Video summary
The presentation addresses the fundamental geomorphic question of how rivers incise through bedrock while simultaneously transporting sediment, a process governed by the balance between rock erosion and sediment supply. The speaker explains that river systems exist on a spectrum ranging from detachment-limited regimes, where the rate of rock erosion is the primary constraint and the channel bed remains relatively clean, to transport-limited regimes, where the river's capacity to move sediment is equal to or less than the available supply, resulting in a bed blanketed by material. Historically, models like the stream power incision model focused on detachment limits, but later developments introduced a "cover term" to account for sediment inhibition of erosion. The speaker argues that various existing models can be mathematically reworked into forms similar to this linear decline model, yet they often contain hidden flaws in how they handle the transition between these two limiting conditions.
A critical issue identified is the flawed parameterization used in popular models like SPACE to determine whether a system is detachment or transport limited. These models rely on a ratio involving sediment settling velocity divided by rainfall rate, which creates a physically unrealistic scenario where even small amounts of sediment would theoretically force a river into a transport-limited state immediately. The speaker demonstrates that this disconnect between the parameter controlling the regime shift and the parameters controlling sediment thickness leads to bizarre behaviors in simulations. Specifically, when a model is forced through a thick layer of sediment and then uplifted, it may exhibit non-physical responses such as nickpoints sweeping downstream while rock is being exposed, or failing to correctly simulate the gradual transition from a sediment-covered bed to bare rock at steady state.
To resolve these inconsistencies, the speaker proposes that all river incision models should be unified under a single conceptual framework derived from the linear decline model. The solution involves explicitly tracking sediment depth as a separate variable and ensuring that the parameters governing transient dynamics (the shift between detachment and transport limits) are mathematically linked to those governing steady-state sediment flux and erodability differences. By resetting the derivation of models like SPACE to define these relationships correctly, future versions can accurately simulate how rivers respond to changes in uplift rates without exhibiting the erratic behaviors caused by decoupled parameters. The talk concludes that while current models have been useful tools for researchers, a conceptual fix is required to ensure they behave logically across both transient and steady-state conditions, allowing for more reliable predictions of landscape evolution.
Read the full video transcript
Well, good morning. And as you can see,
it's a little bit of a surprise that uh
I'm speaking first today. Brian couldn't
be here. So, um at least I'm talking on
a topic that Brian has worked on a lot.
Um many of you that that know me have
commented or asked,
why are you here? Why are you giving a
talk? You are not a modeler. And that is
still true. though uh CSDMS and LAN lab
played a really important role in my
research and uh in my teaching using the
the modules and bothering a lot of your
staff to help me figure stuff out as a
newbie. Oh, and I should mention uh
Annie uh Thompson who's here my
co-conspirator in putting this together,
but she never got a chance to see the
talk, so it's all my fault. She has a
nice organ poster for you, I think,
tonight. All right. So, the topic is how
do rivers cut their way down through
rock? And one of the things they have to
do is they can't they don't only have to
cut their way through rock. They got to
transport all the sediment away.
Sediment can provide tools to increase
erosion. We're not going to actually
talk about today. Today, in many
environments, the role they play is by
blanketing the bed and inhibiting
erosion. So, this something we've
actually known about for a long time.
Gilbert talked about it back from his
work in the Henry Mountains. Um, and
Alan Howard kind of nailed the problem
in about 1980 describing in general
that you can have a whole slider between
what we call detachment limited
situations where the incision into the
evolution of the bedrock channels is all
about eroding the rock. So those are
cases where the sediment transport
capacity is way higher than the sediment
supply. So it's generally a clean bed.
At the other end of the spectrum, the
sediment transport capacity is about
equal to the sediment flux and you get a
transport limited system. So we're going
to look at at these kind of problems.
And on the detachment limited end, at
least those of you that that play in
fluial landscapes would be very familiar
with the stream power incision models.
This K and roadability coefficient area.
A is the drainage area and S is the
local slope. M&N are fixed uh exponents.
So it's been around for quite a while
and then about late 90s people started
worrying about the role of sediment a
lot of inspired by Gilbert's early work
and some of Alan Howard's early work as
well to recognize that that coefficient
of erosion is actually a function of the
sediment flux and this f ofqsclar
proposed that as you go across that
slider of sediment flux is near zero or
the sediment capacity is much higher
than the sediment apply to QS over QC
equals 1, we get to transport limited,
you would just have a linear decline. So
the more sediment there is, is more it's
inhibiting erosion. Okay? And so this uh
kicked up a model that we called the
linear decline model. Uh Greg and I from
a paper in 2002, Nicole had a nice paper
looking at this and other models back in
2006.
um where you have just that linear
decline described in that term in
brackets. That's what we call the cover
term. All right. So with that context,
there have been quite a few new models
trying to handle what do we do with
sediment flu uh involvement in bedrock
incision. And you know my role I've
never been a modeler, but I'm the one
that bugs the modelers, right? So I'm
always my role has always been try to
okay, let's dissect this. Let's figure
out exactly how it works and let's try
to break it. Okay, so I'm here to say
that I found a way. I broke one of our
my favorite models, but I know now how
to fix it as well. Um well, it turns out
uh all of these models can actually be
reworked. Spend a little time doing the
algebra back into the exact same form as
the linear decline model where I've just
made the K in red because it's different
in each model. And I got this little F
factor that pops in there. That's only
one model has something that f factor
and we're going to talk about that.
