Calculation of mountain lakes outburst hydrographsLomonosov Moscow State UniversityFaculty of GeographyFIRST VINOGRADOV'S READINGS. FUTURE OF HYDROLOGY Saint-Petersburg, 2013Kidyaeva Vera

The importance of the mountain lakes studies

Parts of the mountain lakes research1. Potentially hazardous lakes search 2. Surveying and monitoring 3. Morphometrical and hydrological characteristics determination 4. Regional relations determination5. Potential outburst possibility evaluation 6. Scenarios of the outbursts7. Lake outburst hydrographs calculation/evaluation 8. Mathematical simulation of floods or debris flows9. Spatial distribution of the flood or debris flow parameters 10. Intensity and hazard zoning in river valley11. Social and infrastructure vulnerability assessment 12. Risk evaluation

Objects

Mountain lakesGlacialBarrierice-dammedmoraine dammedproglacialrock, and etc.Caused by:lanslides, mudslidesdebris flows, and etc.Study areas: Central Caucasus, Russia (Elbrus region) & Sichuan Province, China (region of the 12.05 Wenchuan earthquake)

Outburst or overflow hydrographs and maximum discharge evaluation field surveysempirical formulas and methodswater-balance methodsmathematical and hydraulic outburst modelshydrodynamic modeling

Measured hydrographs

PositionDistance from Tangjiashan Dam, kmPeak discharge, m3/sOccurrence timeTangjiashan dam0650012:30Beichuan hydrologic station4.6654012:50Tongkou hydrologic station26.0621013:50

Modeling the outburst flood that occurred in 10-12 of June 2008 after the artificial cut at the dam the dam

Empirical formulasProbable maximum discharge of sudden breaks of ice dams:Qmax = W/t (1) or for moraine-dammed lakes:Qmax = 2W/t (2)Haeberli, W. 1983. Frequency and characteristics of glacier floods in the Swiss Alps. Annals of Glaciology, 4: 8590.Huggel, C. et. al. 2002. Remote sensing based assessment of hazards from glacier lake outbursts: a case study in the Swiss Alps. Canadian Geotechnical Journal, 39: 316330.Clague, J.J., and Mathews, W.H. 1973. The magnitude of Jkulhlaups. Journal of Glaciology, 12: 501504.Subglacial drainage of ice dammed lakes:Qmax maximum discharge, m3/s, W - volume in m3, t - drainage duration in seconds, t =1000 s for maximum estimates(3)

Ice-dammed glacial lake outburst 11 august 2006Parameters:Estimated volume of the flood 420 000 m3Maximum discharge of the flood 20 m3/sVolumetric concentration of thedebris flow 0.42 Water-balance method based on field surveys Q, m3/sChernomorets S., Petrakov D., Tutubalina O. 2007 Glacial lake outburst in the north-eastern slope of Mount Elbrus August 11, 2006: the forecast, the eventand the consequences// Materials of glaciological studies. 102. P.211215.

Results

Mathematical and hydraulic models 0 - water density, 1000 kg/m3 - water and ice density, 850-910 kg/m3g - gravitational acceleration, 9.81 m/s2r - latent heat of fusion of ice, 334 000 J/kgl - length of the tunnel, 550 mh - excess between entrance and the exit of the tunnel, 61 mW0 - volume of the lake before the outburst, 821 000 m3a, m - morphometrical parameters of the lake C0 - specific mass heat capacity of water, 4190 J/kg t - lake water temperature, 2,5 Computational model by Yu. B. Vinogradov for outburst through ice tunnel: for Bashkara lake

Gnezdilov Ju., Ivashchenko E., Krasnikh N. 2007 Evaluation of a hypothetical ouburst of the Lake Bashkara // Proceedings of "Sevkavgiprovodhoz", Issue 17, p.127-149.Mathematical and hydraulic models lake

Computational model for a step-shaped schematized lake hollow by V.Mochalov and I.Zuckerman Mathematical and hydraulic models W volume of the lake, m3S- surface area, m2Z depth, mZ depth of the spillway, mk spillway koef. erosion intensity koef., m-2 Tangjiashan barrier lake

Mathematical and hydraulic models 17t, h036vs.Tangjiashan barrier lake outburst, 10-12 of June 2008 ?

