Jordan, with limited rainfall, has per capita water availability of 135 m3/yr making it one of the water-poorest countries in the world. We analyzed the most comprehensive modern rainfall data set to date, consisting of 44 years of daily measurements from 58 stations primarily in the western, populated and agricultural portion of Jordan over the period 1970–2013 to assess temporal trends, variability, and spatial patterns. From 1995 to 2013, 13 of 19 years showed rainfall less than the mean, which has a probability <8.35% of chance occurrence. We used nonparametric statistical analysis and found 38 of 58 stations experienced an annual rainfall decrease at an average rate of 1.2 mm/yr. Over all 58 stations, the average decrease was 0.41 mm/yr. The annual coefficient of variation of daily rainfall showed a long-term increase of ∼2–3% at 90% of stations. Analysis of annual variance of daily rainfall suggests decreasing variance in the low rainfall areas to the southwest and east and increasing variance in the high rainfall areas to the northwest, a pattern consistent with principal component analysis. Strict multiple hypothesis testing procedures using the k-familywise error rate approach reinforced and confirmed the statistically significant regional rainfall decline as well as the spatial patterns of increasing and decreasing rainfall variability.
Jordan is among a handful of the most water scarce countries in the world [Raddad, 2005] and changes in rainfall will directly impact its economic development [Talozi, 2007]. Climate modeling studies have identified Jordan and the surrounding region as a potential hot spot for increases in temperature and changes in precipitation patterns [Evans, 2009; Samuels et al., 2011]. These potential changes pose a significant threat to a water scarce country with a history of heavy socioeconomic burdens that have taxed national water supplies, most recently in the form of a tremendous influx of Syrian refugees [El-Naser, 2009; Ministry of Planning and International Cooperation and United Nations, 2013]. Water supply is limited to 12 h per week in much of the urbanized regions of the country. Largely arid, most of the eastern portion of the country receives rainfall <50–100 mm/yr, while much of the northwestern region receives >300 mm/yr (Figure 1). The Intergovernmental Panel on Climate Change [IPCC, 2014] and Black  predict declining rainfall in the Middle East during the next several decades. These predictions need to be monitored and updated according to measured trends to inform nationwide planning and management of Jordan's very scarce water resources to meet both public supply and agriculture needs.
Several prior efforts have studied rainfall trends in Jordan. The structural characteristics of annual rainfall at 14 stations in Jordan from 1953 to 2002 were examined by Dahamsheh and Aksoy  who reported no trend in annual rainfall. Hamdi et al.  analyzed precipitation from six stations with records ending in 2005 and also found no significant trend in rainfall at any station. Freiwan and Kadioğlu  studied precipitation trends for 14 stations with records ranging from 33 to 78 years all ending in 2000. They found an average decline in annual precipitation of 0.40 mm/yr but only one station's trend was statistically significant. Al-Mashagbah and Al-Farajat  analyzed kriged rainfall data from 25 stations for 1980–2007. They found an average decrease of 0.18 mm/yr (p < 0.05) for three stations each characterized by low rainfall. Ghanem  studied the rainfall characteristics of Amman based on 11 stations with data from 1956 to 2006 and suggested an average decrease of 0.40 mm/yr, but this trend was not statistically significant at any station. Ghanem  analyzed 14 stations for periods ranging from 10 to 50 years (up to 2007) that showed a decrease in annual rainfall in most of Jordan. That work analyzed seven of those stations for annual trends and found an average decrease of 0.11 mm/yr, with four stations showing a statistically significant (p < 0.10) decrease of 0.61 mm/yr. Overall, these studies analyzed data from a limited number of stations and the few reported statistically significant declines in annual rainfall were in the range of 0.18–0.61 mm/yr. In addition, prior studies have shown either no trend or an overall decreasing rainfall trend ranging from 0.11 to 0.40 mm/yr but they were not statistically significant. No trends in rainfall variance over time were reported.
In this work, we use a comprehensive 44 year daily rainfall data set from 58 stations covering 1970–2013 to assess the interannual trends and spatial patterns in rainfall, variability of daily rainfall, and maximum daily rainfall. Our results focus on 58 stations covering the urbanized and agricultural western portion of the country, as rainfall data were not available in the very arid, low-population eastern portion of Jordan. We use nonparametric statistical tests to quantify the magnitude of these trends and multiple hypothesis testing to stringently evaluate statistical significance since many hypothesis tests are being performed simultaneously. In addition, we identify regional trend patterns.
