Drought Forecasting using Markov Chain Model and Artificial Neural Networks

Water resources management is a complex task. It requires accurate prediction of inflow to reservoirs for the optimal management of surface resources, especially in arid and semi-arid regions. It is in particular complicated by droughts. Markov chain models have provided valuable information on drought or moisture conditions. A complementary method, however, is required that can both evaluate the accuracy of the Markov chain models for predicted drought conditions, and forecast the values for ensuing months. To that end, this study draws on Artificial Neural Networks (ANNs) as a data-driven model. The employed ANNs were trained and tested by means of a statistically-based input selection procedure to accurately predict reservoir inflow and consequently drought conditions. Thirty three years’ data of inflow volume on a monthly time resolution were selected to enable calculation of the standardized streamflow index (SSI) for the Markov chain model. Availability of hydro-climatic data from the Doroodzan reservoir in the Fars province, Iran, allowed us to develop a reservoir specific ANN model. Results demonstrated that both models accurately predicted drought conditions, by employing a randomization procedure that facilitated the selection of the required data for the ANN to forecast reservoir inflow close to the observed values over a validation period. The results confirmed that combining the two models improved short-term prediction reliability. This was in contrast to single model applications that resulted into substantial uncertainty. This research emphasized the importance of the correct selection of data or data mining, prior to entering a specific modeling routine.     

Assessment of Hydrological Drought Revisited

A variety of indices for characterising hydrological drought have been devised which, in general, are data demanding and computationally intensive. On the contrary, for meteorological droughts very simple and effective indices such as the Standardised Precipitation Index (SPI) have been used. A methodology for characterising the severity of hydrological droughts is proposed which uses an index analogous to SPI, the Streamflow Drought Index (SDI). Cumulative streamflow is used for overlapping periods of 3, 6, 9 and 12 months within each hydrological year. Drought states are defined which form a non-stationary Markov chain. Prediction of hydrological drought based on precipitation is also investigated. The methodology is validated using reliable data from the Evinos river basin (Greece). It can be easily applied within a Drought Watch System in river basins with significant storage works and can cope with the lack of streamflow data.     

Prediction of SPI Drought Class Transitions Using Markov Chains

Using the SPI relative to 67 years data sets, a Markov chains approach has been utilized for several locations in Alentejo, southern Portugal, to characterize the stochasticity of droughts, which allowed predicting the transition from a class of severity to another up to 3 months ahead. Markov models were applied using both the homogeneous and non-homogeneous formulations. The results of the application of the Markov models are presented and discussed, showing in particular the usefulness of adopting a non-homogeneous formulation, which allows to differentiate predictions in relation to the initial month considered, thus understanding the probable evolution of a drought as influenced by the climate and, in particular, the seasonality of rainfall. However, these results, which are promising in view of drought management, require further developments and to be associated with other predictive tools of stochastic or physical nature. Possible approaches on using predictions of drought class transitions in view of drought risk management are also discussed.     

Analysis of multi‐year drought and high inflow events into the eildon storage

This article presents information from an analysis of the multi‐year drought and high flow durations obtained from a historical time series (1891–1989) of annual inflows aggregated from all streams and rivers flowing into the Eildon Storage, a major storage for irrigation water in Northern Victoria, South‐East Australia. The drought and high inflow duration sequences are found to be affected by the fluctuating climatic cycle, called the Southern Oscillation. The multi‐year drought and high inflow duration sequences are analysed first through a model with IID observations in the annual runoff and second, through a first order auto‐regressive Markov model with a two‐state Markov chain with time homogeneous transition assumption. An alternative approach is taken to estimate the termination rate of multi‐year drought and high inflow duration sequences, based on frequency analysis and the basic concepts of reliability theory. This approach confirms the initial findings.     

