Common Properties with Distance, to be used with setup.prop.1D
Description
Functions that define an yproperty as a function of the onedimensional xcoordinate. These routines can be used to specify properties and parameters as a function of distance, e.g. depth in the water column or the sediment.
They make a transition from an upper (or upstream) zone, with value
y.0
to a lower zone with a value y.inf
.
Particularly useful in combination with setup.prop.1D

p.exp
: exponentially decreasing transitiony=y0+(y0yinf)*exp(max(0,(xx0))/xa

p.lin
: linearly decreasing transitiony=y0 ; y=y0(y0yinf)(xxl)/xatt ; y = yinf
for 0 ≤q x ≤q x_L, x_L ≤q x ≤q x_L + x_{att} and (x ≥q x_L + x.att ) respectively.

p.sig
: sigmoidal decreasing transitiony=yinf+(y0yinf)exp((xxL)/(0.25xatt)) / (1+exp((xxL)/(0.25xatt)))
Usage
1 2 3 
Arguments
x 
the xvalues for which the property has to be calculated. 
y.0 
the yvalue at the origin 
y.inf 
the yvalue at infinity 
x.L 
the xcoordinate where the transition zone starts;
for 
x.att 
attenuation coefficient in exponential decrease, or the size of the transition zone in the linear and sigmoid decrease 
Details
For p.lin
, the width of the transition zone equals x.att
and
the depth where the transition zone starts is x.L
.
For p.sig
, x.L
is located the middle of the smooth transition zone of approaximate width x.att
.
For p.exp
, there is no clearly demarcated transition zone;
there is an abrupt change at x.L
after which the property
exponentially changes from y.0
towards y.L
with attenuation
coefficient x.att
; the larger x.att
the less steep the change.
Value
the property value, estimated for each xvalue.
Author(s)
Filip Meysman <filip.meysman@nioz.nl>, Karline Soetaert <karline.soetaert@nioz.nl>
Examples
1 2 3 4 5 