GLEON Metabolism 1
GLEON WORKING GROUP
These tasks are associated with one subgroup under the GLEON Metabolism 1 Working Group, better known as the Catchment-Lake Age-of-Carbon THEORY Subgroup .
Participants: Tom Harmon, Paul Hanson, Gopal Bhatt, Stuart Jones, Sam Oliver, Hilary Dugan, Roxanna Ayllon, Yang Cui
===Workflow=== (outcome of G16 breakout sessions)
- Develop Conceptual Model [Tom, Paul, Gopal]
- Paul and Gopal reach out for AoW code
- Translation to r-coding: AoW to rAoW (ruh’ ow!) [Stuart, Sam, Hilary, Gopal]
- Lit. review targeting carbon transformation rates [Roxanna, Yang]
- Define model space [Sam]
- Lit. review of prospective study gradients [Roxanna, Kevin]
- Gradient Sensitivity Analysis (TBD at later date)
Skype Mtg #1 (12/30/14)
Attendees: Tom H, Kevin R, Stuart J, Hilary D
Summary - At G16, we decided to attempt to develop and use an Age of Carbon approach based on Duffy (2010), and use it to explore lake metabolism-catchment connections. In this Skype meeting, we revisited the method and Tom noted some good papers to read for people who want to come up to speed on the approach. Then, we discussed our approach to exploring the solution space of the "age" models we plan to develop.
The method is based on moment analysis, and results in relatively simple expressions (mathematically) for quantifying the age of water in idealized watersheds. Although Duffy (2010) opens the door to reactive transport, he stuck mainly with the age of water or conservative tracers. We decided to try to (1) reproduce the first two cases in Duffy (2010) and (2) extend the analysis to include 1st order decay of organic carbon constituents. The two cases involve a simplistic watershed characterized by a volume V and flow Q, and a similar but slightly more complex ideal watershed characterized by a mobile (Vm) and immobile (Vim) volumes--we decided that his might be one level of complexity that would be interesting to explore. Stuart and Tom are starting to work on the equations and Stuart (post-meeting) had some luck getting started with developing the solutions in Mathematica). Eventually, we may wish to develop R-scripts.
In terms of the solutions space, we discussed a broad approach associated with exploring key lake-catchment parameters. Kevin suggested the Wisconsin LTER lakes as a good set of lakes because they have long-term data on both the lakes and the catchments, and there is a reasonably good variety between Northern and Southern Wisconsin in terms of land use, vegetation, soils and geology. We decided to go with this suggestion and Kevin is getting some data organized. --Tom Harmon (talk) 12:23, 7 January 2015 (PST)
NOTE: Chris and his group have a good page on this site chronicling the approach in the paper and extending it: http://www.organicdatascience.org/ageofwater/index.php/Develop_mathematical_model_of_age_of_water_and_carbon#Concept
Post-Skype Mtg #1 Development
Paul requested the Mathematica scripts from Chris Duffy, and Chris is happy to help. Chris requested that Tom and Gopal sit in on their (Paul, Chris and Yolanda Gil) Organic Data Science project meeting. This will be an opportunity to learn a little more about Chris's analysis and we can fill him in on our proposed approach (and get some good feedback!). --Tom Harmon (talk) 12:23, 7 January 2015 (PST)
Skype Mtg #2 (02/18/2015)
Attendees: Tom, Paul, Stuart, Sam, Hilary
Summary: Stuart described version 1.0 of the the r-Age of Carbon (r-AoC) script and made the script available to the working group. Version 1.0 (based on Duffy 2010) currently includes:
(1) A conservative tracer model that doesn’t consider age; to remind myself and anyone else how these work; (2) The conservative tracer model that includes Chris’s age moment; (3) An adaptation of #2 with a first-order decay added; and (4) A model that allows for dynamic control volume, first order decay, and events in inlet discharge or concentration. This last model (4) is a general model that can recreate the special cases #2 and #3 above. With the decay parameter (d) set to zero, model (4) can recreate figures 2, 3, and 4 from Duffy 2010.