21st Century Drought Scenarios for the UK

A 6-month drought severity index (DSI6) is applied to each of the 11-member perturbed-physics ensemble (HadRM3-PPE-UK) monthly precipitation dataset from 1950 to 2100 to investigate projected 21st century droughts in the UK. Four main drought characteristics are investigated: intensity, drought covariance, frequency of drought months and frequency of drought events at a given duration. Changes in these characteristics are analysed for 30-year periods: 1970–1999 (1980s), 2010–2039 (2020s), 2040–2069 (2050s) and 2070–2099 (2080s) and described in terms of their seasonal behaviour, for both moderate and extreme droughts. Projections of drought characteristics are expressed in the forms of ensemble-mean change relative to the 1980s and model consensus, and analysed over 23 water resource regions. In general, drought characteristics show profound increases (and widespread) for the 2050s and 2080s with larger change occurring during the wet season and under moderate drought conditions. Drought covariance sees greater increase during the dry season with greater change magnitude (but less widespread) under extreme drought conditions. Results also show that droughts can persist over long durations. However, the projected frequency of droughts at longer durations is low compared with droughts with shorter duration of persistence. Water resource regions (WWRs) mostly show negative change in drought characteristics, except for drought covariance. However, intensity and duration of droughts also generally increase over most of the WRRs in England, which are already highly exploited. Of particular relevance to water management, results from this ensemble have a strong influence on dry season water availability, especially in parts of England.     

水文干旱与气象干旱临界转变条件的判定及响应关系

水文干旱与气象干旱的响应关系对于建立健全干旱监测预报系统具有重要意义。基于区域水文干旱指数(SHI)与标准化降水指数(SPI),结合游程理论和非线性关系模型分析喀什河流域水文干旱与气象干旱的特征、响应关系及驱动因素。结果表明:水文干旱的年平均干旱历时和干旱烈度大于气象干旱,且随着SPI和SHI时间尺度的增加,识别出的干旱历时和干旱烈度也有所增加。基于三参数(log 3 P1)对数函数(Logarithm)模型可以更好地表征两者的响应关系。在3个月尺度下,气象干旱历时至少为1. 10个月且干旱的烈度至少为0. 83时,将诱发水文干旱;在6个月尺度下,气象干旱历时至少为1. 60个月且干旱的烈度至少为0. 91时,易发生水文干旱。     

Changing Pattern of Droughts during Cropping Seasons of Bangladesh

There has been a growing concern on temporal variations on drought characteristics due to climate change. This study compares meteorological drought characteristics for two different periods to quantify the temporal changes in seasonal droughts of 18 weather stations of the country. Fifty-five years rainfall and temperature data are divided into two different thirty-year periods, 1961–1990 and 1985–2014 and standardized precipitation evapotranspiration index (SPEI) for those periods are calculated to assess the changes. Four seasons in this study are selected as two major crop growing seasons namely, Rabi (November to April) and Kharif (May to October) and two critical periods for crop growth in term of water supply namely critical Rabi (March–April) and critical Kharif (May). Results show that moderate, extreme, and severe Rabi droughts has increased in 11, 9, and 4 stations out of 18 stations, respectively, and Kharif severe and extreme droughts has increased in 8 and 9 stations, respectively, In addition, the frequency analysis shows that the return periods have decreased during 1985–2014 at the stations where it was high during 1961–1990 and vice versa. This has made the spatial distribution of return periods of droughts more uniform over the country for most of the seasons. Increased return period of droughts in highly drought prone north and northwest Bangladesh has caused decrease in average frequency of droughts. Consequently, this result corresponds that Bangladesh experiences fewer droughts in recent years. Trend analysis of rainfall and temperature data reveals that significant increase of mean temperature and no significant change in rainfall in almost all months have increased the frequency of droughts in the regions where droughts were less frequent.     