Hydrodynamic simulationThe Tangjiashan Barrier Lake overflow in case of huge rockfall (volume > 106 m3). The dam is stable

Methodology:two-dimensional hydrodynamic simulation, using River model by V. Belikov, A. MiliteevSaint-Venant equations

u - longitudinal component of flow velocity

v transverse component of flow velocity

q - additional inflow

_1256566703.unknown

Irregular rectangular-triangular gridDigital terrain model of the valleylakedamriverbed

Simulated overflow discharge at the dam of the Tangjiashan Lake, the highest peak 5000 m3/s

3

116.38129

122.55221

130.63011

5154.38356

1226.52405

1070.46494

552.56495

282.05089

37.88916

557.64044

515.1128

349.37426

172.8164

231.54021

263.95213

385.88162

448.20623

392.85898

297.79385

283.93505

349.23678

376.36808

357.42892

316.61284

283.70565

265.77522

286.55436

315.48448

311.54275

281.02199

267.95552

281.89155

305.57325

319.56722

319.34552

312.5185

311.80612

322.48181

335.3399

338.66801

330.62084

320.21768

315.21069

316.32185

318.74407

316.89862

309.83374

303.50073

303.77751

309.63732

315.08977

316.42662

314.75521

313.25632

313.8226

315.69236

316.20582

313.53267

308.79561

304.70533

302.75231

302.26013

301.6684

300.2338

298.65276

298.20911

299.29547

300.98926

302.06725

302.16434

301.83079

301.7361

301.99145

302.13043

301.64692

300.53764

299.30347

298.43204

297.95733

297.5464

296.93826

296.21544

295.67074

295.48014

295.5309

295.54859

295.3622

295.02559

294.69615

294.43626

294.14941

293.69012

293.0141

292.2196

291.45317

290.78504

290.17939

289.57386

288.96914

288.43331

288.03052

287.75623

287.54094

287.30993

287.03563

286.7355

286.42863

286.10271

285.72385

285.27604

284.77471

284.26125

283.76979

283.30836

282.86712

282.43963

282.03357

281.66188

281.32647

281.01248

280.69798

280.36818

280.02113

279.66143

279.29064

278.90431

278.49765

278.07256

277.63851

277.2066

276.78313

276.36841

275.96081

275.56108

275.17249

274.79735

274.43397

274.07718

273.72166

273.36461

273.00573

272.64506

272.28124

271.91212

271.53671

271.15637

270.7741

270.39277

270.01405

269.63855

269.26688

268.90008

268.53912

268.18403

267.83348

267.48542

267.1379

266.78983

266.4407

266.08986

265.7366

265.38063

265.02233

264.6627

264.30302

263.94423

263.58728

263.23269

262.88071

262.53154

262.18523

261.8414

261.49945

261.15872

260.81861

260.4787

260.13873

259.79843

259.45779

259.11708

258.77659

258.43659

258.09742

257.75939

257.42272

257.08761

256.75412

256.42223

256.09181

255.76267

255.43459

255.1074

254.78089

254.45494

254.12941

253.80423

253.47936

253.15475

252.83067

252.50737

252.18482

251.86315

251.54245

251.22278

250.90422

250.58687

250.27065

249.95536

249.64091

249.32725

249.01433

248.70208

248.39046

248.07942

247.76894

247.45908

247.14992

246.84152

246.53389

246.22704

245.92103

245.61594

245.31172

245.00842

244.70604

244.40448

244.10374

243.80378

243.50455

243.20601

242.90814

242.61092

242.31436

242.01848

241.7233

241.42885

241.13513

240.84215

240.54994

240.25846

239.96767

239.67733

239.38782

239.09953

238.81168

238.52462

238.23839

237.95299

237.66822

237.38411

237.10079

236.81804

236.53591

236.2545

235.97382

235.69381

235.41447

235.13589

234.85802

234.58083

234.30432

234.02838

233.75307

233.47848

233.20465

232.9315

232.659

232.38717

232.11603

231.84559

231.57588

231.30687

231.03852

230.77081

230.50375

230.23735

229.9716

229.7065

229.44202

