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SUMMARY:The equations of landscape formation:  review and a new model - Al
 exander Chen (SAMSI\, University of North Carolina)
DTSTART:20130411T140000Z
DTEND:20130411T150000Z
UID:TALK43963@talks.cam.ac.uk
CONTACT:Carola-Bibiane Schoenlieb
DESCRIPTION:In this talk\, we start by reviewing some models for\nlandscap
 e evolution\, many of which are hybrid models\, combining\nfundamental phy
 sical laws with empirical modeling. Such models can be\nvalid near equilib
 rium. Nevertheless\, this situation is not\nsatisfactory from the mathemat
 ical standpoint\, since such models will\nbe valid only for a given landsc
 ape or class of landscapes.\n\nWe propose a simple landscape model\, deduc
 ed from mathematical\nprinciples\, coping with the main features of all mo
 dels. This model\nsingles out three spatially distributed scalar state var
 iable\, namely\nthe landscape elevation\, the water elevation\, and the se
 diment\nconcentration in water. These state variables are linked by three\
 npartial differential equations. Two of these equations are mere\nconserva
 tion laws. A third equation copes with the three main features\nidentified
  in the literature as the main phenomena shaping a\nlandscape:  erosion\, 
 sedimentation and creep.\n\nNumerical results show that a variety of commo
 n landscape features can\nbe reproduced. Furthermore changing various para
 meters in the model\ncan alter the morphology of the landscape and the var
 ious features\nobserved\, even for the same initial landscape. The conject
 ured\nmathematical instability and non-uniqueness of landscape evolution i
 s\nillustrated numerically. On the other hand numerical stability of real\
 nlandscape topographies under realistic values for their evolution is\nals
 o observed. Lastly\, the model presented also shows promise in the\nfield 
 of channel network restoration\, as river networks tend to become\nsharper
  with the proper choice of parameters in the erosion model.
LOCATION:MR 14\, CMS
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