Symbol
|
Definition
|
Units
|
|
|
surface area of element i
|
acres
|
[CO2]s
|
saturation concentration of carbon dioxide
|
mole/L
|
[CO32?]
|
carbonate ion
|
mole/L
|
[H+]
|
hydronium ion
|
mole/L
|
[H2CO3*]
|
sum of dissolved carbon dioxide and carbonic acid
|
mole/L
|
[HCO3?]
|
bicarbonate ion
|
mole/L
|
[OH?]
|
hydroxyl ion
|
mole/L
|
a
|
velocity rating curve coefficient
|
dimensionless
|
a"
|
mean atmospheric transmission coefficient after scattering and absorption
|
Dimensionless
|
a’
|
mean atmospheric transmission coefficient
|
Dimensionless
|
a1
|
atmospheric molecular scattering coefficient for radiation transmission
|
dimensionless
|
Aa
|
atmospheric long-wave radiation coefficient
|
dimensionless
|
Ab
|
atmospheric long-wave radiation coefficient
|
mmHg-0.5 or mb-0.5
|
ab
|
bottom algae
|
mgA/m2
|
Ac
|
cross-sectional area
|
m2
|
ad
|
coefficient correcting dam reaeration for water quality
|
dimensionless
|
Alk
|
alkalinity
|
eq L?1 or mgCaCO3/L
|
ap
|
phytoplankton
|
mgC/L
|
ap
|
phytoplankton concentration
|
mgA/m3
|
at
|
atmospheric attenuation
|
dimensionless
|
atc
|
atmospheric transmission coefficient
|
dimensionless
|
B
|
average element width
|
m
|
b
|
velocity rating curve exponent
|
dimensionless
|
B0
|
bottom width
|
m
|
bd
|
coefficient correcting dam reaeration for dam type
|
dimensionless
|
c1
|
Bowen's coefficient
|
0.47 mmHg/oC
|
cf
|
fast reacting CBOD
|
mgO2/L
|
cf
|
fast CBOD in the overlying water
|
gO2/m3
|
Cgb(T)
|
temperature-dependent maximum photosynthesis rate
|
mgA/(m2 d)
|
CH4,1
|
methane concentration in the aerobic sediment layer
|
gO2/m3
|
CL
|
fraction of sky covered with clouds
|
dimensionless
|
cnps,i,j
|
jth non-point source concentration for element i
|
oC
|
Cp
|
specific heat of water
|
cal/(g oC)
|
cps,i,j
|
jth point source concentration for element i
|
oC
|
cs
|
slowly reacting CBOD
|
mgO2/L
|
Cs
|
saturation concentration of methane
|
mgO2/L
|
CSOD
|
the amount of oxygen demand generated by methane oxidation
|
gO2/m2/d
|
cT
|
total inorganic carbon
|
mole L?1
|
c'T,i?1
|
concentration of inorganic carbon entering element below a dam
|
mgO2/L
|
d
|
dust attenuation coefficient
|
dimensionless
|
Dd
|
pore water diffusion coefficient
|
m2/d
|
Dp
|
diffusion coefficient for bioturbation
|
m2/d
|
E’i
|
bulk dispersion coefficient between elements i and i + 1
|
m3/d
|
eair
|
air vapor pressure
|
mm Hg
|
elev
|
elevation above sea level
|
m
|
En
|
numerical dispersion
|
m2/d
|
Ep,i
|
longitudinal dispersion between elements i and i + 1
|
m2/s
|
eqtime
|
equation of time: the difference between mean solar time and true solar time when located on the reference longitude of the time zone considered
|
minutes
|
es
|
saturation vapor pressure at water surface
|
mmHg
|
f
|
photoperiod
|
fraction of day
|
fdai
|
fraction of ammonium in dissolved form in sediment layer i
|
dimensionless
|
fdpi
|
fraction of inorganic phosphorus in dissolved form in sediment layer i
|
dimensionless
|
FLp
|
phytoplankton growth attenuation due to light
|
dimensionless
|
Foxc
|
attenuation of CBOD oxidation due to low oxygen
|
dimensionless
|
Foxdn
|
enhancement of denitrification at low oxygen concentration
|
dimensionless
|
Foxna
|
attenuation due to low oxygen
|
dimensionless
|
Foxrb
|
attenuation due to low oxygen
|
