APPENDIX A: NOMENCLATURE

8 APPENDIX A: NOMENCLATURE

Symbol Definition Units

A acres , i surface area of reach i acres [CO 2 ] s saturation concentration of carbon dioxide

mole/L

2 [CO −

3 ] carbonate ion mole/L [H + ] hydronium ion mole/L

[H 2 CO 3 *] sum of dissolved carbon dioxide and carbonic acid mole/L [HCO −

3 ] bicarbonate ion mole/L [OH − ]

hydroxyl ion mole/L

a velocity rating curve coefficient dimensionless a"

mean atmospheric transmission coefficient after dimensionless scattering and absorption

a ’ mean atmospheric transmission coefficient dimensionless

a 1 atmospheric molecular scattering coefficient for radiation dimensionless transmission

A a atmospheric long-wave radiation coefficient dimensionless

A -0.5

b atmospheric long-wave radiation coefficient mmHg or mb

b bottom algae gD/m

c cross-sectional area m

a d coefficient correcting dam reaeration for water quality dimensionless Alk alkalinity 1 eq L − or

mgCaCO 3 /L

a p phytoplankton mgC/L

a 3 p phytoplankton concentration mgA/m

a t atmospheric attenuation dimensionless

a tc atmospheric transmission coefficient dimensionless

B average reach width m

b velocity rating curve exponent dimensionless

B 0 bottom width m

b d coefficient correcting dam reaeration for dam type dimensionless

1 Bowen's coefficient

0.47 mmHg/ C

c f fast reacting CBOD mgO 2 /L

f fast CBOD in the overlying water gO 2 /m

gb (T) temperature-dependent maximum photosynthesis rate gD/(m d) CH 3 4,1 methane concentration in the aerobic sediment layer

gO 2 /m

C L fraction of sky covered with clouds dimensionless

c o nps , i , j jth non-point source concentration for reach i

C o p specific heat of water cal/(g C)

c o ps , i , j jth point source concentration for reach i

c s slowly reacting CBOD mgO 2 /L

C s saturation concentration of methane mgO 2 /L CSOD 2 the amount of oxygen demand generated by methane gO

2 /m /d oxidation

T total mole L − c' T,i − 1 concentration of inorganic carbon entering reach below a

c inorganic carbon

mgO 2 /L dam

QUAL2K

97 November 25, 2003 97 November 25, 2003

dimensionless

d pore water diffusion coefficient

m /d

D 2 p diffusion coefficient for bioturbation

m /d

E’ 3

i bulk dispersion coefficient between reaches i and i + 1

m /d

e air air vapor pressure

mm Hg

elev elevation above sea level

E 2 n numerical dispersion

m /d

E p,i longitudinal dispersion between reaches i and i + 1

m 2 /s

eqtime equation of time: the difference between mean solar time

minutes

and true solar time when located on the reference longitude of the time zone considered

e s saturation vapor pressure at water surface

mmHg

f photoperiod

fraction of day

f dai fraction of ammonium in dissolved form in sediment

dimensionless

layer i

f dpi fraction of inorganic phosphorus in dissolved form in

dimensionless

sediment layer i

F Lp phytoplankton growth attenuation due to light

dimensionless

F oxcf attenuation of CBOD oxidation due to low oxygen

dimensionless

F oxdn enhancement of denitrification at low oxygen

dimensionless

concentration

F oxna attenuation due to low oxygen

dimensionless

F oxrb attenuation due to low oxygen

dimensionless

F oxrp attenuation due to low oxygen

dimensionless

f pai fraction of ammonium in particulate form in sediment

dimensionless

layer i

f ppi fraction of inorganic phosphorus in particulate form in

dimensionless

sediment layer i

F u fraction unionized ammonia

g acceleration due to gravity

= 9.81 m/s 2

gX mass of element X

H water depth

H water depth

H d drop in water elevation for a dam

H i thickness of sediment layer i m

H sed sediment thickness

cm

I(0) 2 solar radiation at water surface cal/cm /d

0 extraterrestrial radiation

cal/cm /d

J 2 an net atmospheric longwave radiation flux

cal/(cm d)

J 2 br longwave back radiation flux from water

cal/(cm d)

c conduction flux

cal/(cm d)