That's the source of its issues. All
those same models can also be rewritten
into this form that you if you're
familiar with this literature, you've
seen it a lot. So you basically that
bracketed term that's the cover effect
that you can rewrite those same
equations and you'll have an erosion
term that looks just like the stream
power incision model is minus a
deposition term. Okay, so all those
models can be put in either format and
rather than walking through each one,
I'm just going to break all the rules
and just have this slide covered in
equations. Okay, but I figured this
group is the one place I can probably do
that. So the SQ model from DV and log
just has those particular values of that
K and that G um following you on at all
to to call it G. fastcape G just a
different K otherwise the same um I
guess I should back up and mention KD is
the erosion of rock ks is the
erodability of the sediment okay so it's
a big kind of a fundamental adaptation
of that uh uh ka ta model to apply it to
incision bedrock then her garden shared
stream power model that one has just
slightly different values it's
fundamentally difference in the in the G
value, but I'm going to talk about those
in a second. Well, then kind of my
favorite model that unfortunately I've
been able to break the space model. It's
the best in the sense that it's the only
one that keeps track of the role of
sediment, keeps track of the sediment
separately. How thick is a sediment
pile? All of these can deposit. If that
if that deposition term is greater than
the erosion term, you actually grade the
bed. However, in all these models, they
treat that degraded material as if it's
rock.
So, you're kind of violating all kinds
of stuff. If you had a sediment, if you
had an accumulation phase and then
reinced
is more erodable and keeps track of
where the sediment is. And so, it can be
written the same form. That's the one
took me a long time to figure out. It's
kind of obvious when you realize it
could be uh complex form for what the K
is a much more general K. Now,
interestingly,
space at steady state collapses to a
different looking form. And this is the
nature of where where you can break it.
For transient dynamics, that G, the
thing that sets the balance between your
erosion deposition terms, that value of
that G, that tells you are you
detachment limited, are you transport
limited?
in for a transient problem that's
controlled by this VS over RS. That's
the supposed to be the sedimentation
rate, the settling velocity and the rate
of rainfall. But at steady state, it
takes a value that looks like one of the
other models. It's a fundamentally
different control on what's happening at
steady state and whether you've got
transient dynamics. So that's what we're
gonna dive into to real. I do want to
start with just a comment on this is
this slider what controls that slider.
So in many of these models it's the um
settling velocity of sediment divided by
the rainfall rate which is kind of
nutty. I mean I it took me a long I
really have not been able to swallow
this. Um it's an effective parameter
because it does let you go from
detachment limited to transport limited
but what does it mean? So if you take
that settling velocity is order 1 meter
per second. Okay, you can argue about
the details but it's something like 1
meter a second for gravel. Rainfall rate
order 1 meter per year. So the value of
that is 10 million.
And it turns out as soon as it's 100,
you're totally transport limited. So all
these models if taken literally say
always always they're all transport
limited. We know observations feel
that's not the case. There's many
behaviors that indicate you're somewhere
on that spectrum towards detachment
limited. Um so I do think that it
creates a false impression because it
makes you think rainfall rate really
sets like wetter places are going to be
more um detachment limited and I don't
think that's true or at least we don't
know whether that's true. Um so a more
sensible one is the one that comes out
of the shared stream power model. the
coefficient of erosion versus the
coefficient for transport. That's
ultimately what works. Okay, so let's
just take a look at these. Just a
reminder,
what is this G value? And it's different
for some models. I'm showing you for the
shared stream power model that Annie
developed, ran that code. And on many
plots, I'm going to show you the
elevation profile, right? This plot.
Then also show you the channel steepness
against distance. So the channel
steepness is the local slope corrected
for the drainage area. And what you see
if I have it a low value of G, it's
detachment limited. And you can see you
have this discrete nick point that goes
sweeping up the system and therefore
kind of a stair step, a step function in
the channel steepness.
