Lake Okeechobee System Operating Manual

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DRAFT
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### Lake Okeechobee System Operating Manual (WQ Subteam)

#### .fancy[DRAFT - Caloosahatchee River Estuary Nutrient Loading Model]

#### Addendum to [2020-09-18 presentation](https://owper-tech.github.io/slides/LOSOM/ENLM/Julian_LOSOM_ENLM#1), response to comments

FDEP - Office of Water Policy and Ecosystem Restoration

January 14, 2021

???
- Answer to comments provided during meeting and post-meeting comments

---
name: questions

#### General Comments

Link to [2020-09-18 presentation](https://owper-tech.github.io/slides/LOSOM/ENLM/Julian_LOSOM_ENLM#1).

General comments on FDEP presentation dated 9/18/2020

The use of water quality models for LOSOM evaluations:

* What do models look like with hurricane years included?

*	Is modeling necessary since historical data exist and can be applied to the flow values that will be simulated during the LOSOM evaluations?

* Models are inaccurate and tend to estimate values closer to averages than to extremes - which occur in real life – and have a significant effect on water quality.

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Comments on FDEP presentation dated 9/18/2020 recieved from Gary Goforth

The use of water quality models for LOSOM evaluations:

1.	Is unnecessary since historical data exist and can be applied to the flow values that will be simulated during the LOSOM evaluations.

2.	Is inaccurate and tends to estimate values closer to averages than to extremes - which occur in real life – and have a significant effect on water quality.

3.	Leads to a waste of time as people argue over the models; particularly a model from FDEP – the people who mislead the public annually using their erroneous BMAP models and claiming that water quality is significantly better than it really is (compared to measured data).
--->

???
other comments from Goforth
Also: 
1.	Why did FDEP ignore the St Lucie Estuary?
 - Response: If attended presentation you would have this information, St Lucie models are currently under developement.
2.	Why did FDEP ignore the public health and safety impacts of lake discharges to the estuaries that contain toxic blue green algae?
 - Response: was not the emphasis of the presentation/work.
3.	FDEP arbitrarily excluded years with major hurricanes – 9 years out of a 38-year data set – almost 25% of the period of record.  They actually assume that hurricanes don’t happen and don’t affect water quality – not surprised by this absurd assumption from FDEP.  If their models can’t handle the realty of hurricanes then they should abandon the models and rely on historical data.
 - Response: Models were developed to estimate water quality based on system operations. Response to hurricane the system is generally operated in a different manner (quickly to make storage available for run-off)
4.	There was no mention of TP and TN TMDLs for the estuaries.
 - Response: TMDLs are a seperate process and require specifics 
5.	There was no mention of how the model will be used during LOSOM evaluations.
 - Response: Discussed during presentation
6.	The model ignores total suspended sediment which causes significant damages to the estuaries, e.g., smothers seagrasses.
 - Response: CRE estuary is light limited more from CDOM than particulate

---

#### Model Comparisons

Absolute and Relative measures of error were used to compare models.

- Absolute error - Root Mean Square Error (RMSE) or Residual Residual Standard error (RSE or `$\sigma$`)

- Relative error - coefficient of determination ( `$R^{2}$`)

.pull-left[

.small[
Root Mean Square Error (RMSE)

`\begin{align*}
RMSE = \sqrt{ \frac{\sum_{i=1}^{n}( X_{i} - \hat{X_{i}} )^{2} }{n} }
\end{align*}`

Residual Standard error (RSE)

`\begin{align*}
RSE = \sqrt{ \frac{\sum_{i=1}^{n}( X_{i} - \hat{X_{i}} )^{2} }{df} }
\end{align*}`

.small[
`$X_{i}$`: Oberseved value

`$\hat{X_{i}}$`: Predicted value

`$n$`: Number of observations

`$df$`: Model residual degrees of freedom
]

* Values closer to zero represent model prediction closer to observed.
]
]

.pull-right[

.small[
`$R^{2}$`

`\begin{align*}
R^{2} = 1- { \frac{RSS}{TSS} }
\end{align*}`

Adjusted `$R^{2}$` ( `$R^{2}_{adj.}$` )

`\begin{align*}
R^{2}_{adj.} = 1- \left[{ \frac{(1-R^{2})(n-1)}{n-K-1} }\right]
\end{align*}`

.small[

`$RSS$`: Residual sum of squares

`$TSS$`: Total sum of squares

`$n$`: Number of observations

`$K$`: Kumber of variables

]

* Represents the proportion of the variance explained by the model.

]
]

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Root Mean Square Difference (RMSD)

`\begin{align*}
RMSD = \sqrt{ \frac{\sum_{i=1}^{n}( \hat{X_{A,i}} - \hat{X_{B,i}} )^{2} }{n} }
\end{align*}`

Where:

`$\hat{X_{A}}$` and `$\hat{X_{B}}$` model estimates for each model

- Average difference (or bias) of predictions between models as a percentage was estimated.
-->

???
RSME different from Residual Standard error (sigma)

`sqrt( sum(residuals(fit)^2) / fit$df.residual ) `

R2 assumes that every single variable explains the variation in the dependent variable. The adjusted R2 tells you the percentage of variation explained by only the independent variables that actually affect the dependent variable.

