Data Sources

Field measurements of instantaneous water level and discharge are available for the S-12s (S-12 A, B, C and D) and retrieved from USGS NWIS. Field measurements and rating curve information was provided by USGS (via DOI) for the L-31N Mile-1 flow monitoring location. Published rating curves are only available for the S12 structures and were retrieve from USGS NWIS. Rated and calculated flow measurements for S-333, S-334 and S-356 were provided by SFWMD.

Methods

The stage-discharge relationship (i.e. rating curve) was applied to instantaneous water level measurements to determine an Rated Instantons Flow value which was compared with the measured flow value. The uncertainty analysis focused on field collected data during the period of the most recent rating curve as identified below. Consistent with Walker (2018), linear models were fit to measured and rated instantaneous flow values for each structure using the lm() function in the base R-package. Using the output provided by the linear model, error associated with the slope of the model was estimated using the standard error of the slope term and the slope value calculated as a percent (Eq. 1). This slope error term is considered the low-estimate of error. Error attributed to the model via the residual errors (measured flow - rated flow) using the models residual standard error and the mean measured value (\(\overline{Q_{m}}\); Eq. 2). Finally, total error (or high-estimate) incorporates error associated with the slope and residuals (Eq. 3).

\[ Slope\ SE\ (\%) = \frac{Slope\ Standard\ Error}{Slope} \times 100 \qquad \qquad \text{(Eq. 1)} \] \[ Model\ RSE\ (\%) = \frac{Residual\ Standard\ Error}{\overline{Q_{m}}} \times 100 \qquad \qquad \text{(Eq. 2)} \] \[ Total\ Error\ (\%) = \sqrt{Slope\ SE^{2} + Model\ RSE^{2}} \qquad \qquad \text{(Eq. 3)}\]

Notes:

¹ Linear models were fit to S-12s and L-31N Mile-1 where slope and intercept values were estimated.

² Error terms associated with S-333, S-334 and S-356 were derived using liner models with an x-intercept (\(\beta_{0}\)) set to zero.

³ Limited field measurement data was available for S-356, however it is assumed that error is relatively low from this structure given that flow is estimated from pump rate (RPMs) versus discharge.

Flow Calibration Uncertainty Results

summary(S12A.lm)

## 
## Call:
## lm(formula = discharge_va ~ DEP, data = S12A.dat)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -79.274 -19.309  -5.834  23.280  88.578 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -16.71640   14.36069  -1.164    0.255    
## DEP           0.94701    0.03474  27.256   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 36.71 on 26 degrees of freedom
##   (30 observations deleted due to missingness)
## Multiple R-squared:  0.9662, Adjusted R-squared:  0.9649 
## F-statistic: 742.9 on 1 and 26 DF,  p-value: < 2.2e-16

# plot(S12A.lm) # Default linear model diagnostic plots

# Global Validation of Linear Models Assumptions
## From: Peña and Slate (2006) Global Validation of Linear Model Assumptions. Journal of the American Statistical Association 101:341–354.

gvlma(S12A.lm)

## 
## Call:
## lm(formula = discharge_va ~ DEP, data = S12A.dat)
## 
## Coefficients:
## (Intercept)          DEP  
##     -16.716        0.947  
## 
## 
## ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
## USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
## Level of Significance =  0.05 
## 
## Call:
##  gvlma(x = S12A.lm) 
## 
##                       Value p-value                   Decision
## Global Stat        10.70042 0.03015 Assumptions NOT satisfied!
## Skewness            0.07045 0.79068    Assumptions acceptable.
## Kurtosis            0.17213 0.67823    Assumptions acceptable.
## Link Function       4.23048 0.03970 Assumptions NOT satisfied!
## Heteroscedasticity  6.22736 0.01258 Assumptions NOT satisfied!

summary(S12B.lm)

## 
## Call:
## lm(formula = discharge_va ~ DEP, data = S12B.dat)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -49.154 -14.048  -2.042  16.063  43.846 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -33.33763   10.96329  -3.041   0.0046 ** 
## DEP           1.03321    0.02896  35.671   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 25.19 on 33 degrees of freedom
##   (38 observations deleted due to missingness)
## Multiple R-squared:  0.9747, Adjusted R-squared:  0.974 
## F-statistic:  1272 on 1 and 33 DF,  p-value: < 2.2e-16

