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.     

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     

Evaluation and comparison of interpolated gauge rainfall data and gridded rainfall data in Florida,USA

A variety of spatially continuous rainfall products are available but little evaluation of their accuracy has been published for areas with high spatial variability in rainfall. Five gridded rainfall products (PRISM, RTMA, and the interpolated Florida Automated Weather Network, FAWN, rainfall layers based on three interpolated methods) were assessed for Florida State. Point-to-pixel and pixel-to-pixel comparisons were performed to compare the five products. On average, the PRISM and RTMA products resulted in a better fit with the daily FAWN rainfall datasets, while FAWN-based interpolated products resulted in a better fit with the monthly FAWN rainfall datasets based on point-to-pixel analysis. Inverse distance weighting and ordinary kriging methods performed slightly better than the thin plate spline method in predicting daily rainfall. In general, monthly and seasonal rainfall amounts from PRISM and RTMA products were higher and lower, respectively, than reference rainfall amounts from FAWN gauge stations and FAWN-based interpolated products.     

Estimation of rainfall distribution for the southwestern region of Saudi Arabia

Abstract

Rainfall is the most important input parameter for water resource planning and hydrological studies because flood risk assessment, rainfall harvesting and runoff estimation depend on the rainfall distribution within a region. Due to practical and economic factors, it is not possible to site rainfall stations everywhere, so representative rainfall stations are sited at specific locations. Rainfall distribution is then estimated from such stations. In this study, rainfall distribution in the southwestern region of Saudi Arabia was estimated using kriging, co-kriging and inverse distance weighted (IDW) methods. Historical records of rainfall from 47 stations for the period 1965–2010 and the altitude of these stations were used. The study shows that co-kriging is a better interpolator than the kriging and IDW methods, with a better correlation between actual and estimated monthly average rainfall for the region.     

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     

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.     

Net rainfall estimation by the inversion of a geomorphology-based transfer function and discharge deconvolution

The assessment of net rainfall, defined as the intermediate hydrological variable linked in between the hillslope and the river network, is a challenge. This paper presents a method for net rainfall estimation, using inverse modelling associated to a geomorphology-based transfer function. The analysis is carried out in semi-arid Tunisia, with a dataset from event discharges in a mesoscale dryland basin. A complete sensitivity analysis is developed, along with a discussion of validity limits for simplifying assumptions and the identification of paths for improvement. This work could be relevant for data-scarce areas, thanks to the use of simple dynamic conceptualization and being based on observable geomorphological features, adjusted to the available data and knowledge.     

Geospatial blending to improve spatial mapping of precipitation with high spatial resolution by merging satellite‐based and ground‐based data

Estimating accurate spatial distribution of precipitation is important for understanding the hydrologic cycle and various hydro‐environmental applications. Satellite‐based precipitation data have been widely used to measure the spatial distribution of precipitation over large extents, but an improvement in accuracy is still needed. In this study, three different merging techniques (Conditional Merging, Geographical Differential Analysis and Geographical Ratio Analysis) were used to merge precipitation estimations from Communication, Ocean and Meteorological Satellite (COMS) Rainfall Intensity data and ground‐based measurements. Merged products were evaluated with varying rain‐gauge network densities and accumulation times. The results confirmed that accuracy of detecting quantitative rainfall was improved as the accumulation time and network density increased. Also, the impact of spatial heterogeneity of precipitation on the merged estimates was investigated. Our merging techniques reproduced accurate spatial distribution of rainfall by adopting the advantages of both gauge and COMS estimates. The efficacy of the merging techniques was particularly pronounced when the spatial heterogeneity of hourly rainfall, quantified by variance of rainfall, was greater than 10 mm²/accumulation time². Among the techniques analysed, Conditional Merging performed the best, especially when the gauge density was low. This study demonstrates the utility of the COMS Rainfall Intensity product, which has a shorter latency time (1 h) and higher spatio‐temporal resolution (hourly, 4 km by 4 km) than other widely used satellite precipitation products in estimating precipitation using merging techniques with ground‐based point measurements. The outcome has important implications for various hydrologic modelling approaches, especially for producing near real‐time products. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

Spatial downscaling of TRMM precipitation data based on the orographical effect and meteorological conditions in a mountainous area

