PartⅤ. 일차원 하천수질모형 (QUAL2K)

제1장 서론

QUAL2K는 하천수질을 모의하기 위한 정상상태의 1차원 모형으로서 QUAL2E를 현대적으로 개정한 것이다. QUAL2E 모형은 현재 국내는 물론 외국에서도 널리 이용되고 있는 하천모형이다. 그러나 QUAL2E 모형은 SOD(sediment oxygen demand)를 0차나 일정량으로 처리하였고 부착조류에 의한 용존산소 변화와 부유 조류 사멸시 발생하는 유기물(SOD)이 고려되지 않았으며, 용존산소가 부족한 상태에서 반응이 활발한 탈질화 과정이 포함되지 않아 이들 반응에 의해 수질이 영향을 받는 하천에 적용하기에는 한계가 있다. 그리고 QUAL2E 모형의 모의 가능한 구간수는 최대 50개, 계산요소는 구간당 20개로서 전체개수는 500개, 연결 지류수는 최대 9개, 점오염원, 비점오염원은 최대 50개로 제한되어 있어 여러 개의 지류를 가진 대형하천에는 적용하기 어려운 단점이 있다.

이러한 단점을 보완하기 위해 미국 EPA에서는 QUAL2K 모형을 Microsoft Windows 환경에서 VBA(Visual Basic for Application)를 이용하여 프로그래밍하였다. Excel을 이용하여 모의결과를 그래프로 나타낼 수 있어 사용자가 더욱 쉽게 이용할 수 있고 결과를 한눈에 알아볼 수 있게 되었다.

QUAL2E와는 달리 Standard Element의 길이가 동일하지 않아도 되며, 유기물 지표인 CBOD를 slow CBOD와 fast CBOD로 분리하여 모의하고 입자성 유기물질을 별도로 모의하고 있다. 저산소에서는 산화반응을 계산하지 않으며, 탈질화는 1차반응으로 이루어지고 DO와 영양염에 대하여 수층-퇴적층 반응관계를 고려하고 있다. QUAL2K는 대형하천에도 적용가능하고 QUAL2E가 포함하지 못한 기작들을 포함하게 됨으로써 수질관리 효율을 더욱 높일 수 있게 되었다.  QUAL2K 모형은 16가지의 수질항목을 모의할 수 있으며 구성성분은 <표 5.1-1>과 같다.

QUAL2K 모형의 보정 대상 반응계수는 <표 5.1-2>와 같다. 모의 대상 수질항목인 DO, fCBOD, NH4, NO3, T-N, T-P의 생성 및 소멸에 관련된 파라미터로 민감도 분석결과 모의결과에 큰 영향을 미치는  반응계수들이며 시행착오법을 이용하여 반응계수들을 산정하였다.

표 5.1-1 QUAL2K 모형의 주변수

Variable	Symbol	Unit
Conductivity	s	μmhos
Inorganic suspendid solids	mi	mgD/L
Dissolved oxygen	o	mgO2/L
Slowly reacting CBOD	cs	mgO2/L
Fast reacting CBOD	cf	mgO2/L
Dissolved organic nitrogen	no	μgN/L
Ammonia nitrogen	na	μgN/L
Nitrate nitrogen	nn	μgN/L
Dissolved organic phosphorus	po	μgP/L
Inorganic phosphorus	pi	μgP/L
Phytoplankton	ap	μgP/L
Detritus	mo	mgD/L
Pathogen	χ	cfu/100mL
Alkalinity	Alk	mgCaCO3/L
Total inorganic carbon	ct	mole/L
Bottom algae	ab	gD/m2

표 5.1-2 모형의 주요 보정 파라미터

Parameter	Value	Units	Symbol
Hydrolysis rate	0.2	/d	khc
Oxidation rate	0.9	/d	kdc
Hydrolysis	0.05	/d	khn
Nitrification	0.9	/d	kna
Denitrification	0.1	/d	kdn
Sediment denitrification transfer coeff	0.8	m/d	vdi
Hydrolysis	0.1	/d	khp
Max Growth	2.5	/d	kgp
Respiration	0.02	/d	krp
Death	0.02	/d	kdp
Settling velocity	0.04	m/d	va
Max Growth	60	gD/m2/d	Cgb
Respiration	0.5	/d	krb
Death	0.5	/d	kdb
Dissolution	5	/d	kdt
Setteling velocity	0.2	m/d	vdt

제2장 QUAL2K 모형의 원리

2.1 모형의 개요

QUAL2K 모형은 16가지의 수질항목을 모의할 수 있으면 구성성분은 <표 5.2.1-1>과 같다.

표 5.2.1-1 QUAL2K 모형의 주변수

Variable	Symbol	Unit
Conductivity	s	μmhos
Inorganic suspendid solids	mi	mgD/L
Dissolved oxygen	o	mgO2/L
Slowly reacting CBOD	cs	mgO2/L
Fast reacting CBOD	cf	mgO2/L
Dissolved organic nitrogen	no	μgN/L
Ammonia nitrogen	na	μgN/L
Nitrate nitrogen	nn	μgN/L
Dissolved organic phosphorus	po	μgP/L
Inorganic phosphorus	pi	μgP/L
Phytoplankton	ap	μgP/L
Detritus	mo	mgD/L
Pathogen	χ	cfu/100mL
Alkalinity	Alk	mgCaCO3/L
Total inorganic carbon	ct	mole/L
Bottom algae	ab	gD/m2

자료: QUAL2K Documention and Manual (US-EPA 2003)

물질수지 방정식(물질이동식)은 다음과 같이 표현할 수 있다.

[eqn: {dc _{i}} over {dt} = {Q _{i-1}} over {V _{i}} C _{i-1} - {Q _{i}} over {V _{i}} C _{i} + {Q _{ab,i}} over {V _{i}} C _{i} + {E _{i-1} ^{prime }} over {V _{i}} (C _{i-1} -C _{i} )+ {E _{i} ^{prime }} over {V _{i}} (C _{i+1} -C _{i} )+ {W _{i}} over {V _{i}} +S _{i}]

축적   유입량     유출량   취수량              확산      외부부하량 생성 소멸

여기서, [eqn: C _{i}] = 구간 i 지점에서 농도 [mg/L]

[eqn: C _{i-1}] = 구간 i 지점에서 농도[mg/L]

[eqn: Q _{i}]r = 구간 i 에서 구간 i+1 으로 유출되는 유량 [[eqn: m ^{3}]/d]

[eqn: Q _{i-1}] = 상류구간에저 i-1로 유입되는 유량 [[eqn: m ^{3}]/d]

[eqn: Q _{ab,i}] = 구간 i에서 유출되는 점취수원과 비점취수원 총 유출량

[eqn: V _{i}] = 구간 i 의 체적 [[eqn: m ^{3}]]

[eqn: E _{i} ^{prime }] = 구간 i 와 구간 I+1의 확산계수 [[eqn: m ^{3}]/d]

[eqn: W _{i}] = 구간 I 로 유입되는 외부부하량 [g/d]

[eqn: S _{i}] = 반응과 이송으로 인해 생성/소멸 되는 양 [g/[eqn: m ^{3}]/d]

2.2 물질이송

1) 이송

QUAL2K에서는 QUAL2E와 같이 정상 부등류로 가정하며 i 구간에 대한 물수지는 다음과 같이 나타낸다.