Now if we do the same thing, so this is
just a channel starting at a low initial
case increasing the uplift rate by a
factor of five. If I have a mix case and
this is something we showed way back in
2002, you have an initial nickpoint move
through the system and you can see those
nick points here or in the KSN a big
step and then it changes over and
becomes transport limited and becomes if
you see Nicole's nodding because this is
stuff she also did in a lot of her
modeling to show the ramifications of
some of this. And if you just bump that
G up to 10, you're almost fully into
transport limited conditions. All right,
so very fundamentally different
behavior. So what's happening? This
complex figure is trying to capture a
lot of things.
The fundamental thing that's really
controlling are you detachment limited
or transport limited is that ratio of
the sediment flux the sediment carrying
capacity. That's really what it comes
down to. That's controlled in these
models by the value of G. So uh the G is
on a log scale here and for just normal
at steady state it's the black line and
just makes that nice sigmoidal. So you
can see once G is as low as a 100th you
really your QS on QC is at zero. At one
you're at 50%. Right? They're about your
ability to transport sediment and your
ability to erode the rock are equal. And
once it gets up to 100 you're all the
way bas basically just sediment
blanketed. Well in a transient what
happens and if you've read some of
Nicole's early work you're going to know
this. Let's just do a case of uplift
rate increase. What happens? The channel
steepens at the outlet, but the whole
cachement hasn't responded yet. That so
the QS on QC goes down, shifts you down
to here. So it's effectively the same as
if your GH changed during the transient
by a factor of 10 for this factor of 10
change in uplift rate. Anyway, so maybe
I don't want to belabor that one, but um
generally if you increase uplift rate,
your system becomes more detachment
limited. And if you decrease uplift
rate, it becomes more transport limited
during the transient.
Now let's look at what goes wrong with
the space model. Okay. So in the space
model, well first let's just look again
at that normal case. I'm going to take a
case where I use a G value of 100. So it
should be fully transport limited.
There's going to be no nick points.
Okay? And so if I keep the erodability
of rock and roadability of sediment the
same or I use one of the other models
that assume that anyway I'm going to be
on the solid black line. This one I just
showed you on the last plot. And so if
I'm at GH of 100 means I pop up there
and my QS on QC is near one. I'm
basically transport limited. However, if
I use just a factor of uh a thousand
difference in the roadability of
sediment to rock, which is not an
extreme value, I think it should be that
or more. Um then I can be right there
and that same thing is going to be
transport limited but have only 10%
cover of sediment on the bed. So
everything you see in the field is going
to look like a detachment limited
system, but it's still going to behave
in a transport limited way. I've kind of
got a lot overloaded in here. So it's
basically shift that all over to there
as if the G value was a thousand times
less.
I'm not going to belabor this show a
number of different ways. I can let you
guys look at that. But to finalize on
this, I know I'm blown through that. I
spent so much time building those
animations. Um
but of course I overloaded my talk like
anyone's need always, right? But anyway,
um
the the trick is that there's a G value
that you set that sets whether it's
transport limited or not and then G
times the ratio of KD to KS that
dictates how thick the sediment is and
what the QS on QC ratio. So you break
the link between those two that
intuitively should be there. So let's
look there are some actual consequences
of this. Even at steady state there are
consequences of this. So this is a
steady state where I just have an uplift
rate boundary right there between a low
uplift and a high uplift upstream. Okay.
And if we just look at the upper plot on
here, this is a case where I left
sediment and rock and roadability the
same. So space and other models like the
shared stream power model are identical.
Okay. Now space additionally the red
line is the top of the bedrock. So it
shows you the thickness of sediment and
I've just exaggerated it so you can see
it in this plot. So it's thick sediment
downstream. So all that extra erosion
upstream. Right now if I just keep
everything the same but make KS more
erodable than KD that just changed the
slope. So I've adjusted things. So I
have the same slope in the upstream
part. The slope downstream is way less
because the that KS greater than KD
gives me a basically a high transport
coefficient. So I got a low sediment
flux, got a thin aluvial cover and a
much lower transport slope. So it's a
completely different channel profile,
completely different relief in the whole
catchment
because of that disconnect happening
there. Okay. Now, other thing I want to
test to really show you where it really
breaks is um if you remember this case I
showed you before for a mixed bedrock
channel subject to an increase in uplift
rate, there should be an initial nick
point that covers about half of the
change in channel steepness and then a
really diffusive gradual increase. You
can see on both those plots. So let's
imagine a scenario
um
one that Nicole and I actually tr
struggled to model a long time ago um
of initial low relief channel that has a
thick pile of sediment
and what happens when I then trigger a
pulse of uplift through that. So I'll
make a 200 thick meter pile of sediment
and I'm going to put it through that
same process. So here it is. I start it,
right? I'm in sizing into 200 meters of
sediment. It's got to be transport
limited. But in the space model, if I
had G at one, it's going to behave like
a mix model even though it's incising
through rock. So it gives you that
initial nickpoint response.
And then it does a really this is just
the first 10 time steps and then the
next time steps does a really wacky
thing of where the channel you get this
downstream. This is going from blue to
red through time across with time.
