A Study of the Error Covariance Matrix of Radar Rainfall Estimates in Stratiform Rain (original) (raw)
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Effect of radar-rainfall uncertainties on the spatial characterization of rainfall events
Journal of Geophysical Research, 2010
1] Remotely sensed precipitation products, due to their large areal coverage and high resolution, have been widely used to provide information on the spatiotemporal structure of rainfall. However, it is well known that these precipitation products also suffer from large uncertainties that originate from various sources. In this study, we selected radar-rainfall (RR) data corresponding to 10 warm season events over a 256 × 256 km 2 domain with a data resolution of 4 × 4 km 2 in space and 1 h in time. We characterized their spatial structure using correlation function, power spectrum, and moment scaling function. We then employed a recently developed RR error model and rainfall generator to obtain an ensemble of probable rainfall fields that are consistent with the RR estimation error structure. We parameterized the spatial correlation functions with a two-parameter power exponential function, the Fourier spectra with a power law function, and the moment scaling functions with the universal multifractal model. The parameters estimated from the ensemble were compared with those obtained from the RR products to quantify the impact of radar-rainfall estimation errors on the spatial characterization of rainfall events. From the spatial correlation and power spectrum analyses, we observed that RR estimation uncertainties introduce spurious correlations with greater impact for the smaller scales. The RR errors also significantly bias the estimation of the moment scaling functions.
The accuracy of rainfall estimates by radar as a function of range
Quarterly Journal of the Royal Meteorological Society, 1992
High-spatial-resolution data were collected for nearby convective storms by using a volume scanning weather radar with 200 m resolution, and for stratiform events by using a high-resolution (20 m) vertically pointing radar. Errors in the estimation of rainfall by the scanning radar, due to the radar beam intersecting or overshooting features such as the bright band, were simulated by using these high-resolution images. It was found that these effects define a maximum useful range for the radar that is a strong function of the prevailing meteorological conditions (e.g. bright-band height, intense cell diameter and height). Sudden changes in bright-band height over short times and the large scatter observed in its thickness limit the accuracy with which corrections for the vertical profile of reflectivity may be precalculated in stratiform rain events. A scheme for using a vertically pointing radar to produce these corrections in real time is proposed. The convective events show enough significant storm-to-storm variability that caution is required in extending the useful range of the radar too far.
Statistical Analysis of Radar Rainfall Error Propagation
Journal of Hydrometeorology, 2004
The prediction uncertainty of a hydrologic model is closely related to model formulation and the uncertainties in model parameters and inputs. Currently, the foremost challenges concern not only whether hydrologic model outputs match observations, but also whether or not model predictions are meaningful and useful in the contexts of land use and climate change. The latter is difficult to determine given that model inputs, such as rainfall, have errors and uncertainties that cannot be entirely eliminated. In this paper the physically based simulation methodology developed by Sharif et al. is used to expand this investigation of the propagation of radar rainfall estimation errors in hydrologic simulations. The methodology includes a physics-based mesoscale atmospheric model, a three-dimensional radar simulator, and a two-dimensional infiltration-excess hydrologic model. A time series of simulated three-dimensional precipitation fields over a large domain and a small study watershed are used, which allows development of a large set of rainfall events with different rainfall volumes and vertical reflectivity profiles. Simulation results reveal dominant range-dependent error sources, and frequent amplification of radar rainfall estimation errors in terms of predicted hydrograph characteristics. It is found that in the case of Hortonian runoff predictions, the variance of hydrograph prediction error due to radar rainfall errors decreases for all radar ranges as the event magnitude increases. However, errors in Hortonian runoff predictions increase significantly with range, particularly beyond about 80 km, where the reflectivity signal is increasingly dominated by three-dimensional rainfall heterogeneity with increasing range under otherwise ideal observing conditions.