[eqn: Q _{i} =Q _{i-1} +Q _{"in",i} -Q _{ab,i}]

여기서, [eqn: Q _{i}] = 구간 i에서 구간 k로 유출되는 유량 [[eqn: m ^{3}]/d]

[eqn: Q _{i-1}] = 상류구간에서 i-1로 유입되는 유량 [[eqn: m ^{3}]/d]

[eqn: Q _{i`n,`i}] = 구간 i 로 유입되는 점오염원과 비점오염원 총 유입량

[eqn: Q _{ab,`i}] = 구간 i에서 유출되는 점취수원과 비점취수원 총 유출량

각 구간에 유속, 수심 및 단면적 등 수리학적 특성 값은 QUAL2E 모형과 같은 방법인 연속방정식과 Manning 공식이 사용되었다. QUAL2K에서 새롭게 적용한 Weir를 이용하여 구하는 방식도 있다.

2) 확산

[eqn: E _{p,`i} =0.011 {U _{i} ^{2} B _{i} ^{2}} over {H _{i} U _{i} ^{AST }}]

[eqn: U _{i} ^{AST } = sqrt {gH _{i} S _{i}}]

여기서, [eqn: E _{p,`i}] = 구간 i 와 구간 k 사이의 종확산계수 [[eqn: m ^{3}]/s]

[eqn: U _{i}] = 유속 [m/s]

[eqn: B _{i}] = 너비 [m]

[eqn: H _{i}] = 평균수심 [m]

[eqn: U _{i} ^{AST }] = 전단유속 (m/s)

g = 중력가속도 [9.81m/[eqn: S ^{2}]]

S = 수로 기울기 [무차원]

2.3 반응역학

QUAL2K 모형의 반응 및 물질 흐름도는 다음 그림과 같다.

그림 5.2.3-1 QUAL2K 모형의 반응 및 물질 흐름

※자료 : QUAL2K Documentation and Manual(US-EPA, 2003)

※주 - 용해(ds), 가수분해(h), 산화(x), 질산화(n), 탈질화(dn), 광합성(P), 사멸(d), 호흡(r), 재포기(re), 침전(s), 퇴적층산소요구량(sod), 획적층 무기탄소 흐를(cf), 상태변수

1) 유기물질의 화학양론비 (Stoichiometry)

Chapra(1997)는 다음과 같은 유기물의 화학양론비를 제안하였다.

100gD : 40gC : 7200mgN : 1000mgA

[eqn: r _{xy} = {gX} over {gY}]

여기서, D, C, N, P, A는 각각 건조유기고형물(detritus dry weight), 탄소(carbon), 질소(nitrogen), 인(phosphorus), 조류(chlorophyll a)의 농도이다.

gX = X 의 물질의 무게 , gY = Y 의 물질의 무게

예를 들어 1mgA의 부유조류의 사멸로 인해 발생하는 건조 고형유기물에 대한 화학양론비는 다음과 같다.

[eqn: r _{da} = {100gD} over {1000mgA} =0.1 {gD} over {mgA}]

2) BOD-DO, 유기고형물의 모델링

- 유기고형물([eqn: m _{0}])

[eqn: S _{mo} =r _{da} k _{dp} (T)a _{p} +k _{db} (T)a _{b} -k _{dt} (T)m _{o} - {v _{dt}} over {H} m _{o}]

축적 조류사멸   부착조류사멸 유기물용해 유기물침전

여기서, [eqn: k _{dt}](T) = 온도에 따른 유기고형물 용해속도[[eqn: d ^{-1}]]

[eqn: v _{dt}]유기고형물 침전속도[m/d]

- BOD

- slow CBOD([eqn: C _{s}]) -

[eqn: S _{cs} =r _{od} k _{dt} (T)m _{o} -k _{hc} (T)c _{s} -F _{oxcf} k _{dcs} (T)c _{s}]

축적 유기물용해    가수분해      산화

여기서, [eqn: k _{hc} (T)] = 온도체 따른 sCBOD 가수 분해율[[eqn: d ^{-1}]]

[eqn: k _{dcs} (T)] = 온도에 따른 sCBOD 가수 산화율[[eqn: d ^{-1}]]

[eqn: F_oxcf] = 저산소로 인한 산화율 보정 계수[무차원]

- Fast sCBOD([eqn: C _{f}]) -

[eqn: S _{cf} =k _{hc} (T)c _{s} `````-`````F _{oxcf} k _{dc} (T)c _{f} `````-````r _{ondn} (1-F _{oxdn} )k _{dn} (T)n _{n}]

축적 sCBOD가수분해  fCBOD산화           탈질화

여기서, [eqn: k _{dc}] = 온도에 따른 fCBOD 산화율[[eqn: d ^{-1}]]

[eqn: k _{oxdn}] =전산소로 인한 탈질율 보정 계수[무차원]

- DO(0)

[eqn: S _{o} =r _{oa}]PhytoPhoto + [eqn: r _{od}]BotAlgPhoto - [eqn: r _{oc}]FastCOxid - [eqn: r _{oc}]SlowCOxid - [eqn: r _{on}]

NH4Nitr - [eqn: r _{oa}]PhytoResp - [eqn: r _{od}]BotAlgResp + OxReaer

OxReaer [eqn: =k _{a} (T) LEFT ( o _{s} (T,elev)-o RIGHT )]

[eqn: o _{s} (T,elev)=e ^{lno _{s} (T,0)} (1-0.0001148elev)]

[eqn: lno _{s} (T,0)=-139.34411+ {1.575701 TIMES 10 ^{5}} over {T _{a}} - {6.642308 TIMES 10 ^{7}} over {T _{a} ^{2}}]

[eqn: + {1.243800 TIMES 10 ^{10}} over {T _{a} ^{3}} - {8.621949 TIMES 10 ^{11}} over {T _{a} ^{4}}]

여기서, [eqn: k _{a} (T)] = 온도에 따른 제포기 계수[[eqn: d ^{-1}]]

[eqn: o _{s} (T,elev)] = T 온도와 elev해발고도에서 산소포화농도[mg[eqn: O _{2}]/L]

[eqn: lno _{s} (T,0)] = 순수한 물 1atm에서 용존 산소 포화농도[mg[eqn: O _{2}]/L]

[eqn: T _{a}] = 절도 온도[K]

재포기 공식은 0'Conner-Dobbins, Owens-Gibbs, Churchill 공식 등을 사용하였다. QUAL2K 모형에서는 H < 0.61m 이면 Owens-Gibbs공식을 사용하고, H > 0.61m , H > 3.45[eqn: U ^{2.5}] 이면 0'Conner-Dobbins 공식을 사용하고 두 가지 경우 다 해당되지 않으면 Churchill 공식을 사용하도록 하는 내부 선택사항이 있다.

