doppler Velocimeter, LDV)為主，其運作
原理與聲波式流速儀同為都卜勒效應，僅波之型態由聲波換成光波，常應用於實驗室高精
度量測單點流速時使用(黃偉哲，2002)。其優點為毋須放置探頭於流體內，故不干擾流況，
且流速測定與流體性質無關(如溫度、壓力、相態)(黃文旭，1976)；George(1973)使用 LDV
量測不同流況之流體，並與計算之理論值進行比較，結果顯示實驗結果與流體移動之理論
相符。惟 LDV 適用於實驗室而不適合野外測量。

6.雷達波流速儀(微波及電波)

電 磁 波 依 其 頻 率 範 圍 可 分 為 光 波 、 微 波 及 無 線 電 波 … 等 波 段 ， 由 於 無 線 電 波 (Radio
Wave)之頻率為 3 Hz 至 300 GHz，而微波(Microwave)之頻率僅 300 MHz 至 300 GHz，被含
蓋於無線電波之範圍內，故雷達測速儀可依其發射波之頻率分為微波雷達與無線電波雷達
等二種。而流速觀測用之雷達測速儀多為微波雷達，李明靜(2003)、許盈松(2006)、朱木壽
(2010)…等均分別使用不同波段長度之微波雷達觀測河川流速，其結論均對河川高流量觀
測有正面之評價；惟本方法僅可測得河川表面之流速，於精度方面易受環境(風速、降雨干
擾)之影響為其缺點。

.221.

Plant et al. (2005)指出都卜勒雷達遙測技術之優勢為全天候、日夜均可使用(Radar
Measurement of Waves and Currents in the Nearshore Zone)，可架設於各種平台進行觀測，且
流速範圍 0.1 m/s 以內為準確。美國地質調查所(USGS)與華盛頓大學在 Lewis, Toutle, 與
Cowlitz 三條河川進行現地觀測實驗，結果顯示機載雷達具有可於遠距迅速測量之優點
(Melcher et al., 2002)。William (2008)整理近年流量觀測技術研究論文指出，高頻雷達(HF
radars)為近來廣受重視的新技術並常與傳統之流速觀測方式進行比較；李明靜(2003)使用岸
置式微波雷達系統觀測曾文溪與淡水河之流速並與傳統流速計測量比較；宋長虹等(2010)
亦使用微波雷達系統觀測科羅莎、鳳凰、辛樂克及薔蜜等四次颱風期間曾文溪及頭前溪之
洪峰流量，上述研究結果顯示微波雷達系統觀測流量之誤差平均值均低於 10%，顯示雷達
波之準確度值得信賴。惟手持式雷達波流速儀之觀測俯角與水平方向為極為敏感之控制條
件，若俯角超過 40 度或未與河川流向垂直正交，其觀測誤差將有明顯增大之趨勢(許盈松
等，2006；Plant et al., 2005)；且此觀測法在水面非常平靜之條件下將會無法測得流速資料
(Plant et al., 2005)。

2.2
流水速度為單位時間內水流經過之距離，河流、渠道中通常用的流速單位為 m/sec，

可用來計算流量；由於水路中流速各處不同，所以流速測量一般分為點流速、垂線平均流
速與表面流速三種。量測流速最直接方法為使用流速儀(點流速)測量或於岸上、橋上施放
浮標觀測水流之表面流速；其中，流速儀量測流速之準確性較高，惟儀器受流速限制，當
洪水流速超過其使用範圍時，則建議改以浮標法替代之。一般而言，測量時若觀測河川流
速小於 1.5 m/sec，水深小於 1 m 且現場環境適合進入河道時，則可將流速儀固定於測桿上
以手持使用方式實施涉(水)測；反之，若河道條件無法實施涉測，則建議改以橋面觀測。

流速觀測最主要的目標乃直接或間接測得垂向的平均流速，應用不同的流速儀觀測均
可直接或間接量測計算而得。以點流速觀測而言，可依據水深或準確度的要求實施單點法、
二點法、三點法的觀測，即深測點位置為水面下 0.2 倍、0.6 倍、0.8 倍水深處進行施測，
並依(2)-(4)式推估垂向平均流速；適用的流速儀包含旋槳式流速儀、旋杯式流速儀、電磁
式流速儀及 ADV 等。垂線平均流速直接觀測則可透過 ADP 直接觀測獲得，觀測過程，ADP
可於垂向水深的不同節點處發射聲波並直接平均計算為平均垂向流速；表面流速則可利用
浮標法或雷達波流速儀觀測而得，惟需推求表面流速與平均流速之關係式或簡易修正係數
後，間接計算而得。

Vav = V0.6 ..............................................................................................................................(2)

Vav = (V0.8+V0.2)/2 ................................................................................................................(3)

Vav = (V0.8+2V0.6+V0.2)/4 ......................................................................................................(4)

.222.

