 Okay, please, please everybody, take a seat, you hear me, please, back to order, okay I have a few announcements before we start, after this Jean's talk there'll be a persuasion and beer would come in the room over there, be right there, there are several things that you have to respect here, so if you get a beer here you have to show you ID, okay, there's no exception that's a rule here at Colorado University, so everybody has to show their ID, even me, look, so everybody's gonna be here and showing the ID and you get a beer, you cannot go outside of these rooms here, okay, you have to stay in these rooms, please stay in the rooms because we don't want the people here, the staff to get a bad rep with the rest of the university, okay, so be nice and stay in the rooms, there's enough space here, the posters are here, so stay here, okay, and also don't worry there are parties outside but you know if you don't get out of the room you're not gonna get beat up, so stay in the room and you know it's gonna be fun, okay, so now we're gonna go on with the workshop and we're gonna have a talk by Jean-Bron about parametrizing surface processes and their response to tectonic climatic forces, thank you, thank you for the invitation, it's a pleasure to be here, so like the previous two speakers I'm a transfuge from geodynamics tectonic modeling into surface processes modeling and what I'd like to do today is address my colleagues, my former colleague of the geodynamics tectonics community, modeling community, by making the assumption that geomorphologists have done their job and they have produced parametrizations or equations that do actually represent or have a predictive power in terms of representing out-surface processes and I'm going to take those explain them very briefly and mostly use them to show the consequences they have for this coupling between tectonics erosion and I must say climate because back in the days this limb that we were trying to show and then we trying to demonstrate using models in erosion and tectonics really was trying to relate tectonics to climate and another thing I'll show that so let's start by looking at the response of surface processes and potentially feedback to tectonics forces and to do that I'll simply do what I've already started to tell us and others that think of our origin mountain building as a cycle been in the geomorphology research for many many years and was maybe more recently expressed by Howard and from the tectonics point of view they also realize that there may be some link with surface processes so that you can get to this idea of a steady state with uplift tectonics and erosion proposed by Jemison and Roman in 1998. So the idea if you take a model or if you think about the real world that you have a region that which uplift is caused by many convergence between two plates and the uplift causes erosion and you go to the surface and after some time you reach steady state with erosion and we think for example that this is happening in New Zealand in the southern part of New Zealand. I won't say much about it but it is already a lot about New Zealand but if you just look at the rate at which it has been converging and for how long it has been converging total convergence is on the other hundred kilometers and the mountain is tiny but clearly you must have reached some kind of steady state. How long did it take to get to this steady state? You can actually say in New Zealand it didn't take more than a few million years at most because we know when the conversion started and we also know roughly when the stronger graphic control actually happened. So we have an idea of when the present day topography and it didn't take more than a couple of minutes. Now the end of the cycle is if you stop uplifting it just dies away. You move the topography by and as I will show you in a moment for many origins actually it looks like that stage lasts much longer than the growth. As an example I'll just take the Pyrenees which you may know and I'll be friends in Spain or Syria and the rest of Europe. Collision stopped there about 25 million years ago and if you look at the Pyrenees they are still a pretty substantial topography feature and if you compare the Pyrenees to the Southern Alps you actually ski on both. So they are very similar in height and shape. So I'm going to do a little bit of math so you don't worry I'm going to explain and I just wanted to get the essence of it not the detail. So one way we model erosion is by using the stream parallel which we say is incision by rivers and we say that erosion is proportional to drainage area and slope to some power. In the care here we've also put precipitation which you can take out which mean precipitation and which also it must be to the same power as A. So what I've done here is I've actually solved that equation for you and looked at time versus height and as I told you as you go and look at the height it grows until you reach some kind of steady state then it stops and then if I remove the uplift then it decayes away. What I've done here is actually scaled the height by what this is mean height but you can just think of this being the height divided or the maximum height scaled by the final height. I don't want to reach a steady state. For the stream parallel if you use that equation you can actually figure out what the actually the theoretical value of that maximum height is and what you can also do is figure out the response time tau which is also a function struck from the equation and the key thing what you do when you dimensionalize your model parameters or your variables here if you scale h by h0 and t by tau you can actually vary the value of uk and s the power exponent you will always get the same curve. What's interesting is that you can also show that tau here is simply h0 divided by