Statistics and Nutrient Levels

Julie Stahli

Metro Wastewater Reclamation District

March 2010

MMI

Version 3 lacks a lot of the problems that previous versions contained.

Statistically, the model distinguishes reference sites from stressed sites.

The level chosen as the level of impaired is statistically generous.

MMI

MMI Issues (based on Metro Data) Comments should focus on implementation

Sites with low scores should be put on the M&E list and multiple samples should be taken.

Implementation should be based on median of all MMI scores over the course of five years.

We have seen substantial variation at a single site.

Big rivers need alternative indexes when sites are found in the “yellow zone”.

Sample DataType Year 31st 64th Up CC 88th 120th – H 124th 160th Ft Lupton Cty Rd 18

Kick 1993   25.98 27.59            

Kick 2003   54.56 17.44            

Kick 2004       16.82   21.61 26.33 31.36  

Kick 2005               35.24 35.67

Kick 2006 17.76 44.56 18.96 19.52   17.52 28.61    

Kick 2007 42.6 43.94   23.44          

Kick 2008   32.1 19.84   41.65 35.54      

Kick 2009 22.29 53.42 24.74 9.94 19.86 17.37 19.24 33.93 43.5

Med 22.3 44.3 19.8 18.2 30.8 19.6 26.3 33.9 39.6

Blue indicates attainment, red indicates impaired

Big Rivers

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60

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0.000 0.001 0.010 0.100 1.000 10.000

TP Median

MM

I

Large

Small

Unknown

Small Plains

Lets assume that the MMI is valid and can be related to nutrient concentrations to form TP and TN limits….

Regression analysis

Lots of types of regression analysis linear Multi-linear regression logistic regression etc

Regression analysis

Each type has restrictions on how it is used based on the assumptions we can make about the data.

Evaluate the assumptions to determine whether or not the model is valid or appropriate. Example assumptions

The relationship is linear in nature. The errors are independent and normally

distributed. The model is the best available for describing the

relationship.

Regression analysis

After the model is developed, we evaluate the model to see how useful it is

Tools for evaluation: R2 value Goodness of fit for data Confidence intervals Residual mean-squared error

Ideally, a model on which decisions are based are both valid and useful.

Quantile Regression

Breaks up the data into quantiles and forms an individual regression for each one.

Used with the wedge plot.

Quantile Regression

Typically, no assumptions are necessary. Lots of decisions are made during the modeling

process. Typically, goodness of fit is evaluated in two ways:

examining whether or not the slope is different from zero

The P value for the model (is it significant) Results are not predictive. Can’t really determine whether or not the model is

valid or useful.

Quantile Regression

Quantile Regression

Used to explore patterns in data that cannot be seen using more traditional methods.

Designed to be used in exactly the same way that CDPHE is using it – to illuminate an effect that may be muddied by lots of other variables.

There is no way to evaluate whether or not the model is right or wrong, good or bad and should be considered as part of a

weight of evidence approach.

Quantile Regression

What else do we use?

We don’t believe there is a better tool to solve the nutrient problem.

Especially for Phosphorus.

What??!?

The uncertainty in the model needs to be acknowledged. Using this method should not set

precedent for future usage where other options may be available.

In repeating their methods, we found that choices were made that are not scientifically valid.

CDPHE Review

Quantile Regression Slope

Problems

Using log scale. Using only the warm data to define the slope. Using the 90th percentile without biological

reason (85% is more commonly used). Nitrogen is difficult because of lack of data.

Unless otherwise noted, all limits would apply to Warm streams and rivers.

Log Scale Issues

Normal regression Using a log-scale

Quantile Slope

Does Not Cross Zero

Good P-value

Final Valuemg/L

0.05 -0.93683 Yes No N/A

0.25 -6.19878 Yes Yes 0.237

0.50 -10.9204 Yes Yes 0.143

0.75 -11.386 Yes Yes 0.139

0.85 -10.1523 Yes Yes 0.150

0.90 -10.4541 Yes Yes 0.147

0.95 -10.6691 Yes Yes 0.145

Quantile Slope

Does Not Cross Zero

Good P-value

Final Valuemg/L

0.05 -6.128 Yes No N/A

0.25 -16.018 Yes Yes 0.263

0.50 -25.208 Yes Yes 0.195

0.75 -26.127 Yes Yes 0.191

0.85 -24.666 Yes Yes 0.198

0.90 -25.764 Yes Yes 0.192

0.95 -26.07 No Yes N/A

Using only warm data

Using all data Using warm data

***Both using log scales to make comparable

Quantile Slope

Does Not Cross Zero

Good P-value

Final Valuemg/L

0.05 -0.93683 Yes No N/A

0.25 -6.19878 Yes Yes 0.237

0.50 -10.9204 Yes Yes 0.143

0.75 -11.386 Yes Yes 0.139

0.85 -10.1523 Yes Yes 0.150

0.90 -10.4541 Yes Yes 0.147

0.95 -10.6691 Yes Yes 0.145

Quantile Slope

Does Not Cross Zero

Good P-value

Final Valuemg/L

0.05 -2.461 No No N/A

0.25 -3.074 No No N/A

0.50 -5.205 Yes No N/A

0.75 -10.34 Yes Yes 0.148

0.85 ** did not run N/A

0.90 -11.96 Yes Yes 0.135

0.95 -9.722 Yes Yes 0.155

Cold data

Quantile SlopeDoes Not Cross Zero

Good P-value

Final Valuemg/L

0.05 1.7374 No No N/A

0.25 -3.6333 No No N/A

0.50 -1.9215 No No N/A

0.75 -3.9878 No No N/A

0.85 -5.4538 Yes Yes 0.202

0.90 -3.9919 No No N/A

0.95 -6.2549 No No N/A

Warm – 0.9 -11.96 Yes Yes 0.090

All – 0.9 -25.76 Yes Yes 0.1819

Recommendation

Quantile SlopeDoes Not Cross Zero

Good P-value

Final Valuemg/L

0.05 -6.128 Yes No N/A

0.25 -16.018 Yes Yes 0.263

0.50 -25.208 Yes Yes 0.195

0.75 -26.127 Yes Yes 0.191

0.85 -24.666 Yes Yes 0.198

0.90 -25.764 Yes Yes 0.192

0.95 -26.07 No Yes N/A

Nitrogen

Nitrogen

Valid models with the normal data if cold and warm are looked at together as recommended for Phosphorus.

Strongest scientific model (at 0.9 quantile) gives TN value of 2.06 mg/L.

Currently there is a paucity of data and I think we could argue for more information after the implementation of ammonia and nitrite criteria.

Caveats

I am not an expert in quantile regression and may have missed some qualifying assumptions.

All of the relationships we are discussing are tenuous at best, but may qualify as best current scientific opinion.

Thank you….

Questions???