A comparison of gauge and radar precipitation data for simulating an extreme hydrological event in the Severn Uplands,UK

This paper provides a comparison of gauge and radar precipitation data sources during an extreme hydrological event. November–December 2006 was selected as a time period of intense rainfall and large river flows for the Severn Uplands, an upland catchment in the United Kingdom. A comparison between gauge and radar precipitation time‐series records for the event indicated discrepancies between data sources, particularly in areas of higher elevation. The HEC‐HMS rainfall‐runoff model was selected to assess the accuracy of the precipitation to simulate river flows for the extreme event. Gauge, radar and gauge‐corrected radar rainfall were used as model inputs. Universal cokriging was used to geostatistically interpolate gauge data with radar and elevation data as covariates. This interpolated layer was used to calculate the mean‐field bias and correct the radar composites. Results indicated that gauge‐ and gauge‐corrected radar‐driven models replicated flows adequately for the extreme event. Gauge‐corrected flow predictions produced an increase in flow prediction accuracy when compared with the raw radar, yet predictions were comparative in accuracy to those using the interpolated gauge network. Subsequent investigations suggested this was due to an adequate spatial and temporal resolution of the precipitation gauge network within the Severn Uplands. Results suggested that the six rain gauges could adequately represent precipitation variability of the Severn Uplands to predict flows at an approximately equal accuracy to that obtained by radar. Temporally, radar produced an increase in flow prediction accuracy in mountainous reaches once the gauge time step was in excessive of an hourly interval. Copyright © 2010 John Wiley & Sons, Ltd.     

Spatial patterns in thunderstorm rainfall events and their coupling with watershed hydrological response

Weather radar systems provide detailed information on spatial rainfall patterns known to play a significant role in runoff generation processes. In the current study, we present an innovative approach to exploit spatial rainfall information of air mass thunderstorms and link it with a watershed hydrological model. Observed radar data are decomposed into sets of rain cells conceptualized as circular Gaussian elements and the associated rain cell parameters, namely, location, maximal intensity and decay factor, are input into a hydrological model. Rain cells were retrieved from radar data for several thunderstorms over southern Arizona. Spatial characteristics of the resulting rain fields were evaluated using data from a dense rain gauge network. For an extreme case study in a semi-arid watershed, rain cells were derived and fed as input into a hydrological model to compute runoff response. A major factor in this event was found to be a single intense rain cell (out of the five cells decomposed from the storm). The path of this cell near watershed tributaries and toward the outlet enhanced generation of high flow. Furthermore, sensitivity analysis to cell characteristics indicated that peak discharge could be a factor of two higher if the cell was initiated just a few kilometers aside.     

Distributed hydrological modelling using weather radar in gauged and ungauged basins

Distributed hydrological modelling using space–time estimates of rainfall from weather radar provides a natural approach to area-wide flood forecasting and warning at any location, whether gauged or ungauged. However, radar estimates of rainfall may lack consistent, quantitative accuracy. Also, the formulation of hydrological models in distributed form may be problematic due to process complexity and scaling issues. Here, the aim is to first explore ways of improving radar rainfall accuracy through combination with raingauge network data via integrated multiquadric methods. When the resulting gridded rainfall estimates are employed as input to hydrological models, the simulated river flows show marked improvements when compared to using radar data alone. Secondly, simple forms of physical–conceptual distributed hydrological model are considered, capable of exploiting spatial datasets on topography and, where necessary, land-cover, soil and geology properties. The simplest Grid-to-Grid model uses only digital terrain data to delineate flow pathways and to control runoff production, the latter by invoking a probability-distributed relation linking terrain slope to soil absorption capacity. Model performance is assessed over nested river basins in northwest England, employing a lumped model as a reference. When the distributed model is used with the gridded radar-based rainfall estimators, it shows particular benefits for forecasting at ungauged locations.     