you divided by rho prime and rho prime is something that measures the efficiency of isostasis. So it really is a function of the elastic plate thickness that you assume if you are on the half-liter sphere there is no isostasis and then every time you roll one kilometer the topography goes down by one kilometer if you're in local isostasis every time you roll a kilometer you remove less topography. So the key about this is that you can actually derive the value of how long it takes to get to steady state simply from the final topography the uplift rate and this isostatic factor and if you assume that a mountain has reached steady state then the erosion rate must be equal to the uplift rate. So what I've done here is quite simple is I've actually used thermochronology efficient track dating to estimate the present day erosion rate in many mountain belts and assume that for most of these we must be very close to steady state so that must be equal to you. I can measure the height of the mountain with the maps and then or the rebound or the isostatic effect I just look at either global compilation or local studies that give me the elastic plate thickness and if you do that then what you can do is regardless of what you assume as an erosional process if I come back one slide in this equation now we don't have to assume anything about the erosional process okay what happens is that you can predict the originic time scale or the response time the time it takes to actually get to equilibrium for all these mountain belts and approximation but I believe quite a bit and you see that it ranges from let's say one million year maybe for the west coast of New Zealand to something of the order of 15 million so in the range one to 10 million which is also what seems to be observed by looking at what I said for example even but also the sedimentary record sees that when do you reach this constant sedimentary flux coming out of here and you can see well one thing that I've done with that is actually try to answer a question that all of my former friends and colleagues from the geodynamic community ask me they say oh do you have an erosion model that I can put on top of my tonic model so I give them you know the stream power law or version of it and then they ask me oh what should I use for k m and m and I go hmm okay it depends okay the only thing we know the thing we know that the ratio m over m is about 0.4 0.45 okay but you don't know very much okay what I've done here and I look back at the expression for the time scale and you see that if from it if I then this is only it's independent of the process but if I assume that the stream power law is the process you can look simply at the relationship between these two and the power between the two should give me the value of n so if n equals one for example how should not depend on you yeah we know that so I've done that and you can do a fit and what you find is that best fit values too this assumes somehow that you know there's a global value for n which we know is kind of not true I'm not saying that you know I can tell you that the value m is two in all the mountains well but what you can do with this is actually provide to the modelers a tectonic modelers with a low okay an erosion low with numbers in them that would give them the right mountain height or an average mountain height on earth okay and but also it does it provides them with a with a good time scale for the evolution of the system as a function of the uplift and the isostasia you can do a little bit better even by trying to fit both k and n assuming that there are kind of absolute values for k and n and in that case you get slightly lower value n so the question you could ask are you should have told the one because you know n equals one is much easier in your role and then you figure out a k that that kind of fits there and they shouldn't worry because n the power there only really matters about you know if you are interested in the shape of nickpoints in rivers which a guy in tectonic doesn't care well it's not that simple because what happened I'm just showing you here two model runs okay in which I've simply changed n equals one and n equals two and I've scaled the case so that I know topography is the same as they said okay so you run the models they get to steady state and then after a few million years well you stop but you and then you go and decrease what you notice actually is that depending on n the rate at which the topography disappears much different and the higher n the longer your you know rendment of topography and you can show actually that because you turn you off you comes off then you don't have any more a typical exponential increase or decrease so you get actually a power load and you can show that that power load actually becomes an exponential when n equals one but is strongly dependent on n and you can think about if you want to recast that into any kind of you know erosion model doesn't have to be this extreme power load what really matters is how topography all the slope all the curvature which power it appears in the ocean and that will really determine this asymmetry between the growth phase and the decay phase and this may be explained in part with isostasis because isostasis tends also to increase the length of both the growth and the decay phase why we have ancient mountain belt like the southeastern islands in australia or the Pyrenees that can survive for tens of millions of years whereas the evidence is that the growth stage is much shorter okay now as i said the cool thing about linking erosion to tectonics is that in fact it links climate came up with this things saying like you know a mountain will look completely differently if it's on and the equator or at the pole so i want to talk now and go back to this idea of what happened now when we