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Monitoring and Analyzing Water Resources: Identifying Trends in Water Quality Parameters, Study notes of Statistics

An overview of trend monitoring and analysis in water resources, focusing on the identification and measurement of trends in water quality parameters. various methods for visualizing trends, selecting appropriate statistical tests, and calculating non-parametric statistics. It also discusses issues to consider when doing trend monitoring, such as data quality, time frame, and exogenous variables.

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Box Plot of Workshop Participants Concentration
VS Time of Day
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Trend Analysis and Presentation
Trend Monitoring
What is it and why do we do it?
Trend monitoring looks for changes in environmental
parameters over time periods (E.g. last 10 years) or in space
(e.g. as you move downstream)
***
*** Created with StatPlus™ Software
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Box Plot of Workshop Participants Concentration

VS Time of Day

Time of Day

Percent Total Concentration

Trend Monitoring

What is it and why do we do it?

Trend monitoring looks for changes in environmental

parameters over time periods (E.g. last 10 years) or in space

(e.g. as you move downstream)


***** Created with StatPlus™ Software**

How to find a trend

Visual-

Good News... Graphing or mapping data for people to see is the

easiest way to communicate trends, especially to a non-technical

crowd.

Bad News… No way of “measuring” that there is a trend or how

big it is.

Statistical-

Good News…Can identify hard to see trends and gives a number

that is defensible and repeatable.

Bad News…Easy to do wrong and hard to figure out.

Be vewy, vewy quiet…I’m hunting fow a twend

http://www.barbneal.com/elmer.asp

Average 7 day max by River Mile
River Mile
Avgerage 7 Day Max for July 2000

Visual methods for displaying trends

Time/area series scatter plot Bar Graphs

Time series smoothed scatter plot Time/area series box plot of statistics*

  • From Helsel D.R. and R.M. Hirsch. 1991 Statistical Methods in Water Resources.

Techniques of Water-Resources Investigations of the USGS Book 4. Chapter A

p. 287

(^1 ) (^3 ) 5 (^7 ) 9 10

May

June

July

August

Sept

October

0

500

1000

1500

2000

2500

Concentration
(MPN/100mL)
Site Number
Month

Summer 2000 E.coli Concentrations

The Trouble with Graphs

  • People tend to focus on the outliers and not on more subtle

changes

  • Gradual trends are hard to detect by eye
  • Seasonal variation and exogenous variables can mask trends

in a parameter.

  • Viewers can “see what they want to see” sometimes

http://dnr.metrokc.gov/wlr/waterres/streams/northtrend.htm

Statistical Trend Analysis Methods

Type of statistic depends on data characteristics- To test if an existing data

set is “normally” distributed you may (a) plot a histogram of the results; or (b) conduct

tests for normality like the Shapiro-Wilk W test, the Filliben’s statistic, or the

studentized rage test (EPA, 2000, p. 4-6).

Parametric- Statistics for normally distributed data.

Includes regression of parameter against time or spatial

measure, like river mile. Parametric statistics are rarely

appropriate for environmental samples without massaging

data. See the USGS guide by Helsel and Hirsch for

descriptions of using regression.

Nonparametric- Statistics that are not as dependent on

assumptions about data distribution. Generally the safer

statistics to use, but are not as readily available. Test

include the Kendall test for presence of consistent trend,

Sen slope test for measure of magnitude of slope, and

Wilcoxon-Mann-Whitney step trend analysis.

Things to watch out for with statistical analysis

*** From Helsel D.R. and R.M. Hirsch. 1991 Statistical Methods**

in Water Resources. Techniques of Water-Resources

Investigations of the USGS Book 4. Chapter A3 p.

  • Verify and document that all assumptions have been tested

and met. Failure to do so, may lead to misleading results

  • The easiest test to do, OLS regression, is usually not

appropriate.

  • More robust, non-parametric tests like the seasonal Kendall

test are not readily available and can be computationally

demanding.

  • Finding no trend may only mean your data was insufficient to

find the trend.

  • Infrequent use of statistical

methods often requires

relearning fairly complicated

procedures every year. If

you do use a statistical

package, keep excellent

notes of what you do and

why.

Four OLS regression charts with the same R

2 , slope,

and intercept*


How to Calculate Non-Parametric Statistics

Kendall Test to determine if a significant trend exists see EPA

guide QA/G-9 pages 4-16 to 4-

XY Plot of data vs time

Yearly Value

Some Units

Year Units

2000 5

2001 6

2002 11

2003 8

2004 10

Sen Slope or Kendall-Theil line to measure the magnitude of

the trend see USGS Statistical Methods for Water Resources

pages 266 - 267

What type of trend analysis is right for you to use?

What would you need for temperature trend monitoring? Is there an

exogenous variable?

What about changes in other water quality parameters?

How could changes in monitoring schedule impact trends?

Example Bob has been monitoring DO in the morning at a site for 3 years. He adds

4 new sites to his route and now visits his old site in the afternoon every visit. Now

samples are collected in the pm. What impact will this have on your ability to track

trends? What could you do to correct the problem?

DO Saturation in Willamette R. at Portland S.P. & S. Railroad Bridge

Issues to consider when doing trend monitoring

• Consistent data quality- Trend monitoring assumes that the same or equivalent

methods and protocols are used for all the monitoring.

• Time frame & number of samples- 5 years of monthly data for WQ monotonic

trend analysis (Lettenmaier et.al., 1982); for step trends, at least 2 years of monthly

data before and after management change (Hirsch, 1982). (Statistic should be pre-

defined in QAPP to make sure you have everything you need.)

• Seasonality- Parameters that vary naturally in different seasons of the year

require special statistics or “de-seasonalization”.

• Type of data distribution (Is your data Normal?)*- If your data is not

normally distributed, you need to use a non-parametric statistical test.

Trend Monitoring...

The devil is in the details

  1. Based on Aroner, E.R. 2000 WQHYDRO Environmental Data Analysis Technical App. p. 146
  • Issue most applicable to statistical analysis

2 / 12 / 19906 / 27 / 199111 / 8 / 19923 / 23 / 19948 / 5 / 1995 Date

50

60

70

80

90

OWQI...month

50

60

70

80

90

OWQI...annual

OWQI...month OWQI...annual

ComparisonofTrends:Annualvs.MonthlyData

WillametteRiveratNewbergBridge

Issues to consider when doing trend monitoring

1

  • Similar variance across data set-* Statistical methods require consistent

sampling frequency (i.e., constant number of samples per period, equally spaced

across the period) to minimize variance.

  • Minimal missing observations-* Missing observations may invalidate some

tests by changing variance.

  • Outliers- Statistical tests designed for normal distributions are very sensitive to

outliers

  • Serial correlation-* Each result must be independent of other samples (across

time and space).

  • Exogenous variables- Parameters like conductivity and pH can be greatly

impacted by exogenous parameters, like stream discharge or time of day,

respectively. Changes in these exogenous variables may impact trends you

measure in the parameter of interest. To remove these impacts develop a

regression between the two variables. Calculate the residuals (the difference

between the measured value and value predicted by the regression) and then run

the trend analysis on the residuals.

  • Differences in detection limits-* Changing detection limits might fool the

statistic into thinking concentrations are decreasing (make sure you have a way to

statistically handle changing detection limits}.

  1. Based on Aroner, E.R. 2000 WQHYDRO Environmental Data Analysis Technical Appendix

p. 146

  • Issue most applicable to statistical analysis