A cascade approach to continuous rainfall data generation at point locations

High-resolution temporal rainfall data sequences serve as inputs for a range of applications in planning, design and management of small (especially urban) water resources systems, including continuous flow simulation and evaluation of alternate policies for environmental impact assessment. However, such data are often not available, since their measurements are costly and time-consuming. One alternative to obtain high-resolution data is to try to derive them from available low-resolution information through a disaggregation procedure. This study evaluates a random cascade approach for generation of high-resolution rainfall data at a point location. The approach is based on the concept of scaling in rainfall, or, relating the properties associated with the rainfall process at one temporal scale to a finer-resolution scale. The procedure involves two steps: (1) identification of the presence of scaling behavior in the rainfall process; and (2) generation of synthetic data possessing same/similar scaling properties of the observed rainfall data. The scaling identification is made using a statistical moment scaling function, and the log–Poisson distribution is assumed to generate the synthetic rainfall data. The effectiveness of the approach is tested on the rainfall data observed at the Sydney Observatory Hill, Sydney, Australia. Rainfall data corresponding to four different successively doubled resolutions (daily, 12, 6, and 3 h) are studied, and disaggregation of data is attempted only between these successively doubled resolutions. The results indicate the presence of multi-scaling behavior in the rainfall data. The synthetic data generated using the log–Poisson distribution are found to exhibit scaling behaviors that match very well with that for the observed data. However, the results also indicate that fitting the scaling function alone does not necessarily mean reproducing the broader attributes that characterize the data. This observation clearly points out the extreme caution needed in the application of the existing methods for identification of scaling in rainfall, especially since such methods are also prevalent in studies of the emerging satellite observations and thus in the broader spectrum of hydrologic modeling.     

Stochastic simulation of droughts. Part 1: point droughts

The number of drought events derived from the historic streamflow or rainfall series will be limited and produce results that are not very reliable. This study proposes a drought simulation methodology that uses a long sequence of synthetically generated monthly streamflow/rainfall series, from which it is possible to drive a large sample of drought events and the prediction of drought characteristics will be reliable. The modified Herbst method has been used to identify droughts in the generated streamflow and rainfall series. The drought simulation procedure is illustrated with a case study of the Bhadra reservoir catchment in Karnataka State, India. Monthly droughts were derived from both historic and generated monthly streamflow and rainfall series. The important drought characteristics were determined and the suitable probability distribution for each parameter was arrived at after studying seven different probability models. The use of the probability curves thus derived has been illustrated with examples (referred to in Part 1 as ‘point droughts’). Similarly, the development and application of stochastic models for the prediction of regional drought parameters have been illustrated with examples in the accompanying paper (Part 2: regional droughts). Copyright © 2007 John Wiley & Sons, Ltd.     

Application of linear stochastic models for drought forecasting in the Büyük Menderes river basin, western Turkey

In the present study, a seasonal and non-seasonal prediction of the Standardized Precipitation Index (SPI) time series is addressed by means of linear stochastic models. The methodology presented here is to develop adequate linear stochastic models known as autoregressive integrated moving average (ARIMA) and multiplicative seasonal autoregressive integrated moving average (SARIMA) to predict drought in the Büyük Menderes river basin using SPI as drought index. Temporal characteristics of droughts based on SPI as an indicator of drought severity indicate that the basin is affected by severe and more or less prolonged periods of drought from 1975 to 2006. Therefore, drought prediction plays an important role for water resources management. ARIMA modeling approach involves the following three steps: model identification, parameter estimation, diagnostic checking. In model identification step, considering the autocorrelation function (ACF) and partial autocorrelation function (PACF) results of the SPI series, different ARIMA models are identified. The model gives the minimum Akaike Information Criterion (AIC) and Schwarz Bayesian Criterion (SBC) is selected as the best fit model. Parameter estimation step indicates that the estimated model parameters are significantly different from zero. Diagnostic check step is applied to the residuals of the selected ARIMA models and the results indicated that the residuals are independent, normally distributed and homoscedastic. For the model validation purposes, the predicted results using the best ARIMA models are compared to the observed data. The predicted data show reasonably good agreement with the actual data. The ARIMA models developed to predict drought found to give acceptable results up to 2 months ahead. The stochastic models developed for the Büyük Menderes river basin can be employed to predict droughts up to 2 months of lead time with reasonably accuracy.     

