Hydrological model sensitivity to parameter and radar rainfall estimation uncertainty

Radar estimates of rainfall are being increasingly applied to flood forecasting applications. Errors are inherent both in the process of estimating rainfall from radar and in the modelling of the rainfall–runoff transformation. The study aims at building a framework for the assessment of uncertainty that is consistent with the limitations of the model and data available and that allows a direct quantitative comparison between model predictions obtained by using radar and raingauge rainfall inputs. The study uses radar data from a mountainous region in northern Italy where complex topography amplifies radar errors due to radar beam occlusion and variability of precipitation with height. These errors, together with other error sources, are adjusted by applying a radar rainfall estimation algorithm. Radar rainfall estimates, adjusted and not, are used as an input to TOPMODEL for flood simulation over the Posina catchment (116 km²). Hydrological model parameter uncertainty is explicitly accounted for by use of the GLUE (Generalized Likelihood Uncertainty Estimation). Statistics are proposed to evaluate both the wideness of the uncertainty limits and the percentage of observations which fall within the uncertainty bounds. Results show the critical importance of proper adjustment of radar estimates and the use of radar estimates as close to ground as possible. Uncertainties affecting runoff predictions from adjusted radar data are close to those obtained by using a dense raingauge network, at least for the lowest radar observations available. Copyright © 2004 John Wiley & Sons, Ltd.     

Daily hydrological modeling in the Amazon basin using TRMM rainfall estimates

Rainfall measurements by conventional raingauges provide relatively accurate estimates at a few points of a region. The actual rainfield can be approximated by interpolating the available raingauge data to the remaining of the area of interest. In places with relatively low gauge density such interpolated rainfields will be very rough estimates of the actual events. This is especially true for tropical regions where most rainfall has a convective origin with high spatial variability at the daily level. Estimates of rainfall by remote sensing can be very useful in regions such as the Amazon basin, where raingauge density is very low and rainfall highly variable. This paper evaluates the rainfall estimates of the Tropical Rainfall Measuring Mission (TRMM) satellite over the Tapajós river basin, a major tributary of the Amazon. Three-hour TRMM rainfall estimates were aggregated to daily values and were compared with catch of ground-level precipitation gauges on a daily basis after interpolating both data to a regular grid. Both daily TRMM and raingauge-interpolated rainfields were then used as input to a large-scale hydrological model for the whole basin; the calculated hydrographs were then compared to observations at several streamgauges along the river Tapajos and its main tributaries. Results of the rainfield comparisons showed that satellite estimates can be a practical tool for identifying damaged or aberrant raingauges at a basin-wide scale. Results of the hydrological modeling showed that TRMM-based calculated hydrographs are comparable with those obtained using raingauge data.     

Hydrological appraisal of rainfall estimates from radar,satellite, raingauge and satellite–gauge combination on the Qinhuai River Basin,China

ABSTRACT

Multisource rainfall products can be used to overcome the absence of gauged precipitation data for hydrological applications. This study aims to evaluate rainfall estimates from the Chinese S-band weather radar (CINRAD-SA), operational raingauges, multiple satellites (CMORPH, ERA-Interim, GPM, TRMM-3B42RT) and the merged satellite–gauge rainfall products, CMORPH-GC, as inputs to a calibrated probability distribution model (PDM) on the Qinhuai River Basin in Nanjing, China. The Qinhuai is a middle-sized catchment with an area of 799 km². All sources used in this study are capable of recording rainfall at high spatial and temporal resolution (3 h). The discrepancies between satellite and radar data are analysed by statistical comparison with raingauge data. The streamflow simulation results from three flood events suggest that rainfall estimates using CMORPH-GC, TRMM-3B42RT and S-band radar are more accurate than those using the other rainfall sources. These findings indicate the potential to use satellite and radar data as alternatives to raingauge data in hydrological applications for ungauged or poorly gauged basins.     

Sensitivity analysis of the hydrological response of the Gaping River basin to radar-raingauge quantitative precipitation estimates

Abstract

The generation of reliable quantitative precipitation estimations (QPEs) through use of raingauge and radar data is an important issue. This study investigates the impacts of radar QPEs with different densities of raingauge networks on rainfall–runoff processes through a semi-distributed parallel-type linear reservoir rainfall–runoff model. The spatial variation structures of the radar QPE, raingauge QPE and radar-gauge residuals are examined to review the current raingauge network, and a compact raingauge network is identified via the kriging method. An analysis of the large-scale spatial characteristics for use with a hydrological model is applied to investigate the impacts of a raingauge network coupled with radar QPEs on the modelled rainfall–runoff processes. Since the precision in locating the storm centre generally represents how well the large-scale variability is reproduced; the results show not only the contribution of kriging to identify a compact network coupled with radar QPE, but also that spatial characteristics of rainfalls do affect the hydrographs.

