https://experimental-hydrology.net/wiki/api.php?action=feedcontributions&user=Mcmillanhk&feedformat=atomExperimental Hydrology Wiki - User contributions [en]2024-03-29T15:01:16ZUser contributionsMediaWiki 1.35.0https://experimental-hydrology.net/wiki/index.php?title=Water_quality_uncertainty_(phosphorus)&diff=2542Water quality uncertainty (phosphorus)2012-12-18T02:38:22Z<p>Mcmillanhk: /* References */</p>
<hr />
<div><br />
== Typical quantitative results of water quality uncertainty studies: Phosphorus. ==<br />
<br />
This table originated from McMillan et al. (2012) but is now open to the community to add to and use as a resource.<br />
<br />
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<br />
<br />
{| {{table}}<br />
| align="center" style="background:#f0f0f0;"|'''Uncertainty Type'''<br />
| align="center" style="background:#f0f0f0;"|'''Estimation Method'''<br />
| align="center" style="background:#f0f0f0;"|'''Magnitude'''<br />
| align="center" style="background:#f0f0f0;"|'''Location'''<br />
| align="center" style="background:#f0f0f0;"|'''Reference'''<br />
|- valign="top"<br />
| 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)<br />
|- valign="top"<br />
| 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<br />
|- valign="top"<br />
| 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<br />
|- valign="top"<br />
| ||||-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.||<br />
|- valign="top"<br />
| 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)<br />
|- valign="top"<br />
| 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)||||<br />
|- valign="top"<br />
| 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)||||<br />
|- valign="top"<br />
| 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)<br />
|- valign="top"<br />
| Storm load; effect of minimum flow threshold for sampling||Professional judgement based on Harmel et al. (2002)||±1-81 %||||Harmel et al. (2006)<br />
|- valign="top"<br />
| Storm load; uncertainty due to manual sampling||||±5-25 % (dissolved); ±15-50 % & more (suspended)||||Quoted in Harmel et al. (2006): Slade (2004)<br />
|- valign="top"<br />
| Storm load; uncertainty due to automatic sampling (intake)||||0-17 % (TP); 0 % (DP)||||Quoted in Harmel et al. (2006): Martin et al. (1992)<br />
|- valign="top"<br />
| Storm load; uncertainty due to automatic sampling (timing)||||-65 to 51 %||||Quoted in Harmel et al. (2006)<br />
|- valign="top"<br />
| Storm load; effect of sample preservation & storage||||-64 to 92 % (TP); -52 to 600 % (DP)||||<br />
|- valign="top"<br />
| Storm load; analytical uncertainty||||Up to ±400 % (DP); -2 to 16 % (PP)||||<br />
|- valign="top"<br />
| 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)<br />
|- valign="top"<br />
| 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)<br />
|- valign="top"<br />
| 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)<br />
|- valign="top"<br />
| 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)<br />
|- valign="top"<br />
| Analytical errors||PDF, coefficient of variation||Normal, 6 % (TP, SRP)||||Quoted in Rode & Suhr (2007): Clesceri et al. (1998)<br />
|- valign="top"<br />
| 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)<br />
|- valign="top"<br />
| Instantaneous concentration; analytical uncertainty||Difference to quality control standard||±5 %||Lough Mask catchment, Ireland||Donohue & Irvine (2008)<br />
|- valign="top"<br />
| 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)||||<br />
|- valign="top"<br />
| 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||||<br />
|- valign="top"<br />
| 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<br />
|- valign="top"<br />
| 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||||<br />
|- valign="top"<br />
| 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)<br />
|- valign="top"<br />
| 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)<br />
|- valign="top"<br />
| 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)<br />
|- valign="top"<br />
| 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)<br />
|- valign="top"<br />
| 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)<br />
|- valign="top"<br />
| 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)<br />
|- valign="top"<br />
| 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)<br />
|}<br />
<br />
== References ==<br />
<br />
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.<br />
<br />
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.<br />
<br />
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.<br />
<br />
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.<br />
<br />
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.<br />
<br />
Donohue, I., Irvine, K., 2008. Quantifying variability within water samples: The need for adequate subsampling. Water Research, 42(1-2): 476-482.<br />
<br />
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.<br />
<br />
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.<br />
<br />
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.<br />
<br />
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.<br />
<br />
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. <br />
<br />
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.<br />
<br />
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.<br />
<br />
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.<br />
<br />
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.<br />
<br />
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<br />
<br />
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.<br />
<br />
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.<br />
<br />
McMillan, H., Krueger, T., Freer, J., 2012. Benchmarking observational uncertainties for hydrology: Rainfall, river discharge and water quality. Hydrological Processes 26(26): 4078–4111<br />
<br />
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.<br />
<br />
Rode, M., Suhr, U., 2007. Uncertainties in selected river water quality data. Hydrology and Earth System Sciences, 11(2): 863-874.<br />
<br />
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.<br />
<br />
Slade, R. M., 2004. General Methods, Information, and Sources for Collecting and Analyzing Water-Resources Data. CD-ROM. Copyright 2004 Raymond M. Slade, Jr. <br />
<br />
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.<br />
<br />
[[Category:Uncertainty]]</div>Mcmillanhkhttps://experimental-hydrology.net/wiki/index.php?title=Water_quality_uncertainty_(nitrogen)&diff=2541Water quality uncertainty (nitrogen)2012-12-18T02:37:58Z<p>Mcmillanhk: /* References */</p>
<hr />
<div><br />
== Typical quantitative results of water quality uncertainty studies: Nitrogen. ==<br />
<br />
This table originated from McMillan et al. (2012) but is now open to the community to add to and use as a resource.<br />
<br />
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<br />
<br />
{| {{table}}<br />
| align="center" style="background:#f0f0f0;"|'''Uncertainty Type'''<br />
| align="center" style="background:#f0f0f0;"|'''Estimation Method'''<br />
| align="center" style="background:#f0f0f0;"|'''Magnitude'''<br />
| align="center" style="background:#f0f0f0;"|'''Location'''<br />
| align="center" style="background:#f0f0f0;"|'''Reference'''<br />
|- valign="top"<br />
| 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)<br />
|- valign="top"<br />
| 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<br />
|- valign="top"<br />
| ||||-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.||<br />
|- valign="top"<br />
| 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)<br />
|- valign="top"<br />
| Storm load; effect of minimum flow threshold for sampling||Professional judgement based on Harmel et al. (2002)||±1-81 %||||Harmel et al. (2006)<br />
|- valign="top"<br />
| Storm load; uncertainty due to manual sampling||||±5-25 % (dissolved); ±15-50 % & more (suspended)||||Quoted in Harmel et al. (2006): Slade (2004)<br />
|- valign="top"<br />
| Storm load; uncertainty due to automatic sampling (intake)||||0 % (TN); 0-4 % (DN)||||Quoted in Harmel et al. (2006): Martin et al. (1992)<br />
|- valign="top"<br />
| Storm load; uncertainty due to automatic sampling (timing)||||-65 to 51 %||||Quoted in Harmel et al. (2006)<br />
|- valign="top"<br />
| Storm load; effect of sample preservation & storage||||-90 to 83 % (NH3-N); -65 to 71 % (NO3-N); -84 to 49 % (TKN)||||<br />
|- valign="top"<br />
| Storm load; analytical uncertainty||||Up to ±400 % (DN); ±4-30 % (PN)||||<br />
|- valign="top"<br />
| 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)<br />
|- valign="top"<br />
| 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)<br />
|- valign="top"<br />
| 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)<br />
|- valign="top"<br />
| Instantaneous concentration (NH4-N); analytical uncertainty||Mean SD||5-8 %||||<br />
|- valign="top"<br />
| 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||<br />
|- valign="top"<br />
| 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)<br />
|- valign="top"<br />
| Instantaneous concentration; analytical uncertainty||Difference to quality control standard||±5 %||Lough Mask catchment, Ireland||Donohue & Irvine (2008)<br />