229.17812

228.91476

228.65203

228.38997

228.12854

227.86773

227.60758

227.34804

227.08913

226.8309

226.57336

226.31649

226.06025

225.80462

225.54964

225.29534

225.04171

224.78875

224.53642

224.28474

224.03371

223.78334

223.53361

223.28451

223.03602

222.78815

222.54088

222.29425

222.04825

221.80287

221.55969

221.31713

221.0752

220.83388

220.59317

220.35308

220.11359

219.8747

219.6364

219.3987

219.16159

218.92507

218.68914

218.4538

218.21906

217.98491

217.75136

217.5184

217.28604

217.05427

216.82309

216.59251

216.36251

216.13309

215.90426

215.676

215.44833

215.22123

214.9947

214.76874

214.54333

214.31842

214.09405

213.87027

213.6471

213.42449

213.20246

212.981

212.76012

212.53979

212.32008

212.10094

211.88236

211.66441

211.44707

211.23034

211.01425

210.79877

210.58391

210.36967

210.15605

209.94307

209.73074

209.51907

209.30821

209.09815

208.88871

208.67985

208.47147

208.26364

208.05629

207.84939

207.64302

207.43719

207.2318

207.0268

206.82218

206.61809

206.41467

206.21133

206.00844

205.80596

205.60391

205.40235

205.2013

205.00073

204.80063

204.60099

204.4018

204.20307

204.00478

203.80694

203.60951

203.4125

203.2159

203.0197

202.82386

202.62843

202.43343

202.23887

202.04479

201.85117

201.658

201.46527

201.27297

201.0811

200.88965

200.69863

200.50803

200.31784

200.12804

199.93866

199.74969

199.56114

199.37299

199.18526

198.99793

198.81101

198.6245

198.4384

198.2527

198.06741

197.88251

197.698

197.51386

197.33004

197.1467

196.96381

196.78131

196.59921

196.41751

196.23619

196.05527

195.8748

195.69473

195.51503

195.33567

195.1567

194.97812

194.79993

194.62213

194.44471

194.26766

194.091

193.91472

193.73884

193.56333

193.38819

193.21342

193.03899

192.86491

192.69113

192.51762

192.34449

192.17175

191.99939

191.82742

191.65583

191.48461

191.31379

191.14338

190.97338

190.80375

190.63447

190.46553

190.29694

190.12872

189.96087

189.79337

189.62621

189.4594

189.29294

189.12685

188.9611

188.7957

188.63061

188.4658

188.30116

188.13687

187.97304

187.80972

187.64677

187.48413

187.32181

187.15983

186.99823

186.83703

186.67617

186.51559

186.3553

186.19534

186.03575

185.87651

185.71761

185.55903

185.40078

185.24288

185.08534

184.92817

184.77133

184.61481

184.45862

184.30276

184.14724

183.99205

183.83718

183.68261

183.52836

183.37444

183.22084

183.06756

182.91461

182.76196

182.60964

182.45765

182.30599

182.15465

182.00364

181.85294

181.70256

181.55251

181.40277

181.25335

181.10424

180.95544

180.80695

180.65877

180.51091

180.36335

180.2161

180.06916

179.92253

179.7762

179.63019

179.48449

179.33909

179.19399

179.0492

178.9047

178.7605

178.61659

178.47295

178.3296

178.18654

178.04377

177.90128

177.75908

177.61719

177.47561

177.33433

177.19336

177.0527

176.91234

176.77228

176.63251

176.49303

176.35384

176.21493

176.07631

175.93797

175.79991

175.66214

175.52466

175.38746

175.25055

175.11393

174.9776

174.84155

174.70578

174.5703

174.43509

174.30016

174.16551

174.03113

173.89703

173.76319

173.62962

173.49631

173.36326

173.23048

173.09797

172.96573

172.83375

172.70206

172.57064

172.43949

172.30863

172.17804

172.04773

171.91769

171.78792

171.65841

171.52917

171.40019

171.27147

171.14301

171.01481

170.88688

170.75921

170.6318

170.50466

170.37777

170.25115

170.1248

169.9987

169.87286

169.74727

Q_3dam

time, hour

calculated discharge, m3/c

z1_50