式中：Vav 係指垂向平均流速；V0.2、V0.6、V0.8 係指水面下 0.2 倍水深處、0.6 倍水
深處、0.8 倍水深處之流速觀測值。

上述傳統機械式流速儀之流速量測方法，屬於點流速的觀測方式；浮標法、電磁式流
速儀、超音波流速儀(ADV)、光波式(雷射)流速儀及雷達波流速儀等流速儀亦均同屬點觀測
類別之方式，但浮標法及雷達波流速儀屬表面流之觀測法，其餘觀測方式均需依前述之流
速測量方法進行。而 ADP/ADCP 超音波流速儀則屬垂線流速剖面觀測類別之流速儀。

2.3

河川流量測定主要利用通水斷面及流速測量結果計算而得，一般使用面積-流速法來估
算，茲將步驟簡述如下。

1.一般可依河道寬度不同將全斷面分為若干垂直子斷面，量測每一部份的斷面積 ai (m2)
及平均流速 vi (m/sec)，計算出垂直子斷面的流量，將子斷面之流量累加即為河川流量，
計算公式如下：

Q = a1 v1 +a2 v2 +‥‥‥+an vn =Σav ................................................................................(5)
式中：Q 為河川流量、an 為子斷面積、vn 為子斷面流速。

2.若以平均斷面法計算流量，各子斷面平均流速 vi 可由現場測定後，根據其結果計算各
部分流量之總和，如圖 1 所示，即

Q =Σqi =Σvi．di．bi；i=1,2,3,…n...................................................................................(6)
式中：qi 為子斷面流量、di 為子斷面水深、bi 為子斷面寬度

3.當水流方向未與橫斷面垂直，應將測得之流速修正為垂向流速，進行角度校正以獲得
修正之流量；當水位有變化時，應另計算校正水位。

h= 1 n ......................................................................................................................... (7)
Q
∑ qihi

i =1

式中：hi 為各子斷面之水位，h 為修正後之水位。

.223.

圖 1 平均斷面法量測示意圖

3.1
雷達(Radar)一詞源自於 Radio Detection and Ranging(無線電偵測與定距)，1935 年

Watson-Watt 提出使用擴大機接收脈衝無線電發射後之回聲，同年於英國 Daventry 進行實
驗，並證實利用無線電波偵測物體距離與速度為可行之方法(Penley, 2002)，之後此技術於
二戰時期即被廣泛的應用。其測速之原理與聲波、光波相同，均為都卜勒效應，此理論係
為 1842 年奧地利科學家都卜勒(Doppler)發現波源和觀察者有相對運動時，觀察者接受到波
的頻率與波源發出的頻率並不相同的現象；依據頻率之發射方式可分為脈衝式及連續波式
(CW)，其中脈衝式雷達具大範圍同步測量水面流速分佈之能力，且不受天候及發射角量測
之影響，故可克服高流量觀測時常見之困難(李明靜，2003)。反觀連續波式雷達流速儀係
連續發射雷達波為量測機制，且發射功率與天線較小故可架設於橋梁上進行連續性之長期
自動觀測；其偵測原理為利用微波斜射至待測水體之水面，一小部份之微波被水面波浪之
迎波面反射，儀器之天線接收因反射而產生之都卜勒移頻訊號，並計算其反射信號與發射
信號之頻率差，即可計算波浪之位移流速(許盈松等，2006)。
3.2

本研究採用雷達波流速儀作為非接觸式流速觀測的設備，本研究使用之設備為美國
Stalker 公司生產之手持式雷達波流速儀(SRV)，具有體積小、重量輕、便於攜帶等特點，
俗稱雷達測速槍，無須固定於橋面，因手持式的特性，可因應洪峰前後造成流路改變，便

.224.