|- valign="top"<br />
| 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||||<br />
|- valign="top"<br />
| 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||||<br />
|- valign="top"<br />
| 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<br />
|- valign="top"<br />
| 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||||<br />
|- valign="top"<br />
| 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)<br />
|- valign="top"<br />
| 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)<br />
|- valign="top"<br />
| 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)<br />
|}<br />
<br />
== References ==<br />
<br />
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.<br />
<br />
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.<br />
<br />
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.<br />
<br />
Donohue, I., Irvine, K., 2008. Quantifying variability within water samples: The need for adequate subsampling. Water Research, 42(1-2): 476-482.<br />
<br />
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.<br />
<br />
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.<br />
<br />
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.<br />
<br />
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.<br />
<br />
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.<br />
<br />
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.<br />
<br />
McMillan, H., Krueger, T., Freer, J., 2012. Benchmarking observational uncertainties for hydrology: Rainfall, river discharge and water quality. Hydrological Processes 26(26): 4078–4111<br />
<br />
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.<br />
<br />
Rode, M., Suhr, U., 2007. Uncertainties in selected river water quality data. Hydrology and Earth System Sciences, 11(2): 863-874.<br />
<br />
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.<br />
<br />
Slade, R. M., 2004. General Methods, Information, and Sources for Collecting and Analyzing Water-Resources Data. CD-ROM. Copyright 2004 Raymond M. Slade, Jr.<br />
<br />
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.<br />
<br />
[[Category:Uncertainty]]</div>Mcmillanhkhttps://experimental-hydrology.net/wiki/index.php?title=Suspended_solids_uncertainty&diff=2540Suspended solids uncertainty2012-12-18T02:37:40Z<p>Mcmillanhk: /* References */</p>
<hr />
<div><br />
== Typical quantitative results of water quality uncertainty studies: Suspended solids. ==<br />
<br />
This table originated from McMillan et al. (2012) but is now open to the community to add to and use as a resource.<br />
<br />
PDF = probability density function; RMSE = root mean square error; WY = water year<br />
<br />
{| {{table}}<br />
| align="center" style="background:#f0f0f0;"|'''Uncertainty Type'''<br />
| align="center" style="background:#f0f0f0;"|'''Estimation Method'''<br />
| align="center" style="background:#f0f0f0;"|'''Magnitude'''<br />
| align="center" style="background:#f0f0f0;"|'''Location'''<br />
| align="center" style="background:#f0f0f0;"|'''Reference'''<br />
|- valign="top"<br />
| Instantaneous concentration||Relative difference between auto & manual dublicates||Auto sample within 10 % of manual sample||Devon, UK||Walling & Teed (1971)<br />
|- valign="top"<br />
| 8-year load; effect of estimation method||Bias relative to reference load from daily data (1974/75-1981/82); 12 methods tested; 6 sampling frequencies simulated via sub-sampling||-22 to 10 %||Euphrates (444000 km2) at Haditha, Iraq. Ave. annual precipitation <100 mm (South) – 800 mm (north), ave. annual discharge 776 m3 s-1, ave. annual sediment load 1.4 107 t.||Al-Ansari et al. (1988); values calculated from original absolute values<br />
|- valign="top"<br />
| 8-year load; effect of sampling frequency||||-4 to 6 %||||<br />
|- valign="top"<br />
| Instantaneous concentration; effect of cross-section sampling method||Average coefficient of variation with respect to depth- & width-integrated reference concentration||25 %||Various in USA||Horowitz et al. (1990); values calculated from original table<br />
|- valign="top"<br />
| Instantaneous concentration; horizontal cross-section variation||Average coefficient of variation with respect to 5-point average||26 %||||<br />
|- valign="top"<br />
| Instantaneous concentration; sampler effect||Difference between two samplers (EPIC – USGS)||36 % initially, then -1 to -15 %||Humber catchment, UK||Evans et al. (1997); values gleaned from original graph<br />
|- valign="top"<br />
| Concentration exceedance frequency; effect of distribution assumption given censored data||Absolute difference between lognormal & normal models||0-3%, increasing with censoring||Little Cataraqui Creek (45 km2), Kingston Township, Ontario, Canada. Half urban, half forested, flat, ave. annual precipitation 900 mm (~22% snow).||van Buren et al. (1997)<br />
|- valign="top"<br />
| Load; effect of distribution assumption given censored data||Relative difference between lognormal & normal models, relative to lognormal model||25-37 % (calculated from original table)||||<br />
|- valign="top"<br />
| Instantaneous load; horizontal & vertical cross-section variation||Error of point turbidity measurement compared to width- & depth- integrated sample||-2.18 to -14.3 %||Humber catchment, UK, 8 sites (484.3-8231 km2). Wide range of geology, climate, soils and land cover, ave. annual precipitation 600 (east) – 1600 (Pennine Hills) mm.||Wass & Leeks (1999); values from original table<br />
|- valign="top"<br />
| 5-year load; effect of rating curve choice and sampling frequency||Bias relative to reference load from daily data (1979-1983); 4 rating curves tested; 4 sampling frequencies simulated via sub-sampling||-56 to 10 %||Rhine catchment above Rees, Germany (165000 km2), 5 locations. Temperate climate, 600 (lower Rhine) – 2500 (Alpes) mm precipitation, ave. annual discharge 2300 m3 s-1, ave. annual sediment load 3.14 106 t.||Asselman (2000)<br />
|- valign="top"<br />
| Annual & 5-year load; effect of rating curve choice and sampling frequency||Bias relative to reference load from daily data; 4 rating curves tested; 12 subsets of data used to construct rating curves; various sampling frequencies simulated via sub-sampling||WY 1996-2000: -7 to 6 % at 50 d down to -3 % at 1 d; WY 1989 (low flow year): -10 to 3 % at 30 d down to -6 % at 1 d; WY 1995 (median flow year): -11 to 7 % at 30 d down to -1 % at 1 d; WY1982 (high flow year): -11 to 8 % at 30 d down to 3 % at 1 d||Mississippi at Thebes, Illinois, USA (1847188 km2), 01/10/1980-30/09/2000||Horowitz (2003); values gleaned from original graphs<br />
|- valign="top"<br />
| ||||WY 1989-1993: -7 to 13 % at 50 d down to 2 % at 1 d; WY 1976 (low flow year): -11 to 10 % at 50 d down to 0 % at 1 d; WY 1980 (median flow year): -15 to 5 % at 30 d down to -3 % at 1 d; WY1987 (high flow year): -15 to 10 % at 30 d down to -5 % at 1 d||Rhine at Maxau, Germany (50200 km2), 31/10/1973-30/10/1993||<br />
|- valign="top"<br />
| Annual load; effect of temporal sampling method||Relative error with respect to reference method (composite sampling)||-9.1 to 2.7 %||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)<br />
|- valign="top"<br />
| Storm load; effect of minimum flow threshold for sampling||Professional judgement based on Harmel et al. (2002)||±1-81 %||||Harmel et al. (2006)<br />
|- valign="top"<br />
| Storm load; uncertainty due to manual sampling||||±15-50 % & more||||Quoted in Harmel et al. (2006): Slade (2004)<br />
|- valign="top"<br />
| Storm load; uncertainty due to automatic sampling (intake)||||14-33 %||||Quoted in Harmel et al. (2006): Martin et al. (1992)<br />
|- valign="top"<br />
| Storm load; uncertainty due to automatic sampling (timing)||||-65 to 51 %||||Quoted in Harmel et al. (2006)<br />
|- valign="top"<br />
| Storm load; analytical uncertainty||95 % confidence interval||-9.8 to 5.1 % (sandy); -5.3 to 4.4 % (fine)||||Quoted in Harmel et al. (2006): Gordon et al. (2000)<br />
|- valign="top"<br />
| Annual load; effect of sampling frequency||Bias relative to reference load from daily data (1961-1988); 28 sampling frequencies (2-30 d) simulated via sub-sampling (50 repeats, multiple years)||±30 % at 30 d (central 80 % from repeats & multiple years); decreasing with increasing sampling frequency||Mississippi at St Louis, Missouri, USA (251121 km2). Ave. annual discharge 20.1 l s-1 km-2, ave. annual sediment load 447 t yr-1 km-2.||Moatar et al. (2006); values gleaned from original graph; results from 35 more stations in USA and EU reported as well<br />
|- valign="top"<br />
| Instantaneous concentration||Coefficient of variation between dublicates||33 % (at 15 mg l-1); 10 % (at 242 mg l-1); 0.76 % (at 1707 mg l-1)||||Rode & Suhr (2007)<br />
|- valign="top"<br />
| Analytical errors||PDF, coefficient of variation||Lognormal, 13 %||||Quoted in Rode & Suhr (2007)<br />
|- valign="top"<br />
| Storm load; 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||-52 to 19 %||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<br />
|- valign="top"<br />
| Storm load; effect of sampling frequency||||-25 to 30 % at 1 sample per event; decreasing exponentially with increasing sampling frequency||||<br />