C , G 1 flux of labile dissolved carbon

gO 2 /m /d

J 2 CH 4 Flux of methane from sediments to the overlying water

gO 2 /m /d

J 2 CH 4, d flux of dissolved methane generated in anaerobic

gO 2 /m /d

sediments corrected for methane gas formation J 2 CH 4, T carbon diagenesis flux corrected for denitrification

gO 2 /m /d

e evaporation flux

cal/(cm d)

h air-water heat flux

cal/(cm d)

QUAL2K

98 November 25, 2003

J 2 N nitrogen diagenesis flux gN/m /d J 2 O 2, dn oxygen equivalents consumed during denitrification

gO 2 /m /d J 2 P phosphorus diagenesis flux

gP/m /d J 2 POC , G 1 the flux of labile POC delivered to the anaerobic

gO 2 /m /d sediment layer J POM the downward flux of POM

− 2 − gD m 1 d J 2

si sediment-water heat flux cal/(cm d) J 2

sn net solar shortwave radiation flux cal/(cm d) k(T)

temperature dependent first-order reaction rate /d K 1 acidity constant for dissociation of carbonic acid K 2 acidity constant for dissociation of bicarbonate K a equilibrium coefficient for ammonium dissociation

k a (T) temperature-dependent oxygen reaeration coefficient /d k ac (T)

temperature-dependent carbon dioxide reaeration /d coefficient k db (T)

temperature-dependent bottom algae death rate /d k dc (T)

temperature-dependent fast CBOD oxidation rate /d k dn (T) temperature-dependent denitrification rate

/d k dp (T)

temperature-dependent phytoplankton death rate /d k dt (T)

temperature-dependent detritus dissolution rate /d k dx (T)

temperature-dependent pathogen die-off rate /d k 1

e light extinction coefficient /m k eb a background coefficient accounting for extinction due to

/m water and color k gp (T)

maximum photosynthesis rate at temperature T /d K H Henry's constant

mole/(L atm) k hc (T)

temperature-dependent slow CBOD hydrolysis rate /d k hn (T)

temperature-dependent organic nitrogen hydrolysis rate /d k 3 hnxb preference coefficient of bottom algae for ammonium

mgN/m k 3 hnxp preference coefficient of phytoplankton for ammonium

mgN/m k hp (T)

temperature-dependent organic phosphorus hydrolysis /d rate K L 12 pore water diffusion mass transfer coefficient

m/d K Lb bottom algae light parameter K Lp phytoplankton light parameter

ly/d K 3 M , Dp oxygen half-saturation constant for bioturbation

gO 2 /m k na (T)

temperature-dependent nitrification rate for ammonia /d nitrogen

K 3 NH 4 ammonium half-saturation constant gN/m K NH 4, O 2 oxygen half-saturation constant

mgO 2 /L k POC , G 1 the mineralization rate of labile POC

− d 1 k rb (T)

temperature-dependent bottom algae respiration rate /d k rp (T)

temperature-dependent phytoplankton respiration rate /d k sNb nitrogen half-saturation constant for bottom algae

µ gN/L k sNp nitrogen half-saturation constant for phytoplankton

µ gN/L K socf parameter for oxygen dependency of fast CBOD oxidation K sodn parameter for oxygen dependency of denitrification

QUAL2K

99 November 25, 2003

K sona parameter for oxygen dependency of nitrification k sPb phosphorus half-saturation constant for bottom algae

µ gP/L k sPp phosphorus half-saturation constant for phytoplankton

µ gP/L K w acidity constant for dissociation of water L at latitude

radians L lm longitude of local meridian

degrees localTime local standard time

minutes L sm longitude of standard meridian

degrees m

optical air mass dimensionless mgY

mass of element Y mg m i inorganic suspended solids

mgD/L

i the solids concentration in sediment layer i gD/m m o detritus

mgD/L m 3 o detritus concentration

gD/m n Manning roughness coefficient n a ammonia nitrogen

mgN/L

a the ammonium concentration in the overlying water mgN/m n au unionized ammonia nitrogen

mgN/L n fac atmospheric turbidity factor

dimensionless NH 3

4, i the concentration of total ammonium in sediment layer i gN/m n n nitrate nitrogen

mgN/L

n nitrate concentration in the overlying water mgN/m n o dissolved organic nitrogen

mgN/L NO 3

3, i nitrate concentration in layer i gN/m npai

total number of non-point abstractions outflows from dimensionless reach i npsi

total number of non-point sources inflows to reach i dimensionless NSOD 2 the amount of oxygen demand generated by nitrification gO