---

#### Inclusion vs Exclusion of Hurricane Years

`\begin{align*}
TP Load_{S79} = Q_{C43 Basin} +  Q_{S77} + Mean  Lake  Stage
\end{align*}`

- Data error in initally presented model

- No data transformations needed, and fit the assumptions of the statistical test

- Model Fit Summary:

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0.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-e1b0737f{width:144px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(255, 255, 255, 0.00);border-top: 1.00px solid rgba(255, 255, 255, 0.00);border-left: 1.00px solid rgba(255, 255, 255, 0.00);border-right: 1.00px solid rgba(255, 255, 255, 0.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-e1b07380{width:72px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(255, 255, 255, 0.00);border-top: 1.00px solid rgba(255, 255, 255, 0.00);border-left: 1.00px solid rgba(255, 255, 255, 0.00);border-right: 1.00px solid rgba(255, 255, 255, 0.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-e1b07381{width:86px;background-color:transparent;vertical-align: middle;border-bottom: 2.00px solid rgba(0, 0, 0, 1.00);border-top: 2.00px solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-e1b07382{width:58px;background-color:transparent;vertical-align: middle;border-bottom: 2.00px solid rgba(0, 0, 0, 1.00);border-top: 2.00px solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-e1b07383{width:144px;background-color:transparent;vertical-align: middle;border-bottom: 2.00px solid rgba(0, 0, 0, 1.00);border-top: 2.00px solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-e1b07384{width:144px;background-color:transparent;vertical-align: middle;border-bottom: 2.00px solid rgba(0, 0, 0, 1.00);border-top: 2.00px solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-e1b07385{width:72px;background-color:transparent;vertical-align: middle;border-bottom: 2.00px solid rgba(0, 0, 0, 1.00);border-top: 2.00px solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}</style><table style='border-collapse:collapse;'><thead><tr style="overflow-wrap:break-word;"><td colspan="8"class="cl-e1b0737f">Model fit statistics for the S-79 total phosphorus load models using all available data and excluding hurricane years.</td></tr><tr style="overflow-wrap:break-word;"><td class="cl-e1b07383">Modela</td><td class="cl-e1b07382">R²</td><td class="cl-e1b07382">Adj R²</td><td class="cl-e1b07382">σb </td><td class="cl-e1b07385">F-Statistic</td><td class="cl-e1b07382">ρ-value</td><td class="cl-e1b07384">DOF (Model, Residuals)</td><td class="cl-e1b07381">Observations</td></tr></thead><tbody><tr style="overflow-wrap:break-word;"><td class="cl-e1b04c85">All Data</td><td class="cl-e1b04c82">0.80</td><td class="cl-e1b04c82">0.78</td><td class="cl-e1b04c82">49112</td><td class="cl-e1b04c86">29.84</td><td class="cl-e1b04c82"><0.01</td><td class="cl-e1b04c84">3, 22</td><td class="cl-e1b04c83">26</td></tr><tr style="overflow-wrap:break-word;"><td class="cl-e1b04c8b">Hurricane Years Excluded</td><td class="cl-e1b04c87">0.74</td><td class="cl-e1b04c87">0.69</td><td class="cl-e1b04c87">74805</td><td class="cl-e1b04c8a">14.90</td><td class="cl-e1b04c87"><0.01</td><td class="cl-e1b04c89">3, 16</td><td class="cl-e1b04c88">20</td></tr><tr style="overflow-wrap:break-word;"><td colspan="8"class="cl-e1b0737f">a Total Phosphorus Load Model (WY1982 - 2019)</td></tr><tr style="overflow-wrap:break-word;"><td colspan="8"class="cl-e1b0737f">b σ = Residual Standard Error</td></tr><tr style="overflow-wrap:break-word;"><td colspan="8"class="cl-e1b0737f"> Models based on 70:30 train:test approach</td></tr></tbody></table></div>

---
name: S79TPMod
#### Inclusion vs Exclusion of Hurricane Years

`\begin{align*}
TP Load_{S79} = Q_{C43 Basin} +  Q_{S77} + Mean  Lake  Stage
\end{align*}`

