Significance of AIC differences for precipitation intensity distributions

Chain dependent models for daily precipitation typically model the occurrence process as a Markov chain and the precipitation intensity process using one of several probability distributions. It has been argued that the mixed exponential distribution is a superior model for the rainfall intensity process, since the value of its information criterion (Akaike information criterion or Bayesian information criterion) when fit to precipitation data is usually less than the more commonly used gamma distribution. The differences between the criterion values of the best and lesser models are generally small relative to the magnitude of the criterion value, which raises the question of whether these differences are statistically significant. Using a likelihood ratio statistic and nesting the gamma and mixed exponential distributions in a parent distribution, we show indirectly that generally the superiority of the mixed exponential distribution over the gamma distribution for modeling precipitation intensity is statistically significant. Comparisons are also made with a common-a gamma model, which are less informative.     

Estimation and spatial interpolation of rainfall intensity distribution from the effective rate of precipitation

Great emphasis is being placed on the use of rainfall intensity data at short time intervals to accurately model the dynamics of modern cropping systems, runoff, erosion and pollutant transport. However, rainfall data are often readily available at more aggregated level of time scale and measurements of rainfall intensity at higher resolution are available only at limited stations. A distribution approach is a good compromise between fine-scale (e.g. sub-daily) models and coarse-scale (e.g. daily) rainfall data, because the use of rainfall intensity distribution could substantially improve hydrological models. In the distribution approach, the cumulative distribution function of rainfall intensity is employed to represent the effect of the within-day temporal variability of rainfall and a disaggregation model (i.e. a model disaggregates time series into sets of higher solution) is used to estimate distribution parameters from the daily average effective precipitation. Scaling problems in hydrologic applications often occur at both space and time dimensions and temporal scaling effects on hydrologic responses may exhibit great spatial variability. Transferring disaggregation model parameter values from one station to an arbitrary position is prone to error, thus a satisfactory alternative is to employ spatial interpolation between stations. This study investigates the spatial interpolation of the probability-based disaggregation model. Rainfall intensity observations are represented as a two-parameter lognormal distribution and methods are developed to estimate distribution parameters from either high-resolution rainfall data or coarse-scale precipitation information such as effective intensity rates. Model parameters are spatially interpolated by kriging to obtain the rainfall intensity distribution when only daily totals are available. The method was applied to 56 pluviometer stations in Western Australia. Two goodness-of-fit statistics were used to evaluate the skill—daily and quantile coefficient of efficiency between simulations and observations. Simulations based on cross-validation show that kriging performed better than other two spatial interpolation approaches (B-splines and thin-plate splines).     

Analyse fréquentielle régionale des précipitations journalières maximales annuelles au Québec,Canada / Regional frequency analysis of annual maximum daily precipitation in Quebec,Canada

Abstract

Abstract A complete regional analysis of daily precipitations is carried out in the southern half of the province of Quebec, Canada. The first step of the regional estimation procedure consists of delineating the homogeneous regions within the area of study and testing for homogeneity within each region. The delineation of homogeneous regions is based on using L-moment ratios. A simulation-based testing of statistical homogeneity allows one to verify the inter-site variability. The second step of the procedure deals with the identification of the regional distribution and the estimation of its parameters. The General Extreme Value (GEV) distribution was identified as an appropriate parent distribution. This distribution has already been recommended by several previous research studies for regional frequency analysis of precipitation extremes. The parameters of the GEV distribution are estimated based on the computation of the regional L-CV, L-C_S and the mean of annual maximal daily precipitations. The third step consists of the estimation of precipitation quantiles corresponding to various return periods. The final procedure allows for the estimation of these quantiles at sites where no precipitation information is available. The use of a jack-knife resampling procedure with data from the province of Quebec allows one to demonstrate the robustness and efficiency of the regional estimation procedure. Values of the root mean square error were below 10% for a return period of 20 years, and 20% for a return period of 100 years.     