2 /m /d o dissolved oxygen

mgO 2 /L

o 3 the dissolved oxygen concentration in the overlying gO

2 /m water o’ i − 1 oxygen concentration entering a reach below a dam

mgO 2 /L o 3

crit critical oxygen concentration for sediment phosphorus gO 2 /m sorption o s (T, elev)

saturation concentration of oxygen at temperature, T, and mgO 2 /L elevation above sea level, elev P wetted perimeter

m P ab preference for ammonium as a nitrogen source for

dimensionless bottom algae pai

total number of point abstractions from reach i dimensionless P ap preference for ammonium as a nitrogen source for

dimensionless phytoplankton

PAR(z) photosynthetically available radiation (PAR) at depth z ly/d below water surface p atm atmospheric pressure

mm Hg p CO 2 atmospheric partial pressure of carbon dioxide

atm p i inorganic phosphorus

µ gP/L

i the inorganic phosphorus in the overlying water mgP/m p o dissolved organic phosphorus

µ gP/L

QUAL2K

November 25, 2003

PO 3

4, i the concentration of total inorganic phosphorus in

gP/m

sediment layer i POC 3

2, G 1 the concentration of the labile fraction of POC in the

gO 2 /m

anaerobic sediment layer POC 3 R reference G1 concentration for bioturbation

gC/m

psi total number of point sources to reach i

dimensionless

p wc mean daily atmospheric precipitable water content

3 Q flow 3 m /s or m /d Q 3

ab , i total outflow from reach due to point and nonpoint

m /d

abstractions Q 3

i outflow from reach i into reach i + 1

m /d

Q 3 in , i total inflow into reach from point and nonpoint sources

m /d

Q 3 npa , i , j jth non-point abstraction outflow from reach i

m /d

Q 3 nps , i , j jth non-point source inflow to reach i

m /d

Q 3 pa , i , j jth point abstraction outflow from reach i

m /d

Q 3 ps , i , j jth point source inflow to reach i

m /d

r normalized radius of earth’s orbit (i.e., ratio of actual

dimensionless

earth-sun distance to mean earth-sun distance r cndn ratio of oxygen equivalents lost per nitrate nitrogen that

gO 2 /gN

is denitrified r d ratio of deficit above and below dam

dimensionless

r da the ratio of dry weight to chlorophyll a gD/mgA R L longwave reflection coefficient

dimensionless

r oc ratio of oxygen consumed per organic carbon oxidized to

gO 2 /gC

carbon dioxide r oca ratio of oxygen generated per organic carbon produced

gO 2 /gC

by photosynthesis when nitrate is taken up r ocn ratio of oxygen generated per organic carbon produced

gO 2 /gC

by photosynthesis when ammonia is taken up r on the ratio of oxygen to nitrogen consumed during

= 4.57 gO 2 /gN

nitrification r on '

ratio of oxygen consumed per ammonia nitrogen

gO 2 /gN

converted by nitrification/denitrification to nitrogen gas r on ’

the ratio of oxygen to nitrogen consumed for total = 1.714 gO 2 /gN conversion of ammonium to nitrogen gas via nitrification/denitrification R s albedo or reflectivity (fraction of solar radiation that is

dimensionless

reflected) S channel slope

dimensionless s chloride

mgCl/L s

mass transfer coefficient between the water and the

m/d

aerobic sediments S 0 bottom slope

m/m S 2

b , i sources and sinks of constituent due to reactions for

gD/m /d

bottom algae

i sources and sinks of constituent due to reactions and g/m /d or mg/m /d mass transfer mechanisms for water constituents

SOD 2 the sediment oxygen demand gO

2 /m /d

SOD 2 s the supplemental sediment oxygen demand

gO 2 /m /d

QUAL2K

November 25, 2003

SOD 2 t total sediment oxygen demand = SOD + SOD s gO 2 /m /d s s channel side slope

m/m t time

d T water o temperature C

T water o temperature C T o

,w,f water temperature

T a absolute temperature

T o air air temperature

T o air,f air temperature

d dew-point temperature

i temperature in reach i

timezone time zone indicates local time zone in relation to hours Greenwich Mean Time (GMT) (negative in western hemisphere)