The lack of high resolution precipitation data has posed great challenges to the study and management of extreme rainfall events. Satellite-based rainfall products with large areal coverage provide a potential alternative source of data where in situ measurements are not available. However, the mismatch in scale between these products and model requirements has limited their application and demonstrates that satellite data must be downscaled before being used. This study developed a statistical spatial downscaling scheme based on the relationships between precipitation and related environmental factors such as local topography and pre-storm meteorological conditions. The method was applied to disaggregate the Tropical Rainfall Measuring Mission (TRMM) 3B42 products, which have a resolution of 0.25° × 0.25°, to 1 × 1 km gridded rainfall fields. The TRMM datasets in accord with six rainstorm events in the Xiao River basin were used to validate the effectiveness of this approach. The downscaled precipitation data were compared with ground observations and exhibited good agreement with r² values ranging from 0.612 to 0.838. In addition, the proposed approach provided better results than the conventional spline and kriging interpolation methods, indicating its promise in the management of extreme rainfall events. The uncertainties in the final results and the implications for further study were discussed, and the needs for additional rigorous investigations of the rainfall physical process prior to institutionalizing the use of satellite data were highlighted.     

Spatial,inter and intra‐annual variability of the Upper Blue Nile Basin rainfall

In this study, monthly and annual Upper Blue Nile Basin rainfall data were analyzed to learn the rainfall statistics and its temporal and spatial distribution. Frequency analysis and spatial characterization of rainfall in the Upper Blue Nile Basin are presented. Frequency analysis was performed on monthly basin rainfall. Monthly basin average rainfall data were computed from a network of 32 gauges with varying lengths of records. Monthly rainfall probability distribution varies from month to month fitting Gamma‐2, Normal, Weibull and Log‐Normal distributions. The January, July, October and November basin rainfall fit the Gamma‐2 probability distribution. The February, June and December ones fit Weibull distribution. The March, April, May and August rainfall fit Normal distribution. The September rainfall fits Log‐Normal distribution. Upper Blue Nile Basin is relatively wet with a mean annual rainfall of 1423 mm (1960–2002) with a standard deviation of 125 mm. The annual rainfall has a Normal probability distribution. The 100‐year‐drought basin annual rainfall is 1132 mm and the 100‐year‐wet basin annual rainfall is 1745 mm. The dry season is from November through April. The wet season runs from June through September with 74% of the annual rainfall. October and May are transition months. Monthly and annual rainfalls for return periods 2‐, 5‐, 10‐, 25‐, 50‐ and 100‐year dry and wet patterns are presented. Spatial distribution of annual rainfall over the basin is mapped and shows high variation with the southern tip receiving as high as 2049 mm and the northeastern tip as low as 794 mm annual average rainfall. Copyright © 2009 John Wiley & Sons, Ltd.     

Assessment of regional estimation error by canonical residual kriging

Various regional flood frequency analysis procedures are used in hydrology to estimate hydrological variables at ungauged or partially gauged sites. Relatively few studies have been conducted to evaluate the accuracy of these procedures and estimate the error induced in regional flood frequency estimation models. The objective of this paper is to assess the overall error induced in the residual kriging (RK) regional flood frequency estimation model. The two main error sources in specific flood quantile estimation using RK are the error induced in the quantiles local estimation procedure and the error resulting from the regional quantile estimation process. Therefore, for an overall error assessment, the corresponding errors associated with these two steps must be quantified. Results show that the main source of error in RK is the error induced into the regional quantile estimation method. Results also indicate that the accuracy of the regional estimates increases with decreasing return periods. Copyright © 2010 John Wiley & Sons, Ltd.     

Seasonal evaluation of rainfall estimation by four cumulus parameterization schemes and their sensitivity analysis

