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Table 7 Regression coefficients at different integration times for three empirical methods

From: Rain rate modeling of 1-min from various integration times in South Korea

Sites

5- to 1-min

10- to 1-min

20- to 1-min

a

b

c

d

a

b

c

d

a

b

c

d

Chebl and Rahman

 Gwangju

−17.310

0.73800

1.132

43.170

0.7784

1.0140

1.185

−8.234

−5.422

0.368

1.435

74.160

 Daegu

1.365

−0.01046

−0.359

91.610

3.2690

−0.0086

−2.288

40.390

−4482.000

1.078

1.474

923.900

 Daejeon

0.002

−0.00774

1.120

−5.060

−41.3400

0.9106

1.186

−5.278

1.313

1.064

1.271

−8.465

 Busan

4.602

4.89800

1.118

−110.900

−15.6000

4.6630

1.139

−26.910

0.003

−0.431

0.987

8.064

 Seogwipo

−1211.000

1.08700

1.085

433.600

0.1059

−0.0027

0.975

15.620

4.738

0.003

−3.521

0.013

 Seoul

−2.586

0.05670

2.668

45.650

5.2160

2.7980

1.289

−245.800

−17.970

2.911

1.480

−453.400

 Ulsan

0.173

0.76840

0.985

0.910

28.4200

0.0001

−27.470

−0.020

−0.141

3.589

0.702

571.600

 Incheon

−386.700

0.93300

1.098

410.200

−3.3240

10.6400

1.157

−139.600

−44.460

2.476

1.153

−29.150

 Chuncheon

−0.232

0.77940

1.075

1.790

−5719.0000

1.1340

1.254

966.700

−3289.000

1.033

1.491

895.900

 Average

−179.076

1.02692

1.103

101.219

−637.9416

2.3498

−2.397

66.319

−870.327

1.343

0.719

220.291

Third order polynomial fit

 Gwangju

−0.0002625

0.0573600

−2.785

82.220

−0.00052400

0.11020000

−6.020

145.600

−0.00056630

0.11110000

−5.441

122.700

 Daegu

0.0002814

−0.0614300

5.417

−92.990

0.00046860

−0.10280000

8.426

−156.500

0.00074800

−0.14550000

10.780

−197.700

 Daejeon

−0.0003028

0.0663900

−3.393

94.290

−0.00043420

0.09233000

−4.862

120.900

−0.00075870

0.15210000

−8.134

177.700

 Busan

0.0000145

−0.0011420

1.155

−6.092

−0.00019510

0.05392000

−3.261

106.100

−0.00017430

0.05149000

−3.158

104.900

 Seogwipo

−0.0000840

0.0185500

−0.143

22.060

−0.00012210

0.02355000

−0.233

20.880

−0.00005324

0.00657900

1.028

−5.658

 Seoul

−0.0000755

0.0212400

−0.352

26.140

0.00005647

−0.00577400

1.554

−15.610

0.00091930

−0.14930000

9.788

−173.800

 Ulsan

0.0000548

−0.0239100

3.389

−62.770

0.00001800

−0.01718000

3.034

−56.490

0.00001578

−0.01106000

2.237

−30.670

 Incheon

0.0000155

−0.0018370

1.180

−5.497

0.00131900

−0.27220000

19.770

−427.600

0.00226000

−0.44290000

29.850

−619.800

 Chuncheon

0.0001048

−0.0207000

2.400

−27.110

−0.00040220

0.07533000

−2.927

63.840

0.00028430

−0.05043000

4.607

−70.850

 Average

−0.0000282

0.0060579

0.763

3.361

0.00002050

−0.00473600

1.720

−22.098

0.00029720

−0.05310233

4.617

−77.020

Model 1

 Gwangju

−0.00000312800

0.00069080000

−0.04747

2.11800

−0.0000075820

0.0015920000

−0.104

3.283

−0.00000834800

0.00159900000

−0.094

2.886

 Daegu

0.00000689500

−0.00153400000

0.10790

−1.23600

0.0000139400

−0.0030070000

0.205

−3.157

0.00002826000

−0.00545800000

0.339

−5.501

 Daejeon

−0.00000463700

0.00104500000

−0.07348

2.70700

−0.0000065480

0.0014380000

−0.097

3.183

−0.00001869000

0.00363200000

−0.223

5.485

 Busan

−0.00000001072

0.00000876500

0.00100

0.94870

−0.0000027210

0.0006997000

−0.054

2.330

−0.00000299900

0.00078050000

−0.060

2.494

 Seogwipo

−0.00000094210

0.00019790000

−0.01171

1.22800

−0.0000006942

0.0000989500

−0.002

0.985

0.00000007355

−0.00008346000

0.011

0.761

 Seoul

−0.00000084370

0.00018960000

−0.00897