Editor Z.W. Kundzewicz; Guest editor R.J. Moore

Citation Pan, T.-Y., Li, M.-Y., Lin, Y.-J., Chang, T.-J., Lai, J.-S., and Tan, Y.-C., 2014. Sensitivity analysis of the hydrological response of the Gaping River basin to radar-raingauge quantitative precipitation estimates. Hydrological Sciences Journal, 59 (7), 1335–1352. http://dx.doi.org/10.1080/02626667.2014.923969     

Automatic sampling of stream water during storm events in small remote catchments

In order to study the relationship between water composition and stream flow rate, it is desirable to sample at a frequency related to flow rate, especially during storm events. In a rural catchment of 18 ha near Oxford, the rate of rainfall was found to be linearly related to discharge on the rising limb of the stream hydrograph. A sampling system was therefore designed in which electrical pulses from a tipping-bucket raingauge were used to initiate and control the action of an automatic water sampler. A threshold rainfall intensity is set above which sampling commences. Sampling then continues at regular increments of rainfall until the intensity drops below the threshold, after which sampling occurs at regular intervals during the period that the stream flow reverts to normal. The CMOS electrical circuits which control the sampling also operate a cassette tape recorder which records the time of each tip of the raingauge and operation of the sampler. Since the sytem is designed to impose very little additional load on the battery which powers the water sampler, and can operate unattended for at least a fortnight, it is ideal for use in small, remote catchments. The system has been extended to include measurements of water temperature and could provide other measurements as well.     

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.     

Empirically-based modeling of spatial sampling uncertainties associated with rainfall measurements by rain gauges

In the quantitative evaluation of radar-rainfall products (maps), rain gauge data are generally used as a good approximation of the true ground rainfall. However, rain gauges provide accurate measurements for a specific location, while radar estimates represent areal averages. Because these sampling discrepancies could introduce noise into the comparisons between these two sensors, they need to be accounted for. In this study, the spatial sampling error is defined as the ratio between the measurements by a single rain gauge and the true areal rainfall, defined as the value obtained by averaging the measurements by an adequate number of gauges within a pixel. Using a non-parametric scheme, the authors characterize its full statistical distribution for several spatial (4, 16 and 36 km²) and temporal (15 min and hourly) scales.     

Radar rainfall uncertainty modelling influenced by wind

Radar‐based estimates of rainfall are affected by many sources of uncertainties, which would propagate through the hydrological model when radar rainfall estimates are used as input or initial conditions. An elegant solution to quantify these uncertainties is to model the empirical relationship between radar measurements and rain gauge observations (as the ‘ground reference’). However, most current studies only use a fixed and uniform model to represent the uncertainty of radar rainfall, without consideration of its variation under different synoptic regimes. Wind is such a typical weather factor, as it not only induces error in rain gauge measurements but also causes the raindrops observed by weather radar to drift when they reach the ground. For this reason, as a first attempt, this study introduces the wind field into the uncertainty model and designs the radar rainfall uncertainty model under different wind conditions. We separate the original dataset into three subsamples according to wind speed, which are named as WDI (0–2 m/s), WDII (2–4 m/s) and WDIII (>4 m/s). The multivariate distributed ensemble generator is introduced and established for each subsample. Thirty typical events (10 at each wind range) are selected to explore the behaviours of uncertainty under different wind ranges. In each time step, 500 ensemble members are generated, and the values of 5th to 95th percentile values are used to produce the uncertainty bands. Two basic features of uncertainty bands, namely dispersion and ensemble bias, increase significantly with the growth of wind speed, demonstrating that wind speed plays a considerable role in influencing the behaviour of the uncertainty band. On the basis of these pieces of evidence, we conclude that the radar rainfall uncertainty model established under different wind conditions should be more realistic in representing the radar rainfall uncertainty. This study is only a start in incorporating synoptic regimes into rainfall uncertainty analysis, and a great deal of more effort is still needed to build a realistic and comprehensive uncertainty model for radar rainfall data. Copyright © 2014 John Wiley & Sons, Ltd.     