Stuart also mentioned that it may be a relatively straightforward extension of the script to enable us to add more 'compartments' to the model (e.g., epilimnion and hypolimnion, fast groundwater and slow groundwater, etc.).
Most of the group remarked that they were still digesting the "age" approach in Duffy (2010), and we charged everyone with practicing with r-AoC and, using the Wisconsin LTER lake-catchment data compiled by Kevin, try to come up with some potential applications of the AoC approach.
Paul suggested, and we all agreed, that once we become more familiar with the approach and r-AoC, we could try to gather for a concentrated effort/workshop aimed at crafting some research objectives, sorting out tasks, and making a leap in progress. We also agreed that it would be great to involve Chris Duffy soon to help with ideas and directions.--Tom Harmon (talk) 19:31, 25 March 2015 (PDT)
Skype Mtg #3 (03/25/2015)
Attendees: Tom, Sam, Hilary, Roxanna, Kevin, Paul
Summary: Picking up from the previous meeting, a couple of us presented what we had been able to get done with r-AoC.
Sam noted that there were some errors in the LTER data summary spreadsheet; Kevin will revisit that and resend the spreadsheet.
Sam ran r-AoC for several of the LTER lakes, and we talked through the results, mainly trying to get everyone a feel for the model output (focusing mostly on concentration and age time series outputs). Sam posted the plots from these simulations as .pdf files (see Task tree at top of the page: Decay examples).
Tom ran r-AoC for the catchment side of the problem. He first developed a simple expression for catchment turnover rate (inverse of residence time) based on Darcy's Law. The approach assumes the groundwater (GW) gradient is the same as the ground surface gradient, and that the soil permeability is applicable for groundwater (homogeneous sediments). These two parameters provide the 1D GW flux and that flux divided by a horizontal travel distance provides a rough estimate of the catchment residence time. For the horizontal travel distance, he proposed using the 0.5*sqrt(TrW_Area), where TrW_Area is the catchment area (so roughly half the distance to the lake in a square basin--we can obviously do better than this using GIS tools if we think it's fruitful to pursue). The estimated residence times for the LTER lake catchments ranged from 1.6 years (Big Muskellunge) to 541 years (Mendota) [note: these are quite different from my verbal report (conversion error!) and seem a little long(?)--need to be rechecked]. Tom did not yet post his methods and results, but will do so well before the next meeting.
The group feels like there is some interesting science to be done using the AoC approach and will continue to develop ideas and test simulations. We recognized that we are deficient in terms of key parameters like the carbon decay constants (d). Roxanna is going to start a literature review in this area, looking for other estimates or approaches to making these estimates for temperate lakes and catchments. Hilary will try to point us to some isotope papers that might help us come up to speed on the subject of carbon age in a catchment-lake system, and to constrain/check our model parameters. Paul added the point that we may end up turning this challenge around by using the model to inform hypotheses about carbon ages.
We need a repository for papers, so Tom agreed to share a Drop Box folder with everyone. Coming soon.
Lastly, we pushed the next meeting back 1 week to April 22 due to some travel conflicts (sorry about that! --Tom)--Tom Harmon (talk) 19:31, 25 March 2015 (PDT)
Skype Mtg #4 (04/22/2015)
Attendees: Tom, Hilary, Roxanna, Stuart, Paul
Summary: Discussion of literature review to date, and next steps with r-AoC modeling effort.
We started by briefly pointing out Tom's results from r-AoC for an idealized catchment, and whether this was looking like a reasonable approach. The takeaway was that it might be a reasonable approach, but there is probably a better way to estimate the length scale, which may be biasing the turnover rates to be a bit fast. Tom will explore the spatial data for a couple of the lake catchments.
Roxanna has started on the literature review. She is focusing on organic carbon reaction rates in lakes and catchments. She will post paper information on the wiki, and group members will let her know if they have trouble getting copies. More difficult-to-find material will be put in the group's Drop Box folder (everyone should have received an invitation to a shared folder--let Tom know if you need the link). One interesting paper is the one by Gergel et al (1999), which provides a broad look at DOC-lake connections in terms of watershed characteristics--good for everyone to have a look if they haven't seen this paper before. Roxanna and Tom are scheduling a side-mtg to discuss how to attack the literature from the r-AoC modeling perspective.