change climate and how does the earth the surface processes here react and potentially and you know there's a lot of debate you know whether this is actually happening when you for example look at the cooling of the climate in the late senozoic did it really change the erosion of the surface of the earth maybe the type of erosion from fluvially dominated and also did it change the efficiency of erosion so i'm going to take the opportunity to very briefly introduce our best models for the glacial erosion it's in a way much simpler first because it assumes that erosion here so again the change of height with time is uplift minus erosion erosion by glaciers is really proportional to sliding velocity of the ice the way how the ice slides and unlike the k and the n of the m of the stream paulo kg and l i actually quite well and i won't go through the detail of how it's done but several methods quite different methods came up with very very similar numbers or l roughly two and kg you know i don't remember the number but two is about you know whatever okay it's a value of k which i can't remember if i have so what we have to do the difficult part of the glacial erosion is that you have to model the glaciers that requires a mass balance between accumulation and deformation and accumulation we kind of have a good idea that it depends on altitude and we all use this concept of equilibrium line it which is the point where accumulation equals and the problem is that then we have to predict the flow of the ice we know kind of rheology the ice quite well against depending on another n and then slow it's about three but what we don't really know especially are these factors that determine how the ice is sliding basically a question of friction to the ice that's the least well constrained problem so i'm going to take that and i'm going to look at well what happens now if you assume climate changes and we are going to assume cyclic variations in climate and i'm going to model them by mapping that into elay variation elacrylamide it varies up and down in response to climate change and so what we can do is model solving these equations the shape of a glacier on a mountain profile and then we can change the elay and we can change the accumulation rate in this case and you can show how the the shape of the glacier changes and the effect it has on erosion what's really interesting is in this case again we can pull timescales out of the equation i showed you earlier and there are actually here two timescales when you change the elay when you change the climate first you change the ice there's a response time of the ice through the climate change then you change the ice with ultimately start to change the erosion change the shape of the mountain on which the ice you get to a new state so that is another timescale what i will call the erosion elay ocean erosion and you can show because we know k g quite well that the response time of the ice is of the order of a few hundred to a few thousand years whereas the erosional response time is much longer from ten thousand years to ten million and we also know don't don't remember that if you want to remember anything remember this focus on the erosional timescales that it must scales as the accumulation rates in minus two first of one over technology right and in the case of where elay calls to which is the most likely it also scales with the inverse of the so with frederick herman you know we've done this work together and eric is here we deal as well we've actually run many models and tried to find out what we call the shape of this gain well i should tell you very simply what the gain is we force the system with a periodic signal in elay altitude at various periods and for each period we look how much does the sedimentary flux coming out of the mountain changes with time if you have no gain it means that i'm changing the climate the flux doesn't change if the gain is one it means that if i change the climate by 10 percent the sedimentary flux is going to change by 10 percent the gain is high so what you see then in all cases you get no gain at short periods high gain in middle range period and low gain again at high a long period the reason is simple here you are going faster than the response time of the ice so the ice doesn't have the time to change and cannot transmit the signal to the erosion at the other end here if you go very very very slowly in changing the climate the ice is the time to change the glaciers the time to change the way it erodes and it remains always a steady state with the uplift and again you don't see anything happening to the flux and you can show according to you know the rules that i've given you from the various timescale that different uplift rates will have different gain function and assuming different mean accumulation rate will have different gain function so in other words if you force the signal let's say milankovic cycles okay we produce milankovic cycle different mountains depending on how fast there are plifting and what is the mean accumulation rate will have totally different very different response to the same forcing in the climate and you can go in from deeper and see if we now feed our model with the known cyclicity in climate which could arrive here from the limo cooling curve of the lacy nodoic and can transform that into variation in elay and put that in our model and what we see so what what is shown here are powers okay so this is power versus period and you can see this is the forcing so this is actually a spectrum of this the forcing and you can see the 40 000 100 000 year cycles but you can also see in the blue here this is the long-term cooling of the and then we apply that and we look at the gain that produces or the power in terms of sediment flux coming out of the mountain and you can see that