Research Article Variability and Trend of Annual Maximum

Research ArticleVariability and Trend of Annual Maximum Daily Rainfall inNorthern Algeria

Abderrahmane Nekkache Ghenim and Abdesselam Megnounif

ldquoEau et Ouvrage dans Leur Environnementrdquo Laboratory Tlemcen University BP 230 13000 Tlemcen Algeria

Correspondence should be addressed to Abderrahmane Nekkache Ghenim anghenimyahoofr

Received 3 November 2015 Accepted 7 June 2016

Academic Editor Robert Tenzer

Copyright copy 2016 A N Ghenim and A Megnounif This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

The daily rainfall dataset of 35 weather stations covering the north of Algeria was studied for a period up to 43 years recordedafter 1970s The variability and trends in annual maximum daily rainfall (AMDR) time series and their contributions in annualrainfall (AR) were investigated The analysis of the series was based on statistical characteristics Burnrsquos seasonality procedureMann-Kendall test and linear regression technique The contribution of the AMDR to AR analysis was subjected to both theBuishand test and the double mass curve technique The AMDR characteristics reveal a strong temporal irregularity and have awide frequency of occurrence in the months of November and December while the maximum intensity occurred in October Theobserved phenomenon was so irregular that there was no dominant season and the occurrence of extreme event can arrive at anytime of the year The AMDR trends showed that only six of 35 stations have significant trend For other stations no clear trend washighlighted This result was confirmed by the linear regression procedure On the contrary the contribution of AMDR in annualtotals exhibited a significant increasing trend for 57 of the sites studied with a growth rate of up to 50

1 Introduction

Rainfall is a fundamental element of climate which is forseveral decades in perpetual mutations For most regionsaround the Mediterranean these changes resulted in signif-icant rainfall deficits [1 2] accompanied by an increase ofexceptional events such as severe droughts and devastatingfloods [3 4] The Mediterranean environments typical ofsemiarid regions that enjoy a rather pleasant climate withsunshine and its fine weather can suffer hazardous situa-tions since several regions are regularly struck by severerainstorms Such events are highly variable in the time andspace [5] and often lasted less than one day [6] Thereforethe critical parameter of these rainstorms is the maximumdaily rainfall rather than the total rainfall The annualmaximum daily rainfall is defined as an extreme instancewith critical duration for a watershed region or state [7]In the hydrological year the daily maximum rainfall is theparameter considered to assess the immediate impact on thehydrological response of streams flooding cities soil erosiondams silting and agricultural production [8 9]

Located on the southern shore of the MediterraneanAlgeria suffers a semiarid to arid climate Despite a droughtthat has lasted for over three decades brief intense anddevastating floods often affect cities Due to the intensity ofrainfall events that typically last less than 24 hours and thevulnerability of urban areas the floods have caused damageand significant loss of human lives The only flood thatoccurred in the city of Algiers inNovember 2001 caused some740 casualties [10ndash12]

The objective of this study is to contribute to the knowl-edge of the variability of annual maximum daily rainfall andits changes in the north of Algeria A particular attention ispaid to detect possible trends characterizing AMDR seriesand to evaluate changes in AMDR contribution to annualtotals

2 Study AreaMaterials and Methods

The study area is the north of Algeria and covers 15 of thetotal surface of the country (238 million km2) The length

Hindawi Publishing CorporationInternational Journal of GeophysicsVolume 2016 Article ID 6820397 11 pageshttpdxdoiorg10115520166820397

2 International Journal of Geophysics

12

3

45

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1078

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11

12

13

1617

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221415

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24

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26 27 29

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31

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3534

25 35 45 55 65 75

1

19 20

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221415

23

24

25

26 27 29

28 30

31

32

33

3534

150 300 450 600 750 900

(a)

(b)

23

45

6

1078

9

11

12

13

1617

1836∘N

35∘N

35∘N

36∘N

9∘E8

∘E7∘E6

∘E5∘E4

∘E3∘E2

∘E1∘W 0

∘1∘E

9∘E8

∘E7∘E6

∘E5∘E4

∘E3∘E2

∘E1∘W 0

∘1∘E 60

∘40

∘20

∘0∘

20∘

40∘

20∘

0∘

20∘

Algeria

Study area

Figure 1 Locations of rainfall stations in northernAlgeria andmean values intervals of annual rainfall (a) and annualmaximumdaily rainfall(b)

of the Mediterranean coastline is about 1200 km Because ofits geographic position and its mountainous nature rainfallshows strongest contrasts between the various areas Thisregion has a high spatial and temporal climatic variabilityknown as the Mediterranean climate Intra-annual rainfallis irregular and most rains fall between October and Aprilwhile infrequent and local storms occur in the dry seasonfrom July to October

Rainfall data were collected by the National Agencyof the Hydraulic Resources (ARNH) (httpwwwanrhdz)Because there were too many gaps after colonial period inthe 1960s and where the number of years of observationswas too low for statistical purposes many station series werediscarded from the data set As a result only 35 rainfall serieswere selected (Figure 1)

The data collected are a set of daily rainfall series forthe period after 1970 They include less than 5 of gapsThese are replaced by the values of the station which hasthe best correlation The data were tested for their qualitycontrol The suspect data were cross-checked with thoseof nearby stations (some are not used in this study) Thearithmetic sum of daily heights recorded is the annual rainfallvalue (AR) while the daily maximum observed during theyear represents the annual maximum daily rainfall (AMDR)Data were aggregated according to hydrological year fromSeptember to August The selected stations are described bythe geographical coordinates number of years of observationand statistical characteristics (Table 1)

In the Mediterranean region it is unlikely that rainstormlasts more than 24 hours [6] So the annual maximumdaily rainfall (AMDR) series may be introduced to study

the distribution of extreme precipitation occurrences withina year To examine the regularity for such series we appliedthe seasonality as described by Burn [13] This methodused to estimate the timing and regularity of floods wasthen transposed to extreme rainfall in particular AMDR[14] It assesses the degree of similarity of watersheds inrelation to the hydrological response or the occurrence ofextreme rainfall Burnrsquos vector defined by (120579 119903) represents thevariability of the date of occurrence of all extremes events Itsdirection is the mean date of the occurrence of the extremesevents and the modulus is the variability around the meanvalue The dates of the AMDR occurrence are based on thecalendar year January 1 is the 1st day and December 31 is the365th day

Each date 119895119894was replaced by an angle

120579119894= 119895119894

2120587

36525 120579119894isin 0 75

∘ 360

∘ (1)

The obtained series covers the unit circle where each term canbe described in polar coordinates as a vector (cos 120579

119894 sin 120579119894)

where 120579119894indicates the direction expressed in radians Follow-

ing the Burn approach the Cartesian coordinates 119909119894= cos 120579

119894

and 119910119894= sin 120579

119894 are used to evaluate Burnrsquos vector defined

by (120579 119903) the mean direction and mean modulus given by thefollowing equations

120579 = arctg(119910

119909) 120579 isin [0

∘ 360∘]

119903 = radic1199092+ 1199102 119903 isin [0 1]

(2)

International Journal of Geophysics 3

Table 1 Descriptive statistic of AMDR in northern Algeria

Number Station 119873Coordinates Average AR (mm) AMDR (mm)