We spent the final part of the meeting discussing how to modify r-AoC to encompass different catchment compartments, such as groundwater, runoff (streamflow), and direct precipitation input to the lake. The notion is that r-AoC will incorporate boxes for these compartments, and these boxes will flow into the lake box. At this stage, we are avoiding connection/feedbacks between the catchment boxes. For example, we are assuming groundwater-stream connections are negligible. We will try to keep the model as simple as possible, but no simpler (to paraphrase A. Einstein). Stuart cooked up a diagram to capture our first stab at the conceptual model here: File:GLEON AoC 4-22-15.pdf. Tom will try to generate the equations for this conceptual model and pass them to Stuart for comment and revision. Then they will circulate to the group for feedback, and start on the code revisions.
Lastly, everyone was excited about the possibility of trying to get together for 2 or 3 days this summer/early fall (winter/early spring for Roxanna!). If we can get the code and research objectives focused in the next couple of months, we think we could make a lot of progress in a concentrated effort together. Tom is going to look for some potential dates and will send out a Doodle poll soon.
Next Skype mtg is Wed May 20 at same time as usual: 9AM PDT = 11AM CDT...local times may vary! --Tom Harmon (talk) 11:06, 22 April 2015 (PDT)
Skype Mtg #5 (05/20/2015)
Attendees: Tom, Roxanna, Stuart, Hilary
Summary: Discussion of revised modeling direction and next steps in terms of good lake-catchment systems to examine with the revised model.
Advancing from our conceptual model here: File:GLEON AoC 4-22-15.pdf, Tom generated the equations for to describe (I)parallel 1D reactive transport (plug flow/no-dispersion with 1st order decay) of OM via (i) groundwater and (ii) stream pathways into (II) a well-mixed reactive lake model (also 1st order decay). The general idea is to look at rates of transport compared to rates of decay in order to get a feeling for which pathways will be most important in determining carbon age. The equations are here File:TH GW stream precip lake model.pdf. Stuart coded this up in R for this model. NOTE: currently no carbon age output from the model (working toward that)--for now, concentration time series output.
Here is a brief description of the R code (filename = GW_stream_precip_lake_model_5-20-15.R):
Lines 12-26: Define a custom function to be used with the numerical integrator that simulates a single time step of the model *currently the model tracks volume as a state variable, but keeps V constant (i.e. Qout=sum(Qins) *wouldn’t be hard to add a variable volume, but with the constant inputs currently used (see below) doesn’t make sense
Lines 28-39: Where parameters that I think we want to explore the effect of can be defined, including catchment area, lake area, mean depth, decay parameters, water input, surface-groundwater split, and initial GW and SW carbon concentrations
Lines 42-58: Calculation of derived parameters and definition of some other necessary parameters. Many of the parameters defined in this section are those that I would consider “regional”, rather than lake specific, including GW hydraulic conductivity, stream velocity, etc. There are also two very cursory functions included here that estimate groundwater and stream flowpath lengths from catchment area; one from a very simple conceptualization and the other from a paper.
Lines 60-68: Initialization of model parameters and initial conditions and then actually integrating the model (Line 68). If you mess with parameter values above, you will need to rerun line 60 if you want the parameter changes to be used when simulating.
Lines 70-73: Generates a very simple time series plot of volume and C concentration.
We decided that this summer everyone could try out the model and suggest improvements and/or new directions. We also decided to focus on a few Wisconsin LTER lakes for which there is good groundwater and stream information for flows, hydraulic gradients, and (intermittently) DOM/DOC/TOC/etc concentrations.
Next meeting: A few of us (Tom, Stuart) plan to get together at the Gordon Research Conference in June, including touching base with other prongs of the Metabolism WG effort (Beverley W., Denise B., etc).