於直接前往水流處觀測。該設備之雷達波屬於連續波雷達，因此操作時會即時傳回表面流
速值，並直接平均觀測時間內之平均表面流速值，表面流速穩定者，則數值變動幅度小，
當表面流況複雜時，流速即時變化幅度大，因此需持續觀測較長時間或重複觀測以維持準
確性，SRV 儀器規格及外觀如表 1、圖 2 所示。

表 1 手持式雷達波流速儀(SRV)規格

No. 項目 詳細資料

1 測量範圍 0.2 0-18.00 m/s

2 測量精度 ± 0.03 m/s

3 計時範圍 0-99.9 sec

4 計時精度 0.1 sec

5 最大測量距離 100 m

6 發射角度 12°

7 發射功率 500 mW

8 發射頻率 Ka band，34.7 GHz

9 工作溫度 -30~+70℃

10 電源 鋰電池，可持續觀測 6 小時

圖 2 雷達波流速儀 SRV

3.3
為避免使用不同流速儀進行測量時產生之設備誤差，造成流速測定結果之準確性降

低，故流速觀測設備均須定期進行校正檢核；本研究為評估 SRV 的測量流速的準確性，並
與其他流速儀一併比較，2011 年於水利規劃試驗所(以下簡稱水規所)之流速設備校正標準
渠道進行儀器流速觀測值之校正，校正流速儀器分別為旋槳式流速儀、超音波流速儀及雷
達波流速儀等三項設備；旋槳式流速儀安裝於水面 30 cm 處、ADP 安裝於水面下 5 cm 以
觀測垂向平均速度、SRV 則固定垂直角度約 15 度觀測(仿現場觀測最小角度)。上述 3 種流

.225.

速儀均以水規所標準渠槽之台車速度為標準速度，速度試驗範圍為 0.301-4.000 m/s，共計
進行 9 種流速範圍之實驗，每次測試均重複實驗 3 次，取平均值作為該流速之實測值；以
渠槽台車速度作為流速的標準流速，並進一步將 3 種流速儀之實測數據與台車速度(標準流
速)以線性迴歸及非線性迴歸(一元二次方程)的型式推估不同流速儀器的校正式，表示公式
如(8)式、式(9)。

線性迴歸式：Vst=aVi ± b..................................................................................................(8)

非線性迴歸式：Vst=aVi2 ± bVi ± c..................................................................................(9)

式中：Vst 為校正後之標準流速(m/s)、Vi 為流速儀實測流速(m/s)、a, b, c 均為迴歸係數。

流速校正實驗結果如表 2 及圖 3 所示，結果顯示旋槳式流速儀、超音波流速儀及雷達
波流速儀等三項設備之準確性最佳者為雷達波流速儀(SRV)，平均誤差僅-1.48 %；其次為
旋槳式流速儀 (-5.49 %)，測量期間穩定性最佳者為旋槳式流速儀，不同流速之誤差量變動
幅度最小，ADP 的量測誤差最大，平均約-10.63 %，其原因應為測試時間過短，ADP 測得
數據樣本數過少(取 30 筆)所致；本實驗發現 3 種流速儀均有流速低估現象，因此以(8)-(9)
式修正為標準流速，旋槳式流速儀之流速修正式如(10)-(11)式所示；ADP 之流速修正式如
(12)-(13)式所示；SRV 之流速修正式如(14)-(15)式所示。

表 2 流速儀校正實驗結果一覽

No. 台車速度 流速儀量測流速 (m/s) 誤差百分比 (%)
(m/s)
1 0.301 旋槳式 SRV ADP 旋槳式 SRV ADP
2 0.501
3 1.001 0.280 0.300 0.278 -7.52 -0.35 -8.20
4 1.502
5 1.999 0.470 0.500 0.460 -6.51 -0.12 -8.72
6 2.499
7 2.999 0.960 0.925 0.919 -4.29 -1.79 -8.95
8 3.500
9 4.000 1.430 1.500 1.373 -5.02 -0.12 -9.38
平均
2.034 1.910 1.950 1.822 -4.66 -2.51 -9.70

2.380 2.400 2.302 -5.01 -4.14 -8.56

2.850 2.950 2.645 -5.24 -1.67 -13.38

3.307 3.467 3.153 -5.84 -0.95 -10.99

3.797 3.933 3.396 -5.36 -1.69 -17.78

1.931 1.992 1.817 -5.49 -1.48 -10.63

.226.