# plot(S12B.lm) # Default linear model diagnostic plots

# Global Validation of Linear Models Assumptions

gvlma(S12B.lm)

## 
## Call:
## lm(formula = discharge_va ~ DEP, data = S12B.dat)
## 
## Coefficients:
## (Intercept)          DEP  
##     -33.338        1.033  
## 
## 
## ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
## USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
## Level of Significance =  0.05 
## 
## Call:
##  gvlma(x = S12B.lm) 
## 
##                      Value p-value                   Decision
## Global Stat        5.35750 0.25254    Assumptions acceptable.
## Skewness           0.04188 0.83785    Assumptions acceptable.
## Kurtosis           0.35517 0.55120    Assumptions acceptable.
## Link Function      4.43817 0.03514 Assumptions NOT satisfied!
## Heteroscedasticity 0.52227 0.46987    Assumptions acceptable.

summary(S12C.lm)

## 
## Call:
## lm(formula = discharge_va ~ DEP, data = S12C.dat)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -357.96  -58.39   -8.22   52.20  329.49 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -45.84760   22.41453  -2.045   0.0427 *  
## DEP           1.08534    0.03002  36.153   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 98.25 on 139 degrees of freedom
##   (37 observations deleted due to missingness)
## Multiple R-squared:  0.9039, Adjusted R-squared:  0.9032 
## F-statistic:  1307 on 1 and 139 DF,  p-value: < 2.2e-16

# plot(S12C.lm) # Default linear model diagnostic plots

# Global Validation of Linear Models Assumptions

gvlma(S12C.lm)

## 
## Call:
## lm(formula = discharge_va ~ DEP, data = S12C.dat)
## 
## Coefficients:
## (Intercept)          DEP  
##     -45.848        1.085  
## 
## 
## ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
## USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
## Level of Significance =  0.05 
## 
## Call:
##  gvlma(x = S12C.lm) 
## 
##                      Value   p-value                   Decision
## Global Stat        80.4051 1.110e-16 Assumptions NOT satisfied!
## Skewness            0.8292 3.625e-01    Assumptions acceptable.
## Kurtosis           17.1761 3.407e-05 Assumptions NOT satisfied!
## Link Function      22.1147 2.568e-06 Assumptions NOT satisfied!
## Heteroscedasticity 40.2851 2.195e-10 Assumptions NOT satisfied!

summary(S12D.lm)

## 
## Call:
## lm(formula = discharge_va ~ DEP, data = S12D.dat)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -452.40  -84.84  -11.83   72.49  339.95 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 153.48601   21.93460   6.997 5.84e-11 ***
## DEP           0.74278    0.02883  25.768  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 125.5 on 169 degrees of freedom
##   (52 observations deleted due to missingness)
## Multiple R-squared:  0.7971, Adjusted R-squared:  0.7959 
## F-statistic:   664 on 1 and 169 DF,  p-value: < 2.2e-16

# plot(S12D.lm) # Default linear model diagnostic plots

# Global Validation of Linear Models Assumptions

gvlma(S12D.lm)

## 
## Call:
## lm(formula = discharge_va ~ DEP, data = S12D.dat)
## 
## Coefficients:
## (Intercept)          DEP  
##    153.4860       0.7428  
## 
## 
## ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
## USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
## Level of Significance =  0.05 
## 
## Call:
##  gvlma(x = S12D.lm) 
## 
##                     Value   p-value                   Decision
## Global Stat        19.291 0.0006889 Assumptions NOT satisfied!
## Skewness            1.567 0.2106547    Assumptions acceptable.
## Kurtosis            3.048 0.0808184    Assumptions acceptable.
## Link Function      10.334 0.0013062 Assumptions NOT satisfied!
## Heteroscedasticity  4.342 0.0371805 Assumptions NOT satisfied!

summary(S333.lm)

## 
## Call:
## lm(formula = Q.cfs ~ 0 + X.cfs, data = S333.dat)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -97.71 -50.98 -34.79  -2.66 187.78 
## 
## Coefficients:
##       Estimate Std. Error t value Pr(>|t|)    
## X.cfs  0.82913    0.01396   59.41   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 73.84 on 33 degrees of freedom
## Multiple R-squared:  0.9907, Adjusted R-squared:  0.9905 
## F-statistic:  3529 on 1 and 33 DF,  p-value: < 2.2e-16

