Nutrient Transport Modelling in the Daugava River Basin - DiVA Portal
Nutrient Transport Modelling in the Daugava River Basin - DiVA Portal
Nutrient Transport Modelling in the Daugava River Basin - DiVA Portal
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
whereN k0 = N k (0)With <strong>in</strong>creas<strong>in</strong>g time, equation E2 approaches an asymptotic value as <strong>the</strong> depletion rateapproaches <strong>the</strong> accumulation rate:N = lim N ( t)= nk , maxk kt→∞/ β(E3)Assum<strong>in</strong>g that N k (t) reaches 90 % of its maximum value <strong>in</strong> 20 days, <strong>the</strong> equations canbe solved for . The result is = 0.12, which is <strong>the</strong> value that is used here.Equation E2 can be written for a time <strong>in</strong>terval of one day, which is <strong>the</strong> form that is usedby <strong>the</strong> GWLF model:N−0.12= N e + ( n / 0.12)(1 ek , t+ 1 ktk−−0.12)(E4)By add<strong>in</strong>g a negative term to <strong>the</strong> right hand side of this equation, <strong>the</strong> effect of wash offis <strong>in</strong>cluded:N−0.12−0.12k , t+ 1= Nkte+ ( nk/ 0.12)(1 − e ) −Wkt(E5)whereW kt = runoff load from land use k on day t [kg/ha]The runoff nutrient load at a wash off event is a function of <strong>the</strong> amount of accumulatednutrients at <strong>the</strong> time and <strong>the</strong> runoff flow:Wkt.12= w [ N e + ( n / 0.12)(1 − ektkt−0 −0.12k)](E6)where−1.81Q w ktkt= 1 − e(E7)Equation E7 is based on <strong>the</strong> assumption that 1.27 cm of runoff will wash off 90 % ofaccumulated pollutants.Monthly runoff loads of urban nutrients are thus given by:SUm=∑∑( Wkt⋅ARk)kdmt=1(E8)35