depending on the uplift rate or the accumulation rate you can amplify some periods of some field will disappear so for example in low accumulating area so the ice rain or precipitation are low you really get a big response to the long-term cooling whereas if you are in a very high uplift area you really amplify the 100 000 year cycle it's really important to do and then what you can do you can do a bit more math if you want and take other processes like back to the stream power law you can look at the hill slope diffusion or propagation of a weathering front and you can derive the value or the stream power law of the time scales that are of interest and you can also in those cases do it for the glacial erosion get analytical functions for this gain function the key though is that they vary on they depend on many things the mean precipitation the mean accumulation they also depend in some cases on the length of the system all that to say that if I look at this is one of these gain functions that I'm plotting we have little hope in my opinion to actually see a global signal of the effect of climate change on erosion because basically if you sit in the middle of the ocean and look at the sedimentary core and see oh do I see actually the Mirankovic cycle the flux of sediment to the ocean with some proxy you are unlikely to see it because every part of the system is going to respond differently to the same forcing and I haven't said that but there's also there's a gain function there's also a phase function and not only some of them will amplify or not amplify the signal some of them will actually offset big question we discussed today is also look we try to couple surface processes with tectonics there's a big difference in scale I'm going to get down to it where there's a huge difference in time scale because as we kind of know in geomorphology surface surface processes rated with your efficiency not only depend on mean precipitation or mean you know slow accumulation but also on its variability on the weather so you know and ideally you would want to run your models with a time step like of a day rainfall changes from day to day of course especially if you want to couple them to 3d geodynamic models it's not going to be really helpful to do that and and what we do obviously is we use statistics I want to show you that and before I do that I want to show you that what I said earlier that you know climate really matters we've actually had difficulties not the modelers do that easily but the guys do the observations actually show us then when you change the climate erosion gets better when it rains more does it erode better that's data and this is now precipitation demutation rate and you know let's judge of that now that's a bit biased because obviously I said it's not only precipitation uplift rate matters slope matters and this says oh no it doesn't matter okay but what I want to explore with you is also how does variability in climate matters why would it be important but it is important in the original processes because there are thresholds so if you have this boulder in the middle of a river this is a slide from Eric nice you can realize that it's not going to move until until the discharge in the river reach some critical value and so clearly many processes in the surface of the earth are characterized by a threshold and therefore the variability of the flow becomes really important because what will really matter are the large event that will go above the threshold move the material from rivers or in glaciers or on tip so we have to have a statistical approach to do that as I said and the typical thing that we do and Greg he has been one of the people doing this first try to characterize the discharge in rivers is a statistical with the statistical properties is to look at distribution of discharge given point and so you know this distribution that gives us the frequency of a given discharge in a river there to other discharge and you see what I'm showing again this is an animation from Eric cool animation that shows different sets of discharge probability density function that are all characterized by the same mean but obviously have different variability white one is much more variable with more event of very large size and small size the narrow one have much less probability and you see now if I have a threshold in discharge to move that rock you can see that high variability implies high erosion rate low variability so I've summarized this here erosion efficiency slightly must be a function of the threshold but it should also be a question a function of the shape of that so the variability and you can show also on the slope of what's called the pale though more math and this is about 10 seconds on the on the Eric for his PhD actually shown that you can do that like others have done it for him but he's also shown that you can do it using a family one of the solution functions of discharge in rivers that fits much better observe distribution and it involves a couple of parameters that you can actually extract from looking at recession curves in river sit in a river and you look at what the discharge is doing after a big flooding is that you end up with variability and another parameter B and you can show that these depend mostly on the response timescale of a catchman which must be related to evapotranspiration or maybe vegetation and properties of soil properties of the catchman the frequency of storm and the strength of the storm so the cool thing about this too is that you can relate not only can get to discharge and related to climatic run you can go from precipitation to discharge and after having done that you can fall back onto a pure stream parallel okay a stream probably that means that erosion rate is propelled to slope area and you've started to untangle what