# plot(S333.lm) # Default linear model diagnostic plots

# Global Validation of Linear Models Assumptions
## From: Peña and Slate (2006) Global Validation of Linear Model Assumptions. Journal of the American Statistical Association 101:341–354. Code modified for intercept-free linear model application.

gvlma.int0(S333.lm)

## 
## Call:
## lm(formula = Q.cfs ~ 0 + X.cfs, data = S333.dat)
## 
## Coefficients:
##  X.cfs  
## 0.8291  
## 
## 
## ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
## USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
## Level of Significance =  0.05 
## 
## Call:
##  NULL 
## 
##                     Value p-value                   Decision
## Global Stat        6.3666  0.1734    Assumptions acceptable.
## Skewness           4.6809  0.0305 Assumptions NOT satisfied!
## Kurtosis           0.1340  0.7143    Assumptions acceptable.
## Link Function      0.1612  0.6880    Assumptions acceptable.
## Heteroscedasticity 1.3904  0.2383    Assumptions acceptable.

summary(S334.lm)

## 
## Call:
## lm(formula = Q.cfs ~ 0 + X.cfs, data = S334.dat)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -77.609  -4.822   3.685  26.102  48.913 
## 
## Coefficients:
##       Estimate Std. Error t value Pr(>|t|)    
## X.cfs  0.71170    0.01933   36.81 7.17e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 34.88 on 11 degrees of freedom
## Multiple R-squared:  0.9919, Adjusted R-squared:  0.9912 
## F-statistic:  1355 on 1 and 11 DF,  p-value: 7.169e-13

# plot(S334.lm) # Default linear model diagnostic plots

# Global Validation of Linear Models Assumptions
## From: Peña and Slate (2006) Global Validation of Linear Model Assumptions. Journal of the American Statistical Association 101:341–354. Code modified for intercept-free linear model application.

gvlma.int0(S334.lm)

## 
## Call:
## lm(formula = Q.cfs ~ 0 + X.cfs, data = S334.dat)
## 
## Coefficients:
##  X.cfs  
## 0.7117  
## 
## 
## ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
## USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
## Level of Significance =  0.05 
## 
## Call:
##  NULL 
## 
##                      Value p-value                Decision
## Global Stat        4.01453 0.40404 Assumptions acceptable.
## Skewness           0.28753 0.59181 Assumptions acceptable.
## Kurtosis           0.06906 0.79271 Assumptions acceptable.
## Link Function      3.20185 0.07355 Assumptions acceptable.
## Heteroscedasticity 0.45609 0.49946 Assumptions acceptable.

summary(S356.lm)

## 
## Call:
## lm(formula = Q.cfs ~ 0 + X.cfs, data = S356.dat)
## 
## Residuals:
##       1       2       4       7 
##  3.2261 -0.4377 -2.3388  1.1669 
## 
## Coefficients:
##       Estimate Std. Error t value Pr(>|t|)    
## X.cfs 0.966097   0.003301   292.7  8.8e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.41 on 3 degrees of freedom
##   (6 observations deleted due to missingness)
## Multiple R-squared:      1,  Adjusted R-squared:      1 
## F-statistic: 8.566e+04 on 1 and 3 DF,  p-value: 8.796e-08

# plot(S356.lm) # Default linear model diagnostic plots

# Global Validation of Linear Models Assumptions
## From: Peña and Slate (2006) Global Validation of Linear Model Assumptions. Journal of the American Statistical Association 101:341–354. Code modified for intercept-free linear model application.

gvlma.int0(S356.lm)

## 
## Call:
## lm(formula = Q.cfs ~ 0 + X.cfs, data = S356.dat)
## 
## Coefficients:
##  X.cfs  
## 0.9661  
## 
## 
## ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
## USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
## Level of Significance =  0.05 
## 
## Call:
##  NULL 
## 
##                     Value p-value                   Decision
## Global Stat        5.9782 0.20079    Assumptions acceptable.
## Skewness           0.2501 0.61700    Assumptions acceptable.
## Kurtosis           0.2224 0.63721    Assumptions acceptable.
## Link Function      4.8766 0.02722 Assumptions NOT satisfied!
## Heteroscedasticity 0.6290 0.42770    Assumptions acceptable.

summary(L31N_1.lm)