|- valign="top"<br />
| Instantaneous concentration||Absolute difference between auto & manual dublicates||0-100 mg 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, 250 x 37 cm weir box.||Krueger et al. (2009)<br />
|- valign="top"<br />
| Storm concentrations & load||Total probable error (median in parentheses) based on RMSE propagation method||12-26(18) % (concentrations); 15-35(20) % (load)||Various in USA (2.2-5506 ha)||Harmel et al. (2009) based on Harmel et al. (2006)<br />
|- valign="top"<br />
| Concentration exceedance frequency||Uncertainty range based on bootstrapping low resolution data||Approx.10 %||Den Brook catchment (48 ha), Devon, UK. Dystric Gleysol soil, intensive grazing, ave. annual precipitation 1050 mm, flashy response, underdrained.||Bilotta et al. (2010); values gleaned from original graph<br />
|- valign="top"<br />
| Flow-weighted mean concentration (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)||||Krueger et al. (2012)<br />
|}<br />
<br />
== References ==<br />
<br />
Al-Ansari, N.A., Asaad, N.M., Walling, D.E., Hussan, S.A., 1988. The suspended sediment discharge of the River Euphrates at Haditha, Iraq: An assessment of the potential for establishing sediment rating curves. Geografiska Annaler, Series A, Physical Geography, 70(3): 203-213.<br />
<br />
Asselman, N. E. M., 2000. Fitting and interpretation of sediment rating curves. Journal of Hydrology, 234(3-4): 228-248.<br />
<br />
Bilotta, G.S., Krueger, T., Brazier, R.E., Butler, P., Freer, J., Hawkins, J.M.B., Haygarth, P.M., Macleod, C.J.A., Quinton, J.N., 2010. Assessing catchment-scale erosion and yields of suspended solids from improved temperate grassland. Journal of Environmental Monitoring, 12(3): 731-739.<br />
<br />
Evans, J.G., Wass, P.D., Hodgson, P., 1997. Integrated continuous water quality monitoring for the LOIS river programme. Science of the Total Environment, 194: 111-118.<br />
<br />
Gordon, J. D., Newland, C.A., Gagliardi, S.T., 2000. Laboratory performance in the sediment laboratory quality-assurance project, 1996-98. USGS Water Resources Investigations Report 99-4184. Washington, D.C.: USGS.<br />
<br />
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.<br />
<br />
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.<br />
<br />
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.<br />
<br />
Horowitz, A.J., 2003. An evaluation of sediment rating curves for estimating suspended sediment concentrations for subsequent flux calculations. Hydrological Processes, 17(17): 3387-3409.<br />
<br />
Horowitz, A.J., Rinella, F.A., Lamothe, P., Miller, T.L., Edwards, T.K., Roche, R.L., Rickert, D.A., 1990. Variations in suspended sediment and associated trace-element concentrations in selected riverine cross-sections. Environmental Science & Technology, 24(9): 1313-1320.<br />
<br />
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.<br />
<br />
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<br />
<br />
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.<br />
<br />
McMillan, H., Krueger, T., Freer, J., 2012. Benchmarking observational uncertainties for hydrology: Rainfall, river discharge and water quality. Hydrological Processes 26(26): 4078–4111<br />
<br />
Moatar, F., Person, G., Meybeck, M., Coynel, A., Etcheber, H., Crouzet, P., 2006. The influence of contrasting suspended particulate matter transport regimes on the bias and precision of flux estimates. Science of the Total Environment, 370(2-3): 515-531.<br />
<br />
Rode, M., Suhr, U., 2007. Uncertainties in selected river water quality data. Hydrology and Earth System Sciences, 11(2): 863-874.<br />
<br />
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.<br />
<br />
Slade, R. M., 2004. General Methods, Information, and Sources for Collecting and Analyzing Water-Resources Data. CD-ROM. Copyright 2004 Raymond M. Slade, Jr.<br />
<br />
van Buren, M.A., Watt, W.E., Marsalek, J., 1997. Application of the log-normal and normal distributions to stormwater quality parameters. Water Research, 31(1): 95-104.<br />
<br />
Walling, D.E., Teed, A., 1971. A simple pumping sampler for research into suspended sediment transport in small catchments. Journal of Hydrology, 13: 325-337.<br />
<br />
Wass, P.D., Leeks, G.J.L., 1999. Suspended sediment fluxes in the Humber catchment, UK. Hydrological Processes, 13(7): 935-953.<br />
<br />
[[Category:Uncertainty]]</div>Mcmillanhkhttps://experimental-hydrology.net/wiki/index.php?title=Stage_measurement_uncertainty&diff=2539Stage measurement uncertainty2012-12-18T02:37:16Z<p>Mcmillanhk: /* References */</p>
<hr />
<div><br />
== Typical quantitative results of discharge uncertainty studies: Stage Uncertainty. ==<br />
<br />
This table originated from McMillan et al. (2012) but is now open to the community to add to and use as a resource.<br />
<br />
SD = standard deviation<br />
<br />
{| {{table}}<br />
| align="center" style="background:#f0f0f0;"|'''Uncertainty Type'''<br />
| align="center" style="background:#f0f0f0;"|'''Estimation Method'''<br />
| align="center" style="background:#f0f0f0;"|'''Magnitude'''<br />
| align="center" style="background:#f0f0f0;"|'''Location'''<br />
| align="center" style="background:#f0f0f0;"|'''Reference'''<br />
|- valign="top"<br />
| Stage uncertainty||Comparison with neighbouring stations||SD of 25 mm||Netherlands gauging network||Van der Made (1982)<br />
|- valign="top"<br />
| Effect of unstable bed||Expert knowledge; uncertainty for individual measurement||±10 %||Estimate for locations with shifting sand or moving dunes||Sauer & Meyer (1992)<br />
|- valign="top"<br />
| Instrument precision||Review of previous studies; uncertainty for individual measurement||±3-10.8 mm or ±0.1-2 %||||Quoted in Harmel et al. (2006)<br />
|- valign="top"<br />
| Instrument precision||Expert knowledge||Range ±10 mm; local oscillations of water surface can add additional uncertainty of ±20 mm||Typical example of natural rivers||Dottori et al. (2009)<br />
|- valign="top"<br />
| Instrument precision: Float in stilling well||||6 mm||||Quoted in Herschy (1998): Ackers et al. (1978)<br />
|- valign="top"<br />
| Instrument precision: Pressure transducer ||||1.4-40 mm||||Herschy (1998)<br />
|- valign="top"<br />
| Stage uncertainty||Expert knowledge of typical uncertainties||4 mm (high accuracy) to 15 mm (low accuracy)||Norwegian Water Resources & Energy Directorate||Petersen-Øverleir & Reitan (2005)<br />
|- valign="top"<br />
| Stage uncertainty||Observed fluctuation||2-5 mm||Rowden Experimental Research Platform (1 ha fields), Devon, UK. 250 x 37 cm weir box, stainless steel 45° V-Notch, float (Model 6541, Unidata), stilling well, ave. annual precipitation 1055 mm.||Krueger et al. (2010)<br />
|- valign="top"<br />
| Instrument precision||Manufacturer cited random uncertainty||2.5 mm (Trutrack, Model PLUT-HR Water level recorder)||Hillslope (172 m2), WS10 catchment, HJA Experimental Forest, Oregon, USA||Graham et al. (2010)<br />
|- valign="top"<br />
| ||||0.3 mm (Model 2 Stevens Instruments Position Analog Transmitter)||WS10 catchment (10.2 ha), HJA Experimental Forest, Oregon, USA. Mediterranean climate, rainfall 2200 mm yr-1, slopes 30-45 °.||<br />
|- valign="top"<br />
| Stage uncertainty||Nominal uncertainty||3 mm||||Hamilton & Moore (2012)<br />
|}<br />
<br />
== References ==<br />
<br />
Ackers, P., 1978. Weirs and flumes for flow measurement. Wiley, Chichester.<br />
<br />
Dottori, F., Martina, M.L.V., Todini, E., 2009. A dynamic rating curve approach to indirect discharge measurement. Hydrology and Earth System Sciences, 13(6): 847-863.<br />
<br />
Graham, C.B., van Verseveld, W., Barnard, H.R., McDonnell, J.J., 2010. Estimating the deep seepage component of the hillslope and catchment water balance within a measurement uncertainty framework. Hydrological Processes, 24(25): 3878–3893.<br />
<br />
Hamilton, A.S., Moore, R.D., 2012. Quantifying Uncertainty in Streamflow Records. Canadian Water Resources Journal, 37(1): 3-21.<br />
<br />
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.<br />
<br />
Herschy, R.W., 1998. Hydrometry : Principles and practices. Wiley, Chichester.<br />
<br />
Krueger, T., Freer, J., Quinton, J.N., Macleod, C.J.A., Bilotta, G.S., Brazier, R.E., Butler, P., Haygarth, P.M., 2010. Ensemble evaluation of hydrological model hypotheses. Water Resources Research, 46: W07516.<br />
<br />
McMillan, H., Krueger, T., Freer, J., 2012. Benchmarking observational uncertainties for hydrology: Rainfall, river discharge and water quality. Hydrological Processes 26(26): 4078–4111<br />
<br />
Petersen-Øverleir, A., Reitan, T., 2005. Uncertainty in flood discharges from urban and small rural catchments due to inaccurate head measurement. Nordic Hydrology, 36(3): 245-257.<br />
<br />
Sauer, V.B., Meyer, R.W., 1992. Determination of error in individual discharge measurements, U.S. Geological Survey Open-File Report 92–144.<br />
<br />
van der Made, J.E., 1982. Determination of the accuracy of water level observations, Proceedings of the Exeter Symposium. IAHS Publications 134, pp. 172-184.<br />
<br />