timeQ_3damQ_4_BeichuanQ5_MagunyanQ2_Tongkou

47.992790.00116.38129119.72728125.26706129.30437

48.005350.01122.55221130.8591136.88322135.23911

48.025410.03774.51728132.26119147.33857155.77878

48.045440.05827.16964134.50058147.71902155.51629

48.065540.07146.70893135.89292147.78114155.20314

48.085540.0950.13852137.30728147.69037155.02374

48.105650.11478.71213138.12306147.59003154.88837

48.125720.13444.80731138.28841147.48227154.77461

48.145780.15134.9346138.09553147.37044154.67485

48.165850.17138.20736137.8397147.26064154.58365

48.185880.19229.72106137.63717147.15634154.49692

48.205970.21122.35437137.48946147.05763154.41059

48.226040.23159.97717137.3738146.96334154.32142

48.246090.25275.59986137.27113146.87282154.22824

48.266170.27287.33974137.17318146.78535154.13105

48.286250.29187.61655137.0796146.70016154.03068

48.306380.31209.12116136.99202146.61682153.92865

48.326390.33278.59636136.91044146.5351153.82667

48.346510.35255.00729136.83352146.45489153.72625

48.366570.37245.54344136.75969146.37574153.62802

48.386660.39261.43585136.68818146.2973153.53226

48.406740.41240.6149136.61879146.21971153.43952

48.426750.43201.85305136.55253146.1425153.34926

48.446830.45208.30284136.49523146.06589153.26161

48.466910.47229.49061136.45787145.98982153.17619

48.486960.49218.65829136.45951145.9147153.09309

48.5070.51198.67105136.53096145.8399153.01127

48.527070.53199.25288136.71965145.76538152.93033

48.547190.55204.72815137.08851145.69125152.85007

48.567230.57202.81464137.71629145.61747152.77021

48.587290.59208.7438138.70106145.54397152.69043

48.607340.61216.98603140.1474145.47071152.61054

48.627380.63213.26991142.14339145.39776152.53048

48.647430.65207.85154144.72046145.32556152.45067

48.667490.67216.72649147.88442145.25366152.37058

48.687560.69229.3801151.59038145.18161152.28968

48.707630.71233.14639155.70006145.10987152.2085

48.727670.73232.73724160.07373145.03839152.12703

48.747710.75233.51563164.59908144.96717152.04531

48.767750.77231.87273169.19332144.89623151.96341

48.78780.79230.83497173.77698144.82556151.88141

48.807840.81233.3313178.26254144.75514151.79934

48.827880.83233.42167182.56673144.68494151.71724

48.84790.85227.56041186.62606144.61495151.63516

48.867920.87220.71115190.40198144.54515151.55314

48.887950.89217.26054193.87508144.47553151.47122

48.907990.91216.48054197.03824144.40607151.38943

48.928040.93216.91225199.89291144.33675151.30777

48.948090.95218.00656202.44594144.26756151.22626

48.968140.97218.62213204.70748144.1985151.1449

48.98820.99218.33649206.69078144.12957151.06371

49.008261.01219.15236208.4122144.0608150.9827

49.028331.03222.07889209.89542143.99265150.90239

49.048411.05225.08202211.19424143.92471150.82224

49.068481.07226.19656212.3134143.85705150.74226

49.088551.09225.6394213.23976143.78975150.66244

49.108621.11224.21357213.97166143.72294150.58276

49.128691.13222.47785214.52479143.65677150.50322

49.148761.15221.02796214.92415143.59145150.42381

49.168831.17219.79939215.20335143.52722150.34452

49.18891.19218.07035215.37803143.46438150.26531

49.208981.21215.78835215.45819143.40327150.18618

49.229061.23213.84003215.45028143.34432150.1071

49.249141.25212.91312215.36678143.28799150.02807

49.269231.27212.92069215.23184143.23481149.94907

49.289321.29213.40752215.06568143.18536149.87008

49.309411.31213.98072214.87572143.14028149.79111

49.329511.33214.46172214.66632143.10022149.71213

49.349611.35214.95788214.44325143.06591149.63315

49.369711.37215.66569214.21511143.03808149.55416

49.389811.39216.48615213.99036143.0175149.47517

49.409911.41217.03932213.77178143.00492149.39617

