docs/index.md

In troyhill/TTFF: A Comparison of Multiple Versions of the Tamiami Trail Flow Formula

title: Model comparison layout: template filename: index

Estimating flow across Tamiami Trail

The Tamiami Trail Flow Formula (TTFF) provides weekly flow targets for water moving from Water Conservation Area 3A (WCA3A) into Everglades National Park (ENP). Flows are calculated based on seven water management structures: S12A, S12B, S12C, S12D, S333, S333N, and S334. This page and the accompanying R package compare different approaches to modeling these flows. These approaches use data from a network of stage, potential evapotranspiration (PET), and rainfall gauges in WCA3A and ENP. Estimates from each model for the current week are shown immediately below, followed by descriptions of the individual approaches.

 

The information shown on this page is intended solely for educational purposes. The multiple regression model described below is the TTFF model reported in Appendix H of the 2020 Combined Operational Plan's Environmental Impact Statement. Nonetheless, the output described below may differ from official TTFF targets. For official TTFF targets, users are referred to the South Florida Water Management District's TTFF reports.

Current model values:

Figure 1. Observed flows into ENP during the past nine months (black line). Values shown are the average combined daily flow in a given week (average daily flow at five structures, summed for each week and then divided by 7). Flow estimates generated using multiple linear regression (red), segmented regression (blue), and principal component analysis (green) are also shown.

 

Model performance

Figure 2. Relationships between observed flows during the past year and values predicted by each model. Flow estimates generated using multiple linear regression (red), segmented regression (blue), and principal component analysis (green).

 

 

Model descriptions

Multiple linear regression

This formula operates on a subset of available rainfall, precipitation, and PET stations and has the form:

 

 

where:

Qtsum is the target flow (S12A/B/C/D + S333 + S333N - S334) for the current (upcoming) week, t (cfs),

Stavg1 is the spatial average of observed stages (ft, NGVD) at WCA3A stages A-3, A-4 and A3-28 for the start of the current week t,

Stnesrs2 is observed stage (ft, NGVD) at ENP stage NESRS2 for the start of the current week,

Qt-1 is the sum of observed flows for the previous week (cfs),

Rt is the average weekly rainfall (in) for WCA3A and BCNP for current week t,

PETt is the potential evaporation (in) at the Tamiami Trail Station (3AS3WX), and

ZAt is the Zone A regulation stage (ft, NGVD) value for time step t (beginning of current week).

Coefficients and associated standard errors:

| Parameter | B1 | B2 | B3 | B4 | B5 | B6 | | :--- | :----: | :----: | :----: | :----: | :----: | ---: | | Coefficient | 318.42 | -44.62 | 0.644 | 24.32 | -96.31 | -221.79 | | Standard Error | 18.22 | 18.50 | 0.016 | 7.23 | 28.83 | 13.67 | | t value | 17.5 | -2.4 | 39.4 | 3.4 | -3.3 | -16.2 |

Adjusted R2: 0.93

 

Segmented multiple linear regression

A two-variable segmented regression model has also been proposed. The data used in the model are stages in northeast Shark River Slough and WCA3A, with data breakpoints set where stages in northeast Shark River Slough reach 7.0' and 7.9' NGVD. This model follows the form:

Q = B0 + B1 * SWCA3A + B2 * SNESRS for SNESRS < 7.0

Q = B0 + B1 * SWCA3A + B3 * SNESRS for 7.0 < SNESRS < 7.9

Q = B0 + B1 * SWCA3A + B4 * SNESRS for SNESRS > 7.9

Coefficients and associated standard errors:

| Parameter | B0 | B1 | B2 | B3 | B4 | | :--- | :----: | :----: | :----: | :----: | ---: | | Coefficient | -3625.80 | 451.00 | 12.33 | 869.79 | 2132.31 | | Standard Error | 187.66 | 21.71 | 26.46 | 75.39 | 328.95 | | t value | -19.3 | 20.8 | 0.5 | 11.5 | 6.6 |

Adjusted R2: 0.74

 

Principal component analysis

This approach uses all available data. PCA reduces the dimensionality of the full dataset to a smaller number of statistically independent synthetic variables. A PCA is applied to a training dataset and then the model is used on recent data to generate a flow prediction.

The six-dimension PCA used here has the following form:

 

Coefficients and associated standard errors:

| Parameter | B0 | B1 | B2 | B3 | B4 | B5 | B6 | | :--- | :----: | :----: | :----: | :----: | :----: | :----: | ---: | | Coefficient | 721.6 | 344.1 | 145.3 | 105.5 | -134.2 | 150.6 | 97.7 | | Standard Error | 5.8 | 1.7 | 3.2 | 3.4 | 3.5 | 3.8 | 4.8 | | t value | 124.8 | 201.1 | 45.2 | 30.7 | -38.0 |39.1 | 20.3 |

Adjusted R2: 0.96

 

 

R package installation and usage

The R package containing data and sample analysis can be installed from GitHub:

install.packages("devtools")
devtools::install_github("troyhill/TTFF")

This R package has the data from all rainfall, PET, and stage stations included in the analysis done by the COP modeling subteam in spring of 2019. The analysis presented above can be generated using this R script.

troyhill/TTFF documentation built on Aug. 9, 2021, 6:35 p.m.