Modelling bivariate rainfall distribution and generating bivariate correlated rainfall data in neighbouring meteorological subdivisions using copula

The rainfall patterns of neighbouring meteorological subdivisions of India are similar because of similar climatological and geographical characteristics. Analysing the rainfall pattern separately for these meteorological subdivisions may not always capture the correlation and tail dependence. Furthermore, generating the multivariate rainfall data separately may not preserve the correlation. In this study, copula method is used to derive the bivariate distribution of monsoon rainfall in neighbouring meteorological subdivisions. Different Archimedean copulas are used for this purpose and the best copula is selected based on nonparametric test and tail dependence coefficient. The fitted copula is then applied to derive the bivariate distribution, joint return period and conditional distribution. Bivariate rainfall data is generated with the fitted copula and it is observed with the increase of sample size, the generated data is able to capture the correlation as well as tail dependence. The methodology is demonstrated with the case study of two neighbouring meteorological subdivisions of North‐East India: Assam and Meghalaya meteorological subdivision and Nagaland, Manipur, Mizoram and Tripura meteorological subdivision. Copyright © 2010 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.     

Analyses of the warm season rainfall climatology of the northeastern US using regional climate model simulations and radar rainfall fields

We examine the warm season (April-September) rainfall climatology of the northeastern US through analyses of high-resolution radar rainfall fields from the Hydro-NEXRAD system and regional climate model simulations using the weather research and forecasting (WRF) model. Analyses center on the 5-year period from 2003 to 2007 and the study area includes the New York-New Jersey metropolitan region covered by radar rainfall fields from the Fort Dix, NJ WSR-88D. The objective of this study is to develop and test tools for examining rainfall climatology, with a special focus on heavy rainfall. An additional emphasis is on rainfall climatology in regions of complex terrain, like the northeastern US, which is characterized by land-water boundaries, large heterogeneity in land use and cover, and mountainous terrain in the western portion of the region. We develop a 5-year record of warm season radar rainfall fields for the study region using the Hydro-NEXRAD system. We perform regional downscaling simulations for the 5-year study period using the WRF model. Radar rainfall fields are used to characterize the interannual, seasonal and diurnal variation of rainfall over the study region and to examine spatial heterogeneity of rainfall. Regional climate model simulations are characterized by a wet bias in the rainfall fields, with the largest bias in the high-elevation regions of the model domain. We show that model simulations capture broad features of the interannual, seasonal, and diurnal variation of rainfall. Model simulations do not capture spatial gradients in radar rainfall fields around the New York metropolitan region and land-water boundaries to the east. The model climatology of convective available potential energy (CAPE) is used to interpret the regional distribution of warm season rainfall and the seasonal and diurnal variability of rainfall. We use hydrologic and meteorological observations from July 2007 to examine the interactions of land surface processes and rainfall from a regional perspective.     

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.     

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.     

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

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

Spatial rainfall model using a pattern classifier for estimating missing daily rainfall data

Missing data in daily rainfall records are very common in water engineering practice. However, they must be replaced by proper estimates to be reliably used in hydrologic models. Presented herein is an effort to develop a new spatial daily rainfall model that is specifically intended to fill in gaps in a daily rainfall dataset. The proposed model is different from a convectional daily rainfall generation scheme in that it takes advantage of concurrent measurements at the nearby sites to increase the accuracy of estimation. The model is based on a two-step approach to handle the occurrence and the amount of daily rainfalls separately. This study tested four neural network classifiers for a rainfall occurrence processor, and two regression techniques for a rainfall amount processor. The test results revealed that a probabilistic neural network approach is preferred for determining the occurrence of daily rainfalls, and a stepwise regression with a log-transformation is recommended for estimating daily rainfall amounts.     

Quantifying climate internal variability using an hourly ensemble generator over South Korea

Identifying climate internal variability (CIV) generated by non-linear interactions and feedbacks among many components of the climate system is essential and challenging because of its irreducible and unpredictable characteristics. A range of studies have addressed this issue; however, these studies focused on the first order moments of few representative climate variables at relatively larger spatial and temporal scales. To investigate the magnitude and the spatial pattern of CIV relevant at finer spatial (point) and temporal (hourly) scales, CIV is assessed over a 30-year period in South Korea by analyzing 100-member ensemble generated using an hourly weather generator and a bootstrapping approach. Statistics addressing the first and second order moments, occurrences, and extremes are successfully verified at various temporal scales. The CIV is then estimated by the ‘detrended’ and ‘differenced’ methods for the four metrics proposed at different scales that signify rainfall volume, maxima, and occurrence. Consequently, the implications of this study are the following: (1) the estimation of CIV using bootstrapped ensembles often fails to represent the proper uncertainty range, resulting in high chances of underestimating extreme statistics, such as the maximum rainfall depth; (2) regardless of which of the two methods is used, no significant difference in the CIV estimation is observed; and (3) a temporal scale-dependency is observed for the proposed metrics used to identify the magnitude and the seasonal pattern of the CIV—the utility of an hourly time series and its associated extreme properties deserves significant attention. Ultimately, the spatial mapping and grouping of CIV will provide valuable information to identify which regions have high variability compared to climatological norms and thus are more vulnerable to extremes, and will serve as a guide for planning adaptation and mitigation measures against future extreme events.     