圖 3 不同流速儀校正實驗之性能比較圖

旋槳式流速儀 1：Vst,p = 1.0543 Vp - 0.0029；R2=1.0000............................................. (10)
旋槳式流速儀 2：Vst,p = 0.0049Vp2 + 1.0347 Vp + 0.0097；R2=1.0000 ......................... (11)
ADP1：Vst,u = 1.1524Vu - 0.0599；R2=0.9971.............................................................. (12)
ADP2：Vst,u = 0.0484Vu2 + 0.9762 Vu + 0.0444；R2=0.9984 ......................................... (13)
SRV1：Vst,s = 1.0133 Vs + 0.0155；R2=0.9994 ............................................................. (14)
SRV2：Vst,s = -0.0084Vs2 + 1.0478 Vs - 0.0076；R2=0.9995.......................................... (15)
式中：上標 1 及 2 分別為線性迴歸及非線性迴歸成果；Vst 為校正後之標準流速(m/s)、

Vp 為旋槳式流速儀實測流速(m/s)、Vu 為 ADP 實測流速(m/s)、Vs 為 SRV 實測流
速(m/s)。
3.4
3.3 節為 SRV 及旋槳式流速儀及 ADP 之校正實驗，因此應用上述 3 種流速儀觀測之實
測值經(10)-(15)式修正即可換算為標準速度。本文茲將上述 3 種流速儀推估垂向平均流速
方式說明如下：
1.旋槳式流速儀仍須使用單點法、二點法或三點法分別觀測點流速後再經(10)式或(11)式
校正後，代入(2)-(4)式即可得垂向平均流速，如(16)-(18)式所示。
V(av,st) = V(0.6,st,p) ........................................................................................................ (16)
V(av,st) = (V(0.8,st,p)+V(0.2,st,p))/2 ..................................................................................... (17)
V(av,st) = (V(0.8,st,p)+2V(0.6,st,p)+V(0.2,st,p))/4 ..................................................................... (18)
2.ADP 因具備垂向平均流速觀測特性，因此僅需將現場實測值經(10)式或(11)式校正，即
為垂向平均流速，如(19)式。

.227.

V(av,st) = Vst,u ............................................................................................................. (19)
3.SRV 亦為點觀測的方式，但同時具備非接觸式觀測的特性，僅需觀測表面流速，因此

需再建立表面流速與垂向平均流速之關係式，因此本研究於 2011 年於打鹿坑測站、永
興橋測站進行現地流速試驗，以修正後之旋槳式流速儀實測值配合 3 點法作為垂向平
均流速代表值，並同時以 SRV 觀測表面流速，本文茲將試驗數據以線性迴歸及非線性
迴歸(一元二次方程)建立 SRV 之表面流速與垂向平均流速之關係式，如(20)-(21)式。

V(av,s) = 0.8852 V(st,s) +0.0066；R² = 0.9143 ............................................................... (20)
V(av,s) = 0.548V(st,s)2 + 1.528V(st,s)；R² = 0.9353 .......................................................... (21)

4.1
本研究 2011 年應用雷達波流速儀以表面流觀測方法進行流速觀測及流量測定，應用區

域為中港溪、後龍溪、大安溪、烏溪及濁水溪等 15 處經濟部水利署中區水資源局管轄流量
測站(詳圖 4)；本研究採 2011 年之全年度觀測數據進行案例探討，各測站之觀測次數及觀
測數據如表 3 所示。茲將上述各流域之測站以流速別區分為高流速、中流速與低流速等三
類測站；其中玉峰橋、中山橋、瑞草橋、象鼻大橋及福興橋等測站均屬於高流速測站，平
均流速約 0.89 (m/s)；烏溪橋、自治橋、集泉橋、永興橋及打鹿坑等測站為中流速測站，平
均流速約 0.39 (m/s)；平安橋、北勢大橋、南崗大橋、溪南橋及南雲大橋等測站則為低流速
測站，平均流速僅 0.28 (m/s)。

.228.

中港溪 平安

後龍溪 北勢大 永興橋

集泉橋 打鹿
象鼻大橋
自治 大安溪
溪南

烏溪

福興
烏溪

南崗

濁水溪 中山
玉峰大橋
南雲大橋

瑞草橋

圖 4 應用區域之測站分佈一覽

.217.