A statistical methodology for assessing the long‐term effects of antecedent drought conditions on stream runoff: applications to the Piedmont Province,southeastern United States

A method was developed to investigate the long‐term (months‐to‐years) effects (both magnitude and duration) of antecedent rainfall upon subsequent runoff coefficients (RCs) or runoff/rainfall ratios. The method was applied to a four‐state region (Georgia, South Carolina, North Carolina, and Virginia) within the southeastern Piedmont Province of the United States and incorporated a 59‐year data set of 19 United States Geological Survey stream gages and 57 National Climatic Data Center rain gages. The method was designed to facilitate statistical comparisons [Mann–Whitney rank sum tests] between various groups of normalized runoff coefficients (NRCs) representing 6–36 month periods which differed in terms of antecedent rainfall conditions. The results of this study show that under all subsequent rainfall conditions, with the exception of excess rainfall, a 1‐year period of antecedent drought lowered NRCs for at least 1 year following the drought. The principal finding of this study is that a year‐long drought period within the southeastern Piedmont Province lowers NRCs by ～25% during the following year when rainfall returns to normal. In most cases, RCs are significantly lower during the second year following a drought than they would be when anteceded by normal rainfall; however, the effects of drought wane during this period. This is a statistical and regional method that can be modified to other study areas; however, it cannot be used to predict storm‐event rainfall–runoff relationships for any specific basin. Copyright © 2010 John Wiley & Sons, Ltd.     

Evaluation, modification, and application of the Effective Drought Index to 200-Year drought climatology of Seoul, Korea

In this paper, progressive methods for assessing drought severity from diverse points of view were conceived. To select a fundamental drought index, the performances of the Effective Drought Index (EDI) and 1-, 3-, 6-, 9-, 12-, and 24-month Standardized Precipitation Indices (SPIs) were compared for drought monitoring data accumulated over 200-year period from 1807 to 2006 for Seoul, Korea. The results confirmed that the EDI was more efficient than the SPIs in assessing both short and long-term droughts.We then proposed the following methods for modifying and supplementing the EDI: (1) CEDI, a corrected EDI that considers the rapid runoff of water resources after heavy rainfall; (2) AEDI, an accumulated EDI that considers the drought severity and duration of individual drought events; and (3) YAEDI, a year-accumulated negative EDI representing annual drought severity. In addition to these indices, to more accurately measure and diagnose droughts, we proposed the utilization of (4) the Available Water Resources Index (AWRI), an existing index that expresses the actual amount of available water.Using the improved methods above, we assessed and summarized important droughts that have occurred in Seoul over the 200 years from 1807 to 2006.     

Fractal analysis of rainfall observed in two different climatic regions

Abstract

The importance of high-resolution rainfall data to understand the intricacies of the dynamics of hydrological processes and describe them in a sophisticated and accurate way has been increasingly realized. The present study investigates the general suitability of fractal (or scaling) theory for understanding the rainfall behaviour and transforming rainfall data from one time scale to another. The study, employing a multi-fractal approach, follows the research undertaken earlier by the author (Sivakumar, 2000) employing a mono-fractal approach in which some preliminary indication as to the possibility of existence of (multi-) fractals was obtained. Rainfall data of three different resolutions, six-hourly, daily, and weekly, observed over a period of 25 years in two different climatic regions: a subtropical climatic region (Leaf River basin, Mississippi, USA); and an equatorial climatic region (Singapore) are analysed. The existence of multi-fractal behaviour in the rainfall data is investigated using (a) the power spectrum method; (b) the empirical probability distribution function (PDF) method; (c) the statistical moment scaling method; and (d) the probability distribution multiple scaling (PDMS) method. The results achieved from all these methods for the six different rainfall data sets considered indicate the existence of multi-fractal behaviour of rainfall observed in Leaf River basin and Singapore, providing further support to the results obtained using the mono-fractal approach (Sivakumar, 2000). The suitability of a multi-fractal framework to characterize the behaviour of rainfall observed in the above two significantly different climatic regions, subtropical and equatorial, seems to suggest the general suitability of the fractal theory for transforming rainfall from one time scale to another. Investigations with rainfall data from several other climatic regions are underway with a view to strengthening the above conclusions.     