you put in the K when you put in the K depends only on moments of that and in the case of beef especially beef we have an analytical solution so you can actually almost do a simple stream parallel make build with build into it the link between variability of climate and time is running um does it matter okay does it matter really I told you what you need a threshold and it is very uncertain type of distribution this is something we just submitted with Eric and you know feedback is really welcome on this great idea that Eric had but what we do here is actually um run millions of models okay assuming all sorts of thresholds all sorts of mean value for the the discharge all sorts of value for the variability in discharge so this parameter u the variability also the parameter b and what is plotted here for each of these models is here is the relative magnitude of the threshold compared to the mean discharge okay so if the mean is if the threshold is at the discharge this is one here and if the threshold is higher you go that way if the threshold is lower than the mean discharge what you see is that the conclusion to this is that variability only matters if the threshold is equal or larger than the mean discharge and you can actually this plot other one is going to detail this is true regardless of what you assume for an equation for erosion you can assume that the relationship between discharge and erosion rate specific discharge is super linear sub linear or even inverted you can have a this is the two and power effect it always predicts the variability here doesn't matter whereas it does matter a lot for these very large variation in erosion rate for the same mean discharge okay it doesn't matter here the threshold is below the mean or it does matter a lot of consequences for the important you know of the erosional system response to changing climate and I want to go through all of them simply to say that you can show with this that low threshold system will be really responding to mean precipitation whereas high threshold system will be proportional to mean and the variability and you can show also that the variability is most likely to be real temperature finally because as you increase the slope of rivers the threshold decreases easier for given discharge if there's already a lot of slope you can show that steep landscapes are less sensitive mountain ranges steep mountain ranges are less sensitive to variability so now I'll finish by something that maybe even more exciting than linking climate electronics but no power fetch but I think a lot of us are moving in that area to actually now look at the link between the evolution of life you know the formation the evolution of biodiversity for example given place on earth and the evolution of the landscape and I'd like to go one step beyond you know and actually link what happens totally it's serious but so we're doing this with two postdoc Catherine Kravitz who's actually here in Boulder and Jaurev Luong and we are looking in specifically at Madagascar which you may know is actually characterized by a very purely biota and especially this concept of microendemic what it means if you look for example here that you see that all of these catchmen what you have is one species of Lemieux occupies every other same ecology so you think you know that would have for a long time ago decided that one better than the others and would take over the whole island no they never even spread over the whole island but they live each of them specifically one catchman but there are exceptions to that and that's the inland catchman where you don't have this microendemic so they all live together but two things are interesting first what I just described the other thing is also the distribution of catchmen in Madagascar quite unusual actually for a spontaneous area a lot of photographer in Madagascar who have this high purge catchmen that are connected to the base level by this narrow valley whereas you have these other catchmen that are more natural although they are very elongated and there's also the reasons that people ecologists have used to explain the microendemic but one thing and I'm going to go into detail of that they relate it to the shape of the of the of the catchmen but also one thing to keep in mind is that if you try to time when this microendemism actually happened so when this variation happened potentially the catchmen wait for example you actually realize this is late late cretaceous I was talking about 16 years ago present this is a very long process it didn't happen overnight and it's mostly related first from like the Madagascar and the arrows I've put there which seem to correspond to this branching events happen are actually relatively well documented relief event in Madagascar uplift but also when it's reorganization that's the work of a so let me now get my crazy explanation of this and it relates to lecture okay so to the strength of the underlying why well an island is creating by rifting or by uplift of an area that's rounded by water okay so when you create the relief by rifting you create a skarpment by the side of the island and these skarmans are going to be rode away and it's going to create unloading at the surface and by isostasis now flexure will distribute that rebound and if you have local isostasis the the thing will remain basically like this sorry you have no isostasis or very strong lithosphere it will remain like this whereas if you have a very weak lithosphere you'll create this this you know very peaky skarpment top in the middle of a saucepan okay towards with all the drainage from so what I've done here to express that in a more clearer fashion that run full model of you know a rectangular Madagascar island okay it's roughly right and I've just changed the elastic technique I'll just let you appreciate