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.     

Rainfall estimation using raingages and radar — A Bayesian approach: 2. An application

In Seo and Smith (this issue), a set of estimators was built in a Bayesian framework to estimate rainfall depth at an ungaged location using raingage measurements and radar rainfall data. The estimators are equivalent to lognormal co-kriging (simple co-kriging in the Gaussian domain) with uncertain mean and variance of gage rainfall. In this paper, the estimators are evaluated via cross-validation using hourly radar rainfall data and simulated hourly raingage data. Generation of raingage data is based on sample statistics of actual raingage measurements and radar rainfall data. The estimators are compared with lognormal co-kriging and nonparametric estimators. The Bayesian estimators are shown to provide some improvement over lognormal co-kriging under the criteria of mean error, root mean square error, and standardized mean square error. It is shown that, if the prior could be assessed more accurately, the margin of improvement in predicting estimation variance could be larger. In updating the uncertain mean and variance of gage rainfall, inclusion of radar rainfall data is seen to provide little improvement over using raingage data only.     

Rainfall estimation using raingages and radar — A Bayesian approach: 1. Derivation of estimators

Procedures for estimating rainfall from radar and raingage observations are constructed in a Bayesian framework. Given that the number of raingage measurements is typically very small, mean and variance of gage rainfall are treated as uncertain parameters. Under the assumption that log gage rainfall and log radar rainfall are jointly multivariate normal, the estimation problem is equivalent to lognormal co-kriging with uncertain mean and variance of the gage rainfall field.The posterior distribution is obtained under the assumption that the prior for the mean and inverse of the variance of log gage rainfall is normal-gamma 2. Estimate and estimation variance do not have closed-form expressions, but can be easily evaluated by numerically integrating two single integrals. To reduce computational burden associated with evaluating sufficient statistics for the likelihood function, an approximate form of parameter updating is given. Also, as a further approximation, the parameters are updated using raingage measurements only, yielding closed-form expressions for estimate and estimation variance in the Gaussian domain.     

Rainfall estimation using raingages and radar — A Bayesian approach: 1. Derivation of estimators

Procedures for estimating rainfall from radar and raingage observations are constructed in a Bayesian framework. Given that the number of raingage measurements is typically very small, mean and variance of gage rainfall are treated as uncertain parameters. Under the assumption that log gage rainfall and log radar rainfall are jointly multivariate normal, the estimation problem is equivalent to lognormal co-kriging with uncertain mean and variance of the gage rainfall field.The posterior distribution is obtained under the assumption that the prior for the mean and inverse of the variance of log gage rainfall is normal-gamma 2. Estimate and estimation variance do not have closed-form expressions, but can be easily evaluated by numerically integrating two single integrals. To reduce computational burden associated with evaluating sufficient statistics for the likelihood function, an approximate form of parameter updating is given. Also, as a further approximation, the parameters are updated using raingage measurements only, yielding closed-form expressions for estimate and estimation variance in the Gaussian domain.With a reduction in the number of radar rainfall data in constructing covariance matrices, computational requirements for the estimation procedures are not significantly greater than those for simple co-kriging. Given their generality, the estimation procedures constructed in this work are considered to be applicable in various estimation problems involving an undersampled main variable and a densely sampled auxiliary variable.     

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.     

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.     

Conditional simulation of remotely sensed rainfall data using a non-Gaussian v-transformed copula

Quantification of rainfall and its spatial and temporal variability is extremely important for reliable hydrological and meteorological modeling. While rain gauge measurements do not provide reasonable areal representation of rainfall, remotely sensed precipitation estimates offer much higher spatial resolution. However, uncertainties associated with remotely sensed rainfall estimates are not well quantified. This issue is important considering the fact that uncertainties in input rainfall are the main sources of error in hydrologic processes. Using an ensemble of rainfall estimates that resembles multiple realizations of possible true rainfall, one can assess uncertainties associated with remotely sensed rainfall data. In this paper, ensembles are generated by imposing rainfall error fields over remotely sensed rainfall estimates. A non-Gaussian copula-based model is introduced for simulation of rainfall error fields. The v-transformed copula is employed to describe the dependence structure of rainfall error estimates without the influence of the marginal distribution. Simulations using this model can be performed unconditionally or conditioned on ground reference measurements such that rain gauge data are honored at their locations. The presented model is implemented for simulation of rainfall ensembles across the Little Washita watershed, Oklahoma. The results indicate that the model generates rainfall fields with similar spatio-temporal characteristics and stochastic properties to those of observed rainfall data.     

