A theoretical drought classification method for the multivariate drought index based on distribution properties of standardized drought indices

Drought indices have been commonly used to characterize different properties of drought and the need to combine multiple drought indices for accurate drought monitoring has been well recognized. Based on linear combinations of multiple drought indices, a variety of multivariate drought indices have recently been developed for comprehensive drought monitoring to integrate drought information from various sources. For operational drought management, it is generally required to determine thresholds of drought severity for drought classification to trigger a mitigation response during a drought event to aid stakeholders and policy makers in decision making. Though the classification of drought categories based on the univariate drought indices has been well studied, drought classification method for the multivariate drought index has been less explored mainly due to the lack of information about its distribution property. In this study, a theoretical drought classification method is proposed for the multivariate drought index, based on a linear combination of multiple indices. Based on the distribution property of the standardized drought index, a theoretical distribution of the linear combined index (LDI) is derived, which can be used for classifying drought with the percentile approach. Application of the proposed method for drought classification of LDI, based on standardized precipitation index (SPI), standardized soil moisture index (SSI), and standardized runoff index (SRI) is illustrated with climate division data from California, United States. Results from comparison with the empirical methods show a satisfactory performance of the proposed method for drought classification.     

Long-term periodic drought modeling

Drought modeling is essential to water resources management and planning. In this study, Fourier spectral analysis is used to examine the cyclic structure for drought patterns and develop a long-term periodic model. A case study for historical precipitation data, obtained from the arid region of Kuwait for the period spanning from January 1967 to December 2009, are converted to drought measurements following the Standardized Precipitation Index (SPI) criterion. The SPI calculations are performed for two time scales of 12 and 24 months. The periodogram technique used for both time scales reveals periodicities of 12, 14, 19, 26, 31, 43, 64, 103 and 258 months. It is advocated here that the 26- and 258-month periods present in the data are attributed, respectively, to a Quasi-Biennial Oscillation pattern and a solar cycle over which the magnetic polarity of the sun first reverses then reverts to its former state. The detected periods are manipulated in the SPI model to produce drought forecasts, which suggest that until the end of year 2024 the climate is considered normal to very wet. This finding may be implemented to assess policy requirements related to water resources management.     

A drought frequency formula

Abstract

The important elements of a drought phenomenon are the longest duration and the largest severity for a desired return period. These elements form a basis for designing water storage systems to cope with droughts. At times, a third element, drought intensity, is also used and is defined as the ratio of severity to duration. The commonly available statistics for the causative drought variables such as annual rainfall or runoff sequences are the mean, the coefficient of variation and the lag one serial correlation coefficient, and occasionally some indication of the probability distribution function (pdf) of the sequences. The extremal values of the duration and severity are modelled in the present paper using information on the aforesaid parameters at the truncation level equal to the mean of the drought sequence, which is generally taken as the truncation level in the analysis of droughts. The drought severity has been modelled as the product of the duration and intensity with the assumption of independence between them. An estimate of drought intensity has been realized from the concept of the truncated normal distribution of the standardized form of the drought sequences in the normalized domain. A formula in terms of the extremal severity and the T-year return period has been suggested similar to the flood frequency formulae, commonly cited in hydrological texts.     

Hydrological identification of drought

The problem of drought identification is considered from a primarily hydrological viewpoint. The problems related to the definition, identification and prediction of drought have not yet been solved. Although rainfall data are analysed as the main indicator and characteristic of drought, other characteristics resulting from a rainfall deficit are also important. A time unit of one month was selected as the most suitable for analysis. Special attention was paid to the selection of truncation levels with respect to their influence on the results of drought identification. Three methods for drought identification were applied to a series of monthly rainfall data in Osijek from January 1882 to December 1990: (1) run analysis; (2) a discrete Markov process; and (3) the percentile method. Although the results of these three methods are encouraging, different methods yielded similar results. Some drawbacks of the application of distribution curves are discussed. Drought events should be identified using a number of different procedures.     