- Final Model

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0.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-e1de915a{width:86px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(255, 255, 255, 0.00);border-top: 1.00px solid rgba(255, 255, 255, 0.00);border-left: 1.00px solid rgba(255, 255, 255, 0.00);border-right: 1.00px solid rgba(255, 255, 255, 0.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-e1deb806{width:108px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(255, 255, 255, 0.00);border-top: 1.00px solid rgba(255, 255, 255, 0.00);border-left: 1.00px solid rgba(255, 255, 255, 0.00);border-right: 1.00px solid rgba(255, 255, 255, 0.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-e1deb807{width:7px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(255, 255, 255, 0.00);border-top: 1.00px solid rgba(255, 255, 255, 0.00);border-left: 1.00px solid rgba(255, 255, 255, 0.00);border-right: 1.00px solid rgba(255, 255, 255, 0.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-e1deb808{width:108px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(255, 255, 255, 0.00);border-top: 1.00px solid rgba(255, 255, 255, 0.00);border-left: 1.00px solid rgba(255, 255, 255, 0.00);border-right: 1.00px solid rgba(255, 255, 255, 0.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-e1deb809{width:86px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(255, 255, 255, 0.00);border-top: 1.00px solid rgba(255, 255, 255, 0.00);border-left: 1.00px solid rgba(255, 255, 255, 0.00);border-right: 1.00px solid rgba(255, 255, 255, 0.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-e1deb80a{width:7px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(255, 255, 255, 0.00);border-top: 1.00px solid rgba(255, 255, 255, 0.00);border-left: 1.00px solid rgba(255, 255, 255, 0.00);border-right: 1.00px solid rgba(255, 255, 255, 0.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-e1deb80b{width:108px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(255, 255, 255, 0.00);border-top: 1.00px solid rgba(255, 255, 255, 0.00);border-left: 1.00px solid rgba(255, 255, 255, 0.00);border-right: 1.00px solid rgba(255, 255, 255, 0.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-e1deb80c{width:86px;background-color:transparent;vertical-align: middle;border-bottom: 2.00px solid rgba(0, 0, 0, 1.00);border-top: 2.00px solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-e1deb80d{width:7px;background-color:transparent;vertical-align: middle;border-bottom: 2.00px solid rgba(0, 0, 0, 1.00);border-top: 2.00px solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-e1deb80e{width:108px;background-color:transparent;vertical-align: middle;border-bottom: 2.00px solid rgba(0, 0, 0, 1.00);border-top: 2.00px solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}</style><table style='border-collapse:collapse;'><thead><tr style="overflow-wrap:break-word;"><td colspan="6"class="cl-e1deb80b">S-79 total phosphorus model results and estimates fitted using all available data during the water year 1982 - 2019 period.</td></tr><tr style="overflow-wrap:break-word;"><td class="cl-e1deb80e"></td><td class="cl-e1deb80c">Estimate</td><td class="cl-e1deb80c">Standard Error</td><td class="cl-e1deb80c">t-value</td><td class="cl-e1deb80c">ρ-value</td><td class="cl-e1deb80d"></td></tr></thead><tbody><tr style="overflow-wrap:break-word;"><td class="cl-e1de9152">(Intercept)</td><td class="cl-e1de9150">127,156.07</td><td class="cl-e1de9150">103,885.73</td><td class="cl-e1de9150">1.22</td><td class="cl-e1de9150">0.23</td><td class="cl-e1de9151"></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-e1de9154">QC43</td><td class="cl-e1de9153">0.20</td><td class="cl-e1de9153">0.05</td><td class="cl-e1de9153">3.72</td><td class="cl-e1de9153">≤ 0.01</td><td class="cl-e1de9155"></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-e1de9154">QS77</td><td class="cl-e1de9153">0.08</td><td class="cl-e1de9153">0.02</td><td class="cl-e1de9153">3.70</td><td class="cl-e1de9153">≤ 0.01</td><td class="cl-e1de9155"></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-e1de9158">Mean Lake Stage</td><td class="cl-e1de9157">-7,689.38</td><td class="cl-e1de9157">9,172.09</td><td class="cl-e1de9157">-0.84</td><td class="cl-e1de9157">0.41</td><td class="cl-e1de9156"></td></tr><tr style="overflow-wrap:break-word;"><td colspan="6"class="cl-e1deb806"></td></tr><tr style="overflow-wrap:break-word;"><td colspan="6"class="cl-e1deb808">Residual standard error: 49112 on 22 degrees of freedom</td></tr><tr style="overflow-wrap:break-word;"><td colspan="6"class="cl-e1deb808">Multiple R-squared: 0.80, Adjusted R-squared: 0.78</td></tr><tr style="overflow-wrap:break-word;"><td colspan="6"class="cl-e1deb808">F-statistic: 29.84 on 22 and 3, ρ-value: ≤ 0.01</td></tr></tbody></table></div>

`\begin{align*}
TP Load_{S79} = 127156 + 0.20 Q_{C43 Basin} + 0.08 Q_{S77} - 7689 Mean  Lake  Stage
\end{align*}`

.footnote[
.small[[Model Diagnostics](#TP_diag) plots]
]

---
name: S79TP_eval1
class: left

#### S-79 Water Quality Model (Total Phosphorus)

`\begin{align*}
TP Load_{S79} = Q_{C43 Basin} +  Q_{S77} + Mean  Lake  Stage
\end{align*}`

.pull-left[
<img src="./resources/C43TPLoad_WY_ActualPred.png" width="1067" style="display: block; margin: auto;" />
Actual versus predicted TP loads at S-79 based on predictive model. Actual and predicted concentration were highly correlated (Spearman’s correlation: r=0.98, `$\rho$`<0.01).
]

--
.pull-right[

Model Fit
  - `$R^{2}_{adj}$` : 0.78
  - RSE : 49112
  
Train:Test
  - Mean Absolute Percent Error: 15 %
  - Min-Max Accuracy: 87 %

]

???
Mean absolute percentage error - lower the better
Min_Max Accuracy - higher the better

---
name: S79TP_eval2
class: left

#### S-79 Water Quality Model (Total Phosphorus)

`\begin{align*}
TP Load_{S79} = Q_{C43 Basin} +  Q_{S77} + Mean  Lake  Stage
\end{align*}`

.pull-left[
<img src="./resources/C43TPLoad_WY_kmodel.png" width="1067" style="display: block; margin: auto;" />
Actual versus predicted TP loads at S-79 with each k-model presented. 
]

--
.pull-right[
k-fold (k=10)

