# Hyporheic Exchange Model: Interface

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breed [ particles particle ] particles-own [ residence-time in-bank? ] globals [Boundary constant maxflux k2 height time-counter time-dx HydrCond2 hm2 Boundary2 xcutoff ChannelVelocity2 depth2] to-report surface-function [ x ] report height * sin ( k2 * x ) + Slope * x end to setup clear-all set constant 240 / (3 * lambda) set k2 ( 360 / (constant * lambda )) set Boundary BedDepth set height (( BedformHeight / 2 ) * constant ) set time-counter 0 set time-dx 100 set HydrCond2 constant * HydrCond set ChannelVelocity2 ChannelVelocity * constant set depth2 depth * constant ifelse (( height * 2 / depth2 ) > .34) [set hm2 .28 * ( ( ChannelVelocity2 ) ^ 2 ) / ( 2 * 9.8 * constant * 100 ) * (( height * 2 / depth2 ) / .34 ) ^ ( 3 / 2 ) ] [set hm2 .28 * ( ( ChannelVelocity2 ) ^ 2 ) / ( 2 * 9.8 * constant * 100 ) * (( height * 2 / depth2 ) / .34 ) ^ ( 3 / 8 ) ] set Boundary2 constant * Boundary set xcutoff constant * lambda * floor( 240 / (constant * lambda)) set maxflux 1.5 * ( max [flux-weighting pxcor] of patches with [pycor = 0] ) ;show maxflux ask patches [ ifelse ( pycor < surface-function (pxcor)) [ set pcolor brown + 2 ] ; sand color [ set pcolor blue - 2 ] ; water color if ( pycor < -1 * boundary2 ) [ set pcolor black ] if ( pxcor > xcutoff ) [ set pcolor black ] if ( pxcor < 0 ) [ set pcolor black ] ] repeat NumParticles [ drop-particle ] do-plot reset-ticks end to-report flux-weighting [ x ] let exp1 1 let exp2 exp ( k2 * (2 * pi / 360 ) * (-2 * boundary2 ) ) let expsum exp1 + exp2 let yvel ((-1 * (cos ( x * k2 )) * ( ( exp1 - exp2) * (k2 * 2 * pi / 360 )) * hm2)) * HydrCond2 / porosity ; let xvel ((k2 * (2 * pi / 360 ) * ( sin ( x * k2 )) * ( expsum ) * hm2 ) ) * HydrCond2 / porosity; let derivative (( (1) * height * 2 * pi / (constant * lambda )) * cos ( ( x) * k2 ) ) report derivative * xvel - yvel end to-report random-flux-weighted-x let x random-float xcutoff let threshold random-float maxflux ; number bigger than any flux-weighting value while [ threshold > flux-weighting x ] [ set x random-float xcutoff set threshold random-float maxflux ] report x end to drop-particle create-particles 1 [ set xcor random-flux-weighted-x set ycor surface-function xcor set in-bank? true set residence-time 0 set size .5 set color green set shape "circle" stamp set size 2 if (show-paths?) [ pd ] ] end to go ask particles with [ in-bank? ] [ move ] if re-drop? [ while [ count particles with [ in-bank? ] < NumParticles ] [ drop-particle ] ] set time-counter time-counter + time-dx if (not re-drop?) [ do-plot ] tick end to move let ycor2 ycor - surface-function( xcor ) let exp1 exp ( k2 * (2 * pi / 360 ) * ycor2 ) let exp2 exp ( k2 * (2 * pi / 360 ) * (-2 * boundary2 - ycor2 ) ) let exp3 exp ( k2 * (2 * pi / 360 ) * (-2 * boundary2) ) let expsum exp1 + exp2 let yvel ((-1 * (cos ( xcor * k2 )) * ( ( exp1 - exp2) * (k2 * 2 * pi / 360 )) * hm2)) / (1 + exp3) * HydrCond2 / porosity ; let xvel ((k2 * (2 * pi / 360 ) * ( sin ( xcor * k2 )) * ( expsum ) * hm2 ) ) / (1 + exp3) * HydrCond2 / porosity; set xcor xcor + time-dx * (xvel - HydrCond2 * Slope / (porosity * (1 + Slope ^ 2))) ; / constant if (ycor + yvel > max-pycor) [ show "big problem -- particle lost above screen" die ] if (ycor + yvel < min-pycor) [ ;show "Oh no, I'm lost!" die ] set ycor ycor + time-dx * (yvel - (HydrCond2 * Slope ^ 2) / (porosity * (1 + Slope ^ 2))); + HydrCond2 / porosity );/ constant set residence-time residence-time + time-dx if xcor >= xcutoff [ pen-up set ycor ycor - Slope * xcutoff set xcor xcor - xcutoff if show-paths? [pen-down] ] if xcor <= 0 [ pen-up set ycor ycor + Slope * xcutoff set xcor xcor + xcutoff if show-paths? [pen-down] ] set in-bank? (ycor <= surface-function xcor) ifelse (in-bank?) [ set color blue ] [ set color magenta ; show residence-time set size 0.5 ; we want them to stamp them right on the function, for better visuals set ycor surface-function xcor stamp ht ] end to do-plot if (count particles != 0) [ set-current-plot "Cumulative Residence Time" if time-counter > time-dx [set-plot-x-range 0 1 + round (log (1 + Median [residence-time] of particles) 10 ) * 3] ; keep increasing y-range, proportionally to number of particles ;set-plot-y-range 0 (ceiling (count particles / 1900)) set-plot-y-range 0 1 ;set-histogram-num-bars 54 ;histogram [ residence-time ] of particles with [ not in-bank? ] plotxy (log (( time-counter + 1 )) 10) ( count particles with [ in-bank? ] / count particles ) ] end to export-residence-times let file user-new-file if ( file != false ) [ if ( file-exists? file ) [ file-delete file ] file-open file ] let res-time-list [ residence-time ] of particles with [ not in-bank? ] foreach res-time-list [ file-type ? file-type "\r\n" ] file-close end

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## Attached files

File | Type | Description | Last updated | |
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Hyporheic Exchange Model: Interface.png | preview | image | about 5 years ago, by Susa Stonedahl | Download |

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