This function uses the Lamberte-Beere law to predict the depth in metres a given proportion of surface Photosynthetically Active Radiation (PAR) penetrates to.
depth(light = seq(0.01, 1, length = 500), KdPAR = 0.05, shade = 1)
| light | The proportion of surface irradiance (PAR), between 0 and 1. Defaults to a vector of light values. |
|---|---|
| KdPAR | The average light attenuation coefficient of the water column above the reef. Defaults to 0.05. |
| shade | Additional shading at the seafloor, such as bathymetric effects, between 0 (no light available) and 1 (all light available). Defaults to 1 (all light available). |
A depth in metres. When a single light value is provided, a single value is returned. You can pass a vector of light levels for a vector of depths.
The function takes the average light attenuation coefficient (KdPAR) of the water column above a reef and a proportion between 0 and 1 of surface PAR. The Lamberte-Beer law is then used to predict the depth in metres this light environment occurs at.
A shading parameter can be used to scale how much of the light which reaches the seafloor is available to the benthos. According to (Lesser et al., 2018) the shading effect of reef slope at a vertical wall is to limit surface irradiance to 25% (shade = 0.25). The default behaviour is for there to be no shading (Shade = 1). When shading is more severe, the function will return a shallower depth. This is as the function is predicting the depth you would find your specified light level in the shaded environment.
Leaving shade unspecified makes this function equivalent to the "Depth_function" in (Laverick et al. 2020).
Specifying shading makes this function equivalent to the "Shade_function" in (Laverick et al., 2020).
Lamberte-Beer law
Lesser
Laverick
# Specifying a single light value and light # attenuation returns a single depth. depth(light = 0.1, KdPAR = 0.03)#> [1] 76.75284# By defualt there is no shading. You can # switch this on by passing a value. depth(light = 0.1, KdPAR = 0.03, shade = 0.8)#> [1] 69.31472# Specifying a vector of light values and light # attenuation returns a vector of depths. depth(light = seq(0.0065, 1, length = 500), KdPAR = 0.03)#> [1] 167.86510340 158.95835414 151.93664066 146.13977696 141.20324877 #> [6] 136.90437923 133.09712003 129.68048244 126.58171781 123.74668029 #> [11] 121.13397940 118.71126362 116.45276615 114.33763086 112.34873867 #> [16] 110.47186483 108.69506111 107.00819453 105.40259730 103.87079730 #> [21] 102.40630778 101.00346137 99.65727765 98.36335643 97.11779096 #> [26] 95.91709682 94.75815315 93.63815375 92.55456619 91.50509728 #> [31] 90.48766388 89.50036798 88.54147542 87.60939753 86.70267533 #> [36] 85.81996573 84.96002965 84.12172148 83.30397995 82.50582004 #> [41] 81.72632582 80.96464419 80.21997922 79.49158715 78.77877195 #> [46] 78.08088132 77.39730309 76.72746199 76.07081677 75.42685753 #> [51] 74.79510339 74.17510027 73.56641900 72.96865349 72.38141912 #> [56] 71.80435122 71.23710377 70.67934812 70.13077182 69.59107762 #> [61] 69.05998247 68.53721665 68.02252292 67.51565578 67.01638078 #> [66] 66.52447381 