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.     

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.     

A comparative analysis of rain-gauge and radar techniques for storm kinematics

This paper presents a comparative analysis between a rain-gauge and a radar storm tracking technique. The rain-gauge technique is based on simulating the storm motion by visualizing the sequence of the isohyetal patterns obtained using rain-gauge data and the radar technique is based on spatial correlation. The rain-gauge method is using 1-min rainfall data and via mpeg technology can display in 3D the storm motion in an animated form. The storm speed and direction are obtained using the rain-gauge method by tracking the advance of the maximum rainfall intensity in time and space. The radar technique determines the velocity vector by specifying the applied spatial shift that maximizes the correlation between every pair of consecutive radar rainfall grids. The comparison between the two techniques showed very good agreement. Based on the results, the rain-gauge technique can be used for studying the historical storm characteristics with sufficient accuracy and can be implemented as a tool for exploring the storm structure within the microscale which is not covered by the available operational radars.     

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.     

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.     

Quantization analysis of weather radar data with synthetic rainfall

Quantization is a process by where continuous signals are transformed into discrete values. It is an important part of the signal processing involved in using weather radar. Technological advances have made it easier to increase the number of quantization levels, as witnessed by the replacement of a 3 bit system by an 8 bit system by the UK Meteorological Office. Research has been conducted in the past demonstrating the error statistics of quantized rainfall, although these studies have used real radar data. The novelty of this study is in using synthetic rain, generated with a Poisson cluster model to represent hourly rainfall, and subsequently disaggregated using a fractal cascade to a fine 5 min time scale. The advantage of this approach is the length of time series that can be generated far outweighs the limited duration of historical rainfall series, especially at such fine time scales. This provides sufficient rainfall data, especially high intensity rainfall, to say something statistically significant about the error statistics. The models are parameterised for different months and also for a non-seasonal set. Rainfall is then generated for a summer case, a winter case, and for the non-seasonal case. It is discovered that the error distribution varies significantly as the parameters change for 3 bit rainfall. This error distribution is relatively constant for 8 bit data, within its working range (up to 126 mm/h). At a fine time scale, such high intensity events are not uncommon. This knowledge is useful when investigating historical radar data at lower quantization levels, for the purpose of flood frequency analysis, and remains relevant, especially, if as some studies have shown, the occurrence of high intensity storms is likely to increase.     

Probabilistic radar rainfall nowcasts using empirical and theoretical uncertainty models

Weather radar has a potential to provide accurate short‐term (0–3 h) forecasts of rainfall (i.e. radar nowcasts), which are of great importance in warnings and risk management for hydro‐meteorological events. However, radar nowcasts are affected by large uncertainties, which are not only linked to limitations in the forecast method but also because of errors in the radar rainfall measurement. The probabilistic quantitative precipitation nowcasting approach attempts to quantify these uncertainties by delivering the forecasts in a probabilistic form. This study implements two forms of probabilistic quantitative precipitation nowcasting for a hilly area in the south of Manchester, namely, the theoretically based scheme [ensemble rainfall forecasts (ERF)‐TN] and the empirically based scheme (ERF‐EM), and explores which one exhibits higher predictive skill. The ERF‐TN scheme generates ensemble forecasts of rainfall in which each ensemble member is determined by the stochastic realisation of a theoretical noise component. The so‐called ERF‐EM scheme proposed and applied for the first time in this study, aims to use an empirically based error model to measure and quantify the combined effect of all the error sources in the radar rainfall forecasts. The essence of the error model is formulated into an empirical relation between the radar rainfall forecasts and the corresponding ‘ground truth’ represented by the rainfall field from rain gauges measurements. The ensemble members generated by the two schemes have been compared with the rain gauge rainfall. The hit rate and the false alarm rate statistics have been computed and combined into relative operating characteristic curves. The comparison of the performance scores for the two schemes shows that the ERF‐EM achieves better performance than the ERF‐TN at 1‐h lead time. The predictive skills of both schemes are almost identical when the lead time increases to 2 h. In addition, the relation between uncertainty in the radar rainfall forecasts and lead time is also investigated by computing the dispersion of the generated ensemble members. Copyright © 2013 John Wiley & Sons, Ltd.     