_Cross-validation error (average k errors)_

<div class="tabwid"><style>.cl-e1f8f7e8{font-family:'Arial';font-size:13px;font-weight:bold;font-style:normal;text-decoration:none;color:rgba(17, 17, 17, 1.00);background-color:transparent;}.cl-e1f8f7e9{font-family:'Arial';font-size:11px;font-weight:normal;font-style:normal;text-decoration:none;color:rgba(17, 17, 17, 1.00);background-color:transparent;}.cl-e1f8f7ea{font-family:'Arial';font-size:7px;font-weight:normal;font-style:normal;text-decoration:none;color:rgba(17, 17, 17, 1.00);background-color:transparent;position: relative;bottom:3px;}.cl-e1f8f7eb{font-family:'Arial';font-size:7px;font-weight:normal;font-style:normal;text-decoration:none;color:rgba(17, 17, 17, 1.00);background-color:transparent;position: relative;top:3px;}.cl-e1f8f7ec{font-family:'Arial';font-size:6px;font-weight:normal;font-style:normal;text-decoration:none;color:rgba(0, 0, 0, 1.00);background-color:transparent;position: relative;bottom:3px;}.cl-e1f8f7ed{font-family:'Arial';font-size:10px;font-weight:normal;font-style:normal;text-decoration:none;color:rgba(0, 0, 0, 1.00);background-color:transparent;}.cl-e1f8f7ee{margin:0;text-align:left;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:2px;padding-top:2px;padding-left:5px;padding-right:5px;line-height: 1.00;background-color:transparent;}.cl-e1f8f7ef{margin:0;text-align:center;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:2px;padding-top:2px;padding-left:5px;padding-right:5px;line-height: 1.00;background-color:transparent;}.cl-e1f8f7f0{margin:0;text-align:left;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 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solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-e1f945d8{width:72px;background-color:transparent;vertical-align: top;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-e1f945d9{width:72px;background-color:transparent;vertical-align: top;border-bottom: 2.00px solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-e1f945da{width:72px;background-color:transparent;vertical-align: middle;border-bottom: 2.00px solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-e1f945db{width:72px;background-color:transparent;vertical-align: middle;border-bottom: 2.00px solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-e1f945dc{width:72px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(255, 255, 255, 0.00);border-top: 1.00px solid rgba(255, 255, 255, 0.00);border-left: 1.00px solid rgba(255, 255, 255, 0.00);border-right: 1.00px solid rgba(255, 255, 255, 0.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-e1f945dd{width:72px;background-color:transparent;vertical-align: middle;border-bottom: 2.00px solid rgba(0, 0, 0, 1.00);border-top: 2.00px solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-e1f945de{width:72px;background-color:transparent;vertical-align: middle;border-bottom: 2.00px solid rgba(0, 0, 0, 1.00);border-top: 2.00px solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}</style><table style='border-collapse:collapse;'><thead><tr style="overflow-wrap:break-word;"><td class="cl-e1f945de"> </td><td class="cl-e1f945de">Parameter</td><td class="cl-e1f945dd">Mean</td><td class="cl-e1f945dd">Min</td><td class="cl-e1f945dd">Max</td></tr></thead><tbody><tr style="overflow-wrap:break-word;"><td rowspan="2"class="cl-e1f945d8">Model</td><td class="cl-e1f945d7">R2adj</td><td class="cl-e1f945d6">0.71</td><td class="cl-e1f945d6">0.62</td><td class="cl-e1f945d6">0.79</td></tr><tr style="overflow-wrap:break-word;"><td class="cl-e1f945d7">RMSE</td><td class="cl-e1f945d6">63,461</td><td class="cl-e1f945d6">41,657</td><td class="cl-e1f945d6">76,864</td></tr><tr style="overflow-wrap:break-word;"><td rowspan="2"class="cl-e1f945d9">Train:Test</td><td class="cl-e1f945d7">MAPE 1</td><td class="cl-e1f945d6">21</td><td class="cl-e1f945d6">16</td><td class="cl-e1f945d6">41</td></tr><tr style="overflow-wrap:break-word;"><td class="cl-e1f945db">MMA 1</td><td class="cl-e1f945da">83</td><td class="cl-e1f945da">78</td><td class="cl-e1f945da">86</td></tr><tr style="overflow-wrap:break-word;"><td colspan="5"class="cl-e1f945dc"> 1 Mean Absolute Percent Error (MAPE) and Min-Max Accuracy (MMA) expressed in percent</td></tr></tbody></table></div>

]

---

#### Inclusion vs Exclusion of Hurricane Years

`\begin{align*}
TN Load_{S79} = Q_{C43 Basin} +  Q_{S77} + Mean  Lake  Stage
\end{align*}`

- No data transformations needed, and fit the assumptions of the statistical test

- Model Fit Summary:

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0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-e21c9ac4{width:58px;background-color:transparent;vertical-align: middle;border-bottom: 2.00px solid rgba(0, 0, 0, 1.00);border-top: 2.00px solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-e21c9ac5{width:144px;background-color:transparent;vertical-align: middle;border-bottom: 2.00px solid rgba(0, 0, 0, 1.00);border-top: 2.00px solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-e21c9ac6{width:144px;background-color:transparent;vertical-align: middle;border-bottom: 2.00px solid rgba(0, 0, 0, 1.00);border-top: 2.00px solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-e21c9ac7{width:72px;background-color:transparent;vertical-align: middle;border-bottom: 2.00px solid rgba(0, 0, 0, 1.00);border-top: 2.00px solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}</style><table style='border-collapse:collapse;'><thead><tr style="overflow-wrap:break-word;"><td colspan="8"class="cl-e21c9824">Model fit statistics for the S-79 total nitrogen load models using all available data and excluding hurricane years.</td></tr><tr style="overflow-wrap:break-word;"><td class="cl-e21c9ac5">Modela</td><td class="cl-e21c9ac4">R²</td><td class="cl-e21c9ac4">Adj R²</td><td class="cl-e21c9ac4">σb </td><td class="cl-e21c9ac7">F-Statistic</td><td class="cl-e21c9ac4">ρ-value</td><td class="cl-e21c9ac6">DOF (Model, Residuals)</td><td class="cl-e21c9ac3">Observations</td></tr></thead><tbody><tr style="overflow-wrap:break-word;"><td class="cl-e21c981b">All Data</td><td class="cl-e21b5e4f">0.95</td><td class="cl-e21b5e4f">0.94</td><td class="cl-e21b5e4f">326435</td><td class="cl-e21c981c">140.19</td><td class="cl-e21b5e4f"><0.01</td><td class="cl-e21c981a">3, 22</td><td class="cl-e21b5e50">26</td></tr><tr style="overflow-wrap:break-word;"><td class="cl-e21c9821">Hurricane Years Excluded</td><td class="cl-e21c981d">0.94</td><td class="cl-e21c981d">0.93</td><td class="cl-e21c981d">410391</td><td class="cl-e21c9820">81.56</td><td class="cl-e21c981d"><0.01</td><td class="cl-e21c981f">3, 16</td><td class="cl-e21c981e">20</td></tr><tr style="overflow-wrap:break-word;"><td colspan="8"class="cl-e21c9824">a Total Nitrogen Load Model (WY1982 - 2019)</td></tr><tr style="overflow-wrap:break-word;"><td colspan="8"class="cl-e21c9824">b σ = Residual Standard Error</td></tr><tr style="overflow-wrap:break-word;"><td colspan="8"class="cl-e21c9824"> Models based on 70:30 train:test approach</td></tr></tbody></table></div>

---
name: S79TNMod

#### Inclusion vs Exclusion of Hurricane Years

`\begin{align*}
TN Load_{S79} = Q_{C43 Basin} +  Q_{S77} + Mean  Lake  Stage
\end{align*}`

- Final Model

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0.00);border-left: 1.00px solid rgba(255, 255, 255, 0.00);border-right: 1.00px solid rgba(255, 255, 255, 0.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-e246035d{width:108px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(255, 255, 255, 0.00);border-top: 1.00px solid rgba(255, 255, 255, 0.00);border-left: 1.00px solid rgba(255, 255, 255, 0.00);border-right: 1.00px solid rgba(255, 255, 255, 0.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-e246035e{width:86px;background-color:transparent;vertical-align: middle;border-bottom: 2.00px solid rgba(0, 0, 0, 1.00);border-top: 2.00px solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-e246035f{width:7px;background-color:transparent;vertical-align: middle;border-bottom: 2.00px solid rgba(0, 0, 0, 1.00);border-top: 2.00px solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-e2460360{width:108px;background-color:transparent;vertical-align: middle;border-bottom: 2.00px solid rgba(0, 0, 0, 1.00);border-top: 2.00px solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}</style><table style='border-collapse:collapse;'><thead><tr style="overflow-wrap:break-word;"><td colspan="6"class="cl-e246035d">S-79 total nitrogen model results and estimates fitted using all available data during the water year 1982 - 2019 period.</td></tr><tr style="overflow-wrap:break-word;"><td class="cl-e2460360"></td><td class="cl-e246035e">Estimate</td><td class="cl-e246035e">Standard Error</td><td class="cl-e246035e">t-value</td><td class="cl-e246035e">ρ-value</td><td class="cl-e246035f"></td></tr></thead><tbody><tr style="overflow-wrap:break-word;"><td class="cl-e245daec">(Intercept)</td><td class="cl-e245daea">27,560.89</td><td class="cl-e245daea">690,496.68</td><td class="cl-e245daea">0.04</td><td class="cl-e245daea">0.97</td><td class="cl-e245daeb"></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-e245daee">QC43</td><td class="cl-e245daed">1.53</td><td class="cl-e245daed">0.35</td><td class="cl-e245daed">4.38</td><td class="cl-e245daed">≤ 0.01</td><td class="cl-e245daef"></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-e245daee">QS77</td><td class="cl-e245daed">1.58</td><td class="cl-e245daed">0.15</td><td class="cl-e245daed">10.48</td><td class="cl-e245daed">≤ 0.01</td><td class="cl-e245daef"></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-e245daf2">Mean Lake Stage</td><td class="cl-e245daf1">20,812.63</td><td class="cl-e245daf1">60,964.10</td><td class="cl-e245daf1">0.34</td><td class="cl-e245daf1">0.74</td><td class="cl-e245daf0"></td></tr><tr style="overflow-wrap:break-word;"><td colspan="6"class="cl-e2460358"></td></tr><tr style="overflow-wrap:break-word;"><td colspan="6"class="cl-e246035a">Residual standard error: 326435 on 22 degrees of freedom</td></tr><tr style="overflow-wrap:break-word;"><td colspan="6"class="cl-e246035a">Multiple R-squared: 0.95, Adjusted R-squared: 0.94</td></tr><tr style="overflow-wrap:break-word;"><td colspan="6"class="cl-e246035a">F-statistic: 140.2 on 22 and 3, ρ-value: ≤ 0.01</td></tr></tbody></table></div>