Modelling radar-rainfall estimation uncertainties using elliptical and Archimedean copulas with different marginal distributions

Abstract

Given that radar-based rainfall has been broadly applied in hydrological studies, quantitative modelling of its uncertainty is critically important, as the error of input rainfall is the main source of error in hydrological modelling. Using an ensemble of rainfall estimates is an elegant solution to characterize the uncertainty of radar-based rainfall and its spatial and temporal variability. This paper has fully formulated an ensemble generator for radar precipitation estimation based on the copula method. Each ensemble member is a probable realization that represents the unknown true rainfall field based on the distribution of radar rainfall (RR) error and its spatial error structure. An uncertainty model consisting of a deterministic component and a random error factor is presented based on the distribution of gauge rainfall conditioned on the radar rainfall (GR|RR). Two kinds of copulas (elliptical and Archimedean copulas) are introduced to generate random errors, which are imposed by the deterministic component. The elliptical copulas (e.g. Gaussian and t-copula) generate the random errors based on the multivariate distribution, typically of decomposition of the error correlation matrix using the LU decomposition algorithm. The Archimedean copulas (e.g. Clayton and Gumbel) utilize the conditional dependence between different radar pixels to obtain random errors. Based on those, a case application is carried out in the Brue catchment located in southwest England. The results show that the simulated uncertainty bands of rainfall encompass most of the reference raingauge measurements with good agreement between the simulated and observed spatial dependences. This indicates that the proposed scheme is a statistically reliable method in ensemble radar rainfall generation and is a useful tool for describing radar rainfall uncertainty.

Editor D. Koutsoyiannis; Associate editor S. Grimaldi     

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.     

IV: EPSAT-NIGER study of rainfall over the Sahel at small time steps using a dense network of recording raingauges

The high density, static memory raingauge network of the EPSAT-NIGER experiment was designed with the aim of: (1) studying the rainfall spatial variability in the Sahel, as may be seen from ground networks of varying density, and (2) providing reference values for the calibration of a C band radar system. A first subset of 37 raingauges was installed in 1988 and the remaining 43 in 1989, thus providing a network of 80 stations, spread over a 100 × 100 km square area. The data analysis is based on the indentification of the structural function for each rainfall event. This permits classification of the events into three main categories with respect to their spatial organization. Furthermore the differences between the shower body and the trail are important and it is shown that the analysis of the spatial organization at the event scale may not be applicable to the calibration of high temporal resolution radar data. Estimation of the areal rainfall over two reference areas is also carried out.     

Impact of spatial rainfall resolution on point-source solute transport modelling

Numerical simulations of unsaturated solute transport from point sources were carried out using HYDRUS-1D. Three different soil types cropped with spring wheat were considered at three different locations in Sweden: Malmö, Norrköping and Petisträsk. Two types of rainfall data were used, point-scale raingauge measurements and a gauge-adjusted weather radar product at four spatial resolutions, 2 × 2, 6 × 6, 10 × 10 and 14 × 14 km². The results showed that differences in the mean solute transport depths were small and not significant, with the exception of Petisträsk. Maximum transport depths were in most cases significantly larger using raingauge data compared to radar data. The results showed that using areal-averaged rainfall input will give solute transport estimations close to those using point-measured data. This shows the great potential in using radar-measured rainfall data in small-scale hydrological applications.     

Spatial-temporal rainfall modelling for flood risk estimation

Some recent developments in the stochastic modelling of single site and spatial rainfall are summarised. Alternative single site models based on Poisson cluster processes are introduced, fitting methods are discussed, and performance is compared for representative UK hourly data. The representation of sub-hourly rainfall is discussed, and results from a temporal disaggregation scheme are presented. Extension of the Poisson process methods to spatial-temporal rainfall, using radar data, is reported. Current methods assume spatial and temporal stationarity; work in progress seeks to relax these restrictions. Unlike radar data, long sequences of daily raingauge data are commonly available, and the use of generalized linear models (GLMs) (which can represent both temporal and spatial non-stationarity) to represent the spatial structure of daily rainfall based on raingauge data is illustrated for a network in the North of England. For flood simulation, disaggregation of daily rainfall is required. A relatively simple methodology is described, in which a single site Poisson process model provides hourly sequences, conditioned on the observed or GLM-simulated daily data. As a first step, complete spatial dependence is assumed. Results from the River Lee catchment, near London, are promising. A relatively comprehensive set of methodologies is thus provided for hydrological application.     

Using microwave links to adjust the radar rainfall field

The final stage in processing radar data so as to arrive at an estimated rain field typically involves a comparison of the preliminary radar-derived estimates of hourly rainfall with those observed by ground-based gauges. Often a mean field bias adjustment will then be applied using an age-weighted average of the individual gauge–radar comparisons. In this paper, a mean field bias adjustment is presented that uses the path-integrated rainfall estimates provided by microwave links together with information from gauges. It is shown to be at least as efficient as the current gauge-based procedure used by the UK Met Office to improve the accuracy of radar-based estimates of rainfall at the ground.     

