Lake Okeechobee Technical Advisory Committee
Water Quality Data Analysis
Long-Term Trends
Spatial Variations
Bloom Frequency vs. Total P
P Mass Balance Modeling
Mass-Balance Data Analysis
Model Formulation
Calibration
TMDL Applications
Presentation to
W. Walker
April 6, 2000
Long-Term Monitoring Stations
#S
#S#S
#S#S
#S
#S
#S
L001
L002
L003
L004L005
L006
L007
L008
Median Values by Station & Year Variable: TP Chl-a TurbidityTrend (%/yr): 2.1% 1.5% 2.3%
Long-Term Water-Quality Trends at Open-Lake Stations
0
20
40
60
80
100
120
140
73 75 77 79 81 83 85 87 89 91 93 95 97 99T
ota
l P (
pp
b)
0
5
10
15
20
25
30
35
40
73 75 77 79 81 83 85 87 89 91 93 95 97 99C
hlo
rop
hyl
l-a
(p
pb
)
0
5
10
15
20
25
30
35
73 75 77 79 81 83 85 87 89 91 93 95 97 99T
urb
idit
y (
ntu
)
North ---------------------------------------------------------->South Central
Trend (%/yr)Station 73-99 80-99 90-99
L001 1.8 * 0.5 1.8 L002 2.3 * 0.5 1.1 L003 2.7 * 0.8 1.4 L004 2.5 * 0.7 1.0 L005 3.6 * 1.6 5.6 *L006 3.3 * 1.7 * 4.0 *L007 2.8 * 1.7 * 4.3 *L008 2.9 * 1.7 * 4.9 *
* significant at p < .05, seasonal kendall test
Long-Term Phosphorus TrendsLake Okeechobee Open-Lake Stations
0
1
2
3
4
5
6
L001 L002 L003 L004 L005 L006 L007 L008
Station
To
tal P
Tre
nd
(
% /
yr )
73-99
80-99
90-99
North -------------------------------------> West --- South -- West Central
Median Concentrations vs. Station & Time Interval
Spatial & Temporal Water Quality Variations at Open Lake Stations
0
20
40
60
80
100
120
140
L001 L002 L003 L004 L005 L006 L007 L008 Lake
To
tal P
(p
pp
)
73-81
82-90
91-99
0
5
10
15
20
25
30
35
40
L001 L002 L003 L004 L005 L006 L007 L008 Lake
Ch
loro
ph
yll-
a (p
pb
)
73-81
82-90
91-99
0
5
10
15
20
25
30
35
40
L001 L002 L003 L004 L005 L006 L007 L008 Lake
Tu
rbid
ity
(ntu
)
73-81
82-90
91-99
Long-Term Trends in Algal Bloom Frequency & Total P
0%
5%
10%
15%
20%
25%
30%
35%
40%
73 75 77 79 81 83 85 87 89 91 93 95 97 99
Blo
om
Fre
qu
ency
(%
)
Chl-a >40 ppb
Chl-a > 60 ppb
0
20
40
60
80
100
120
140
73 75 77 79 81 83 85 87 89 91 93 95 97 99
To
tal P
(p
pb
)
No Data
Algal Bloom Frequencies vs. Total P in Open Lake
0%
1%
2%
3%
4%
5%
6%
7%
8%
9%
10%
0 20 40 60 80 100 120 140
Median Annual Total P (ppb)
An
nu
al B
loo
m F
req
uen
cy (
%) Chl-a > 60 ppb
0%
5%
10%
15%
20%
25%
30%
35%
40%
0 20 40 60 80 100 120 140
Median Annual Total P (ppb)
An
nu
al B
loo
m F
req
uen
cy (
%) Chl-a > 40 ppb
Rainfall35
Inflow Outflow460 Area = 1730 150
Conc = 86Knet = 2.3
Retention 345
Phosphorus Fluxes in metric tons / yearAreas in 1000 acresConcentrations in ppbSettling Rates in m/yr
Phosphorus Mass Balance1973-1998 Average
LAKE
2.0
2.2
2.4
2.6
2.8
3.0
3.2
1970 1975 1980 1985 1990 1995 2000
Year
Mea
n D
epth
(m
)
4-Yr Rolling
1 Year
0
20
40
60
80
100
120
140
1970 1975 1980 1985 1990 1995 2000
Year
Lak
e P
(p
pb
)
4-Yr Rolling
1 Year
0
100
200
300
400
500
