 final talk of the day, which is from Lawrence Vules, and who will be talking about the distribution of lake sizes in Arctic deltas. Hey, good morning. Thanks for introducing me, Professor Moriartri. So let me hide this thing. So yeah, my name is Lawrence. And thanks for being here today. I'm going to speak about the distribution of lake sizes in Arctic deltas. So briefly, why we care about these lakes. Well, Arctic deltas are uniquely characterized by abundant lakes, whereas temperate deltas are not. So this is the Coville River delta here in Alaska. And for reference, and this is the Wax Lake delta, which is in the Gulf coast, sorry, the Gulf of Mexico. So you can see all these lakes that you don't see on other deltas. And little attention has been paid to what the distribution of lake sizes, like the distribution of lake areas is, and what processes might generate the underlying that observed distribution. And in general, that's important if you have lake size parameterized, especially as a nonlinear function in a land surface model for energy budget or methane budget. And also, rapid warming of the Arctic is leading to changes. But it's not exactly clear what those changes are, the magnitude of the changes or the time scale of the changes. So the two questions that we're going to be asking today and addressing are, what is the lake size distribution? And are the distribution characteristics related to climate or hydrogeuro morphology? And these are a couple of the deltas that we studied. So the seven deltas that we studied are pictured here, ringing the Arctic circle. And we go from the McKenzie going in this little circle all the way down to the NSA. So the data set that we use to analyze the deltas is called the global surface water data set. And it's a landsat derived, so it's 30 meter spatial resolution. And it's monthly composited water masks. So you composite several landsat masks to generate a monthly image, so like a July image for a given year. And this is an example of the water masks here over the Kalima Delta. And white shows water and gray shows land. Now, if we went to another year, landsat seven striping and cloud cover make it so there's a lot of no data. And extracting accurate lake or water body areas is really difficult to do when you have all this no data. To extract the water bodies, I'm going to hop over to the schematic, which we'll be revisiting. We identify the connected components of water pixels shown here in blue and ignore the land, basically. And we do this for the summer because you want to minimize the amount of flooding that's on the landscape because we care about lakes and not about all the ephemeral inundation from snowmelt. So we go back to the Kalima and we have extracted these. We've overlaying the water bodies that we've identified in pink. And we look at the histogram of water body areas. And in the literature, people since over the 20th century have hypothesized, well, OK, lakes have power law distribution. They may have a log normal distribution. They might be because you have inundated landscape. And the water body area is not power law and it's not log normal. So that kind of begs the question of what is the water body area PDF? And one thing that's going on, though, is that when we look at the water bodies from this water mask, it includes both wetlands. So areas that are simply wet ephemerally because it's kind of wet that year, and it's rather perennially inundated lakes. And these lakes are generally thermocarsal lakes, is what we're interested in. And the question is, how do you separate the two in your analysis? So the GSW data set that I mentioned, it's actually a temporal stack. So it's from 1999 to 2018, it generates these monthly masks. And we're going to utilize that information to separate the two classes. So imagine we had a given year and then we come back to the schematic, right? We could extract our water body as these six pixels. And we observe it again next year. And there is, now this is land. And maybe that's because the shoreline moved a little bit or it could be a little dry that year. And we go to year three. And all of a sudden, there's a no data pixel for whatever reason from an observation. And we go to year four. And we might have a little uncertainty in how we call the water body, but let's just say we wanna know how often water was present at every point in the landscape. So we take the vertical average here through time. We define the pixel water occurrence, okay? And the pixel water occurrence is the fraction of years that a pixel was classified as water. Yeah. So for this point, you'd have 75% water occurrence everywhere else is 100% water occurrence. You discard the no data, so it's like you didn't have an observation that year. And here you have a 0% water occurrence. Then we go to a year that has really good data quality, like the one I showed you earlier for the Kalima and you outline your water bodies. You then impose that water body mask on the occurrence, pixel water occurrence. And we compute the mean of the pixels and we call that the water body occurrence. So this water body that we identified in say 2016 has a water body occurrence of 96% in this case. Then you simply take a threshold and you say, and we say if the water body occurrence is above theta, it's