Latitude Longitude Average Max Cv Cs1 Pierre du chat 41 1∘2610158405210158401015840W 35∘0810158403710158401015840N 330 46 2554 081 4602 Meffrouche 41 1∘1710158403110158401015840W 34∘5110158401910158401015840N 608 64 1581 050 1303 Bensekrane 37 1∘1310158402610158401015840W 35∘0410158402810158401015840N 377 46 822 036 0464 Ras El Ma 39 0∘4810158403410158401015840W 34∘2910158404110158401015840N 194 25 522 050 0515 S A Benyoub 42 0∘4410158400410158401015840W 34∘5810158403810158401015840N 351 35 772 042 0856 Sarno 41 0∘3510158405210158401015840W 35∘4410158405910158401015840N 357 40 887 045 1487 Hassi Daho 40 0∘3210158402610158401015840W 35∘0510158402810158401015840N 313 38 103 040 2108 Cheurfas 35 0∘1510158400610158401015840W 35∘2410158401510158401015840N 328 38 1144 056 1939 Ain El Hadjer 35 0∘0810158405610158401015840E 34∘4510158402510158401015840N 330 29 616 038 11410 Ghriss 38 0∘0910158405910158401015840E 35∘1410158404610158401015840N 291 31 52 031 07411 Maoussa 35 0∘1410158405310158401015840E 35∘2210158404110158401015840N 292 34 849 044 11612 Oued El Kheir 41 0∘2210158405010158401015840E 35∘5710158400810158401015840N 301 31 944 050 21613 Bekhedda 33 1∘0210158401510158401015840E 35∘2010158403210158401015840N 315 30 644 041 08914 Meured 41 2∘2410158402710158401015840E 36∘2610158405810158401015840N 615 71 1768 051 16215 Djebabra 41 2∘2610158400610158401015840E 36∘2310158404310158401015840N 647 59 1768 054 17916 Ameur El Ain 41 2∘3410158400110158401015840E 36∘2810158403110158401015840N 586 40 83 039 09917 Kolea 41 2∘4610158401910158401015840E 36∘3810158400410158401015840N 606 54 1055 034 09318 Ouzera 41 2∘5010158405010158401015840E 36∘1510158402110158401015840N 571 52 134 046 13819 Hamiz-D9 38 3∘1910158404910158401015840E 36∘3910158402610158401015840N 598 57 1029 038 05620 Lakhdaria 39 3∘3510158401210158401015840E 36∘3710158404010158401015840N 701 61 1174 040 10221 Krsquosob 34 4∘3410158400310158401015840E 35∘4910158403210158401015840N 220 25 535 038 12022 Sidi Yahia 40 4∘3710158401110158401015840E 36∘2510158401910158401015840N 377 35 701 033 10023 Batna 40 6∘1010158402310158401015840E 35∘3310158405310158401015840N 374 36 644 035 04024 El Milia 40 6∘1610158403810158401015840E 36∘4510158402110158401015840N 874 70 2103 052 17025 Ain Tinn 40 6∘2610158402110158401015840E 35∘2210158403910158401015840N 430 47 143 046 24426 Timgad 40 6∘2810158400710158401015840E 35∘2910158405110158401015840N 289 33 937 044 19327 Chelia 43 6∘3910158400310158401015840E 35∘2210158400210158401015840N 481 52 1775 056 26528 Zardasas 41 6∘5310158404810158401015840E 36∘3510158405810158401015840N 658 58 137 054 12429 Ain Mimoun 40 6∘5710158402210158401015840E 35∘2410158405510158401015840N 434 43 1161 041 23230 Helioplolis 41 7∘2610158404410158401015840E 36∘3010158403210158401015840N 596 54 1037 043 07931 Ain Beida 43 7∘2710158400310158401015840E 35∘4710158405010158401015840N 408 40 104 036 22432 Ain Berda 42 7∘3510158404710158401015840E 36∘4110158403010158401015840N 631 53 111 043 09433 Bouchegouf 41 7∘4210158403510158401015840E 36∘2710158403310158401015840N 545 32 120 041 11234 Ain Kerma 41 8∘1110158404610158401015840E 36∘3510158402310158401015840N 712 57 1551 047 14135 Ain Assel 41 8∘2110158405710158401015840E 36∘4610158400310158401015840N 821 60 1427 038 131119873 years of record Cv coefficient of variation Cs coefficient of skewness

where

119909 =1

119899

119899

sum119894=1

cos 120579119894

119910 =1

119899

119899

sum119894=1

sin 120579119894

(3)

When 119903 decrease to zero there is no single dominant seasonand the occurrence of extreme event can arrive at any timeof the year while 119903 = 0 is a virtual value indicating thatextreme events occur on the same dayThe date of occurrence

of extreme events is regular as the modulus approaches theunit more

The annual trend of AMDR series was analyzed byusing two statistical methods the Mann-Kendall test andthe linear regression The nonparametric Mann-Kendall test[15 16] detects the direction of trend patterns in hydrologicalvariables For a time series (119909

119894) of 119899 values each value 119909

119894is

compared with all corresponding 119909119895to compute the sign and

the indices 119894 and 119895 take the respective values 119894 = 1 2 119899 minus 1and 119895 = 119894+1 119894+2 119894+3 119899 Kendallrsquos 119878-statistics is based onthe sum and variance computation In this study an error riskof 5 is accepted that means a probability threshold belowwhich the null hypothesis the trend series is monotonic will


be rejected Thereby the Mann-Kendall test is expected to beless affected by the outliers because its statistic is based on thesign of differences rather than on the values of the randomvariable [17]

The linear regression procedure is a statistical techniquefor estimating the relationships among variables (eg 119883 and119884)The straight line119884 = 119886119883+119887 is obtained by the least squareregression method The slope (119886) indicates the average rateof change in the variable used If the change is significantlydifferent from zero then a real change occurs Positive slopedefines increasing trend while the negative one indicates adecreasing trend

The temporal series of the rate contribution of the AMDRto annual rainfall was subjected to the Buishand test to assesstrends and date of departure of homogeneity [18] The test isa graphical method based on the evolution of the followingequation

CS119896(119883) = sum

119894le119896

119878119894= sum119894le119896

(119883119894minus 119883

119904) (4)

where119883119894is the variable119883 is themean value of the series and

119904 is the standard deviationThe statistical parameter max

119896|CS119896| is a good indicator

of the departure of homogeneity [19] The increasing ordecreasing limbs of both sides of the extremum max

119896|CS119896|

correspond to surplus or deficit periods respectively Sowhen significant change is confirmed we applied the doublemass curve to quantify the surplus or deficit [20]The curve isa straight line whose slope is the proportionality constant Abreak in slope indicates a change of the proportionality [21]The break in slope and the angle formed by two straight linesindicate the date and the degree of change in the behavior ofthe phenomenon

3 Results

In the study sites located in the north of Algeria where adivision in increments of 150mm is shown in Figure 1(a)the average annual rainfall varies from 194mm (Ras El Mastation code number 4) to 874mm (El Milia station codenumber 24) (Table 1) Spatially rainfall is distributed in fourareas [22]

(i) The central highlands Sersou and Ras El Ma regionsthough situated at high altitude are sheltered com-pared to wet currents where rainfall is less than300mm

(ii) The western region of the country is characterizedby a relative sheltered position compared to maritimeinfluences and the low volume of the relief Annualaverages are generally less than 450mm

(iii) The mountainous areas and high interior plains(mountains of Tlemcen in thewest and themountainsof Zaccar and Dahras in the east) are characterized bythe relative importance of total rainfall with annualaverage exceeding 600mm

(iv) The Atlas Tellien region exposed to the north andnorthwest records rainfall amounts that can exceed800mm

For AMDR values a division in increments of 10mm andthe main statistical parameters estimated for all the stationsare shown respectively in Figure 1(b) and Table 1 Spatialvariability of intra-annual averages of AMDR ranges from aminimum of 25mm (station Ras El Ma code number 4) to amaximum of 71mm (Station Meured code number 14) Lowvalues are concentrated on the west side while the high valuesare in the east and center of the country

