Using short hydrological records to characterise extreme drought for water studies could lead to uncertain results. At first, this article introduces a generic model that extends the length of short hydrological records to improve the analysis of drought. Using simulated data, the extension model performance was tested and found to work well and later the model was used to extend the annual precipitation for Reba region back to 1924. The analysis of the extended precipitation shows the occurrence of 23 drought events that is about 50% more than the number of events detected from the analysis of the short historical precipitation. The analysis shows that events of 1 year duration are common while events of 3 years or more are rare. Furthermore, this article proposes a theoretical model that can be used to estimate the number of drought events that may emerge during a fixed period. The model is shown to be reliable, and the estimated drought numbers can be used in planning for the water supply from the traditional water sources. Moreover, the article suggests a few measures to improve the water supply in Jordan during dry conditions.

## INTRODUCTION

Drought is a natural hazard that causes a significant reduction in the water supply below the demand during a specific time (Bonaccorso *et al.* 2003). Each drought event is characterised by its space coverage, water deficit magnitude, duration upon which the deficit continues, and return period that tells how frequent the drought is (Salas *et al.* 2005). In recent decades, drought events have caused economic damage to several sectors including rain fed and irrigated agriculture (Rossi & Cancelliere 2013). It should be noted that the prediction of drought as a natural hazard remains challenging due to uncertainties (Van Huijgevoot *et al.* 2014). One source of the uncertainty could be attributed to the shortness of historical hydrological records used to capture the occurrence of severe drought events.

*et al.*2003; Salas

*et al.*2005; Mishra

*et al.*2009; Cancelliere & Salas 2010). Furthermore, long proxy data that contain natural climatic information, i.e. tree ring indices, have been used extensively in the literature to reconstruct precipitation or stream flow records back in time and later such records were used to track the past occurrence of severe drought episodes not being detected from the short historical records (Touchan

*et al.*1999; Gonzales & Valdes 2003; Akkemik

*et al.*2008; Woodhouse

*et al.*2009; Fang

*et al.*2010; Yang

*et al.*2014). In the literature, the duration as an important feature of the drought has been modelled using the geometric distribution (Shiau & Shen 2001; Salas

*et al.*2005). The probability distribution of the drought of duration

*l*is given as:where

*p*is the conditional probability of observing wet year given that the past year is a dry year.

_{dw}While most of the water resources in the arid region of Jordan are limited and subjected to intensive stresses due to increasing water demand for the population and economic activities, the occurrence of prolonged drought events rapidly enlarges the gap between the limited supply and the water demand. In Jordan, a few drought studies were conducted employing either the drought indices (Hammouri & El-Naqa 2007) or probabilistic modelling (Tarawneh *et al.* 2008, 2009; Tarawneh 2011) to characterise the severity of drought. In addition, tree ring indices were used to augment short precipitation records in Jordan and later were used to capture the past occurrence of extreme meteorological droughts (Touchan *et al.* 1999; Tarawneh & Hadadin 2009). In summary, previous studies conducted in Jordan have characterised the severity of drought in Jordan focusing on the largest drought magnitude, the longest duration upon which the deficit extends, and the frequency of the drought. It should be noted that none of the above mentioned studies have addressed the prediction of drought events in Jordan. Besides the negative impact caused by the drought persistence on the water supply from surface and ground sources, climate change could also induce extra pressure on water resources by limiting the feed water. In the semi-arid region of Jordan, there are few studies that indicated a change in the climate. Smadi & Zghoul (2006) indicated the existence of a downward trend in the annual rainfall amounts for many regions in Jordan. Also, a warming trend in the summer season at a rate of 0.038 °C/year has been detected which would increase the demand on water for irrigating summer crops. In a recent study, Rahman *et al.* (2015) also indicated the decrease in the annual rainfall amounts in Jordan at an average rate of 1.2 mm/yr. Al-Houri (2014) analysed the rainfall in Jordan and indicated a decreasing trend in the duration of the wet season associated with a decrease in the number of rainy days. In summary, due to the nature of the arid region of Jordan, a slight decrease in rainfall due to climate change will ultimately create extra stress on the surface and groundwater storages.