[[Category:Uncertainty]]</div>Mcmillanhkhttps://experimental-hydrology.net/wiki/index.php?title=Rainfall_radar_and_satellite_uncertainty&diff=2538Rainfall radar and satellite uncertainty2012-12-18T02:36:59Z<p>Mcmillanhk: /* References */</p>
<hr />
<div><br />
== Typical quantitative results of rainfall uncertainty studies: Radar and Satellite. ==<br />
<br />
This table originated from McMillan et al. (2012) but is now open to the community to add to and use as a resource.<br />
<br />
RMSE = root mean square error; SD = standard deviation<br />
<br />
{| {{table}}<br />
| align="center" style="background:#f0f0f0;"|'''Uncertainty Type'''<br />
| align="center" style="background:#f0f0f0;"|'''Estimation Method'''<br />
| align="center" style="background:#f0f0f0;"|'''Magnitude'''<br />
| align="center" style="background:#f0f0f0;"|'''Location'''<br />
| align="center" style="background:#f0f0f0;"|'''Reference'''<br />
|-<br />
| '''''Radar'''''<br />
|- valign="top"<br />
| Error between radar estimate and gauge network||Radar RMSE with respect to 30 raingauges||10 % for storms >30 mm after radar bias correction using high quality rain gauge data; when all gauges were used for bias correction without prior quality control RMSE was 10-40 %||ARS Goodwin Creek experimental watershed, Mississippi, USA||Steiner et al. (1999)<br />
|- valign="top"<br />
| Error between radar estimate and gauge network||Standard error of residuals compared with 8 rain gauges in 2 km2 area||50% (low relief) at 4 mm/15 min rain rate; presented graphically for rain rates 0.4-10 mm/15 min||Brue catchment, UK (135 km2). 20-250 m a.s.l., temperate climate, orographic rainfall.||Wood et al. (2000)<br />
|- valign="top"<br />
| ||Standard error of residuals compared with 49 rain gauges in 135 km2 area||55 % at 2km resolution, 60 % at 5 km resolution, for rain rate 4 mm/15 min; presented graphically for rain rates 0.2-8 mm/15 min||||<br />
|- valign="top"<br />
| Error between radar (WSR-88D) estimate and gauge network||SD of the stochastic component of multiplicative error||Conditioned on distance from radar, timescale of observation & season; asymptotic SD at high rainfall rates in the range 0.1-0.7, typically 0.5 for hourly data||Oklahoma, USA. Rainfall 800 mm yr-1, dominated by midlatitude convective systems.||Ciach et al. (2007)<br />
|- valign="top"<br />
| Error between radar (S-band) estimate and gauge network||SD of residuals||Approx. 0.3 (proportion of mean rain rate) for hourly data over 0-100 km distance from radar; values also given for 1, 2, 6, 12 hours & 0-50, 50-100, 0-100 km distances||Cévennes-Vivarais region, France. 200 km *160 km convective and frontal rainfall.||Kirstetter et al. (2010)<br />
|- valign="top"<br />
| Error between radar (WSR-88D) estimate and gauge network||SD of residuals (2 research gauge networks)||0.48 (hourly, 8 km resolution), 1.07 (hourly, 1 km resolution), proportion of mean rain rate; values also given for 15 min, 1 hour at scales 0.5, 1, 2, 4, 8 km||Iowa, USA||Seo & Krajewski (2010); raingauge networks used paired gauges at all sites<br />
|- valign="top"<br />
| Error between radar (X-band) estimate and gauge network||Mean and SD of bias for pixel-based comparison between 2 radars and 20 gauges.||Using a Z-R relationship to estimate rainfall, the mean bias for the 2 radars was -0.24, -0.27; with SD of the relative error 0.46, 0.48.||Southwest Oklahoma, USA. Raingauges – radar distance up to 35 km. Study used 4 storm events of heavy/ broken squall lines with embedded convective cells. ||Vieux and Imgarten (2011)<br />
|-<br />
| '''''Satellite'''''<br />
|- valign="top"<br />
| Bias in estimates of surface rain rate from TRMM (Tropical Rainfall Measuring Mission)||Bayesian modelling approach to estimate SD of each parameter in algorithm used to calculate surface rain rate||SD of combined multiplicative bias in rain rate presented graphically as a function of rain rate: 40-60% at rates up to 18 mm h-1, 150 % at 25 mm h-1,||All oceanic pixels for 10 TRMM orbits||L’Ecuyer and Stephens (2002)<br />
|- valign="top"<br />
| Bias of two NASA satellite products (infrared & passive microwave)||Mean & variance in multiplicative bias at hourly timesteps & 0.25º resolution compared with ground radar||Mean multiplicative hourly bias 0.35-1.09 (with SD of 0.73-0.84) over 4-month study period.||Oklahoma, USA. Southern Plains, 95-100°W, 34-37°N.||Hossain & Anagnostou (2006)<br />
|}<br />
<br />
== References ==<br />
<br />
Ciach, G.J., Krajewski, W.F., Villarini, G., 2007. Product-error-driven uncertainty model for probabilistic quantitative precipitation estimation with NEXRAD data. Journal of Hydrometeorology, 8(6): 1325-1347.<br />
<br />
Hossain, F., Anagnostou, E.N., 2006. Assessment of a multidimensional satellite rainfall error model for ensemble generation of satellite rainfall data. IEEE Geoscience and Remote Sensing Letters, 3(3): 419-423.<br />
<br />
Kirstetter, P.E., Delrieu, G., Boudevillain, B., Obled, C., 2010. Toward an error model for radar quantitative precipitation estimation in the Cevennes-Vivarais region, France. Journal of Hydrology, 394(1-2): 28-41.<br />
<br />
L’Ecuyer, T. S., and G. L. Stephens, 2002. An uncertainty model for Bayesian Monte Carlo retrieval algorithms: Application to the TRMM observing system. Quart. J. Roy. Meteor. Soc.,128, 1713–1737.<br />
<br />
McMillan, H., Krueger, T., Freer, J., 2012. Benchmarking observational uncertainties for hydrology: Rainfall, river discharge and water quality. Hydrological Processes 26(26): 4078–4111<br />
<br />
Seo, B.C., Krajewski, W.F., 2010. Scale dependence of radar rainfall uncertainty: Initial evaluation of NEXRAD's new super-resolution data for hydrologic applications. Journal of Hydrometeorology, 11(5): 1191-1198.<br />
<br />
Steiner, M., Smith, J.A., Burges, S.J., Alonso, C.V., Darden, R.W., 1999. Effect of bias adjustment and rain gauge data quality control on radar rainfall estimation. Water Resources Research, 35(8): 2487-2503.<br />
<br />
Vieux, B.E., Imgarten, J.M., 2011. On the scale-dependent propagation of hydrologic uncertainty using high-resolution X-band radar rainfall estimates. Atmospheric Research. 103: 96-105.<br />
<br />
Wood, S.J., Jones, D.A., Moore, R.J., 2000. Accuracy of rainfall measurement for scales of hydrological interest. Hydrology and Earth System Sciences, 4(4): 531-543.<br />
<br />
[[Category:Uncertainty]]</div>Mcmillanhkhttps://experimental-hydrology.net/wiki/index.php?title=Rainfall_point_measurement_uncertainty&diff=2536Rainfall point measurement uncertainty2012-12-18T02:36:38Z<p>Mcmillanhk: /* References */</p>
<hr />
<div><br />
== Typical quantitative results of rainfall uncertainty studies: Point Measurements. ==<br />
<br />
This table originated from McMillan et al. (2012) but is now open to the community to add to and use as a resource.<br />
<br />
{| {{table}}<br />
| align="center" style="background:#f0f0f0;"|'''Uncertainty Type'''<br />
| align="center" style="background:#f0f0f0;"|'''Estimation Method'''<br />
| align="center" style="background:#f0f0f0;"|'''Magnitude'''<br />
| align="center" style="background:#f0f0f0;"|'''Location'''<br />
| align="center" style="background:#f0f0f0;"|'''Reference'''<br />
|-<br />
| '''''Systematic Errors'''''<br />
|- valign="top"<br />
| Wind loss curves dependent on wind speed & raindrop size ||Theoretical calculation using wind velocity field from wind tunnel experiments||1 mm drops: -10 % (6 m s-1), -40 % (9 m s-1), -80 % (12 m s-1); 2 mm drops: -10 % (9 m s-1), -20 % (12 m s-1); 3-5 mm drops: no effect up to 15 m s-1||||Mueller & Kidder (1972)<br />
|- valign="top"<br />
| Wind loss curves||Comparison with shielded gauge||Approx. linear 1 % under-catch per 1 mph wind speed||Danville, Vermont, USA||Larson & Peck (1974); also wind loss curves for snow<br />
|- valign="top"<br />
| Undercatch for gauge mounted at 1 m height||Comparison with pit gauge||5-16 % average undercatch (over 53-321 events), 0-75 % per storm||USA: Reynolds Creek, Idaho; Pullman, Washington; Sidney, Montana; Ekalaka, Montana||Neff (1977)<br />
|- valign="top"<br />
| Loss due to wind field deformation||WMO literature survey & pit gauge comparisons||2-10 % (rain), 10-50 % (snow)||||Sevruk (1982); extensive literature survey is still widely quoted; correction equations are given dependent on gauge type & meteorological conditions<br />
|- valign="top"<br />
| Wetting loss||||2-15 % (summer), 1-8 % (winter)||||<br />
|- valign="top"<br />
| Evaporation loss from open container||||0-4 %||||<br />
|- valign="top"<br />
| Splash-in/out||||1-2 %||||<br />
|- valign="top"<br />
| Undercatch for shielded gauge at 12 inches height & turf wall gauge||Comparison with pit gauge||5 % (unshielded), 2 % (turf wall) annual undercatch||County Londonderry, Ireland. Lowland, coastal, rainfall 900-1100 mm yr-1.||Essery & Wilcock (1991); 1976-1988<br />
|- valign="top"<br />
| Wind-induced error depending on wind speed, rain drop size distribution & gauge design||Comparison between exposed & pit gauges||2–10 % (hourly data; even after popular correction algorithms)||ARS Goodwin Creek experimental watershed, Mississippi, USA. 21.4 km2, rainfall 1400 mm yr-1, 71-128 m a.s.l.||Sieck et al. (2007)<br />
|- valign="top"<br />
| Tipping error per 1 mm rain||Field calibration with known water delivery rate||Up to 10 % dependent on gauge type & rain rate||||<br />