66.03972057 65.56191598 65.09086363 64.62637533 #> [71] 64.16827067 63.71637654 63.27052682 62.83056192 62.39632854 #> [76] 61.96767924 61.54447224 61.12657107 60.71384434 60.30616547 #> [81] 59.90341248 59.50546775 59.11221783 58.72355323 58.33936825 #> [86] 57.95956081 57.58403227 57.21268729 56.84543369 56.48218229 #> [91] 56.12284680 55.76734370 55.41559209 55.06751364 54.72303241 #> [96] 54.38207481 54.04456950 53.71044725 53.37964093 53.05208535 #> [101] 52.72771726 52.40647521 52.08829953 51.77313223 51.46091695 #> [106] 51.15159891 50.84512482 50.54144288 50.24050266 49.94225509 #> [111] 49.64665243 49.35364817 49.06319702 48.77525489 48.48977879 #> [116] 48.20672684 47.92605822 47.64773313 47.37171275 47.09795923 #> [121] 46.82643564 46.55710595 46.28993498 46.02488840 45.76193269 #> [126] 45.50103514 45.24216376 44.98528733 44.73037533 44.47739796 #> [131] 44.22632605 43.97713114 43.72978535 43.48426144 43.24053279 #> [136] 42.99857331 42.75835752 42.51986045 42.28305770 42.04792535 #> [141] 41.81444001 41.58257876 41.35231916 41.12363925 40.89651748 #> [146] 40.67093278 40.44686448 40.22429232 40.00319646 39.78355744 #> [151] 39.56535620 39.34857402 39.13319257 38.91919387 38.70656028 #> [156] 38.49527448 38.28531950 38.07667868 37.86933567 37.66327443 #> [161] 37.45847920 37.25493452 37.05262522 36.85153639 36.65165339 #> [166] 36.45296184 36.25544763 36.05909688 35.86389597 35.66983151 #> [171] 35.47689035 35.28505955 35.09432641 34.90467843 34.71610335 #> [176] 34.52858908 34.34212376 34.15669573 33.97229349 33.78890577 #> [181] 33.60652147 33.42512966 33.24471959 33.06528071 32.88680261 #> [186] 32.70927505 32.53268797 32.35703145 32.18229574 32.00847123 #> [191] 31.83554846 31.66351814 31.49237109 31.32209830 31.15269087 #> [196] 30.98414006 30.81643724 30.64957393 30.48354176 30.31833250 #> [201] 30.15393801 29.99035032 29.82756154 29.66556390 29.50434975 #> [206] 29.34391155 29.18424187 29.02533337 28.86717884 28.70977115 #> [211] 28.55310329 28.39716832 28.24195943 28.08746989 27.93369306 #> [216] 27.78062239 27.62825142 27.47657380 27.32558323 27.17527352 #> [221] 27.02563857 26.87667233 26.72836886 26.58072228 26.43372681 #> [226] 26.28737672 26.14166638 25.99659021 25.85214271 25.70831847 #> [231] 25.56511213 25.42251839 25.28053205 25.13914795 24.99836100 #> [236] 24.85816618 24.71855853 24.57953315 24.44108520 24.30320991 #> [241] 24.16590256 24.02915849 23.89297310 23.75734183 23.62226021 #> [246] 23.48772379 23.35372819 23.22026908 23.08734218 22.95494326 #> [251] 22.82306814 22.69171270 22.56087286 22.43054458 22.30072388 #> [256] 22.17140682 22.04258951 21.91426811 21.78643880 21.65909783 #> [261] 21.53224148 21.40586607 21.27996798 21.15454361 21.02958941 #> [266] 20.90510187 20.78107751 20.65751290 20.53440465 20.41174940 #> [271] 20.28954382 20.16778463 20.04646858 19.92559246 19.80515309 #> [276] 19.68514732 19.56557204 19.44642417 19.32770068 19.20939854 #> [281] 19.09151478 18.97404645 18.85699064 18.74034444 18.62410501 #> [286] 18.50826952 18.39283518 18.27779921 18.16315887 18.04891145 #> [291] 17.93505427 17.82158467 17.70850002 