Forecasting flash floods using data-based mechanistic models and NORA radar rainfall forecasts

Abstract

Data-based mechanistic (DBM) models can offer a parsimonious representation of catchment dynamics. They have been shown to provide reliable accurate flood forecasts in many hydrological situations. In this work, the DBM methodology is applied to forecast flash floods in a small Alpine catchment. Compared to previous DBM modelling studies, the catchment response is rapid. The use of novel radar-derived ensemble quantitative precipitation forecasts based on analogues to drive the DBM model allows the forecast horizon to be increased to a level useful for emergency response. The characterization of the predictive uncertainty in the resulting hydrological forecasts is discussed and a framework for its representation illustrated.

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

Structural damage detection using empirical-mode decomposition and vector autoregressive moving average model

A method based on empirical-mode decomposition (EMD) and vector autoregressive moving average (VARMA) model is proposed for structural damage detection. The basic idea of the method is that the structural damages can be identified as the abrupt changes in energy distribution of structural responses at high frequencies. Using the time-varying VARMA model to represent the intrinsic mode functions (IMFs) obtained from the EMD of vibration signal, we define a damage index according to the VARMA coefficients. In the two examples given, the Imperial County Services Building and the Van Nuys hotel are used as the benchmark structures to verify the effectiveness and sensitivity of the damage index in real environments with the presence of actual noise. The analysis results show that the damage index can indicate the occurrence and relative severity of structural damages at multiple locations in an efficient manner. The damage index can also be potentially used for structural health monitoring, since it is based on the time-varying VARMA coefficients. Finally, some recommendations for future research are provided.     

A multivariate Bernstein copula model for permeability stochastic simulation

This paper introduces a general nonparametric method for joint stochastic simulation of petrophysical properties using the Bernstein copula. This method consists basically in generating stochastic simulations of a given petrophysical property (primary variable) modeling the underlying empirical dependence with other petrophysical properties (secondary variables) while reproducing the spatial dependence of the first one.This multivariate approach provides a very flexible tool to model the complex dependence relationships of petrophysical properties. It has several advantages over other traditional methods, since it is not restricted to the case of linear dependence among variables, it does not require the assumption of normality and/or existence of moments.In this paper this method is applied to simulate rock permeability using Vugular Porosity and Shear Wave Velocity (S-Waves) as covariates in a carbonate double-porosity formation at well log scale. Simulated permeability values show a high degree of accuracy compared to the actual values.     

Comparing threshold definition techniques for rainfall‐induced landslides: A national assessment using radar rainfall

Translational landslides and debris flows are often initiated during intense or prolonged rainfall. Empirical thresholds aim to classify the rain conditions that are commonly associated with landslide occurrence and therefore improve understating of these hazards and predictive ability. Objective techniques that are used to determine these thresholds are likely to be affected by the length of the rain record used, yet this is not routinely considered. Moreover, remotely sensed spatially continuous rainfall observations are under‐exploited. This study compares and evaluates the effect of rain record length on two objective threshold selection techniques in a national assessment of Scotland using weather radar data. Thresholds selected by ‘threat score’ are sensitive to rain record length whereas, in a first application to landslides, ‘optimal point’ (OP) thresholds prove relatively consistent. OP thresholds increase landslide detection and may therefore be applicable in early‐warning systems. Thresholds combining 1‐ and 12‐day antecedence variables best distinguish landslide initiation conditions and indicate that Scottish landslides may be initiated by lower rain accumulation and intensities than previously thought. © 2017 The Authors. Earth Surface Processes and Landforms published by John Wiley & Sons Ltd.     

