Rainfall distribution function for Libya and rainfall prediction

Abstract

Monthly rainfall amounts are distributed according to different frequency distribution functions in different parts of the world. However, in extremely arid regions gamma probability distribution functions are most often found to fit the existing data well. Libyan monthly rainfall distributions are found to abide by gamma probability distribution function which is confirmed on the basis of chi-square tests. Almost all the rainfall sequences recorded for at least the last 20 years in Libya are investigated statistically and gamma distribution parameters are calculated at existing stations. The shape and scale parameters are then regionalized and hence it becomes possible to find the parameter values at any desired location within the study area and then to generate synthetic sequences according to the gamma distribution. Predictions of 10, 25, 50 and 100 mm rainfall amounts are achieved by this probability function.     

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.     

Comparison of the return period for landslide-triggering rainfall events in Japan based on standardization of the rainfall period

The intensity of rainfall events with potential to cause landslides has varying temporal characteristics. In this study, the time at which the 72-h accumulated rainfall reached its maximum was used to standardize the period of rainfall measurement. The proposed standardization of the rainfall period was used in conjunction with the return level of rainfall intensity, obtained from intensity–duration–frequency curves, to investigate rainfall intensity anomalies associated with 10 hazardous rainfall events that triggered numerous landslides at the regional scale in Japan. These landslides included shallow landslides in volcanic and non-volcanic areas, as well as deep-seated landslides. The rainfall events that triggered the shallow landslides were divided into two types: downpours that repeatedly reached close to the 100-year return level within approximately 3–4 h, and accumulated rainfall that reached close to 200–400 mm over longer time intervals but within 72 h. Lithological differences seemed unrelated to the differences between the two types of shallow-landslide-triggering rainfall; however, precipitation >1000 mm was necessary to trigger deep-seated landslides. Although the characteristics of the hyetographs differed markedly among the landslide-triggering rainfall events, all the landslides could have been triggered when the mean rainfall intensity reached the 100-year rainfall level during the standardized period. Thus, the landslide trigger can be evaluated indirectly based on the increase in the return level of the mean rainfall intensity, which could provide a means for estimating the time of landslide occurrence.     

Predicting rainfall intensity using a genetic algorithm approach

A genetic algorithm rainfall intensity (GARI) model has been developed and used to predict the intensities for given return period. It is a one‐step solution procedure that may not require any mathematical transformation. The problem formulation is given and the genetic algorithm solution of the problem is presented. The results show that the proposed GARI model can be used to solve the rainfall intensity–duration–frequency relations with lowest mean‐squared error between measured and predicted intensities. Predicted intensities are in good agreement between measured and predicted values for given return periods. Copyright © 2006 John Wiley & Sons, Ltd.     

Identification of changes in heavy rainfall events in Ontario,Canada

To assess whether changes in the frequency of heavy rainfall events are occurring over time, annual maximum records from 21 rainfall gauges in Ontario are examined using frequency analysis methods. Relative RMSE and related boxplots are used to characterize assessment for selecting distributions; the Gumbel distribution is verified as one of the most suitable distributions to provide accurate quantile estimates. Records were divided into two time periods, and tested using the Mann-Kendall test and lag-1 autocorrelations to ensure that data in each period are identically distributed. The confidence intervals of design rainfalls for each return period (2, 5, 10, and 25-year) are derived by using resampling method, and compared at 90 % confidence levels. The changes in heavy rainfall intensities are tested at gauges across the Province of Ontario. Several significant decreases in heavy rainfall intensities are identified in central and southern Ontario. Increases in heavy rainfall intensities are identified in gauges at Sioux Lookout and Belleville. The sensitivity analysis of changes identified with respect to the year of splitting indicates changes are occurring during the 1980s and 1990s.     

Trends in the Mediterranean rainfall

Summary The trends appearing in the annual rainfall of the 14 selected coastal and island stations of the Mediterranean were invetigated by running 30-year averages. The periods used as well as the standard deviation, the average variability and the coefficient of variation of the annual rainfall are given for each of the 14 stations. It was found that in the majority of the stations upward and downward trends in the annual rainfall appeared but in a few only stations these trends coincide in the same intervals. A relative similarity appeared in the stations of Marseille-Trieste, Malta-Tunis, Gibraltar-Rome, Nicosia-Limassol and Beyrut-Alexandria. By examination of the three more important maxima and minima in the course of rainfall it was observed that many of them coincide simultaneously at about the same time in the different stations and also that these coincidences occurred near the maximum or minimum of sunspots.     