Through the 35 studied stations the temporal distributionof the annual maximum daily rainfall is irregular Thecoefficients of variation Cv vary between 31 and 81 witha spatial average of 44 The most irregular series Cv above05 are found near the reliefs The stations with the codenumbers 1 and 24 are positioned facing the north and thestations with code numbers 2 4 8 12 14 15 24 27 and 28are positioned facing the south (Figure 1) The largest valuesof 255 and 210mm were recorded respectively in the westregion in station code number 1 in 1999-2000 and at the eastin station code number 24 in 1990-1991 The spatial averageof maximum daily rainfall is about 114mm which represents24 of the spatial average of mean inter annual rainfall

For stations under consideration the skewness coefficient(Cs) has positive values fluctuating from 04 to 46 with aspatial mean of 143Thereby at level confidence of 95 thereis rejection for normal distribution for a majority of stationssince the values of skewness coefficient are above 062 for31 of 35 stations That means low values are more frequentwhile high values are still rare but excessive The pronouncedskewness coefficients occurred at the station Pierre du chat(code number 1)

The difference in positioning stations (near the coastlinefacing the sea at high altitude or between the mountains)prevents a relatively good correlation to the altitude Thespatial variability of rainfall (AR and AMDR) is mainlyinfluenced by latitude (Figure 2) The average increase forAR and AMDR respectively is about 140mm and 25mm to100 km latitude

The occurrence of AMDR was more frequent duringNovember followed by December and January (Figure 3(a))while the peaks in order of importance occurred in OctoberDecember and November (Figure 3(b)) In addition theseasonal concentration index 119903 varies from 003 to 032 withan average of 015 (Figure 4) So there is no single dominantseason and the occurrence of an extreme event can arrive atany time of the year On the other hand Burnrsquos method showsthat AMDR were more concentrated in February through40 of the stations against 20 in October (Figure 4)

The results of the Mann-Kendall test are summarizedin Table 2 and Figure 5(a) At the 95 confidence levelonly 6 of 35 stations show significant trend The stationsRas El Ma Ain Berda and Chelia show an increasing trendwhereas the trend is decreasing in Sarno Ameur El Ain andDjebabra while in the remaining stations no significant trendis observed This finding corroborates the results obtainedby the linear regression analysis (Table 2 and Figure 5(b))


20

30

40

50

60

70

80

100 200 300 400 500

Aver

age A

MD

R (m

m)

Latitude (km) (Lambert coordinates)

R2= 052

Y = 0116X + 1333

(a)

100

200

300

400

500

600

700

800

900

100 200 300 400 500

Aver

age A

R (m

m)


R2= 069

Y = 186X minus 4635

(b)

Figure 2 Relationship of AMDR (a) and AR (b) with latitude in northern Algeria

1 2 3 4 5 6 7 8 9 10 11 12(Months)

Grey monthly occurrence of AMDR for individual stations Black monthly average occurrence of AMDR

0

5

10

15

20

25

30

35

Mon

thly

occ

urre

nce o

f AM

DR

()

(a)

0

50

100

150

200

250

300

1 2 3 4 5 6 7 8 9 10 11 12

Mon

thly

max

imum

AM

DR

valu

es (m

m)

(Months)

Grey monthly maximum AMDR values for individual stationsBlack monthly maximum AMDR values for all stations

(b)

Figure 3 Annual maximum daily rainfall (AMDR) frequency (a) and maximum values (b) at monthly scales

0

30

330

300

6090

120

150

180

210

240270

108

0604

02

04

02

Figure 4 Location of seasonal concentration index 119903 for AMDR The angles 0∘ represents January 1 90∘ represents April 1 180∘ representsJuly 1 and 270∘ represents October 1


Table 2 119875 values and Tau of Mann-Kendall test the slope (119886) of linear regression analysis and AMDR contribution to AR over the periodafter 1970 in the north of Algeria

Number Station Mann-Kendall test Linear regression AMDR contribution to AR119875 value Tau Slope (119886) Date of change deficit (minus) or surplus (+)

1 Pierre du chat 0167 minus0151 +0118 2001 +3492 Meffrouche 0078 minus0193 minus0872 Complex3 Bensekrane 1000 +0002 +0024 1987 +4124 Ras El Ma 0002lowast +0022 +0353 1999 +2295 S A Benyoub 0374 +0104 +0286 1987 +2536 Sarno 0047lowast minus0217 minus0427 Complex7 Hassi Daho 0305 minus0114 minus0027 1997 +2788 Cheurfas 0787 minus0034 +0158 1986 +2969 Ain El Hadjer 0822 minus0029 minus0140 1988 minus17410 Ghriss 0874 minus0024 minus0089 1983 +42611 Maoussa 0287 +0128 +0335 Complex12 Oued El Kheir 0928 +0011 +0032 1997 +18913 Bekhedda 0687 +0051 +0061 1991 +18314 Meured 0240 minus0129 minus0437 Complex15 Djebabra 0001lowast minus0368 minus1223 1985 minus22716 Ameur El Ain lt10minus3lowast minus0431 minus0802 Complex17 Kolea 0574 minus0062 minus0045 1990 +07918 Ouzera 0084 minus0189 minus0588 No trend19 Hamiz-D9 0372 minus0102 minus0349 Complex20 Lakhdaria 0200 minus0145 minus0301 1990 +8521 Krsquosob 0778 minus0036 minus0057 1981 +18422 Sidi Yahia 0577 +0066 +0034 1987 minus18823 Batna 0576 +0063 +0093 No trend24 El Milia 0363 +0101 +0285 1981 +49925 Ain Tinn 0651 +0111 minus0166 1985 +12226 Timgad 0402 +0094 +0275 1992 +10027 Chelia 0013lowast +0265 +0664 No trend28 Zardasas 0357 +0101 +0293 1979 +29629 Ain Mimoun 0807 minus0028 +0042 1986 minus110130 Helioplolis 0200 +0140 +0425 1991 +28131 Ain Beida 0944 minus0009 minus0151 1989 minus12132 Ain Berda 0032lowast +0232 +0601 1987 +14233 Bouchegouf 0094 +0183 +0411 1998 +33234 Ain Kerma 0551 minus0066 minus0255 Complex35 Ain Assel 0142 +0161 +0345 1990 +142lowastTrend statistically significant at 5 level

Indeed for 34 stations the slope (119886) is less than |1| leadingto stationarity of the series The only Djebabra station showsa moderate decreasing trend

The curves resulting from Buishand procedure wereclassified into four distinct cases The first case concerns fiverainfall stations (Ain Beida Ain El Hadjer Sidi Yahia AınMimoun and Djebabra) where Cs

119896curve shows ascending

and descending lambs and the maximum of the Cs119896curve

corresponds to the date of change (Figure 6(a)) The declineof the AMDR contribution to annual rainfall manifested bythe falling lamb was quantified by the double mass curveand varies between 121 and 227 The dates of change were

observed during the 1980s (Table 2)The second case grouped20 rainfall series exhibiting opposite behavior (Figure 6(b))The AMDR contribution has increased significantly (eg atEl Milia station the increase reaches about 50) The datesof change occurred from the end of 1970s to the end of1990s The third case represents seven of 35 rainfall seriesand is manifested by a complex form showing more thanone date of the change However lambs of the Cs

119896curves

were not sufficiently long to apply the double mass method(Figure 6(c)) For the last case three of 35 rainfall series noclear trend can be detected for any rainfall sequence (egOuzera Batna and Chelia) (Figure 6(d))


1

23

4

5

6

107

8

9

11

12

13

1617

18

19 20

21

2214

15

23

24

25

2629

28 30

31

32

33

3534

27

Increasing trendDecreasing trend

No trendStatistically significant at the 5 level

(a) Mann-Kendall trend

1

23

4

5

6

1078

9

11

12

13

1618

20

21

2214

15

23

24

25

2629

28 30

31

32

33

3534

27


17 19

(b) Linear regression trend

Figure 5 Mann-Kendall (a) and linear regression (b) trend ofAMDR over the period after 1970 in northern Algeria

