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Abstract: 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. [Copyright &y& Elsevier]

The estimation of water resources at basin scale requires modelling of all components of the hydrological system. Because of the great uncertainties associated with the estimation of each water cycle component and the large error in budget closure that results, water budget is rarely carried out explicitly. This paper fills the gap in providing a methodology for obtaining it routinely at daily and subdaily time scales. In this study, we use various strategies to improve water budget closure in a small basin of Italian Prealps. The specific objectives are: assessing the predictive performances of different Kriging methods to determine the most accurate precipitation estimates; using MODIS imagery data to assist in the separation of snowfall and rainfall; combining the Priestley-Taylor evapotranspiration model with the Budyko hypothesis to estimate at high resolution (in time and space) actual evapotranspiration (ET); using an appropriate calibration-validation strategy to forecast discharge spatially. For this, 18 years of spatial time series of precipitation, snow water equivalent, rainfall-runoff and ET at hourly time steps are simulated for the Posina River basin (Northeast Italy) using the JGrass-NewAGE system. Among the interpolation methods considered, local detrended kriging is seen to give the best performances in forecasting precipitation distribution. However, detrended Kriging gives better results in simulating discharges. The parameters optimized at the basin outlet over a five-year period show acceptable performances during the validation period at the outlet and at interior points of the basin. The use of the Budyko hypothesis to guide the ET estimation shows encouraging results, with less uncertainty than the values reported in literature. Aggregating at a long temporal scale, the mean annual water budget for the Posina River basin is about 1269 ± 372 mm (76.4%) runoff, 503.5 ± 35.5 mm (30%) evapotranspiration, and − 50 ± 129 mm ( − 4.2%) basin storage from basin precipitation of 1730 ± 344 mm. The highest interannual variability is shown for precipitation, followed by discharge. Evapotranspiration shows less interannual variability and is less dependent on precipitation. [ABSTRACT FROM AUTHOR]

This paper presents novel formulations of Mean field bias (MFB) and local bias (LB) correction schemes that incorporate conditional bias (CB) penalty. These schemes are based on the operational MFB and LB algorithms in the National Weather Service (NWS) Multisensor Precipitation Estimator (MPE). By incorporating CB penalty in the cost function of exponential smoothers, we are able to derive augmented versions of recursive estimators of MFB and LB. Two extended versions of MFB algorithms are presented, one incorporating spatial variation of gauge locations only (MFB-L), and the second integrating both gauge locations and CB penalty (MFB-X). These two MFB schemes and the extended LB scheme (LB-X) are assessed relative to the original MFB and LB algorithms (referred to as MFB-O and LB-O, respectively) through a retrospective experiment over a radar domain in north-central Texas, and through a synthetic experiment over the Mid-Atlantic region. The outcome of the former experiment indicates that introducing the CB penalty to the MFB formulation leads to small, but consistent improvements in bias and CB, while its impacts on hourly correlation and Root Mean Square Error (RMSE) are mixed. Incorporating CB penalty in LB formulation tends to improve the RMSE at high rainfall thresholds, but its impacts on bias are also mixed. The synthetic experiment suggests that beneficial impacts are more conspicuous at low gauge density (9 per 58,000 km 2 ), and tend to diminish at higher gauge density. The improvement at high rainfall intensity is partly an outcome of the conservativeness of the extended LB scheme. This conservativeness arises in part from the more frequent presence of negative eigenvalues in the extended covariance matrix which leads to no, or smaller incremental changes to the smoothed rainfall amounts. [ABSTRACT FROM AUTHOR]

The paper aims to develop researches on the spatial variability of heavy rainfall events estimation using spatial copula analysis. To demonstrate the methodology, short time resolution rainfall time series from Stuttgart region are analyzed. They are constituted by rainfall observations on continuous 30 min time scale recorded over a network composed by 17 raingages for the period July 1989–July 2004. The analysis is performed aggregating the observations from 30 min up to 24 h. Two parametric bivariate extreme copula models, the Husler–Reiss model and the Gumbel model are investigated. Both involve a single parameter to be estimated. Thus, model fitting is operated for every pair of stations for a giving time resolution. A rainfall threshold value representing a fixed rainfall quantile is adopted for model inference. Generalized maximum pseudo-likelihood estimation is adopted with censoring by analogy with methods of univariate estimation combining historical and paleoflood information with systematic data. Only pairs of observations greater than the threshold are assumed as systematic data. Using the estimated copula parameter, a synthetic copula field is randomly generated and helps evaluating model adequacy which is achieved using Kolmogorov Smirnov distance test. In order to assess dependence or independence in the upper tail, the extremal coefficient which characterises the tail of the joint bivariate distribution is adopted. Hence, the extremal coefficient is reported as a function of the interdistance between stations. If it is less than 1.7, stations are interpreted as dependent in the extremes. The analysis of the fitted extremal coefficients with respect to stations inter distance highlights two regimes with different dependence structures: a short spatial extent regime linked to short duration intervals (from 30 min to 6 h) with an extent of about 8 km and a large spatial extent regime related to longer rainfall intervals (from 12 h to 24 h) with an extent of 34 to 38 km. [ABSTRACT FROM AUTHOR]