3) 영양물질과 조류의 모의

- 부유조류(phytoplankton) ([eqn: a _{p}])

[eqn: S _{ap} = mu _{p} a _{p} -k _{rp} (T)a _{p} -k _{dp} (T)a _{p} - {v _{a}} over {H} a _{p}]

축적  광합성  호흡     사멸     침전

여기서, [eqn: mu _{p}] = 부유조류 광합성율[[eqn: d ^{-1}]]

[eqn: k_rp (T)] = 온도에 따른 부유조류 호흡율[[eqn: d ^{-1}]]

[eqn: k_dp (T)] = 온도에 따른 부유조류 사멸율[[eqn: d ^{-1}]]

[eqn: v_a] = 부유조류 침전속도[m/d]

- 부착조류(bottom algae)([eqn: a _{b}])

[eqn: S _{ab} =C _{gb} (T) phi _{Nb} phi _{Lb} -k _{rb} (T)a _{b} -k _{db} (T)a _{b}]

축적     광합성       호흡      사멸

여기서, [eqn: C _{gb} (T)] = 온도에 따른 최대 광합성율[gD/([eqn: m ^{2}]d)]

[eqn: phi _{Nb}] = 부착조류 및 영양 감쇠 인자[0~1 무차원]

[eqn: phi _{Lb}] = 부착조류 및 영양 감쇠 계수[0~1 무차원]

[eqn: k_rb] = 온도에 따른 부착조류 호흡율[[eqn: d ^{-1}]]

[eqn: k_db] = 온도에 따른 부착조류 사멸율[[eqn: d ^{-1}]]

- 용존 유기질소(DON)([eqn: n_a])

[eqn: S _{no} =r _{nd} k _{dt} (T)m _{o} -k _{nn} (T)n _{o}]

축적  유기물용해     가수분해

여기서, [eqn: k_hn]= 온도에 따른 유기질소 가수분해율[[eqn: d ^{-1}]]

- 암모니아성 질소([eqn: n _{a}])

[eqn: S _{na} =k _{hn} (T)n _{o} +r _{na} k _{rp} (T)a _{p} +r _{nd} k _{rb} (T)a _{b} -F _{oxna} k _{n} (T)n _{a}]

축적  DON가수분해  부유조류호흡  부착조류호흡  질산화

[eqn: -r _{na} P _{ap} mu _{p} a _{p} -r _{nd} P _{ab} C _{gb} (T) phi _{Nb} phi _{Lb}]

부유조류광합성  부착조류광합성

여기서, [eqn: k _{n}] = 온도에 따른 질산화율[[eqn: d ^{-1}]]

[eqn: F_oxna] = 저산소로 인한 산화율 보정계수 [무차원]

[eqn: p_ap , p_ab] = 부유조류와 부착조류의 암모니아 선호도

[eqn: P _{ap} = {n _{a} n _{n}} over {(k _{hnxp} +n _{a} )(k _{hnxp} +n _{n} )} + {n _{a} k _{hnxp}} over {(n _{a} +n _{n} )(k _{hnxp} +n _{n} )}]

[eqn: P _{ap} = {n _{a} n _{n}} over {(k _{hnxb} +n _{a} )(k _{hnxb} +n _{n} )} + {n _{a} k _{hnxb}} over {(n _{a} +n _{n} )(k _{hnxb} +n _{n} )}]

[eqn: k _{hnxp} ,k _{hnxb}] = 부유조류와 부착조류의 암모니아 선호계수[mg/N[eqn: m ^{3}]]

- NH3(Unionized Ammonia)

[eqn: n _{au} =F _{u} n _{a}]

여기서, [eqn: n _{au}] = [eqn: NH _{3}] 농도[ugN/L]

[eqn: F_U] = 총 암모니아의 [eqn: NH _{3}] 비율

- 질산성 질소([eqn: n _{n}])

[eqn: S _{"ni"} =F _{oxna} k _{n} (T)n _{a} -(1-F _{oxdn} )k _{dn} (T)n _{n} -r _{na} (1-P _{ap} )- mu _{p} a _{p}]

축적   질산화          탈질화              부유조류광합성

[eqn: -r _{nd} (1-P _{ab} )C _{gb} (T) phi _{Nb} phi _{Lb}]

부착조류 광합성

여기서, [eqn: k _{dn} (T)] = 온도에 따른 질산성질성 탈질화율[[eqn: d ^{-1}]]

[eqn: F _{oxdn}] = 저산소로 인한 탈질화율 보정계수[무차원]

- 용존 유기인(DOP)([eqn: P _{o}])

[eqn: S _{po} =r _{pd} k _{dt} (T)m _{o} -k _{hp} (T)P _{o}]

축적 유기물용존    가수분해

여기서, [eqn: k _{hp} (T)] = 온도에 따른 유기인 가수분해율[[eqn: d ^{-1}]]

- 무기 인([eqn: P _{i}])

[eqn: S _{pi } =k _{hp} (T)P _{o} ````+```r _{pa} k _{rp} (T)a _{p} ````+``r _{pd} k _{rb} (T)a _{b} ````-```r _{pa} mu _{p} a _{p}][eqn: -r _{pd} C _{gb} (T) phi _{Nb} phi _{Lb}]

축적 DOP가수붆해 부유조류호흡 부착조류호흡 부유조류광합성 부착조류광합성

- 무기성 부유물질([eqn: m _{i}])

[eqn: S _{mi} = {v _{i}} over {H} m _{i}]

축적  침전

여기서, [eqn: v _{i}] = 무기성 부유물질 침전속도[m/d]

그 밖에 모델링이 가능한 물질로는 보존성 물질, 병원균, pH, 총 무기 탄소, 알카리도 등이 있다.

4) 퇴적층산소요구량 (SOD)

SOD 흐름은 Di Toro(1991, 1993, 2001)2s)t6)27)의 모형을 기본으로 하였다. 그림 2-4는 입자성유기물(Particulate Organic Matters)이 수체에서 퇴적층으로 침전되어 입자성 유기탄소(POC), 입자성 유기질소(PON), 입자성 유기인(POP) 으로 나누어 반응하는 것을 그림으로 나

타낸 것이다 퇴적층은 않은 호기성층(1mm)과 두꺼운 혐기성층(loom)으로 나누어 모의하였다.

<그림 5.2.3-2> SOD 영양물질 흐름도

※자료 : QUAL2K Documentation and Manual (US-EPA, 2003)

제3장 모형의 특징

QUAL2K (or Q2K) is a river and stream water quality model that is intended to represent a modernized version of the QUAL2E (or Q2E) model (Brown and Barnwell 1987). Q2K is similar to Q2E in the following respects:

• One dimensional. The channel is well-mixed vertically and laterally.

• Branching. The system can consist of a mainstem river with branched tributaries.

• Steady state hydraulics. Non-uniform, steady flow is simulated.

• Diel heat budget. The heat budget and temperature are simulated as a function of meteorology on a diel time scale.

• Diel water-quality kinetics. All water quality variables are simulated on a diel time

scale.

• Heat and mass inputs. Point and non-point loads and withdrawals are simulated.

The QUAL2K framework includes the following new elements:

• Software Environment and Interface. Q2K is implemented within the Microsoft Windows environment. Numerical computations are programmed in Fortran 90. Excel is used as the graphical user interface. All interface operations are programmed in the Microsoft Office macro language: Visual Basic for Applications (VBA).

