Lake Okeechobee System Operating Manual

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DRAFT - 9/18/2020
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### Lake Okeechobee System Operating Manual (WQ Subteam)

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

FDEP - Office of Water Policy and Ecosystem Restoration

September 18, 2020

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- Top down statistical modeling, where we used observed water quality and discharge data to fit a model. 
- Does not account for C-43 reservior but if we assume that the reservior is just (temp) storing basin water and no WQ treatment is occuring then the models can still be applied. 
- Does not account for *potential* nutrient reductions assoicated with the current Basin Action Management Plan(s).

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#### S-79 Water Quality Model

- __Goal:__ Develop a series of water quality models based on hydrodynamic indicators to be used in planning model scenario evaluation for LOSOM using RSMBN.

- __Period of Record:__ May 1981 – April 2019 (WY1982 – 2019)
  - Based on available data.
  - Years with major hurricanes were excluded.

- __Parameters of Interest:__ Total Phosphorus and Total Nitrogen.

- __Predictor Variables:__ Discharge (S77, S78, S79, C43 Basin) converted from ft3 s-1 to Acre-Ft d-1 and Lake Okeechobee stage elevation were considered.

- __Statistical Modeling:__
  - Multiple regression models using training and testing datasets (70:30). 
     - Training dataset: randomly sampled 70% of monthly data 
     - Testing dataset: remaining 30% was used for model testing
  - Verified with k-fold cross-validation linear modeling.

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#### Regional Simulation Model - Basins (RSMBN)

- A link-node application of the Regional Simulation Model (RSM) specific to Lake Okeechobee and Basins.

- \>100 basins/lakes/canals represented
  
  - \>150 connections represented
  
- Used in prior planning efforts.

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Geographical representation of RSM-BN

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- Annual TP and TN loads were estimated by interpolating water quality concentration daily from grab samples collected at each respective structure during days of observed flow (consistent with SFWMD Nutrient Load Program). 
  - Period of Record was restricted to WY 1982 – 2019.

- Major hurricane years were excluded from the dataset.
  - Major hurricane years were identified by major storms centerline that passed within 20 km of the C43 Basins and Lake Okeechobee.

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

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#### S-79 Water Quality Model (Total Phosphorus)
- TP load was square-root transformed to fit the assumptions of linear modeling

- Model assumptions and verified
  - GVLMA (Global Stats = 4.37, `\(\rho\)`=0.36)

- Variance inflation factors (VIF) evaluated for model

- Residuals check for autocorrelation (Breusch-Godfrey test)
  - Breusch-Godfrey (LM test = 0.27, df = 1, `\(\rho\)`=0.60)

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

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

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

- Model Output:

<div class="tabwid"><table style='border-collapse:collapse;'><thead><tr style="overflow-wrap:break-word;"><td style="width:126px;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;"><p style="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;background-color:transparent;">Parameter </td><td style="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;"><p style="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;background-color:transparent;">Estimate</td><td style="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;"><p style="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;background-color:transparent;">Standard Error</td><td style="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;"><p style="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;background-color:transparent;">t-value</td><td style="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;"><p style="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;background-color:transparent;">ρ-value</td><td style="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;"><p style="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;background-color:transparent;">VIF</td></tr></thead><tbody><tr style="overflow-wrap:break-word;"><td style="width:126px;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 1.25px 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;"><p style="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;background-color:transparent;">(Intercept)</td><td style="width:86px;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 1.25px 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;"><p style="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;background-color:transparent;">30.68</td><td style="width:86px;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 1.25px 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;"><p style="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;background-color:transparent;">181.80</td><td style="width:86px;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 1.25px 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;"><p style="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;background-color:transparent;">0.17</td><td style="width:86px;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 1.25px 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;"><p style="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;background-color:transparent;">0.87</td><td style="width:86px;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 1.25px 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;"><p style="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;background-color:transparent;">---</td></tr><tr style="overflow-wrap:break-word;"><td style="width:126px;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;"><p style="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;background-color:transparent;">QC43</td><td style="width:86px;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;"><p style="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;background-color:transparent;">2.17x10-4</td><td style="width:86px;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;"><p style="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;background-color:transparent;">7.33x10-5</td><td style="width:86px;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;"><p style="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;background-color:transparent;">2.95</td><td style="width:86px;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;"><p style="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;background-color:transparent;"><0.01</td><td style="width:86px;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;"><p style="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;background-color:transparent;">2.96</td></tr><tr style="overflow-wrap:break-word;"><td style="width:126px;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;"><p style="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;background-color:transparent;">QS77</td><td style="width:86px;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;"><p style="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;background-color:transparent;">4.16x10-5</td><td style="width:86px;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;"><p style="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;background-color:transparent;">3.07x10-5</td><td style="width:86px;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;"><p style="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;background-color:transparent;">1.36</td><td style="width:86px;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;"><p style="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;background-color:transparent;">0.19</td><td style="width:86px;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;"><p style="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;background-color:transparent;">1.59</td></tr><tr style="overflow-wrap:break-word;"><td style="width:126px;background-color:transparent;vertical-align: middle;border-bottom: 1.25px 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;"><p style="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;background-color:transparent;">Mean Lake Stage</td><td style="width:86px;background-color:transparent;vertical-align: middle;border-bottom: 1.25px 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;"><p style="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;background-color:transparent;">17.07</td><td style="width:86px;background-color:transparent;vertical-align: middle;border-bottom: 1.25px 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;"><p style="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;background-color:transparent;">15.70</td><td style="width:86px;background-color:transparent;vertical-align: middle;border-bottom: 1.25px 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;"><p style="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;background-color:transparent;">1.09</td><td style="width:86px;background-color:transparent;vertical-align: middle;border-bottom: 1.25px 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;"><p style="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;background-color:transparent;">2.89</td><td style="width:86px;background-color:transparent;vertical-align: middle;border-bottom: 1.25px 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;"><p style="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;background-color:transparent;">2.89</td></tr></tbody><tfoot><tr style="overflow-wrap:break-word;"><td colspan="6" style="width:126px;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;"><p style="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;background-color:transparent;"> Residual standard error (σ): 65.71 on 16 degrees of freedom</td></tr><tr style="overflow-wrap:break-word;"><td colspan="6" style="width:126px;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;"><p style="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;background-color:transparent;"> Multiple R²: 0.79; Adj R²: 0.75</td></tr><tr style="overflow-wrap:break-word;"><td colspan="6" style="width:126px;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;"><p style="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;background-color:transparent;"> F-statistic: 20.33 on 3 and 16 DF; ρ-value<0.01</td></tr></tfoot></table></div>