Extreme value statistics for annual minimum and trough-under-threshold precipitation at different spatio-temporal scales

Abstract

The aim of this paper is to quantify meteorological droughts and assign return periods to these droughts. Moreover, the relation between meteorological and hydrological droughts is explored. This has been done for the River Meuse basin in Western Europe at different spatial and temporal scales to enable comparison between different data sources (e.g. stations and climate models). Meteorological drought is assessed in two ways: using annual minimum precipitation amounts as a function of return period, and using troughs under threshold as a function of return period. The Weibull extreme value type 3 distribution has been fitted to both sources of information. Results show that the trough-under-threshold precipitation is larger than the annual minimum precipitation for a specific return period. Annual minimum precipitation values increase with spatial scale, being most pronounced for small temporal scales. The uncertainty in annual minimum point precipitation varies between 68% for the 30-day precipitation with a return period of 100 years, and 8% for the 120-day precipitation with a return period of 10 years. For spatially-averaged values, these numbers are slightly lower. The annual discharge deficit is significantly related to the annual minimum precipitation.

Citation Booij, M. J. & de Wit, M. J. M. (2010) Extreme value statistics for annual minimum and trough-under-threshold precipitation at different spatio-temporal scales. Hydrol. Sci. J. 55(8), 1289–1301.     

Climate change impacts on extreme precipitation of water supply area in Istanbul: use of ensemble climate modelling and geo-statistical downscaling

ABSTRACT

Numerous statistical downscaling models have been applied to impact studies, but none clearly recommended the most appropriate one for a particular application. This study uses the geographically weighted regression (GWR) method, based on local implications from physical geographical variables, to downscale climate change impacts to a small-scale catchment. The ensembles of daily precipitation time series from 15 different regional climate models (RCMs) driven by five different general circulation models (GCMs), obtained through the European Union (EU)-ENSEMBLES project for reference (1960–1990) and future (2071–2100) scenarios are generated for the Omerli catchment, in the east of Istanbul city, Turkey, under scenario A1B climate change projections. Special focus is given to changes in extreme precipitation, since such information is needed to assess the changes in the frequency and intensity of flooding for future climate. The mean daily precipitation from all RCMs is under-represented in the summer, autumn and early winter, but it is overestimated in late winter and spring. The results point to an increase in extreme precipitation in winter, spring and summer, and a decrease in autumn in the future, compared to the current period. The GWR method provides significant modifications (up to 35%) to these changes and agrees on the direction of change from RCMs. The GWR method improves the representation of mean and extreme precipitation compared to RCM outputs and this is more significant, particularly for extreme cases of each season. The return period of extreme events decreases in the future, resulting in higher precipitation depths for a given return period from most of the RCMs. This feature is more significant with downscaling. According to the analysis presented, a new adaption for regulating excessive water under climate change in the Omerli basin may be recommended.     

Extraction of information content from stochastic disaggregation and bias corrected downscaled precipitation variables for crop simulation

We applied a simple statistical downscaling procedure for transforming daily global climate model (GCM) rainfall to the scale of an agricultural experimental station in Katumani, Kenya. The transformation made was two-fold. First, we corrected the rainfall frequency bias of the climate model by truncating its daily rainfall cumulative distribution into the station’s distribution based on a prescribed observed wet-day threshold. Then, we corrected the climate model rainfall intensity bias by mapping its truncated rainfall distribution into the station’s truncated distribution. Further improvements were made to the bias corrected GCM rainfall by linking it with a stochastic disaggregation scheme to correct the time structure problem inherent with daily GCM rainfall. Results of the simple and hybridized GCM downscaled precipitation variables (total, probability of occurrence, intensity and dry spell length) were linked with a crop model for a more objective evaluation of their performance using a non-linear measure based on mutual information based on entropy. This study is useful for the identification of both suitable downscaling technique as well as the effective precipitation variables for forecasting crop yields using GCM’s outputs which can be useful for addressing food security problems beforehand in critical basins around the world.     