`\begin{align*}
TN Load_{S79} = 27561 + 1.53 Q_{C43 Basin} + 1.58 Q_{S77} + 20813 Mean  Lake  Stage
\end{align*}`

.footnote[
.small[[Model Diagnostics](#TN_diag) plots]
]

---
name: S79TN_eval1
class: left

#### S-79 Water Quality Model (Total Nitrogen)

`\begin{align*}
TN Load_{S79} = Q_{C43 Basin} +  Q_{S77} + Mean  Lake  Stage
\end{align*}`

.pull-left[
<img src="./resources/C43TNLoad_WY_ActualPred.png" width="1067" style="display: block; margin: auto;" />
Actual versus predicted TN loads at S-79 based on predictive model. Actual and predicted concentration were highly correlated (Spearman’s correlation: r=0.95, `$\rho$`<0.01).
]

--
.pull-right[

Model Fit
  - `$R^{2}_{adj}$` : 0.94
  - RSE : 326400
  
Train:Test
  - Mean Absolute Percent Error: 9 %
  - Min-Max Accuracy: 92 %

]

???
Mean absolute percentage error - lower the better
Min_Max Accuracy - higher the better

---
name: S79TN_eval2
class: left

#### S-79 Water Quality Model (Total Nitrogen)

`\begin{align*}
TN Load_{S79} = Q_{C43 Basin} +  Q_{S77} + Mean  Lake  Stage
\end{align*}`

.pull-left[
<img src="./resources/C43TNLoad_WY_kmodel.png" width="1067" style="display: block; margin: auto;" />
Actual versus predicted TN loads at S-79 with each k-model presented. 
]

--
.pull-right[
k-fold (k=10)

_Cross-validation error (average k errors)_

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solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-e2613f62{width:72px;background-color:transparent;vertical-align: top;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-e2613f63{width:72px;background-color:transparent;vertical-align: top;border-bottom: 2.00px solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-e2613f64{width:72px;background-color:transparent;vertical-align: middle;border-bottom: 2.00px solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-e2613f65{width:72px;background-color:transparent;vertical-align: middle;border-bottom: 2.00px solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-e2613f66{width:72px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(255, 255, 255, 0.00);border-top: 1.00px solid rgba(255, 255, 255, 0.00);border-left: 1.00px solid rgba(255, 255, 255, 0.00);border-right: 1.00px solid rgba(255, 255, 255, 0.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-e2613f67{width:72px;background-color:transparent;vertical-align: middle;border-bottom: 2.00px solid rgba(0, 0, 0, 1.00);border-top: 2.00px solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-e2613f68{width:72px;background-color:transparent;vertical-align: middle;border-bottom: 2.00px solid rgba(0, 0, 0, 1.00);border-top: 2.00px solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}</style><table style='border-collapse:collapse;'><thead><tr style="overflow-wrap:break-word;"><td class="cl-e2613f68"> </td><td class="cl-e2613f68">Parameter</td><td class="cl-e2613f67">Mean</td><td class="cl-e2613f67">Min</td><td class="cl-e2613f67">Max</td></tr></thead><tbody><tr style="overflow-wrap:break-word;"><td rowspan="2"class="cl-e2613f62">Model</td><td class="cl-e2613f61">R2adj</td><td class="cl-e2613f60">0.93</td><td class="cl-e2613f60">0.89</td><td class="cl-e2613f60">0.96</td></tr><tr style="overflow-wrap:break-word;"><td class="cl-e2613f61">RMSE</td><td class="cl-e2613f60">376,894</td><td class="cl-e2613f60">324,753</td><td class="cl-e2613f60">411,799</td></tr><tr style="overflow-wrap:break-word;"><td rowspan="2"class="cl-e2613f63">Train:Test</td><td class="cl-e2613f61">MAPE 1</td><td class="cl-e2613f60">11</td><td class="cl-e2613f60">7</td><td class="cl-e2613f60">19</td></tr><tr style="overflow-wrap:break-word;"><td class="cl-e2613f65">MMA 1</td><td class="cl-e2613f64">89</td><td class="cl-e2613f64">83</td><td class="cl-e2613f64">93</td></tr><tr style="overflow-wrap:break-word;"><td colspan="5"class="cl-e2613f66"> 1 Mean Absolute Percent Error (MAPE) and Min-Max Accuracy (MMA) expressed in percent</td></tr></tbody></table></div>

]

---

#### Modeled Loads

---
name: POR

#### Using monthly WQ data

.pull-left[

* A suggestion was made to use the existing measured data instead of developing the predictive equation.

* Other restoration planning efforts (i.e. Restoration Strategies) have used this method in the past.