This paper introduces the Standardized Drought Analysis Toolbox (SDAT) that offers a generalized framework for deriving nonparametric univariate and multivariate standardized indices. Current indicators suffer from deficiencies including temporal inconsistency, and statistical incomparability. Different indicators have varying scales and ranges and their values cannot be compared with each other directly. Most drought indicators rely on a representative parametric probability distribution function that fits the data. However, a parametric distribution function may not fit the data, especially in continental/global scale studies. SDAT is based on a nonparametric framework that can be applied to different climatic variables including precipitation, soil moisture and relative humidity, without having to assume representative parametric distributions. The most attractive feature of the framework is that it leads to statistically consistent drought indicators based on different variables. [ABSTRACT FROM AUTHOR]

Abstract: Defining droughts based on a single variable/index (e.g., precipitation, soil moisture, or runoff) may not be sufficient for reliable risk assessment and decision-making. In this paper, a multivariate, multi-index drought-modeling approach is proposed using the concept of copulas. The proposed model, named Multivariate Standardized Drought Index (MSDI), probabilistically combines the Standardized Precipitation Index (SPI) and the Standardized Soil Moisture Index (SSI) for drought characterization. In other words, MSDI incorporates the meteorological and agricultural drought conditions for overall characterization of drought. In this study, the proposed MSDI is utilized to characterize the drought conditions over several Climate Divisions in California and North Carolina. The MSDI-based drought analyses are then compared with SPI and SSI. The results reveal that MSDI indicates the drought onset and termination based on the combination of SPI and SSI, with onset being dominated by SPI and drought persistence being more similar to SSI behavior. Overall, the proposed MSDI is shown to be a reasonable model for combining multiple indices probabilistically. [Copyright &y& Elsevier]

Determining surface precipitation phase is required to properly correct precipitation gage data for wind effects, to determine the hydrologic response to a precipitation event, and for hydrologic modeling when rain will be treated differently from snow. In this paper we present a comparison of several methods for determining precipitation phase using 12years of hourly precipitation, weather and snow data from a long-term measurement site at Reynolds Mountain East (RME), a headwater catchment within the Reynolds Creek Experimental Watershed (RCEW), in the Owyhee Mountains of Idaho, USA. Methods are based on thresholds of (1) air temperature (Ta ) at 0°C, (2) dual Ta threshold, −1 to 3°C, (3) dewpoint temperature (Td ) at 0°C, and (4) wet bulb temperature (Tw ) at 0°C. The comparison shows that at the RME Grove site, the dual threshold approach predicts too much snow, while Ta , Td and Tw are generally similar predicting equivalent snow volumes over the 12year-period indicating that during storms the cloud level is at or close to the surface at this location. To scale up the evaluation of these methods we evaluate them across a 380m elevation range in RCEW during a large mixed-phase storm event. The event began as snow at all elevations and over the course of 4h transitioned to rain at the lowest through highest elevations. Using 15-minute measurements of precipitation, changes in snow depth (zs ), Ta , Td and Tw , at seven sites through this elevation range, we found precipitation phase linked to the during-storm surface humidity. By measuring humidity along an elevation gradient during the storm we are able to track changes in Td to reliably estimate precipitation phase and effectively track the elevation of the rain/snow transition during the event. [ABSTRACT FROM AUTHOR]