2 Jordan's Climate
With a Mediterranean climate, Jordan is characterized by hot and dry summers and relatively short wetter winters (Figure 1). January is typically the coldest month and has the highest rainfall. Temperature varies from 5oC to 10o C in winter, while temperature in August, generally the hottest month, varies from 20oC to 35oC. Based on the 58 stations, mean annual rainfall from 1970 to 2013 was 258 mm/yr with rainfall occurring primarily from October to May, the remaining months being dry. Potential evapotranspiration typically exceeds rainfall. Relatively flat and low elevation areas such as the Jordan Valley suffer significant summer heat whereas high altitude areas located in the north are relatively cool in winter and experience greater rainfall.
Figure 1a shows kriged mean annual rainfall from 1970 to 2013 calculated from data collected at 58 rain gauges (data from Jordan's Ministry of Water and Irrigation) covering the western portion of Jordan. The kriged values were only used to prepare the map shown, not for trend analyses. Figure 1b shows the annual fractional deviation from the 44 year average from the mean of these 58 gauges. Of interest is that since 1995 at these gauges, 13 of 19 years had below average rainfall, while rainfall from 1970 to 1994 had roughly equal numbers of years below and above the long-term average. Furthermore, from 1970 to 1994 consecutive dry periods lasted only 2 years, while afterward dry periods persisted for 4 and 5 years, respectively. Figure 1c displays Jordan's Mediterranean climatic seasonality through the percentage of mean annual rainfall each month for each of the 58 gauging stations.
We use a multivariate statistical approach to assess the trends in four rainfall metrics: (1) annual rainfall; (2) annual variance of daily rainfall; (3) annual coefficient of variation of daily rainfall; and (4) annual maximum daily rainfall. Multivariate statistics, including parametric and nonparametric tests, are often used in climatic time series analysis to detect potential trends [López-Moreno et al., 2010; Sayemuzzaman and Jha, 2014]. We employ nonparametric tests because they are distribution-free and are based on fewer assumptions [Sonali and Nagesh Kumar, 2012].
3.1 Statistical Analysis of Trends and Regionalization of Rainfall
We investigate the presence of multiyear trends in annual rainfall, variance, coefficient of variation, and daily maximum rainfall using Kendall's tau [Kendall, 1990; Mann, 1945]. Kendall's tau is used to represent the degree of relationship between two sets of ranked data, in this case time and rainfall or rainfall statistical characteristics. The Mann-Kendall trend analysis uses Kendall's tau as the basis of a test statistic for a hypothesis test that the slope is different from 0 at a given significance level. We use Sen's slope estimator to investigate the magnitude of the trends in all four rainfall metrics. Sen's slope estimator is a method for robust linear regression that chooses the median slope among all lines through pairs of temporal rainfall or rainfall statistical characteristics data [Sen, 1968; Theil, 1992] as the best trend slope estimator. We prewhitened each time series before testing trends so as to remove lag 1 autocorrelation >0.05 and avoid false rejection of the null hypothesis [Bayazit and Onöz, 2007], adopting the method presented in Zhang et al.  and Gocic and Trajkovic .
To regionalize the rainfall data and assess the spatial pattern of the temporal trends in annual rainfall, we use Principal Component Analysis (PCA). PCA is a data reduction method that finds a reduced number of axes that maximize the explained variance in the data. The first Principal Component (PC1) is the linear function with the highest explained variance, the second (PC2) is the linear function with the second highest explained variance, and so on. For rainfall data, S-mode PCA analysis was employed to yield the correlation between the time series, with rotation to find the optimal components using the VARIMAX strategy [Kaiser, 1958].
3.2 Multiple Hypothesis Testing
We use a modern multiple hypothesis testing procedure to explore the significance of trends in rainfall. We use the k-FWER or k-familywise error rate [Lehmann and Romano, 2005], which is an analog of Type I error in the traditional single hypothesis test. The k-FWER controls the "global" probability of falsely rejecting k or more null hypotheses, and explicitly accounts for the phenomenon that, when testing a large number of hypotheses (considering trends at 58 stations in our case), some of the hypotheses will turn out to be statistically significant by chance. We formally conduct multiple hypothesis tests (MHTs) using k-FWER to determine the strict statistical validity of the apparent trends in three metrics: annual rainfall, annual variance of daily rainfall, and annual coefficient of variation of daily rainfall. For these three metrics, we analyze trends at all 58 stations, performing one hypothesis test for the trend at each station. The tests at each station are conducted independently, so for each test there is a less than 5% (or 10%) chance of incorrectly rejecting the null hypothesis that no counter-trend exists. When performed over 58 stations, we expect trends at three stations to appear significant by chance for p < 0.05, resulting in an incorrect rejection of the null hypothesis (or six for p < 0.10). The k-FWER controls the probability of rejecting a null hypothesis across all the stations given that some would appear significant by chance.