Spatial rainfall estimation by linear and non-linear co-kriging of radar-rainfall and raingage data

The feasibility of linear and nonlinear geostatistical estimation techniques for optimal merging of rainfall data from raingage and radar observations is investigated in this study by use of controlled numerical experiments. Synthetic radar and raingage data are generated with their hypothetical error structures that explicitly account for sampling characteristics of the two sensors. Numerically simulated rainfall fields considered to be ground-truth fields on 4×4 km grids are used in the generation of radar and raingage observations. Ground-truth rainfall fields consist of generated rainfall fields with various climatic characteristics that preserve the space-time covariance function of rainfall events in extratropical cyclonic storms. Optimal mean areal precipitation estimates are obtained based on the minimum variance, unbiased property of kriging techniques under the second order homogeneity assumption of rainfall fields. The evaluation of estimated rainfall fields is done based on the refinement of spatial predictability over what would be provided from each sensor individually. Attention is mainly given to removal of measurement error and bias that are synthetically introduced to radar measurements. The influence of raingage network density on estimated rainfall fields is also examined.     

Spatial rainfall estimation by linear and non-linear co-kriging of radar-rainfall and raingage data

The feasibility of linear and nonlinear geostatistical estimation techniques for optimal merging of rainfall data from raingage and radar observations is investigated in this study by use of controlled numerical experiments. Synthetic radar and raingage data are generated with their hypothetical error structures that explicitly account for sampling characteristics of the two sensors. Numerically simulated rainfall fields considered to be ground-truth fields on 4×4 km grids are used in the generation of radar and raingage observations. Ground-truth rainfall fields consist of generated rainfall fields with various climatic characteristics that preserve the space-time covariance function of rainfall events in extratropical cyclonic storms. Optimal mean areal precipitation estimates are obtained based on the minimum variance, unbiased property of kriging techniques under the second order homogeneity assumption of rainfall fields. The evaluation of estimated rainfall fields is done based on the refinement of spatial predictability over what would be provided from each sensor individually. Attention is mainly given to removal of measurement error and bias that are synthetically introduced to radar measurements. The influence of raingage network density on estimated rainfall fields is also examined.     

Optimal design of rain gauge network in the Middle Yarra River catchment,Australia

Rainfall data are a fundamental input for effective planning, designing and operating of water resources projects. A well‐designed rain gauge network is capable of providing accurate estimates of necessary areal average and/or point rainfall estimates at any desired ungauged location in a catchment. Increasing network density with additional rain gauge stations has been the main underlying criterion in the past to reduce error and uncertainty in rainfall estimates. However, installing and operation of additional stations in a network involves large cost and manpower. Hence, the objective of this study is to design an optimal rain gauge network in the Middle Yarra River catchment in Victoria, Australia. The optimal positioning of additional stations as well as optimally relocating of existing redundant stations using the kriging‐based geostatistical approach was undertaken in this study. Reduction of kriging error was considered as an indicator for optimal spatial positioning of the stations. Daily rainfall records of 1997 (an El Niño year) and 2010 (a La Niña year) were used for the analysis. Ordinary kriging was applied for rainfall data interpolation to estimate the kriging error for the network. The results indicate that significant reduction in the kriging error can be achieved by the optimal spatial positioning of the additional as well as redundant stations. Thus, the obtained optimal rain gauge network is expected to be appropriate for providing high quality rainfall estimates over the catchment. The concept proposed in this study for optimal rain gauge network design through combined use of additional and redundant stations together is equally applicable to any other catchment. © 2014 The Authors. Hydrological Processes published by John Wiley & Sons Ltd.     

Rainfall estimation in the Sahel: the EPSAT-NIGER experiment

Abstract

EPSAT-NIGER (Estimation of Precipitation by SATellite—NIGER experiment) has been designed to improve the understanding of the precipitation systems of Sudano-Sahelian Africa and to develop operational rainfall estimation algorithms for this region. It is based on the combined use of a very dense raingauge network (93 gauges over a study area of 16 000 km₂) and a C-band weather radar system. The experiment is scheduled to last three years, 1990–1992. The network pattern, a regular grid with nodes spaced at 12.5 km and a 16 gauge target area where the distance between stations is decreased to 1 km, has allowed for some preliminary studies on the rainfall distribution at various space and time scales. Whereas the long term average rainfall gradient is uniform, rainfall increasing north to south, a single rainy season can be markedly different. The local variability may be extremely large. That variability is enhanced at smaller sampling time steps and the computation of reference areal rainfall for satellite imagery validation is extremely sensitive to the design of the ground-based validation system. The joint processing of gauge and radar data has led to the identification of a few typical features of the drop size distribution of the African squall lines, which could lead to deriving specific algorithms for radar calibration in this region. The data provided by EPSAT-NIGER will be used in various international projects for the assessment of water input from the atmosphere to the continent over the Sahel.     