49.430011.43217.09416213.56056143.00113149.31715

49.450121.45216.76277213.35831143.00689149.23813

49.470221.47216.29465213.16662143.02296149.15909

49.490321.49215.85506212.98654143.05007149.08004

49.510431.51215.45649212.81859143.08892149.00098

49.530541.53214.99503212.66284143.14015148.92192

49.550641.55214.39746212.51918143.2044148.84285

49.570751.57213.75214212.38743143.28225148.76378

49.590861.59213.23845212.26729143.37426148.6847

49.610961.61212.946212.15836143.48093148.60564

49.631071.63212.81598212.06014143.60271148.52659

49.651181.65212.72841211.9721143.74002148.44757

49.671291.67212.61237211.89376143.89321148.36858

49.69141.69212.49167211.82439144.06257148.28963

49.711511.71212.43864211.7627144.24834148.21073

49.731621.73212.47913211.70703144.45069148.13188

49.751741.75212.5487211.65568144.66974148.05311

49.771851.77212.5458211.60716144.90555147.97442

49.791971.79212.41719211.56014145.15812147.89581

49.812081.81212.18537211.51341145.42739147.81731

49.83221.83211.90503211.46596145.71325147.73892

49.852321.85211.60477211.41696146.01557147.66064

49.872441.87211.26914211.36582146.33411147.5825

49.892561.89210.87044211.31242146.66864147.50451

49.912691.91210.4144211.25729147.01886147.42667

49.932811.93209.95065211.201147.38443147.34899

49.952931.95209.53851211.14366147.76495147.27149

49.973051.97209.20778211.08504148.15999147.19418

49.993171.99208.95004211.02491148.56906147.11705

50.01332.01208.74246210.96358148.99165147.04012

50.033422.03208.57368210.90209149.42724146.96339

50.053552.05208.44833210.84095149.87528146.88686

50.073672.07208.36966210.77982150.33523146.81054

50.09382.09208.32097210.71838150.80655146.73443

50.113922.11208.26842210.65659151.28867146.65854

50.134052.13208.18006210.59504151.78101146.58287

50.154182.15208.04161210.5349152.28298146.50744

50.174182.17207.8574210.4761152.79391146.43224

50.194182.19207.639210.41785153.31147146.35728

50.214182.21207.39376210.35931153.83226146.28259

50.234182.23207.12388210.29983154.35628146.20816

50.254182.25206.83456210.2391154.88482146.13401

50.274192.27206.53999210.177155.41908146.06017

50.294192.29206.26014210.11358155.95966145.98664

50.314192.31206.00874210.04896156.50645145.91346

50.33422.33205.79045209.98334157.05887145.84065

50.35422.35205.59982209.91695157.61609145.76823

50.374212.37205.42865209.85009158.17722145.69625

50.394212.39205.27146209.783158.7415145.62473

50.414222.41205.12536209.71574159.30832145.55374

50.434232.43204.98579209.64827159.87717145.48332

50.454232.45204.84413209.58051160.44765145.41352

50.474242.47204.69042209.51229161.01931145.34444

50.494252.49204.51825209.44328161.59115145.27614

50.514262.51204.32725209.37312162.16206145.2087

50.534272.53204.12148209.30156162.7316145.14221

50.554282.55203.90555209.22837163.29975145.07677

50.57432.57203.68217209.1534163.86663145.01248

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57.695139.70

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57.755399.76146.32578

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57.835739.84146.0059

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137.80815156.7902

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137.23458144.64558155.99664

137.17145144.57128155.90905

137.10843144.49709155.82158

137.04553144.42303155.73422

z1_50

Q_3dam

Q_4_Beichuan

Q5_Magunyan

Q2_Tongkou

z1_40

timeQ_3damQ_4_BeichuanQ5_MagunyanQ2_Tongkou

47.992790.00116.38129119.72728125.26706129.30437

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48.065540.07141.25046135.9056147.78059155.20117