• Model segmentation. Q2E segments the system into river reaches comprised of equally spaced elements. Q2K also divides the system into reaches and elements. However, in contrast to Q2E, the element size for Q2K can vary from reach to reach. In addition, multiple loadings and withdrawals can be input to any element.

• Carbonaceous BOD speciation. Q2K uses two forms of carbonaceous BOD to represent organic carbon. These forms are a slowly oxidizing form (slow CBOD) and a rapidly oxidizing form (fast CBOD).

• Anoxia. Q2K accommodates anoxia by reducing oxidation reactions to zero at low oxygen levels. In addition, denitrification is modeled as a first-order reaction that becomes pronounced at low oxygen concentrations.

• Sediment-water interactions. Sediment-water fluxes of dissolved oxygen and nutrients are simulated internally rather than being prescribed. That is, oxygen (SOD) and nutrient fluxes are simulated as a function of settling particulate organic matter, reactions within the sediments, and the concentrations of soluble forms in the overlying waters.

• Bottom algae. The model explicitly simulates attached bottom algae. These algae have variable stoichiometry.

• Light extinction. Light extinction is calculated as a function of algae, detritus and inorganic solids.

• pH. Both alkalinity and total inorganic carbon are simulated. The river’s pH is then computed based on these two quantities.

• Pathogens. A generic pathogen is simulated. Pathogen removal is determined as a function of temperature, light, and settling.

• Reach specific kinetic parameters. Q2K allows you to specify many of the kinetic parameters on a reach-specific basis.

제4장 모형의 운영

As presently configured, an Excel workbook serves as the interface for QUAL2K. That is, all input and output as well as model execution are implemented from within Excel. All interface functions are programmed in Excel’s macro language: Visual Basic for Applications (VBA). All numerical calculations are implemented in Fortran 90 for speed of execution. The following material provides a step-by-step description of how the model can be set up on your computer and used to perform a simulation.

Step 1: Copy the file, q2kFortranv2_04.zip, to a directory (e.g., C:\). When this file is unzipped, it will set up a subdirectory, q2kFortranv2_04 which includes an Excel file (Q2KMasterFortranv2_04.xls), and an executable file (q2kfortran2_04.exe). The first is the Q2K interface that allows you to run Q2K and display its results. The second is the Fortran executable that actually performs the model computations. Note that after you run the model, some assisting files will be automatically created by the Fortran executable file to exchange information with Excel.

NOTE: Do not delete the .zip file. If for some reason, you modify Q2K in a way that makes it unusable, you can always use the zip file to reinstall the model.

Figure 5.4-1. The Excel Macro Security Level dialogue box. In order to run Q2K, the Medium level of security should be selected.

Step 2: Create a subdirectory off of c:\q2kFortranv2_04 called DataFiles.

Step 3: Open Excel and make sure that your macro security level is set to medium (Figure 4-1). This can be done using the menu commands: Tools → Macro → Security. Make certain that the Medium radio button is selected.

Step 4: Open Q2KMasterFortranv2_04.xls. When you do this, the Macro Security Dialogue Box will be displayed (Figure 4-2).

Step 5: On the QUAL2K Worksheet, go to cell B10 and enter the path to the DataFiles directory: C:\QUAL2K\DataFiles as shown in Figure 4-3.

Figure 5.4-2. The Excel Macro security dialogue box.

In order to run Q2K, the Enable Macros button must be selected. Click on the Enable Macros button.

Figure 5.4-3. The QUAL2K worksheet showing the entry of the file path into cell B10.

Step 6: Click on the Run Fortran button.

If the program does not work correctly…

There are two primary reasons why the program would not work properly. First, you may be using an old version of Microsoft Office. Although Excel is downwardly compatible for some earlier versions, Q2K will not work with very old versions.

Second, you may have made a mistake in implementing the preceding steps. A common mistake is to have mistyped the file path that you entered in cell B10. For example, suppose that you mistyped the path as C:\Q2KFortranv2_04\DataFles. If this is the case, you will receive an error message (Figure 5.4-4).

Figure 5.4-4. An error message that will occur if you type the incorrect file path into cell B10 on the QUAL2K Worksheet.

If this occurs, click OK. This will terminate the run and bring you back to the QUAL2K Worksheet where you can correct the file path entry.

If the program works correctly…

QUAL2K will begin to execute. A window will open showing the progress of the Fortran computations (Figure 5.4-5).

Figure 5.4-5. This window is displayed showing the progress of the model   computations as executed in Fortran. It allows you to follow the progress of a model run.

The program is set up to simulate a fictitious river with a mainstem along with two tributaries. If the program works properly, the following dialogue box will appear when the run is completed:

Press OK and the following dialogue box will be displayed:

This box allows you to choose the parts of the system that you want to plot. As shown, it defaults to the river’s Mainstem. Press OK to see the travel time for the Mainstem. Note that all plots are updated when you press OK.

To switch to see the plots for one of the tributaries, you would press the button on the upper left of the screen

This causes the plot options dialogue box to be displayed. The pulldown can then be used to select another tributary.

Step 7: On the QUAL2K Worksheet click on the Open Old File button. Browse to get to the directory: C:\Q2KFortranv2_04\DataFiles. You should see that a new file has been created with the name that was specified in cell B9 (in the case of the example in Figure 5.4-3, Bogus071504.q2k). Click on the Cancel button to return to Q2K.

Note that every time that Q2K is run, a data file will be created with the file name specified in cell B9 on the QUAL2K Worksheet. The program automatically affixes the extension .q2k to the file name. Since this will overwrite previous versions of the file, make certain to change the file name when you perform a new application.

Now that you have successfully run Q2K on your computer, the following pages are devoted to documenting the science that underlies the model.

제5장 격자망 구성 및 수리학적 해석 방법

The model represents a river as a series of reaches. These represent stretches of river that have constant hydraulic characteristics (e.g., slope, bottom width, etc.). As depicted in Figure 5.5-1, the reaches are numbered in ascending order starting from the headwater of the river’s main stem. Notice that both point and non-point sources and point and non-point withdrawals (abstractions) can be positioned anywhere along the channel’s length.

Figure 5.5-1. QUAL2K segmentation scheme for a river with no tributaries.

For systems with tributaries (Figure 5.5-2), the reaches are numbered in ascending order starting at reach 1 at the headwater of the main stem. When a junction with a tributary is reached, the numbering continues at that tributary’s headwater. Observe that both the headwaters and the tributaries are also numbered consecutively following a sequencing scheme similar to the reaches. Note also that the major branches of the system (that is, the main stem and each of the tributaries) are referred to as segments. This distinction has practical importance because the software provides plots of model output on a segment basis. That is, the software generates individual plots for the main stem as well as each of the tributaries.

Figure 5.5-2. QUAL2K segmentation scheme for (a) a river with tributaries.

The Q2K reach representation in (b) illustrates the reach,

headwater and tributary numbering schemes.

Finally, any model reach can be further divided into a series of equally-spaced elements. As in Figure 5.5-3, this is done by merely specifying the number of elements that are desired.