*x*is the long record, and are the mean values of the short record and long record over the calibration period,

_{t}*b*is the model parameter and

*n*is the extension period. The quality of extensions produced using the linear regression (Equation (2)) relies only on the strength of correlation between the short and the long record, however if the short record exhibits a temporal (serial) correlation, then extensions produced using Equation (2) may not acquire the temporal correlation of the short record, especially when the long record is time independent. Such a drawback could appear in hydrologic studies when river flows that usually show significant serial correlation are reconstructed from a serially independent variable like tree ring data.

_{e}One objective of this article is to present a generic theoretical model that extends the length of short hydrological records while accounting for the temporal correlation of the short variable. It is believed that extending the length of short hydrological records will increase the opportunity to capture more extreme drought events, ultimately, water management studies will be improved. Other objectives are to introduce a simple theoretical model that enables the computation of the number of drought events of specific duration, and to analyze the occurrence of drought in the Raba region, Jordan.

## METHODS

*a*and

*b*are the model parameters. Referring to the simple traditional linear regression (Equation (2)), the proposed model (Equation (3)) with the additional term, , considers the short variable lagged information contained in the past value (time

*t*−1) to predict the current value (time

*t*). Using the method of moments, the model parameters

*a*and

*b*are estimated as (Appendix A, available with the online version of this paper):andwhere

*C*(

*XY*) is the lag-0 covariance between

*y*and

_{t}*x*,

_{t}*C*(

*XX*) is the lag-0 covariance of

*x*,

_{t}*C*(

*XY*) is the lag-1 covariance between

^{−}*x*and the one time step lagged

_{t}*y*,

_{t}*C*(

*YY*) and

*C*(

*YY*) are the lag-0 and lag-1 covariance of

^{−}*y*, respectively.

_{t}*N*and the number of drought events of specific length is

*N*, then the probability that a drought of length

_{l}*l*years occurs is estimated empirically as follows:Equating Equations (1) and (6), simplifying and taking expectation on both sides, then the expected number of drought events of the desired length

*l*is:If the hydrologic variable has fixed length (

*M*years), and let

*p*be the unconditional probability of observing a dry year, then the total number of dry years is

_{d}*p*×

_{d}*M*, which is the sum of lengths for all drought events, i.e.

*N*×

*L*=

*p*×

_{d}*M*. Taking the expectation and rearranging, the expected number of all drought events,

*E*[

*N*] is:where

*E*[

*L*] is the expected length of drought.

*l*years drought events that could emerge during a fixed time period

*M*. Such a fixed period could be any planning time for a water resource system. Furthermore, Equation (9) is useful to develop an expression that estimates the recurrence time (

*R*) of drought events of specific type. Based on the renewal theory of events, Loaiciga & Leipnik (1996) expressed the recurrence time (

*R*) of hydrologic events emerging during a fixed time

*t*as follows:where

*N*is the number of events arising during the period

_{e}*t*. If the number of drought events

*N*is estimated by its expected number (Equation (9)) and noting that

_{e}*t*=

*M*, then the recurrence time (

*R*) is:

Equation (11) is the same expression developed by Salas *et al.* (2005) to evaluate the recurrence time of hydrologic events.

## RESULTS AND DISCUSSION

### Extension model performance

*y*and

_{t}*x*of 0.5, a normally distributed pair (

_{t}*y*and

_{t}*x*) was generated to a length of 150 data points. The mean and standard deviation of both,

_{t}*y*and

_{t}*x*, were selected arbitrarily as 100 and 30, respectively. The serial correlation coefficient of

_{t}*y*was selected as 0.3, i.e. shows significant temporal dependence like stream flows, while the serial correlation coefficient of the predictor variable

_{t}*x*was kept at low value (time independent) similar to most of tree-ring indices used as predictors to extend short precipitation or stream flow records. Out of the

_{t}*y*150 data points, the last 50 (

_{t}*t*= 101, 102, …, 150) were kept aside for model evaluation purposes. Therefore the variable

