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[Linear Models](#lm)

* [Nitrogen loads and chlorophyll, with 3-month cumulative loads](#lm_3N)
* [Nitrogen loads and chlorophyll, with delayed loads](#lm_N)
* [Nitrogen loads and chlorophyll (3-month cumulative loads)](#lm_3N)
* [Nitrogen loads and chlorophyll (concurrent and delayed loads)](#lm_N)
* [Chlorophyll and light](#lm_chl)

[Generalized Additive Models (GAMs)](#gam)
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# Overview {#overview}

The current management paradigm for Old Tampa Bay (OTB) is holds that (1) reducing _external nitrogen loads_ will reduce chlorophyll a concentrations in the OTB water column, (2) reducing _chlorophyll a concentrations_ will improve water clarity, and (3) improved _water clarity_ will stimulate _seagrass growth/recovery_. The management paradigm is based on earlier studies that reported significant correlations between each subsequent pair of covariates, considering data from across Tampa Bay as a whole and/or from Tampa Bay segments including OTB (e.g., Janicki & Wade 1996; Morrison et al. 1996; Greening & Janicki 2016).
The current management paradigm for Old Tampa Bay (OTB) holds that (1) reducing _external nitrogen loads_ will reduce chlorophyll a concentrations in the OTB water column, (2) reducing _chlorophyll a concentrations_ will improve water clarity, and (3) improved _water clarity_ will stimulate _seagrass growth/recovery_. The management paradigm is based on earlier studies that reported significant correlations between each subsequent pair of covariates, considering data from across Tampa Bay as a whole and/or from Tampa Bay segments including OTB (e.g., Janicki & Wade 1996; Morrison et al. 1996; Greening & Janicki 2016).

This document explores statistical relationships between TN loads and chlorophyll-a concentrations and between chlorophyll-a concentrations and Secchi depth at various OTB sub-segments using monthly averaged data between approximately 2000 and 2023 (periods of record vary by data source and variable). The analyses were implemented in R version 4.3.1 (R Core Team 2023).

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Janicki & Wade (1996) developed a linear regression model relating monthly average chlorophyll-a concentrations to cumulative TN loads over a three-month period (the concurrent month and two previous months). The model used data from across Tampa Bay during 1985--1991 and stratified the data by the month of the year and by bay segment, and it produced an R2 value of 0.73. Subsequently, Greening et al. (2014) developed a similar regression model for the 1985–2011 period and observed an R2 value of 0.66.

## Nitrogen loads and chlorophyll, with 3-month cumulative loads {#lm_3N}
## Nitrogen loads and chlorophyll (3-month cumulative loads) {#lm_3N}

We apply a similar approach as Janciki & Wade (1996) to explore relationships between monthly average chlorophyll-a concentrations and TN loads at three OTB sub-segments during the 2000-2021 period. For simplicity, the models below do not stratify by the month of the year, in contrast to the model of Janicki & Wade (1996).

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## Nitrogen loads and chlorophyll, with delayed loads {#lm_N}
## Nitrogen loads and chlorophyl (concurrent and delayed loads) {#lm_N}

This section further explores relationships between chlorophyll-a and TN loads by considering monthly TN loading values at delays of zero through two months across various OTB sub-segments, including the EPC sub-segments and the Pinellas County strata.

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