Delineation of flood generating processes and their hydrological response

Knowledge about flood generating processes can be beneficial for numerous applications. Especially in the context of climate change impact assessment, daily patterns of meteorological and catchment state conditions leading to flood events (i.e., storylines) may be of value. Here, we propose an approach to identify storylines of flood generation using daily weather and snow cover observations. The approach is tested for and applied to a typical pre‐Alpine catchment in the period between 1961 and 2014. Five precipitation parameters were determined that describe temporal and spatial characteristics of the flood associated precipitation events. The catchment's snow coverage was derived using statistical relationships between a satellite‐derived snow cover climatology and station snow measurements. Moreover, (pre‐) event snow melt sums were estimated using a temperature‐index model. Based on the precipitation and catchment state parameters, 5 storylines were identified with a cluster analysis: These are (a) long duration, low intensity precipitation events with high precipitation depths, (b) long duration precipitation events with high precipitation depths and episodes of high intensities, (c) shorter duration events with high or (d) low precipitation intensity, respectively, and (e) rain‐on‐snow events. The event groups have distinct hydrological characteristics that can largely be explained by the storylines' respective properties. The long duration, high intensity storyline leads to the most adverse hydrological response, namely, a combination of high peak magnitudes, high volumes, and long durations of threshold exceedance. The results show that flood generating processes in mesoscale catchments can be distinguished on the basis of daily meteorological and catchment state parameters and that these process types can explain the hydrological flood properties in a qualitative way. Hydrological simulations of daily resolution can thus be analysed with respect to flood generating processes.     

Climate Variability in NW Spain and its Relationship with Water Balance and Streamflow in a Small Headwater Catchment: Preliminary Results

This paper presents preliminary results from an analysis of hydrological variability of a catchment located in Galicia (NW Spain), with particular focus on the effects of climate variability (temperature and precipitation), using daily streamflow data for the period October 2004 to September 2009. The climate variability has been studied by means of data obtained in a meteorological station on the area. The analysis is based on the examination of statistical parameters, flow duration characteristics, baseflow separation and the relationship between measured streamflow and precipitation. The results show that daily, monthly and annual streamflow are highly variable in this catchment. At seasonal scale about 65% of the water flows in winter (33%) and spring (32%) months, although with significant differences between years. This seasonality essentially relates to distribution and characteristics of precipitation episodes. However, there is not a narrow relationship between precipitation and streamflow, because soil moisture conditions have an important role in the hydrological behaviour of the catchment. The baseflow contribution to total streamflow is quite high, with baseflow index values above 0.69, which is consistent with the characteristics of the study area, such as geology (dominated by schist), soils (Umbrisols and Cambisols), vegetation cover (over 65% forest area) and precipitation characteristics (heavy, long duration and low intensity). The flow duration analysis also reveals that the flow regime is dominated by baseflow, recording high flow peaks during a limited period of the year. The study reveals that the major cause of streamflow variability in this catchment is related to precipitation distribution and soil moisture conditions. The results suggest that the Corbeira stream undergoes a reduction in low streamflows and an increase in the frequency of high flows, hence producing an increase in the risks associated with these changes.     

Bayesian estimation of intensity–duration–frequency curves and of the return period associated to a given rainfall event

Intensity–duration–frequency (IDF) curves are used extensively in engineering to assess the return periods of rainfall events and often steer decisions in urban water structures such as sewers, pipes and retention basins. In the province of Québec, precipitation time series are often short, leading to a considerable uncertainty on the parameters of the probabilistic distributions describing rainfall intensity. In this paper, we apply Bayesian analysis to the estimation of IDF curves. The results show the extent of uncertainties in IDF curves and the ensuing risk of their misinterpretation. This uncertainty is even more problematic when IDF curves are used to estimate the return period of a given event. Indeed, standard methods provide overly large return period estimates, leading to a false sense of security. Comparison of the Bayesian and classical approaches is made using different prior assumptions for the return period and different estimation methods. A new prior distribution is also proposed based on subjective appraisal by witnesses of the extreme character of the event.     