Use of Scale Recursive Estimation for assimilation of precipitation data from TRMM (PR and TMI) and NEXRAD

The paper shows an application of Scale Recursive Estimation (SRE) used to assimilate rainfall rates estimated during a storm event from three remote sensing devices. These are the TMI radiometer and the PR radar, carried on board of the TRMM satellite and the KNQA Memphis Weather Surveillance radar, belonging to the NEXRAD network, each one providing rain rate estimates at a different spatial scale. The variability of rain rate process in scales is modeled as a multiplicative random cascade, including spatial intermittence. The observational noise in the estimates is modeled according to a multiplicative error. System estimation, including process and observational noise, is carried out using Maximum Likelihood Estimation implemented by a scale recursive Expectation Maximization (EM) algorithm. As a result, new rainfall rate estimates are obtained that feature decreased estimation error as compared to those coming from each device alone. The performance of the SRE-EM approach is compared with that of the latest methods proposed for data fusion of multisensor estimates. The proposed approach improves the current methods adopted for SRE and provides an alternative for data fusion in the field of precipitation.     

A non-parametric automatic blending methodology to estimate rainfall fields from rain gauge and radar data

Quantitative estimation of rainfall fields has been a crucial objective from early studies of the hydrological applications of weather radar. Previous studies have suggested that flow estimations are improved when radar and rain gauge data are combined to estimate input rainfall fields. This paper reports new research carried out in this field. Classical approaches for the selection and fitting of a theoretical correlogram (or semivariogram) model (needed to apply geostatistical estimators) are avoided in this study. Instead, a non-parametric technique based on FFT is used to obtain two-dimensional positive-definite correlograms directly from radar observations, dealing with both the natural anisotropy and the temporal variation of the spatial structure of the rainfall in the estimated fields. Because these correlation maps can be automatically obtained at each time step of a given rainfall event, this technique might easily be used in operational (real-time) applications. This paper describes the development of the non-parametric estimator exploiting the advantages of FFT for the automatic computation of correlograms and provides examples of its application on a case study using six rainfall events. This methodology is applied to three different alternatives to incorporate the radar information (as a secondary variable), and a comparison of performances is provided. In particular, their ability to reproduce in estimated rainfall fields (i) the rain gauge observations (in a cross-validation analysis) and (ii) the spatial patterns of radar fields are analyzed. Results seem to indicate that the methodology of kriging with external drift [KED], in combination with the technique of automatically computing 2-D spatial correlograms, provides merged rainfall fields with good agreement with rain gauges and with the most accurate approach to the spatial tendencies observed in the radar rainfall fields, when compared with other alternatives analyzed.     

Rainfall stochastic modeling for runoff forecasting

Rainfall fields estimation over a catchment area is an important stage in many hydrological applications. In this context, weather radars have several advantages because a single-site can scan a vast area with very high temporal and spatial resolution. The construction of weather radar systems with dual polarization capability allowed progress on radar rainfall estimation and its hydro-meteorological applications. For these applications of radar data it is necessary to remove the ground clutter contamination with an algorithm based on the backscattering signal variance of the differential reflectivity. The calibration of the GDSTM model (Gaussian Displacements Spatial-Temporal Model), a cluster stochastic generation model in continuous space and time, is herewith presented. In this model, storms arrive in a Poisson process in time with cells occurring in each storm that cluster in space and time. The model is calibrated, using data collected by the weather radar Polar 55C located in Rome, inside a square area of 132 × 132 km², with the radar at the centre. The GDSTM is fitted to sequences of radar images with a time interval between the PPIs scans of 5 min. A generalized method of moment procedure is used for parameter estimation. For the validation of the ability of the model to reproduce internal structure of rain event, a geo-morphological rainfall-runoff model, based on width function (WFIUH), was calibrated using simulated and observed data. Several rainfall fields are generated with the stochastic model and later they are used as input of the WFIUH model so that the forecast discharges can be compared to the observed ones.     