4 Discussion and Conclusion

The data of 35 rainfall stations recorded after 1970 andcovering the north of Algeria reveal that rainfall undergoesan overall downward trend Deficit rate between 20 and40 was estimated in several parts of the country [23ndash27] This decrease in annual rainfall was accompanied bya large temporal irregularity like the Mediterranean region[28 29] In terms of AMDR values coefficients of variationfor the different sites vary at plusmn12 around the average of44 showing a more pronounced irregularity occurrencebut in the same proportions as in other regions [30ndash32]Indeed the skewness values of the time series which showif the empirical distribution of the data follows a normaldistribution are more important in the extreme east of thecountry than in the west and the center (a ratio of 166)All positive values of Cs found indicating that distributionshifted to the left of themedian (Table 1) are of the same orderas those of Chott-Chergui basin in western Algeria [33] Inthis analysis we exclude Pierre du chat station for which anexceptional value of 2554mm has increased all coefficients

For a better understanding of water availability it is veryinteresting to demarcate the quasi-homogeneous climaticzones and identify the climatic subregions in an observationnetwork [34] Nevertheless in the north of Algeria theproximity of the Mediterranean and the variety surroundingreliefs make it difficult to delimiting homogeneous areasMoreover the increased baroclinic instability in saturated air

is closely related to latent heat release and thus to the devel-opment of convective phenomena During the rainy seasonnorthern Algeria is affected by the polar front especially theeast of the country Further south the highlands are generallyaffected by western disturbances following the orographicforcing that causes thunderstorms with heavy rainfall [35]Then the correlation between rainfall and altitude is complexIt may be valid only for limited areas Contrary to that therainfall is positively correlated with latitude and the east ofthe country is much wetter than the west (Figure 2)

For almost all stations mean values of AMDR as wellas AR are two to five times higher for particular years Thisdisparity between the average values and peaks combinedwith statistical parameters cited above is illustrated in Fig-ure 4 according to Burn [13] The seasonal concentrationindex 119903 varies between 003 and 032 showing that there isno single dominant season and the time of the occurrenceof an extreme event is distributed around the year Thisdemonstrates the extent of rainfall irregularity in the south ofthe Mediterranean This is not always the case through otherregions In central Slovakia for example the phenomenonhas a spatiotemporal occurrence more regular [14] Despitethis October and November are the months when the floodsare the deadliest It should be noted thatAlgeria is the countrywhere the number of flood victims is the highest of theMediterranean countries [36]

The examination of AMDR trends using the Mann-Kendall test and linear regression procedure shows thatunlike the annual rainfall undergoing a downward trend inmost of the rainfall stations in Algeria [28 37ndash39] thereis no clear trend to rise or fall in the series of AMDRfor the majority of the sites studied The region of studyis characterized by a great number of complexities relatedto geography and topography where the combination ofthe effects produced makes weather forecasting exceedinglydifficult causing high spatiotemporal variability So likemanyother parts of the Mediterranean area a majority of AMDRseries recorded in the north of Algeria show nonsignificanttrends [38 40 41] However globally AMDR series show anincrease in tendency in the east of the country and a decreasein the centerwhile in thewest the system ismore complicatedand there is nomajority of stations that differs from others Inthis context the IPCC report confirmed that the behavior ofextreme rainfall differs considerably from the annual totals bysome considerable geographical differences in the frequencytiming and magnitude of events [42]

The present study does not converge with the resultsdeveloped by some authors and in the occurrence of extremerainfall forecasts which predict an increase in extreme rainfallin many parts of the world even in areas where the averageannual rainfall has a downward trend [42ndash45] For someauthors this finding is apparently valid for Mediterraneancountries that record rainfall deficits since 3-4 decades [3 28]However our study reveals that not only does the trend ofthe AMDR series depend on global and regional settings butalso it is highly influenced by local geographical character-istics This result corroborates the finding of Tramblay et al[38] and Jones et al [46] who cited the orography influenceas a main cause generating local climatic processes Other


0

2

4

6

8

10

12

0

1

2

3

4

Cum

ulat

ive r

epor

t of A

MD

R co

ntrib

utio

n in

AR

Before date of changeAfter date of change

(Years)20102000199019801970

(Years)20102000199019801970

Csk

(AM

DR

AR)

(a)

0

2Date of change

After date of changeBefore date of change

0

1

2

3

4

Cum

ulat

ive r

epor

t of A

MD

R co

ntrib

utio

n in

AR

(Years)20102000199019801970

(Years)20102000199019801970

minus4

minus2

minus6

minus8

Csk

(AM

DR

AR)

(b)

0

1

2

0

1

2

3

4

5

6

Cum

ulat

ive r

epor

t of A

MD

R co

ntrib

utio

n in

AR

(Years) (Years)2010200019901980197020102000199019801970

minus1

minus2

minus3

minus4

minus5

Csk

(AM

DR

AR)


(c)

0

1

2

3

4

(Years)

0

1

2

3

4

Cum

ulat

ive r

epor

t of A

MD

R co

ntrib

utio

n in

AR

20102000199019801970

(Years)20102000199019801970

minus1

minus2

minus3

minus4

Csk

(AM

DR

AR)

(d)

Figure 6 Buishand and double mass methods applied to AMDR contribution to AR


investigations of extreme rainfall across many countries ofthe globe show that extreme rainfall trend is complex Forexample it had increased in the USA China AustraliaCanada Norway Mexico and Poland [47] where no cleartrend was detected in other regions such as in Brazil andEthiopia [7 48] Although a general trend for drought anda reduction in rainfall intensity was predicted for easternMediterranean [49] the extreme precipitation trend is moremisunderstood as in Jordan [32]

Without having a provided dominant season the AMDRoccurred mainly between October and March (Figure 4)and the highest values were recorded in autumn (Figure 3)Similar results were observed in other Mediterranean siteswhere a slight increase in autumn rainfall was mainly felt inOctober [50 51] leading tomore concentrated rainfall duringthe hydrological year [52]

The relationship between the values of the AMDR andAR in the north of Algeria has experienced significanttemporal changes in most of the studied stations Howeverfour configurations of the relationship between AMDR andAR (Figure 6) are distinguished and seem to be related tothe climate change which operated in the Mediterraneanregion Despite the lack of trend in AMDR series theircontributions in the annual rainfall are on the rise Thisoccurred in 80 of stations spread from the east to the west(not taking into account the stations that submitted a complexor nonsignificant trend behavior) The rate of increase ofthis contribution will be from 8 to about 50 Although therates of reduction of annual precipitation in the post-1970period are higher than 20 formost stations in Algeria somevery high rates of increase in the contribution of the AMDRin annual totals are amplified by extremely high values ofthe recorded AMDR (example of El Milia Station) In thiscontext and by analyzing the contribution of events in annualprecipitation in the north of the Mediterranean De Luis etal [53] reported that in all the studied stations more than37 experienced an increasing contribution against 15withdecreasing contribution

The start of the change leading to the increasing con-tribution of the AMDR to the annual rainfall occurredmainly during the 1980s and 1990s and the AMDR occurredprincipally in the autumn season However this observationismisleading because the decrease of annual rainfall ismainlydue to the sharp diminution of the winter rainfall Indeedthe values of the AMDR that occurred during autumn are inthe same proportions observed in winter (Figure 3) In theMediterranean region Giorgi and Lionello [50] observed asharp falling in the winter rainfall against a small increase inautumnTheymainly attributed the increase in extreme dailyintensities to the reduction of annual precipitation The rateof this reduction was estimated to be more than 30 in thenorthwest of Algeria [54]