Dimensionality reduction in drought modelling

For monitoring hydrological events characterized by high spatial and temporal variability, the number and location of recording stations must be carefully selected to ensure that the necessary information is collected. Depending on the characteristics of each natural process, certain stations may be spurious or redundant, whereas others may provide most of the relevant data. With the objective of reducing the costs of the monitoring system and, at the same time, improving its operational effectiveness, three procedures were applied to identify the minimum network of rain gauge stations able to capture the characteristics of droughts in mainland Portugal. Drought severity is characterized by the standardized precipitation index applied to the timescales of 1, 3, 6 and 12 consecutive months. The three techniques used to reduce the dimensionality of the network of rain gauges were as follows: (i) artificial neural networks with sensitivity analysis, (ii) application of the mutual information criterion and (iii) K‐means cluster analysis using Euclidean distances. The results demonstrated that the best dimensionality reduction method was case dependent in the three regions of Portugal (northern, central and southern) previously identified by cluster analysis. All the reduction techniques lead to the selection of a subset of rain gauges capable of reproducing the original temporal patterns of drought. For specific severe drought events in Portugal in the past, the comparison between drought spatial patterns obtained with the original stations and the selected subset indicated that the subset produced statistically satisfactory results (correlation coefficients higher than 0.6 and efficiency coefficients higher than 0.5). Copyright © 2012 John Wiley & Sons, Ltd.     

Streamflow drought time series forecasting

Drought is considered to be an extreme climatic event causing significant damage both in the natural environment and in human lives. Due to the important role of drought forecasting in water resources planning and management and the stochastic behavior of drought, a multiplicative seasonal autoregressive integrated moving average (SARIMA) model is applied to the monthly streamflow forecasting of the Zayandehrud River in western Isfahan province, Iran. After forecasting 12 leading month streamflow, four drought thresholds including streamflow mean, monthly streamflow mean, 2-, 5-, 10- and 20-year return period monthly drought and standardized streamflow index were chosen. Both observed and forecasted streamflow showed a drought period with different severity in the lead-time. This study also demonstrates the usefulness of SARIMA models in forecasting, water resources planning and management.     

Diagnosing drought using the downstreamness concept: the effect of reservoir networks on drought evolution

To effectively manage hydrological drought, there is an urgent need to better understand and evaluate its human drivers. Using the “downstreamness” concept, we assess the role of a reservoir network in the emergence and evolution of droughts in a river basin in Brazil. In our case study, the downstreamness concept shows the effect of a network of reservoirs on the spatial distribution of stored surface water volumes over time. We demonstrate that, as a consequence of meteorological drought and recovery, the distribution of stored volumes became spatially skewed towards upstream locations, which affected the duration and magnitude of hydrological drought both upstream (where drought was alleviated) and downstream (where drought was aggravated). The downstreamness concept thus appears to be a useful entry point for spatiotemporally explicit assessments of hydrological drought and for determining the likelihood of progression from meteorological drought to a human-modified hydrological drought in a basin.     

Comparison of ten notable meteorological drought indices on tracking the effect of drought on streamflow

ABSTRACT

Ten notable meteorological drought indices were compared on tracking the effect of drought on streamflow. A 730-month dataset of precipitation, temperature and evapotranspiration for 88 catchments in Oregon, USA, representing pristine conditions, was used to compute the drought indices. These indices were correlated with the monthly streamflow datasets of the minimum, maximum and mean discharge, and the discharge monthly fluctuation; it was revealed that the 3-month Z-score drought index (Z3) has the best association with the four streamflow variables. The Mann-Kendall trend detection test applied to the latter index time series mainly highlighted a downward trend in the autumn and winter drought magnitude (DM) and an upward trend in the spring and summer DM (p = 0.05). Finally, the Pettitt test indicated an abrupt decline in the annual and autumn DM, which began in 1984 and 1986, respectively.     

Diagnosing drought using the downstreamness concept: the effect of reservoir networks on drought evolution

ABSTRACT

To effectively manage hydrological drought, there is an urgent need to better understand and evaluate its human drivers. Using the “downstreamness” concept, we assess the role of a reservoir network in the emergence and evolution of droughts in a river basin in Brazil. In our case study, the downstreamness concept shows the effect of a network of reservoirs on the spatial distribution of stored surface water volumes over time. We demonstrate that, as a consequence of meteorological drought and recovery, the distribution of stored volumes became spatially skewed towards upstream locations, which affected the duration and magnitude of hydrological drought both upstream (where drought was alleviated) and downstream (where drought was aggravated). The downstreamness concept thus appears to be a useful entry point for spatiotemporally explicit assessments of hydrological drought and for determining the likelihood of progression from meteorological drought to a human-modified hydrological drought in a basin.     