表 3 2011 年應用 SRV 觀測表面流速成果一覽

No. 流域別 測站 水面寬 斷面積 流速 水位 流量 斷面數 資料量
(m) (m2) (m/s) (m) (cms) (個) (筆)
1 中港溪 14 10
2 永興橋 26.60 4.50 0.33 176.45 1.42 16 8
3 後龍溪 15 10
4 平安橋 11.08 2.74 0.49 38.32 0.26 13 8
5 大安溪 11 16
6 打鹿坑 15.65 2.72 0.36 170.51 0.96 16 14
7 15 8
8 烏溪 北勢大橋 13.84 4.95 0.31 12.43 1.31 12 8
9 12 7
10 象鼻大橋 24.22 15.04 0.90 624.42 14.81 14 11
11 13 10
12 福興橋 16.77 10.50 0.59 266.38 6.50 22 22
13 濁水溪 16 22
15 烏溪橋 29.17 16.88 0.39 87.83 10.11 17 22
16 14 5
南崗大橋 37.86 22.80 0.13 74.79 3.44

溪南橋 83.06 71.35 0.10 23.42 4.54

自治橋 26.06 19.46 0.46 18.61 8.91

集泉橋 28.03 6.90 0.42 20.14 3.02

玉峰橋 113.95 60.32 0.93 263.85 64.57

南雲大橋 36.40 20.70 0.36 115.90 10.68

中山橋 21.21 15.01 1.28 265.47 20.89

瑞草橋 48.40 31.44 0.74 242.32 25.62

註：除資料量為各站之觀測次數，其餘欄位均為觀測結果之平均值。

4.2 SRV

本研究以雷達波流速儀於應用區域內測站進行多次表面流速觀測，以進一步估算流量
及建立流量率定曲線；依據 2011 年一系列觀測經驗顯示，雷達波測速槍與傳統旋槳式流速
儀相比具有量測速度迅速，可確保觀測人員安全優點，其次縮短量測時間有助於避免過長
的觀測時間導致於觀測期間因流量變化過劇而無法決定觀測起迄時間內之代表流量為何？
表面流速之觀測並可透過迅速重複觀測以避免極端值出現，時間較傳統旋槳式流速儀快 3
倍以上，且獲得之流速數據經換算流量後誤差均可達 10 %以內。由於雷達波流速儀為非接
觸式之觀測方式，不受河川中漂流物之破壞或影響觀測，故當河川流速過快、水深過深之
情況下，人員可站於橋面進行觀測，大幅降低失足落水之風險；但 SRV 仍有使用上的限制，
易受外在環境干擾為 SRV 之缺點，因本儀器量測目標為河川之表面流速，故易受表層逆流
之干擾，如橋墩後方或河道兩側之迴流區、低流速測站之河面遭強風吹拂…等均會造成表
層逆流之現象，造成觀測之速度為負值(逆流)；另當流速低於 0.1 m/s 時，應用 SRV 亦不易
觀測流速、降雨期間，攜帶式雷達波流速儀亦會被雨滴干擾，造成測得之流速數據大幅跳
動、無法穩定。故量測期間遭遇降雨或強風等無法作業之情形，均需排除外在干擾因素消

.218.

除後再行測量；橋墩後方及河道兩側迴流校正部分，本研究則使用測深盤進行探測，利用
水流拖曳物體之方式判斷下層水流流向，以確保每一斷面測量點數據之準確性。

流速觀測方法的發展或改良的主要目標均是提高流量測定的準確性及適用性，不同流
速儀有其特性及適用條件；本文使用雷達波流速儀(SRV)配合表面流速觀測法進行河川流量
的測定，經實地測試成果顯示應用雷達波流速儀以觀測表面流速之非接觸式量測法，於高
流速測站或傳統設備不便施測之環境下具快速、安全之特性；且其可大幅減少流量觀測的
時間，以減少因長時間觀測所造成之流量誤差。惟雷達波流速儀於觀測期間易受外在環境
之干擾，故於觀測期間需盡量避免外在環境之干擾，以避免外在因素產生不必要的量測誤
差。依實地觀測結果顯示雷達波流速儀之穩定性、便利性及安全性均較傳統旋槳式流速儀
之量測方式為佳，為一值得推廣的流量測定方式。

1. Crazier, A.H., 1974, “Water Current Meters”, Psmithsonian Institution Press, Washington.
2. George, W.K., Lumley, J.L., “The laser-Doppler velocimeter and its application to the

measurement of turbulence”, J. Fluid Mech., Vol. 60, Part 2, pp. 321-362, 1973.
3. Melcher, N. B., Costa, J. E., Haeni, F. P., Cheng, R. T., Thurman, E. M., Buursink, M., Spicer, K.