17.59579772 17.48347518 #> [296] 17.37152987 17.25995925 17.14876083 17.03793213 16.92747069 #> [301] 16.81737410 16.70763995 16.59826586 16.48924948 16.38058848 #> [306] 16.27228054 16.16432338 16.05671473 15.94945236 15.84253403 #> [311] 15.73595756 15.62972075 15.52382146 15.41825754 15.31302688 #> [316] 15.20812738 15.10355696 14.99931356 14.89539515 14.79179970 #> [321] 14.68852522 14.58556971 14.48293123 14.38060781 14.27859753 #> [326] 14.17689849 14.07550878 13.97442653 13.87364989 13.77317700 #> [331] 13.67300605 13.57313523 13.47356273 13.37428679 13.27530565 #> [336] 13.17661755 13.07822077 12.98011359 12.88229432 12.78476127 #> [341] 12.68751276 12.59054715 12.49386279 12.39745805 12.30133133 #> [346] 12.20548102 12.10990554 12.01460331 11.91957279 11.82481241 #> [351] 11.73032066 11.63609602 11.54213697 11.44844203 11.35500971 #> [356] 11.26183854 11.16892708 11.07627388 10.98387749 10.89173652 #> [361] 10.79984954 10.70821516 10.61683200 10.52569867 10.43481383 #> [366] 10.34417612 10.25378419 10.16363672 10.07373239 9.98406989 #> [371] 9.89464793 9.80546521 9.71652047 9.62781242 9.53933983 #> [376] 9.45110143 9.36309600 9.27532231 9.18777913 9.10046527 #> [381] 9.01337952 8.92652070 8.83988762 8.75347912 8.66729403 #> [386] 8.58133120 8.49558949 8.41006776 8.32476489 8.23967977 #> [391] 8.15481127 8.07015830 7.98571978 7.90149461 7.81748172 #> [396] 7.73368004 7.65008852 7.56670609 7.48353173 7.40056439 #> [401] 7.31780304 7.23524667 7.15289426 7.07074481 6.98879731 #> [406] 6.90705078 6.82550424 6.74415671 6.66300721 6.58205479 #> [411] 6.50129850 6.42073738 6.34037049 6.26019690 6.18021569 #> [416] 6.10042592 6.02082669 5.94141709 5.86219621 5.78316317 #> [421] 5.70431707 5.62565704 5.54718218 5.46889165 5.39078456 #> [426] 5.31286007 5.23511732 5.15755547 5.08017367 5.00297109 #> [431] 4.92594691 4.84910030 4.77243045 4.69593654 4.61961776 #> [436] 4.54347333 4.46750243 4.39170429 4.31607812 4.24062315 #> [441] 4.16533858 4.09022367 4.01527765 3.94049976 3.86588924 #> [446] 3.79144535 3.71716735 3.64305449 3.56910605 3.49532130 #> [451] 3.42169952 3.34823998 3.27494198 3.20180480 3.12882773 #> [456] 3.05601009 2.98335118 2.91085030 2.83850677 2.76631991 #> [461] 2.69428904 2.62241348 2.55069258 2.47912566 2.40771207 #> [466] 2.33645114 2.26534224 2.19438470 2.12357790 2.05292118 #> [471] 1.98241392 1.91205548 1.84184524 1.77178257 1.70186686 #> [476] 1.63209749 1.56247384 1.49299531 1.42366131 1.35447121 #> [481] 1.28542444 1.21652040 1.14775850 1.07913815 1.01065877 #> [486] 0.94231978 0.87412062 0.80606071 0.73813947 0.67035636 #> [491] 0.60271080 0.53520224 0.46783013 0.40059391 0.33349304 #> [496] 0.26652698 0.19969518 0.13299710 0.06643222 0.00000000# By default the function uses the reference light # environment from (Laverick et al., 2020) with no shade. depth()#> [1] 92.10340372 88.48371056 85.41981742 82.76354192 80.41905127 78.32078150 #> [7] 76.42189587 74.68776868 73.09207782 71.61434511 70.23832498 68.95091280 #> [13] 67.74138398 66.60085041 65.52186364 64.49811988 63.52423681 62.59558231 #> [19] 61.70814119 60.85841030 60.04331499 