Dependence of radar quantitative precipitation estimation error on the rain intensity in the Cévennes region,France

Abstract

Radar quantitative precipitation estimates (QPEs) were assessed using reference values established by means of a geostatistical approach. The reference values were estimated from raingauge data using the block kriging technique, and the reference meshes were selected on the basis of the kriging estimation variance. Agreement between radar QPEs and reference rain amounts was shown to increase slightly with the space–time scales. The statistical distributions of the errors were modelled conditionally with respect to several factors using the GAMLSS approach. The conditional bias of the errors presents a complex structure that depends on the space–time scales and the considered geographical sub-domains, while the standard deviation of the errors has a more homogeneous behaviour. The estimation standard deviation of the reference rainfall and the standard deviation of the errors between radar and reference rainfall were found to have the same magnitude, indicating the limitations of the available network in terms of providing accurate reference values for the spatial scales considered (5–100 km²).

Editor D. Koutsoyiannis; Guest editor R.J. Moore

Citation Delrieu, G., Bonnifait, L., Kirstetter, P.-E., and Boudevillain, B., 2013. Dependence of radar quantitative precipitation estimation error on the rain intensity in the Cévennes region, France. Hydrological Sciences Journal, 59 (7), 1300–1311. http://dx.doi.org/10.1080/02626667.2013.827337     

Comparison of radar and gauge precipitation data in watershed models across varying spatial and temporal scales

Precipitation is a key control on watershed hydrologic modelling output, with errors in rainfall propagating through subsequent stages of water quantity and quality analysis. Most watershed models incorporate precipitation data from rain gauges; higher‐resolution data sources are available, but they are associated with greater computational requirements and expertise. Here, we investigate whether the Multisensor Precipitation Estimator (MPE or Stage IV Next‐Generation Radar) data improve the accuracy of streamflow simulations using the Soil and Water Assessment Tool (SWAT), compared with rain gauge data. Simulated flows from 2002 to 2010 at five timesteps were compared with observed flows for four nested subwatersheds of the Neuse River basin in North Carolina (21‐, 203‐, 2979‐, and 10 100‐km² watershed area), using a multi‐objective function, informal likelihood‐weighted calibration approach. Across watersheds and timesteps, total gauge precipitation was greater than radar precipitation, but radar data showed a conditional bias of higher rainfall estimates during large events (>25–50 mm/day). Model parameterization differed between calibrations with the two datasets, despite the fact that all watershed characteristics were the same across simulation scenarios. This underscores the importance of linking calibration parameters to realistic processes. SWAT simulations with both datasets underestimated median and low flows, whereas radar‐based simulations were more accurate than gauge‐based simulations for high flows. At coarser timesteps, differences were less pronounced. Our results suggest that modelling efforts in watersheds with poor rain gauge coverage can be improved with MPE radar data, especially at short timesteps. Published 2013. This article is a U.S. Government work and is in the public domain in the USA.     

Rainfall spatial variability observed by X-band weather radar and its implication for the accuracy of rainfall estimates

The main objective of this paper is to estimate the error in the rainfall derived from a polarimetric X-band radar, by comparison with the corresponding estimate of a rain gauge network. However the present analysis also considers the errors inherent to rain gauge, in particular instrumental and representativeness errors. A special emphasis is addressed to the spatial variability of the rainfall in order to appreciate the representativeness error of the rain gauge with respect to the 1 km square average, typical of the radar derived estimate. For this purpose the spatial correlation function of the rainfall is analyzed.     

A two steps disaggregation method for highly seasonal monthly rainfall

 The need for high resolution rainfall data at temporal scales varying from daily to hourly or even minutes is a very important problem in hydrology. For many locations of the world, rainfall data quality is very poor and reliable measurements are only available at a coarse time resolution such as monthly. The purpose of this work is to apply a stochastic disaggregation method of monthly to daily precipitation in two steps: 1. Initialization of the daily rainfall series by using the truncated normal model as a reference distribution. 2.␣Restructuring of the series according to various time series statistics (autocorrelation function, scaling properties, seasonality) by using a Markov chain Monte Carlo based algorithm. The method was applied to a data set from a rainfall network of the central plains of Venezuela, in where rainfall is highly seasonal and data availability at a daily time scale or even higher temporal resolution is very limited. A detailed analysis was carried out to study the seasonal and spatial variability of many properties of the daily rainfall as scaling properties and autocorrelation function in order to incorporate the selected statistics and their annual cycle into an objective function to be minimized in the simulation procedure. Comparisons between the observed and simulated data suggest the adequacy of the technique in providing rainfall sequences with consistent statistical properties at a daily time scale given the monthly totals. The methodology, although highly computationally intensive, needs a moderate number of statistical properties of the daily rainfall. Regionalization of these statistical properties is an important next step for the application of this technique to regions in where daily data is not available.     