Abstract: The correct identification of homogeneous areas in regional rainfall frequency analysis is fundamental to ensure the best selection of the probability distribution and the regional model which produce low bias and low root mean square error of quantiles estimation. In an attempt at rainfall spatial homogeneity, the paper explores a new approach that is based on meteo-climatic information. The results are verified ex-post using standard homogeneity tests applied to the annual maximum daily rainfall series. The first step of the proposed procedure selects two different types of homogeneous large regions: convective macro-regions, which contain high values of the Convective Available Potential Energy index, normally associated with convective rainfall events, and stratiform macro-regions, which are characterized by low values of the Q vector Divergence index, associated with dynamic instability and stratiform precipitation. These macro-regions are identified using Hot Spot Analysis to emphasize clusters of extreme values of the indexes. In the second step, inside each identified macro-region, homogeneous sub-regions are found using kriging interpolation on the mean direction of the Vertically Integrated Moisture Flux. To check the proposed procedure, two detailed examples of homogeneous sub-regions are examined. [Copyright &y& Elsevier]

Abstract: Hydrological time series increasingly exhibit non-stationarity, e.g., variables such as precipitation and streamflow values do not maintain a consistent mean over long periods, due to natural and anthropogenic changes. Detecting whether such shifts are gradual or abrupt is a growing concern for water resources planning and management. This paper shows that conventional trend and change-point tests do not adequately enable these two types of change to be distinguished. We propose a method for combining the rank correlations of the Mann–Kendall and Pettitt statistics to extract an indicator whose value determines whether a shift observed in a given time series is gradual or abrupt. This method allows the success rate to be independent of the length of record, and it is validated with Monte-Carlo experiments. The limitations caused by the short and noisy nature of hydroclimatic time series are discussed. As an application, the proposed method provides useful insights on changes in hydroclimatic variables in the United States during 1910–2009 using time series from 1217 stations in the United States Hydroclimatic Data Network (USHCN). [Copyright &y& Elsevier]

Abstract: Hydrology requires accurate and reliable rainfall input. Because of the strong spatial and temporal variability of precipitation, estimation of spatially distributed rain rates is challenging. Despite the fact that weather radars provide high-resolution (but indirect) observations of precipitation, they are not used in hydrological applications as extensively as one could expect. The goal of the present review paper is to investigate this question and to provide a clear view of the opportunities (e.g., for flash floods, urban hydrology, rainfall spatial extremes) the limitations (e.g., complicated error structure, need for adjustment) and the challenges for the use of weather radar in hydrology (i.e., validation studies, precipitation forecasting, mountainous precipitation, error propagation in hydrological models). [Copyright &y& Elsevier]

Abstract: This paper considers a class of stochastic point process models, based on doubly stochastic Poisson processes, in the modelling of rainfall. We examine the application of this class of models, a neglected alternative to the widely-known Poisson cluster models, in the analysis of fine time-scale rainfall intensity. These models are mainly used to analyse tipping-bucket raingauge data from a single site but an extension to multiple sites is illustrated which reveals the potential of this class of models to study the temporal and spatial variability of precipitation at fine time-scales. [Copyright &y& Elsevier]

Abstract: Cascades have been used as models of precipitation for nearly 25years yet many basic questions remain unanswered and most applications have been to small or to regional scales. In this paper we revisit some of these issues and present an inter comparison of four global scale data sets each with exceptional characteristics: the hourly (and ≈200km) resolution Climate Prediction Center (CPC) gridded precipitation over the continental US, the three hourly global ECMWF reanalysis stratiform precipitation product at 1.5° resolution, the six hourly Twentieth Century reanalysis at 2° (1871–2008) and an analysis of 5300 orbits (1year) of the Tropical Rainfall Measuring Mission (TRMM) satellite rainfall over ±40° latitude. The data were analysed zonally, meridionally and in time. Each showed cascade structures; in space up to planetary scales and in time up to 5–10days. For each we estimated the moment scaling exponent (K(q)) as well as its characterisation near the mean (C 1) and the effective outer cascade scales. The comparison of the cascade structures in different directions indicate that although anomalies remain, they are relatively isotropic in (horizontal) space–time. For any given direction, the comparison of the different products indicates very similar but not identical scaling properties. In order to be properly inter calibrated at more than a unique resolution, the different products must have the same exponents and outer scales so that - while the similarities are encouraging – the remaining anomalies point to needed improvements in techniques for estimating areal rainfall. Our main conclusion is that the rain rate biases introduced by the measurement techniques are larger than the deviations from perfect log–log linearity (scaling) so that multifractal models will be needed for improving space–time precipitation measurements. Our analyses clarify various fundamental issues. For example, the CPC data show that at “weather” scales smaller than ≈2days in time; H =0.17±0.11 so that rain is apparently not the direct product of a cascade process (which would have H =0). Similarly, for the low frequency weather regime (scales >≈2weeks) we find H ≈−0.42 so that fluctuations tend to decrease rather than increase with scale and display long range statistical dependencies. Finally, we find power law probability tails with exponent q D ≈3 so that the orders of singularity are apparently not bounded, ruling out several model types including microcanonical and log-Poisson models. [Copyright &y& Elsevier]