Letters to the Editor

Abstract

This work investigates historical trends of meteorological drought in Taiwan by means of long-term precipitation records. Information on local climate change over the last century is also presented. Monthly and daily precipitation data for roughly 100 years, collected by 22 weather stations, were used as the study database. Meteorological droughts of different levels of severity are represented by the standardized precipitation index (SPI) at a three-monthly time scale. Additionally, change-point detection is used to identify meteorological drought trends in the SPI series. Results of the analysis indicate that the incidence of meteorological drought has decreased in northeastern Taiwan since around 1960, and increased in central and southern Taiwan. Long-term daily precipitation series show an increasing trend for dry days all over Taiwan. Finally, frequency analysis was performed to obtain further information on trends of return periods of drought characteristics.     

Simulated changes due to global warming in the variability of precipitation, and their interpretation using a gamma-distributed stochastic model

The interannual variability of monthly mean January and July precipitation and its possible change due to global warming are assessed using a five-member ensemble of climate for the period 1871–2100, simulated by the CSIRO Mark 2 global coupled atmosphere–ocean model. In the 1961–1990 climate, for much of the middle to high latitudes the standard deviation of precipitation for both months is roughly proportional to the mean, with the coefficient of variation (C) typically 0.3–0.5. The variability there is shown to be largely consistent with that from a first-order Markov chain model of the daily rainfall occurrence, with the distribution of wet-day amounts approximated by a gamma distribution. Global distributions of Mark 2-based parameters of this stochastic model, commonly used in weather generators, are presented. In low latitudes, however, the variability from the coupled model is typically double that anticipated by the stochastic model, as quantified by an ‘overdispersion ratio’. C often exceeds one at subtropical locations, where rain is less frequent, but sometimes relatively heavy.The standard deviation of monthly mean precipitation S generally increases as the global model warms, with the global mean S in 2071–2100 in January (July) being 9.0% (11.5%) larger than in 1961–1990. Decreases in some subtropical locations occur, particularly where mean precipitation decreases. The global pattern of overdispersion is largely unchanged, however, and the changes in S can be related to those in the stochastic model parameters. Much of the increase in S is associated with increases in the scale parameter of the gamma distribution of wet-day amounts. Changes in C, which is unaffected by this parameter, are generally small. Increases in C in several subtropical bands and over northern midlatitude land in July are related to a decreased frequency of precipitation, and (to a lesser degree) changes in the gamma shape parameter. Some potential applications of the results to downscaling are discussed, and illustrated using observed rainfall from southeast Australia.     

Generating surfaces of daily meteorological variables over large regions of complex terrain

A method for generating daily surfaces of temperature, precipitation, humidity, and radiation over large regions of complex terrain is presented. Required inputs include digital elevation data and observations of maximum temperature, minimum temperature and precipitation from ground-based meteorological stations. Our method is based on the spatial convolution of a truncated Gaussian weighting filter with the set of station locations. Sensitivity to the typical heterogeneous distribution of stations in complex terrain is accomplished with an iterative station density algorithm. Spatially and temporally explicit empirical analyses of the relationships of temperature and precipitation to elevation were performed, and the characteristic spatial and temporal scales of these relationships were explored. A daily precipitation occurrence algorithm is introduced, as a precursor to the prediction of daily precipitation amount. Surfaces of humidity (vapor pressure deficit) are generated as a function of the predicted daily minimum temperature and the predicted daily average daylight temperature. Daily surfaces of incident solar radiation are generated as a function of Sun-slope geometry and interpolated diurnal temperature range. The application of these methods is demonstrated over an area of approximately 400 000 detailed illustration of the parameterization process. A cross-validation analysis was performed, comparing predicted and observed daily and annual average values. Mean absolute errors (MAE) for predicted annual average maximum and minimum temperature were 0.7°C and 1.2°C, with biases of +0.1°C and −0.1°C, respectively. MAE for predicted annual total precipitation was 13.4 cm, or, expressed as a percentage of the observed annual totals, 19.3%. The success rate for predictions of daily precipitation occurrence was 83.3%. Particular attention was given to the predicted and observed relationships between precipitation frequency and intensity, and they were shown to be similar. We tested the sensitivity of these methods to prediction grid-point spacing, and found that areal averages were unchanged for grids ranging in spacing from 500 m to 32 km. We tested the dependence of the results on timestep, and found that the temperature prediction algorithms scale perfectly in this respect. Temporal scaling of precipitation predictions was complicated by the daily occurrence predictions, but very nearly the same predictions were obtained at daily and annual timesteps.     