A bivariate pareto model for drought

Univariate Pareto distributions have been so widely used in hydrology. It seems however that bivariate or multivariate Pareto distributions have not yet found applications in hydrology, especially with respect to drought. In this note, a drought application is described by assuming a bivariate Pareto model for the joint distribution drought durations and drought severity in the State of Nebraska. Based on this model, exact distributions are derived for the inter arrival time, magnitude and the proportion of droughts. Estimates of 2, 5, 10, 20, 50 and 100 year return periods are derived for the three variables, drought duration, drought severity and the pairwise combinations: (drought duration, drought severity), (inter arrival time of drought, proportion of drought) and (drought duration, drought magnitude). These return period estimates could have an important role in hydrology, for example, with respect to measures of vegetation water stress for plants in water-controlled ecosystems.     

A drought outlook study in Korea

Abstract

Techniques are proposed for developing a monthly and weekly drought outlook and the drought outlook components are evaluated. A drought index, the surface water supply index (SWSI) was modified and used for the drought outlook. A water balance model (abcd) was successfully calibrated using a regional regression, including monthly and weekly factors, and was used to convert meteorology to hydrology. For the monthly drought outlook, an ensemble technique was applied, both with and without monthly industrial meteorology information (MIMI). For the weekly drought outlook, a deterministic forecasting technique was applied employing the Global Data Assimilation and Prediction System (GDAPS). The methodologies were applied to the Geum River basin in Korea. While only the weekly outlook using the GDAPS has sufficient forecasting capability to suggest it might be useful, the accuracy of the monthly drought outlook is expected to improve as the climate forecast accuracy increases.

Editor Z.W. Kundzewicz; Associate editor D. Hughes

Citation Kim, Y.-O., Lee, J.-K., and Palmer, R.N., 2012. A drought outlook study in Korea. Hydrological Sciences Journal, 57 (6), 1141–1153.     

Investigating effect of climate change on drought propagation from meteorological to hydrological drought using multi-model ensemble projections

Stochastic Environmental Research and Risk Assessment - Climate change is a main driving force that affects the hydrological cycle, leading to an increase in natural hazards. Among these natural...     

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.     

Critical drought analysis by second-order Markov chain

Exact probability distribution functions (PDF) of critical droughts in stationary second-order Markov chains are derived for finite sample lengths on the basis of the enumeration technique. These PDF are useful in predicting the possible critical drought durations that may result from any hydrologic phenomenon during any future period provided that the second-order Markov chain is representative of the underlying probability generation mechanism. Necessary charts are provided for the expectation and variance of critical droughts. The application of the developed methodology is given for three representative annual flow series from different parts of the world. It is observed that their critical droughts confirm well with the second-order Markov chain.     

广东省干旱灾害空间分布特征

利用1956-2005年126个雨量站逐月降水资料,采用标准化降雨指数和经验正交函数分解法,探讨了广东省干旱灾害空间分布规律.结果表明:广东省虽然总体比较湿润,但局部干旱时有发生,且在空间上存在东西差异、南北差异、中部差异的特点;春旱大致呈自西向东、自北向南逐渐加重的趋势;秋旱空间分布特点与春旱相反,由东向西、由南向北逐渐加重;春旱、秋旱在中部地区也有微弱的差异.     

The survey of climatic drought trend in Iran

Drought is one of the most important natural hazards in Iran. Therefore, drought monitoring has become a point of concern for most of the researchers. In the present study, the changes and trend of drought was surveyed, under the current global climate changes, by non parametric Mann–Kendall statistical test for 42 synoptic stations at different places of Iran. Standardized Precipitation Index (SPI) was calculated to recognize the drought condition at different time scales (3, 6, 9, 12, 18 and 24 months’ time series) for analyzing the drought trend in the recent 30 years. The obtained results have indicated a significant negative trend of drought in many parts of Iran, especially the South-East, West and South-West regions of the country. According to the results, although some parts of Iran such as North (around the Caspian Sea) and Northeast show no significant trend but in other parts of country, the severity of drought has increased during the last 30 years.     

Risk-based drought early warning system in reservoir operation

This paper introduces a risk-based decision process integrated into a drought early warning system (DEWS) for reservoir operation. It is to support policy making under uncertainty for drought management. Aspects of posterior risk, chances of option occurrences and the corresponding options to given chances, are provided to help decision makers to make better decisions. A new risk index is also defined to characterize decision makers’ attitudes toward risk. Decision makers can understand the inclination of attitude associated with any specific probability through accuracy assessment, and learn to adjust their attitudes in decision-making process. As a pioneering experiment, the Shihmen reservoir in northern Taiwan was tested. Over the simulation period (1964–2005), the expected overall accuracy approximated to 77%. The results show that the proposed approach is very practical and should find good use for reservoir operations.