---
name: S79TP 4
class: left

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

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

.pull-left[
<img src="./resources/CRE_WY_TPMod_relaimpo.png" width="70%" style="display: block; margin: auto;" />
Relative importance of each predictor calculated by partitioning R2 by averaging sequential sums of squares over all orders of regressors (Lindeman et al 1979). All metrics are normalized to a sum of 100%.

]
--
.pull-right[

Relative Importance Metrics for the S79 TP Load annual model.

---
name: S79TP 5
class: left

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

`\begin{align*}
\sqrt{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=0.83, `\(\rho\)`<0.01).
]

--
.pull-right[
Train:Test
 - R2: 0.79
 - RMSE: 65.71
 - Mean Absolute Percent Error: 21 %
 - Min-Max Accuracy: 82 %

]

---
name: S79TP 6
class: left

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

`\begin{align*}
\sqrt{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)_
 - R2: 0.79
 - RMSE: 61.0
 - Mean Absolute Percent Error: 24 %
 - Min-Max Accuracy: 82 %
]

---
name: S79TN
class: left

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

---
name: S79TN 2
class: left

#### S-79 Water Quality Model (Total Nitrogen)
- No response variable transformation performed

- Model assumptions and verified
  - GVLMA (Global Stats = 4.77, `\(\rho\)`=0.31)

- Variance inflation factors (VIF) evaluated for model

- Residuals check for autocorrelation (Breusch-Godfrey test)
  - Breusch-Godfrey (LM test = 0.73, df = 1, `\(\rho\)`=0.39)

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

---
name: S79TN 3
class: left

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

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

- Model Output:

