Part I: Coupling Between Climate and Tectonics

What is the Relation Between Climate and Erosion Rate?Between Erosion Rate and Tectonics?Is there a Demonstrable Coupling (with feedback loops) Between Climate and Tectonics?How Strong are the Feedbacks?How Variable Among Mountain Belts?Over what Time and Space Scales does this Coupling Operate?

A ~6-fold Increase!

The Erosion and Rock Uplift Paradox

In an isostatically compensated orogen, most (~5/6 total) rock uplift can be said to be a response to erosion At steady state, rock uplift equals erosion

the two are interchangeable

Thus it makes no sense to discuss how erosion

influences rock uplift rock uplift is erosion,

more or less

If erosion is not driven by rock uplift, but vice-

versa, what does drive erosion? And how is

relief generated?

Resolving the Paradox

Consider Three End-Member Cases:Non-Isostatic, Constant Width Mountain Belt (no root)Isostatic, Constant Width Mountain BeltIsostatic, Self-Similar Orogenic Wedge (Dynamic Adjustment of Range Width)For Each We Will Use a Simplified Erosion Rule to Explore Fundamental BehaviorInter-relationships among Erosion, Rock Uplift Rate, Surface Uplift Rate, Isostatic Compensation, and Topography

Definitions

Uplift rate (of surface or rock) is the vertical component of motion measured relative to a fixed datum (geoid) at the Earths Surface (positive up) Erosion rate is positive downSurface uplift rate is the difference between rock uplift rate and erosion rate

I discuss only regionally averaged quantities

* Rock uplift rate typically varies with depth

*

Defined at the Earths Surface (only)

Non-Isostatic Range: Siwalik Hills, Nepal

W

Uavg = Fa/W

Rock Uplift Determined by Material Flux and Fault Geometry: Erosion Plays no Role in this Simple Case of a Fixed-Width, Non-Isostatic Mountain Belt

Fa

U(x) = f (Fa, structural geometry)

Structural Geometry: Mechanism to Convert Horizontal

Motion into Vertical Motion (Rock Uplift)

The Non-Isostatic, Constant Width Mountain Belt

Fa

W

R

Uavg = Fa/W

Reminder: Only Discuss Average Rock Uplift Rate

(relative to geoid) measured at the Surface --

not internal deformation field

At all times!

Taiwan Central Range

GTOPO30 DEM

Time Since Collision Increases at ~1Ma/60 km from south

Many Narrow Mountain Belts Exhibit 2-Sided Wedge

Geometry Consistent with Critical Taper Theory

Self-Similar Geometry Consistent with Critical Taper Theory

Provides a Simple, Powerful Constraint

80-90% Relief is on Bedrock Channels

Blue lines: drainage area > 1km2; Regime where S = ksA-q

80-90% Relief is on Bedrock Channels

Threshold hillslope gradients dominate no tectonic info

80-90% Relief is on Bedrock Channels

Relief strongly scale-dependent; records: surface roughness, hillslope length, tributary relief, trunk relief

Regional Topographic Slope (tana)

