Because stream water quality is often strongly correlated with flow, it is common to "flow-adjust" the data before testing for time trends (e.g. with the seasonal Kendall test). This is usually done by subtracting an "average" data value at each flow (often determined by fitting a non-parametric LOESS curve to the flow-data or log-flow-data scatter plot).
I have not been able to find a good justification for this practice.
This method makes me nervous, because the very notion of flow-adjustment ASSUMES that there is no change in the flow-data relationship with time. However, we then use this to look for changes with time. At best, this approach is valid only under very restricted conditions, i.e., when the flow-data-relationship and the data trend are additive. This means that trends in the data are the same across the entire flow range. However, trends in waterborne contaminants are usually linked to either surface, shallow or groundwater processes, not all three simultaneously.
Is flow-adjustment fundamentally flawed?
"There is a need for approaches that do not assume that the flow vs. concentration relation is constant with time." (Hirsch et al 2010). This paper has an excellent critical discussion of trend detection methods.
Hirsch, Robert M., Douglas L. Moyer, and Stacey A. Archfield, 2010. Weighted Regressions on Time, Discharge, and Season (WRTDS), With an Application to Chesapeake Bay River Inputs. Journal of the American Water Resources Association (JAWRA) 46(5):857-880. DOI: 10.1111 ⁄j.1752-1688.2010.00482.x
Your concern appears justified.
It seems to me that if you have long-term data to use for trend analysis, there is no need to adjust for flow. You can test for trends in flow and for trends in water quality separately. If there is a trend in water quality and there is also a statistically significant trend in the flow rate, this does not change the validity of the result for water quality trend, but of course may need to be investigated as a contributing causative factor for the water quality trend.
It seems to me that any data adjustment or conditioning is conflating existence of a water quality trend with attribution of that water quality trend.
"There is a need for approaches that do not assume that the flow vs. concentration relation is constant with time." (Hirsch et al 2010). This paper has an excellent critical discussion of trend detection methods.
Hirsch, Robert M., Douglas L. Moyer, and Stacey A. Archfield, 2010. Weighted Regressions on Time, Discharge, and Season (WRTDS), With an Application to Chesapeake Bay River Inputs. Journal of the American Water Resources Association (JAWRA) 46(5):857-880. DOI: 10.1111 ⁄j.1752-1688.2010.00482.x
I had not heard of this approach. Some WQ data is strongly correlated. Others types not so much. The relationship is not always static, and there can be substantial differences at the same flow rate between the rising and falling limbs of the hydrograph, seasonal change, length of time between significant storms and floods, as well as droughts. Management practices and various natural and induced disturbances and impacts can cause shifts. By plotting the flow x and water quality parameter y by year, using different point types or colors by year, one might begin to see trends whether there might be shifting of the water quality -flow relationship. There is only so much detail one may include and assess in normal plots.
Since I am unfamiliar with the flow adjustment use, I would not go so far as suggesting it is flawed, but before I would use, I would be cautious and want to know more. I have not read the Hirsch et al paper suggested.
You might be interested in some papers on end member analysis, such as by Garrett and others, which was used to separate stormflow, baseflow and interflow in the hydrograph.
All water data must show contaminates or the data is incorrect. All water is contaminated.
William F. Hansen yes exactly. There's a Murdoch and Shanley 2006 paper that suggests plotting flow vs concentration year by year. But this requires weekly or better data, and our data is usually monthly. Flow-adjustment has been standard practice in NZ, although I think it is falling out of favour. By the way, we have published a method using end member analysis combined with hydrograph separation, and I am currently extending this to infer flow path trends.
Murdoch, P.S., Shanley, J.B., 2006. Detection of water quality trends at high, median, and low flow in a Catskill Mountain stream, New York, through a new statistical method. Water Resources Research 42. doi:10.1029/2004WR003892
Woodward, S.J.R., Stenger, R., 2018. Bayesian chemistry-assisted hydrograph separation (BACH) and nutrient load partitioning from monthly stream phosphorus and nitrogen concentrations. Stochastic Environmental Research and Risk Assessment 32: 3475–3501, doi:10.1007/s00477-018-1612-3
Interesting. I know what I have used at times to make sense of water quality WQ data may be difficult to describe. Often flow and sometimes WQ needs to be on log scales. 12 readings a year probably would be usable if they sampled varied flows, rising and falling hydrographs, baseflow, seasons. I really used to like Lotus 123, as opposed to Excel. But you might use a specific symbol color for each year. Perhaps triangles for samples taken during rising hydrographs, circles during falling hydrograph. Solid color symbols if taken during growing season, symbols outlined not filled for dormant season. If you wanted to, you could pick the yearly color scheme to start in blues, then greens, yellows, orange, red, brown, and this may help in visualizing shifts. By the time you add log and other unit scales, you might want to plot this on a large GIS type plotter. Make sure you size and bold the symbols as needed. If one can begin to visualize these complex WQ flow relationships and trends, it will be easier to describe or model them. And sometimes, as may be expected for some parameters, the WQ point scatter will be difficult to define beyond natural variability.
I assume you are working with daily averages, but I would be concerned that using this method would become increasingly inaccurate as sampling measurements occur more frequently (5-60 minute range). The whole notion of a "first flush" is dependent on the front-loading of higher contaminant concentrations in the rising limb of the hydrograph, somewhat apart from actual flow rate. Average daily measurements largely obscure the flashiness of smaller order stream flowrates, and would also hide any pulsed contaminant effects occurring at the event scale.
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