R., Hayes, E., Plant, W. J., Keller, W. C., Hayes, K., 2002, “River Discharge Measurements by
Using Helicopter-Mounted Radar”, Geophysical Research Letters, Vol. 29, No. 22,
pp.41-1-41-4.
4. Plant, W.J., Keller, W.C., Hayes, K., 2005, “Measurement of River Surface Currents with
Coherent Microwave Systems” IEEE Trans. Geoscience and Remote Sensing, Vol. 43, No.6,
pp.1242-1257.
5. Rantz, S.E., 1982, “Measurement and Computation of Streamflow: Volume 2. Computation of
Discharge.” Geological Survey Water-Supply Paper 2175. U.S. Government Printing Office,
Washington.
6. Penley, W.H., 2002, “The Early Days of Radar in the UK Notes for Talks.” Web site:
www.penleyradararchives.org.uk/documents/penley/early_radar/ 15th October 2002.
7. USBR, 2001, “Water Measurement Manual.” 3rd Edition, U.S. Department of the Interior,
Bureau of Reclamation.

.219.

8. Williams 3rd, A.J., Heron, M.L., and Anderson, S.P., 2008, “Technology of Water Flow
Measurement Represented by Thirty Years of CMTC”.

9. 王傳益、盧昭堯、徐享崑、馮德榮、蘇志強，1998，「聲波杜卜勒流速儀於台灣河川
流量」，中華水土保持學報，第 29 卷，第 1 期，pp. 23-32。

10. 朱木壽、黃煌煇、呂珍謀、宋長虹、蘇俊明，2010，「非接觸式量測系統於河川流量
觀測之應用」，台灣水利，第 58 卷，第 3 期，pp. 26-33。

11. 宋長虹、朱木壽、劉俞佑、蘇俊明、黃俊仁，2010，「複合式河川流量自動化觀測系
統建構與應用」，水利會訊，第 13 期，pp. 96-113。

12. 李寶根，1966，「流量測量時之浮標觀測法」，台灣水利，第 13 卷，第 4 期，pp. 36-37。
13. 李明靜，2003，「河川表面流速與流量非接觸式量測方法之發展與應用」，國立成功

大學博士論文。
14. 呂珍謀、賴泉基、詹勳全、李嶸泰、陳鴻鈞，2006，「紊流在透水底床之流速特性」，

第 15 屆水利工程研討會，桃園。
15. 許盈松、童琮志、周湘俊、張國強，2006，「微波雷達流速儀觀測特性研究」，臺灣

水利，第 54 卷，第 3 期，pp. 82-91。
16. 黃文旭，1976，「雷射都卜勒測速法」，中國農業工程學報，第 22 卷，第 1 期，pp. 25-28。
17. 黃偉哲，2002，「水流通過透水式橋墩保護工之流況分析」，國立成功大學碩士論文。
18. 陳彥璋、楊翰宗、郭振泰、郭廷鳴，2008，「應用手持式聲波都普勒流速儀量測低水

位之流量」，台灣水利，第 56 卷，第 3 期，pp. 70-77。
19. 陳豐文、陳麒升 a，2008，「鯉魚潭水庫下游景山溪流量率定」，AERC-08-RR-14，

農業工程研究中心研究報告。
20. 陳豐文、陳麒升 b，2008，「山腳工作站苑裡圳流量率定」，AERC-08-RR-15，農業

工程研究中心研究報告。
21. 陳豐文、陳麒升、黃鳳美 c，2008，「西屯工作站廟前圳明渠段之最大通水量推估」，

AERC-08-RR-21，農業工程研究中心研究報告。
22. 陳豐文、陳麒升、游宗桓，2010，「大型巴歇爾量水槽應用於灌溉水路之流量誤差實

測分析」，2010 農業工程研討會論文集，pp.481-496，臺南。
23. 賴建信、許盈松，2004，「普萊氏流速儀率定關係之研究」，台灣水利，第 52 卷，第

1 期，pp. 83-92。
24. 蕭溪盛，1967，「有關水之測定」，台灣水利，第 14 卷，第 4 期，pp. 60-65。

.220.

