Rainfall radar and satellite uncertainty

Typical quantitative results of rainfall uncertainty studies: Radar and Satellite.

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

RMSE = root mean square error; SD = standard deviation

Uncertainty Type	Estimation Method	Magnitude	Location	Reference
Radar
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)
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)
	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
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)
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)
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
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)
Satellite
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)
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)

References

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.

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.

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.

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.

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

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.

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.

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.

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.