T o nps , i , j jth non-point source temperature for reach i

T o ps , i , j jth point source temperature for reach i

trueSolarTime time determined from actual position of the sun in the minutes sky T o

s,i temperature of bottom sediment

t sr time of sunrise

Hr

t ss time of sunset

Hr

T std standard time Hr t t , i travel time from headwater to end of reach i D U mean velocity

m/s U i * shear velocity

m/s

U w wind speed m/s U w,mph wind speed

mph U w,z wind speed at height z w above water surface

m/s

v a phytoplankton settling velocity m/d v a phytoplankton settling velocity

m/d v dt detritus settling velocity

m/d

v dt detritus settling velocity

m/d

v i inorganic suspended solids settling velocity

m/d

i volume of i reach

th

v p pathogen settling velocity

m/d

v pc non-living particulate organic carbon settling velocity

m/d

0 solar constant 2851 cal/cm /d w 2 the burial velocity

m/d

W h,i net heat load from point and non-point sources into reach

cal/d

i W i external loading of constituent to reach i

g/d or mg/d x pathogen

cfu/100 mL z w height above water for wind speed measurements

QUAL2K

November 25, 2003

Greek:

Symbol Definition Units

α depth rating curve coefficient dimensionless α sun’s altitude

radians α d sun’s altitude

degrees α 2 s sediment thermal diffusivity

cm /s α 0 fraction of total inorganic carbon in carbon dioxide

dimensionless α 1 fraction of total inorganic carbon in bicarbonate

dimensionless α 2 fraction of total inorganic carbon in carbonate

dimensionless α i effect of inorganic suspended solids on light attenuation

L/mgD/m α o

effect of particulate organic matter on light attenuation L/mgD/m α p linear effect of chlorophyll on light attenuation

L/ µ gA/m α 2/3 pn non-linear effect of chlorophyll on light attenuation

(L/ µ gA) /m β depth rating curve exponent

dimensionless δ solar declination

radians ∆ π PO 4,1 factor that increases the aerobic sediment layer partition

dimensionless coefficient relative to the anaerobic coefficient ∆ θ v virtual temperature difference between the water and air

°F ∆ t s difference between standard and local civic time

hr ∆ x i length of ith reach

m ε emissivity of water

dimensionless ε clear

emissivity of longwave radiation from the sky with no 0-1 clouds ε sky

emissivity of longwave radiation from the sky with 0-1 clouds

ε a estimated error % φ Lb bottom algae light attenuation

0-1 φ Lp phytoplankton light attenuation

0-1 φ Nb bottom algae nutrient attenuation factor

0-1 φ Np phytoplankton nutrient attenuation factor

0-1 µ p phytoplankton photosynthesis rate

/d ρ 3 density of water g/cm

2 σ 4 Stefan-Boltzmann constant 11.7x10 cal/(cm dK ) τ local hour angle of sun

radians τ th

i residence time of i reach

d θ temperature coefficient for zero and first-order reactions

dimensionless θ am elevation adjusted optical air mass

ω 12 the bioturbation mass transfer coefficient between the m/d sediment layers

π 3 ai the partition coefficient for ammonium in sediment layer m /gD i

π 3 pi the partition coefficient for inorganic phosphorus in m /gD sediment layer i

θ CH 4 temperature correction factor for sediment methane dimensionless oxidation

QUAL2K

November 25, 2003

θ Dd temperature coefficient for porewater diffusion dimensionless θ Dp temperature coefficient for bioturbation diffusion

dimensionless θ NH 4 temperature correction factor for sediment nitrification

dimensionless θ NO 3 sediment denitrification temperature correction factor

dimensionless θ POC , G 1 temperature correction factor for labile POC

dimensionless mineralization

κ CH 4,1 the reaction velocity for methane oxidation in the m/d aerobic sediments

κ NH 4,1 the reaction velocity for nitrification in the aerobic m/d sediments

κ NO 3, i denitrification reaction velocity sediment layer i m/d

QUAL2K

November 25, 2003