so this is a view from the top I'm showing you the catchment they evolved through time and you'll see roughly where the rivers rivers are that really increase the photographic the duration and what do you see is that you know completely different behaviors in terms of catchment and catchment capture in the case of a very high elastic thickness you basically produce something that's more typical of an island with very linear catchment that go all the way all to the main divide if you have a very weak elastic thickness the rebound you get on the normally make the system such that there's actually only one catchment and this is you know sorry that we never see this on earth or we do see that quite often actually for example the orange river in South Africa which trains the whole of the South African cretin is surrounded by these very you know elevated regions that are most likely created by a lecture in the middle here we have these bizarre catchment that really look like Madagascar Madagascar for reference and also as you may have seen during the evolution they are extremely dynamic much more dynamic there's much more capture in this situation compared to what happened either or yet so here we go it's the thickness of the elastic lithosphere kermans microendemism in Madagascar I won't go through I'm already on the time thank you for your attention thank you Jean any questions so great talk Jean you reviewed how different transfer processes have different eigen frequencies and so they have different eigen frequencies right there's a resonance you have an eigen frequency depends on some parameters in some complicated way but in the end there's a frequency now you know if you have something like that right physicists things of course well we just can look at absorption bands and then we know what processes you made the case that that's not possible so I wonder if you could elaborate a little bit on that because why not look at you know forcing we understand like you did in your synthetic models and then look at the sediment record and then divvy out what is the dominant process so I guess you indicated that these eigen frequencies are too close together the overlap there's a wide spectrum why why is that not possible now the point that I said is that it's not possible if you look at the globally integrated signal but if you go at the bottom of any mountain belt and look at the sedimentary flux from the out of it in response to the climate then then yes yes you you will be able I mean that was the purpose of meeting like that and now I published a paper in 2014 where we looked at two geochemical proxies for climate change and erosion we tried to make a point that constrained us to empower law very nice talk thank you so I actually have two questions but first one is kind of more technology so you mentioned you use a game function so what type in function you are using do you think different type in function will influence your conclusions kind of things and the second question is you talk about the variability and mean do you think do you consider like an extreme once like a landslide and debris flow will influence your configuration about was it in condition so the first one the the gain function that we derive that we use are derived from the process if we go back to these gain functions okay are simply derived from the differential equation we have assumed for the function so that's in your stability analysis and the second question is on variability uh yeah uh Eric could respond but I can if you want okay so so the the the key yes you you write a thing conclusion we come to should be and we haven't really done it for each process but should be applicable to any process in which think of it in which there is a threshold and the forcing forcing mechanism when it's painful whether it's you know fall or other things it has a strong variability but it will only matter as I said earlier if the mean of your forcing is close to the question so you can think yeah of landsliding or any process that has a shun killin here um thanks for a dynamic fun talk I want to there's an opportunity maybe to connect to the um the way that coupling might happen one of the things you explored with the gain functions was looking at the el a varying and could you get an increased sediment flux out so now it seems to me you can't sustain that over long term unless for some reason there's a tectonic response and increase the uplift in other words the increase in sediment flux would just be while the morphology adjusts from a fluvial one to a glacial one and it's going to be over so maybe there's an opportunity for testing if there is a dynamic response by looking to see if that is sustained over long yeah so so thing but I fully agree with you that any response step-wise climate change is going to last only a period of time that is coming back to the delivery uh that timescale if you can measure it I think I think telling us a lot about the process I think for personally I think we had a discussion doesn't really really matter how you put things in equation what really matters is that timescale and from a tectonic point of view if you want to really model the shape of the landscape before but if you're really interested only as you say that there are going to be a tectonic feedback tectonics going to change that that's really old even climate change is going to change the topography by that much and over that time step you could even dream of highly simplified original model I believe it was quite a good job if you want to connect them to a really complexion model I have a comment to make as you may know I have three positions more interested in doing modeling surface points linked with tectonics climate life contacting okay we do thank you again because it was great okay the the beer should come I think