Functions that define an y-property as a function of the one-dimensional x-coordinate. 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 transition
y=y0+(y0-yinf)*exp(-max(0,(x-x0))/xa
p.lin
: linearly decreasing transition
y=y0 ; y=y0-(y0-yinf)(x-xl)/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 transition
y=yinf+(y0-yinf)exp(-(x-xL)/(0.25xatt)) / (1+exp(-(x-xL)/(0.25xatt)))
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x |
the x-values for which the property has to be calculated. |
y.0 |
the y-value at the origin |
y.inf |
the y-value at infinity |
x.L |
the x-coordinate 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 |
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.
the property value, estimated for each x-value.
Filip Meysman <filip.meysman@nioz.nl>, Karline Soetaert <karline.soetaert@nioz.nl>
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