Sampling error of areal average rainfall due to radar partial coverage

Areal average rainfall is important as it is used as an input for most rainfall-runoff analysis in Hydrology and Water Resources. Different from traditional methods of using rain gauge data, the use of radar rainfall for the estimation of areal average rainfall is very straightforward. However, in some cases with severe terrain blockages, the value of the incomplete radar information is of serious concern. This study investigated this problem and derived an equation for estimating the error involved in the areal average rainfall due to partial radar coverage of a basin or sub-basin. When only partial radar information is available, the sampling error decreases with increasing radar coverage and the number of radar bin clusters. As an application example, this study considered the Han River Basin with its rainfall observations using the Ganghwa rain radar. Among a total of 24 mid-sized sub-basins in the Han River Basin evaluated, only five sub-basins were fully covered by the radar and three were totally uncovered. The remaining 16 sub-basins were covered partially by radar leading to incomplete radar information. The results show that the sampling error ranged from several % to tens % of standard deviation of the areal average rainfall depending on the relative areal radar coverage.     

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     

Development of an operational rainfall data quality-control scheme based on radar-raingauge co-kriging analysis

Abstract

Automatic raingauge data often serve as an important input to hydrological and weather warning operations. They are not only fundamental in quantitative rainfall analysis, but also act as the ground truth in warning operation and forecast validation. Quality control is required before the data can be used quantitatively due to systematic and random errors. Extremely large random errors and unreasonably small or false zero values can hamper effective monitoring of heavy rain. Yet both are difficult to detect in real-time by objective means. In an attempt to address these problems, a rainfall data quality-control scheme based on radar-raingauge co-kriging analysis was developed. The important threshold values required in the data quality control of 60-min raingauge rainfall were determined from a detailed analysis of the distributions of rainfall residuals defined as the arithmetic difference and the logarithm of the ratio between a raingauge measurement and its co-kriging estimate. The scheme has been developed and is in real-time use in Hong Kong, a coastal city of about 1100 km² area with more than 150 raingauges installed. Geographically, it is located in the subtropics and dominated by heavy convective rainfall in the summer. As a basis of the quality-control scheme, the co-kriging rainfall analysis was shown through a verification exercise to be superior to those obtained by the Barnes analysis and ordinary kriging of raingauge data. The performance of the quality-control algorithm was assessed using selected cases and controlled tests, and was found to be satisfactory, with a high error detection rate for the two targeted types of error. Limitations and operational issues identified during a real-time trial of the quality-control scheme are also discussed.

Citation Yeung, H.Y., Man, C., Chan, S.T., and Seed, A., 2014. Development of an operational rainfall data quality-control scheme based on radar-raingauge co-kriging analysis. Hydrological Sciences Journal, 59 (7), 1285–1299. http://dx.doi.org/10.1080/02626667.2013.839873     

Coupling between weather radar rainfall data and a distributed hydrological model for real-time flood forecasting / Couplage de données pluviométriques issues de radars météorologiques et d’un modèle hydrologique distribué pour la prévision de crue en temps réel