Sustainable water resources management require scientifically sound information on precipitation, as it plays a key role in hydrological responses in a catchment. In recent years, mesoscale weather models in conjunction with hydrological models have gained great attention as they can provide high‐resolution downscaled weather variables. Many cumulus parameterization schemes (CPSs) have been developed and incorporated into three‐dimensional Pennsylvania State University/National Center for Atmospheric Research (PSU/NCAR) mesoscale model 5 (MM5). This study has performed a comprehensive evaluation of four CPSs (the Anthes–Kuo, Grell, Betts–Miller and Kain–Fritsch93 schemes) to identify how their inclusion influences the mesoscale model's precipitation estimation capabilities. The study has also compared these four CPSs in terms of variability in rainfall estimation at various horizontal and vertical levels. For this purpose, the MM5 was nested down to resolution of 81 km for Domain 1 (domain span 21 × 81 km) and 3 km for Domain 4 (domain span 16 × 3 km), respectively, with vertical resolutions at 23, 40 and 53 vertical levels. The study was carried out at the Brue catchment in Southwest England using both the ERA‐40 reanalysis data and the land‐based observation data. The performances of four CPs were evaluated in terms of their ability to simulate the amount of cumulative rainfall in 4 months in 1995 representing the four seasonal months, namely, January (winter), March (spring), July (summer) and October (autumn). It is observed that the Anthes–Kuo scheme has produced inferior precipitation values during spring and autumn seasons while simulations during winter and summer were consistently good. The Betts–Miller scheme has produced some reasonable results, particularly at the small‐scale domain (3 km grid size) during winter and summer. The KF2 scheme was the best scheme for the larger‐scale (81 km grid size) domain during winter season at both 23 and 53 vertical levels. This scheme tended to underestimate rainfall for other seasons including the small‐scale domain (3 km grid size) in the mesoscale. The Grell scheme was the best scheme in simulating rainfall rates, and was found to be superior to other three schemes with consistently better results in all four seasons and in different domain scales. Copyright © 2011 John Wiley & Sons, Ltd.     

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.     

Spatial modelling of rainfall trends using satellite datasets and geographic information system

This study developed a standard methodology for identifying spatial trends using satellite-based raster datasets. It involves the novelty of exploring the capabilities of a geographic information system in implementing the procedures of three trend tests, the Spearman rank order correlation (SROC) test, the Kendall rank correlation (KRC) test and the Mann-Kendall (MK) test, on raster datasets of the Tropical Rainfall Measuring Mission at 0.25° × 0.25° resolution. Comparative evaluation of the three tests revealed fair agreement of a major part of the test results for pre-, post- and non-monsoon and one-day maximum rainfall. Also, similar results from KRC and MK tests were obtained over a considerable area for annual, monsoon and monthly maximum rainfall. These findings suggest the importance of selecting the appropriate test depending on rainfall magnitudes at the chosen time scale and emphasize the robustness of the KRC and MK tests.     

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.     

Spatial distribution and temporal trends of rainfall and erosivity in the Eastern Africa region

Soil erosion by water is one of the main environmental concerns in the drought‐prone Eastern Africa region. Understanding factors such as rainfall and erosivity is therefore of utmost importance for soil erosion risk assessment and soil and water conservation planning. In this study, we evaluated the spatial distribution and temporal trends of rainfall and erosivity for the Eastern Africa region during the period 1981–2016. The precipitation concentration index, seasonality index, and modified Fournier index have been analysed using 5 × 5‐km resolution multisource rainfall product (Climate Hazards Group InfraRed Precipitation with Stations). The mean annual rainfall of the region was 810 mm ranging from less than 300 mm in the lowland areas to over 1,200 mm in the highlands being influenced by orography of the Eastern Africa region. The precipitation concentration index and seasonality index revealed a spatial pattern of rainfall seasonality dependent on latitude, with a more pronounced seasonality as we go far from the equator. The modified Fournier index showed high spatial variability with about 55% of the region subject to high to very high rainfall erosivity. The mean annual R‐factor in the study region was calculated at 3,246 ± 1,895 MJ mm ha^?1 h^?1 yr^?1, implying a potentially high water erosion risk in the region. Moreover, both increasing and decreasing trends of annual rainfall and erosivity were observed but spatial variability of these trends was high. This study offers useful information for better soil erosion prediction as well as can support policy development to achieve sustainable regional environmental planning and management of soil and water resources.     

基于测井、VSP和地面地震数据最佳拟合的子波估计(英文)

本文提出了基于测井、VSP和地震数据拟合的子波估计方法,从输入输出都包含随机噪声的统计模型出发,采用相关性拟合技术来提取子波。拟合度和误差分析为整个过程提供了定量的质量控制手段,可以评估数据拟合和子波估计的可靠性。实际数据试算表明,该方法在含有噪声的实际数据中稳定而有效,在地震频带内的子波估计和数据拟合是可靠的。该方法无需对子波相位和振幅谱进行任何假设,其主要优点在于确定相位的能力。