dimensionless
|
Foxrp
|
attenuation due to low oxygen
|
dimensionless
|
fpai
|
fraction of ammonium in particulate form in sediment layer i
|
dimensionless
|
fppi
|
fraction of inorganic phosphorus in particulate form in sediment layer i
|
dimensionless
|
Fu
|
fraction unionized ammonia
|
|
g
|
acceleration due to gravity
|
= 9.81 m/s2
|
gX
|
mass of element X
|
g
|
H
|
water depth
|
m
|
H
|
water depth
|
m
|
Hd
|
drop in water elevation for a dam
|
m
|
Hi
|
thickness of sediment layer i
|
m
|
Hsed
|
sediment thickness
|
cm
|
I(0)
|
solar radiation at water surface
|
cal/cm2/d
|
I0
|
extraterrestrial radiation
|
cal/cm2/d
|
Jan
|
net atmospheric longwave radiation flux
|
cal/(cm2 d)
|
Jbr
|
longwave back radiation flux from water
|
cal/(cm2 d)
|
Jc
|
conduction flux
|
cal/(cm2 d)
|
JC,G1
|
flux of labile dissolved carbon
|
gO2/m2/d
|
JCH4
|
flux of methane from sediments to the overlying water
|
gO2/m2/d
|
JCH4,d
|
flux of dissolved methane generated in anaerobic sediments corrected for methane gas formation
|
gO2/m2/d
|
JCH4,T
|
carbon diagenesis flux corrected for denitrification
|
gO2/m2/d
|
Je
|
evaporation flux
|
cal/(cm2 d)
|
Ja
|
air-water heat flux
|
cal/(cm2 d)
|
JN
|
nitrogen diagenesis flux
|
gN/m2/d
|
JO2,dn
|
oxygen equivalents consumed during denitrification
|
gO2/m2/d
|
JP
|
phosphorus diagenesis flux
|
gP/m2/d
|
JPOC,G1
|
the flux of labile POC delivered to the anaerobic sediment layer
|
gO2/m2/d
|
JPOM
|
the downward flux of POM
|
gD m?2 d?1
|
Jsi
|
sediment-water heat flux
|
cal/(cm2 d)
|
Jsn
|
net solar shortwave radiation flux
|
cal/(cm2 d)
|
k(T)
|
temperature dependent first-order reaction rate
|
/d
|
K1
|
acidity constant for dissociation of carbonic acid
|
|
K2
|
acidity constant for dissociation of bicarbonate
|
|
Ka
|
equilibrium coefficient for ammonium dissociation
|
|
ka(T)
|
temperature-dependent oxygen reaeration coefficient
|
/d
|
kac(T)
|
temperature-dependent carbon dioxide reaeration coefficient
|
/d
|
kdb(T)
|
temperature-dependent bottom algae death rate
|
/d
|
kdc(T)
|
temperature-dependent fast CBOD oxidation rate
|
/d
|
kdn(T)
|
temperature-dependent denitrification rate
|
/d
|
kdp(T)
|
temperature-dependent phytoplankton death rate
|
/d
|
kdt(T)
|
temperature-dependent detritus dissolution rate
|
/d
|
kdX(T)
|
temperature-dependent pathogen die-off rate
|
/d
|
ke
|
light extinction coefficient
|
/m1
|
keb
|
a background coefficient accounting for extinction due to water and color
|
/m
|
kgp(T)
|
maximum photosynthesis rate at temperature T
|
/d
|
KH
|
Henry's constant
|
mole/(L atm)
|
khc(T)
|
temperature-dependent slow CBOD hydrolysis rate
|
/d
|
khn(T)
|
temperature-dependent organic nitrogen hydrolysis rate
|
/d
|
khnxb
|
preference coefficient of bottom algae for ammonium
|
mgN/m3
|
khnxp
|
preference coefficient of phytoplankton for ammonium
|
mgN/m3
|
khp(T)
|
temperature-dependent organic phosphorus hydrolysis rate
|
/d
|
KL12
|
pore water diffusion mass transfer coefficient
|
m/d
|
KLb
|
bottom algae light parameter
|
|
KLp
|
phytoplankton light parameter
|
ly/d
|
KM,Dp
|
oxygen half-saturation constant for bioturbation
|
gO2/m3
|
kna(T)
|
temperature-dependent nitrification rate for ammonia nitrogen
|
/d
|
KNH4
|
ammonium half-saturation constant
|
gN/m3
|
KNH4,O2
|
oxygen half-saturation constant
