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
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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)
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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
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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
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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
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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
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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
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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
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