Drought Concepts and Characterization

Abstract

A better knowledge of droughts is required to improve water management in water scarce areas. To appropriately cope with droughts, there is the need to adopt adequate concepts relative to droughts and water scarcity, to properly use drought indices that help characterize them, including ones relative to their severity, and to develop prediction tools that may be useful for early warning and that may reduce the respective lead time needed for appropriate response. In this paper, concepts relative to drought and other water scarcity regimes are discussed aiming both to distinguish droughts from other water scarcity regimes and to base a common understanding of the general characteristics of droughts as hazards and disasters. Three main drought indices are described aiming at appropriate characterization of droughts: the theory of runs, the Palmer Drought Severity Index (PDSI), and the Standardized Precipitation Index (SPI). Their application to local and regional droughts in the region of Alentejo, Portugal is presented focusing on the respective comparison and possible adequateness for drought monitoring. Results indicate some difficulties in using the theory of runs, particularly because it requires a subjective definition of thresholds in precipitation and does not provide a standardized classification of severity. Results show that draught characterization with the PDSI and the SPI produce coherent information, but the PDSI is limited relative to the SPI because it requires more data to perform a soil water balance while the SPI needs only precipitation data, which are more easily available in numerous locations. It is concluded that adopting the SPI is appropriate, but there is advantage in combining different indices to characterize droughts.     

Analysis of spatio-temporal evolution of droughts in Luanhe River Basin using different drought indices

Based on the monthly precipitation and air temperature from 1960 to 1989 in the Luanhe River Basin, the standardized precipitation evapotranspiration index(SPEI) and standardized precipitation index(SPI) at three- and six-month time scales and the self-calibrating Palmer drought severity index(sc-PDSI) were calculated to evaluate droughts in the study area. Temporal variations of the drought severity from 1960 to1989 were analyzed and compared based on the results of different drought indices, and some typical drought events were identified. Spatial distributions of the drought severity according to the indices were also plotted and investigated. The results reveal the following: the performances of different drought indices are closely associated with the drought duration and the dominant factors of droughts; the SPEI is more accurate than the SPI when both evaporation and precipitation play important roles in drought events; the drought severity shown by the sc-PDSI is generally milder than the actual drought severity from 1960 to 1989; and the evolution of the droughts is usually delayed according to the scPDSI. This study provides valuable references for building drought early warning and mitigation systems in the Luanhe River Basin.     

A Simplified Model for Predicting Drought Magnitudes: a Case of Streamflow Droughts in Canadian Prairies

The model for prediction of drought magnitudes is based on the multiplicative relationship: drought magnitude (M) = drought intensity (I) × drought duration (L), where I, L, and M are presumed to obey respectively the truncated normal probability distribution function (pdf), the geometric pdf, and the normal pdf. The multiplicative relationship is applied in the standardized domain of the streamflows, named as SHI (standardized hydrological index) sequences, which are treated equivalent to standard normal variates. The expected drought magnitude E(M _T ), i.e. the largest value of M over a sampling period of T-time units (T-year, T-month, and T-week) is predicted for hydrological droughts using streamflow data from Canadian prairies. By suitably amalgamating E(L _T ) with mean and variance of I in the extreme number theorem based relationship, the E(M _T ) is evaluated. Using Markov chain (MC), the E(L _T ) is estimated involving the geometric pdf of L. The Markov chains up to order one (MC-1) were found to be adequate in the proposed model for the annual to weekly time scales. For a given level of drought probability (q) and a sampling period T-time units; the evaluation of E(M _T ) requires only 3 parameters viz. lag-1 autocorrelation (ρ ₁ ), first order conditional probability (q _q , present instant being a drought given past instant was a drought) in SHI sequences and a parameter ø (value 0 to 1), which were estimated from historical data of streamflows. A major strength of the proposed model lies in the use of simple and widely familiar normal and geometric pdfs as its basic building blocks for the estimation of drought magnitudes.     