|-<br />
| '''''Random Errors'''''<br />
|- valign="top"<br />
| Coefficient of variation of random errors||12 co-located standard rain gauges||Approx. 5 % for single storm, independent of total storm rainfall||Mount Cargill, Dunedin, New Zealand. Exposed site at 560 m a.s.l.||Hutchinson (1969)<br />
|- valign="top"<br />
| Coefficient of variation of non-recording gauges||9 co-located recording & non-recording gauges||4-5 % for storms >15 mm (monsoon season thunderstorms)||USDA Walnut Gulch Experimental Watershed, Arizona, USA. 4.4 ha, semi-arid, 1250-1585 m a.s.l. ||Goodrich et al. (1995)<br />
|- valign="top"<br />
| Total error of recording gauge||Standard error between single gauges & average of 15 co-located tipping buckets||Decreases with rain rate & accumulation time, e.g. 4.9 % (5 min) & 2.9 % (15 min) at rain rate of 10 mm h-1||USDA field station in Chickasha, Oklahoma, USA||Ciach (2003)<br />
|}<br />
<br />
== References ==<br />
<br />
Ciach, G.J., 2003. Local random errors in tipping-bucket rain gauge measurements. Journal of Atmospheric and Oceanic Technology, 20(5): 752-759.<br />
<br />
Essery, C.I., Wilcock, D.N., 1991. The variation in rainfall catch from standard UK Meteorological-Office rain-gages - A 12 year case-study. Hydrological Sciences Journal-Journal Des Sciences Hydrologiques, 36(1): 23-34.<br />
<br />
Goodrich, D.C., Faures, J.M., Woolhiser, D.A., Lane, L.J., Sorooshian, S., 1995. Measurement and analysis of small-scale convective storm rainfall variability. Journal of Hydrology, 173(1-4): 283-308.<br />
<br />
Hutchinson, P., 1969. A note on random rain-gauge errors. Journal of Hydrology (NZ), 8(1): 8-10.<br />
<br />
Larson, L.W., Peck, E.L., 1974. Accuracy of precipitation measurements for hydrologic models. Water Resources Research, 10(4): 857-863.<br />
<br />
McMillan, H., Krueger, T., Freer, J., 2012. Benchmarking observational uncertainties for hydrology: Rainfall, river discharge and water quality. Hydrological Processes 26(26): 4078–4111<br />
<br />
Mueller, C.C., Kidder, E.H., 1972. Rain gage catch variation due to air-flow disturbances around a standard rain gage. Water Resources Research, 8(4): 1077-1082.<br />
<br />
Neff, E.L., 1977. How much rain does a rain gauge gauge? Journal of Hydrology, 35: 213-220.<br />
<br />
Sevruk, B., 1982. Methods of correction for systematic error in point precipitation measurement. World Meteorological Organisation, Operational Hydrology Report No. 21, WMO-No.589. Geneva, Switzerland.<br />
<br />
Sieck, L.C., Burges, S.J., Steiner, M., 2007. Challenges in obtaining reliable measurements of point rainfall. Water Resources Research, 43(1): W01420.<br />
<br />
[[Category:Uncertainty]]</div>Mcmillanhkhttps://experimental-hydrology.net/wiki/index.php?title=Rainfall_interpolation_uncertainty&diff=2535Rainfall interpolation uncertainty2012-12-18T02:36:13Z<p>Mcmillanhk: /* References */</p>
<hr />
<div><br />
== Typical quantitative results of rainfall uncertainty studies: Interpolation. ==<br />
<br />
This table originated from McMillan et al. (2012) but is now open to the community to add to and use as a resource.<br />
<br />
SD = standard deviation<br />
<br />
{| {{table}}<br />
| align="center" style="background:#f0f0f0;"|'''Uncertainty Type'''<br />
| align="center" style="background:#f0f0f0;"|'''Estimation Method'''<br />
| align="center" style="background:#f0f0f0;"|'''Magnitude'''<br />
| align="center" style="background:#f0f0f0;"|'''Location'''<br />
| align="center" style="background:#f0f0f0;"|'''Reference'''<br />
|- valign="top"<br />
| Rainfall variability in convective events||48 non-recording gauges on 30 m grid over 4.4 ha catchment||4-14 % variation of mean storm rainfall over 100 m distance; -5.6 % greatest difference between areal mean & 4 co-located central gauges||USDA Walnut Gulch Experimental Watershed, Arizona, USA. 4.4 ha, semi-arid, 1250-1585 m a.s.l.||Goodrich et al. (1995)<br />
|- valign="top"<br />
| Standard error in single gauge measurement vs. gauge network||8 rain gauges within a 2 km2 area||33 % (low relief), 45 % (high relief) at 4 mm/15 min rain rate; 90% confidence bounds on the standard error, dependent on rain rate, are also given graphically||Brue catchment, UK (135 km2). 20-250 m a.s.l., temperate climate, orographic rainfall.||Wood et al. (2000)<br />
|- valign="top"<br />
| ||49 rain gauges in 135 km2 area||65 % at 4 mm/15 min rain rate; presented graphically for rain rates 0.2-8 mm/15 min and for three different gauges||||<br />
|- valign="top"<br />
| SD of rainfall rates within 5 km2 area for accumulation periods between 5 min and 1 hour||5 clusters, each of 12-40 rain gauges||12.2, 12.0, 16.1, 7.7 & 9.8 mm h-1 for 5 min totals over 57-515 days, conditioned on rain rates greater than 0.5 mm h-1||Gauge clusters in Guam, Brazil, Florida, Oklahoma, Iowa||Krajewski et al. (2003); also looked at correlation statistics up to 8 km distance with significant reductions<br />
|- valign="top"<br />
| Multiplier from 3-gauge average to areal mean rainfall||Conditional simulation using 13 raingauges to generate ensemble of spatial rainfall fields||Rainfall multipliers have mean 1.15 ± 0.03, standard deviation 0.27 ± 0.02 when accounting separately for rainfall, runoff and structural uncertainty.||Yzeron catchment (129 km2), Rhone-Alpes region, France. 400-917 m a.s.l.. Rainfall 845 mm yr-1, runoff 150 mm yr-1. ||Renard et al. (2011)<br />
|}<br />
<br />
== References ==<br />
<br />
Goodrich, D.C., Faures, J.M., Woolhiser, D.A., Lane, L.J., Sorooshian, S., 1995. Measurement and analysis of small-scale convective storm rainfall variability. Journal of Hydrology, 173(1-4): 283-308.<br />
<br />
Krajewski, W.F., Ciach, G.J., Habib, E., 2003. An analysis of small-scale rainfall variability in different climatic regimes. Hydrological Sciences Journal-Journal Des Sciences Hydrologiques, 48(2): 151-162.<br />
<br />
McMillan, H., Krueger, T., Freer, J., 2012. Benchmarking observational uncertainties for hydrology: Rainfall, river discharge and water quality. Hydrological Processes 26(26): 4078–4111<br />
<br />
Renard, B., Kavetski, D., Leblois, E., Thyer, M., Kuczera, G., 2011. Towards a reliable decomposition of predictive uncertainty in hydrological modelling : characterizing rainfall errors using conditional simulation, Water Resources Research, 47: W11516. doi:10.1029/2011WR010643<br />
<br />
Wood, S.J., Jones, D.A., Moore, R.J., 2000. Accuracy of rainfall measurement for scales of hydrological interest. Hydrology and Earth System Sciences, 4(4): 531-543.<br />
<br />
[[Category:Uncertainty]]</div>Mcmillanhkhttps://experimental-hydrology.net/wiki/index.php?title=Discharge_uncertainty_(ADCP,_ADV,_LSPIV)&diff=2534Discharge uncertainty (ADCP, ADV, LSPIV)2012-12-18T02:35:46Z<p>Mcmillanhk: /* References */</p>
<hr />
<div><br />
== Typical quantitative results of discharge uncertainty studies: New Measurement Techniques. ==<br />
<br />
This table originated from McMillan et al. (2012) but is now open to the community to add to and use as a resource.<br />
<br />
ADV = acoustic Doppler velocimetry; ADCP = acoustic Doppler current profiling; LSPIV = Large Scale Particle Image Velocimetry; SD = standard deviation<br />
<br />
{| {{table}}<br />
| align="center" style="background:#f0f0f0;"|'''Uncertainty Type'''<br />
| align="center" style="background:#f0f0f0;"|'''Estimation Method'''<br />
| align="center" style="background:#f0f0f0;"|'''Magnitude'''<br />
| align="center" style="background:#f0f0f0;"|'''Location'''<br />
| align="center" style="background:#f0f0f0;"|'''Reference'''<br />
|- valign="top"<br />
| ADCP discharge measurement uncertainty||Relative error of discharge calculated using ADCP vs. current meter and/or rating curve||Mean relative error from multiple transects was -3 to 5 % (from meter) or -7 to 5 % (from rating) dependent on site||USA (5 sites on Illinois, Kankakee, Mississippi and Missouri rivers). Depths 1.1-3.8 m, widths 33-527 m, velocities 0.4-1.3 m s-1.||Mueller (2003)<br />
|- valign="top"<br />
| ||Relative error of discharge calculated using ADCP vs. multiple concurrent current meters||SD of relative error 5.8 %; distributions given from large set of test cases, plus results for alternative measurement set-ups||Multi-location field sites (including USA, Canada, Sweden, Netherlands) plus laboratory testing||Oberg & Mueller (2007)<br />
|- valign="top"<br />
| ADV velocity measurement uncertainty, with & without calibration||Relative error of discharge calculated using ADV velocity (20 min average) vs. impellor velocity (60 s period per sample)||Flow estimates were within 20 % of the current-metered flow for 93 % of samples after calibration (68 % before calibration)||Pontbren, Wales, UK, 5 concrete-lined sections. 3 circular: diameter 0.6-1.6 m, depth 0-0.71 m, velocity 0-3.0 m s-1. 2 rectangular: width 3.17, 4.17 m; depth 0-0.67 m, velocity 0-3.9 m s-1.||McIntyre & Marshall (2008)<br />
|- valign="top"<br />