Sampling errors in radar estimates of rainfall
Journal of Geophysical Research, 2000
The relatively slow rate of application of radar rainfall to operational hydrology is partially due to concerns about the measurement errors. The errors that result in a bias in the field mean have been studied extensively and can to some extent be treated, but errors that manifest themselves as more or less white noise become important when considering what scale is appropriate for spatially distributed hydrological modeling. This paper evaluates the errors that arise in radar estimates of rainfall as a result of temporal sampling, spatial averaging, measuring the field at some distance above the ground, and recording the reflectivity data with a limited radiometric resolution. By far the most significant source of error was found to be due to measuring the field at some height above the ground. The mean standard difference in rainfall rate between fields separated by 1 km in height at 1 km spatial resolution was found to be of the order of 100% of the mean rainfall rate. When the spatial resolution is reduced to 5 km the mean standard difference between the fields with the same 1 km vertical separation fell to about 50% of the mean rainfall rate. Temporal sampling was found to be quite sensitive to the intermittency of the rain field being sampled. The mean standard error caused by 2-min sampling for 10-min accumulations decreased from 14% for scattered rainfall to 8% for widespread rainfall. This deep and well-founded-suspicion of radar data is based on the major differences between the errors inherent in radar and rain gage estimates of mean areal rainfall. The errors in rain gage estimates are related to the number of gages in the area of interest, the spatial distribution of the field being sampled as well as the small-scale topographical features surrounding each gage and the exposure to wind effects [Bradley et al.
Sampling errors in rainfall measurements by weather radar
Advances in Geosciences, 2005
Radar rainfall data are affected by several types of error. Beside the error in the measurement of the rainfall reflectivity and its transformation into rainfall intensity, random errors can be generated by the temporal spacing of the radar scans. The aim of this work is to analize the sensitivity of the estimated rainfall maps to the radar sampling interval, i.e. the time interval between two consecutive radar scans. This analysis has been performed employing data collected with a polarimetric C-band radar in Rome, Italy. The radar data consist of reflectivity maps with a sampling interval of 1 min and a spatial resolution of 300 m, covering an area of 1296 km 2 . The transformation of the reflectivity maps in rainfall fields has been validated against rainfall data collected by a network of 14 raingauges distributed across the study area. Accumulated rainfall maps have been calculated for different spatial resolutions (from 300 m to 2400 m) and different sampling intervals (from 1 min to 16 min). The observed differences between the estimated rainfall maps are significant, showing that the sampling interval can be an important source of error in radar rainfall measurements.
Radar-rainfall error models and ensemble generators
2010
The availability of radar-based rainfall products at high space-time resolutions and over continental scales has greatly advanced our understanding of the rainfall process and its interactions with other hydrological processes across a wide range of scales. However, it is well known that radars provide areal estimates of the rainfall, which are affected by systematic and random errors from various sources. Some of these errors are inherent to the observation system and unavoidable. Therefore, it is important to quantify the uncertainty associated with the radar-based rainfall products and to provide a strong basis for probabilistic quantitative precipitation estimation. Literature in the last four decades abounds with several studies comparing the radar estimates with estimates from other instruments, identifying the radar-rainfall error sources, minimizing the errors, and modeling the uncertainties. This chapter reviews key literature related to the characterization of errors for different space-time scales, rainfall regimes, and geographical settings. The emphasis is on the error models that can be utilized to represent the uncertainty in the form of ensembles. The chapter also lists a few open questions and challenges concerning the statistical structure of radarrainfall errors and the generation of the ensembles.
Atmospheric Research, 2012
Radar precipitation estimates can improve hydrologic prediction over a range of spatial scales represented by both rural and urban basins. Flooding results from the combination of heavy precipitation and the distributed hydraulic and hydrologic characteristics of the basin. Accuracy and spatial scaling of radar estimated rainfall, and its impact at relevant hydrologic scales is an important determinant of hydrologic prediction accuracy and flood forecasting. Results of simulations using archival radar events are used to demonstrate the sources of uncertainty affecting site-specific flood forecasts within the distributed hydrologic model, Vflo. Radar data used in this analysis are derived from both S-band (NEXRAD/88D) and the Collaborative Adaptive Sensing of the Atmosphere (CASA), polarimetric X-band radars. X-band radars have the capability to provide higher spatial and temporal resolution than the conventional radars operating at S-band. However, compared to S-band, X-band radars have shorter wavelengths and suffer from attenuation, or even total extinction of the radar signal at short ranges from the radar. Degradation of precipitation mapping is a serious concern, especially in heavy precipitation over distances associated with watersheds prone to flooding. Compared to rain gauge accumulations, X-band radar polarimetric rainfall estimates were significantly degraded beyond about 15 km from the radars. With rainfall input derived from Xband radars, uncertainty in runoff volume scales with watershed area as a smooth monotonically decreasing function as area increases due to averaging of random errors in the input. Relative to estimates derived from S-band radar, unreliable hydrograph response was produced using X-band polarimetric rainfall estimates as input to a physics-based distributed hydrologic model, especially for watershed areas less than about 20 km 2 .