48.085540.0961.04516137.31826147.68948155.02239

48.105650.11418.0943138.12822147.58887154.887

48.125720.13395.42093138.28782147.48124154.77363

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48.165850.17118.05103137.83715147.25948154.5827

48.185880.19210.45761137.63499147.15507154.49585

48.205970.21118.26352137.48782147.05642154.40949

48.226040.23140.50335137.37249146.96222154.32033

48.246090.25246.31928137.27001146.87184154.22719

48.266170.27264.22763137.17232146.78458154.13018

48.286250.29175.4668137.07901146.69962154.03003

48.306380.31183.32699136.9917146.61651153.92827

48.326390.33253.56204136.91034146.53501153.82655

48.346510.35232.43156136.83312146.45449153.72575

48.366570.37218.97161136.75901146.37506153.62718

48.386660.39233.98164136.68706146.29636153.53113

48.406740.41220.05498136.61662146.21851153.43811

48.426750.43183.32323136.54804146.14153153.34815

48.446830.45186.7686136.48405146.06516153.26078

48.466910.47208.58988136.43032145.98931153.17562

48.486960.49200.29944136.39641145.91394153.09226

48.5070.51181.6765136.39787145.83891153.0102

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48.547190.55188.41533136.61025145.69077152.84956

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48.627380.63196.63935139.06496145.39839152.53118

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48.687560.69208.94158144.2104145.18218152.29032

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48.807840.81211.91561161.97122144.75733151.8019

48.827880.83212.88005165.14218144.6874151.72012

48.84790.85208.27217168.24097144.61767151.63835

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49.008261.01199.65156187.08048144.06553150.98839

49.028331.03201.99358188.55089143.99711150.90787

49.048411.05204.8577189.83883143.92886150.82753

49.068481.07206.18356190.95451143.86078150.74735

49.088551.09205.92977191.9089143.79294150.66732

49.108621.11204.85991192.71347143.72538150.58744

49.128691.13203.37584193.38009143.6582150.5077

49.148761.15202.02155193.92352143.59151150.4281

49.168831.17200.9863194.36634143.52545150.34861

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49.208981.21197.65678194.98718143.39589150.18989

49.229061.23195.81698195.18426143.33284150.11062

49.249141.25194.85817195.31555143.27132150.0314

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49.309411.31195.75268195.3805143.0994149.7939

49.329511.33196.23136195.32138143.04765149.71474

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49.369711.37197.27782195.13341142.95527149.55644

49.389811.39198.05306195.02029142.91568149.47727

49.409911.41198.64272194.90303142.8812149.3981

49.430011.43198.779194.79001142.85238149.31891

49.450121.45198.5326194.68565142.82979149.23972

49.470221.47198.12938194.59104142.81399149.1605

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49.510431.51197.39377194.42235142.80496149.00204

49.530541.53197.02444194.34561142.8128148.9228

49.550641.55196.52883194.27699142.82955148.84356

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49.590861.59195.48071194.1595142.89167148.68507

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49.671291.67194.94171193.97694143.14137148.36827

49.69141.69194.83911193.94178143.23175148.28916

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49.731621.73194.8161193.88352143.44768148.13109

49.751741.75194.8962193.86032143.57356148.05216

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49.83221.83194.46065193.77995144.19846147.73734

49.852321.85194.22171193.75767144.38505147.65891

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49.973051.97192.19675193.56785145.75071147.19153

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50.01332.01191.78157193.48378146.29428147.03717

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50.254182.25190.29415192.91416150.29807146.12877

50.274192.27190.04196192.86454150.67627146.05461

50.294192.29189.7977192.81467151.05943145.98073

50.314192.31189.57733192.76457151.44716145.90714

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50.35422.35189.22196192.66362152.23485145.76088

50.374212.37189.07639192.61275152.63408145.68826

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50.554282.55187.85803192.13443156.26711145.05575

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50.694382.69186.55391191.70629159.13705144.60791

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50.754442.75186.0777191.50231160.35374144.43604

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50.794472.79185.78571191.36105161.15509144.33068

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50.854542.85185.35322191.14295162.33853144.18953

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50.954662.95184.5683190.75915164.24748144.01101

50.974682.97184.40257190.67908164.61904143.98552

50.994712.99184.23617190.59798164.98513143.96391

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137.17145144.57128155.90905163.88943