59.26014196 58.50648476 57.78019920 #> [25] 57.07936657 56.40226309 55.74733439 55.11317398 54.49850508 53.90216517 #> [31] 53.32309270 52.76031576 52.21294227 51.68015145 51.16118641 50.65534773 #> [37] 50.16198772 49.68050550 49.21034256 48.75097891 48.30192954 47.86274144 #> [43] 47.43299078 47.01228048 46.60023802 46.19651343 45.80077753 45.41272028 #> [49] 45.03204936 44.65848884 44.29177794 43.93167001 43.57793144 43.23034084 #> [55] 42.88868816 42.55277391 42.22240851 41.89741161 41.57761154 41.26284469 #> [61] 40.95295508 40.64779389 40.34721897 40.05109452 39.75929065 39.47168311 #> [67] 39.18815291 38.90858606 38.63287327 38.36090974 38.09259485 37.82783201 #> [73] 37.56652839 37.30859477 37.05394533 36.80249748 36.55417172 36.30889147 #> [79] 36.06658293 35.82717496 35.59059893 35.35678863 35.12568013 34.89721171 #> [85] 34.67132374 34.44795856 34.22706046 34.00857553 33.79245162 33.57863823 #> [91] 33.36708649 33.15774907 32.95058007 32.74553504 32.54257086 32.34164574 #> [97] 32.14271910 31.94575157 31.75070496 31.55754215 31.36622710 31.17672480 #> [103] 30.98900121 30.80302326 30.61875878 30.43617648 30.25524592 30.07593750 #> [109] 29.89822238 29.72207249 29.54746051 29.37435981 29.20274445 29.03258917 #> [115] 28.86386933 28.69656090 28.53064048 28.36608522 28.20287284 28.04098160 #> [121] 27.88039028 27.72107818 27.56302507 27.40621122 27.25061733 27.09622458 #> [127] 26.94301456 26.79096929 26.64007119 26.49030309 26.34164818 26.19409003 #> [133] 26.04761259 25.90220013 25.75783728 25.61450901 25.47220058 25.33089758 #> [139] 25.19058591 25.05125176 24.91288159 24.77546216 24.63898050 24.50342390 #> [145] 24.36877989 24.23503627 24.10218108 23.97020260 23.83908933 23.70882999 #> [151] 23.57941355 23.45082915 23.32306618 23.19611419 23.06996296 22.94460246 #> [157] 22.82002283 22.69621440 22.57316768 22.45087336 22.32932229 22.20850550 #> [163] 22.08841416 21.96903962 21.85037336 21.73240704 21.61513244 21.49854150 #> [169] 21.38262630 21.26737904 21.15279208 21.03885789 20.92556907 20.81291836 #> [175] 20.70089861 20.58950278 20.47872397 20.36855538 20.25899032 20.15002222 #> [181] 20.04164460 19.93385111 19.82663547 19.71999154 19.61391323 19.50839458 #> [187] 19.40342973 19.29901288 19.19513835 19.09180052 18.98899389 18.88671301 #> [193] 18.78495254 18.68370722 18.58297184 18.48274131 18.38301057 18.28377468 #> [199] 18.18502875 18.08676797 17.98898758 17.89168292 17.79484938 17.69848241 #> [205] 17.60257755 17.50713038 17.41213656 17.31759180 17.22349187 17.12983261 #> [211] 17.03660991 16.94381971 16.85145803 16.75952093 16.66800451 16.57690495 #> [217] 16.48621846 16.39594132 16.30606985 16.21660042 16.12752944 16.03885339 #> [223] 15.95056877 15.86267215 15.77516014 15.68802937 15.60127654 15.51489840 #> [229] 15.42889170 15.34325329 15.25798000 15.17306875 15.08851648 15.00432015 #> [235] 14.92047679 14.83698345 14.75383721 14.67103521 14.58857461 14.50645259 #> [241] 14.42466640 14.34321330 14.26209058 14.18129558 14.10082566 14.02067821 #> [247] 13.94085066 13.86134047 13.78214512 13.70326212 13.62468904 13.54642343 #> [253] 13.46846290 13.39080508 