You've got a nickpoint going sweeping
downstream.
And that's as the rock is getting almost
exposed to the surface as you're
stripping the sediment off and starts to
change behavior so that it's um anyway
it's a really bizarre little response
and then when the rock is finally
exposed at the outlet then you get a
nickpoint sweeping up through the system
of it steepening up. So kind of crazy
behavior that happens in this model. Um
so let's just pop forward a kind of
We can fix this by
first off I can achieve the say this is
the same plot I showed you before. Let's
zoom in on here and I'm going to fix all
of the other models by adding the
ability to track sediment depth first
off. So this is just a plot showing you
the black lines on top are the shared
stream power model. Now with a component
an element added to track the sediment
thickness and it matches space exactly
where KS and KD are equal to what are
equal. Um that's my boundary between
those two. Now I can force it in a
little transient where I step the uplift
rate boundary downstream. Do a little
crazy thing. I'm I'm of course way out
of time, but the thing I just want to
emphasize, there's a complicated pattern
that happens. I move the uplift rate
boundary to there. So now I'm moving
that sediment, thick sediment up and
eroding it off. The two models with no
difference between rock and sediment are
identical. The black dash lines are on
top of the colored lines. I guess is all
you can really see right now. But I can
also add that sediment is more easily
erodable into this kind of model. And
then you'll see so in this case the
black lines are the case where they were
equal. The blue line is the surface in
the case where they are not equal. And
the red is the
uh the bed surface where they're not
equal. So in that case you don't get as
much of a step. You're eroding it faster
as you carve down into that sediment.
Anyway, not enough time to really
explain what's happening there, but
let's just pop past that.
So, we can do the same experiment with
this other model, which we can do this
fix in space, and I've talked to Charlie
Schau about that, and we're going to
work on that. We start with that same
initial lowleaf landscape, uplift it
through the 200 meters of sediment, and
the first time steps here, you can see a
perfectly transport limited response.
There's no nickpoint in the system
anywhere. The channel steepnesses are
just broadly increasing mostly at the
downstream end and then propagating
upstream. A very transport limited
response like you might expect. And then
as soon as you start exposing rock near
the outlet, you get a nick point that
goes propping up propagating up through
the system. And then eventually oh this
is actually now that so that's all I
wanted to show you for that evolution.
And this is the sediment depths plotted
down below. So in the first phase,
sediment depth is just decreasing,
especially at the outlet. By the time
it's thin enough, that's when you get
into the second phase of the nickpoint
actually sweeps up. Anyway, you can have
it all and not have any of the problems
that were um
exposed. So I'm out of time. I'll just
throw up the conclusions for you to have
a look at and uh hopefully that was at
least moderately amusing to get you
started on your day.
>> Thank you very much, Kevin. Um we have
time for one or two questions
if there are questions.
>> Um so I following
you're varying the ratio
to
right but then
is that correct
>> that's correct because they are separate
in the model
oh I should repeat the question Nicole
was asking you are varying the ratio of
sediment erodability to rocket roability
independently from the G parameter that
determines the model is transport
limited or not and yes and the answer
was yes because that's encoded into
space that it has to be that way
but it's not
like a real
gra
second you can't set it that way, but
technically satellite velocity would
think would be tied to
the chaos.
So, this is something
you can sort of one or the other and get
>> they should be drawn together. And this
is what sent me on a a year of headaches
working with Annie. We knew what should
happen. It shouldn't it should be a
whole like non-dimensional number. You
can either change KSKD or you can change
VS over R and you should get the same
thing. But then it didn't happen. And it
finally it's because of just the
original derivation of the model built
on the CQ model that VS overall sediment
velocity relative to rainfall that
dictates the transient dynamics no
matter what independent of that KS and
KD ratio. The KS and KD changes the
slope. It changes the steady state
sediment flux all this kind of stuff. So
then it it just breaks apart and doesn't
behave like the way it should. But it's
easy if you go back once you recognize
all the models like can be thought of as
a variance of the linear decline model.
If you kind of go back to the beginning
of space and reset let's define it from
there and go forward those things will
all be uh linked together and everything
will behave beautifully. So I believe a
space 2.0 or 3.0 know whatever it's
going to be will do all the beautiful
things that it does and won't have any
of the weird behavior that we managed to
uh squeeze out of it.
Even though they're not
chaos and what you call cheap
in the Right.
>> Yes.
>> It ought to.
>> Yeah. Except it doesn't work because
that's what we thought and we set off
down that path that just will everything
be fine. But cuz in the end if you're
running a transient like a dynamic
evolving thing it's just VS overr
uniquely they control it.
So that that's the thing but it's easily
well I don't know if it's easily fixed
numerically but it's easily fixed
conceptually.