a lake, if it's below theta, it's a wetland. And in the analysis I'm gonna present, and the results I'm gonna present, we use a theta of 0.85. So if a water body has an occurrence of 85%, it's a lake and that allows for some ephemerality on the edges. And if it's below, it's a wetland. And we do sensitivity analysis and our results are all robust for a range of thetas, at least from 80 to 90%. Okay, so come back to the Kalima and we have this occurrence map that we generated. And here are some examples of lakes versus wetlands. And blue here is water or 100% occurrence and brown is 0% occurrence of its land. And we come back to the histogram earlier and we can decompose the histogram into fractions of lakes versus fractions of wetlands as a function of area. And we see that obviously these two have different fractions of smaller water bodies or mostly wetlands. And the thing is if we wanna study the size distribution, we need to go directly to the PDFs, right? And the PDF is the probability density function. So we want what's the probability density function of lakes. So each of these curves is normalized area under the curve one. And I'm gonna focus on the lakes today and I'll simply tell you that the wetlands have a very different size distribution. So coming, we're gonna move that plot over to the left now and we look at the PDF and we say, well, that's an interesting looking PDF. And we look at the exceedance probability and we say, what if it's a log normal distribution and we fit it and it's fit and it's significant at the 90% level? There's a truncation parameter here because we don't look at water bodies less than six pixels because we don't trust their area. And we've managed to fit a log normal distribution on the Kalima. If we go back to all seven deltas and I'm not gonna show the fitted distributions here because it would look terrible. And we look at all seven curves here, all seven PDFs and all seven exceedance probabilities, all seven deltas have log normal distributions of lake areas. So once we control for ephemeral water bodies, we are able to detect a log normal distribution of lake areas on Arctic deltas. Furthermore, I've colored these according to delta latitude at the apex of the delta. If we look at these seven deltas, we could qualitatively observe that but as you get further north, it seems that the distribution has shifted further to the right. If we pull up the mean lake area and plot it versus latitude, we observe a weekly significant trend in mean lake area. So the mean area trends with latitude is 10 to some small coefficient and that means as you go over about five degrees latitude, lake area increases by about 30%. And this again is a weekly significant relationship. So this, we're not 100% sure why. We have some hypotheses that the further north you are, the longer lakes are able to be sustained on the landscape and there's greater ice content and this is something we're investigating further. So why the law, and I'm gonna step back now and say why the log normal distribution and why does all the deltas that we analyzed have a log normal distribution in the Arctic. Well, generally a thermocarse lakes grow via thermal abrasion of lakes shorelines. So if we assume that the growth of these lakes is proportional to the volume or heat content of the lakes, it's inversely proportional to the lateral surface area, we can show, and I have the equations hidden, that the area at a given time plus one is equal to a growth rate times the area at time T. Now, T is a random variable because we don't know the growth rate and it fluctuates from year to year and given a certain hydrologic climatologic state, some fluctuations in temperature, precipitation, soil properties, et cetera will be random, right? So if you integrate this to a long time T, this is a known proportionality model and it leads you to a log normal distribution and that's why we observe the log normal distribution and this was originally proposed by Viktorov for an English version of the paper it's in 2015. So in summary, we present this water body classification technique to distinguish perennial lakes from ephemeral wetlands using the global surface water time stack. Lake areas in Arctic belt is our log normally distributed and it's explained by this proportional growth model of thermocarse lake expansion. And lastly, there's evidence for increasing lake size with delta latitude, which we think is related to lakes being able to stay in the landscape longer and there being greater ice content the further north that you get. So thank you for your time and my email is below if you have any questions and I'll take any questions now. I see there's the chat is blowing up. Yes, we have a talk from Shelby who says or a question from Shelby who says great talk. That's interesting that you noted a subtle increase in lake area with delta latitude. I'm interested if you noticed or explored geophysical properties of the delta in relation to lake area, i.e. delta shape size number of active river channels. No, we've only so far investigated the lake size distribution on the deltas and we'll be following up on that but Anastasia Polurias at Los Alamos has done quite a bit of work and she had a paper in JGR this year exploring that. You can take a look at her paper.