大气季节内振荡的活动与江淮流域夏季旱涝

观测资料的分析极为清楚地表明,江淮流域的夏季降水有着极为明显的低频变化,周期为30-60d和近20d的振荡是其最基本的特征,尤其是在多雨的年份.对应江淮夏季多雨(涝)年和少雨(旱)年,大气环流的分析表明其大气季节内振荡(IS0)的形势有着显著的差异.例如在多雨(少雨)年,在长江以南的850hPa上为一个低频(IS0)反气旋(气旋)性环流控制,而中国北部和日本一带为气旋(反气旋)性环流,从而在江淮流域形成较强的低频辐合(辐散)气流;在200hPa的青藏高原上却为一个低频气旋(反气旋)性环流所控制.分析还表明,对应多雨年,在江淮流域有明显的由中高讳度向南传播和由低玮度向北传播的大气低频振荡的汇合情况;而对应于少雨年,由中高纬度向南传播的低频系统较不明显,在江淮流域低频系统的汇合也较为不清楚.     

21st Anniversary of the Bulletin

Abstract

The drought event which reached severe levels in 1972 and 1973 caused a major disaster in the Sahalian and sub-Sahalian zones in Africa. This disaster has drawn attention to the need for data surveys and detailed studies for meaningful long-term measures to combat the effects of future droughts.

The study reported in this paper is an attempt to assess the hydrological aspects of the drought event in Nigeria in 1972 and 1973. There exist relatively long and reliable records of rainfall within the drought zone, while records for runoff, water level and groundwater are few and far between. Data available are analysed to determine evidence of trend and persistence (short and long-term). An examination of the rainfall records showed that extreme dry years at all the stations tended to recur at about the same time. The time interval between these extreme dry years was about 30 years. It was also observed from the spectral analysis of the records that most of the spectra for all the stations showed a generally high level of variance at low frequency.

The limited information on runoff and groundwater precludes a detailed statistical analysis from being carried out on the annual series of runoff. However, the runoff data at some stations snowed that the magnitude of runoff in the drought year 1972/1973 was about 22–72 per cent of the average value for the length of record available (about eight years). Moreover, the long-term water-level record of Lake Chad revealed a similar trend for the occurrence of extreme dry years to that observed in the rainfall record.     

Integrating TRMM and MODIS satellite with socio-economic vulnerability for monitoring drought risk over a tropical region of India

Drought is a recurring feature of the climate, responsible for social and economic losses in India. In the present work, attempts were made to estimate the drought hazard and risk using spatial and temporal datasets of Tropical Rainfall Measuring Mission (TRMM) and Moderate Resolution Imaging Spectroradiometer (MODIS) in integration with socio-economic vulnerability. The TRMM rainfall was taken into account for trend analysis and Standardized Precipitation Index (SPI) estimation, with aim to investigate the changes in rainfall and deducing its pattern over the area. The SPI and average rainfall data derived from TRMM were interpolated to obtain the spatial and temporal pattern over the entire South Bihar of India, while the MODIS datasets were used to derive the Normalized Difference Vegetation Index (NDVI) deviation in the area. The Geographical Information System (GIS) is taken into account to integrate the drought vulnerability and hazard, in order to estimate the drought risk over entire South Bihar. The results indicated that approximately 36.90% area is facing high to very high drought risk over north-eastern and western part of South Bihar and need conservation measurements to combat this disaster.     