1.12400

0.0000010330

−0.0002241000

0.021

0.456

0.00001399000

−0.00254100000

0.162

−2.378

 Ulsan

0.00000095570

−0.00036440000

0.03484

0.11350

0.0000001916

−0.0001705000

0.020

0.473

0.00000006879

−0.00004612000

0.006

0.915

 Incheon

0.00000034290

−0.00008152000

0.00787

0.78030

0.0000159800

−0.0033830000

0.236

−4.455

0.00002703000

−0.00539600000

0.352

−6.574

 Chuncheon

0. 00000156600

−0.00033680000

0.02354

0.54900

−0.0000064710

0.0012230000

−0.067

2.204

0.00000916100

−0.00177400000

0.116

−1.118

 Average

0.00000002201

−0.00002051722

0.00373

0.92583

0.0000007920

−0.0001925500

0.018

0.589

0.00000539404

−0.00103189778

0.068

−0.337

Sites

30- to 1-min

60- to 1-min

a

b

c

d

a

b

c

d

Chebl and Rahman

 Gwangju

13.050

−0.004

−12.270

0.101

0.001

−0.516

1.220

−25.240

 Daegu

−5135.000

1.064

1.621

996.200

−90.760

0.533

2.165

454.900

 Daejeon

0.005

−0.433

1.039

48.890

0.028

1.046

1.427

−26.920

 Busan

−148.900

5.111

1.245

−245.200

−7.097

7.725

1.268

−252.400

 Seogwipo

1.281

0.011

−0.039

93.690

−7.269

1.194

1.049

91.700

 Seoul

0.014

−0.380

0.862

74.740

5.116

2.823

1.690

−605.900

 Ulsan

58.940

3.524

0.717

556.200

5.590

0.226

0.132

−913.400

 Incheon

−12.030

2.825

1.212

−182.800

0.710

1.017

1.171

−29.160

 Chuncheon

−133.300

0.621

1.811

468.400

−3290.000

0.972

1.921

975.200

 Average

−595.105

1.371

−0.423

201.136

−375.965

1.669

1.338

−36.802

Third order polynomial fit

 Gwangju

−0.00043350

0.08480000

−3.826

92.290

0.00028730

−0.03606000

3.077

−34.280

 Daegu

−0.00029600

0.01206000

3.624

−94.220

−0.01276000

1.77700000

−76.950

1103.000

 Daejeon

0.00266400

−0.37620000

18.600

−262.900

0.01033000

−1.50900000

73.190

−1119.000

 Busan

−0.00002500

0.01923000

−0.783

46.990

0.00149900

−0.31010000

22.500

−490.800

 Seogwipo

−0.00001095

−0.00142800

1.489

−12.950

−0.00003418

0.00503300

0.958

0.313

 Seoul

0.00448700

−0.73490000

41.400

−733.200

−0.00012310

0.07349000

−4.201

103.3 00

 Ulsan

0.00001323

−0.00829000

1.634

−7.223

0.00005752

−0.02056000

2.519

−27.090

 Incheon

0.00407000

−0.80480000

53.800

−1144.000

0.00339900

−0.67410000

45.380

−963.900

 Chuncheon

−0.00072290

0.10450000

−2.639

37.110

−0.00220900

0.29200000

−9.363

112.500

 Average

0.00108288

−0.18944756

12.589

−230.900

0.00004962

−0.04469967

6.346

−146.217

Model 1

 Gwangju

−0.00000667000

0.00128300000

−0.0756

2.5780

0.00000877500

−0.00141400000

0.08129

−0.32120

 Daegu

0.00001930000

−0.00427400000

0.2982

−5.0810

−0.00028400000

0.03620000000

−1.62800

23.86000

 Daejeon

0.00001809000

−0.00205100000

0.0678

0.6327

0.00016300000

−0.02523000000

1.18100

−17.22000

 Busan

−0.00000154700

0.00045000000

−0.0343

1.8360

0.00001705000

−0.00365300000

0.25900

−5.03200

 Seogwipo

0.00000040390

−0.00013980000

0.0135

0.7558

−0.00000008082

−0.00000528700

0.00200

1.05700

 Seoul

0.00006708000

−0.01158000000

0.6467

−11.0000

−0.00000258100

0.00088110000

−0.04907

1.81200

 Ulsan

0.00000001307

0.00000295300

−0.0056

1.3830

0.00000025710

−0.00006486000

−0.00071

1.25200

 Incheon

0.00005004000

−0.01016000000

0.6629

−13.4000

0.00004937000

−0.01013000000

0.66720

−13.62000

 Chuncheon

−0.00000859100

0.00094650000

−0.0124

0.8382

−0.00003320000

0.00392800000

−0.11420

1.94300

 Average

0.00001534655

−0.00283581633

0.1735

−2.3841

−0.00000904552

0.00005688367

0.04428

−0.69658