Figure 5.5-3. If desired, any model reach can be further subdivided

into a series of n equal-length elements.

5.1 물수지

As described in the last section, Q2K’s most fundamental unit is the element. A steady-state flow balance is implemented for each model element as (Figure 5.5-3)

[eqn: Q _{i} =Q _{i-1} +Q _{"in" ,i} -Q _{out,t}]                                     (1)

where

[eqn: Q _{i}] = outflow from element i into the downstream element i+1,

[eqn: Q _{i-1}] = inflow from the upstream element i–1,

[eqn: Q _{"in",i}] is the total inflow into the element from point and nonpoint sources,

[eqn: Q _{out,i}] is the total outflow from the element due to point and nonpoint withdrawals.

Figure 5.5.1-1. Element flow balance.

The total inflow from sources is computed as

[eqn: Q _{"in",i} = sum _{j=1} ^{"psi"} Q _{ps,i,j} + sum _{j=1} ^{"npsi"} Q _{nps,i,j}]                                 (2)

where

[eqn: Q _{ps,i,j}] is the jth point source inflow to element i,

psi is the total number of point sources to element i,

[eqn: Q _{nps,i,j}] is the jth non-point source inflow to element iI,

npsi is the total number of non-point source inflows to element i.

The total outflow from withdrawals is computed as

[eqn: Q _{out,i} = sum _{j=1} ^{"p"a"i"} Q _{pa,i,j} + sum _{j=1} ^{"np"a"i"} Q _{npa,i,j}]                               (3)

where

[eqn: Q _{pa,i,j}] is the jth point withdrawal outflow from element i,

pai is the total number of point withdrawals from element i,

[eqn: Q _{npa,i,j}] is the jth non-point withdrawal outflow from element i,

npai is the total number of non-point withdrawal flows from element i.

The non-point sources and withdrawals are modeled as line sources. As in Figure 5.5-5, the non-point source or withdrawal is demarcated by its starting and ending kilometer points. Its flow is then distributed to or from each element in a length-weighted fashion.

Figure 5.5.1-2. The manner in which non-point source flow is

distributed to an element.

5.2 수리 특성

Once the outflow for each element is computed, the depth and velocity are calculated in one of three ways: weirs, rating curves, and Manning equations. The program decides among these options in the following manner:

• If weir height and width are entered, the weir option is implemented.

• If the weir height and width are zero and rating curve coefficients are entered (a and α), the rating curve option is implemented.

• If neither of the previous conditions is met, Q2K uses the Manning equation.

1) Weirs

Figure 5.5-6 shows how weirs are represented in Q2K. Note that a weir can only occur at the end of a reach consisting of a single element. The symbols shown in Figure 5.12.5-5 are defined as:

[eqn: H _{i}] = the depth of the element upstream of the weir [m],

[eqn: H _{i+1}] = the depth of the element downstream of the weir [m],

[eqn: elev2 _{i}] = the elevation above sea level of the tail end of the upstream element [m],

[eqn: elev1 _{i+1}] = the elevation above sea level of the head end of the downstream element [m],

[eqn: H _{w}] = the height of the weir above [eqn: elev2 _{i}] [m],

[eqn: H _{d}] = the drop between the elevation above sea level of the surface of element i and element i+1 [m],

[eqn: H _{h}] = the head above the weir [m],

[eqn: B _{w}] = the width of the weir [m].

Note that the width of the weir can differ from the width of the element, [eqn: B _{i}].

Figure 5.5.1-3 A sharp-crested weir occurring at the boundary between two reaches.

For a sharp-crested weir where [eqn: H _{h} /H _{w} <0.4], flow is related to head by (Finnemore and Franzini 2002)

[eqn: Q _{i} =1.83B _{w} H _{h} ^{3/2}]                                            (4)

where [eqn: Q _{i}] is the outflow from the element upstream of the weir in m3/s, and [eqn: B_w] and [eqn: H_h] are in m. Equation (4) can be solved for

[eqn: H _{h} = LEFT ( {Q _{i}} over {1.83B _{w}} RIGHT ) ^{2/3}]                                           (5)

This result can then be used to compute the depth of element i,

[eqn: H _{i} =H _{w} +H _{h}]                                               (6)

and the drop over the weir

[eqn: H _{d} =elev2 _{i} +H _{i} -elev1 _{i+1} -H _{i+1}]                            (7)

Note that this drop is used to compute oxygen and carbon dioxide gas transfer due to the weir.

The cross-sectional area, velocity, surface area and volume of element i can then be computed as

[eqn: A _{c,i} =B _{i} H _{i}]                                                 (8)

[eqn: U _{i} = {Q _{i}} over {A _{c,i}}]                                                  (9)

[eqn: A _{s,i} =B _{i} DELTA x _{i}]

[eqn: V _{i} =B _{i} H _{i} DELTA x _{i}]

where [eqn: B _{i}] = the width of element i, [eqn: DELTA x _{i}] = the length of element i. Note that for reaches with weirs, the reach width must be entered. This value is entered in the column AA (labeled "Bottom Width") of the Reach Worksheet.

2) Rating Curves

Power equations can be used to relate mean velocity and depth to flow,

[eqn: U=aQ ^{b}]                                                  (10)

[eqn: H= alpha Q ^{beta }]                                                  (11)

where [eqn: a,````b,```` alpha ,```` beta] are empirical coefficients that are determined from velocity-discharge and stage-discharge rating curves, respectively. The values of velocity and depth can then be employed to determine the cross-sectional area and width by

[eqn: A _{c} = {Q} over {U}]

[eqn: B= {A _{c}} over {H}]

The surface area and volume of the element can then be computed as

[eqn: A _{s} =B DELTA x]

[eqn: V=BH DELTA x]

The exponents [eqn: b] and [eqn: beta] typically take on values listed in Table 5.12.5-1. Note that the sum of [eqn: b] and [eqn: beta] must be less than or equal to 1. If this is not the case, the width will decrease with increasing flow. If their sum equals 1, the channel is rectangular.

Table 5.5.1-1. Typical values for the exponents of rating curves used to

determine velocity and depth from flow (Barnwell et al. 1989).

Equation	Exponent	Typical value	Range
[eqn: U=aQ ^{b}]	[eqn: b]	0.43	0.4-0.6
[eqn: H= alpha Q ^{beta }]	[eqn: beta]	0.45	0.3-0.5

In some applications, you might want to specify constant values of depth and velocity that do not vary with flow. This can be done by setting the exponents [eqn: b] and [eqn: beta] to zero and setting [eqn: a] equal to the desired velocity and [eqn: alpha] equal to the desired depth.

3) Manning Equation

Each element is idealized as a trapezoidal channel (Figure 5.5.1-4). Under conditions of steady flow, the Manning equation can be used to express the relationship between flow and depth as

[eqn: Q= {S _{0} ^{1/2}} over {n} {A _{c} ^{5/3}} over {P ^{2/3}}]                                        (14)

where

[eqn: Q] = flow [m3/s],

[eqn: S_0] = bottom slope [m/m],

[eqn: n] = the Manning roughness coefficient,

[eqn: A _{c}] = the cross-sectional area [m2],

P = the wetted perimeter [m].