13.31344764 13.23638825 13.15962463 13.08315452 #> [259] 13.00697567 12.93108589 12.85548298 12.78016479 12.70512917 12.63037402 #> [265] 12.55589725 12.48169678 12.40777059 12.33411664 12.26073294 12.18761752 #> [271] 12.11476842 12.04218370 11.96986146 11.89779980 11.82599686 11.75445077 #> [277] 11.68315972 11.61212188 11.54133547 11.47079872 11.40050986 11.33046716 #> [283] 11.26066890 11.19111339 11.12179894 11.05272388 10.98388657 10.91528538 #> [289] 10.84691869 10.77878490 10.71088244 10.64320973 10.57576523 10.50854741 #> [295] 10.44155474 10.37478572 10.30823886 10.24191270 10.17580577 10.10991662 #> [301] 10.04424383 9.97878598 9.91354167 9.84850951 9.78368812 9.71907614 #> [307] 9.65467223 9.59047504 9.52648326 9.46269557 9.39911068 9.33572731 #> [313] 9.27254417 9.20956000 9.14677357 9.08418362 9.02178894 8.95958831 #> [319] 8.89758053 8.83576440 8.77413874 8.71270238 8.65145417 8.59039296 #> [325] 8.52951759 8.46882696 8.40831994 8.34799542 8.28785231 8.22788952 #> [331] 8.16810596 8.10850058 8.04907230 7.98982009 7.93074291 7.87183971 #> [337] 7.81310949 7.75455122 7.69616391 7.63794655 7.57989817 7.52201777 #> [343] 7.46430441 7.40675710 7.34937490 7.29215687 7.23510207 7.17820957 #> [349] 7.12147844 7.06490779 7.00849669 6.95224425 6.89614959 6.84021182 #> [355] 6.78443007 6.72880346 6.67333114 6.61801225 6.56284595 6.50783140 #> [361] 6.45296776 6.39825421 6.34368994 6.28927412 6.23500595 6.18088464 #> [367] 6.12690938 6.07307940 6.01939392 5.96585216 5.91245335 5.85919673 #> [373] 5.80608155 5.75310705 5.70027250 5.64757716 5.59502030 5.54260118 #> [379] 5.49031909 5.43817331 5.38616315 5.33428788 5.28254682 5.23093927 #> [385] 5.17946454 5.12812195 5.07691084 5.02583051 4.97488032 4.92405958 #> [391] 4.87336766 4.82280390 4.77236765 4.72205828 4.67187513 4.62181759 #> [397] 4.57188502 4.52207681 4.47239233 4.42283097 4.37339213 4.32407519 #> [403] 4.27487957 4.22580465 4.17684986 4.12801461 4.07929831 4.03070038 #> [409] 3.98222026 3.93385736 3.88561114 3.83748102 3.78946645 3.74156687 #> [415] 3.69378173 3.64611050 3.59855262 3.55110756 3.50377479 3.45655377 #> [421] 3.40944398 3.36244489 3.31555600 3.26877677 3.22210670 3.17554529 #> [427] 3.12909202 3.08274640 3.03650792 2.99037610 2.94435044 2.89843045 #> [433] 2.85261566 2.80690558 2.76129972 2.71579763 2.67039882 2.62510284 #> [439] 2.57990920 2.53481746 2.48982716 2.44493783 2.40014903 2.35546031 #> [445] 2.31087122 2.26638132 2.22199017 2.17769733 2.13350236 2.08940484 #> [451] 2.04540433 2.00150041 1.95769266 1.91398066 1.87036398 1.82684222 #> [457] 1.78341496 1.74008179 1.69684231 1.65369611 1.61064279 1.56768195 #> [463] 1.52481319 1.48203612 1.43935035 1.39675549 1.35425115 1.31183696 #> [469] 1.26951252 1.22727746 1.18513140 1.14307397 1.10110480 1.05922351 #> [475] 1.01742974 0.97572312 0.93410330 0.89256991 0.85112258 0.80976098 #> [481] 0.76848474 0.72729351 0.68618694 0.64516468 0.60422639 0.56337173 #> [487] 0.52260036 0.48191193 0.44130611 0.40078256 0.36034096 0.31998097 #> [493] 0.27970226 0.23950451 0.19938738 0.15935057 0.11939374 0.07951658 #> [499] 0.03971877 0.00000000