4.1 Regionalization Using Principal Component Analysis
PCA was used to explore the spatial patterns of the variance in annual rainfall over time. Figure 2 shows the results of the PCA for annual rainfall over the 44 years of record. The two most significant principal components explain nearly 74% of the variance in annual rainfall. The first principal component accounts for 38% of interannual variance in rainfall and strongly correlates with stations located in the southwest (Figure 2a). Its factor score (Figure 2b) shows a decreasing trend with time. The second principal component accounts for 36% of variance and strongly correlates with stations located in the northwest (Figure 2c). Its factor score (Figure 2d) shows an increasing trend. Figures 2a and 2c show the Pearson R correlation of each interannual rainfall trend with factor scores 1 and 2, respectively. The southwest stations have a decreasing trend over time and the northwest stations an increasing trend.
4.2 Annual Rainfall Trend
Based on the Mann-Kendall trend analysis and Sen's slope estimator at all 58 stations, 38 show decreasing rainfall trends averaging 1.2 mm/yr. Of these, three show a statistically significant decreasing trend at p < 0.05 and six others show a significant decreasing trend at p < 0.10. The remaining 20 of 58 stations show an increasing annual rainfall trend, but only one is statistically significant at p < 0.05 or p < 0.10. Figure 3a maps the Kendall's tau values according to magnitude and the p-values of Kendall's tau. Three of the four stations exhibiting a significant trend (p < 0.05) are located in the drier southwest and east (annual rainfall averaging 94 mm/yr). Figure 3b shows the magnitudes of the trend in rainfall from Sen's slope estimator, ordered based on each station's mean annual rainfall ranging from 37 to 592 mm/yr. The average indicates a decrease of 0.41 mm/yr considering all 58 stations, and among the statistically significant values the decrease is 1.45 mm/yr (p < 0.05) and 1.84 mm/yr (p < 0.10), respectively. The significant declining trends are 3–10 times greater in magnitude than those from prior studies. Our analysis shows that during the last 19 years of record, 13 of these stations experienced rainfall less than the 44 year mean (Figure 1b). As a first approximation to understand the significance of this annual sequence, a standard binomial test indicates a probability < 8.35% of this sequence occurring by chance.
Figures 3c and 3d display annual trends in variance of daily rainfall. Of the statistically significant (p < 0.05) variance trends, six stations increased and four stations decreased. The mapped trends suggest variance decreased in the low rainfall areas to the east and southwest where rainfall is below the annual median of 220 mm/yr, and variance increased in the northwest region where rainfall is above the median. The spatial patterns of annual rainfall shown in Figures 2a and 2b display a rough spatial correspondence to the decreasing and increasing trends shown here in annual variance of daily rainfall (Figure 3c).
4.3 Trends in Coefficient of Variation and Daily Maximum Rainfall
Figure 4a shows that the annual coefficient of variation (CV) of daily rainfall has increased throughout most of the country over the 44 year period of record at the 58 stations. Figure 4b also shows that 52 of the stations indicate an increasing trend in CV, 13 of which are statistically significant (p < 0.05). None of the six stations showing a decline in CV are statistically significant. All but one of the stations with a statistically significant increase in CV lie in the northwest “high” rainfall area. For the 13 stations showing statistically significant trends, the average annual increase in CV is 3.02% and for all 58 stations the average increase is 1.75%.
Figures 4c and 4d indicate that the annual maximum daily rainfall has increased in the higher rainfall areas in the northwest and has decreased at stations in the drier areas in the east and southwest. Eleven stations show statistically significant (p < 0.05) trends in maximum daily rainfall. Of these, three stations are in the lower rainfall regions and eight are in the higher rainfall region.
4.4 Multiple Hypothesis Tests
We implemented the strict multiple hypothesis testing procedure for annual rainfall, variance, and CV. To test the “global” decreasing trend in annual rainfall, we performed one-sided hypothesis tests at both 5% and 10% levels of significance at each of the 58 stations and use these results in a k-FWER multiple hypothesis testing procedure. We consider the trend at each station to be characterized by a linear model: Annual rainfall, R(t)= β0+β1*(t) for t =1,2, . . .,44 years, where β0 is the rainfall trend intercept (in 1970) and β1 is the slope of the trend indicating a change in rainfall at that station. Our null hypothesis, HR0: β1≥0, is that rainfall has increased or remained the same over the 44 years. Our alternative hypothesis, HR1: β1<0, is that rainfall has decreased (trended downward) over the 44 years. The hypothesis test for β1 is performed with the nonparametric Kendall's tau as previously described. We then tested the global null hypothesis of a nondecreasing trend in annual rainfall, using the k-FWER to control the probability of rejecting the null hypothesis due to chance occurrence when performing many hypothesis tests. This global null hypothesis of a nondecreasing trend in annual rainfall is rejected at the 10% level as three stations have significant decreasing trends in rainfall beyond chance occurrence. However, at the 5% level k-FWER could not reject the global null hypothesis.