|
mgO2/L
|
kPOC,G1
|
the mineralization rate of labile POC
|
d?1
|
krb(T)
|
temperature-dependent bottom algae respiration rate
|
/d
|
krp(T)
|
temperature-dependent phytoplankton respiration/excretion rate
|
/d
|
ksNb
|
nitrogen half-saturation constant for bottom algae
|
?gN/L
|
ksNp
|
nitrogen half-saturation constant for phytoplankton
|
?gN/L
|
Ksocf
|
parameter for oxygen dependency of fast CBOD oxidation
|
|
Ksodn
|
parameter for oxygen dependency of denitrification
|
|
Ksona
|
parameter for oxygen dependency of nitrification
|
|
ksPb
|
phosphorus half-saturation constant for bottom algae
|
?gP/L
|
ksPp
|
phosphorus half-saturation constant for phytoplankton
|
?gP/L
|
Kw
|
acidity constant for dissociation of water
|
|
Lat
|
latitude
|
radians
|
Llm
|
longitude of local meridian
|
degrees
|
localTime
|
local standard time
|
minutes
|
Lsm
|
longitude of standard meridian
|
degrees
|
m
|
optical air mass
|
dimensionless
|
mgY
|
mass of element Y
|
mg
|
mi
|
inorganic suspended solids
|
mgD/L
|
mi
|
the solids concentration in sediment layer i
|
gD/m3
|
mo
|
detritus
|
mgD/L
|
mo
|
detritus concentration
|
gD/m3
|
n
|
Manning roughness coefficient
|
|
na
|
the ammonium concentration in the overlying water
|
mgN/m3
|
nau
|
unionized ammonia nitrogen
|
mgN/m3
|
nfac
|
atmospheric turbidity factor
|
dimensionless
|
NH4,i
|
the concentration of total ammonium in sediment layer i
|
gN/m3
|
nn
|
nitrate concentration in the overlying water
|
mgN/m3
|
no
|
organic nitrogen
|
mgN/m3
|
NO3,i
|
nitrate concentration in layer i
|
gN/m3
|
npai
|
total number of non-point withdrawals outflows from element i
|
dimensionless
|
npsi
|
total number of non-point sources inflows to element i
|
dimensionless
|
NSOD
|
the amount of oxygen demand generated by nitrification
|
gO2/m2/d
|
o
|
dissolved oxygen
|
mgO2/L
|
o
|
the dissolved oxygen concentration in the overlying water
|
gO2/m3
|
o’i?1
|
oxygen concentration entering an element below a dam
|
mgO2/L
|
ocrit
|
critical oxygen concentration for sediment phosphorus sorption
|
gO2/m3
|
os(T, elev)
|
saturation concentration of oxygen at temperature, T, and elevation above sea level, elev
|
mgO2/L
|
P
|
wetted perimeter
|
m
|
Pab
|
preference for ammonium as a nitrogen source for bottom algae
|
dimensionless
|
pai
|
total number of point withdrawals from element i
|
dimensionless
|
Pap
|
preference for ammonium as a nitrogen source for phytoplankton
|
dimensionless
|
PAR(z)
|
photosynthetically available radiation (PAR) at depth z below water surface
|
ly/d
|
patm
|
atmospheric pressure
|
mm Hg
|
pCO2
|
atmospheric partial pressure of carbon dioxide
|
atm
|
pi
|
inorganic phosphorus
|
?gP/L
|
pi
|
the inorganic phosphorus in the overlying water
|
mgP/m3
|
po
|
organic phosphorus
|
?gP/L
|
PO4,i
|
the concentration of total inorganic phosphorus in sediment layer i
|
gP/m3
|
POC2,G1
|
the concentration of the labile fraction of POC in the anaerobic sediment layer
|
gO2/m3
|
POCR
|
reference G1 concentration for bioturbation
|
gC/m3
|
psi
|
total number of point sources to element i
|
dimensionless
|
pwc
|
mean daily atmospheric precipitable water content
|
|
Q
|
flow
|
m3/s or m3/d
|
Qout,i
|
total outflow from element due to point and nonpoint withdrawals
|
m3/d
|
Qi
|
outflow from element i into element i + 1