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] A Longobardi and P Villani ldquoTrend analysis of annual andseasonal rainfall time series in the Mediterranean areardquo Inter-national Journal of Climatology vol 30 no 10 pp 1538ndash15462010

[2] P T Nastos ldquoTrends and variability of precipitation within theMediterranean region based on Global Precipitation Climatol-ogy Project (GPCP) and ground based datasetsrdquo in Advances inthe Research of Aquatic Environment vol 1 pp 67ndash74 Springer2011

[3] P Alpert T Ben-Gai A Baharad et al ldquoThe paradoxicalincrease of Mediterranean extreme daily rainfall in spite ofdecrease in total valuesrdquo Geophysical Research Letters vol 29no 11 pp 1ndash31 2002

[4] A Bodini and Q A Cossu ldquoVulnerability assessment ofCentral-East Sardinia (Italy) to extreme rainfall eventsrdquoNaturalHazards and Earth System Science vol 10 no 1 pp 61ndash72 2010

[5] S Beguerıa SMVicente-Serrano J I Lopez-Moreno and JMGarcıa-Ruiz ldquoAnnual and seasonal mapping of peak intensitymagnitude and duration of extreme precipitation events acrossa climatic gradient northeast Spainrdquo International Journal ofClimatology vol 29 no 12 pp 1759ndash1779 2009

[6] T Haktanir S Bajabaa and M Masoud ldquoStochastic analyses ofmaximum daily rainfall series recorded at two stations acrossthe Mediterranean Seardquo Arabian Journal of Geosciences vol 6no 10 pp 3943ndash3958 2013

[7] J R Porto de Carvalho E D Assad A F de Oliveira and HSilveira Pinto ldquoAnnual maximum daily rainfall trends in themidwest southeast and southern Brazil in the last 71 yearsrdquoWeather and Climate Extremes vol 5 no 1 pp 7ndash15 2014

[8] M J M Romkens K Helming and S N Prasad ldquoSoil erosionunder different rainfall intensities surface roughness and soilwater regimesrdquo Catena vol 46 no 2-3 pp 103ndash123 2002

[9] X-C Zhang and W-Z Liu ldquoSimulating potential response ofhydrology soil erosion and crop productivity to climate changein Changwu tableland region on the Loess Plateau of ChinardquoAgricultural and Forest Meteorology vol 131 no 3-4 pp 127ndash142 2005

[10] G J Tripoli C M Medaglia S Dietrich et al ldquoThe 9-10November 2001 Algerian flood a numerical studyrdquo Bulletin ofthe American Meteorological Society vol 86 no 9 pp 1229ndash1235 2005

[11] S Argence D Lambert E Richard et al ldquoHigh resolutionnumerical study of the Algiers 2001 flash flood sensitivityto the upper-level potential vorticity anomalyrdquo Advances inGeosciences vol 7 pp 251ndash257 2006

[12] N Sohne J-P Chaboureau S Argence D Lambert and ERichard ldquoObjective evaluation of mesoscale simulations of theAlgiers 2001 flash flood by the model-to-satellite approachrdquoAdvances in Geosciences vol 7 pp 247ndash250 2006

[13] D H Burn ldquoCatchment similarity for regional flood frequencyanalysis using seasonality measuresrdquo Journal of Hydrology vol202 no 1ndash4 pp 212ndash230 1997

[14] J Szolgay J Parajka S Kohnova andKHlavcova ldquoComparisonof mapping approaches of design annual maximum dailyprecipitationrdquo Atmospheric Research vol 92 no 3 pp 289ndash3072009

[15] H BMann ldquoNonparametric tests against trendrdquo Econometricavol 13 pp 245ndash259 1945

[16] M G Kendall Rank Correlation Methods Charles GriffinLondon UK 4th edition 1975


[17] D R Helsel and R M Hirsch Statistical Methods in WaterResources vol 529 Elsevier AmsterdamTheNetherlands 1992

[18] T A Buishand ldquoSome methods for testing the homogeneity ofrainfall recordsrdquo Journal of Hydrology vol 58 no 1-2 pp 11ndash271982

[19] D Raes D Mallants and Z Song ldquoRAINBOW a softwarepackage for analysing hydrologic datardquo inHydraulic EngineeringSoftware VI W R Blain Ed pp 525ndash534 ComputationalMechanics Publication Boston Mass USA 1996

[20] C F Merriam ldquoA comprehensive study of the rainfall onthe Susquehanna Valleyrdquo Transactions American GeophysicalUnion vol 18 no 2 pp 471ndash476 1937

[21] W-W Zhao B-J Fu Q-H Meng Q-J Zhang and Y-HZhang ldquoEffects of land-use pattern change on rainfall-runoffand runoff-sediment relations a case study in Zichang water-shed of the Loess Plateau of Chinardquo Journal of EnvironmentalSciences vol 16 no 3 pp 436ndash442 2004

[22] AMedjerab and LHenia ldquoRegionalisation des pluies annuellesdans lrsquoAlgerie nord-occidentalerdquo Revue Geographique de lrsquoEstvol 45 no 2 pp 1ndash12 2005

[23] H Meddi and M Meddi ldquoVariabilite des precipitationsannuelles du Nord-Ouest de lrsquoAlgerierdquo Secheresse vol 20 no1 pp 57ndash65 2009

[24] A N Ghenim AMegnounif A Seddini andA Terfous ldquoFluc-tuations hydropluviometriques du bassin versant de lrsquoOuedTafna a Beni Bahdel (Nord Ouest Algerien)rdquo Secheresse vol 21no 2 pp 115ndash120 2010

[25] A N Ghenim and A Megnounif ldquoAnalyse des precipitationsdans le Nord-Ouest Algerienrdquo Secheresse vol 24 no 2 pp 107ndash114 2013

[26] A N Ghenim and A Megnounif ldquoAmpleur de la secheressedans le bassin drsquoalimentation du barrage Meffrouche (Nord-Ouest de lrsquoAlgerie)rdquo Geographie Physique et Environnement(Physio-Geo) vol 7 pp 35ndash49 2013

[27] A Dahmani and M Meddi ldquoImpact of rainfall deficiency onwater resources in the plain Ghriss Wilaya of Mascara (West ofAlgeria)rdquoAmerican Journal of Scientific and Industrial Researchvol 2 no 5 pp 755ndash760 2011

[28] C M Philandras P T Nastos J Kapsomenakis K C DouvisG Tselioudis andC S Zerefos ldquoLong termprecipitation trendsand variability within the Mediterranean regionrdquo Natural Haz-ards and Earth System Sciences vol 11 no 12 pp 3235ndash32502011

[29] H Reiser and H Kutiel ldquoRainfall uncertainty in the Mediter-ranean time series uncertainty and extreme eventsrdquoTheoreti-cal and Applied Climatology vol 104 no 3-4 pp 357ndash375 2011

[30] C Maciel Vaz ldquoTrend analysis in annual maximum dailyrainfall seriesrdquo Tech Rep Universidade Tecnica de LisboaLisbon Portugal 2008

[31] S Deka M Borah and SC Kakaty ldquoDistributions of annualmaximum rainfall series of north-east Indiardquo European WaterPublications vol 27-28 pp 3ndash14 2009

[32] K A Al-Qudah and A A Smadi ldquoTrends in maximumdaily rainfall in marginal desert environment signs of climatechangerdquo American Journal of Environmental Sciences vol 7 no4 pp 331ndash337 2011

[33] B Habibi M Meddi and A Boucefiane ldquoAnalyse frequentielledes pluies journalieres maximalesrdquo Cas du Bassin Chott-Chergui Nature amp Technologie vol 8 pp 41ndash48 2013