Abstract: The availability of in situ measurements of precipitation in remote locations is limited. As a result, the use of satellite measurements of precipitation is attractive for water resources management. Combined precipitation products that rely partially or entirely on satellite measurements are becoming increasingly available. However, these products have several weaknesses, for example their failure to capture certain types of precipitation, limited accuracy and limited spatial and temporal resolution. This paper evaluates the usefulness of several commonly used precipitation products over data scarce, complex mountainous terrain from a water resources perspective. Spatially averaged precipitation time series were generated or obtained for 16 sub-basins of the Paute river basin in the Ecuadorian Andes and 13 sub-basins of the Baker river basin in Chilean Patagonia. Precipitation time series were generated using the European Centre for Medium Weather Range Forecasting (ECMWF) 40year reanalysis (ERA-40) and the subsequent ERA-interim products, and the National Centers for Environmental Prediction/National Center for Atmospheric Research reanalysis dataset 1 (NCEP R1) hindcast products, as well as precipitation estimation from Remotely Sensed Information using Artificial Neural Networks (PERSIANN). The Tropical Rainfall Measurement Mission (TRMM) 3B42 is also used for the Ecuadorian Andes. These datasets were compared to both spatially averaged gauged precipitation and river discharge. In general, the time series of the remotely sensed and hindcast products show a low correlation with locally observed precipitation data. Large biases are also observed between the different products. Hydrological verification based on river flows reveals that water balance errors can be extremely high for all evaluated products, including interpolated local data, in basins smaller than 1000km2. The observations are consistent over the two study regions despite very different climatic settings and hydrological processes, which is encouraging for extrapolation to other mountainous regions. [Copyright &y& Elsevier]

Abstract: In regions with saline groundwater, fresh water lenses may develop due to rainwater infiltration. The amount of fresh water that is available for e.g. agricultural crops depends on the thickness of the lens and the extent of mixing between fresh and saline water. In this paper, we consider the mixing of fresh water and upward moving saline ground water in low-lying deltaic areas. The parameters that dominate the flow and transport problem are investigated using dimensionless groups and scaled sensitivities. We characterize the numerically simulated thicknesses of the lens and of the mixing zone by spatial moments. Rayleigh number and mass flux ratio, which is the ratio of the salt water seepage and the precipitation, determine the thickness of the fresh water lens. The local thickness of the mixing zone is mainly influenced by the dispersive/diffusive groups and the mass flux ratio. In addition, convergence of streamlines towards an outflow boundary affects the thickness, particularly in the vicinity of this boundary. Analytical and numerical steady state solutions for lens thickness are compared, taking into account upward seepage, for the two cases with and without a density difference between lens and underlying groundwater. Agreement between the numerical and analytical solutions for the lens thickness is good except when the mass flux ratio becomes small. For zero mass flux ratio, it is implicitly assumed in the analytical solution that salt water is stagnant, and that is unrealistic. Relative contributions of longitudinal and transversal hydrodynamic dispersion and diffusion to the thickness of the mixing zone are quantified numerically for different phases of lens formation. Longitudinal dispersion dominates in the early stages of lens formation, while diffusion and transversal dispersion dominate at steady state. [ABSTRACT FROM AUTHOR]

Abstract: Spatio-temporal estimation of precipitation over a region is essential to the modeling of hydrologic processes for water resources management. The changes of magnitude and space–time heterogeneity of rainfall observations make space–time estimation of precipitation a challenging task. In this paper we propose a Box–Cox transformed hierarchical Bayesian multivariate spatio-temporal interpolation method for the skewed response variable. The proposed method is applied to estimate space–time monthly precipitation in the monsoon periods during 1974–2000, and 27-year monthly average precipitation data are obtained from 51 stations in Pakistan. The results of transformed hierarchical Bayesian multivariate spatio-temporal interpolation are compared to those of non-transformed hierarchical Bayesian interpolation by using cross-validation. The software developed by [11] is used for Bayesian non-stationary multivariate space–time interpolation. It is observed that the transformed hierarchical Bayesian method provides more accuracy than the non-transformed hierarchical Bayesian method. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]