<div class="tabwid"><table style='border-collapse:collapse;'><thead><tr style="overflow-wrap:break-word;"><td style="width:126px;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;"><p style="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;background-color:transparent;">Parameter </td><td style="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;"><p style="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;background-color:transparent;">Estimate</td><td style="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;"><p style="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;background-color:transparent;">Standard Error</td><td style="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;"><p style="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;background-color:transparent;">t-value</td><td style="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;"><p style="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;background-color:transparent;">ρ-value</td><td style="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;"><p style="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;background-color:transparent;">VIF</td></tr></thead><tbody><tr style="overflow-wrap:break-word;"><td style="width:126px;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 1.25px 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;"><p style="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;background-color:transparent;">(Intercept)</td><td style="width:86px;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 1.25px 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;"><p style="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;background-color:transparent;">5.20x104</td><td style="width:86px;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 1.25px 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;"><p style="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;background-color:transparent;">1.14x106</td><td style="width:86px;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 1.25px 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;"><p style="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;background-color:transparent;">-0.05</td><td style="width:86px;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 1.25px 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;"><p style="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;background-color:transparent;">0.96</td><td style="width:86px;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 1.25px 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;"><p style="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;background-color:transparent;">---</td></tr><tr style="overflow-wrap:break-word;"><td style="width:126px;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;"><p style="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;background-color:transparent;">QC43</td><td style="width:86px;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;"><p style="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;background-color:transparent;">2.42</td><td style="width:86px;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;"><p style="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;background-color:transparent;">0.46</td><td style="width:86px;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;"><p style="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;background-color:transparent;">5.27</td><td style="width:86px;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;"><p style="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;background-color:transparent;"><0.01</td><td style="width:86px;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;"><p style="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;background-color:transparent;">2.96</td></tr><tr style="overflow-wrap:break-word;"><td style="width:126px;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;"><p style="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;background-color:transparent;">QS77</td><td style="width:86px;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;"><p style="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;background-color:transparent;">1.16</td><td style="width:86px;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;"><p style="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;background-color:transparent;">0.19</td><td style="width:86px;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;"><p style="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;background-color:transparent;">6.02</td><td style="width:86px;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;"><p style="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;background-color:transparent;"><0.01</td><td style="width:86px;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;"><p style="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;background-color:transparent;">1.59</td></tr><tr style="overflow-wrap:break-word;"><td style="width:126px;background-color:transparent;vertical-align: middle;border-bottom: 1.25px 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;"><p style="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;background-color:transparent;">Mean Lake Stage</td><td style="width:86px;background-color:transparent;vertical-align: middle;border-bottom: 1.25px 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;"><p style="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;background-color:transparent;">2.35x103</td><td style="width:86px;background-color:transparent;vertical-align: middle;border-bottom: 1.25px 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;"><p style="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;background-color:transparent;">9.83x104</td><td style="width:86px;background-color:transparent;vertical-align: middle;border-bottom: 1.25px 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;"><p style="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;background-color:transparent;">0.02</td><td style="width:86px;background-color:transparent;vertical-align: middle;border-bottom: 1.25px 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;"><p style="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;background-color:transparent;">0.98</td><td style="width:86px;background-color:transparent;vertical-align: middle;border-bottom: 1.25px 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;"><p style="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;background-color:transparent;">2.89</td></tr></tbody><tfoot><tr style="overflow-wrap:break-word;"><td colspan="6" style="width:126px;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;"><p style="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;background-color:transparent;"> Residual standard error (σ): 4.11x105 on 16 degrees of freedom</td></tr><tr style="overflow-wrap:break-word;"><td colspan="6" style="width:126px;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;"><p style="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;background-color:transparent;"> Multiple R²: 0.93; Adj R²: 0.92</td></tr><tr style="overflow-wrap:break-word;"><td colspan="6" style="width:126px;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;"><p style="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;background-color:transparent;"> F-statistic: 73.87 on 3 and 16 DF; ρ-value<0.01</td></tr></tfoot></table></div>

---
name: S79TN 4
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/CRE_WY_TNMod_relaimpo.png" width="70%" style="display: block; margin: auto;" />
Relative importance of each predictor calculated by partitioning R2 by averaging sequential sums of squares over all orders of regressors (Lindeman et al 1979). All metrics are normalized to a sum of 100%.

]

--
.pull-right[

Relative Importance Metrics for the S79 TN Load annual model.

---
name: S79TN 5
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 TP 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[
Train:Test
 - R2: 0.93
 - RMSE: 4.11x105
 - Mean Absolute Percent Error: 10 %
 - Min-Max Accuracy: 92 %

]

---
name: S79TN 6
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 TP loads at S-79 with each k-model presented. 
]

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

_Cross-validation error (average k errors)_
 - R2: 0.94
 - RMSE: 3.57x105
 - Mean Absolute Percent Error: 11 %
 - Min-Max Accuracy: 90 %
]

---
name: WQMods
class: left

#### S-79 Water Quality Models

Annual observed versus predicted ( `\(\pm\)` 95% CI) S-79 load during the period of record (WY1982 – WY 2019) with hurricane years identified.

???
- Caloosahatchee TMDL is 412 thousand kg/Yr (908,6094 lbs/Y)
- TMDL includes S79 and tidal basin.

---
name: WQMods2
class: left

#### S-79 Water Quality Models

Annual observed versus predicted ( `\(\pm\)` 95% CI) S-79 load during the period of record (WY1982 – WY 2019) with hurricane years identified.

---
name: RSM
class: left

#### S-79 Water Quality Models

### Application of model with RSM-BN outputs1

__Provisional RSM BN outputs with POR extension. For demonstration/testing purposes only.__

---
name: RSM2
class: left

#### S-79 Water Quality Models

### Application of model with RSM-BN outputs1

__Provisional RSM BN outputs with POR extension. For demonstration/testing purposes only.__

---
name: last slide
class: left

### Acknowledgements

#### Data

<img src="https://www.sfwmd.gov/sites/default/files/documents/sfwmd-seal-hq.png" width="10%" />
South Florida Water Management District ([DBHYDRO](https://www.sfwmd.gov/science-data/dbhydro))

#### Slides

* HTML [Slide deck](https://swampthingecology.org/slides/20200918_LOSOM_ENLM/Julian_LOSOM_ENLM.html) &copy; Julian (2020) [![Creative Commons License](https://i.creativecommons.org/l/by/4.0/88x31.png)](http://creativecommons.org/licenses/by/4.0/)

* RMarkdown [Source](https://github.com/SwampThingPaul/LOSOM_ENLM)

<img src="https://floridadep.gov/system/files/styles/general_page_images__scaled_to_900_pixels_/private/media-folders/media-root/in-house-graphic-DEP%20Logo%20color%20Large.png?itok=wm1GoIhx" width="15%" style="display: block; margin: auto;" />
<center>Draft FDEP Work Product</center>