| Mobile LSPIV instantaneous velocity & discharge measurement uncertainty||Relative error from theoretical velocity field based on 27 error sources; case study comparison with rating curve & ADCP methods||Theoretical errors in velocity from 10-35 % at 95 % confidence level; case study gave discharge error at 2 % compared to rating curve & 5.5 % compared to ADCP||Analysis of typical conditions. Case study at Clear Creek near Coralville, Iowa, USA. 20 m wide, 0.7 m deep, stage 1.2 and velocity 5.2 m s-1 during study.||Kim et al. (2008)<br />
|- valign="top"<br />
| Simulated LSPIV measurements against theoretical true values||Error variance obtained via linear regression of simulated vs. true values||5 % under normal conditions, increasing to 17 % with a high tilt angle (70º)||Numerical simulation||Hauet et al. (2008)<br />
|- valign="top"<br />
| LSPIV instantaneous discharge measurements during high flows compared with rating curve & current meter reference values||Relative error at a number of observation times||47 % at low flows, 13-23 % on rising limb, 2 % during stable high flow period||River Arc, France, during dam release operation. Discharge range 10-150 m3 s-1, width 60-70 m, gravel-bed river.||Jodeau et al. (2008)<br />
|- valign="top"<br />
| Microwave & UHF Doppler Radars uncertainty in instantaneous discharge measurement||Correlation coefficients between radar measurements & conventional rating curve methods over 16-week period||0.883, 0.969, 0.992 dependent on Doppler radar system||Cowlitz River, Washington, USA(5800 km2). Width 92 m, depth 2-7 m.||Costa et al. (2006)<br />
|}<br />
<br />
== References ==<br />
<br />
Costa, J.E., Cheng, R.T., Haeni, F.P., Melcher, N., Spicer, K.R., Hayes, E., Plant, W., Hayes, K., Teague, C., Barrick, D., 2006. Use of radars to monitor stream discharge by noncontact methods. Water Resources Research, 42(7): W07422.<br />
<br />
Hauet, A., Creutin, J.D., Belleudy, P., 2008. Sensitivity study of large-scale particle image velocimetry measurement of river discharge using numerical simulation. Journal of Hydrology, 349(1-2): 178-190.<br />
<br />
Jodeau, M., Hauet, A., Paquier, A., Le Coz, J., Dramais, G., 2008. Application and evaluation of LS-PIV technique for the monitoring of river surface velocities in high flow conditions. Flow Measurement and Instrumentation, 19(2): 117-127.<br />
<br />
Kim, Y., Muste, M., Hauet, A., Krajewski, W.F., Kruger, A., Bradley, A., 2008. Stream discharge using mobile large-scale particle image velocimetry: A proof of concept. Water Resources Research, 44(9): W09502.<br />
<br />
McIntyre, N., Marshall, M., 2008. Field verification of bed-mounted ADV meters. Proceedings of the Institution of Civil Engineers-Water Management, 161(4): 199-206.<br />
<br />
McMillan, H., Krueger, T., Freer, J., 2012. Benchmarking observational uncertainties for hydrology: Rainfall, river discharge and water quality. Hydrological Processes 26(26): 4078–4111 <br />
<br />
Mueller, D.S., 2003. Field evaluation of boat-mounted acoustic Doppler instruments used to measure streamflow. Proceedings of the IEEE/OES Seventh Working Conference on Current Measurement Technology. IEEE, New York, 30-34 pp.<br />
<br />
Oberg, K., Mueller, D.S., 2007. Validation of streamflow measurements made with acoustic Doppler current profilers. Journal of Hydraulic Engineering-ASCE, 133(12): 1421-1432.<br />
<br />
[[Category:Uncertainty]]</div>Mcmillanhkhttps://experimental-hydrology.net/wiki/index.php?title=Discharge_uncertainty&diff=2533Discharge uncertainty2012-12-18T02:35:12Z<p>Mcmillanhk: /* References */</p>
<hr />
<div><br />
== Typical quantitative results of discharge uncertainty studies: Discharge Uncertainty. ==<br />
<br />
This table originated from McMillan et al. (2012) but is now open to the community to add to and use as a resource.<br />
<br />
PDF = probability density function; RMSE = root mean square error; SD = standard deviation<br />
<br />
{| {{table}}<br />
| align="center" style="background:#f0f0f0;"|'''Uncertainty Type'''<br />
| align="center" style="background:#f0f0f0;"|'''Estimation Method'''<br />
| align="center" style="background:#f0f0f0;"|'''Magnitude'''<br />
| align="center" style="background:#f0f0f0;"|'''Location'''<br />
| align="center" style="background:#f0f0f0;"|'''Reference'''<br />
|-<br />
| '''''Instantaneous Discharge Uncertainty'''''<br />
|- valign="top"<br />
| Single discharge measurement uncertainty when using method of verticals with current meter||SD of relative discharge error calculated from individual uncertainty components||2.3 % using 30 verticals with measurements at 0.2 & 0.8 depth points; other combinations also given||Columbia River, USA (5 sites)||Carter & Anderson (1963)<br />
|- valign="top"<br />
| Single discharge measurement uncertainty using velocity-area method||95 % confidence bounds on relative uncertainty, from literature review||4-17 % for 35-5 verticals at 0.25 m s-1; 5-40 % for velocities 0.5-0.05 m s-1. ||Various||Pelletier (1988)<br />
|- valign="top"<br />
| Single discharge measurement uncertainty under ice||Difference between USGS & Water Survey of Canada instantaneous flow measurements attributed to different setup of current meter on rod or in suspension||2-17 %||Red river at Emerson, Manitoba, Canada (104000 km2). Slope 0.04-0.25 m km-1, mean discharge 94.2 m3 s-1, when under ice 20 m3 s-1, drains glacial plain with moraines.||Pelletier (1989)<br />
|- valign="top"<br />
| Combination of stage error & components of discharge error for wading or cable methods||Standard error computed by root-mean-square of component uncertainties: those derived from previous studies, manufacturer citations and expert knowledge.||2.4 % (Good Cable); 4.0 % (Good Wading); 19 % (Poorest measurements)||||Sauer & Meyer (1992)<br />
|- valign="top"<br />
| Single discharge measurement uncertainty: effect of reducing number of verticals||Halving number of verticals||Approx. 5 % (given as graph relating to % reduction in verticals)||23 sites in UK North-East||Whalley (2001)<br />
|- valign="top"<br />
| Epistemic single discharge measurement uncertainty using current meter for velocity-area method||Combined uncertainty values from expert opinion & previous studies||6 %||Typical example||Herschy (2002)<br />
|- valign="top"<br />
| Single discharge measurement uncertainty: Salt dilution gauging ||SD of instantaneous discharge measured using salt dilution, deviation from rating curve developed using both salt dilution and current metering.||5 %||Stephanie Creek, Vancouver Island, BC, Canada (8.6 km2). Steep rocky creek.||Hudson & Fraser (2002)<br />
|- valign="top"<br />
| ||||7.1%||Flume Creek, Sunshine Coast, BC, Canada (118 ha). Steep creek.||<br />
|- valign="top"<br />
| ||||±42-84 %||South Fork catchment (780 km2), Iowa, USA||<br />
|- valign="top"<br />
| Single discharge measurement uncertainty||Typical bias determined from replicates||<-4 %||||Hamilton & Moore (2012)<br />
|-<br />
| '''''Rating Curve and Combined Uncertainty'''''<br />
|- valign="top"<br />
| Random errors associated with power law rating curves||RMSE of component uncertainties||1.9 % in instantaneous or average daily discharge, 0.5 % in average monthly discharge||Mangawhero at Ore Ore, New Zealand. Mean discharge 13m3 s-1||Dymond & Christian (1982)<br />
|- valign="top"<br />
| Deviation between theoretical & measured rating curve (with current meter)||||20 % at low flows (0.2 m above station datum), 10 % at higher flows||Sprint, UK. Flat-vee crump profile weir structure.||Whalley (2001)<br />
|- valign="top"<br />
| Deviation between theoretical rating curve accounting for non-steady flow & measured discharge (also given for empirical rating curve)||Coefficient of variation calculated from 55 discharge measurements||10 % (in-bank flows); 36% (including out-of-bank flows) ||Illinois River, USA. Low gradient river, discharge 38-3480 m3 s-1, two gauge (slop-stage-discharge) rating station.||Schmidt & Yen (2008)<br />
|- valign="top"<br />
| Total instantaneous discharge uncertainty caused by interpolation / extrapolation of rating curve, unsteady flow conditions & seasonal changes in roughness||95 % uncertainty bounds for relative error calculated through combination of three error components||6.2 % at 1000 m3 s-1 to 42.8 % at 12000 m3 s-1, average 25.6 %||Po River, Italy (70000 km2). Channel width 200-500 m, depth 10-15 m, slope 0.02, floodplain width 1000-3000 m.||Di Baldassarre & Montanari (2009)<br />
|- valign="top"<br />
| Total instantaneous discharge uncertainty caused by rating curve uncertainty||Relative error compared to manual measurements||1-20 % (average 8.76 %), negatively related to stage||Hillslope (172 m2), WS10 catchment, HJA Experimental Forest, Oregon, USA. Stilling well with 30° V-Notch Weir.||Graham et al. (2010); values calculated from original figures<br />
|- valign="top"<br />
| ||||Average 3.6 %, not related to stage||WS10 catchment (10.2 ha), HJA Experimental Forest, Oregon, USA. 90° V-Notch Weir||<br />
|- valign="top"<br />
| Total instantaneous discharge uncertainty caused by gauging errors & rating curve form / extrapolation||Estimate of upper & lower discharge bounds for any given stage through combination of component errors||Relative error from 100 % (low flows) to 10 % (low-mid flows) to 20 % (high flows)||Rowden Experimental Research Platform (1 ha fields), Devon, UK. 250 x 37 cm weir box, stainless steel 45° V-Notch, bucket method & electromagnetic flowmeter (Magflo Mag 5100, Siemens), ave. annual precipitation 1055 mm.||Krueger et al. (2010)<br />