]

.pull-right[
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1.00);padding-bottom:2px;padding-top:2px;padding-left:5px;padding-right:5px;line-height: 1.00;background-color:transparent;}.cl-e27a4b63{margin:0;text-align:center;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:2px;padding-top:2px;padding-left:5px;padding-right:5px;line-height: 1.00;background-color:transparent;}.cl-e27a4b64{margin:0;text-align:left;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:0;padding-top:0;padding-left:0;padding-right:0;line-height: 1.00;background-color:transparent;}.cl-e27a4b65{width:36px;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-e27a4b66{width:108px;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-e27a4b67{width:108px;background-color:transparent;vertical-align: middle;border-bottom: 2.00px solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-e27a4b68{width:36px;background-color:transparent;vertical-align: middle;border-bottom: 2.00px solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-e27b8528{width:36px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(255, 255, 255, 0.00);border-top: 1.00px solid rgba(255, 255, 255, 0.00);border-left: 1.00px solid rgba(255, 255, 255, 0.00);border-right: 1.00px solid rgba(255, 255, 255, 0.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-e27b8529{width:108px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(255, 255, 255, 0.00);border-top: 1.00px solid rgba(255, 255, 255, 0.00);border-left: 1.00px solid rgba(255, 255, 255, 0.00);border-right: 1.00px solid rgba(255, 255, 255, 0.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-e27b852a{width:36px;background-color:transparent;vertical-align: middle;border-bottom: 2.00px solid rgba(0, 0, 0, 1.00);border-top: 2.00px solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-e27b852b{width:108px;background-color:transparent;vertical-align: middle;border-bottom: 2.00px solid rgba(0, 0, 0, 1.00);border-top: 2.00px solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}</style><table style='border-collapse:collapse;'><thead><tr style="overflow-wrap:break-word;"><td class="cl-e27b852a">Month </td><td class="cl-e27b852b">Total Phosphorus (μg L⁻¹) a</td><td class="cl-e27b852b">Total Nitrogen (mg L⁻¹) a</td></tr></thead><tbody><tr style="overflow-wrap:break-word;"><td class="cl-e27a4b65">Jan</td><td class="cl-e27a4b66">97 ± 28 (58)</td><td class="cl-e27a4b66">1.40 ± 0.36 (56)</td></tr><tr style="overflow-wrap:break-word;"><td class="cl-e27a4b65">Feb</td><td class="cl-e27a4b66">89 ± 21 (49)</td><td class="cl-e27a4b66">1.71 ± 2.54 (49)</td></tr><tr style="overflow-wrap:break-word;"><td class="cl-e27a4b65">Mar</td><td class="cl-e27a4b66">93 ± 25 (54)</td><td class="cl-e27a4b66">1.28 ± 0.32 (55)</td></tr><tr style="overflow-wrap:break-word;"><td class="cl-e27a4b65">Apr</td><td class="cl-e27a4b66">102 ± 26 (51)</td><td class="cl-e27a4b66">1.25 ± 0.62 (50)</td></tr><tr style="overflow-wrap:break-word;"><td class="cl-e27a4b65">May</td><td class="cl-e27a4b66">129 ± 37 (55)</td><td class="cl-e27a4b66">1.34 ± 0.26 (55)</td></tr><tr style="overflow-wrap:break-word;"><td class="cl-e27a4b65">Jun</td><td class="cl-e27a4b66">179 ± 67 (49)</td><td class="cl-e27a4b66">1.57 ± 0.57 (49)</td></tr><tr style="overflow-wrap:break-word;"><td class="cl-e27a4b65">Jul</td><td class="cl-e27a4b66">179 ± 66 (56)</td><td class="cl-e27a4b66">1.47 ± 0.28 (56)</td></tr><tr style="overflow-wrap:break-word;"><td class="cl-e27a4b65">Aug</td><td class="cl-e27a4b66">166 ± 41 (55)</td><td class="cl-e27a4b66">1.43 ± 0.18 (54)</td></tr><tr style="overflow-wrap:break-word;"><td class="cl-e27a4b65">Sep</td><td class="cl-e27a4b66">161 ± 49 (53)</td><td class="cl-e27a4b66">1.47 ± 0.24 (51)</td></tr><tr style="overflow-wrap:break-word;"><td class="cl-e27a4b65">Oct</td><td class="cl-e27a4b66">128 ± 33 (50)</td><td class="cl-e27a4b66">1.43 ± 0.19 (50)</td></tr><tr style="overflow-wrap:break-word;"><td class="cl-e27a4b65">Nov</td><td class="cl-e27a4b66">109 ± 26 (56)</td><td class="cl-e27a4b66">1.43 ± 0.27 (55)</td></tr><tr style="overflow-wrap:break-word;"><td class="cl-e27a4b68">Dec</td><td class="cl-e27a4b67">97 ± 35 (46)</td><td class="cl-e27a4b67">1.37 ± 0.22 (46)</td></tr><tr style="overflow-wrap:break-word;"><td colspan="3"class="cl-e27b8528"> a Mean ± Std Dev (N)</td></tr><tr style="overflow-wrap:break-word;"><td colspan="3"class="cl-e27b8528"> POR: Jan 1981 - April 2019</td></tr><tr style="overflow-wrap:break-word;"><td colspan="3"class="cl-e27b8528"> Station ID: S79</td></tr><tr style="overflow-wrap:break-word;"><td colspan="3"class="cl-e27b8528"> Data Source: SFWMD DBHydro</td></tr></tbody></table></div>
]

---

#### Monthly POR Estimates

- Pair monthly mean TP and TN concentrations with discharge volumes to estimate load (See [prior slide](#POR)).

---

#### Monthly POR Estimates

- How does POR estimates approach match up?