600
700
800
900
1000
1970 1975 1980 1985 1990 1995 2000
Year
To
tal P
Lo
ad (
mt/
yr)
4-Yr Rolling
1 Year
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
1970 1975 1980 1985 1990 1995 2000
Year
P R
esid
ence
Tim
e (
yrs
)
4-Yr Rolling
1 Year
0.0
2.0
4.0
6.0
8.0
10.0
12.0
1970 1975 1980 1985 1990 1995 2000
Year
Wat
er R
esid
ence
Tim
e (
yrs
)
4-Yr Rolling
1 Year
Net Settling Rate 1 Year & 4-Year Rolling Averages
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
2.0 2.2 2.4 2.6 2.8 3.0 3.2
Mean Depth (m)
Kn
et (
m/y
r)
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
1970 1975 1980 1985 1990 1995 2000
Year
Kn
et (
m/y
r)
Latmos
Linflow Qnet Clake
Lremoved
Knet Area Clake
Water Balance:
Qnet = Qout + dV/dt = Qin + Qprec - Qevap
Mass Balance:
Linflow + Latmos - Lremoved = Qnet Clake + Knet Area Clake
TMDL Calculation:
TMDL = Qnet Ctarget + Knet Area Ctarget
= Linflow + Latmos - Lremoved
Linflow = TMDL - Latmos + Lremoved
Model Calibration to 4-Year Rolling Averages, 1973 - 1998:
Knet = 4.76 exp [ -.063 ( Year - 1975 ) ] R2 = 0.97
Clake = Total Load / ( Qnet + Knet Area ) R2 = 0.90
Hydrologic Conditions for TMDL Calculations (1973-1998 Means):
Qnet = 1751 hm3/yr
Area = 1730 km2
Clake
Lake Okeechobee Steady-State P Balance Model
Model: Knet = 4.76 exp [ -.063 ( Year - 1975 ) ] R2 = 0.97
Clake = Total Load / ( Qnet + Knet Area ) R2 = 0.90
Lake Okeechobee Phosphorus Balance ModelFour-year Rolling Averages
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
1975 1980 1985 1990 1995 2000
Year
Kn
et (
m/y
r)
0
20
40
60
80
100
120
1975 1980 1985 1990 1995 2000
Year
Lak
e P
Co
nc
(pp
b)
Lake Okeechobee Phosphorus Balance ModelOne-Year & Four-Year Rolling Averages
0
20
40
60
80
100
120
140
1970 1975 1980 1985 1990 1995 2000
Year
Lak
e P
Co
nc
(pp
b)
Obs - 1 Yr
Obs - 4 Yr
Pred - 4 yr
0
1
2
3
4
5
6
7
8
9
1970 1975 1980 1985 1990 1995 2000
Year
Kn
et (
m/y
r)
Obs - 1 Yr
Obs - 4 Yr
Pred - 4 yr
Residuals Plots Observed - Predicted Concs 4-Year Rolling Averages
-10
-8
-6
-4
-2
0
2
4
6
8
10
1970 1975 1980 1985 1990 1995 2000
Year
Co
nc
Res
idu
al (
pp
b)
-10
-8
-6
-4
-2
0
2
4
6
8
10
2.2 2.4 2.6 2.8 3.0
Mean Depth (m)
Co
nc
Res
idu
al (
pp
b)
-10
-8
-6
-4
-2
0
2
4
6
8
10
250 350 450 550 650
External Load (mt/yr)
Co
nc
Res
idu
al (
pp
b)
-10
-8
-6
-4
-2
0
2
4
6
8
10
1.5 2.0 2.5 3.0 3.5
Inflow (e9 m3/yr)
Co
nc
Res
idu
al (
pp
b)
-10
-8
-6
-4
-2
0
2
4
6
8
10
-20 -10 0 10 20 30 40
Load Increase (mt/yr over 4 years)
Co
nc
Res
idu
al (
pp
b)
-10
-8
-6
-4
-2
0
2
4
6
8
10
100 150 200 250 300
Iinflow Conc (ppb)
Co
nc
Res
idu
al (
pp
b)
Rainfall
3336
73-77 94 - 98
Inflow Outflow
441 Conc = 54 106 83
502 305
Knet = 4.3 1.2
Retention 391 82%
233 43%
Phosphorus Loads in metric tons / year
Concentrations in ppb
Settling Rates in m/yr
Phosphorus Mass BalancesHistorical Conditions
Net Settling Rate Decreasing @ ~ 6% / year