Assessing spatially dependent errors in radar rainfall estimates for rainfall-runoff simulation

Weather radar been widely employed to measure precipitation and to predict flood risks. However, it is still not considered accurate enough because of radar errors. Most previous studies have focused primarily on removing errors from the radar data. Therefore, in the current study, we examined the effects of radar rainfall errors on rainfall-runoff simulation using the spatial error model (SEM). SEM was used to synthetically generate random or cross-correlated errors. A number of events were generated to investigate the effect of spatially dependent errors in radar rainfall estimates on runoff simulation. For runoff simulation, the Nam River basin in South Korea was used with the distributed rainfall-runoff model, Vflo?. The results indicated that spatially dependent errors caused much higher variations in peak discharge than independent random errors. To further investigate the effect of the magnitude of cross-correlation among radar errors, different magnitudes of spatial cross-correlations were employed during the rainfall-runoff simulation. The results demonstrated that a stronger correlation led to a higher variation in peak discharge up to the observed correlation structure while a correlation stronger than the observed case resulted in lower variability in peak discharge. We concluded that the error structure in radar rainfall estimates significantly affects predictions of the runoff peak. Therefore, efforts to not only remove the radar rainfall errors, but to also weaken the cross-correlation structure of the errors need to be taken to forecast flood events accurately.     

Seasonal copula models for the analysis of glacier discharge at King George Island,Antarctica

Modelling glacier discharge is an important issue in hydrology and climate research. Glaciers represent a fundamental water resource when melting of ice and snow contributes to runoff. Glaciers are also studied as natural global warming sensors. GLACKMA association has implemented one of their Pilot Experimental Catchment areas at the King George Island in the Antarctica which records values of the liquid discharge from Collins glacier. In this paper, we propose the use of time-varying copula models for analyzing the relationship between air temperature and glacier discharge, which is clearly non constant and non linear through time. A seasonal copula model is defined where both the marginal and copula parameters vary periodically along time following a seasonal dynamic. Full Bayesian inference is performed such that the marginal and copula parameters are estimated in a one single step, in contrast with the usual two-step approach. Bayesian prediction and model selection is also carried out for the proposed model such that Bayesian credible intervals can be obtained for the conditional glacier discharge given a value of the temperature at any given time point. The proposed methodology is illustrated using the GLACKMA real data where there is, in addition, a hydrological year of missing discharge data which were not possible to measure accurately due to problems in the sounding.     

A simple model for spatial rainfall fields

Spatial rainfall amounts accumulated over short to medium periods of time, say a few days, tend to have a probabilistic structure with very distinctive features. Some of these that are specially relevant for the purpose of spatial modeling are the presence of mixed sampling distributions, right skewed distributions conditional on rainfall occurrence, and a complex spatial association structure. The goal of this work is to construct a family for the bivariate distributions of spatial rainfall fields that incorporates these distinctive features. It is based on the separate modeling of spatial occurrence of rainfall and the spatial distribution of positive rainfalls. The main properties of the bivariate distributions are derived, and some properties of the random field realizations are illustrated through simulation. Some limitations of the proposed model are also discussed.     

Assimilating Doppler radar observations with an ensemble Kalman filter for convection-permitting prediction of convective development in a heavy rainfall event during the pre-summer rainy season of South China

This study examines the effectiveness of an ensemble Kalman filter based on the weather research and forecasting model to assimilate Doppler-radar radial-velocity observations for convection-permitting prediction of convection evolution in a high-impact heavy-rainfall event over coastal areas of South China during the pre-summer rainy season. An ensemble of 40 deterministic forecast experiments(40 DADF) with data assimilation(DA) is conducted, in which the DA starts at the same time but lasts for different time spans(up to 2 h) and with different time intervals of 6, 12, 24, and 30 min. The reference experiment is conducted without DA(NODA).To show more clearly the impact of radar DA on mesoscale convective system(MCS)forecasts, two sets of 60-member ensemble experiments(NODA EF and exp37 EF) are performed using the same 60-member perturbed-ensemble initial fields but with the radar DA being conducted every 6 min in the exp37 EF experiments from 0200 to0400 BST. It is found that the DA experiments generally improve the convection prediction. The 40 DADF experiments can forecast a heavy-rain-producing MCS over land and an MCS over the ocean with high probability, despite slight displacement errors. The exp37 EF improves the probability forecast of inland and offshore MCSs more than does NODA EF. Compared with the experiments using the longer DA time intervals, assimilating the radial-velocity observations at 6-min intervals tends to produce better forecasts. The experiment with the longest DA time span and shortest time interval shows the best performance.However, a shorter DA time interval(e.g., 12 min) or a longer DA time span does not always help. The experiment with the shortest DA time interval and maximum DA window shows the best performance, as it corrects errors in the simulated convection evolution over both the inland and offshore areas. An improved representation of the initial state leads to dynamic and thermodynamic conditions that are more conducive to earlier initiation of the inland MCS and longer maintenance of the offshore MCS.     

Spatial reconstruction of rainfall fields from rain gauge and radar data

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