Water quality uncertainty (nitrogen)

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Typical quantitative results of water quality uncertainty studies: Nitrogen.

This table originated from McMillan et al. (2012) but is now open to the community to add to and use as a resource.

BFI = base flow index; DIN = dissolved inorganic nitrogen; DN = dissolved nitrogen; PDF = probability density function; PN = particulate nitrogen; RMSE = root mean square error; SD = standard deviation; TKN = total Kjeldahl nitrogen; TN = total nitrogen

Uncertainty Type Estimation Method Magnitude Location Reference
Annual load (NO3-N); effect of sampling frequency 8 d routine sampling compared to 2 h composite (8 15 min sub-samples; Nov 1974 – May 1975); all via rating curve Bias 18 % River Main at Andraid, Co. Antrim, Northern Ireland (709 km2). Basaltic glacial till geology, 10% arable, 53% grassland, 24% rough grazing, population 54549 (65% connected to sewer), ave. annual precipitation 1181 mm, flashy response. Stevens & Smith (1978)
Annual load (TN); effect of estimation method & sampling frequency Bias relative to interpolated stage-triggered instantaneous load timeseries (2-15 min during rising stage, 1-4 h during falling stage, 4-24 h during baseflow); 13 estimation methods tested; 7 sampling frequencies simulated via sub-sampling -20 to 30 % at 12 samples per year down to -12 to 10 % at 104 samples per year; high-flow biased stratified sampling more biased and less precise Gelbæk catchment (8.5 km2), Eastern Jutland, Denmark. Lowland, low baseflow, high event-responsiveness, ave. discharge 232 mm. Kronvang & Bruhn (1996); results gleaned from original graphs
-11 to 25 % at 12 samples per year down to -2 to 9 % at 104 samples per year; high-flow biased stratified sampling more biased and less precise Gjern Å catchment (103 km2), Eastern Jutland, Denmark. Lowland, high baseflow, low event-responsiveness, ave. discharge 361 mm.
Annual load (NO3-N); effect of temporal sampling method Relative error with respect to reference method (composite sampling) -9.2 to 2 % USDA-ARS Grassland Soil & Water Research Laboratory (4.6-125.1 ha), Texas, USA. Vertisol soil, 2-4 % slope, mixed land cover. Harmel & King (2005)
Storm load; effect of minimum flow threshold for sampling Professional judgement based on Harmel et al. (2002) ±1-81 % Harmel et al. (2006)
Storm load; uncertainty due to manual sampling ±5-25 % (dissolved); ±15-50 % & more (suspended) Quoted in Harmel et al. (2006): Slade (2004)
Storm load; uncertainty due to automatic sampling (intake) 0 % (TN); 0-4 % (DN) Quoted in Harmel et al. (2006): Martin et al. (1992)
Storm load; uncertainty due to automatic sampling (timing) -65 to 51 % Quoted in Harmel et al. (2006)
Storm load; effect of sample preservation & storage -90 to 83 % (NH3-N); -65 to 71 % (NO3-N); -84 to 49 % (TKN)
Storm load; analytical uncertainty Up to ±400 % (DN); ±4-30 % (PN)
Total uncertainty (TN) PDF, mean, SD Normal, 0, 10 % Odense basin (1190 km2), Denmark. Glacial/interglacial sediment geology, low rolling hills, ave. annual precipitation/evapotranspiration 900/600 mm. Refsgaard et al. (2006)
Total analytical uncertainty (NH4-N) SD based on lab standards 4-19 %, decreasing with concentration 2 streams in Victoria, Australia, 1 forested, 1 urbanised. Hanafi et al. (2007)
Instantaneous concentration (NO3-N); analytical uncertainty SD 0, 40, 50, 50 µg l-1 at 100, 200, 800, 2100 µg l-1, respectively Rode & Suhr (2007)
Instantaneous concentration (NH4-N); analytical uncertainty Mean SD 5-8 %
Instantaneous concentration (NH4-N); horizontal cross-section variation Variation from 10-point cross-section average Up to 50 % & more Elbe river at Dom Muehlenholz, Germany
Analytical errors PDF, coefficient of variation Normal, 5 % (NO3, Cadmium Reduction Method); normal, 2.5 % (NO3, Electrode Method); normal, 4 % (NO3, Ion Chromatography); normal, 6 % (NO2); normal, 11 % (NH4) Quoted in Rode & Suhr (2007): Clesceri et al. (1998)
Instantaneous concentration; analytical uncertainty Difference to quality control standard ±5 % Lough Mask catchment, Ireland Donohue & Irvine (2008)
Instantaneous concentration; effect of lab sub-sampling Coefficient of variation with respect to 3-sub-sample average (95 % confidence interval) 9.6-11.2 % (TN), 71.8-82 % (lakes) & 77-82.2 % (rivers) attributable to sub-sample variability; 4-6.6 % (DIN), 53.4-71.2 % (lakes) & 67.7-75.1 % (rivers) attributable to sub-sample variability
Instantaneous concentration; effect of lab sub-sampling Mean minimum detectable difference between mean concentrations of two sets of 10 replicate sub-samples from same sample 0.2 mg l-1 (TN); 0.02 mg l-1 (DIN); gleaned from original graphs
Storm load (TN); effect of estimation method Bias relative to reference load from 1-6 h data (2 events in Sep 1994 & Nov 1999); 6 estimation methods tested; continuous thinning of data down to 1 sample per event -22 to 11 % Vène catchment, France (67 km2). Karst geology overlain by clay, mixed fruit/vegetables and urban land cover. Salles et al. (2008); values gleaned from original graphs
Storm load; effect of sampling frequency -25 to 20 % (TN), -25 to 10 % (NO3-N) at 1 sample per event; decreasing exponentially with increasing sampling frequency
Storm concentrations & load Total probable error (median in parentheses) based on RMSE propagation method 13-102(17) % (NO3-N concentrations); 14-103(22) % (NO3-N load); 14-104(23) % (TN concentrations); 15-105(27) % (TN load) Various in USA (2.2-5506 ha) Harmel et al. (2009) based on Harmel et al. (2006)
Annual load (TON); effect of sampling frequency Bias relative to reference load from stratified data (2-4 per d when dry, up to 8 per d when wet; Feb 2005 – Jan 2006); 5 sampling frequencies simulated via sub-sampling -4.2 to 11.2 % (monthly); -3.5 to 3.9 % (fortnightly); -1.8 to 3.5 % (weekly); -0.5 to 0.9 % (daily); -0.1 to 0.3 % (12 h) Frome at East Stoke, UK (414 km2), Mainly chalk geology, mainly grassland & cereals land cover, one town, ave. annual precipitation 1020 mm, ave. annual discharge 6.38 m3 s-1, BFI 0.84. Bowes et al. (2009)
Precision of various high frequency nutrient analysers As stated by manufacturer ±5 % of range (NH4-N & NO3-N, WTWTM VARiON; NH4-N & NO3-N, GreenspanTM Aqualab; NO3-N, YSITM YSI96000); ±3 % of range (TN, NH4-N, NO3-N & NO2-N, SysteaTM Micromac C; NO3-N & NO2-N, S::canTM Spectroanalyser); ±2 % of range (NH4-N & NO3-N, EnvirotechTM AutoLAB/MicroLAB; NH4-N, NO3-N & NO2-N, FIALabTM SIA; NO3-N, SatlanticTM ISUS) Bende-Michl & Hairsine (2010)