Spatio-temporal analysis of daily,seasonal and annual precipitation concentration in Jharkhand state,India

Nowadays, climate change and global warming have led to changes in the distribution of precipitation, which affect on the availability of water resources. Therefore, investigating the temporal and spatial variations of precipitation in the previous period is highly important in the future planning for flood control and local management of water resources. Considering the importance of this issue, in the present study, the precipitation concentration indices have been used for analysing precipitation changes at daily, seasonal, and annual time scales in the period of 1971 to 2011 over the Jharkhand state, India. Also, Modified Mann–Kendall test has used to study the trend of precipitation concentration indices in annual and seasonal time scales. The result shows a highly irregular and non-uniform distribution in the annual scale. For the seasonal scale an irregular and non-uniform distribution has been also observed, although the summer had a better situation than other seasons. For daily scale, none of the stations had a regular concentration and in the northeast and southern parts of the study area, there have been more irregularities. Furthermore, the results of investigating annual precipitation trend showed a combination of increasing and decreasing trend over the study area. The results of this study can be applied to manage water supplies, drainage projects, construct collection structures of urban flood, develop plans to prevent soil erosion, and designing appropriate plans to cope with drought conditions.     

Frequency analysis of precipitation extremes in Heihe River basin based on generalized Pareto distribution

Precipitation extremes could cause a series of social, environmental and ecological problems. This paper, taking Heihe River basin, the second largest inland river basin in China, as the study area, focused on the frequency analysis of precipitation extremes based on the historical daily precipitation records (1960–2010) at nine stations. Generalized Pareto distribution (GPD) was employed for fitting the peaks over threshold (POT) series, in which Hill plot, percentile method and the average annual occurrence number were used to select the threshold in GPD. Maximum likelihood estimate and L-moment were used to estimate the parameters. The inherent assumptions for POT series were investigated by auto-correlation coefficient, Mann–Kendall test, Spearman’s ρ test, cumulative deviation test and Worsley likelihood ratio test. 10, 20, 50 and 100 year precipitation extremes for Heihe River basin were calculated and analyzed as well. It was found the POT series derived from several methods involved were approximately independent and stationary, and GPD could give a satisfactory fit to the POT series for each station. For the upper and lower reaches, the frequency of precipitation extremes at long return periods (20, 50 year or longer) presented increasing in recent years, and the intensity of the highest precipitation were getting stronger as well. The intensity of the highest precipitation extremes for the lower reach (21 and 35 %) increased higher than those for the upper reach (10 and 11 %). For the middle reach, the frequency of precipitation extremes (over 20 year return level) was not found to be increased. The uneven spatial and temporal distribution of precipitation extremes for the basin especially for the upper and lower reaches were getting more and more serious, which would bring great challenges for the local water allocation and management.     