|- valign="top"<br />
| Total instantaneous discharge uncertainty caused by gauging error, rating curve form / extrapolation & instability of rating curve||Estimate of complete instantaneous discharge PDF for any given stage||Relative error from 46 % (low flows) to 10 % (mid-high flows) to 15 % (flood flows), average 22 %||Wairau River, New Zealand (3825 km2). Elevation 0-2309 m a.s.l., braided reach, 100 m width.||McMillan et al. (2010)<br />
|- valign="top"<br />
| Total instantaneous discharge uncertainty caused by gauging error & instability of rating curve||Estimates of upper & lower instantaneous discharge bounds for any given stage using uncertain time-varying rating curve||Difference from constant rating curve ranged from -60 to 90 % (low flows) to ±20 % (mid-high flows); mean daily discharge error -43 % to +73 %. Effect of using only 3 stage measurements / day to calculate mean daily discharge: ±17 %||Choluteca River, Honduras (1766 km2). Mountainous, 660 – 2320 m a.s.l., precipitation mainly convective.||Westerberg et al. (2011)<br />
|-<br />
| '''''Time-averaged Discharge Uncertainty'''''<br />
|- valign="top"<br />
| Total uncertainty of daily discharge||PDF, mean, SD ||Normal, 0, 10 %||Odense basin (1190 km2), Denmark. Low rolling hills, elevation 0-100 m a.s.l.||Refsgaard et al. (2006)<br />
|- valign="top"<br />
| Relative uncertainty of daily & annual discharge estimates in rivers subject to icing||Statistical analysis of uncertainty in the parameters of the fitted quadratic rating curves & ice correction coefficients||Where cross sections assumed stable: 8-25 % for low flows, 2-5 % for high flows (variation for different rivers); where cross section not stable (e.g. with ice): 10-21 % with high frequency gaugings, 15-45 % under the worst conditions in the record||6 largest Eurasian Arctic Rivers (248000-2950000 km2). Mean discharge 2200-18400 m3 s-1.||Shiklomanov et al. (2006)<br />
|- valign="top"<br />
| Monthly discharge uncertainty||Probable error range||±42 %||Small watershed near Riesel, Texas, USA||Harmel & Smith (2007) based on Harmel et al. (2006)<br />
|- valign="top"<br />
| Daily discharge uncertainty||||±42 %; ±100-200 % for low flows; ±100 % for high flows||Reynolds Creek catchment (239 km2), Idaho, USA||<br />
|- valign="top"<br />
| Storm discharge uncertainty||Total probable error based on RMSE propagation method||2-19 %||Various in USA (2.2-5506 ha)||Harmel et al. (2009) based on Harmel et al. (2006)<br />
|- valign="top"<br />
| Deep seepage uncertainty in steady state (as residual water balance component)||Relative uncertainty based on propagation of component uncertainties||57 % (under steady state); 32 % (during irrigation); 34 % (during irrigation + 5 days); 35 % (during irrigation + 10 days)||Hillslope (172 m2), WS10 catchment, HJA Experimental Forest, Oregon, USA. Stilling well with 30° V-Notch Weir.||Graham et al. (2010); values calculated from original figures<br />
|- valign="top"<br />
| ||||84 % (under steady state); 62 % (during irrigation); 93 % (during irrigation + 5 days); 155 % (during irrigation + 10 days)||WS10 catchment (10.2 ha), HJA Experimental Forest, Oregon, USA. 90° V-Notch Weir||<br />
|- valign="top"<br />
| Daily discharge; effect of manual stage reading||Manually minus automatically derived discharge||Up to ±10-50 %||Lillooet River near Pemberton, British Columbia, Canada. Nivo-glacial.||Hamilton & Moore (2012)<br />
|- valign="top"<br />
| Monthly discharge; effect of manual stage reading||||Up to 5-10 %<br />
|}<br />
<br />
== References ==<br />
<br />
Carter, R.W., Anderson, I.E., 1963. Accuracy of current meter measurements. Journal of the Hydraulics Division, 89(4): 105-115.<br />
<br />
Di Baldassarre, G., Montanari, A., 2009. Uncertainty in river discharge observations: a quantitative analysis. Hydrology and Earth System Sciences, 13(6): 913-921.<br />
<br />
Dymond, J.R., Christian, R., 1982. Accuracy of discharge determined from a rating curve. Hydrological Sciences Journal-Journal Des Sciences Hydrologiques, 4(12): 493-504.<br />
<br />
Graham, C.B., van Verseveld, W., Barnard, H.R., McDonnell, J.J., 2010. Estimating the deep seepage component of the hillslope and catchment water balance within a measurement uncertainty framework. Hydrological Processes, 24(25): 3878–3893.<br />
<br />
Hamilton, A.S., Moore, R.D., 2012. Quantifying Uncertainty in Streamflow Records. Canadian Water Resources Journal, 37(1): 3-21.<br />
<br />
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.<br />
<br />
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.<br />
<br />
Harmel, R.D., Smith, P.K., 2007. Consideration of measurement uncertainty in the evaluation of goodness-of-fit in hydrologic and water quality modeling. Journal of Hydrology, 337(3-4): 326-336.<br />
<br />
Herschy, R.W., 2002. The uncertainty in a current meter measurement. Flow Measurement and Instrumentation, 13(5-6): 281-284.<br />
<br />
Hudson R, Fraser J., 2002. Alternative methods of flow rating in small coastal streams. Forest Research Extension Note EN-014 (Hydrology). Vancouver Forest Region.<br />
<br />
Krueger, T., Freer, J., Quinton, J.N., Macleod, C.J.A., Bilotta, G.S., Brazier, R.E., Butler, P., Haygarth, P.M., 2010a. Ensemble evaluation of hydrological model hypotheses. Water Resources Research, 46: W07516.<br />
<br />
McMillan, H., Freer, J., Pappenberger, F., Krueger, T., Clark, M., 2010. Impacts of uncertain river flow data on rainfall-runoff model calibration and discharge predictions. Hydrological Processes, 24(10): 1270-1284.<br />
<br />
McMillan, H., Krueger, T., Freer, J., 2012. Benchmarking observational uncertainties for hydrology: Rainfall, river discharge and water quality. Hydrological Processes 26(26): 4078–4111 <br />
<br />
Pelletier, P.M.., 1988. Uncertainties in the determination of river discharge: A literature review. Canadian Journal of Civil Engineering, 15: 834-850.<br />
<br />
Pelletier, P. M., 1989. Uncertainties in streamflow measurement under winter ice conditions a case study: The Red River at Emerson, Manitoba, Canada, Water Resour. Res., 25(8), 1857–1867, doi:10.1029/WR025i008p01857.<br />
<br />
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.<br />
<br />
Sauer, V.B., Meyer, R.W., 1992. Determination of error in individual discharge measurements, U.S. Geological Survey Open-File Report 92–144.<br />
<br />
Shiklomanov, A.I., Yakovleva, T.I., Lammers, R.B., Karasev, I.P., Vörösmarty, C.J., Linder, E., 2006. Cold region river discharge uncertainty - Estimates from large Russian rivers. Journal of Hydrology, 326(1-4): 231-256.<br />
<br />
Schmidt, A.R., Yen, B.C., 2008. Theoretical development of stage-discharge ratings for subcritical open-channel flows. Journal of Hydraulic Engineering-ASCE, 134(9): 1245-1256.<br />
<br />
Westerberg, I., Guerrero, J.L., Seibert, J., Beven, K.J., Halldin, S., 2011. Stage-discharge uncertainty derived with a non-stationary rating curve in the Choluteca River, Honduras. Hydrological Processes, 25(4): 603-613.<br />
<br />
Whalley, N., Iredale, R.S., Clare, A.F., 2001. Reliability and uncertainty in flow measurement techniques - Some current thinking. Physics and Chemistry of the Earth Part C-Solar-Terrestial and Planetary Science, 26(10-12): 743-749.<br />
<br />
[[Category:Uncertainty]]</div>Mcmillanhkhttps://experimental-hydrology.net/wiki/index.php?title=Stage_measurement_uncertainty&diff=2385Stage measurement uncertainty2012-10-28T10:59:19Z<p>Mcmillanhk: /* References */</p>
<hr />
<div><br />
== Typical quantitative results of discharge uncertainty studies: Stage Uncertainty. ==<br />
<br />
This table originated from McMillan et al. (2012) but is now open to the community to add to and use as a resource.<br />
<br />
SD = standard deviation<br />
<br />
{| {{table}}<br />
| align="center" style="background:#f0f0f0;"|'''Uncertainty Type'''<br />
| align="center" style="background:#f0f0f0;"|'''Estimation Method'''<br />
| align="center" style="background:#f0f0f0;"|'''Magnitude'''<br />
| align="center" style="background:#f0f0f0;"|'''Location'''<br />
| align="center" style="background:#f0f0f0;"|'''Reference'''<br />
|- valign="top"<br />
| Stage uncertainty||Comparison with neighbouring stations||SD of 25 mm||Netherlands gauging network||Van der Made (1982)<br />
|- valign="top"<br />
| Effect of unstable bed||Expert knowledge; uncertainty for individual measurement||±10 %||Estimate for locations with shifting sand or moving dunes||Sauer & Meyer (1992)<br />
|- valign="top"<br />
| Instrument precision||Review of previous studies; uncertainty for individual measurement||±3-10.8 mm or ±0.1-2 %||||Quoted in Harmel et al. (2006)<br />
|- valign="top"<br />
| Instrument precision||Expert knowledge||Range ±10 mm; local oscillations of water surface can add additional uncertainty of ±20 mm||Typical example of natural rivers||Dottori et al. (2009)<br />
|- valign="top"<br />
| Instrument precision: Float in stilling well||||6 mm||||Quoted in Herschy (1998): Ackers et al. (1978)<br />
|- valign="top"<br />
| Instrument precision: Pressure transducer ||||1.4-40 mm||||Herschy (1998)<br />
|- valign="top"<br />