農地重劃績效評估模式探討 .221.

農地重劃績效評估模式探討

Study On Performance Assessment Models Of Agricultural Land
Consolidation

農業工程研究中心 內政部土地重劃工程處 農業工程研究中心 農業工程研究中心

約聘助理研究員 副處長 助理研究員兼室長 顧問

鄭世才 劉昌文 簡文煥 陳獻

S.T. Cheng C.W. Liu W.H. Jen S. Chen

摘要

台灣農地重劃自民國 47 年(1957)起，成功試辦台南市仁德區大甲及屏東縣萬丹社皮等
二區農地重劃後，在台灣各地全面推行至 99 年(2010)底止，已經歷時 52 年，共計辦理 804
區，面積超過 39.0 萬公頃，不但促進農地生產力，提高農民所得，繁榮農村經濟，績效至
為顯著。惟早期台灣農地重劃目標著重於產量提高與降低成本，並未考量農地環境資源維
護及永續，而在日本及德國已紛採兼顧自然景觀、生態保護、文化保存、娛樂休閒及能源
供給之綜合性發展，近年來台灣農地重劃亦仿效其他國家朝向環境資源維護及永續發展之
方向。然而目前台灣現有效益分析方法仍沿用早期農地重劃之分析法，對於多元化之農地
重劃無法有效呈現完整之效益，因此本研究探討現有農地重劃效益分析模式，蒐集台灣、
日本及德國相關法規、經營作業與效益評估等之差異性，探討台灣地區合適之績效評估方
式，以符合政府及農民經濟條件與受益農民負擔能力，並作為未來二次重劃時之效益評估
參考。

關鍵字：農地重劃效益、效益分析

Abstract

Since 1957 the agricultural land consolidation (ALC) projects in Taiwan were initiated at Dajia
area of Rende District in Tainan City and Shepi area of Wandan Township in Pintung County, the
similar projects have been extended to the areas spreading over Taiwan. As of 2010, a total of 804
areas covering about 390,000 ha were implemented the ALC projects. The prominent benefits realized
included upgrading of farmland productivity, increase of farmers’ incomes, and prospering rural
economy.The early ALC projects focus on the increase in production and reduce costs, and did not

本篇論文原刊載於「農業工程研討會」，2012，10 月。

.222. 一○一年度研究年報

consider the maintenance and sustainability of environmental resources of agricultural land, while in
Japan and Germany have been successively adopted to take into account the natural landscape,
ecological protection, cultural preservation, recreation and leisure, and energy supplycomprehensive
development.Taiwan's existing effectiveness analysis methods still in use early ALC the analysis
method for diversification of agricultural land readjustment can not be effectively rendered the
integrity of benefit, therefore this study investigate the existing agricultural land readjustment
effectiveness analysis mode, collect Taiwan, Japan and Germany, related laws and regulations,
business operations and benefit assessment of the differences to explore the Taiwan area of
performance assessment methods, to comply with the government and farmers' economic conditions
and benefit farmers affordability, and reference point for evaluating the effectiveness of the future of
secondary rezoning.
Keywords：The benefits of the agricultural land consolidation , Benefit analysis

一、前言

農地重劃係將一定區域內經濟效益較低之農地加以重新規劃整理，建立標準坵塊，並
透過土地交換分合，讓原本分散之耕地得以集中，使每一坵塊土地均能直接灌溉、排水及
臨路，以徹底改善農業生產環境，充分發揮農地整體效益，達到提高經濟經營效率之目的。
台灣農業重劃自民國 47 年(1957)起，成功試辦台南市仁德區大甲及屏東縣萬丹社皮等二區
農地重劃後，在台灣各地全面推行至 99 年(2010)底止，已歷 52 年，計辦理 804 區，面積
超過 39 萬公頃，不但促進農地生產力，提高農民所得，繁榮農村經濟，績效至為顯著。惟
其量化資料不甚齊全，需藉由實地調查所得資料，以利於農地重劃效益評估。本研究擬就
農地重劃特性，分析、參酌國外重劃工法，提出明確量化農地重劃之效益，用以評估爾後
欲進行重劃農地之必要性。