Model and parameter uncertainty in IDF relationships under climate change

Quantifying distributional behavior of extreme events is crucial in hydrologic designs. Intensity Duration Frequency (IDF) relationships are used extensively in engineering especially in urban hydrology, to obtain return level of extreme rainfall event for a specified return period and duration. Major sources of uncertainty in the IDF relationships are due to insufficient quantity and quality of data leading to parameter uncertainty due to the distribution fitted to the data and uncertainty as a result of using multiple GCMs. It is important to study these uncertainties and propagate them to future for accurate assessment of return levels for future. The objective of this study is to quantify the uncertainties arising from parameters of the distribution fitted to data and the multiple GCM models using Bayesian approach. Posterior distribution of parameters is obtained from Bayes rule and the parameters are transformed to obtain return levels for a specified return period. Markov Chain Monte Carlo (MCMC) method using Metropolis Hastings algorithm is used to obtain the posterior distribution of parameters. Twenty six CMIP5 GCMs along with four RCP scenarios are considered for studying the effects of climate change and to obtain projected IDF relationships for the case study of Bangalore city in India. GCM uncertainty due to the use of multiple GCMs is treated using Reliability Ensemble Averaging (REA) technique along with the parameter uncertainty. Scale invariance theory is employed for obtaining short duration return levels from daily data. It is observed that the uncertainty in short duration rainfall return levels is high when compared to the longer durations. Further it is observed that parameter uncertainty is large compared to the model uncertainty.     

A bivariate gamma distribution for use in multivariate flood frequency analysis

A gamma distribution is one of the most frequently selected distribution types for hydrological frequency analysis. The bivariate gamma distribution with gamma marginals may be useful for analysing multivariate hydrological events. This study investigates the applicability of a bivariate gamma model with five parameters for describing the joint probability behavior of multivariate flood events. The parameters are proposed to be estimated from the marginal distributions by the method of moments. The joint distribution, the conditional distribution, and the associated return periods are derived from marginals. The usefulness of the model is demonstrated by representing the joint probabilistic behaviour between correlated flood peak and flood volume and between correlated flood volume and flood duration in the Madawask River basin in the province of Quebec, Canada. Copyright © 2001 John Wiley & Sons, Ltd.     

Multisite generalization of a daily stochastic precipitation generation model

The familiar chain-dependent-process stochastic model of daily precipitation, consisting of a two-state, first-order Markov chain for occurrences and a mixed exponential distribution for nonzero amounts, is extended to simultaneous simulation at multiple locations by driving a collection of individual models with serially independent but spatially correlated random numbers. The procedure is illustrated for a network of 25 locations in New York state, with interstation separations ranging approximately from 10 to 500 km. The resulting process reasonably reproduces various aspects of the joint distribution of daily precipitation observations at the modeled locations. The mixed exponential distributions, in addition to providing substantially better fits than the more conventional gamma distributions, are convenient for representing the tendency for smaller amounts at locations near the edges of wet areas. Means, variances, and interstation correlations of monthly precipitation totals are also well reproduced. In addition, the use of mixed exponential rather than gamma distributions yields interannual variability in the synthetic series that is much closer to the observed.     

Frequency analysis of climate extreme events in Zanjan, Iran

In this study, generalized extreme value distribution (GEV) and generalized Pareto distribution (GPD) were fitted to the maximum and minimum temperature, maximum wind speed, and maximum precipitation series of Zanjan. Maximum (minimum) daily and absolute annual observations of Zanjan station from 1961 to 2011 were used. The parameters of the distributions were estimated using the maximum likelihood estimation method. Quantiles corresponding to 2, 5, 10, 25, 50, and 100 years return periods were calculated. It was found that both candidate distributions fitted to extreme events series, were statistically reasonable. Most of the observations from 1961 to 2011 were found to fall within 1–10 years return period. Low extremal index (θ) values were found for excess maximum and minimum temperatures over a high threshold, indicating the occurrence of consecutively high peaks. For the purpose of filtering the dependent observations to obtain a set of approximately independent threshold excesses, a declustering method was performed, which separated the excesses into clusters, then the de-clustered peaks were fitted to the GPD. In both models, values of the shape parameters of extreme precipitation and extreme wind speed were close to zero. The shape parameter was less negative in the GPD than the GEV. This leads to significantly lower return period estimates for high extremes with the GPD model.