## 
## Call:
## lm(formula = discharge_va ~ DEP, data = L31N_1.dat)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -222.037  -47.599    5.281   37.886  209.267 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 18.73287   19.47297   0.962     0.34    
## DEP          0.90339    0.03743  24.137   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 97.8 on 58 degrees of freedom
## Multiple R-squared:  0.9095, Adjusted R-squared:  0.9079 
## F-statistic: 582.6 on 1 and 58 DF,  p-value: < 2.2e-16

# plot(L31N_1.lm) # Default linear model diagnostic plots

# Global Validation of Linear Models Assumptions

gvlma(L31N_1.lm)

## 
## Call:
## lm(formula = discharge_va ~ DEP, data = L31N_1.dat)
## 
## Coefficients:
## (Intercept)          DEP  
##     18.7329       0.9034  
## 
## 
## ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
## USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
## Level of Significance =  0.05 
## 
## Call:
##  gvlma(x = L31N_1.lm) 
## 
##                      Value  p-value                   Decision
## Global Stat        13.0057 0.011248 Assumptions NOT satisfied!
## Skewness            0.2720 0.601960    Assumptions acceptable.
## Kurtosis            0.0862 0.769066    Assumptions acceptable.
## Link Function       2.9578 0.085463    Assumptions acceptable.
## Heteroscedasticity  9.6896 0.001853 Assumptions NOT satisfied!

summary(L31N_3.lm)

## 
## Call:
## lm(formula = discharge_va ~ DEP, data = L31N_3.dat)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -133.285  -38.421   -3.242   46.653  159.215 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  6.22267   14.13276    0.44    0.662    
## DEP          0.99498    0.02485   40.04   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 59.35 on 50 degrees of freedom
## Multiple R-squared:  0.9698, Adjusted R-squared:  0.9692 
## F-statistic:  1603 on 1 and 50 DF,  p-value: < 2.2e-16

# plot(L31N_3.lm) # Default linear model diagnostic plots

# Global Validation of Linear Models Assumptions

gvlma(L31N_3.lm)

## 
## Call:
## lm(formula = discharge_va ~ DEP, data = L31N_3.dat)
## 
## Coefficients:
## (Intercept)          DEP  
##       6.223        0.995  
## 
## 
## ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
## USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
## Level of Significance =  0.05 
## 
## Call:
##  gvlma(x = L31N_3.lm) 
## 
##                       Value p-value                Decision
## Global Stat        4.242667 0.37416 Assumptions acceptable.
## Skewness           0.148099 0.70036 Assumptions acceptable.
## Kurtosis           0.004131 0.94875 Assumptions acceptable.
## Link Function      0.581322 0.44579 Assumptions acceptable.
## Heteroscedasticity 3.509115 0.06103 Assumptions acceptable.

summary(L31N_4.lm)

## 
## Call:
## lm(formula = discharge_va ~ DEP, data = L31N_4.dat)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -244.147  -42.429    4.724   56.076  191.979 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -18.09110   18.58688  -0.973    0.335    
## DEP           1.02541    0.03517  29.157   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 76.7 on 55 degrees of freedom
## Multiple R-squared:  0.9392, Adjusted R-squared:  0.9381 
## F-statistic: 850.1 on 1 and 55 DF,  p-value: < 2.2e-16

# plot(L31N_4.lm) # Default linear model diagnostic plots

# Global Validation of Linear Models Assumptions

gvlma(L31N_4.lm)

## 
## Call:
## lm(formula = discharge_va ~ DEP, data = L31N_4.dat)
## 
## Coefficients:
## (Intercept)          DEP  
##     -18.091        1.025  
## 
## 
## ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
## USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
## Level of Significance =  0.05 
## 
## Call:
##  gvlma(x = L31N_4.lm) 
## 
##                     Value   p-value                   Decision
## Global Stat        20.040 0.0004904 Assumptions NOT satisfied!
## Skewness            1.281 0.2576398    Assumptions acceptable.
## Kurtosis            1.888 0.1693718    Assumptions acceptable.
## Link Function       7.926 0.0048727 Assumptions NOT satisfied!
## Heteroscedasticity  8.944 0.0027839 Assumptions NOT satisfied!

summary(L31N_5.lm)

## 
## Call:
## lm(formula = discharge_va ~ DEP, data = L31N_5.dat)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -129.12  -39.33  -13.28   19.53  503.90 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  3.02057   21.42833   0.141    0.888    
## DEP          1.01703    0.03892  26.134   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 91.79 on 51 degrees of freedom
## Multiple R-squared:  0.9305, Adjusted R-squared:  0.9292 
## F-statistic:   683 on 1 and 51 DF,  p-value: < 2.2e-16