*y*was considered the short variable of 100 data points length (

_{t}*n*= 100). The proposed and the simple linear regression models were used to estimate the extensions for

*t*= 101, 102, …, 150. The extended part (

*t*= 101, 102, …, 150) was combined with the short part

*y*(

_{t}*t*= 1, 2, …,100) forming the combined record and the serial correlation was computed and checked versus the serial correlation of the short (

*y*). The performance statistic was computed. Since the proposed record extension model targets the production of extensions that will preserve the serial correlation of the short record, then the model performs well if the statistic is close to 1. The same procedure was repeated 1,000 times and finally the expected value of the performance statistic was computed. The same simulation experiments and analysis procedure were repeated at cross correlation values 0.65, 0.8 and 0.9. Figure 2 shows the expected value of the performance statistic computed using extensions predicted by the proposed and the traditional linear regression models at different cross correlation values.

_{t}The expected value of the performance statistic computed from extensions achieved using the traditional regression model (Figure 2) is always less than 1, i.e. the traditional regression model generated extensions that failed to preserve the serial correlation of the short record. In that case, extended values were affected somehow by the independence feature of the long record (*x _{t}*). The effect of the independence feature of the long record (

*x*) on the generated values increases as the cross correlation increases, i.e. as the power of the information transfer increases. In conclusion, the performance statistic shown in Figure 2 indicates that extensions produced using the traditional regression model did not maintain the serial correlation of the original short record (

_{t}*y*). As the cross correlation between the short (predicted) and the long record (predictor) increases, the characteristics of the predicted short variable are highly affected by the features of the long recorded variable rather than preserving the features of the original variable. Regarding the performance of the proposed record extension model, Figure 2 shows a consistent performance statistic that is very close to 1 regardless of the variation in the cross correlation values. Although the quality of the information transferred is highly affected by the cross correlation between the

_{t}*x*and

_{t}*y*, the additional term in Equation (3) maintained the serial correlation of the short variable (

_{t}*y*). In general, the proposed extension model succeeded to produce extensions that maintain the original short record serial correlation. Other statistics to measure the performance of both models to generate extensions that preserve features like the mean, variance, cross correlation and sum of squared error were also computed (results are not shown). In general, the analysis of results indicates the ability of both models to generate extensions that reproduce the mean, variance, and sum of squared error of the short variable.

_{t}### Analysis of multiyear drought events in Raba

*a*and

*b*, were estimated over the model calibration period (1953–2012) using Equations (4) and (5). The parameter

*a*

*=*0.132 and

*b*= 0.973. The combined precipitation series for Raba (1924–2012) consists of the historical part (1953–2012) and the extended part (1924–1952). Figure 3 shows the combined annual precipitation series for Raba region truncated at the level of the long-term mean.

The combined annual precipitation series shown in Figure 3 was truncated at the level of the long-term mean to identify drought events. Similarly, the historical precipitation for Raba was also truncated at the level of the long-term mean for drought characterisation. In the arid region of Jordan, the selection of the long-term mean as a truncation level could be an appropriate choice due to water scarcity, i.e. any small deviation below the average precipitation reduces the water amounts supplied to the rain fed agricultural activities. The analysis of the truncated historical precipitation (1953–2012) indicated the occurrence of 15 drought events, among them the 5-year drought and the 6-year drought that occurred during the periods 1975–1980 and 1958–1963 respectively (Figure 3). On the other hand, the analysis of the truncated combined annual precipitation series (1924–2012) indicated the occurrence of 23 drought events, which is around 1.5 times larger than the number of drought events detected from the analysis of the historical precipitation. Among the 23 drought events, there are two severe drought events each lasting 5 years during the periods 1975–1979 and 1930–1934, and one severe 6-year drought event during the period 1958–1963 (Figure 3). In order to investigate the distribution of the drought events in Raba region, the number of events and their occurrence probability were obtained from the analysis of both truncated precipitation series. Table 1 shows the number of detected drought events and their occurrence probability against the drought length. In general, drought events of short duration like the 1-year and probably the 2-year events, are the common (frequent) types of drought in Raba region with occurrence probability of 0.57 and 0.17 for the 1- and 2-year events respectively. Events of the duration of 3 years or more, although they do occur, are a less common type of drought with low occurrence probability, i.e. *P*[*L* ≥3 years] = 0.26. The distribution of drought events of 2 years or more detected from the analysis of the historical precipitation appears to be inconsistent (Table 1) compared to events detected from the combined precipitation (relatively long record), which attributed to the limited number of historical drought events observed.