137.10843144.49709155.82158163.79442

137.04553144.42303155.73422163.69948

z1_40

Q_3dam

Q_4_Beichuan

Q5_Magunyan

Q2_Tongkou

z2_40

timeQ_3damQ_4_BeichuanQ5_MagunyanQ2_Tongkou

47.992790.00116.38129119.72728125.26706129.30437

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48.065540.071226.52405135.90176147.7807155.20197

48.085540.091070.46494137.31448147.68976155.02289

48.105650.11552.56495138.1278147.58889154.88705

48.125720.13282.05089138.28761147.48122154.77363

48.145780.1537.88916138.09352147.3696154.67415

48.165850.17557.64044137.8385147.26011154.58321

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48.205970.21349.37426137.48826147.05678154.4098

48.226040.23172.8164137.37273146.96247154.32055

48.246090.25231.54021137.27012146.87199154.22732

48.266170.27263.95213137.17209146.78443154.12996

48.286250.29385.88162137.07852146.69921154.02951

48.306380.31448.20623136.99089146.61576153.92731

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48.346510.35297.79385136.83229146.45364153.72468

48.366570.37283.93505136.7583146.37429153.62622

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48.406740.41376.36808136.61734146.21799153.43748

48.426750.43357.42892136.5531146.14121153.34777

48.446830.45316.61284136.50339146.06478153.26035

48.466910.47283.70565136.49167145.98891153.17517

48.486960.49265.77522136.56551145.91364153.09193

48.5070.51286.55436136.81194145.83884153.01011

48.527070.53315.48448137.3759145.76435152.92921

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48.827880.83315.21069243.11357144.6861151.71859

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48.928040.93303.50073271.96021144.3391151.31052

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48.968140.97309.63732279.15261144.20134151.14816

48.98820.99315.08977281.89575144.13271151.06724

49.008261.01316.42662284.1796144.0643150.98648

49.028331.03314.75521286.03038143.99617150.90588

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49.068481.07313.8226288.59876143.86137150.74521

49.088551.09315.69236289.44725143.79512150.66513

49.108621.11316.20582290.06599143.73006150.5852

49.128691.13313.53267290.4929143.66661150.5054

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49.229061.23301.6684290.79282143.39673150.10789

49.249141.25300.2338290.59122143.35857150.02856

49.269231.27298.65276290.39062143.32837149.94925

49.289321.29298.20911290.21305143.30748149.86996

49.309411.31299.29547290.06479143.29735149.79068

49.329511.33300.98926289.93679143.29949149.71141

49.349611.35302.06725289.81631143.31547149.63214

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49.389811.39301.83079289.54999143.39531149.47358

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49.430011.43301.99145289.34001143.54989149.31497

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49.530541.53298.43204289.05741144.34798148.9182

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49.812081.81293.69012289.24699150.88647147.80931

49.83221.83293.0141289.2145151.62931147.7306

49.852321.85292.2196289.16786152.40841147.65202

49.872441.87291.45317289.11246153.22234147.57357

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49.912691.91290.17939288.99258154.93164147.41713

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50.053552.05287.30993288.5649161.85951146.87531

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50.234182.23283.76979287.83686172.3442146.19762

50.254182.25283.30836287.74834173.59634146.12422

50.274192.27282.86712287.65818174.86919146.05126

50.294192.29282.43963287.56618176.16091145.9788

50.314192.31282.03357287.47213177.4662145.90689

50.33422.33281.66188287.37579178.77225145.8356

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50.434232.43280.02113286.84841185.38477145.49153

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50.474242.47279.29064286.61102188.0897145.36193

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50.614322.61276.36841285.65188197.58842144.97162

50.634342.63275.96081285.5001198.93298144.92733

50.654352.65275.56108285.34516200.27494144.88687

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50.81452.81272.64506284.00598210.33748144.75264

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50.934632.93270.39277282.90384217.40781144.98495

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52.016994.02251.86315270.6734258.9941181.42182

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52.157444.16249.64091268.88267261.69853190.85723

52.177514.18249.32725268.62459262.04463192.2015

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52.3184.32247.14992266.80443264.196