|
m3/d
|
Qin,i
|
total inflow into element from point and nonpoint sources
|
m3/d
|
Qnpa,i,j
|
jth non-point withdrawal outflow from element i
|
m3/d
|
Qnps,i,j
|
jth non-point source inflow to element i
|
m3/d
|
Qpa,i,j
|
jth point withdrawal outflow from element i
|
m3/d
|
Qps,i,j
|
jth point source inflow to element i
|
m3/d
|
r
|
normalized radius of earth’s orbit (i.e., ratio of actual earth-sun distance to mean earth-sun distance
|
dimensionless
|
rcndn
|
ratio of oxygen equivalents lost per nitrate nitrogen that is denitrified
|
gO2/gN
|
rd
|
ratio of deficit above and below dam
|
dimensionless
|
rda
|
the ratio of dry weight to chlorophyll a
|
gD/mgA
|
RL
|
longwave reflection coefficient
|
dimensionless
|
roc
|
ratio of oxygen consumed per organic carbon oxidized to carbon dioxide
|
gO2/gC
|
roca
|
ratio of oxygen generated per organic carbon produced by photosynthesis when nitrate is taken up
|
gO2/gC
|
rocn
|
ratio of oxygen generated per organic carbon produced by photosynthesis when ammonia is taken up
|
gO2/gC
|
ron
|
the ratio of oxygen to nitrogen consumed during nitrification
|
= 4.57 gO2/gN
|
ron'
|
ratio of oxygen consumed per ammonia nitrogen converted by nitrification/denitrification to nitrogen gas
|
gO2/gN
|
ron’
|
the ratio of oxygen to nitrogen consumed for total conversion of ammonium to nitrogen gas via nitrification/denitrification
|
= 1.714 gO2/gN
|
Rs
|
albedo or reflectivity (fraction of solar radiation that is reflected)
|
dimensionless
|
S
|
channel slope
|
dimensionless
|
s
|
chloride
|
mgCl/L
|
s
|
mass transfer coefficient between the water and the aerobic sediments
|
m/d
|
S0
|
bottom slope
|
m/m
|
Sb,i
|
sources and sinks of constituent due to reactions for bottom algae
|
mgA/m2/d
|
Si
|
sources and sinks of constituent due to reactions and mass transfer mechanisms for water constituents
|
g/m3/d or mg/m3/d
|
SOD
|
the sediment oxygen demand
|
gO2/m2/d
|
SODs
|
the supplemental sediment oxygen demand
|
gO2/m2/d
|
SODt
|
total sediment oxygen demand = SOD + SODs
|
gO2/m2/d
|
ss
|
channel side slope
|
m/m
|
t
|
time
|
d
|
T
|
water temperature
|
oC
|
T
|
water temperature
|
oC
|
T,w,f
|
water temperature
|
oF
|
Ta
|
absolute temperature
|
K
|
Tair
|
air temperature
|
oC
|
Tair,f
|
air temperature
|
oF
|
Td
|
dew-point temperature
|
oC
|
Ti
|
temperature in element i
|
oC
|
timezone
|
time zone indicates local time zone in relation to Greenwich Mean Time (GMT) (negative in western hemisphere)
|
hours
|
Tnps,i,j
|
jth non-point source temperature for element i
|
oC
|
Tps,i,j
|
jth point source temperature for element i
|
oC
|
trueSolarTime
|
time determined from actual position of the sun in the sky
|
minutes
|
Ts,i
|
temperature of bottom sediment
|
oC
|
tsr
|
time of sunrise
|
Hr
|
tss
|
time of sunset
|
Hr
|
Tstd
|
standard time
|
Hr
|
tt,i
|
travel time from headwater to end of element i
|
D
|
U
|
mean velocity
|
m/s
|
Ui*
|
shear velocity
|
m/s
|
Uw
|
wind speed
|
m/s
|
Uw,mph
|
wind speed
|
mph
|
Uw,z
|
wind speed at height zw above water surface
|
m/s
|
va
|
phytoplankton settling velocity
|
m/d
|
va
|
phytoplankton settling velocity
|
m/d
|
vdt
|
detritus settling velocity
|
m/d
|
vdt
|
detritus settling velocity
|
m/d
|
vi
|
inorganic suspended solids settling velocity
|
m/d
|
Vi
|
volume of ith element
