UPDATES: March 2011

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Influence of non-detects on TMDL mass loading calculations

March 2011 (volume 6 - issue 3)

Contributed by Masoud Kayhanian, Department of Civil and Environmental Engineering, University of California - Davis (recipient of the 2010 J.S. Braun/Braun Intertec Professorship from the University of Minnesota)

Partially funded by Caltrans Division of Environmental Analysis

Often, fractions of stormwater chemical constituents are not detected above laboratory detection limits and are reported as non-detect (ND). Constituents that are often reported with higher numbers of non-detects in stormwater runoff include dissolved nutrients, dissolved metals, pesticides, herbicides and other organic compounds. For certain analyses, these ND data cannot be ignored as they provide necessary information. Analyzing data with non-detects can also be challenging, especially when computing for total maximum daily load (TMDL) mass loading calculations. The methodologies to deal with ND data include: (1) substitute ND = 0, (2) substitute ND = detection limit, (3) substitute ND = ½ detection limit, (4) regression on order statistics (ROS) method, (5) maximum likelihood estimation (MLE) method, (6) Cohen’s method and (7) USEPA delta log method. The first method is not reasonable. The second and third methods are non-scientific, although commonly used by practitioners and municipalities. The remaining methods are based on valid and accepted statistical approaches.

Application of these methods results in different estimates of constituent mean concentration that will, in turn, affect mass loading computation. To demonstrate the variability in mean values on load calculations, the dissolved As, Cr, Ni and Pb data from a highway runoff characterization study in California is used. An example calculation for a watershed with hypothetical TMDL load regulations for various metals is shown in Figure 1.

Figure 1: Mass loading for a watershed with a hypothetical metal TMDL for dissolved As, Cr, Ni and Pb (note: the horizontal line is the assumed hypothetical TMDL; the legend for each metal is associated with column bars from left to right)  

Results revealed that, depending on the number of NDs and the method of data analysis, differences up to 70 percent have been observed in mean values. Differences in TMDL were, as shown in Figure 1, found to have significant impacts on estimation of dissolved metal mass loading. In some cases, depending on the method of data analysis, the TMDL can either be met or violated for the same data set. For this test case, the ROS and MLE data analysis methods were found to be superior compared with other statistical methods. The conclusion of this short exercise is that when a large number of runoff data contain non-detects, it is better to use reliable statistical methods. These should be used consistently on a statewide basis, otherwise we can expect different TMDL outcomes. This consistent method of data analysis will also be beneficial when employed on national basis. The ROS method has been developed for practitioner use and information on this method can be found under "Data Analysis Tool" at this link. For additional information the readers are encouraged to look at the following two references.


  • Kayhanian, M., A. Singh, and S. Meyer (2002). "Impact of Non-Detect on Water Quality Data on Estimation of Constituent Mass Loading." Water Science and Technology, Vol. 45, No. 9, 219-225.
  • Shumway R. H., A. S. Azari, and M. Kayhanian (2002). "Statistical Approaches to Estimating Mean Water Quality Concentrations with Detection Limits." Environmental Science and Technology, Vol. 36, No. 15, 3345-3353.


We want to hear from you!!!

Let us know your thoughts, experiences, and questions by posting a comment. To get you thinking, here are a few questions: 

  • Do you think non-detect will be an issue in the future TMDL calculation? 
  • If yes, substituting ½ detection limit is the most practical method or do we need to use a science-based method?