Drought forecasting using the Standardized Precipitation Index

Unlike other natural disasters, drought events evolve slowly in time and their impacts generally span a long period of time. Such features do make possible a more effective drought mitigation of the most adverse effects, provided a timely monitoring of an incoming drought is available. Among the several proposed drought monitoring indices, the Standardized Precipitation Index (SPI) has found widespread application for describing and comparing droughts among different time periods and regions with different climatic conditions. However, limited efforts have been made to analyze the role of the SPI for drought forecasting. The aim of the paper is to provide two methodologies for the seasonal forecasting of SPI, under the hypothesis of uncorrelated and normally distributed monthly precipitation aggregated at various time scales k. In the first methodology, the auto-covariance matrix of SPI values is analytically derived, as a function of the statistics of the underlying monthly precipitation process, in order to compute the transition probabilities from a current drought condition to another in the future. The proposed analytical approach appears particularly valuable from a practical stand point in light of the difficulties of applying a frequency approach due to the limited number of transitions generally observed even on relatively long SPI records. Also, an analysis of the applicability of a Markov chain model has revealed the inadequacy of such an approach, since it leads to significant errors in the transition probability as shown in the paper. In the second methodology, SPI forecasts at a generic time horizon M are analytically determined, in terms of conditional expectation, as a function of past values of monthly precipitation. Forecasting accuracy is estimated through an expression of the Mean Square Error, which allows one to derive confidence intervals of prediction. Validation of the derived expressions is carried out by comparing theoretical forecasts and observed SPI values by means of a moving window technique. Results seem to confirm the reliability of the proposed methodologies, which therefore can find useful application within a drought monitoring system.     

加权马尔可夫链在银川地区降雨量预测中的应用

依据1960年～2008年银川地区的年降雨量资料,采用均值一标准差分级法,对其进行状态分级,分为枯水年、偏枯年、平水年、偏丰年和丰水年5个状态。根据马尔可夫链预测方法,验证了该降水序列满足马氏性,并以规范化的各阶自相关系数为权,建立了适用于银川地区年降雨量的加权马尔可夫链预测模型,实例验证结果令人满意。在此基础上结合模糊集理论中的级别特征值,预测了银川地区2009年及2010年的年降雨量。预测结果表明：银川地区2009年为偏枯年,年降雨量为150．45mm;2010年为平水年,年降雨量为177．38mm。最后采用平稳分布估计年降雨量各状态的重现期,结果显示银川地区年降雨量处于平水年和偏枯年的可能性较大。     

Effect of Air Temperature on Historical Trend of Long-Term Droughts in Different Climates of Iran

Effective monitoring of drought plays an important role in water resources planning and management, especially under global warming effect. The aim of this paper is to study the effect of air temperature on historical long-term droughts in regions with diverse climates in Iran. To this end, monthly air temperature (T) and precipitation (P) data were gathered from 15 longest record meteorological stations in Iran covering the period 1951–2014. Long-term meteorological droughts behavior was quantified using two different drought indices, i.e. the Standardized Precipitation Index (SPI) and the Standardized Precipitation Evapotranspiration Index (SPEI). Linear and non-linear trends in T, P, SPI and SPEI were evaluated using non-parametric and parametric statistical approaches such as non-modified and modified Mann-Kendall Test, Theil-Sen approach, and simple regression. The results indicated that the significant trends for temperature are approximately all increasing (0.2 °C to 0.5 °C per decade), and for precipitation are mostly decreasing (?7.2 mm to ?14.8 mm per decade). It was also indicated that long-term drought intensities monitored by the SPI and SPEI have had significant downward trend (drought intensification with time) at most stations of interest. The observed trends in the SPI series can be worsen if air temperature (in addition to precipitation) participates in drought monitoring as SPEI. In arid and extra arid climates, it was observed that temperature has strong effects on historical drought characteristics when comparing the SPI and SPEI series. Due to the determinative role of temperature in mostly dry regions like Iran, the study suggests using the SPEI rather than SPI for more effective monitoring of droughts.     