[34] J Guiot ldquoSur la determination des regions climatiques quasihomogenesrdquo Revue de Statistique Appliquee vol 34 no 2 pp15ndash34 1986

[35] A Benhamrouche D Boucherf R Hamadache L Bendah-mane J Martin-Vide and J Teixeira Nery ldquoSpatial distributionof the daily precipitation concentration index in AlgeriardquoNatural Hazards and Earth System Sciences vol 15 no 3 pp617ndash625 2015

[36] M C Llasat M Llasat-Botija M A Prat et al ldquoHigh-impactfloods and flash floods in Mediterranean countries the FLASHpreliminary databaserdquo Advances in Geosciences vol 23 pp 47ndash55 2010

[37] A Bakreti I Braud E Leblois andA Benali ldquoAnalyse conjointedes regimes pluviometriques et hydrologiques dans le bassin dela Tafna (Algerie Occidentale)rdquo Hydrological Sciences Journalvol 58 no 1 pp 133ndash151 2013

[38] Y Tramblay S ElAdlouni andE Servat ldquoTrends and variabilityin extreme precipitation indices over maghreb countriesrdquo Nat-ural Hazards and Earth System Sciences vol 13 no 12 pp 3235ndash3248 2013

[39] M Lazri and S Ameur ldquoAnalysis of the time trends of pre-cipitation over mediterranean regionrdquo International Journal ofInformation Engineering and Electronic Business vol 6 no 4pp 38ndash44 2014

[40] G Villarini ldquoAnalyses of annual and seasonal maximum dailyrainfall accumulations for Ukraine Moldova and RomaniardquoInternational Journal of Climatology vol 32 no 14 pp 2213ndash2226 2012

[41] T S Stephenson L A Vincent T Allen et al ldquoChanges inextreme temperature and precipitation in the Caribbean region1961ndash2010rdquo International Journal of Climatology vol 34 no 9pp 2957ndash2971 2014

[42] IPCC ldquoSpecial Report onManaging the risks of extreme eventsand disasters to advance climate change adaptation(SREX)rdquo inA Special Report of Working Group I and Working Group II ofthe Intergovernmental Panel on Climate Change C B Field VBarros T F Stocker et al Eds p 582 Cambridge UniversityPress New York NY USA 2012

[43] D H Burn R Mansour K Zhang and P HWhitfield ldquoTrendsand variability in extreme rainfall events in British ColumbiardquoCanadianWater Resources Journal vol 36 no 1 pp 67ndash82 2011

[44] E M Douglas and C A Fairbank ldquoIs precipitation in NorthernNew England becoming more extreme statistical analysisof extreme rainfall in Massachusetts New Hampshire andMaine and updated estimates of the 100-year stormrdquo Journal ofHydrologic Engineering ASCE vol 16 no 3 pp 203ndash217 2011

[45] S Westra L V Alexander and F W Zwiers ldquoGlobal increasingtrends in annual maximum daily precipitationrdquo Journal ofClimate vol 26 no 11 pp 3904ndash3918 2013

[46] M R Jones S Blenkinsop H J Fowler and C G KilsbyldquoObjective classification of extreme rainfall regions for the UKand updated estimates of trends in regional extreme rainfallrdquoInternational Journal of Climatology vol 34 no 3 pp 751ndash7652014

[47] P Y Groisman T R Karl D R Easterling et al ldquoChanges inthe probability of heavy precipitation important indicators ofclimatic changerdquo Climatic Change vol 42 no 1 pp 243ndash2831999

[48] M A Degefu andW Bewket ldquoVariability and trends in rainfallamount and extreme event indices in the Omo-Ghibe RiverBasin Ethiopiardquo Regional Environmental Change vol 14 no 2pp 799ndash810 2014

[49] COikonomouH A FlocasMHatzaki D N Asimakopoulosand C Giannakopoulos ldquoFuture changes in the occurrence of


extreme precipitation events in eastern Mediterraneanrdquo GlobalNest Journal vol 10 no 2 pp 255ndash262 2008

[50] F Giorgi and P Lionello ldquoClimate change projections for theMediterranean regionrdquo Global and Planetary Change vol 63no 2-3 pp 90ndash104 2008

[51] C Norrant and A Douguedroit ldquoTendances des precipitationsmensuelles et quotidiennes dans le sud-est mediterraneenfrancais (1950-511999-2000)rdquo Climatologie vol 1 pp 45ndash642004

[52] A Megnounif and A N Ghenim ldquoRainfall irregularity andits impact on the sediment yield in Wadi Sebdou watershedAlgeriardquo Arabian Journal of Geosciences vol 9 no 4 pp 1ndash152016

[53] M De Luis J Raventos J R Sanchez J C Gonzalez J Cortinaand M F Garcia-Cano ldquoEvent contribution to annual precipi-tation a trend analysisrdquo in Proceedings of the 2nd InternationalConference on Climate andWater pp 290ndash300 Espoo Finland1998

[54] A N Ghenim Ecoulements et Transports Solides dans lesRegions Semi-Arides Editions Universitaires Europeennes2012

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of


EarthquakesJournal of


Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining


Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of


Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering


GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of


OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in


MineralogyInternational Journal of


MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Geological ResearchJournal of


Geology Advances in


12

3

45

6

1078

9

11

12

13

1617

18

19 20

21

221415

23

24

25

26 27 29

28 30

31

32

33

3534

25 35 45 55 65 75

1

19 20

21

221415

23

24

25

26 27 29

28 30

31

32

33

3534

150 300 450 600 750 900

(a)

(b)

23

45

6

1078

9

11

12

13

1617

1836∘N

35∘N

35∘N

36∘N

9∘E8

∘E7∘E6

∘E5∘E4

∘E3∘E2

∘E1∘W 0

∘1∘E

9∘E8

∘E7∘E6

∘E5∘E4

∘E3∘E2

∘E1∘W 0

∘1∘E 60

∘40

∘20

∘0∘

20∘

40∘

20∘

0∘

20∘

Algeria

Study area

Figure 1 Locations of rainfall stations in northernAlgeria andmean values intervals of annual rainfall (a) and annualmaximumdaily rainfall(b)

of the Mediterranean coastline is about 1200 km Because ofits geographic position and its mountainous nature rainfallshows strongest contrasts between the various areas Thisregion has a high spatial and temporal climatic variabilityknown as the Mediterranean climate Intra-annual rainfallis irregular and most rains fall between October and Aprilwhile infrequent and local storms occur in the dry seasonfrom July to October

Rainfall data were collected by the National Agencyof the Hydraulic Resources (ARNH) (httpwwwanrhdz)Because there were too many gaps after colonial period inthe 1960s and where the number of years of observationswas too low for statistical purposes many station series werediscarded from the data set As a result only 35 rainfall serieswere selected (Figure 1)

The data collected are a set of daily rainfall series forthe period after 1970 They include less than 5 of gapsThese are replaced by the values of the station which hasthe best correlation The data were tested for their qualitycontrol The suspect data were cross-checked with thoseof nearby stations (some are not used in this study) Thearithmetic sum of daily heights recorded is the annual rainfallvalue (AR) while the daily maximum observed during theyear represents the annual maximum daily rainfall (AMDR)Data were aggregated according to hydrological year fromSeptember to August The selected stations are described bythe geographical coordinates number of years of observationand statistical characteristics (Table 1)

