Water quality uncertainty (phosphorus)

Typical quantitative results of water quality uncertainty studies: Phosphorus.

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; DP = dissolved phosphorus; FRP(X µm) = filtered reactive phosphorus (filter size); PDF = probability density function; PP = particulate phosphorus; RMSE = root mean square error; SD = standard deviation; SRP = soluble reactive phosphorus; TIP = total inorganic phosphorus; TP = total phosphorus

Uncertainty Type	Estimation Method	Magnitude	Location	Reference
Annual load; 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 -43 % (TP); 12 % (SRP)	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; effect of estimation method & sampling frequency	Bias relative to reference load from daily data (Mar 1976 to 28 Feb 1977); 3 sampling frequencies simulated via sub-sampling (222-680 repeats); 3-11 estimation methods tested	Average bias, biweekly: -2 to 20 %; Average bias, bi-weekly biased to high flows: 0-2 %; Average bias, bi-weekly biased to low flows: -1 to 2 %	Grand River at Eastmanville, Michigan, USA (13550 km2). Cropland; ave. discharge 101 m3 s-1; ave. annual TP load 1730 kg P d-1.	Dolan et al. (1981); values calculated from original absolute values
Annual load (TP); 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	-50 to 150 % at 12 samples per year down to -30 to 40 % 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
		-30 to 110 % at 12 samples per year down to -10 to 10 % 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.
Instantaneous concentration; analytical uncertainty	Standard uncertainty (square root of variance)	0.25 µg l-1 (FRP(0.2 µm)); 0.32 µg l-1 (TP)	Latrobe River catchment, Victoria, Australia	Lovell et al. (2001)
Instantaneous concentration; spot sampling uncertainty	Standard uncertainty (square root of variance) based on 3 repeats	2.09 µg l-1 (FRP(0.2 µm)); 1.05 µg l-1 (TP)
Instantaneous concentration; effect of spatial variation within 100 m reach	Standard uncertainty (square root of variance) based on 6 sampling spots	20.8 µg l-1 (FRP(0.2 µm)); 18.6 µg l-1 (TP)
Annual load; effect of temporal sampling method	Relative error with respect to reference method (composite sampling)	-9.2 to 2 % (PO4-P)	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)		0-17 % (TP); 0 % (DP)		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		-64 to 92 % (TP); -52 to 600 % (DP)
Storm load; analytical uncertainty		Up to ±400 % (DP); -2 to 16 % (PP)
Flow-weighted mean concentration (TIP, weekly)	Triangular fuzzy number	±40 % support	Crighton Royal Farm (0.5 ha fields), Dumfries, Scotland, UK. Silty clay loam soil, grassland, macropore flow, ave. annual precipitation 1054 mm.	Beven et al. (2006)
Total uncertainty	PDF, mean, SD	Normal, 0, 12 % (TP)	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	SD based on lab standards	5-15 % (PO4-P), decreasing with concentration	2 streams in Victoria, Australia, 1 forested, 1 urbanised.	Hanafi et al. (2007)
Instantaneous concentration; horizontal cross-section variation	Coefficient of variation with respect to 10-point cross-section average	7 % (SRP)	Elbe river at Dom Muehlenholz, Germany	Rode & Suhr (2007)
Analytical errors	PDF, coefficient of variation	Normal, 6 % (TP, SRP)		Quoted in Rode & Suhr (2007): Clesceri et al. (1998)
Daily load	Total probable error based on RMSE propagation method	<10 % (TP)	Various in Illinois, USA. Glacial moraine geology, Mollisol soil, flat, mainly corn & soybean land cover, underdrained.	Gentry et al. (2007) based on Harmel et al. (2006)
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)	6.4-8 % (TP); 6.1-7.5 % (SRP) (both almost 100 % 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	2 µg l-1 (TP); 0.4 µg l-1 (SRP); gleaned from original graphs
Storm load (TP); 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	-38 to 36 %	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 30 % (TP, PP), -25 to 65 % (SRP) 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	13-103(19) % (PO4-P concentrations); 14-104(23) % (PO4-P load); 16-104(24) % (TP concentrations); 17-105(27) % (TP load)	Various in USA (2.2-5506 ha)	Harmel et al. (2009) based on Harmel et al. (2006)
Concentrations & load	Total probable error based on RMSE propagation method	27 % (PO4-P concentrations); 28 % (PO4-P load)		Quoted in Harmel et al. (2009): Keener et al. (2007)
Instantaneous concentration (TP)	Absolute difference between auto & manual dublicates	0-400 µg l-1; decreasing with flow	Rowden Experimental Research Platform (1 ha fields), Devon, UK. Dystric Gleysol soil, 7-9 % slope, grassland, ave. annual precipitation 1055 mm, surface soil P ~540 mg kg-1, 250 x 37 cm weir box.	Krueger et al. (2009)
Annual load; 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	Monthly: -21.3 to 35.2 % (TP); -10.6 to 27.9 % (SRP); Fortnightly: -17.5 to 28.1 % (TP); -11 to 15.3 % (SRP); Weekly: -11.6 to 15.4 % (TP); -4.9 to 6.5 % (SRP); Daily: 0 to 4 % (TP); -2.1 to 2.5 % (SRP); 12h: -1.9 to 0.7 % (TP); -0.9 to 1.1 % (SRP)	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	±2 % of range (PO4-P, GreenspanTM Aqualab; PO4-P, EcotechTM FIA NUT1000; PO4-P, FIALabTM SIA); ±3 % of range (TP & PO4-P, SysteaTM Micromac C; PO4-P, EnvirotechTM AutoLAB/MicroLAB)		Bende-Michl & Hairsine (2010)
Annual load (TP); effect of temporal sampling method	Bias relative to interpolated 20 min instantaneous load timeseries	Median bias of various methods -50 to +30 %	Co. Monaghan, Ireland (5 km2). Drumlin soils, grassland, flashy, point sources.	Jordan & Cassidy (2011)
Flow-weighted mean concentration (TP, hourly)	Trapezoidal fuzzy number based on analysis of bulk uncertainty as function of number of sub-samples for three timesteps	±10 % core (5-6 samples per hour); ±50 % support (1 sample per hour)	Den Brook catchment (48 ha), Devon, UK. Dystric Gleysol soil, intensive grazing, ave. annual precipitation 1050 mm, flashy response, underdrained.	Krueger et al. (2012)