Bende-Michl, U., Hairsine, P.B., 2010. A systematic approach to choosing an automated nutrient analyser for river monitoring. Journal of Environmental Monitoring, 12(1): 127-134.

Bowes, M. J., Smith, J.T., Neal, C., 2009. The value of high-resolution nutrient monitoring: A case study of the River Frome, Dorset, UK. Journal of Hydrology, 378(1-2): 82-96.

Clesceri, L.S., Greenberg, A.E., Eaton, A.D., (Editors), 1998. Standard methods for the examination of water & wastewater. American Public Health Association, American Water Works Association and Water Environment Federation. 20th edition.

Donohue, I., Irvine, K., 2008. Quantifying variability within water samples: The need for adequate subsampling. Water Research, 42(1-2): 476-482.

Hanafi, S., Grace, M., Webb, J.A., Hart, B., 2007. Uncertainty in nutrient spiraling: Sensitivity of spiraling indices to small errors in measured nutrient concentration. Ecosystems, 10(3): 477-487.

Harmel, R.D., Cooper, R.J., Slade, R.M., Haney, R.L., Arnold, J.G., 2006. Cumulative uncertainty in measured streamflow and water quality data for small watersheds. Transactions of the ASABE, 49(3): 689-701.

Harmel, R.D., King, K.W., 2005. Uncertainty in measured sediment and nutrient flux in runoff from small agricultural watersheds. Transactions of the ASAE, 48(5): 1713-1721.

Harmel, R.D., Smith, D.R., King, K.W., Slade, R.M., 2009. Estimating storm discharge and water quality data uncertainty: A software tool for monitoring and modeling applications. Environmental Modelling & Software, 24(7): 832-842.

Kronvang, B., Bruhn, A.J., 1996. Choice of sampling strategy and estimation method for calculating nitrogen and phosphorus transport in small lowland streams. Hydrological Processes, 10(11): 1483-1501.

Martin, G. R., Smoot, J. L., White, K. D., 1992. A comparison of surface-grab and cross-sectionally integrated stream-water-quality sampling methods. Water Environ. Res. 64(7): 866-876.

McMillan, H., Krueger, T., Freer, J., 2012. Benchmarking observational uncertainties for hydrology: Rainfall, river discharge and water quality. Hydrological Processes 26(26): 4078–4111

Refsgaard, J.C., van der Keur, P., Nilsson, B., Mueller-Wohlfeil, D.I., Brown, J., 2006. Uncertainties in river basin data at various support scales - Example from Odense Pilot River Basin. Hydrology Earth System Sciences Discussions, 3(4): 1943-1985.

Rode, M., Suhr, U., 2007. Uncertainties in selected river water quality data. Hydrology and Earth System Sciences, 11(2): 863-874.

Salles, C., Tournoud, M.G., Chu, Y., 2008. Estimating nutrient and sediment flood loads in a small Mediterranean river. Hydrological Processes, 22(2): 242-253.

Slade, R. M., 2004. General Methods, Information, and Sources for Collecting and Analyzing Water-Resources Data. CD-ROM. Copyright 2004 Raymond M. Slade, Jr.

Stevens, R. J., Smith, R.V., 1978. A comparison of discrete and intensive sampling for measuring the loads of nitrogen and phosphorus in the river main, County Antrim. Water Research, 12(10): 823-830.