In the Mediterranean region it is unlikely that rainstormlasts more than 24 hours [6] So the annual maximumdaily rainfall (AMDR) series may be introduced to study

the distribution of extreme precipitation occurrences withina year To examine the regularity for such series we appliedthe seasonality as described by Burn [13] This methodused to estimate the timing and regularity of floods wasthen transposed to extreme rainfall in particular AMDR[14] It assesses the degree of similarity of watersheds inrelation to the hydrological response or the occurrence ofextreme rainfall Burnrsquos vector defined by (120579 119903) represents thevariability of the date of occurrence of all extremes events Itsdirection is the mean date of the occurrence of the extremesevents and the modulus is the variability around the meanvalue The dates of the AMDR occurrence are based on thecalendar year January 1 is the 1st day and December 31 is the365th day

Each date 119895119894was replaced by an angle

120579119894= 119895119894

2120587

36525 120579119894isin 0 75

∘ 360

∘ (1)

The obtained series covers the unit circle where each term canbe described in polar coordinates as a vector (cos 120579

119894 sin 120579119894)

where 120579119894indicates the direction expressed in radians Follow-

ing the Burn approach the Cartesian coordinates 119909119894= cos 120579

119894

and 119910119894= sin 120579

119894 are used to evaluate Burnrsquos vector defined

by (120579 119903) the mean direction and mean modulus given by thefollowing equations

120579 = arctg(119910

119909) 120579 isin [0

∘ 360∘]

119903 = radic1199092+ 1199102 119903 isin [0 1]

(2)





where

119909 =1

119899

119899

sum119894=1

cos 120579119894

119910 =1

119899

119899

sum119894=1

sin 120579119894

(3)





119894is







CS119896(119883) = sum

119894le119896

119878119894= sum119894le119896

(119883119894minus 119883

119904) (4)





119896|CS119896|


3 Results













20

30

40

50

60

70

80

100 200 300 400 500

Aver

age A

MD

R (m

m)


R2= 052

Y = 0116X + 1333

(a)

100

200

300

400

500

600

700

800

900

100 200 300 400 500

Aver

age A

R (m

m)


R2= 069

Y = 186X minus 4635

(b)


1 2 3 4 5 6 7 8 9 10 11 12(Months)


0

5

10

15

20

25

30

35

Mon

thly

occ

urre

nce o

f AM

DR

()

(a)

0

50

100

150

200

250

300

1 2 3 4 5 6 7 8 9 10 11 12

Mon

thly

max

imum

AM

DR

valu

es (m

m)

(Months)


(b)


0

30

330

300

6090

120

150

180

210

240270

108

0604

02

04

02












119896curves



1

23

4

5

6

107

8

9

11

12

13

1617

18

19 20

21

2214

15

23

24

25

2629

28 30

31

32

33

3534

27




1

23

4

5

6

1078

9

11

12

13

1618

20

21

2214

15

23

24

25

2629

28 30

31

32

33

3534

27


17 19











0

2

4

6

8

10

12

0

1

2

3

4

Cum

ulat

ive r

epor

t of A

MD

R co

ntrib

utio

n in

AR


(Years)20102000199019801970

(Years)20102000199019801970

Csk

(AM

DR

AR)

(a)

0

2Date of change


0

1

2

3

4

Cum

ulat

ive r

epor

t of A

MD

R co

ntrib

utio

n in

AR

(Years)20102000199019801970

(Years)20102000199019801970

minus4

minus2

minus6

minus8

Csk

(AM

DR

AR)

(b)

0

1

2

0

1

2

3

4

5

6

Cum

ulat

ive r

epor

t of A

MD

R co

ntrib

utio

n in

AR

(Years) (Years)2010200019901980197020102000199019801970

minus1

minus2

minus3

minus4

minus5

Csk

(AM

DR

AR)


(c)

0

1

2

3

4

(Years)

0

1

2

3

4

Cum

ulat

ive r

epor

t of A

MD

R co

ntrib

utio

n in

AR

20102000199019801970

(Years)20102000199019801970

minus1

minus2

minus3

minus4

Csk

(AM

DR

AR)

(d)







Competing Interests


References



































































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in





where

119909 =1

119899

119899

sum119894=1

cos 120579119894

119910 =1

119899

119899

sum119894=1

sin 120579119894

(3)





119894is







CS119896(119883) = sum

119894le119896

119878119894= sum119894le119896

(119883119894minus 119883

119904) (4)





119896|CS119896|


3 Results













20

30

40

50

60

70

80

100 200 300 400 500

Aver

age A

MD

R (m

m)


R2= 052

Y = 0116X + 1333

(a)

100

200

300

400

500

600

700

800

900

100 200 300 400 500

Aver

age A

R (m

m)


R2= 069

Y = 186X minus 4635

(b)


1 2 3 4 5 6 7 8 9 10 11 12(Months)


0

5

10

15

20

25

30

35

Mon

thly

occ

urre

nce o

f AM

DR

()

(a)

0

50

100

150

200

250

300

1 2 3 4 5 6 7 8 9 10 11 12

Mon

thly

max

imum

AM

DR

valu

es (m

m)

(Months)


(b)


0

30

330

300

6090

120

150

180

210

240270

108

0604

02

04

02












119896curves



1

23

4

5

6

107

8

9

11

12

13

1617

18

19 20

21

2214

15

23

24

25

2629

28 30

31

32

33

3534

27




1

23

4

5

6

1078

9

11

12

13

1618

20

21

2214

15

23

24

25

2629

28 30

31

32

33

3534

27


17 19











0

2

4

6

8

10

12

0

1

2

3

4

Cum

ulat

ive r

epor

t of A

MD

R co

ntrib

utio

n in

AR


(Years)20102000199019801970

(Years)20102000199019801970

Csk

(AM

DR

AR)

(a)

0

2Date of change


0

1

2

3

4

Cum

ulat

ive r

epor

t of A

MD

R co

ntrib

utio

n in

AR

(Years)20102000199019801970

(Years)20102000199019801970

minus4

minus2

minus6

minus8

Csk

(AM

DR

AR)

(b)

0

1

2

0

1

2

3

4

5

6

Cum

ulat

ive r

epor

t of A

MD

R co

ntrib

utio

n in

AR

(Years) (Years)2010200019901980197020102000199019801970

minus1

minus2

minus3

minus4

minus5

Csk

(AM

DR

AR)


(c)

0

1

2

3

4

(Years)

0

1

2

3

4

Cum

ulat

ive r

epor

t of A

MD

R co

ntrib

utio

n in

AR

20102000199019801970

(Years)20102000199019801970

minus1

minus2

minus3

minus4

Csk

(AM

DR

AR)

(d)







Competing Interests


References



































































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in





CS119896(119883) = sum

119894le119896

119878119894= sum119894le119896

(119883119894minus 119883

119904) (4)





119896|CS119896|


3 Results













20

30

40

50

60

70

80

100 200 300 400 500

Aver

age A

MD

R (m

m)


R2= 052

Y = 0116X + 1333

(a)

100

200

300

400

500

600

700

800

900

100 200 300 400 500

Aver

age A

R (m

m)


R2= 069

Y = 186X minus 4635

(b)


1 2 3 4 5 6 7 8 9 10 11 12(Months)


0

5

10

15

20

25

30

35

Mon

thly

occ

urre

nce o

f AM

DR

()

(a)

0

50

100

150

200

250

300

1 2 3 4 5 6 7 8 9 10 11 12

Mon

thly

max

imum

AM

DR

valu

es (m

m)

(Months)


(b)


0

30

330

300

6090

120

150

180

210

240270

108

0604

02

04

02












119896curves



1

23

4

5

6

107

8

9

11

12

13

1617

18

19 20

21

2214

15

23

24

25

2629

28 30

31

32

33

3534

27




1

23

4

5

6

1078

9

11

12

13

1618

20

21

2214

15

23

24

25

2629

28 30

31

32

33

3534

27


17 19











0

2

4

6

8

10

12

0

1

2

3

4

Cum

ulat

ive r

epor

t of A

MD

R co

ntrib

utio

n in

AR


(Years)20102000199019801970

(Years)20102000199019801970

Csk

(AM

DR

AR)