| Stage uncertainty||Expert knowledge of typical uncertainties||4 mm (high accuracy) to 15 mm (low accuracy)||Norwegian Water Resources & Energy Directorate||Petersen-Øverleir & Reitan (2005)<br />
|- valign="top"<br />
| Stage uncertainty||Observed fluctuation||2-5 mm||Rowden Experimental Research Platform (1 ha fields), Devon, UK. 250 x 37 cm weir box, stainless steel 45° V-Notch, float (Model 6541, Unidata), stilling well, ave. annual precipitation 1055 mm.||Krueger et al. (2010)<br />
|- valign="top"<br />
| Instrument precision||Manufacturer cited random uncertainty||2.5 mm (Trutrack, Model PLUT-HR Water level recorder)||Hillslope (172 m2), WS10 catchment, HJA Experimental Forest, Oregon, USA||Graham et al. (2010)<br />
|- valign="top"<br />
| ||||0.3 mm (Model 2 Stevens Instruments Position Analog Transmitter)||WS10 catchment (10.2 ha), HJA Experimental Forest, Oregon, USA. Mediterranean climate, rainfall 2200 mm yr-1, slopes 30-45 °.||<br />
|- valign="top"<br />
| Stage uncertainty||Nominal uncertainty||3 mm||||Hamilton & Moore (2012)<br />
|}<br />
<br />
== References ==<br />
<br />
Ackers, P., 1978. Weirs and flumes for flow measurement. Wiley, Chichester.<br />
<br />
Dottori, F., Martina, M.L.V., Todini, E., 2009. A dynamic rating curve approach to indirect discharge measurement. Hydrology and Earth System Sciences, 13(6): 847-863.<br />
<br />
Graham, C.B., van Verseveld, W., Barnard, H.R., McDonnell, J.J., 2010. Estimating the deep seepage component of the hillslope and catchment water balance within a measurement uncertainty framework. Hydrological Processes, 24(25): 3878–3893.<br />
<br />
Hamilton, A.S., Moore, R.D., 2012. Quantifying Uncertainty in Streamflow Records. Canadian Water Resources Journal, 37(1): 3-21.<br />
<br />
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.<br />
<br />
Herschy, R.W., 1998. Hydrometry : Principles and practices. Wiley, Chichester.<br />
<br />
Krueger, T., Freer, J., Quinton, J.N., Macleod, C.J.A., Bilotta, G.S., Brazier, R.E., Butler, P., Haygarth, P.M., 2010. Ensemble evaluation of hydrological model hypotheses. Water Resources Research, 46: W07516.<br />
<br />
McMillan, H., Krueger, T., Freer, J., 2012. Benchmarking observational uncertainties for hydrology: Rainfall, river discharge and water quality. Hydrological Processes.<br />
<br />
Petersen-Øverleir, A., Reitan, T., 2005. Uncertainty in flood discharges from urban and small rural catchments due to inaccurate head measurement. Nordic Hydrology, 36(3): 245-257.<br />
<br />
Sauer, V.B., Meyer, R.W., 1992. Determination of error in individual discharge measurements, U.S. Geological Survey Open-File Report 92–144.<br />
<br />
van der Made, J.E., 1982. Determination of the accuracy of water level observations, Proceedings of the Exeter Symposium. IAHS Publications 134, pp. 172-184.<br />
<br />
[[Category:Uncertainty]]</div>Mcmillanhkhttps://experimental-hydrology.net/wiki/index.php?title=Rainfall_radar_and_satellite_uncertainty&diff=2384Rainfall radar and satellite uncertainty2012-10-28T10:58:38Z<p>Mcmillanhk: /* References */</p>
<hr />
<div><br />
== Typical quantitative results of rainfall uncertainty studies: Radar and Satellite. ==<br />
<br />
This table originated from McMillan et al. (2012) but is now open to the community to add to and use as a resource.<br />
<br />
RMSE = root mean square error; SD = standard deviation<br />
<br />
{| {{table}}<br />
| align="center" style="background:#f0f0f0;"|'''Uncertainty Type'''<br />
| align="center" style="background:#f0f0f0;"|'''Estimation Method'''<br />
| align="center" style="background:#f0f0f0;"|'''Magnitude'''<br />
| align="center" style="background:#f0f0f0;"|'''Location'''<br />
| align="center" style="background:#f0f0f0;"|'''Reference'''<br />
|-<br />
| '''''Radar'''''<br />
|- valign="top"<br />
| Error between radar estimate and gauge network||Radar RMSE with respect to 30 raingauges||10 % for storms >30 mm after radar bias correction using high quality rain gauge data; when all gauges were used for bias correction without prior quality control RMSE was 10-40 %||ARS Goodwin Creek experimental watershed, Mississippi, USA||Steiner et al. (1999)<br />
|- valign="top"<br />
| Error between radar estimate and gauge network||Standard error of residuals compared with 8 rain gauges in 2 km2 area||50% (low relief) at 4 mm/15 min rain rate; presented graphically for rain rates 0.4-10 mm/15 min||Brue catchment, UK (135 km2). 20-250 m a.s.l., temperate climate, orographic rainfall.||Wood et al. (2000)<br />
|- valign="top"<br />
| ||Standard error of residuals compared with 49 rain gauges in 135 km2 area||55 % at 2km resolution, 60 % at 5 km resolution, for rain rate 4 mm/15 min; presented graphically for rain rates 0.2-8 mm/15 min||||<br />
|- valign="top"<br />
| Error between radar (WSR-88D) estimate and gauge network||SD of the stochastic component of multiplicative error||Conditioned on distance from radar, timescale of observation & season; asymptotic SD at high rainfall rates in the range 0.1-0.7, typically 0.5 for hourly data||Oklahoma, USA. Rainfall 800 mm yr-1, dominated by midlatitude convective systems.||Ciach et al. (2007)<br />
|- valign="top"<br />
| Error between radar (S-band) estimate and gauge network||SD of residuals||Approx. 0.3 (proportion of mean rain rate) for hourly data over 0-100 km distance from radar; values also given for 1, 2, 6, 12 hours & 0-50, 50-100, 0-100 km distances||Cévennes-Vivarais region, France. 200 km *160 km convective and frontal rainfall.||Kirstetter et al. (2010)<br />
|- valign="top"<br />
| Error between radar (WSR-88D) estimate and gauge network||SD of residuals (2 research gauge networks)||0.48 (hourly, 8 km resolution), 1.07 (hourly, 1 km resolution), proportion of mean rain rate; values also given for 15 min, 1 hour at scales 0.5, 1, 2, 4, 8 km||Iowa, USA||Seo & Krajewski (2010); raingauge networks used paired gauges at all sites<br />
|- valign="top"<br />
| Error between radar (X-band) estimate and gauge network||Mean and SD of bias for pixel-based comparison between 2 radars and 20 gauges.||Using a Z-R relationship to estimate rainfall, the mean bias for the 2 radars was -0.24, -0.27; with SD of the relative error 0.46, 0.48.||Southwest Oklahoma, USA. Raingauges – radar distance up to 35 km. Study used 4 storm events of heavy/ broken squall lines with embedded convective cells. ||Vieux and Imgarten (2011)<br />
|-<br />
| '''''Satellite'''''<br />
|- valign="top"<br />
| Bias in estimates of surface rain rate from TRMM (Tropical Rainfall Measuring Mission)||Bayesian modelling approach to estimate SD of each parameter in algorithm used to calculate surface rain rate||SD of combined multiplicative bias in rain rate presented graphically as a function of rain rate: 40-60% at rates up to 18 mm h-1, 150 % at 25 mm h-1,||All oceanic pixels for 10 TRMM orbits||L’Ecuyer and Stephens (2002)<br />
|- valign="top"<br />
| Bias of two NASA satellite products (infrared & passive microwave)||Mean & variance in multiplicative bias at hourly timesteps & 0.25º resolution compared with ground radar||Mean multiplicative hourly bias 0.35-1.09 (with SD of 0.73-0.84) over 4-month study period.||Oklahoma, USA. Southern Plains, 95-100°W, 34-37°N.||Hossain & Anagnostou (2006)<br />
|}<br />
<br />
== References ==<br />
<br />
Ciach, G.J., Krajewski, W.F., Villarini, G., 2007. Product-error-driven uncertainty model for probabilistic quantitative precipitation estimation with NEXRAD data. Journal of Hydrometeorology, 8(6): 1325-1347.<br />
<br />
Hossain, F., Anagnostou, E.N., 2006. Assessment of a multidimensional satellite rainfall error model for ensemble generation of satellite rainfall data. IEEE Geoscience and Remote Sensing Letters, 3(3): 419-423.<br />
<br />
Kirstetter, P.E., Delrieu, G., Boudevillain, B., Obled, C., 2010. Toward an error model for radar quantitative precipitation estimation in the Cevennes-Vivarais region, France. Journal of Hydrology, 394(1-2): 28-41.<br />
<br />
L’Ecuyer, T. S., and G. L. Stephens, 2002. An uncertainty model for Bayesian Monte Carlo retrieval algorithms: Application to the TRMM observing system. Quart. J. Roy. Meteor. Soc.,128, 1713–1737.<br />
<br />
McMillan, H., Krueger, T., Freer, J., 2012. Benchmarking observational uncertainties for hydrology: Rainfall, river discharge and water quality. Hydrological Processes.<br />
<br />
Seo, B.C., Krajewski, W.F., 2010. Scale dependence of radar rainfall uncertainty: Initial evaluation of NEXRAD's new super-resolution data for hydrologic applications. Journal of Hydrometeorology, 11(5): 1191-1198.<br />
<br />
Steiner, M., Smith, J.A., Burges, S.J., Alonso, C.V., Darden, R.W., 1999. Effect of bias adjustment and rain gauge data quality control on radar rainfall estimation. Water Resources Research, 35(8): 2487-2503.<br />
<br />
Vieux, B.E., Imgarten, J.M., 2011. On the scale-dependent propagation of hydrologic uncertainty using high-resolution X-band radar rainfall estimates. Atmospheric Research. 103: 96-105.<br />
<br />
Wood, S.J., Jones, D.A., Moore, R.J., 2000. Accuracy of rainfall measurement for scales of hydrological interest. Hydrology and Earth System Sciences, 4(4): 531-543.<br />
<br />
[[Category:Uncertainty]]</div>Mcmillanhk