From 4.3 m/yr in 1973-1977 to 1.2 m/yr in 1994-1998
Model residuals independent of depth, flow, & load
Explains 90% of variance in 4-yr rolling average conc
Implied time scales of sediment response:
Half-life (50% Response) 11 years90% Response 36 years
Potential Causal Factors:
Gradual accumulation & recycling of P
Decrease in lake area caused by dike
Decrease in calcium levels (?)
Recycling aggravated by increased water depths
wave action - resuspension
intermittent stratification &O2 loss (?)
increased light-limitation of algal growth
loss of rooted vegetation
increased horizontal transport
Reversible?
Decrease external P load
Decrease water depth
Remove sediment
Re-establish vegetation
Conservative Assumption for TMDL Calculation:
Use 1994-1998 settling rate
Steady-State Settling Rate may be lower
Effect of changes in water level?
Lake Okeechobee P Balance Results
Variable Units 73-98 73-77 94-98 84-96
Knet m/yr 2.32 4.31 1.22 1.65
Design Conditions ( 1973 - 1999 ) Means
Qnet hm3/yr 1750.6 1750.6 1750.6 1750.6
Qin hm3/yr 2564.5 2564.5 2564.5 2564.5
Area km2 1729.8 1729.8 1729.8 1729.8
Volume e9m3 4.7 4.7 4.7 4.7
Zmean m 2.70 2.70 2.70 2.70
Qs m/yr 1.01 1.01 1.01 1.01
Atmos P Load mg/m2-yr 20 20 20 20
Atmos P Load mt/yr 34.6 34.6 34.6 34.6
Historical Linflow mt/yr 460.2 460.2 460.2 460.2
TMDL Calculations
Lake Target Conc ppb 40.0 40.0 40.0 40.0
Ltotal = TMDL mt/yr 230.9 368.3 154.1 184.2
Latmos mt/yr 34.60 34.6 34.6 34.6
Linflow mt/yr 196.3 333.7 119.5 149.6
Cinflow ppb 76.5 130.1 46.6 58.3
Loutflow mt/yr 70.0 70.0 70.0 70.0
Load Reduction mt/yr 263.9 126.5 340.7 310.6
Load Reduction % 57% 27% 74% 67%
P Retention mt/yr 161 298 84 114
WC P Res Time years 0.81 0.51 1.21 1.01
Calibration Period
Lake Okeechobee TMDL Calculation
0
50
100
150
200
250
300
350
400
73-98 73-77 94-98 84-96
Calibration Period
TM
DL
( m
ton
s / y
r )
Tributary Atmospheric
0
20
40
60
80
100
120
140
73-98 73-77 94-98 84-96
Calibration Period
Tri
b In
flo
w C
on
c (p
pb
)
0%
10%
20%
30%
40%
50%
60%
70%
80%
73-98 73-77 94-98 84-96
Calibration Period
Lo
ad R
edu
ctio
n
0.0
1.0
2.0
3.0
4.0
5.0
73-98 73-77 94-98 84-96
Calibration Period
Kn
et (
m/y
r)
Rainfall35
1973-1998Historical Inflow Outflow
460 120 Area = 427 70Conc = 40
Reduction Knet = 1.2341
Retention 84Load Reduction 74%TMDL 154 mt/yrTarget Inflow Load 120 mt/yrTarget Inflow Conc 47 ppb
Phosphorus Fluxes in metric tons / year, Areas in 1000 Acres, Concentrations in ppb
Settling Rate in m/yr, Calibrated to 1994-1998 Data
LAKE
Phosphorus Mass BalanceTMDL - E X A M P L E
Area = 0Cin = 47
Cout = 4Knet = 20
Rainfall0 0 0 35
Post-Historical BMP Inflow
460 120 120 0BMP's Area = 0
Area = 427 Cin = 0341 C = 40 Cout = 4
Outflow Knet = 1.2 Knet = 40BMP Load Reduction 74% 70 0TMDL 154 mt/yr
Target Inflow Load 120 mt/yr Retention 84 0Target Inflow Conc 47 ppb ?