W

Chart212.152155.69825017.1001412.152155.698250.320.1254486517.1001412.152155.698250.320.2508972917.1001412.152155.698250.320.3396028817.1001412.152155.781618750.320.4650515317.1001412.1548455.9160750.5378250.5905001717.1001412.235518756.050531251.075650.7159488617.1001412.31619256.18498751.6134750.8046543617.1001412.396866256.319443752.15130.8933599617.10283512.477546.45392.6891250.9820655617.16737412.558213756.588356253.226951.1075142617.23191312.63888756.72281253.7647751.1962198617.29645212.719561256.857268754.30261.2849253617.36099112.8002356.9917254.8404251.4103740617.4255312.880908757.126181255.378251.4990796617.49006912.96158257.26063755.9160751.6245282617.55460813.042256257.395093756.45391.7499769617.61914713.122937.529556.9917251.8386825617.68368613.203603757.664006257.529551.9273881617.74822513.28427757.79846258.0673752.0160936617.81276413.364951257.932918758.60522.1415423617.87730313.4456258.0673759.1430252.2669909617.94184213.526298758.201831259.680852.3556965618.00638113.60697258.336287510.2186752.4444021618.0709213.687646258.4707437510.75652.5331077618.13545913.768328.605211.2943252.6218133618.19999813.848993758.7396562511.832152.7105189618.26453713.92966758.874112512.3699752.8359675618.32907614.010341259.0085687512.90782.9614162618.39361514.0910159.14302513.4456253.0868648618.45815414.171688759.2774812513.983453.2123135618.52269314.25236259.411937514.5212753.3377621618.58723214.333036259.5463937515.05913.4264677618.65177114.413719.6808515.5969253.5519163618.7163114.494383759.8153062516.134753.6406219618.78084914.57505759.949762516.6725753.7660706618.84538814.6557312510.0842187517.21043.8547762618.90992714.73640510.21867517.7482253.9802248618.97446614.8170787510.3531312518.286054.1056735619.03900514.897752510.487587518.8238754.1943790619.10354414.9784262510.6220437519.36174.3198277619.16808315.059110.756519.8995254.4085333619.23262220.437354.4972389619.29716120.9751754.6226875619.361721.5134.748136264.873584864.999033565.087739065.213187765.301893365.390598965.479304565.568010065.656715665.745421265.834126865.959575566.085024166.210472866.335921466.461370066.586818766.712267366.800972966.926421667.051870267.140575867.229281467.317987067.443435667.568884367.694332967.783038567.871744167.960449768.049155368.137860968.226566568.315272068.403977668.492683268.618131968.743580568.869029268.994477869.119926569.245375169.370823769.459529369.548234969.636941069.725646069.814352069.9398000610.0285060610.1539550610.2426600610.3681090610.4568140610.5455200610.6342260610.7229310610.8116370610.9370850611.0257910611.1144970611.2399450611.3286510611.4540990611.5428050611.6682540611.7937020611.8824080612.0078570612.0965620612.1852680612.2739730612.3626790612.4513850612.5768330612.6655390612.7542440612.8796930613.0051420613.1305900613.2560390613.3814880613.5069360613.6323850613.7578340613.8832820613.9719880614.0974360614.2228850614.3115910614.4370390614.5624880614.6879370614.7766420614.8653480614.9540530615.0427590615.1314650615.2201700615.3088760615.3975810615.4862870615.5749920615.7004410615.8258900615.9145950616.0400440616.1654930616.2909410616.3796470616.4683520616.5570580616.6457640616.7712120616.8599180616.9486230617.0373290617.1260350617.2147400617.3401890617.4656380617.5543430617.6430490617.7317540617.8204600617.9091650617.9978710618.0865770618.1752820618.2639880618.3894360618.5148850618.6403340618.7657820618.8912310618.9799370619.0686420619.1573480619.2460530619.3715020619.4602080619.5489130619.6743620619.7998100619.9252590620.0139650620.1026700620.1913760620.2800810620.3687870620.4942360620.6196840620.7451330620.8705820620.9960300621.0847360621.1734410621.2988900621.4243390621.51304406Rhcschematic ridge profilexcDistance from Divide (km)Elevation (km)1.48003853192.07130043212.91.13944914131.48003853192.07130043212.5660149152.751.13944914131.48003853192.07130043212.5660149152.61.13944914131.48003853192.07130043212.5660149152.51.13944914131.48003853191.97194568762.5660149152.41.13944914131.47650610811.84303747432.33775195732.31.13944914131.38068378741.73870860492.0005775332.2511.13944914131.29970492751.65054091231.78453240762.181.13944914131.22929409381.5738794141.62215575752.11.13591671741.16682350571.505863051.49073998582.11.05789129271.11055579431.44460021821.37968131692.0670.99004846061.05927901221.38877138131.28311619532.0060.92985627991.0121122131.33741738781.19744074421.9530.87564074670.96839381521.28981792471.12027224461.90.8262341150.92761362691.24541750821.04994856791.90.78078756840.88936945641.20377824250.98526153811.8860.73866365410.85333831811.16454846910.92530382731.820.69937078790.81925669231.12744127460.86937573161.780.66252144660.78690661181.0922193420.81692566411.740.62780442460.75610561771.05868401450.76751066541.70.5949658130.72669935671.02666723650.72076933081.70.56379559440.69855602450.99602550290.67640272851.70.53411796430.6715621270.9666352440.63416062471.6590.50578419910.64561919840.9383892530.59383133121.6080.47866730170.62064122920.91119388480.5552340851.5540.4526579170.59655262480.8849668340.51821323371.50.42766117070.57328656890.8596353530.48263373661.50.403594190.55078369890.83513480880.44837763551.4710.38038413750.52899102260.81140750540.41534125611.4330.35796663390.50786102780.78840171240.38343296311.3950.33628448130.48735094190.76607086030.35257134321.3570.31528662060.46742211440.74437286730.32268372041.3280.29492727230.44803949660.72326957330.29370493391.30.27516522380.42917120210.70272626130.26557632321.2930.25596323410.4107881330.68271125010.23824488061.2660.2372875330.39286365920.66319554570.21166253881.240.2191073970.37537334390.64415254180.18578556711.2260.20139478930.3582947060.62555776170.1605740591.20.18412405120.3416070140.60738863340.13599149261.1730.16727163710.32529110690.58962429490.1120043541.160.15081588590.30932923730.57224542330.08858181151.1330.13473682210.29370493390.5552340850.06569543281.1330.11901598360.04331893941.1390.10363627030.02142799171.080.088581811501.0531.02610.9861.0210.9770.9330.920.9060.90.90.90.90.90.90.90.8940.8570.8170.7760.70.70.70.70.70.70.70.70.70.6910.6790.6630.6610.6850.690.6920.6940.6950.6990.6870.50.50.50.540.50.50.50.50.50.4980.4950.4830.4770.4630.4660.4510.4370.4310.4390.4350.4040.3980.3850.3780.3650.3590.3390.3260.3490.3270.30.30.30.30.30.30.30.30.30.30.30.30.30.30.30.30.30.20.20.20.20.10.10.10.10.10.10.10.10.10.10.10.10.10.10.10.10.10.10.10.10.10.10.10.10.10.10.10.10.10.10.10.10.10.10.10.10.10.10.10.10.10.10.10.0840.060.0440.030.020.020.020.020.020.020.020.0130.010.010.010.010.010.010.010.010.010.0080.0070.0060.0040.0020.001Topo Envelop CalcsParametersx/Lx (km)z (km)x T1x' T1z T1x T2x' T2z T2x T3x' T3z T3Taiwan DataDist(km) DElev (km) DDist (km) CElev (km) CDist (km) AElev (km) AParameters%LL (km)zmax (km)Parameters%LL (km)zmax (km)Parameters%LL (km)zmax (km)Ahnert DataLzmaxParametersU mm/yrKzmax (km)ParametersU mm/yrKzmax (km)ParametersU mm/yrKzmax (km)0.151.40857020520.150.70428510260.150.35214255138.50.770.529.05588016030.10012304730.558.05140187890.20003810660.5116.10280375780.4000762133L (m)215130.0010.322.56601491532017.100141.139449141332012.152151.48003853193205.698252.071300432102.903.402.067L (m)500000.2101.87776441L (m)500000.2100.938882205L (m)500000.2100.469441102590.9L (m)50000182.13974862710.2830436348L (m)500001116.10280375780.4000762133L (m)500001164.19415970380.5657932068m/n0.50.00250.322.56601491532017.100141.139449141332012.152151.48003853193205.698252.07130043210.125448652.750.125448653.3620.0887055892.033m/n0.50.3152.1784014497m/n0.50.3151.0892007248m/n0.50.3150.54460036249.61.16m/n0.51.5150.85449508390.5198263366m/n0.51.5174.15420563670.6001143199m/n0.51.5201.09595500970.6929523283n10.0050.322.566014915032017.100141.139449141332012.152151.48003853193205.698252.07130043210.250897292.60.214154233.3260.177411182n10.4202.4043562603n10.4201.2021781301n10.4200.601089065111.51n0.6672232.20560751560.8001524266n12232.20560751560.8001524266n22232.20560751560.8001524266U (mm/yr)50.010.322.5660149151.047919007132017.100141.139449141332012.152151.48003853193205.698252.07130043210.339602882.50.302859823.290.302859821.974U (mm/yr)80.5252.5872275401U (mm/yr)40.5251.29361377U (mm/yr)20.5250.64680688515.51.16U (mm/yr)42.5324.46292321681.1180599734U (mm/yr)42.5290.25700939451.0001905332U (mm/yr)42.5259.61376158080.8945976091U (m/yr)0.0050.0250.5378252.33775195730.626922185332017.100141.139449141332012.152151.48003853193205.698252.07130043210.465051532.40.391565413.2540.391565411.957U (m/yr)0.0080.6302.7417709457U (m/yr)0.0040.6301.3708854729U (m/yr)0.0020.6300.6854427364183.2U (m/yr)0.0043426.45929970471.4695271452U (m/yr)0.0043348.30841127351.2002286399U (m/yr)0.0043284.39262691310.9799825808k [m]0.0000120.051.075652.0005775330.4017015332017.100141.139449141332012.152151.48003853193205.698252.07130043210.590500172.30.4802713.2180.517014061.931k [m]0.000020.7352.8761458928k [m]0.000020.7351.4380729464k [m]0.000020.7350.719036473218.51.2k [m]0.00009268943.5537.33804248661.8516018764k [m]0.000023.5406.35981315241.4002667465k [m]0.00000023.5307.17914526051.0585021659k-area [m]6.690.0751.6134751.78453240760.301913540732017.100141.139449141332012.152151.4800385319403.368755.781618751.97194568760.715948862.2510.568976593.1820.605719651.9k-area [m]6.690.8402.9953673469k-area [m]6.690.8401.4976836735k-area [m]6.690.8400.7488418367202.35k-area [m]6.694656.4354659342.2619971868k-area [m]6.694464.41121503131.6003048532k-area [m]6.694328.38831940771.1315864137K161.0926402140.12.15131.62215575750.244346714532017.100141.1394491413322.69512.1548451.4765061081537.8255.9160751.84303747430.804654362.180.694425243.0660.731168291.866K154.64893460540.9453.1027509745K77.32446730270.9451.5513754873K38.66223365140.9450.7756877436252.35h1.6674.5783.21766752512.6988733129h1.6674.5522.46261691021.8003429598h1.6674.5348.30841127351.20022863990.1252.6891251.49073998580.2064959213322.69517.1028351.1359167174403.3687512.235518751.3806837874672.281256.050531251.73870860490.893359962.10.783130823.0390.856616941.821503.20060970641501.60030485321500.8001524266254.21-hm/n0.16655917.24300915433.1607084231-hm/n0.16655580.51401878912.00038106651-hm/n0.16655367.14930260631.2651520717T12581.560.153.226951.37968131690.1795474766387.23417.1673741.0578912927484.042512.31619251.2997049275806.73756.18498751.65054091230.982065562.10.871836413.0130.945322531.8h1.6671.1553.2906247767h1.6671.1551.6453123883h1.6671.1550.8226561942292.52Xc3205.51058.13823890583.6462163364Xc3205.5638.5654206682.2004191731Xc3205.5385.06943717291.326902687T1 end19361.70.1753.7647751.28311619530.1592998673451.77317.2319130.9900484606564.7162512.396866251.2292940938941.193756.319443751.5738794141.107514262.0670.96054231.07077121.81-hm/n0.16651.2603.37405877521-hm/n0.16651.2601.68702938761-hm/n0.16651.2600.8435146938353.65061205.58246675734.15429130486696.61682254692.400457279806402.19191001951.3859046567T23226.950.24.30261.19744074420.1434825448516.31217.2964520.9298562799645.3912.477541.16682350571075.656.45391.505863051.196219862.0061.049247631.19621981.783Xc(m)3201.3653.4518853732Xc(m)3201.3651.7259426866Xc(m)3201.3650.8629713433352.706.51359.29595361244.6839693812UKN41006.5754.66822442582.60049538646.5418.61461217391.4424953011T2 end15059.10.2254.8404251.12027224460.1307556858580.85117.3609910.8756407467726.0637512.558213751.11055579431210.106256.588356251.44460021821.284925361.9531.17469622.9991.32166851.7481.4703.524872131.4701.7624360651.4700.8812180325405.48871519.0319995185.23440046737812.71962630472.80053349317434.41691330561.4969481188T35378.250.255.378251.04994856790.1202752379645.3917.425530.826234115806.737512.63888751.05927901221344.56256.72281251.38877138131.410374061.91.30014492.9971.41037411.7141.5753.59363544461.5751.79681772231.5750.8984088611504.337.51684.57090906675.80482751947.5870.77102818363.00057159977.5449.6642254021.5494885113T3 end10756.50.2755.9160750.98526153810.1114818218709.92917.4900690.7807875684887.4112512.719561251.0121122131479.018756.857268751.33741738781.499079661.91.42559352.9631.49907961.71.6803.65867822881.6801.82933911441.6800.9146695572604.481855.71539613686.39457071338928.82243006253.20060970648464.41121503131.6003048532z(T1 end)0.08858181150.36.45390.92530382730...