Multifractal analysis as a tool for validating a rainfall model

A multifractal analysis was carried out in order to validate the simulation of hourly rainfall records of a local climate model for the Iberian Peninsula. Observed and simulated hourly rainfall data from four locations in Andalusia (southern Spain) were used to carry out the study. In order to detect the influence of the length of the data series on the results, two different sizes were used for the real data: 4 years, and 20 years. The results show that algebraic tails are required to fit the probability distribution of extreme rain event sizes, and rain and dry event durations for both kinds of rainfall data. Similar results are found for the extreme rain event sizes and dry event durations fits when the real and synthetic data are considered. Nevertheless, some differences appear in the cases of rain event durations. The detection of the presence of a first‐order multifractal phase transition associated with a critical moment in the empirical moment scaling exponent function and the results of the extreme rain event sizes fits, reveal that real rainfall is a self‐organized criticality (SOC) process. That behaviour is less evident in the simulated rainfall series. The same ‘synoptic maximum’ value was found for each place with both types of rainfall data. A time clustering analysis was carried out applying the count‐based periodogram and the Fano factor methods. Some periodicities have been detected in the periodograms, especially for the longest real rainfall data series. Copyright © 2007 John Wiley & Sons, Ltd.     

Evaluating the performance of climate models in reproducing the hydrological characteristics of rainfall events

ABSTRACT

Rainfall events largely control hydrological processes occurring on and in the ground, but the performance of climate models in reproducing rainfall events has not been investigated enough to guide selection among the models when making hydrological projections. We proposed to compare the durations, intensities, and pause periods, as well as depths of rainfall events when assessing the accuracy of general circulation models (GCMs) in reproducing the hydrological characteristics of observed rainfall. We also compared the sizes of design storm events and the frequency and severity of drought to demonstrate the consequences of GCM selection. The results show that rainfall and extreme hydrological event projections could significantly vary depending on climate model selection and weather stations, suggesting the need for a careful and comprehensive evaluation of GCM in the hydrological analysis of climate change. The proposed methods are expected to help to improve the accuracy of future hydrological projections for water resources planning.     

Adaptive Neuro-Fuzzy Inference System for drought forecasting

Drought causes huge losses in agriculture and has many negative influences on natural ecosystems. In this study, the applicability of Adaptive Neuro-Fuzzy Inference System (ANFIS) for drought forecasting and quantitative value of drought indices, the Standardized Precipitation Index (SPI), is investigated. For this aim, 10 rainfall gauging stations located in Central Anatolia, Turkey are selected as study area. Monthly mean rainfall and SPI values are used for constructing the ANFIS forecasting models. For all stations, data sets include a total of 516 data records measured between in 1964 and 2006 years and data sets are divided into two subsets, training and testing. Different ANFIS forecasting models for SPI at time scales 1–12 months were trained and tested. The results of ANFIS forecasting models and observed values are compared and performances of models were evaluated. Moreover, the best fit models have been also trained and tested by Feed Forward Neural Networks (FFNN). The results demonstrate that ANFIS can be successfully applied and provide high accuracy and reliability for drought forecasting.     

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.     

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.     

Stochastic simulation of droughts. Part 2: regional droughts

In Part 1 we demonstrated the applicability of stochastic models to predicting the characteristics of point drought events within any planning period by means of a case study (Mohan S, Sahoo PK (2007) Hydrological Processes 21 : this issue). In addition, studies on regional droughts are important in the context of regional level planning and evolving management strategies. The small number of drought events from a particular streamflow or rainfall series, when subjected to statistical analysis in order to predict future occurrences, produces results that are not very reliable. To overcome this difficulty, we propose using a long sequence of synthetically generated annual rainfall series at various rain‐gauge stations of a region, and multiyear regional droughts were derived from both historic and generated series. The key parameters for a successful regional multiyear drought study are the critical area ratio and the critical level, and the area affected by the drought can be ascertained using these parameters. The important regional drought parameters were determined and their suitable probability distributions were arrived at by studying a total of nine possible probability models; these models can be used in predicting the longest regional drought duration and the greatest regional drought severity with a given return period. The effect of change of critical parameters on the regional drought parameters is also studied and reported. Copyright © 2007 John Wiley & Sons, Ltd.     