. | Number of events (probability) . | |
---|---|---|

Drought length (year) . | Combined precipitation 1924–2012 . | Historical precipitation 1953–2012 . |

1 | 13 (0.57) | 8 (0.53) |

2 | 4 (0.17) | 2 (0.13) |

3 | 2 (0.09) | 2 (0.13) |

4 | 1 (0.04) | 1 (0.07) |

5 | 2 (0.09) | 1 (0.07) |

6 | 1 (0.04) | 1 (0.07) |

. | Number of events (probability) . | |
---|---|---|

Drought length (year) . | Combined precipitation 1924–2012 . | Historical precipitation 1953–2012 . |

1 | 13 (0.57) | 8 (0.53) |

2 | 4 (0.17) | 2 (0.13) |

3 | 2 (0.09) | 2 (0.13) |

4 | 1 (0.04) | 1 (0.07) |

5 | 2 (0.09) | 1 (0.07) |

6 | 1 (0.04) | 1 (0.07) |

*M*= 60 years). At first, the unconditional and conditional probabilities

*p*and

_{d}*p*were estimated from the truncated historical precipitation. The probabilities

_{dw}*p*and

_{d}*p*are 0.528 and 0.472, respectively. Using Equation (9) with

_{dw}*M*= 60, the expected number of drought events were computed against the drought length. Figure 4 shows the number of observed (actual) drought events and their expected number computed using Equation (9) versus the length of drought during the historical precipitation period for Raba region. Figure 4 shows the reliability of Equation (9) to closely estimate the number of the observed drought events of specific length during a fixed period. The total number of estimated drought events is 14.6 events, which is very close to the total number of observed events (15 events). For the most common type of events, the 1-year drought, the expected number is seven events compared to eight observed events (Figure 4). The discrepancy between the expected and the observed 2-year drought events shown in Figure 4 is attributed to the limited number (two events) of drought detected from the analysis of the short historical precipitation.

The merit of using Equation (9) to estimate the number of drought events during a specified time arises from its simplicity and the usefulness of its product to water resource management studies. It shows flexibility to accommodate any planning period, for example *M* could be 5, 10, 15 years. Therefore, Equation (9) can be used to construct charts that display the expected number of drought events that could occur in any region given simple statistics like *p _{d}* and

*p*.

_{dw}In order to estimate the recurrence time of the common drought events in Raba region, Equation (11) has been used. Given the probabilities *p _{d}* and

*p*, the recurrence times for events with a duration of 1 and 2 years are 8.5 and 16.1 years, respectively, whereas the less common events (3 years or more) have recurrence times of more than 30 years.

_{dw}### Measures to reduce the impact of drought and climate change on the water supply

Due to shortage in the water supply from the limited natural water resources, the Ministry of Water and Irrigation in Jordan has constructed several macro-scale rainwater harvesting projects during the past few decades. Such projects were designed for different tasks including groundwater basin recharge and fresh water supply for municipal, agricultural, and industrial sectors. Table 2 shows the storage capacity and the purpose of rainwater harvesting for selected projects in Jordan.