Figure 5.5.1-4. Trapezoidal channel.

The cross-sectional area of a trapezoidal channel is computed as

[eqn: A _{c} =[B _{0} +0.5(s _{s1} +s _{s2} )H]H]                            (15)

where [eqn: B _{0}] = bottom width [m], [eqn: s _{s1}] and [eqn: s _{s2}] = the two side slopes as shown in Figure 12 [m/m], and [eqn: H] = element depth [m].

The wetted perimeter is computed as

[eqn: P=B _{0} +H sqrt {s _{s1} ^{2} +1} +H sqrt {s _{s2} ^{2} +1}]                       (16)

After substituting Eqs. (15) and (16), Eq. (14) can be solved iteratively for depth (Chapra and Canale 2002),

[eqn: H _{k} = {(Qn) ^{3/5} LEFT ( B _{0} +H _{k-1} sqrt {s _{s1} ^{2} +1} +H _{k-1} sqrt {s _{s2} ^{2} +1} RIGHT ) ^{2/5}} over {S ^{3/10} [B _{0} +0.5(s _{s1} +s _{s2} )H _{k-1} ]}]     (17)

where [eqn: k=1,2,...,n], where [eqn: n] = the number of iterations. An initial guess of [eqn: H _{0} =0] is employed. The method is terminated when the estimated error falls below a specified value of 0.001%. The estimated error is calculated as

[eqn: varepsilon _{a} = LEFT | {H _{k+1} -H _{k}} over {H _{k+1}} RIGHT | TIMES 100%]                              (18)

The cross-sectional area can be determined with Eq. (15) and the velocity can then be determined from the continuity equation,

[eqn: U= {Q} over {A _{c}}]                                               (19)

The average element width, [eqn: B] [m], can be computed as

[eqn: B= {A _{c}} over {H}]                                               (20)

The top width, [eqn: B_1] [m], can be computed as

[eqn: B _{1} =B _{0} +(s _{s1} +s _{s2} )H]

The surface area and volume of the element can then be computed as

[eqn: A _{s} =B _{1} DELTA x]

[eqn: V=BH DELTA x]

Suggested values for the Manning coefficient are listed in Table 5.12.5-2. Manning’s [eqn: n] typically varies with flow and depth (Gordon et al. 1992). As the depth decreases at low flow, the relative roughness increases. Typical published values of Manning’s n, which range from about 0.015 for smooth channels to about 0.15 for rough natural channels, are representative of conditions when the flow is at the bankfull capacity (Rosgen, 1996). Critical conditions of depth for evaluating water quality are generally much less than bankfull depth, and the relative roughness may be much higher.

Manning’s [eqn: n] typically varies with flow and depth (Gordon et al. 1992). As the depth decreases at low flow, the relative roughness increases. Typical published values of Manning’s [eqn: n], which range from about 0.015 for smooth channels to about 0.15 for rough natural channels, are representative of conditions when the flow is at the bankfull capacity (Rosgen, 1996). Critical conditions of depth for evaluating water quality are generally much less than bankfull depth, and the relative roughness may be much higher.

Table 5.5.1-2. The Manning roughness coefficient for various open channel

surfaces (from Chow et al. 1988).

MATERIAL	n
Man-made channels
Concrete	0.012
Gravel bottom with sides:
Concrete	0.020
mortared stone	0.023
Riprap	0.033
Natural stream channels
Clean, straight	0.025-0.04
Clean, winding and some weeds	0.03-0.05
Weeds and pools, winding	0.05
Mountain streams with boulders	0.04-0.10
Heavy brush, timber	0.05-0.20

4) Waterfalls

In Section 3.2.1, the drop of water over a weir was computed. This value is needed in order to compute the enhanced reaeration that occurs in such cases. In addition to weirs, such drops can also occur at waterfalls (Figure 5.5.1-5). Note that waterfalls can only occur at the end of a reach.

Figure 5.5.1-5. A waterfall occurring at the boundary between two reaches.

QUAL2K computes such drops for cases where the elevation above sea level drops abruptly at the boundary between two reaches. Equation (7) is used to compute the drop. It should be noted that the drop is only calculated when the elevation above sea level at the downstream end of a reach is greater than at the beginning of the next downstream reach; that is, [eqn: elev2 _{i} >elev1 _{i+1}].

5.3 체류 시간

The residence time of each element is computed as

[eqn: tau _{k} = {V _{k}} over {Q _{k}}]                                               (21)

where [eqn: tau _{k}] = the residence time of the kth element [d], [eqn: V _{k}] = the volume of the kth element [m3] = [eqn: A _{c,k} DELTA x _{k}], [eqn: A _{c,k}] = the cross-sectional area of the kth element [m2], and [eqn: DELTA x _{k}] = the length of the kth element [m]. These times are then accumulated to determine the travel time along each of the river’s segments (that is, either the main stem or one of the tributaries). For example, the travel time from the headwater to the downstream end of the jth element in a segment is computed as,

[eqn: t _{t,j} = sum _{k=1} ^{j} tau _{k}]                                             (22)

where [eqn: t _{t,j}] = the travel time [d].

5.4 종방향 분산

Two options are used to determine the longitudinal dispersion for a boundary between two elements. First, the user can simply enter estimated values on the Reach Worksheet. If the user does not enter values, a formula is employed to internally compute dispersion based on the channel’s hydraulics (Fischer et al. 1979),

[eqn: E _{p,i} =0.011 {U _{i} ^{2} B _{i} ^{2}} over {H _{i} U _{i} ^{*}}]                                     (23)

where [eqn: E _{p,i}] = the longitudinal dispersion between elements i and i+1 [m2/s], [eqn: U _{i}] = velocity [m/s], [eqn: B _{i}] = width [m], [eqn: H _{i}] = mean depth [m], and [eqn: U _{i} ^{*}] = shear velocity [m/s], which is related to more fundamental characteristics by

[eqn: U _{i} ^{*} = sqrt {gH _{i} S _{i}}]                                         (24)

where [eqn: g] = acceleration due to gravity [= 9.81 m/s2] and [eqn: S] = channel slope [dimensionless].

After computing or prescribing [eqn: E _{p,i}], the numerical dispersion is computed as

[eqn: E _{n,i} = {U _{i} DELTA x _{i}} over {2}]                                         (25)

The model dispersion [eqn: E _{i}] (i.e., the value used in the model calculations) is then computed as follows:

• If [eqn: E _{n,i} LEQ E _{p,i}], the model dispersion, [eqn: E _{i}] is set to [eqn: E _p,i - E_n,i].

• If [eqn: E _{n,i} >E _{p,i}]E, the model dispersion is set to zero.

For the latter case, the resulting dispersion will be greater than the physical dispersion. Thus, dispersive mixing will be higher than reality. It should be noted that for most steady-state rivers, the impact of this overestimation on concentration gradients will be negligible. If the discrepancy is significant, the only alternative is to make element lengths smaller so that the numerical dispersion becomes smaller than the physical dispersion.