We followed a similar procedure to analyze the trend in the annual coefficient of variation of daily rainfall, CV(t), under the null hypothesis that CV has decreased or remained the same at each station, HCV0: β1≤0, and the alternative hypothesis that HCV1: β1>0, where β1 is the trend. The same type of analysis was performed on annual variance in daily rainfall, testing two additional hypotheses. One hypothesis, HVL1, is that variance decreased at the 25 stations measuring less than the stations' median rainfall (220 mm/yr) over the 44 years of record, with HVL0: β1≥0 and HVL1: β1<0; the other hypothesis, HVH1, is that variance increased at the 33 stations measuring rainfall greater than the median value with HVH0: β1≤0 and HVL1: β1>0.
Multiple hypothesis tests for the trend in CV showed that the global null hypothesis of a non-increasing trend is rejected at the 5% level and five stations have a significant increasing trend (eight stations at the 10% level). Tests for trends in variance support the global hypotheses that variance decreased for stations below the median annual rainfall and increased for stations above the median rainfall. In both cases, the k-FWER tests at the 5% level resulted in two stations having trends that reject the null hypothesis. At the 10% level, the k-FWER tests resulted in clear rejection of the global null hypothesis and very strong corroboration of the hypothesized variance trends. There were four stations with a significant decreasing trend for stations with rainfall below the median annual rainfall and six stations having a significant increasing trend for stations above the median annual rainfall. The modern multiple hypothesis testing approach, though much more stringent, confirms the large number of significant results identified in our individual trend analyses are very unlikely to have occurred by chance alone.
We analyzed the most complete and comprehensive modern set of daily rainfall data from Jordan to date, consisting of 58 stations in the western portion of the country. We estimated temporal trends and spatial patterns in annual rainfall, variance of daily rainfall, coefficient of variation of daily rainfall, and maximum daily rainfall. In particular, at stations in the northwest portion of the country, the annual rainfall rate and variance have generally increased, whereas at stations primarily in the south they have generally decreased. During the 44 year study period (1970–2013), the rate of decrease is 0.41 mm/yr over all 58 stations and 1.45–1.84 mm/yr for those records showing a statistically significant trend at p < 0.05 and p < 0.10, respectively. The value over all stations is consistent with prior studies, but our statistically significant values exceed by over threefold those previously reported ranging from 0.11 to 0.61 mm/yr annual decline in rainfall. The decline in annual rainfall for the 1995–2013 drought period has only <8.35% probability of occurring by chance.
Two trends in variability were analyzed: annual variance of daily rainfall and annual coefficient of variation of daily rainfall. Decreasing trends in variance appear in low rainfall to the east and southwest with average rainfall of 137 mm/yr, and the stations that show increasing variance trends appear in the northwest with average rainfall of 349 mm/yr. Stations measuring rainfall below the annual median were more likely to exhibit a decrease in variance, while those measuring rainfall above the median showed an increase in variance. This pattern is consistent with principal component analysis which regionalized the stations based on annual rainfall variance. The most striking result appeared in the annual coefficient of variation of daily rainfall (CV). Approximately 90% of stations showed an increase in CV over time, and of the remaining stations none showed a statistically significant (p < 0.10) decrease. The annual increase in CV is ∼2–3%. The northwest region showed the most significant increase in CV.
Strict multiple hypothesis tests using the k-FWER reinforced single hypothesis tests and confirmed a statistically significant trend across the stations of a decline in annual rainfall at the 10% level but not at the 5% level, an increase in the annual coefficient of variation of daily rainfall at the 5% level, and spatially increasing (northwest) and decreasing (southwest and east) trends in the annual variance of daily rainfall at the 5% level. This work provides a benchmark for future studies aimed at quantifying changes in rainfall magnitude and variability in Jordan, and may be of value in future rainfall trend analyses conducted for the rest of the Middle East. This information is important to water managers who are planning for future water needs in the face of increasing demographic pressures on water supplies and an ongoing drought, which has now lasted more than a decade. Water planners need to track data that might indicate the beginnings of a structural change in rainfall as predicted with significant uncertainty by models presented by the IPCC .
This work was supported by the National Science Foundation (NSF) under grant GEO/OAD-1342869 to Stanford University as part of a Belmont Forum project on water security. NSF support for the effort of B. Rajaratnam was provided by AGS-1003823 to Stanford University. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. Additional support was obtained through a UPS Foundation grant to Stanford University. We also thank Stanford's Woods Institute for the Environment for its support of the Global Freshwater Initiative. We are grateful to the Jordanian Ministry of Water and Irrigation for providing the rainfall data and other information. Rainfall data used in this paper may be obtained from the Ministry of Water and Irrigation of Jordan (http://www.mwi.gov.jo).