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Conceptual Models and Paleoclimate Fall Schedule 2016

We meet this semester on Wednesdays from 1:00-2:00 pm Eastern time. 

Wednesday, October 19th, 1-2 PM eastern time: Kaitlin Hill presents. Here is the webex link for the meeting https://renci.webex.com/renci/j.php?MTID=m902b1284d4907c673b6df5e7e7298801

Title: Energy Balance Models, by North, Cahalan, and Coakley

Abstract: I'll give an overview of North, Cahalan, and Coakley's 1981 survey paper, through Section 3 (pp. 91 to 102). I'll focus on the different types of energy balance models they analyze and their general results. If there is time, I would like to compare their results with those of the more recent 2015 paper by Wagner and Eisenman.

Kaitlin's slides: https://mcrn.hubzero.org/groups/conceptual/File:Kaitlin_North_Cahalan_Coakley_2016_10_19.pdf

Wednesday, October 26th, 1-2 PM eastern time: Dave Camp presents, Part I. Here is the webex link for the meeting https://renci.webex.com/renci/j.php?MTID=m0a77561a00fec2d1d36259901b866878

Title: Modeling Glacial Cycles: Open Questions and Interesting Dynamics

Abstract:  The glacial cycles of Pliocene and Pleistocene provide a rich environment for investigating the use of conceptual models to test physical hypotheses. The observational records contain features for which many distinct sets of underlying processes have been proposed. Therefore, there are many competing low-complexity models for such phenomena involving a wide range of mathematical approaches. A key question therefore arises: how can we use the sparse data records to select amongst the myriad models? More precisely, how can we isolate the empirical information used to tune a model from that which is used to validate a model?  A number of fundamental mathematics issues can impede our ability to address these questions. For example, many of the low-complexity models display a sensitivity to character of external forcing (both dynamical or stochastic.)

The Mid-Pliestocene Transition (MPT) provides a useful test case to explore these issues. I will give an overview of some of wide range of conceptual models for the MPT and show some recent work in using model-data comparison for model selection. I will also discuss recent work in how the underlying geometric structure of such models interacts with periodic deterministic forcing and with stochastic forcing.

Wednesday, November 2nd, 1-2 PM eastern time: Dave Camp presents, Part II. Here is the webex link for the meeting https://renci.webex.com/renci/j.php?MTID=m49832e1cda46c7921bedc4d95356a546

Wednesday, November 9th, 1-2 PM eastern time: Jim Walsh presents. Here is the webex link for the meeting https://renci.webex.com/renci/j.php?MTID=me160d3ce34cbb0d7616fa34a6e812f31

Title: Diffusive heat transport in the Budyko-Widiasih model

Abstract: We pick up where Kaitlin left off in her presentation on October 19th (an overview of North, Cahalan, and Coakley's 1981 survey paper (twigs?)). We then incorporate diffusive heat transport into Budyko's model when coupled with Widiasih's ice line equation. We compare and contrast previous work on this coupled model with the diffusive heat transport approach. Time permitting, we present a nonsmooth system arising when modeling the great glacial episodes of the Neoproterozoic Era with diffusive heat transport in the Budyko-Widiasih model.

Jim's slides: https://mcrn.hubzero.org/groups/conceptual/File:Walsh11092016.pdf

Wednesday, November 16th, 1-2 PM eastern time: Group discussion. Here is the webex link for the meeting https://renci.webex.com/renci/j.php?MTID=m47a5c14ca1a8beff3ea018b8eab89535

Wednesday, November 30th, **12 noon - 1 PM eastern time**: Hans Engler & Hans Kaper present (Part I). Here is the webex link for the meeting https://renci.webex.com/renci/j.php?MTID=md541f31bb3e518da71c1a77b6ecf6331

Title: A dynamical systems approach to the Pleistocene climate - Part I of II

Abstract: In 1990, K. Maasch and B. Saltzman introduced a three-dimensional dynamical system to explain the glacial cycles of the Pleistocene Epoch. The model incorporates interactions between the Earth’s oceans, atmosphere, and cryosphere. They showed numerically that a particular slow drift of some of the system parameters, together with orbital forcing, can result in system behavior that exhibits the mid-Pleistocene transition to large-amplitude limit cycles, plausible temporal wave forms for ice and CO2, and correct phase relations between the system variables. 

In this presentation, we briefly review the Maasch-Saltzman model and show that a reduced two-dimensional version of the model already exhibits the most salient dynamical features of the full model. In particular, we show that there exist large-amplitude limit cycles in a large portion of the parameter space.

Hans' slides: https://mcrn.hubzero.org/groups/conceptual/File:MCRN-Paleoseminar-2016-1.pdf

Wednesday, December 7th, **12 noon - 1 PM eastern time**: Hans Engler & Hans Kaper present (Part II). Here is the webex link for the meeting https://renci.webex.com/renci/j.php?MTID=m81f12b75c87d4361658d09869ea86a88

Title: A dynamical systems approach to the Pleistocene climate - Part II of II

Abstract:In this presentation we continue the analysis of the Pleistocene climate model proposed by Maasch and Saltzman, focusing on the original three-dimensional dynamical system. We show that the observed mid-Pleistocene transition to large-amplitude oscillations can be triggered by two different mechanisms, namely the delayed loss of stability of a critical point or the disappearance of a weakly unstable critical point. Both mechanisms are due to a single slowly varying parameter.

Hans' slides: https://mcrn.hubzero.org/groups/conceptual/File:MCRN-Paleoseminar-2016-2.pdf