Assimilation of Doppler Weather Radar Radial Velocity and Reflectivity Observations in WRF-3DVAR System for Short-Range Forecasting of Convective Storms

In this paper the impact of Doppler weather radar (DWR) reflectivity and radial velocity observations for the short range forecasting of a tropical storm and associated rainfall event have been examined. Doppler radar observations of a tropical storm case that occurred during 29–30 October 2006 from SHARDWR (13.6° N, 80.2° E) are assimilated in the WRF 3DVAR system. The observation operator for radar reflectivity and radial velocity is included within latest version of WRF 3DVAR system. Keeping all model physics the same, three experiments were conducted at a horizontal resolution of 30?km. In the control experiment (CTRL), NCEP Final Analysis (FNL) interpolated to the model grid was used as the initial condition for 48-h free forecast. In the second experiment (NODWR), 6-h assimilation cycles have been carried out using all conventional (radiosonde and surface data) and non-conventional (satellite) observations from the Global Telecommunication System (GTS). The third experiment (DWR) is the same as the second, except Doppler radar radial velocity and reflectivity observations are also used in the assimilation cycle. Continuous 6-h assimilation cycle employed in the WRF-3DVAR system shows positive impact on the rainfall forecast. Assimilation of DWR data creates several small scale features near the storm centre. Additional sensitivity experiments were conducted to study the individual impact of reflectivity and radial velocity in the assimilation cycle. Radar data assimilation with reflectivity alone produced large analysis response on both thermodynamical and dynamical fields. However, radial velocity assimilation impacted only on dynamical fields. Analysis increments with radar reflectivity and radial velocity produce adjustments in both dynamical and thermodynamical fields. Verification of QPF skill shows that radar data assimilation has a considerable impact on the short range precipitation forecast. Improvement of the QPF skill with radar data assimilation is more clearly seen in the heavy rainfall (for thresholds >7?mm) event than light rainfall (for thresholds of 1 and 3?mm). The spatial pattern of rainfall is well simulated by the DWR experiment and is comparable to TRMM observations.     

Spatial reconstruction of rainfall fields from rain gauge and radar data

Rainfall is a phenomenon difficult to model and predict, for the strong spatial and temporal heterogeneity and the presence of many zero values. We deal with hourly rainfall data provided by rain gauges, sparsely distributed on the ground, and radar data available on a fine grid of pixels. Radar data overcome the problem of sparseness of the rain gauge network, but are not reliable for the assessment of rain amounts. In this work we investigate how to calibrate radar measurements via rain gauge data and make spatial predictions for hourly rainfall, by means of Monte Carlo Markov Chain algorithms in a Bayesian hierarchical framework. We use zero-inflated distributions for taking zero-measurements into account. Several models are compared both in terms of data fitting and predictive performances on a set of validation sites. Finally, rainfall fields are reconstructed and standard error estimates at each prediction site are shown via easy-to-read spatial maps.     

The effect of differences between rainfall measurement techniques on groundwater and discharge simulations in a lowland catchment

Several rainfall measurement techniques are available for hydrological applications, each with its own spatial and temporal resolution and errors. When using these rainfall datasets as input for hydrological models, their errors and uncertainties propagate through the hydrological system. The aim of this study is to investigate the effect of differences between rainfall measurement techniques on groundwater and discharge simulations in a lowland catchment, the 6.5‐km² Hupsel Brook experimental catchment. We used five distinct rainfall data sources: two automatic raingauges (one in the catchment and another one 30 km away), operational (real‐time and unadjusted) and gauge‐adjusted ground‐based C‐band weather radar datasets and finally a novel source of rainfall information for hydrological purposes, namely, microwave link data from a cellular telecommunication network. We used these data as input for the, a recently developed rainfall‐runoff model for lowland catchments, and intercompared the five simulated discharges time series and groundwater time series for a heavy rainfall event and a full year. Three types of rainfall errors were found to play an important role in the hydrological simulations, namely: (1) Biases, found in the unadjusted radar dataset, are amplified when propagated through the hydrological system; (2) Timing errors, found in the nearest automatic raingauge outside the catchment, are attenuated when propagated through the hydrological system; (3) Seasonally varying errors, found in the microwave link data, affect the dynamics of the simulated catchment water balance. We conclude that the hydrological potential of novel rainfall observation techniques should be assessed over a long period, preferably a full year or longer, rather than on an event basis, as is often done. Copyright © 2016 The Authors. Hydrological Processes. Published by John Wiley & Sons Ltd.     