Project name . | Capacity (MCM) . | Purpose . | Notes . |
---|---|---|---|

Mujib dam reservoir | 32 | Supply fresh water for agriculture and industry | Collecting the winter flood and base flow of the Mujib valley |

Wala dam reservoir | 9 | Supply fresh water for agriculture and recharging groundwater | Collecting winter flood |

Qutrana dam reservoir | 4.2 | Supply fresh water for agriculture | Collecting winter flood |

Project name . | Capacity (MCM) . | Purpose . | Notes . |
---|---|---|---|

Mujib dam reservoir | 32 | Supply fresh water for agriculture and industry | Collecting the winter flood and base flow of the Mujib valley |

Wala dam reservoir | 9 | Supply fresh water for agriculture and recharging groundwater | Collecting winter flood |

Qutrana dam reservoir | 4.2 | Supply fresh water for agriculture | Collecting winter flood |

*et al.*2015) detected after 1995, Figure 5 shows the potential reduction in the total annual rainfall amount over Jordan after 1995. Figure 5 shows that the feed water has decreased from the long-term average value of 7,300 MCM in 1995 to nearly 6,550 MCM in 2013, which is approximately a 10% reduction due to the change in the climate. In a country where water is scarce, such a reduction is remarkable.

The following measures, if implemented, could contribute to reducing the devastating impact of drought persistence, the effect of the change in climate, and the increasing demand on the water sector in Jordan. Therefore the following is recommended:

Embed drought persistence in water release policies from surface water resources. In a previous study (Tarawneh 2011), it was concluded that unplanned water releases combined with less attention to drought persistence possibly contributed to the remarkable decline in the water storage in the Mujib dam reservoir during the years 2008 and 2009, upon which the water supply reached a critical level.

Develop new water sources. It could be time in Jordan to develop new water sources to compensate the lowering trend in the annual rainfall amount as a result of climate change and the increasing demand on water. One promising potential source that could provide unlimited amounts of fresh water is sea water desalination. Current desalination practices in Jordan are running at a modest scale in the Jordan Valley after desalting the brackish in small scale private units. The Red Sea-Dead Sea canal project has been implemented, which targets the restoration of the Dead Sea water level and hydropower energy production through conveying seawater to the Dead Sea. After desalination, it is expected that the project will provide Jordan with around 500 MCM of fresh water per year.

Adapt economic incentive plan to encourage water savings and the efficient use of water in irrigation where huge amounts of fresh water are usually consumed. Introducing new irrigation techniques and properly rehabilitating the existing aged water distribution systems are essential measures for saving water. The current water loss percentage reaches 42%, which is relatively high. Further reduction in the loss rate is needed which can be achieved through incentives, probably lowering the price of water when less water is used.

Adapt proper crop changing policy during the dry periods. While around 60% of the water released from surface and groundwater sources in Jordan is used mainly to irrigate crops, irrigating less water demanding crops would possibly lessen the water shortage problem during dry periods. Drought studies would help in advising farmers to adapt less water demanding crops that could survive under dry conditions.

## CONCLUSIONS

Long dry periods threaten the water supply of traditional water resources in Jordan. To reduce the uncertainty in drought characterisation due to using short hydrological records, this article introduces a generic record extension model that augments short hydrologic records while preserving the features of the hydrologic variable. Using simulation experiments, the model performance was tested at different cross correlation values and extensions produced were found to preserve the characteristics of the original variable. Therefore such a model can be used to extend the length of short hydrologic records targeting the improvement of drought characterisation. Furthermore, the article presents a simple theoretical model that facilitates the estimation of the number of drought events that could emerge during a fixed time. The proposed model was tested to foretell the number of drought events that occurred in Raba region. Such a model can be used to estimate the number of drought events needed for water resources management studies.

After extending the length of the Raba precipitation record, the analysis of the extended precipitation indicates the occurrence of 23 drought events, the longest is a 6-year event. However, events of short duration, one and 2 years, are the common type of events in Raba with recurrence time of 8.5 and 16 years, respectively. While part of the water shortage in Jordan is attributed to a drought persistence problem, it is recommended that the water sector institutions in Jordan consider drought persistence when planning for water releases. Moreover, the reduction in precipitation due to climate change increases the gap between water supply and demand. Therefore, it is recommended to develop new water sources in Jordan through increasing desalination practices to provide fresh water to compensate for the increasing water demand and the lowering trend in the rainfall amounts due to climate change. Furthermore, more efforts are needed to save water through rehabilitating existing water distribution systems, adapting economic incentives to encourage the efficient use of water, and adapting proper crop changing policy during the dry periods.