Abstract

Abstract After the destructive flood in 1998, the Chinese government planned to build national weather radar networks and to use radar data for real-time flood forecasting. Hence, coupling of weather radar rainfall data and a hydrological (Xinanjiang) model became an important issue. The present study reports on experience in such coupling at the Shiguanhe watershed. After having corrected the radar reflectivity and the attenuation data, the weather radar rainfall was estimated and then corrected in real time using a Kalman filter. In general, the precipitation estimated from weather radar is reasonably accurate in most of the catchment investigated, after corrections as above. Compared to the results simulated by raingauge data, the simulations based on the weather radar data are of similar accuracy. Present research results show that rainfall estimated from the weather radar, the radar data correction method, the method of coupling, and the Xinanjiang model lend themselves well to application in operational real-time flood forecasting.     

Estimation of tropical cyclone parameters and wind fields from SAR images

The traditional method of Synthetic Aperture Radar(SAR)wind field retrieval is based on an empirical relation between the near surface winds and the normalized radar backscatter cross section to estimate wind speeds,where this relation is called the geophysical model function(GMF).However,the accuracy rapidly decreases due to the impact of rainfall on the measurement of SAR and the saturation of backscattered intensity under the condition of tropical cyclone.Because of no available instrument synchronously monitoring rain rate on the satellite platform of SAR,we have to derive the precipitation of the SAR observation time from non-simultaneous passive microwave observations of rain in combination with geostationary IR images,and then use the model of rain correction to remove the impact of rain on SAR wind field measurements.For the saturation of radar backscatter cross section in high wind speed conditions,we develop an approach to estimate tropical cyclone parameters and wind fields based on the improved Holland model and the SAR image features of tropical cyclone.To retrieve the low-to-moderate wind speed,the wind direction of tropical cyclone is estimated from the SAR image using wavelet analysis.And then the maximum wind speed and the central pressure of tropical cyclone are calculated by a least square minimization of the difference between the improved Holland model and the low-to-moderate wind speed retrieved from SAR.In addition,wind fields are estimated from the improved Holland model using the above-mentioned parameters of tropical cyclone as input.To evaluate the accuracy of our approach,the SAR images of typhoon Aere,typhoon Khanun,and hurricane Ophelia are used to estimate tropical cyclone parameters and wind fields,which are compared with the best track data and reanalyzed wind fields of the Joint Typhoon Warning Center(JTWC)and the Hurricane Research Division(HRD).The results indicate that the tropical cyclone center,maximum wind speed,and central pressure are generally consistent with the best track data,and wind fields agree well with reanalyzed data from HRD.     

Detection of mean-field bias of the radar rain rate using rain gauges available within a small portion of radar umbrella: a case study of the Donghae (East Sea) radar in Korea

Observation of a storm approaching from the ocean to the in-land area is very important for the flood forecasting. Radar is generally used for this purpose. However, as rain gauges are mostly located within the in-land area, detection of the mean-field bias of radar rain rate cannot be easily made. This problem is obviously different from that with evenly-spaced rain gauges over the radar umbrella. This study investigated the detection problem of mean-field bias of radar rain rate when rain gauges are available within a small portion of radar umbrella. To exactly determine the mean-field bias, i.e. the difference between the radar rain rate and the rain gauge rain rate, the variance of the difference between two observations must be small; thus, a sufficient number of observations are indispensable. Therefore, the problem becomes determining the number of rain gauges that will satisfy the given accuracy, that being the variance of the difference between two observations. The dimensionless error variance derived by dividing the expected value of the error variance by the variance of the areal average rain rate was introduced as a criteria to effectively detect the mean field bias. Here, the variance of the areal average rain rate was assumed to be the climatological one and the expectation for the error variance could be changed depending one the sampling characteristics. As an example, this study evaluated the rainfall observation over the East Sea by the Donghae radar. About 6.8 % of the entire radar umbrella covered in-land areas, where the rain gauges were available. It was found that, to limit the dimensionless error variance to 2 %, a total of 26 rain gauges are required for the entire radar umbrella; whereas, a total of 24 rain gauges would be required within the in-land area with available for the rain gauge data.