Estimation of rainfall from infrared‐microwave satellite data for basin‐scale hydrologic modelling

The infrared‐microwave rainfall algorithm (IMRA) was developed for retrieving spatial rainfall from infrared (IR) brightness temperatures (TBs) of satellite sensors to provide supplementary information to the rainfall field, and to decrease the traditional dependency on limited rain gauge data that are point measurements. In IMRA, a SLOPE technique (ST) was developed for discriminating rain/no‐rain pixels through IR image cloud‐top temperature gradient, and 243K as the IR threshold temperature for minimum detectable rainfall rate. IMRA also allows for the adjustment of rainfall derived from IR‐TB using microwave (MW) TBs. In this study, IMRA rainfall estimates were assessed on hourly and daily basis for different spatial scales (4, 12, 20, and 100 km) using NCEP stage IV gauge‐adjusted radar rainfall data, and daily rain gauge data. IMRA was assessed in terms of the accuracy of the rainfall estimates and the basin streamflow simulated by the hydrologic model, Sacramento soil moisture accounting (SAC‐SMA), driven by the rainfall data. The results show that the ST option of IMRA gave accurate satellite rainfall estimates for both light and heavy rainfall systems while the Hessian technique only gave accurate estimates for the convective systems. At daily time step, there was no improvement in IR‐satellite rainfall estimates adjusted with MW TBs. The basin‐scale streamflow simulated by SAC‐SMA driven by satellite rainfall data was marginally better than when SAC‐SMA was driven by rain gauge data, and was similar to the case using radar data, reflecting the potential applications of satellite rainfall in basin‐scale hydrologic modelling. Copyright © 2010 John Wiley & Sons, Ltd.     

Modeling radar-rainfall estimation uncertainties using parametric and non-parametric approaches

There are large uncertainties associated with radar estimates of rainfall, including systematic errors as well as the random effects from several sources. This study focuses on the modeling of the systematic error component, which can be described mathematically in terms of a conditional expectation function. The authors present two different approaches: non-parametric (kernel-based) and parametric (copula-based). A large sample (more than six years) of rain gauge measurements from a dense network located in south-west England is used as an approximation of the true ground rainfall. These data are complemented with rainfall estimates by a C-band weather radar located at Wardon Hill, which is about 40 km from the catchment. The authors compare the results obtained using the parametric and non-parametric schemes for four temporal scales of hydrologic interest (5 and 15 min, hourly and three-hourly) by means of several different performance indices and discuss the strengths and weaknesses of each approach.     

Flood simulation using the gauge‐adjusted radar rainfall and physics‐based distributed hydrologic model

This paper reports the results of an investigation into flood simulation by areal rainfall estimated from the combination of gauged and radar rainfalls and a rainfall–runoff model on the Anseong‐cheon basin in the southern part of Korea. The spatial and temporal characteristics and behaviour of rainfall are analysed using various approaches combining radar and rain gauges: (1) using kriging of the rain gauge alone; (2) using radar data alone; (3) using mean field bias (MFB) of both radar and rain gauges; and (4) using conditional merging technique (CM) of both radar and rain gauges. To evaluate these methods, statistics and hyetograph for rain gauges and radar rainfalls were compared using hourly radar rainfall data from the Imjin‐river, Gangwha, rainfall radar site, Korea. Then, in order to evaluate the performance of flood estimates using different rainfall estimation methods, rainfall–runoff simulation was conducted using the physics‐based distributed hydrologic model, Vflo^?. The flood runoff hydrograph was used to compare the calculated hydrographs with the observed one. Results show that the rainfall field estimated by CM methods improved flood estimates, because it optimally combines rainfall fields representing actual spatial and temporal characteristics of rainfall. Copyright © 2008 John Wiley & Sons, Ltd.     

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.     

Evaluating the performance of ground-based and remotely sensed near real-time rainfall fields from a hydrological perspective

Abstract

The South African Weather Service (SAWS) issues routine experimental, near real-time rainfall maps from daily raingauge networks, radar networks and satellite images, as well as merged rainfall fields. These products are potentially useful for near real-time forecasting, especially in areas of fast hydrological response, and also to simulate the “now state” of various hydrological state variables such as soil moisture content, streamflow, and reservoir inflows. The purpose of this paper is to evaluate their skill as inputs to hydrological simulations and, in particular, the skill of the merged field in terms of better hydrological results relative to the individual products. Rainfall fields derived from raingauge, radar, satellite, conditioned satellite and the merged (gauge/radar/satellite) were evaluated for two selected days with relatively high amounts of rainfall, as well as for a continuous period of 90 days in the Mgeni catchment, South Africa. Streamflows simulated with the ACRU model indicate that the use of raingauge as well as merged fields of satellite/raingauge and satellite/radars/raingauge provides relatively realistic rainfall results, without much difference in their hydrological outputs, whereas the radar and raw satellite information by themselves cannot be used in operational hydrological application in their current status.

Citation Ghile, Y., Schulze, R. & Brown, C. (2010) Evaluating the performance of ground-based and remotely sensed near real-time rainfall fields from a hydrological perspective. Hydrol. Sci. J. 55(4), 497–511.