Sediment Removal ?P Loads in metric tons / year, Areas in 1000 acres, Concentrations in ppb, Settling Rates in m/yr
STA's
LAKE STA
Phosphorus Mass BalanceTMDL with Controls - Example 1
Area = 20Cin = 69
Cout = 21Knet = 20
Rainfall84 26 59 35
Post-Historical BMP Inflow
460 178 120 0BMP's Area = 0
Area = 427 Cin = 0282 C = 40 Cout = 4
Outflow Knet = 1.2 Knet = 40BMP Load Reduction 61% 70 0TMDL 154 mt/yr
Target Inflow Load 120 mt/yr Retention 84 0Target Inflow Conc 47 ppb ?
Sediment Removal ?P Loads in metric tons / year, Areas in 1000 acres, Concentrations in ppb, Settling Rates in m/yr
STA's
LAKE STA
Phosphorus Mass BalanceTMDL with Controls - Example 2
Area = 20Cin = 114
Cout = 33Knet = 20
Rainfall138 40 98 35
Post-Historical BMP Inflow
460 292 194 101BMP's Area = 20
Area = 427 Cin = 50168 C = 40 Cout = 13
Outflow Knet = 1.2 Knet = 40BMP Load Reduction 37% 70 27TMDL 154 mt/yr
Target Inflow Load 194 mt/yr Retention 84 74Target Inflow Conc 76 ppb ?
Sediment Removal ?P Loads in metric tons / year, Areas in 1000 acres, Concentrations in ppb,
STA's
LAKE STA
Phosphorus Mass BalanceTMDL with Controls - Example 3
TMDL = External Load + Atmospheric Load - Load Removed by STA
TMDL Components:
External Load Requirements:
Load Allocations with Parallel STA
-200
-150
-100
-50
0
50
100
150
200
250
300
0 5 10 15 20 25 30 35 40
STA Area (acres)
P L
oad
(m
ton
s/yr
)
TMDL
External Inflow
Atmospheric
STA Removal
0
20
40
60
80
100
120
0 5 10 15 20 25 30 35 40
STA Area (acres)
Tar
get
In
flo
w C
on
c (p
pb
)
0%
10%
20%
30%
40%
50%
60%
70%
80%E
xter
nal
Lo
ad R
edu
ctio
n (
%)
Inflow Conc
Load Reduc
Sensitivity of TMDL Calculation to Atmospheric LoadsCalibration Period: 94-98
PreviousVariable Units Assumed StudiesAtmospheric Load mg/m2-yr 20.0 43.3Atmospheric Load mt/yr 34.6 75.0Average Rainfall m/yr 1.07 1.07Bulk Concentration ppb 18.7 40.5
Atm Load Knet Conc R2 TMDL L Reduc Linflow Cinflowmg/m2-yr m/yr -- mt/yr % mt/yr ppb
1.22 0.90 154 74% 120 4710 1.12 0.89 148 72% 130 5120 1.22 0.90 154 74% 120 4730 1.31 0.90 161 76% 109 4240 1.40 0.90 167 79% 98 3850 1.50 0.90 174 81% 87 3460 1.59 0.90 180 83% 76 3070 1.69 0.90 187 86% 66 26