# plot(L31N_5.lm) # Default linear model diagnostic plots

# Global Validation of Linear Models Assumptions

gvlma(L31N_5.lm)

## 
## Call:
## lm(formula = discharge_va ~ DEP, data = L31N_5.dat)
## 
## Coefficients:
## (Intercept)          DEP  
##       3.021        1.017  
## 
## 
## ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
## USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
## Level of Significance =  0.05 
## 
## Call:
##  gvlma(x = L31N_5.lm) 
## 
##                        Value   p-value                   Decision
## Global Stat        768.76734 0.000e+00 Assumptions NOT satisfied!
## Skewness           114.06199 0.000e+00 Assumptions NOT satisfied!
## Kurtosis           632.28978 0.000e+00 Assumptions NOT satisfied!
## Link Function        0.04036 8.408e-01    Assumptions acceptable.
## Heteroscedasticity  22.37521 2.243e-06 Assumptions NOT satisfied!

summary(L31N_7.lm)

## 
## Call:
## lm(formula = discharge_va ~ DEP, data = L31N_7.dat)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -155.75  -38.45   -0.23   29.19  426.67 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 17.51415   12.45380   1.406    0.163    
## DEP          0.92071    0.02024  45.487   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 68.47 on 106 degrees of freedom
## Multiple R-squared:  0.9513, Adjusted R-squared:  0.9508 
## F-statistic:  2069 on 1 and 106 DF,  p-value: < 2.2e-16

# plot(L31N_7.lm) # Default linear model diagnostic plots

# Global Validation of Linear Models Assumptions

gvlma(L31N_7.lm)

## 
## Call:
## lm(formula = discharge_va ~ DEP, data = L31N_7.dat)
## 
## Coefficients:
## (Intercept)          DEP  
##     17.5142       0.9207  
## 
## 
## ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
## USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
## Level of Significance =  0.05 
## 
## Call:
##  gvlma(x = L31N_7.lm) 
## 
##                       Value p-value                   Decision
## Global Stat        853.4621 0.00000 Assumptions NOT satisfied!
## Skewness            98.9271 0.00000 Assumptions NOT satisfied!
## Kurtosis           750.8519 0.00000 Assumptions NOT satisfied!
## Link Function        0.3144 0.57500    Assumptions acceptable.
## Heteroscedasticity   3.3686 0.06645    Assumptions acceptable.

Summary of Results

A code chunk example of the analysis performed, this is specfic to the USGS data for the S12A structure.

USGS.site="254543080491101"
S12A.rating=readNWISrating(USGS.site,type="exsa");#DEP=Discharge - CFS; INDEP=Stage - FT
S12A.rating$INDEP=with(S12A.rating,INDEP+SHIFT)

rate.date.begin=date.fun(paste(substr(attributes(S12A.rating)$comment[32],27,30),substr(attributes(S12A.rating)$comment[32],31,32),substr(attributes(S12A.rating)$comment[32],33,34),sep="-"));
rate.date.begin
WY(rate.date.begin+ddays(1),"Fed")

S12A.inst.Q=readNWISmeas(USGS.site,startDate=sdate.usgs,endDate=edate.usgs)
S12A.inst.Q$measurement_dt=date.fun(S12A.inst.Q$measurement_dt)
S12A.inst.Q$WY=WY(S12A.inst.Q$measurement_dt,"Fed")
S12A.inst.Q=merge(S12A.inst.Q,S12A.rating[,c("INDEP","DEP")],by.x="gage_height_va",by.y="INDEP",all.x=T)
S12A.dat=subset(S12A.inst.Q,WY%in%seq(WY(rate.date.begin+ddays(1),"Fed"),2017,1))

plot(discharge_va~DEP,S12A.dat)
S12A.lm=lm(discharge_va~DEP,S12A.dat)
mod.val=gvlma(S12A.lm)

Metadata - Session Info

• Originally Complied: 10/08/2018; Edited: 10/22/2018
• R version 3.4.1 (2017-06-30) — Single Candle
• R-packages used in this analysis include plyr (Ver 1.8.4), openxlsx (Ver 4.0.17), dataRetrieval (Ver 2.7.3), lubridate (Ver 1.7.4) and gvlma (Ver 1.0.0.2).