(a)

0

2Date of change


0

1

2

3

4

Cum

ulat

ive r

epor

t of A

MD

R co

ntrib

utio

n in

AR

(Years)20102000199019801970

(Years)20102000199019801970

minus4

minus2

minus6

minus8

Csk

(AM

DR

AR)

(b)

0

1

2

0

1

2

3

4

5

6

Cum

ulat

ive r

epor

t of A

MD

R co

ntrib

utio

n in

AR

(Years) (Years)2010200019901980197020102000199019801970

minus1

minus2

minus3

minus4

minus5

Csk

(AM

DR

AR)


(c)

0

1

2

3

4

(Years)

0

1

2

3

4

Cum

ulat

ive r

epor

t of A

MD

R co

ntrib

utio

n in

AR

20102000199019801970

(Years)20102000199019801970

minus1

minus2

minus3

minus4

Csk

(AM

DR

AR)

(d)







Competing Interests


References



































































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in


20

30

40

50

60

70

80

100 200 300 400 500

Aver

age A

MD

R (m

m)


R2= 052

Y = 0116X + 1333

(a)

100

200

300

400

500

600

700

800

900

100 200 300 400 500

Aver

age A

R (m

m)


R2= 069

Y = 186X minus 4635

(b)


1 2 3 4 5 6 7 8 9 10 11 12(Months)


0

5

10

15

20

25

30

35

Mon

thly

occ

urre

nce o

f AM

DR

()

(a)

0

50

100

150

200

250

300

1 2 3 4 5 6 7 8 9 10 11 12

Mon

thly

max

imum

AM

DR

valu

es (m

m)

(Months)


(b)


0

30

330

300

6090

120

150

180

210

240270

108

0604

02

04

02












119896curves



1

23

4

5

6

107

8

9

11

12

13

1617

18

19 20

21

2214

15

23

24

25

2629

28 30

31

32

33

3534

27




1

23

4

5

6

1078

9

11

12

13

1618

20

21

2214

15

23

24

25

2629

28 30

31

32

33

3534

27


17 19











0

2

4

6

8

10

12

0

1

2

3

4

Cum

ulat

ive r

epor

t of A

MD

R co

ntrib

utio

n in

AR


(Years)20102000199019801970

(Years)20102000199019801970

Csk

(AM

DR

AR)

(a)

0

2Date of change


0

1

2

3

4

Cum

ulat

ive r

epor

t of A

MD

R co

ntrib

utio

n in

AR

(Years)20102000199019801970

(Years)20102000199019801970

minus4

minus2

minus6

minus8

Csk

(AM

DR

AR)

(b)

0

1

2

0

1

2

3

4

5

6

Cum

ulat

ive r

epor

t of A

MD

R co

ntrib

utio

n in

AR

(Years) (Years)2010200019901980197020102000199019801970

minus1

minus2

minus3

minus4

minus5

Csk

(AM

DR

AR)


(c)

0

1

2

3

4

(Years)

0

1

2

3

4

Cum

ulat

ive r

epor

t of A

MD

R co

ntrib

utio

n in

AR

20102000199019801970

(Years)20102000199019801970

minus1

minus2

minus3

minus4

Csk

(AM

DR

AR)

(d)







Competing Interests


References



































































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in











119896curves



1

23

4

5

6

107

8

9

11

12

13

1617

18

19 20

21

2214

15

23

24

25

2629

28 30

31

32

33

3534

27




1

23

4

5

6

1078

9

11

12

13

1618

20

21

2214

15

23

24

25

2629

28 30

31

32

33

3534

27


17 19











0

2

4

6

8

10

12

0

1

2

3

4

Cum

ulat

ive r

epor

t of A

MD

R co

ntrib

utio

n in

AR


(Years)20102000199019801970

(Years)20102000199019801970

Csk

(AM

DR

AR)

(a)

0

2Date of change


0

1

2

3

4

Cum

ulat

ive r

epor

t of A

MD

R co

ntrib

utio

n in

AR

(Years)20102000199019801970

(Years)20102000199019801970

minus4

minus2

minus6

minus8

Csk

(AM

DR

AR)

(b)

0

1

2

0

1

2

3

4

5

6

Cum

ulat

ive r

epor

t of A

MD

R co

ntrib

utio

n in

AR

(Years) (Years)2010200019901980197020102000199019801970

minus1

minus2

minus3

minus4

minus5

Csk

(AM

DR

AR)


(c)

0

1

2

3

4

(Years)

0

1

2

3

4

Cum

ulat

ive r

epor

t of A

MD

R co

ntrib

utio

n in

AR

20102000199019801970

(Years)20102000199019801970

minus1

minus2

minus3

minus4

Csk

(AM

DR

AR)

(d)







Competing Interests


References



































































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in


1

23

4

5

6

107

8

9

11

12

13

1617

18

19 20

21

2214

15

23

24

25

2629

28 30

31

32

33

3534

27




1

23

4

5

6

1078

9

11

12

13

1618

20

21

2214

15

23

24

25

2629

28 30

31

32

33

3534

27


17 19











0

2

4

6

8

10

12

0

1

2

3

4

Cum

ulat

ive r

epor

t of A

MD

R co

ntrib

utio

n in

AR


(Years)20102000199019801970

(Years)20102000199019801970

Csk

(AM

DR

AR)

(a)

0

2Date of change


0

1

2

3

4

Cum

ulat

ive r

epor

t of A

MD

R co

ntrib

utio

n in

AR

(Years)20102000199019801970

(Years)20102000199019801970

minus4

minus2

minus6

minus8

Csk

(AM

DR

AR)

(b)

0

1

2

0

1

2

3

4

5

6

Cum

ulat

ive r

epor

t of A

MD

R co

ntrib

utio

n in

AR

(Years) (Years)2010200019901980197020102000199019801970

minus1

minus2

minus3

minus4

minus5

Csk

(AM

DR

AR)


(c)

0

1

2

3

4

(Years)

0

1

2

3

4

Cum

ulat

ive r

epor

t of A

MD

R co

ntrib

utio

n in

AR

20102000199019801970

(Years)20102000199019801970

minus1

minus2

minus3

minus4

Csk

(AM

DR

AR)

(d)







Competing Interests


References



































































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in


0

2

4

6

8

10

12

0

1

2

3

4

Cum

ulat

ive r

epor

t of A

MD

R co

ntrib

utio

n in

AR


(Years)20102000199019801970

(Years)20102000199019801970

Csk

(AM

DR

AR)

(a)

0

2Date of change


0

1

2

3

4

Cum

ulat

ive r

epor

t of A

MD

R co

ntrib

utio

n in

AR

(Years)20102000199019801970

(Years)20102000199019801970

minus4

minus2

minus6

minus8

Csk

(AM

DR

AR)

(b)

0

1

2

0

1

2

3

4

5

6

Cum

ulat

ive r

epor

t of A

MD

R co

ntrib

utio

n in

AR

(Years) (Years)2010200019901980197020102000199019801970

minus1

minus2

minus3

minus4

minus5

Csk

(AM

DR

AR)


(c)

0

1

2

3

4

(Years)

0

1

2

3

4

Cum

ulat

ive r

epor

t of A

MD

R co

ntrib

utio

n in

AR

20102000199019801970

(Years)20102000199019801970

minus1

minus2

minus3

minus4

Csk

(AM

DR

AR)

(d)







Competing Interests


References



































































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in






Competing Interests


References



































































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in



















































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in

















Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in










Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in

Documents

Research Article Variability and Trend of Annual Maximum