Stochastic–conceptual analysis of near‐surface hydrological response

The stochastic–conceptual rainfall–runoff simulator (SCRRS) developed by R. A. Freeze in 1980 was used in this study to demonstrate quantitatively the interplay of the factors that control the occurrence of overland flow by the Horton and Dunne mechanisms. The simulation domain and input data for the SCRRS simulations reported here were abstracted from the R‐5 catchment (Chickasha, OK) data sets. The results illustrate that the identification of a dominant hydrological response process may not be as simple as a singular Horton or Dunne characterization. The SCRRS simulations show that the Horton and Dunne processes can (i) occur simultaneously at different locations during a given rainfall event, (ii) change from one process to the other with time depending on the characteristics of the rainfall event, and (iii) be strongly dependent on the initial conditions. Copyright © 2001 John Wiley & Sons, Ltd.     

Is a chaotic multi‐fractal approach for rainfall possible?

An Erratum has been published for this article in Hydrological Processes 15 (12) 2001, 2381–2382. Applications of the ideas gained from fractal theory to characterize rainfall have been one of the most exciting areas of research in recent times. The studies conducted thus far have nearly unanimously yielded positive evidence regarding the existence of fractal behaviour in rainfall. The studies also revealed the insufficiency of the mono‐fractal approaches to characterizing the rainfall process in time and space and, hence, the necessity for multi‐fractal approaches. The assumption behind multi‐fractal approaches for rainfall is that the variability of the rainfall process could be directly modelled as a stochastic (or random) turbulent cascade process, since such stochastic cascade processes were found to generically yield multi‐fractals. However, it has been observed recently that multi‐fractal approaches might provide positive evidence of a multi‐fractal nature not only in stochastic processes but also in, for example, chaotic processes. The purpose of the present study is to investigate the presence of both chaotic and fractal behaviours in the rainfall process to consider the possibility of using a chaotic multi‐fractal approach for rainfall characterization. For this purpose, daily rainfall data observed at the Leaf River basin in Mississippi are studied, and only temporal analysis is carried out. The autocorrelation function, the power spectrum, the empirical probability distribution function, and the statistical moment scaling function are used as indicators to investigate the presence of fractal, whereas the presence of chaos is investigated by employing the correlation dimension method. The results from the fractal identification methods indicate that the rainfall data exhibit multi‐fractal behaviour. The correlation dimension method yields a low dimension, suggesting the presence of chaotic behaviour. The existence of both multi‐fractal and chaotic behaviours in the rainfall data suggests the possibility of a chaotic multi‐fractal approach for rainfall characterization. Copyright © 2001 John Wiley & Sons, Ltd.     

Ensemble rainfall forecasting with numerical weather prediction and radar‐based nowcasting models

The overall objective of this study is to improve the forecasting accuracy of the precipitation in the Singapore region by means of both rainfall forecasting and nowcasting. Numerical Weather Predication (NWP) and radar‐based rainfall nowcasting are two important sources for quantitative precipitation forecast. In this paper, an attempt to combine rainfall prediction from a high‐resolution mesoscale weather model and a radar‐based rainfall model was performed. Two rainfall forecasting methods were selected and examined: (i) the weather research and forecasting model (WRF); and (ii) a translation model (TM). The WRF model, at a high spatial resolution, was run over the domain of interest using the Global Forecast System data as initializing fields. Some heavy rainfall events were selected from data record and used to test the forecast capability of WRF and TM. Results obtained from TM and WRF were then combined together to form an ensemble rainfall forecasting model, by assigning weights of 0.7 and 0.3 weights to TM and WRF, respectively. This paper presented results from WRF and TM, and the resulting ensemble rainfall forecasting; comparisons with station data were conducted as well. It was shown that results from WRF are very useful as advisory of anticipated heavy rainfall events, whereas those from TM, which used information of rain cells already appearing on the radar screen, were more accurate for rainfall nowcasting as expected. The ensemble rainfall forecasting compares reasonably well with the station observation data. Copyright © 2012 John Wiley & Sons, Ltd.