Abstract: The main objective of this paper is to estimate the error in the rainfall derived from a polarimetric X-band radar, by comparison with the corresponding estimate of a rain gauge network. However the present analysis also considers the errors inherent to rain gauge, in particular instrumental and representativeness errors. A special emphasis is addressed to the spatial variability of the rainfall in order to appreciate the representativeness error of the rain gauge with respect to the 1km square average, typical of the radar derived estimate. For this purpose the spatial correlation function of the rainfall is analyzed. The data set consists of 1-year radar data collected by the X-band polarimetric radar HYDRIX®, located in Beauce region (80km south of Paris). All data were processed in real time using the ZPHI® algorithm. A dense 25 rain gauge network provided ground comparison data. The various sources of uncertainties (instrumental and representativeness) are then analyzed and quantified for each sensor. [Copyright &y& Elsevier]

Abstract: Flash-flood warning models can save lives and protect various kinds of infrastructure. In dry climate regions, rainfall is highly variable and can be of high-intensity. Since rain gauge networks in such areas are sparse, rainfall information derived from weather radar systems can provide useful input for flash-flood models. This paper presents a flash-flood warning model which utilizes radar rainfall data and applies it to two catchments that drain into the dry Dead Sea region. Radar-based quantitative precipitation estimates (QPEs) were derived using a rain gauge adjustment approach, either on a daily basis (allowing the adjustment factor to change over time, assuming available real-time gauge data) or using a constant factor value (derived from rain gauge data) over the entire period of the analysis. The QPEs served as input for a continuous hydrological model that represents the main hydrological processes in the region, namely infiltration, flow routing and transmission losses. The infiltration function is applied in a distributed mode while the routing and transmission loss functions are applied in a lumped mode. Model parameters were found by calibration based on the 5 years of data for one of the catchments. Validation was performed for a subsequent 5-year period for the same catchment and then for an entire 10-year record for the second catchment. The probability of detection and false alarm rates for the validation cases were reasonable. Probabilistic flash-flood prediction is presented applying Monte Carlo simulations with an uncertainty range for the QPEs and model parameters. With low probability thresholds, one can maintain more than 70% detection with no more than 30% false alarms. The study demonstrates that a flash-flood warning model is feasible for catchments in the area studied. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]

Abstract: This paper describes a data assimilation method that uses observations of snow covered area (SCA) to update hydrologic model states in a mountainous catchment in Colorado. The assimilation method uses SCA information as part of an ensemble Kalman filter to alter the sub-basin distribution of snow as well as the basin water balance. This method permits an optimal combination of model simulations and observations, as well as propagation of information across model states. Sensitivity experiments are conducted with a fairly simple snowpack/water-balance model to evaluate effects of the data assimilation scheme on simulations of streamflow. The assimilation of SCA information results in minor improvements in the accuracy of streamflow simulations near the end of the snowmelt season. The small effect from SCA assimilation is initially surprising. It can be explained both because a substantial portion of snowmelts before any bare ground is exposed, and because the transition from 100% to 0% snow coverage occurs fairly quickly. Both of these factors are basin-dependent. Satellite SCA information is expected to be most useful in basins where snow cover is ephemeral. The data assimilation strategy presented in this study improved the accuracy of the streamflow simulation, indicating that SCA is a useful source of independent information that can be used as part of an integrated data assimilation strategy. [Copyright &y& Elsevier]

The uncertainty in forecasted precipitation remains a major source of uncertainty in real time flood forecasting. Precipitation uncertainty consists of uncertainty in (i) the magnitude, (ii) temporal distribution, and (iii) spatial distribution of the precipitation. This paper presents a methodology for propagating the precipitation uncertainty through a deterministic rainfall-runoff-routing model for flood forecasting. It uses fuzzy set theory combined with genetic algorithms. The uncertainty due to the unknown temporal distribution of the precipitation is achieved by disaggregation of the precipitation into subperiods. The methodology based on fuzzy set theory is particularly useful where a probabilistic forecast of precipitation is not available. A catchment model of the Klodzko valley (Poland) built with HEC-1 and HEC-HMS was used for the application. The results showed that the output uncertainty due to the uncertain temporal distribution of precipitation can be significantly dominant over the uncertainty due to the uncertain quantity of precipitation. [Copyright &y& Elsevier]