A stochastic integral equation analog of rainfall-runoff processes for evaluating modeling uncertainty

In this paper a very general rainfall-runoff model structure (described below) is shown to reduce to a unit hydrograph model structure. For the general model, a multi-linear unit hydrograph approach is used to develop subarea runoff, and is coupled to a multi-linear channel flow routing method to develop a link-node rainfall-runoff model network. The spatial and temporal rainfall distribution over the catchment is probabilistically related to a known rainfall data source located in the catchment in order to account for the stochastic nature of rainfall with respect to the rain gauge measured data. The resulting link node model structure is a series of stochastic integral equations, one equation for each subarea. A cumulative stochastic integral equation is developed as a sum of the above series, and includes the complete spatial and temporal variabilities of the rainfall over the catchment. The resulting stochastic integral equation is seen to be an extension of the well-known single area unit hydrograph method, except that the model output of a runoff hydrograph is a distribution of outcomes (or realizations) when applied to problems involving prediction of storm runoff; that is, the model output is a set of probable runoff hydrographs, each outcome being the results of calibration to a known storm event.     

A stochastic integral equation analog of rainfall-runoff processes for evaluating modeling uncertainty

In this paper a very general rainfall-runoff model structure (described below) is shown to reduce to a unit hydrograph model structure. For the general model, a multi-linear unit hydrograph approach is used to develop subarea runoff, and is coupled to a multi-linear channel flow routing method to develop a link-node rainfall-runoff model network. The spatial and temporal rainfall distribution over the catchment is probabilistically related to a known rainfall data source located in the catchment in order to account for the stochastic nature of rainfall with respect to the rain gauge measured data. The resulting link node model structure is a series of stochastic integral equations, one equation for each subarea. A cumulative stochastic integral equation is developed as a sum of the above series, and includes the complete spatial and temporal variabilities of the rainfall over the catchment. The resulting stochastic integral equation is seen to be an extension of the well-known single area unit hydrograph method, except that the model output of a runoff hydrograph is a distribution of outcomes (or realizations) when applied to problems involving prediction of storm runoff; that is, the model output is a set of probable runoff hydrographs, each outcome being the results of calibration to a known storm event.     

Adjustment of wind-drift effect for real-time systematic error correction in radar rainfall data

An effective bias correction procedure using gauge measurement is a significant step for radar data processing to reduce the systematic error in hydrological applications. In these bias correction methods, the spatial matching of precipitation patterns between radar and gauge networks is an important premise. However, the wind-drift effect on radar measurement induces an inconsistent spatial relationship between radar and gauge measurements as the raindrops observed by radar do not fall vertically to the ground. Consequently, a rain gauge does not correspond to the radar pixel based on the projected location of the radar beam. In this study, we introduce an adjustment method to incorporate the wind-drift effect into a bias correlation scheme. We first simulate the trajectory of raindrops in the air using downscaled three-dimensional wind data from the weather research and forecasting model (WRF) and calculate the final location of raindrops on the ground. The displacement of rainfall is then estimated and a radar–gauge spatial relationship is reconstructed. Based on this, the local real-time biases of the bin-average radar data were estimated for 12 selected events. Then, the reference mean local gauge rainfall, mean local bias, and adjusted radar rainfall calculated with and without consideration of the wind-drift effect are compared for different events and locations. There are considerable differences for three estimators, indicating that wind drift has a considerable impact on the real-time radar bias correction. Based on these facts, we suggest bias correction schemes based on the spatial correlation between radar and gauge measurements should consider the adjustment of the wind-drift effect and the proposed adjustment method is a promising solution to achieve this.