제6장 모형의 구성 요소

6.1 구성 요소 및 물질 평형

The model constituents are listed in Table 5.6.1-1

Table 5.6.1-1 Model state variables

Variable	Symbol	Units*
Conductivity	s	µmhos
Inorganic suspended solids	mi	mgD/L
Dissolved oxygen	o	mgO2/L
Slowly reacting CBOD	cs	mgO2/L
Fast reacting CBOD	cf	mgO2/L
Organic nitrogen	no	µgN/L
Ammonia nitrogen	na	µgN/L
Nitrate nitrogen	nn	µgN/L
Organic phosphorus	po	µgP/L
Inorganic phosphorus	pi	µgP/L
Phytoplankton	ap	µgA/L
Detritus	mo	mgD/L
Pathogen	X	cfu/100 mL
Alkalinity	Alk	mgCaCO3/L
Total inorganic carbon	cT	mole/L
Bottom algae biomass	ab	mgA/m2
Bottom algae nitrogen	INb	mgN/m2
Bottom algae phosphorus	IPb	mgP/m2

For all but the bottom algae variables, a general mass balance for a constituent in an element is written as (Figure 5.6-1)

[eqn: {dc _{i}} over {dt} = {Q _{i-1}} over {V _{i}} c _{i-1} - {Q _{i}} over {V _{i}} c _{i} - {Q _{out,i}} over {V-i} c _{i}]

[eqn: + {E _{i-1} ^{prime }} over {V _{i}} (c _{i-1} -c _{i} )+ {E _{i} ^{prime }} over {V _{i}} (c _{i+1} -c _{i} )+ {W _{i}} over {V _{i}} +S _{i}]      (26)

where [eqn: W _{i}] = the external loading of the constituent to element i [g/d or mg/d], and [eqn: S _{i}] = sources and sinks of the constituent due to reactions and mass transfer mechanisms [g/m3/d or mg/m3/d].

Figure 5.6.1-1 Mass balance.

The external load is computed as

[eqn: W _{i} = sum _{j=1} ^{"psi"} Q _{ps,i,j} c _{"psi",j} + sum _{j=1} ^{npsi} Q _{nps,i,j} c _{npsi,j}]                    (27)

where [eqn: c _{ps,i,j}] is the jth point source concentration for element i [mg/L or µg/L], and [eqn: c _{nps,i,j}] is the jth non-point source concentration for element i [mg/L or µg/L].

For bottom algae, the transport and loading terms are omitted,

[eqn: {da _{b,t}} over {dt} =S _{b,i}]                                           (28)

[eqn: {dIN _{b}} over {dt} =S _{bN,i}]                                          (29)

[eqn: {dIP _{b}} over {dt} =S _{bP,i}]                                          (30)

where [eqn: S _{b,i}] = sources and sinks of bottom algae biomass due to reactions [mgA/m2/d], [eqn: S _{bN,i}] = sources and sinks of bottom algae nitrogen due to reactions [mgN/m2/d], and [eqn: S _{bP,i}] = sources and sinks of bottom algae phosphorus due to reactions [mgP/m2/d]. The sources and sinks for the state variables are depicted in Figure 5.6-2 (note that the internal levels of nitrogen and phosphorus in the bottom algae are not depicted). The mathematical representations of these processes are presented in the following sections.

Figure 5.6.1-2. Model kinetics and mass transfer processes. The state variables are defined in Table 3. Kinetic processes are dissolution (ds), hydrolysis (h), oxidation (ox), nitrification (n), denitrification (dn), photosynthesis (p), death (d), and respiration/excretion (r). Mass transfer processes are reaeration (re), settling (s), sediment oxygen demand (SOD), sediment exchange (se), and sediment inorganic carbon flux (cf). Note that the subscript x for the stoichiometric conversions stands for chlorophyll a (a) and dry weight (d) for phytoplankton and bottom algae, respectively.

6.2 생화학적 반응

1) Biochemical Reactions

The following chemical equations are used to represent the major biochemical reactions that take place in the model (Stumm and Morgan 1996):

Plant Photosynthesis and Respiration:

Ammonium as substrate:

[eqn: 106CO _{2} +16NH _{4} ^{+} +HPO _{4} ^{2-} +108H _{2} O LRARROW C _{106} H _{263} O _{110} N _{16} P _{1} +107O _{2} +14H ^{+}]

Nitrate as substrate:

[eqn: 106CO _{2} +16NO _{3} ^{-} +HPO _{4} ^{2-} +122H _{2} O+18H ^{+} LRARROW C _{106} H _{263} O _{110} N _{16} P _{1} +138O _{2}]

Nitrification:

[eqn: NH _{4} ^{+} +2O _{2} -> NO _{3} ^{-} +H _{2} O+2H ^{+}]

Denitrification:

[eqn: 5CH _{2} O+4NO _{3} ^{-} +4H ^{+} -> 5CO _{2} +2N _{2} +7H _{2} O]

Note that a number of additional reactions are used in the model such as those involved with simulating pH and unionized ammonia. These will be outlined when these topics are discussed later in this document.

2) Stoichiometry of Organic Matter

The model requires that the stoichiometry of organic matter (i.e., phytoplankton and detritus) be specified by the user. The following representation is suggested as a first approximation (Redfield et al. 1963, Chapra 1997),

100gD : 40 gC : 7200 mgN : 1000mgP : 1000mgA

where gX = mass of element X [g] and mgY = mass of element Y [mg]. The terms D, C, N, P, and A refer to dry weight, carbon, nitrogen, phosphorus, and chlorophyll [eqn: a], respectively. It should be noted that chlorophyll a is the most variable of these quantities with a range of approximately 500-2000 mgA (Laws and Chalup 1990, Chapra 1997).

These values are then combined to determine stoichiometric ratios as in

[eqn: r _{xy} = {gX} over {gY}]

For example, the amount of detritus (in dry weight) that is released due to the death of 1 mgA of phytoplankton can be computed as

[eqn: r _{da} = {100gD} over {1000mgA} =0.1 {gD} over {mgA}]

6.3 복합 변수

In addition to the model's state variables, Q2K also displays several composite variables that are computed as follows:

Total Organic Carbon (mgC/L):

[eqn: "TOC"= {c _{s} +c _{f}} over {r _{oc}} +r _{ca} a _{p} +r _{cd} m _{o}]

Total Nitrogen (µgN/L):

[eqn: TN=n _{o} +n _{a} +n _{n} +r _{na} a _{p}]

Total Phosphorus (µgP/L):

[eqn: TP=p _{o} +p _{i} +r _{pa} a _{p}]

Total Kjeldahl Nitrogen (µgN/L):

[eqn: TKN=n _{o} +n _{a} +r _{na} a _{p}]

Total Suspended Solids (mgD/L):

[eqn: TSS=r _{da} a _{p} +m _{o} +m _{i}]

Ultimate Carbonaceous BOD (mgO2/L):

[eqn: CBOD _{u} =c _{s} +c _{f} +r _{oc} r _{ca} a _{p} +r _{oc} r _{cd} m _{o}]

6.4 모형의 주변수와 입력 자료의 관계

For all but slow and fast CBOD (cf and cs), there exists a relatively straightforward relationship between the model state variables and standard water-quality measurements. These are outlined next. Then we discuss issues related to the more difficult problem of measuring CBOD.