.pull-left[
<img src="./resources/C43_WYObsPredloads_annualcomp.png" width="100%" style="display: block; margin: auto;" />
]

.pull-right[

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1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-e2966dea{width:108px;background-color:transparent;vertical-align: middle;border-bottom: 2.00px solid rgba(0, 0, 0, 1.00);border-top: 2.00px solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-e2966deb{width:72px;background-color:transparent;vertical-align: middle;border-bottom: 2.00px solid rgba(0, 0, 0, 1.00);border-top: 2.00px solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-e2966dec{width:36px;background-color:transparent;vertical-align: middle;border-bottom: 2.00px solid rgba(0, 0, 0, 1.00);border-top: 2.00px solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}</style><table style='border-collapse:collapse;'><thead><tr style="overflow-wrap:break-word;"><td colspan="4"class="cl-e2966de8">Root mean standard error for models and period of record estimates.</td></tr><tr style="overflow-wrap:break-word;"><td class="cl-e2966deb">Model</td><td class="cl-e2966dea">Estimate Method</td><td class="cl-e2966de9">RMSE 1</td><td class="cl-e2966dec">NS 2</td></tr></thead><tbody><tr style="overflow-wrap:break-word;"><td rowspan="3"class="cl-e296469d">TP Load</td><td class="cl-e296469f">Model - All Data</td><td class="cl-e296469e">45,177</td><td class="cl-e296469c">0.80</td></tr><tr style="overflow-wrap:break-word;"><td class="cl-e296469f">Model - Hur. Ex.</td><td class="cl-e296469e">66,908</td><td class="cl-e296469c">0.75</td></tr><tr style="overflow-wrap:break-word;"><td class="cl-e296469f">POR Est.</td><td class="cl-e296469e">73,439</td><td class="cl-e296469c">0.64</td></tr><tr style="overflow-wrap:break-word;"><td rowspan="3"class="cl-e29646a0">TN Load</td><td class="cl-e296469f">Model - All Data</td><td class="cl-e296469e">300,277</td><td class="cl-e296469c">0.95</td></tr><tr style="overflow-wrap:break-word;"><td class="cl-e296469f">Model - Hur. Ex.</td><td class="cl-e296469e">367,065</td><td class="cl-e296469c">0.95</td></tr><tr style="overflow-wrap:break-word;"><td class="cl-e29646a2">POR Est.</td><td class="cl-e29646a3">405,274</td><td class="cl-e29646a1">0.91</td></tr><tr style="overflow-wrap:break-word;"><td colspan="4"class="cl-e2966de8"> 1 RMSE value for POR Est. calculated using observed values versus annual estimated values using monthly mean concentrations</td></tr><tr style="overflow-wrap:break-word;"><td colspan="4"class="cl-e2966de8"> 2 NS = Nash-Sutcliffe coefficient</td></tr></tbody></table></div>

]

???
Nash-Sutcliff - estimates the ratio of error variance of the modeled versus observed timeseries.

---

- Monthly POR estimate inject much more variability than modeled values (all data or hurricanes excluded) for estimating TP and TN loads.

---

#### Flow-Weighted Mean Concentrations
<img src="./resources/C43_WYObsPredFWM_annual.png" width="80%" style="display: block; margin: auto;" />

---

#### Future Work

- Finalize models.
 
 - Develop St Lucie Estuary (S-80) Models.
 
 - Apply models to RSM-BN to evaluate changes in nutrient loads relative to baseline conditions.

---
class: inverse

---
name: TP_diag

**S79 TP Model diagnostics**

.pull-left[

<img src="./resources/S79_TPModel_diag.png" width="1600" style="display: block; margin: auto;" />
.small[S79 TP model diagnostics plots (Top Left: Residuals vs Fitted, Bottom Left: Normal Q-Q, Top Right: Scale-Location, Bottom right: Residuals vs leverage.).]

.small[

- GVLMA (Global Stats = 3.36, `$\rho$` =0.50)

- Shapiro-Wilk normality test (W=0.92, `$\rho$` =0.05)

]

.pull-right[

<img src="./resources/S79_TPModResid_ACF.png" width="100%" style="display: block; margin: auto;" />
.small[S79 TP Model residual Autocorrelation Function.]

.small[

- Breusch-Godfrey (LM test = 0.06, df = 1, `$\rho$`=0.80)

]

.footnote[
.small[[TP Model](#S79TPMod) plots]
]

---
name: TN_diag

**S79 TN Model diagnostics**

.pull-left[

<img src="./resources/S79_TNModel_diag.png" width="1600" style="display: block; margin: auto;" />
.small[S79 TN model diagnostics plots (Top Left: Residuals vs Fitted, Bottom Left: Normal Q-Q, Top Right: Scale-Location, Bottom right: Residuals vs leverage.).]

.small[

- GVLMA (Global Stats = 6.25, `$\rho$` =0.18)

- Shapiro-Wilk normality test (W=0.94, `$\rho$` =0.12)

]

.pull-right[

<img src="./resources/S79_TNModResid_ACF.png" width="100%" style="display: block; margin: auto;" />
.small[S79 TN Model residual Autocorrelation Function.]

.small[

- Breusch-Godfrey (LM test = 0.19, df = 1, `$\rho$`=0.66)

]

.footnote[
.small[[TN Model](#S79TNMod) plots]
]