Droughts Prediction: a Methodology Based on Climate Seasonal Forecasts

This study proposes a methodology for the drought assessment based on the seasonal forecasts. These are climate predictions of atmospheric variables, such as precipitation, temperature, wind speed, for upcoming season, up to 7 months. In regions particularly vulnerable to droughts and to changes in climate, such as the Mediterranean areas, predictions of precipitation with months in advance are crucial for understanding the possible shifts, for example, in water resource availability. Over Europe, practical applications of seasonal forecasts are still rare, because of the uncertainties of their skills; however, the predictability varies depending on the season and area of application. In this study, we describe a methodology which integrates, through a statistical approach, seasonal forecast and reanalysis data to assess the climate state, i.e. drought or not, of a region for predefined periods in the next future, at monthly scale. Additionally, the skill of the forecasts and the reliability of the released climate state assessment are estimated in terms of the false rate, i.e. the probability of missing alerts or false alarms. The methodology has been first built for a case study in Zakynthos (Greece) and then validated for a case study in Sicily (Italy). The selected locations represent two areas of the Mediterranean region often suffering from drought and water shortage situations. Results showed promising findings, with satisfying matching between predictions and observations, and false rates ranging from 1 to 50%, depending on the selected forecast period.

     

Projected Changes of Future Extreme Drought Events under Numerous Drought Indices in the Heilongjiang Province of China

Effective drought prediction methods are essential for the mitigation of adverse effects of severe drought events. This study utilizes the Reconnaissance Drought Index, Standardized Precipitation Index and Standardized Precipitation Evapotranspiration Index to assess the occurrence of future drought events in the study area of the Heilongjiang province of China over a period of 2016–2099. The drought indices were computed from the meteorological data (temperature, precipitation) generated by the global climate model (HadCM3A2). Moreover, Mann-Kendall trend test was applied for the assessment of future climatic trends and detecting probable differences in the behaviour of various drought indices. Drought forecasting periods has been divided into three categories: the early phase (1916–2030), middle phase (2031–2060) and late phase (2061–2099). The occurrence of future droughts is also ranked according to their intensity (mild, moderate, severe and extreme drought). Based on the drought results, more number of drought events are expected to occur during 12-month drought analysis are, RDI during 2084–2098 (DD = 14, DS = ?1.38), SPEI during 2084–2098 (DD = 14, DS = ?1.33) and SPI during 2084–2095 (DD = 12, DS = ?1.19). The 1st and 2nd months of the years studied predicted a warming trend, while the 7th, 8th, and 9th months predicted a wetter trend. Finally, it was observed that RDI is more sensitive to drought and indicated a high percentage of years under severe and extreme drought conditions during the drought frequency analysis. Conclusively, this study provides a strategies for water resources management and monitoring of droughts, in which drought indices like RDI can play a central role.     

加权马尔可夫链在降水状况预测中的应用

在介绍加权马尔可夫链预测方法的基础上,以郑州市1951~1994年降雨量资料为例,采用均值标准差分级法进行旱涝指标值分级,把这44年资料划分成雨涝、偏涝、正常、偏旱、干旱5种状态,应用加权马尔可夫链对该地区旱涝状态进行预测和分析,结果表明该方法预测结果与实际情况相吻合。     

Predicting Drought Magnitudes: A Parsimonious Model for Canadian Hydrological Droughts