|
m3
|
vp
|
pathogen settling velocity
|
m/d
|
vpc
|
non-living particulate organic carbon settling velocity
|
m/d
|
W0
|
solar constant
|
2851 cal/cm2/d
|
w2
|
the burial velocity
|
m/d
|
Wh,i
|
net heat load from point and non-point sources into element i
|
cal/d
|
Wi
|
external loading of constituent to element i
|
g/d or mg/d
|
X
|
pathogen
|
cfu/100 mL
|
zw
|
height above water for wind speed measurements
|
m
|
Symbol
|
Definition
|
Units
|
|
a
|
depth rating curve coefficient
|
dimensionless
|
a
|
sun’s altitude
|
radians
|
?d
|
sun’s altitude
|
degrees
|
?s
|
sediment thermal diffusivity
|
cm2/s
|
?0
|
fraction of total inorganic carbon in carbon dioxide
|
dimensionless
|
?1
|
fraction of total inorganic carbon in bicarbonate
|
dimensionless
|
?2
|
fraction of total inorganic carbon in carbonate
|
dimensionless
|
?i
|
effect of inorganic suspended solids on light attenuation
|
L/mgD/m
|
?o
|
effect of particulate organic matter on light attenuation
|
L/mgD/m
|
?p
|
linear effect of chlorophyll on light attenuation
|
L/?gA/m
|
?pn
|
non-linear effect of chlorophyll on light attenuation
|
(L/?gA)2/3/m
|
?path
|
pathogen light efficiency factor
|
dimensionless
|
b
|
depth rating curve exponent
|
dimensionless
|
d
|
solar declination
|
radians
|
??PO4,1
|
factor that increases the aerobic sediment layer partition coefficient relative to the anaerobic coefficient
|
dimensionless
|
|
virtual temperature difference between the water and air
|
°F
|
?ts
|
difference between standard and local civic time
|
hr
|
?xi
|
length of ith element
|
m
|
e
|
emissivity of water
|
dimensionless
|
?clear
|
emissivity of longwave radiation from the sky with no clouds
|
0-1
|
?sky
|
emissivity of longwave radiation from the sky with clouds
|
0-1
|
?a
|
estimated error
|
%
|
?Lb
|
bottom algae light attenuation
|
0-1
|
?Lp
|
phytoplankton light attenuation
|
0-1
|
?Nb
|
bottom algae nutrient attenuation factor
|
0-1
|
?Np
|
phytoplankton nutrient attenuation factor
|
0-1
|
?p
|
phytoplankton photosynthesis rate
|
/d
|
r
|
density of water
|
g/cm3
|
s
|
Stefan-Boltzmann constant
|
11.7×10-8 cal/(cm2 d K4)
|
t
|
local hour angle of sun
|
radians
|
?i
|
residence time of ith element
|
d
|
q
|
temperature coefficient for zero and first-order reactions
|
dimensionless
|
?am
|
elevation adjusted optical air mass
|
|
?12
|
the bioturbation mass transfer coefficient between the sediment layers
|
m/d
|
?ai
|
the partition coefficient for ammonium in sediment layer i
|
m3/gD
|
?pi
|
the partition coefficient for inorganic phosphorus in sediment layer i
|
m3/gD
|
?CH4
|
temperature correction factor for sediment methane oxidation
|
dimensionless
|
?Dd
|
temperature coefficient for porewater diffusion
|
dimensionless
|
?Dp
|
temperature coefficient for bioturbation diffusion
|
dimensionless
|
?NH4
|
temperature correction factor for sediment nitrification
|
dimensionless
|
?NO3
|
sediment denitrification temperature correction factor
|
dimensionless
|
?POC,G1
|
temperature correction factor for labile POC mineralization
|
dimensionless
|
?CH4,1
|
the reaction velocity for methane oxidation in the aerobic sediments
|
m/d
|
?NH4,1
|
the reaction velocity for nitrification in the aerobic sediments
|
m/d
|
?NO3,i
|
denitrification reaction velocity sediment layer i
|
m/d
|