A multiplier-based method of generating stochastic areal rainfall from point rainfalls

Catchment modelling for water resources assessment is still mainly based on rain gauge measurements as these are more easily available and cover longer periods than radar and satellite-based measurements. Rain gauges however measure the rain falling on an extremely small proportion of the catchment and the areal rainfall obtained from these point measurements are consequently substantially uncertain. These uncertainties in areal rainfall estimation are generally ignored and the need to assess their impact on catchment modelling and water resources assessment is therefore imperative. A method that stochastically generates daily areal rainfall from point rainfall using multiplicative perturbations as a means of dealing with these uncertainties is developed and tested on the Berg catchment in the Western Cape of South Africa. The differences in areal rainfall obtained by alternately omitting some of the rain gauges are used to obtain a population of plausible multiplicative perturbations. Upper bounds on the applicable perturbations are set to prevent the generation of unrealistically large rainfall and to obtain unbiased stochastic rainfall. The perturbations within the set bounds are then fitted into probability density functions to stochastically generate the perturbations to impose on areal rainfall. By using 100 randomly-initialized calibrations of the AWBM catchment model and Sequent Peak Analysis, the effects of incorporating areal rainfall uncertainties on storage-yield-reliability analysis are assessed. Incorporating rainfall uncertainty is found to reduce the required storage by up to 20%. Rainfall uncertainty also increases flow-duration variability considerably and reduces the median flow-duration values by an average of about 20%.     

A Bayesian analysis of the Gumbel distribution: an application to extreme rainfall data

With the objective of modelling annual rainfall maximum intensities in different geographical zones of Chile, we have created a Bayesian inference method for the generalized extreme value type I distribution (Gumbel distribution). We considered an uninformative prior distribution for the location parameter, μ, and three different prior distributions for the scale parameter, σ. Under these conditions we obtained the posterior distribution of (μ, σ) and associated summary statistics such as modes, expected values, quantiles and credibility intervals. In order to predict and estimate return periods, we obtained the posterior distribution of future observations, its expected value, quantiles and credibility intervals. To obtain several of these posterior summary measures it was necessary to utilize both numerical and Laplace approximations. Furthermore we estimate return period curves and intensity–duration–frequency curves.     

Greatest observed one-day point and areal rainfall of India

The greatest one-day rain amounts recorded at individual stations in the country during the last 41-year period from 1940 onwards were examined for all observatories as well as State rain-gauge stations in an attempt to bring out up-to-date information on the greatest recorded point rainfall for the duration of one day. Outstanding one-day point rainfall amounts recorded prior to 1940 were also examined and have been included in this note along with their date and year of occurrence by way of comparison. A generalized chart has been prepared based on the percentage ratios of the greatest one-day rainfall to the mean annual rainfall of about 300 observatory stations distributed uniformly over the entire country. On the basis of Depth-Area-Duration (DAD) analyses of the most severe rainstorms which occurred over different plain areas of the country, it has been found that the 2 July, 1941, rainstorm gave the highest areal rain depths in the country for different areas. Comparison with similar areal rain depths of the tropical USA has shown that rain depths of the July, 1941, rainstorm were higher for all areas excepting the areas of 500 sq. miles (1295 sq. km) and 1000 sq. miles (2590 sq. km).     

WATER MANAGEMENT—A GENERAL REPORT

Abstract

This analysis was undertaken to develop appropriate extreme flood design criteria for a nuclear power plant at Halileh, near Bushehr, Iran, adjacent to the Persian Gulf. Graphical relationships presented provide a convenient means of estimating the probable maximum precipitation and the 2- to 100-year return period rainfall events with durations from 5 min to 24 h. The relationships may be applied for drainage areas up to 25 km². Probable maximum precipitation and 2- to 100-year return period rainfall events were estimated. Precipitation depth-duration relationships were derived.     