二、台灣、日本、德國農地重劃差異性

台灣農地重劃偏重於區塊整理及農路水路之整建，而德國及日本，除農路水路整建外，
並因應需求有土壤改良及地下排水等，甚至有因需求做二次以上重劃者。茲比較三國之法
源目的、實施範圍、做法及同一區域重劃次為如表 1 所示。以上係扼要說明三地區重劃差
異。本研究蒐集之地區對重劃效益評估方式，藉以分析比較為何德國及日本，至今非常重
視農地重劃，且有 2 次甚至於有 3 次重劃。有關台灣、日本與德國農地重劃法規及其做法
如表 2～表 4 所示；而目標、做法、經費分擔及施作工法比較之。參酌各國文獻，整理如
下表 5：

農地重劃績效評估模式探討 .223.

表 1 台灣、日本、德國農地重劃規劃

地區 台灣 日本 德國
法源依據
農地重劃條例 土地改良法 農地重劃法
目的
第3條 第1條 第1條
實施範圍
做法 配合今後農業發展之 實施農用地之改良、開 改善農林生產與工作條
需要
同一區域 發、保育及集團化，以及 件，提高農地一般用途，
重劃次數
農業生產基盤整備與開 促進鄉村之發展。

發，提高農業生產效率，

擴大農生產種類及改善

農業結構。

耕地以水田為主 耕地、農村及多目標農地 耕地、農村及多目標農地

大致相同 隨需求變化 隨需求變化

一次及早期重劃工程 視需要有二次以上 視需要有二次以上
更新改善

表 2 台灣農地重劃法規與做法

年代 法規 做法

1930 年 土地法 全國土地分類

1939 年 都市計畫法 改善居民生活環境，並促進
市、鎮、鄉街有計畫之均衡
發展

1946 年 土地重劃辦法 農地重劃參考法源
1951 年
1953 年 耕地三七五減租條例 促進土地及天然資源之保育
1954 年 實施耕者有其田條例 利用，及人口與產業之合理
1974 年 平均地權條例 分布
區域計畫法
1980 年
農地重劃條例 農地重劃有較明確且獨立法
源依據

2003 年 農地重劃區農路水路工程設 納入具涵養水資源及維護原

施規劃設計標準 有重劃區生態考量

表 3 日本農地重劃法規與做法

年代 法規 做法
明治 32 年
耕地整理法 解決高農地租金小面積耕地

.224. 一○一年度研究年報

大正 8 年 開墾助成法 以糧食增產為目標
昭和 24 年(1949 年)
昭和 36 年(1961 年) 土地改良法 地主解體，農地開放

平成 11 年(1999 年) 農地基本法 因 1965 年以後稻米生產過剩，以農地重
劃之方式，將水田轉作成多目標農地，
2001 年 並朝大坵塊方向重劃。
2004 年
2005 年 食料、農業、農村基本法 四大基本理念：
1.糧食安定供給。
2.多方面機能。
3.農業永續發展。
4.農村振興。

土地改良法修訂 納入環境考量

景觀法訂定 農地、農村事業納入景觀考量。

新制定糧食、農業、農村 糧食安定供應、環境永續發展。
基本法

表 4 德國農地重劃法規與做法

年代 法規 做法
1955 年
1989 年 主要政策有：

農業基本法 1.實施農地重劃。
2.從事農地轉移管制。
3.促進農地的租佃。
4.鼓勵農場一子繼承。
5.促進個別農場之發展。
6.鼓勵老農退出生產。

鄉村農業促進法 1.在強化家庭農場之結構及其競爭力。

2. 在 避 免 農 業 集 中 化 生 產 之 趨 勢 以 及 農 業 工
廠化的生產方式。

3.在維護自然生態，減輕環境負荷。

表 5 台灣、日本、德國之差異性比較表

台灣 日本 德國

目 改 革 農 業 生 產 環 1.農 場 規 模 擴 大 ， 促 進 農 地 聯 合 經 1.加強農業的公共投資，改
標 境，擴大農場經營 營。 善農業生產與工作環

規模，推行農業機 境，以適應結構變遷之要