References

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.

Beven, K., Page, T., McGechan, M., 2006. Uncertainty estimation in phosphorus models. In: Radcliffe, D.E., Cabrera, M.L. (Eds.), Modeling phosphorus in the environment. CRC Press, Boca Raton, pp. 131-160.

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.

Dolan, D. M., Yui, A.K., Geist, R.D., 1981. Evaluation of river load estimation methods for total phosphorus. Journal of Great Lakes Research, 7(3): 207-214.

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

Gentry, L.E., David, M.B., Royer, T.V., Mitchell, C.A., Starks, K.M., 2007. Phosphorus transport pathways to streams in tile-drained agricultural watersheds. Journal of Environmental Quality, 36(2): 408-415.

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.

Jordan, P., Cassidy, R., 2011. Technical Note: Assessing a 24/7 solution for monitoring water quality loads in small river catchments. Hydrology and Earth System Sciences, 15(10): 3093-3100.

Keener, V.W., Ingram, K.T., Jacobson, B., Jones, J.W., 2007. Effects of El-Nino / Southern Oscillation on simulated phosphorus loading in South Florida. Trans. ASABE 50 (6), 2081–2089.

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.

Krueger, T., Quinton, J.N., Freer, J., Macleod, C.J.A., Bilotta, G.S., Brazier, R.E., Butler, P., Haygarth, P.M., 2009. Uncertainties in data and models to describe event dynamics of agricultural sediment and phosphorus transfer. Journal of Environmental Quality, 38(3): 1137-1148.

Krueger, T., Quinton, J.N., Freer, J., Macleod, C.J.A., Bilotta, G.S., Brazier, R.E., Hawkins, J.M.B., Haygarth, P.M., 2012. Comparing empirical models for sediment and phosphorus transfer from soils to water at field and catchment scale under data uncertainty. European Journal of Soil Science. doi:10.1111/j.1365-2389.2011.01419.x

Lovell, B., McKelvie, I.D., Nash, D., 2001. Sampling design for total and filterable reactive phosphorus monitoring in a lowland stream: considerations of spatial variability, measurement uncertainty and statistical power. Journal of Environmental Monitoring, 3(5): 463-468.

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.