A multiplicative relationship, drought magnitude (M) = drought intensity (I) × drought duration or length (L) is used as a basis for predicting the largest expected value of hydrological drought magnitude, E(M _T ) over a period of T-year (or month). The prediction of E(M _T ) is carried out in terms of the SHI (standardized hydrological index, tantamount to standard normal variate) sequences of the annual and monthly streamflow time series. The probability distribution function (pdf) of I (drought intensity) was assumed to follow a truncated normal. The drought length (L _c ) was taken as some characteristic duration of the drought period, which is expressible as a linear combination of the expected longest (extreme) duration, E(L _T ) and the mean duration, L _m of droughts and is estimated involving a parameter ø (range 0 to 1). The drought magnitude (deficit-sum, M) has been assumed to follow a gamma pdf, in view of the observed behavior of M. The model M = I × L has been invoked via two approximations, viz. Type-1 involves only mean of I and Type-2 involves both mean and variance of I through the theorem of extremes of random numbers of random variables. The E(L _T ) were obtained using the Markov chain (MC) model of an appropriate order, which turned out to be zero order Markov chain (MC-0) at the annual time scale. At the monthly time scale, the E(L _T ) was best represented by MC-0 for SHI sequences with low value of lag-1 autocorrelation (ρ?<?0.3) and first order Markov chain (MC-1) for SHI sequences with ρ?>?0.3. At low cutoff levels (q?≤?0.2), the trivial relationship E(M _T ) = E(I) × E(L _T ) i.e. without considerations of the extreme number theorem and the pdf of M yielded satisfactory results.     

A New Method for Joint Frequency Analysis of Modified Precipitation Anomaly Percentage and Streamflow Drought Index Based on the Conditional Density of Copula Functions

In this study, a new method was proposed to model the occurrence of related variables based on the conditional density of copula functions. The proposed method was adopted to investigate the dynamics of meteorological and hydrological droughts in the Zarinehroud basin, southeast of Lake Urmia, during the period 1994–2015. For this purpose, the modified precipitation anomaly percentage and streamflow drought indices were extracted. Finally, the joint frequency analysis of duration-duration and severity-severity characteristics of meteorological and hydrological droughts was analyzed. Analysis of 7 different copulas used to create the joint distribution in the Zarinehroud basin indicated that the Frank copula had the best performance in describing the relationship between the meteorological and hydrological drought severities and durations. By examining the results of the bivariate analysis of duration-duration of meteorological and hydrological droughts at different stations, the expected meteorological and hydrological drought durations were estimated in the years ahead. For example, at Chalkhmaz station, 4- to 7-month duration for the hydrological drought and 9- to 12-month duration for the meteorological drought is expected in the years ahead. The joint frequency analysis of drought characteristics allows to determine the meteorological and hydrological drought characteristics at a single station at the same time using joint probabilities. Also, the results indicated that by knowing the conditional density, the hydrological drought characteristics can be easily estimated for the given meteorological drought characteristics. This could provide users and researchers useful information about the probabilistic behavior of drought characteristics for optimal operation of surface water.

     

近50年来浙江省干旱规律时空分析

利用浙江省近50年降水资料,基于最优区域旱涝指标采用克里金空间插值方法对浙江省旱涝进行时空规律分析和等级评定。结果表明,浙江省发生干旱频繁,两年一旱,发生大旱以上的频率较高,连旱严重,近年干旱有加重的趋势;同时干旱呈现明显的区域性,发生重旱时波及范围广,各分区发生干旱频率在16%~26%之间,仅有4个分区不易波及。     

Future Hydrological Drought Analysis Considering Agricultural Water Withdrawal Under SSP Scenarios

Hydrological drought is assessed through river flow, which depends on river runoff and water withdrawal. This study proposed a framework to project future hydrological droughts considering agricultural water withdrawal (AWW) for shared socioeconomic pathway (SSP) scenarios. The relationship between AWW and potential evapotranspiration (PET) was determined using a deep belief network (DBN) model and then applied to estimate future AWW using projections of the twelve global climate models (GCMs). 12 GCMs were bias-corrected using the quantile mapping method, climate variables were generated, and river flow was estimated using the soil and water assessment tool (SWAT) model. The standardized runoff index (SRI) was used to project the changes in hydrological drought characteristics. The results revealed a higher occurrence of severe droughts in the future. Droughts would be more frequent in the near future (2021–2060) than in the far future (2061–2100) and more severe when AWW is considered. Droughts would also be more severe for SSP5-8.5 than for SSP2-4.5. The study revealed that the increased PET due to rising temperatures is the primary cause of the increased drought frequency and severity. The AWW will accelerate the drought severities in the future in the Yeongsan River basin.