1) Non-CBOD Variables and Data

The following are measurements that are needed for comparison of non-BOD variables with model output:

TEMP = temperature (oC)

TKN = total kjeldahl nitrogen (µgN/L) or TN = total nitrogen (µgN/L)

NH4 = ammonium nitrogen (µgN/L)

NO2 = nitrite nitrogen (µgN/L)

NO3 = nitrate nitrogen (µgN/L)

CHLA = chlorophyll a (µgA/L)

TP = total phosphorus (µgP/L)

SRP = soluble reactive phosphorus (µgP/L)

TSS = total suspended solids (mgD/L)

VSS = volatile suspended solids (mgD/L)

TOC = total organic carbon (mgC/L)

DOC = dissolved organic carbon (mgC/L)

DO = dissolved oxygen (mgO2/L)

PH = pH

ALK = alkalinity (mgCaCO3/L)

COND = specific conductance (µmhos)

The model state variables can then be related to these measurements as follows:

s = COND

mi = TSS – VSS or TSS – rdc (TOC – DOC)

o = DO

no = TKN – NH4 – rna CHLA or no = TN – NO2 – NO3 – NH4 – rna CHLA

na = NH4

nn = NO2 + NO3

po = TP – SRP – rpa CHLA

pi = SRP

ap = CHLA

mo = VSS – rda CHLA or rdc (TOC – DOC) – rda CHLA

pH = PH

Alk = ALK

2) Carbonaceous BOD

The interpretation of BOD measurements in natural waters is complicated by three primary factors:

• Filtered versus unfiltered. If the sample is unfiltered, the BOD will reflect oxidation of both dissolved and particulate organic carbon. Since Q2K distinguishes between dissolved (cs and cf) and particulate (mo and ap) organics, an unfiltered measurement alone does not provide an adequate basis for distinguishing these individual forms. In addition, one component of the particulate BOD, phytoplankton (ap) can further complicate the test through photosynthetic oxygen generation.

• Nitrogenous BOD. Along with the oxidation of organic carbon (CBOD), nitrification also contributes to oxygen depletion (NBOD). Thus, if the sample (a) contains reduced nitrogen and (b) nitrification is not inhibited, the measurement includes both types of BOD.

• Incubation time. Short-term, usually 5-day, BODs are typically performed. Because Q2K uses ultimate CBOD, 5-day BODs must be converted to ultimate BODs in a sensible fashion.

We suggest the following as practical ways to measure CBOD in a manner that accounts for the above factors and results in measurements that are compatible with Q2K.

Filtration. The sample should be filtered prior to incubation in order to separate dissolved from particulate organic carbon.

Nitrification inhibition. Nitrification can be suppressed by adding a chemical inhibiting agent such as TCMP (2-chloro-6-(trichloro methyl) pyridine. The measurement then truly reflects CBOD. In the event that inhibition is not possible, the measured value can be corrected for nitrogen by subtracting the oxygen equivalents of the reduced nitrogen (=ron×TKN) in the sample. However, as with all such difference-based adjustments, this correction may exhibit substantial error.

Incubation time. The model is based on ultimate CBOD, so two approaches are possible: (1) use a sufficiently long period so that the ultimate value is measured, or (2) use a 5-day measurement and extrapolate the result to the ultimate. The latter method is often computed with the formula

[eqn: CBODFNU= {CBODFN5} over {1-e ^{-k _{1} 5}}]

where CBODFNU = the ultimate dissolved carbonaceous BOD [mgO2/L], CBODFN5 = the 5-day dissolved carbonaceous BOD [mgO2/L], and k1 = the CBOD decomposition rate in the bottle [/d].

It should be noted that, besides practical considerations of time and expense, there may be other benefits from using the 5-day measurement with extrapolation, rather that performing the longer-term CBOD. Although extrapolation does introduce some error, the 5-day value has the advantage that it would tend to minimize possible nitrification effects which, even when inhibited, can begin to be exerted on longer time frames.

If all the above provisions are implemented, the result should correspond to the model variables by

[eqn: c _{f} +c _{s} =CBODFNU]

Slow versus Fast CBOD. The final question relates to discrimination between fast and slow CBODU. Although we believe that there is currently no single, simple, economically-feasible answer to this problem, we think that the following 2 strategies represent the best current alternatives.

Option 1) Represent all the dissolved, oxidizable organic carbon with a single pool (fast CBOD). The model includes parameters to bypass slow CBOD. If no slow CBOD inputs are entered, this effectively drops it from the model. For this case,

[eqn: c _{f`} =CBODFNU]

[eqn: c _{s} =0]

Option 2) Use an ultimate CBOD measurement for the fast fraction and compute slow CBOD by difference with a DOC measurement. For this case,	[eqn: c _{f} =CBODFNU]

[eqn: c _{s} =r _{oc} DOC-CBODFNU]

Option 2 works very nicely for systems where two distinct types of CBOD are present. For example, sewage effluent and autochthonous carbon from the aquatic food chain might be considered as fast CBOD. In contrast, industrial wastewaters such as pulp and paper mill effluent or allochthonous DOC from the watershed might be considered more recalcitrant and hence could be lumped into the slow CBOD fraction. In such case, the hydrolysis rate converting the slow into the fast fraction could be set to zero to make the two forms independent.

For both options, the CBODFNU can either be (a) measured directly using a long incubation time or (b) computed by extrapolation with Eq. 75. In both situations, a time frame of several weeks to a month (i.e., a 20- to 30-day CBOD) is probably a valid period in order to oxidize most of the readily degradable organic carbon. We base this assumption on the fact that bottle rates for sewage-derived organic carbon are on the order of 0.05 to 0.3/d (Chapra 1997). As in Figure 5.6-3, such rates suggest that much of the readily oxidizable CBOD will be exerted in about 20 to 30 days.

Figure 5.6.4-1 Progression of CBOD test for various levels of the bottle decomposition rate.

In addition, we believe that practitioners should consider conducting long-term CBOD tests at 30°C rather than at the commonly employed temperature of 20°C. The choice of 20°C originated from the fact that the average temperature of most receiving waters and wastewater treatment plants in the temperate zone in summer is approximately 20°C. If the CBOD measurement is intended to be used for regulation or to assess treatment plant performance, it makes sense to standardize the test at a particular temperature. And for such purposes, 20°C is as reasonable a choice as any. However, if the intent is to measure an ultimate CBOD, anything that speeds up the process while not jeopardizing the measurement's integrity would seem beneficial.

The saprophytic bacteria that break down nonliving organic carbon in natural waters and sewage thrive best at temperatures from 20°C to 40°C. Thus, a temperature of 30°C is not high enough that the bacterial assemblage would shift to thermophilic organisms that are atypical of natural waters and sewage. The benefit should be higher oxidation rates which would result in shorter analysis times for CBOD measurements. Assuming that a Q10 ≅ 2 is a valid approximation for bacterial decomposition, a 20-day BOD at 30°C should be equivalent to a 30-day BOD at 20°C.