Influence of rainfall spatial variability on flood prediction

This paper deals with the sensitivity of distributed hydrological models to different patterns that account for the spatial distribution of rainfall: spatially averaged rainfall or rainfall field. The rainfall data come from a dense network of recording rain gauges that cover approximately 2000 km² around Mexico City. The reference rain sample accounts for the 50 most significant events, whose mean duration is about 10 h and maximal point depth 170 mm. Three models were tested using different runoff production models: storm-runoff coefficient, complete or partial interception. These models were then applied to four fictitious homogeneous basins, whose sizes range from 20 to 1500 km². For each test, the sensitivity of the model is expressed as the relative differences between the empirical distribution of the peak flows (and runoff volumes), calculated according to the two patterns of rainfall input: uniform or non-uniform. Differences in flows range from 10 to 80%, depending on the type of runoff production model used, the size of the basin and the return period of the event. The differences are generally moderate for extreme events. In the local context, this means that uniform design rainfall combining point rainfall distribution and the probabilistic concept of the areal reduction factor could be sufficient to estimate major flood probability. Differences are more significant for more frequent events. This can generate problems in calibrating the hydrological model when spatial rainfall localization is not taken into account: a bias in the estimation of parameters makes their physical interpretation difficult and leads to overestimation of extreme flows.     

New estimates of future changes in extreme rainfall across the UK using regional climate model integrations. 2. Future estimates and use in impact studies

Under enhanced greenhouse conditions, climate models suggest an increase in rainfall intensities in the northern Hemisphere. Major flood events in the UK during autumn 2000 and central Europe in August 2002, have focussed attention on the dramatic impacts these changes may have on many sectors of society. In the companion paper [Fowler et al., J. Hydrol. (2004) this issue], we suggested that the HadRM3H model may be used with some confidence to estimate extreme rainfall distributions, showing good predictive skill in estimating statistical properties of extreme rainfall during the baseline period, 1961–1990. In this study, we use results from the future integration of HadRM3H (following the IPCC SRES scenario A2 for 2070–2100) to assess possible changes in extreme rainfall across the UK using two methods: regional frequency analysis and individual grid box analysis. Results indicate that for short duration events (1–2 days), event magnitude at a given return period will increase by 10% across the UK. For longer duration events (5–10 days), event magnitudes at given return periods show large increases in Scotland (up to +30%), with greater relative change at higher return periods (25–50 years). In the rest of the UK, there are small increases in the magnitude of more frequent events (up to +10%) but reductions at higher return periods (up to −20%). These results provide information to alter design storm depths to examine climate change impacts on various structures. The uncertainty bounds of the estimated changes and a ‘scaling’ methodology are additionally detailed. This allows the estimation of changes for the 2020s, 2050s and 2080s, and gives some confidence in the use of these estimates in impact studies.     

Incorporating rainfall intensity into daily rainfall records for simulating runoff and infiltration into soil profiles

Hydrological modelling often implies the use of rainfall data. Its quality and resolution directly affect the accuracy of the simulation results. This study illustrates that a simple approach of incorporating rainfall intensity information in daily rainfall records significantly improves the simulation of surface runoff and rainfall infiltration into soil profiles. The procedure is developed using a frequency analysis on rainfall data of the Royal Meteorological Institute of Belgium, collected with a resolution of 10 min and for a consecutive period of 61 years. The frequency analysis of the data allowed the incorporation of rainfall intensity information into daily rainfall records. To test the effect of this approach the surface runoff and water flow into three different soil types was simulated using the HYDRUS‐1D model for a typical dry, normal and wet year. The simulation results whereby the observed 10‐min rainfall data was used as input were considered as the reference. Comparative analysis revealed that the simulations using the 10 min rainfall data deducted from the incorporation of rainfall intensity into daily rainfall records, deviate a maximum 1·2% from the reference and produce much better results than the Soil Conservation Service (SCS) runoff curve‐number method because rainfall intensity is considered in the procedure presented. The SCS curve‐number method typical overestimates surface runoff during periods of low rainfall intensity (winter) and underestimate runoff during periods of high rainfall intensities (summer). Copyright © 2002 John Wiley & Sons, Ltd.     

Calibration of an oscillating nozzle‐type rainfall simulator

Nozzle‐type rainfall simulators are commonly used in hydrologic and soil erosion research. Simulated rainfall intensity, originating from the nozzle, increases as the distance between the point of measurement and the source is decreased. Hence, rainfall measured using rain gauges would systematically overestimate the rainfall received at the ground level. A simple model was developed to adjust rainfall measured anywhere under the simulator to plot‐wide average rainfall at the ground level. Nozzle height, plot width, gauge diameter and height, and gauge location are required to compute this adjustment factor. Results from 15 runs at different rain intensities and durations, and with different rain gauge layouts, showed that a simple average of measured rain would overestimate the plot‐wide rain by about 20 per cent. Using the adjustment factor to convert measured rainfall for individual gauges before averaging improved the estimate of plot‐wide rainfall considerably. For the 15 runs considered, overall discrepancy between actual and measured rain is reduced to less than 1 per cent with a standard error of 0·97 mm. This model can be easily tested in the ?eld by comparing rainfall depths of different sized gauges. With the adjustment factor they should all give very similar values. Copyright © 2003 John Wiley & Sons, Ltd.     

Spatial mapping of drought in Zambia using regional frequency analysis

Regional frequency analysis based on L-moments was applied to assess the spatial extent of meteorological droughts in tandem with their return periods in Zambia. Weather station monthly rainfall data were screened to form homogeneous sub-regions-, validated by a homogeneity criterion and fitted by a generalized extreme value distribution using goodness-of-fit test statistics. Predictor equations at regional scale for L-moment ratios and mean annual precipitation were developed to generate spatial maps of meteorological drought recurrences. The 80% of normal rainfall level and two thresholds of 60% and 70% were synonymous with moderate and severe droughts, respectively. Droughts were more severe in the south than in the north of Zambia. The return periods for severe and moderate droughts showed an overlapping pattern in their occurrence at many locations, indicating that in certain years droughts can affect the entire country. The extreme south of Zambia is the most prone to drought.     

Non-stationary future return levels for extreme rainfall over Extremadura (southwestern Iberian Peninsula)

Based on a previous study for temperature, a new method for the calculation of non-stationary return levels for extreme rainfall is described and applied to Extremadura, a region of southwestern Spain, using the peaks-over-threshold approach. Both all-days and rainy-days-only datasets were considered and the 20-year return levels expected in 2020 were estimated taking different trends into account: first, for all days, considering a time-dependent threshold and the trend in the scale parameter of the generalized Pareto distribution; and second, for rainy days only, considering how the mean, variance, and number of rainy days evolve. Generally, the changes in mean, variance and number of rainy days can explain the observed trends in extremes, and their extrapolation gives more robust estimations. The results point to a decrease of future return levels in 2020 for spring and winter, but an increase for autumn.     

Elevation effects on rainfall: A stochastic model

The variation in point precipitation with elevation is investigated using an event-based stochastic model of thunderstorm rainfall and empirical data. Parameters of the model correspond to the number of events per unit of time and the depth of rainfall per event. An increase in precipitation with elevation may be due to an increase in the number of events, in the amount of rainfall per event or to some combination of both possibilities. The distribution of the number of events per season is assumed to be a Poisson variate while the distribution of point rainfall depths may be taken as geometric. The summation of a random number of random variables is used to represent seasonal point precipitation. Assuming that the two parameters of the model increase linearly with elevation, then total seasonal rainfall increases as a quadratic polynomial with elevation. The use of the model allows one to obtain the return period of storm rainfall of a given magnitude despite a short historical record. An independent set of data was used to verify the procedure.     

Tree ring information and rainfall characteristic for landslide in the Kobe District,Japan

Heavy rainfall on the south side of the Rokko Mountains has often caused severe landslides and debris flows. Analysis of the annual summation of rainfall in excess of 100 mm/day shows that the rainfall in this area has dominant periodicities of about 25–30, 10–13, and 5–7 years. The period of about 25–30 years corresponds to that of occurrence of the natural disasters produced by heavy rainfall; years when the maximum rainfall correspond to years when there have been severe landslides and debris flows in the area. Temporal change in this rainfall may provide a first approximation for erosional force. Analyses of tree ring width from these mountains indicate that the sequences have a dominant periodicity of about 25–30 years. Cross-spectral analyses for rainfall and ring width in this area show high coherency for the periods of about 25–30 years; evidence that variations in the ring width may be used as proxy data for erosional force.     

Temporal and spatial variation of annual rainfall on the island of Crete,Greece

Annual rainfall records from the island of Crete in Greece were used with the aid of a geographical information system (GIS) to study the temporal and spatial rainfall characteristics. The GIS was used to produce a digital elevation model, delineate watersheds and estimate the areal rainfall from a network of raingauges by using different interpolation schemes. The rainfall–elevation correlation was significant, suggesting an orographic type of precipitation for the island. The rainfall records for the majority of the stations were found to fit the normal distribution. Deviation from normal for the rest of the records was attributed to the wettest year of 1977–1978. The year 1989–1990 was the driest, and most rainfall records showed a decrease in rainfall over 30 years with higher negative rainfall gradients at the higher elevations. Frequency analysis of the rainfall records was used to estimate areal rainfall for the island of Crete and its main watersheds for return periods of 2, 5 and 10 years. Copyright © 2003 John Wiley & Sons, Ltd.