Chapter Five AL-Qadisiya Journal For Engineering Sciences ,Vol. 6.No 3 Year 2013 492 ESTIMATION OF DOKAN RESERVOIR RELIABILITY USING STREAM FLOW DATA GENERATION TECHNIQUES Ruqaya K.M. Al-Masudi College of Engrg., Babylon Univ., Babil, Iraq Ruqaya2008@yahoo.com Abstract In the present study, two procedures of capacity-yield are applied to estimate the reliability of Dokan reservoir using data generation techniques. These procedures are the probability matrix (Gould) procedure, and the behavior analysis. Vulnerability, and resilience, are also calculated in the second procedure .The data is generated by using four approaches ,namely ,Thomas-Fiering model with log –transformation (TF-log), Two-Tier model (TTM), modified Two-Tier model (MTTM) and modified Fragment model (MFM).These models are tested and compared with the historical data. It is concluded that among these four procedures the Thomas-Fiering model with log –transformation is the most appropriate for representing the Dokan reservoir inflow .Three factors are examined to determine their influence on the minimum storage estimate .These are the length of stochastically generated sequence, the initial state of storage ,and the starting month. The results reported here show that sequences as long as 10,000 years or more may be needed to minimize the effects of these factors. ستخلصمال . هاذه بنساتخدا البنناانا المدلاد لتخمانط اتتمنيياة اا ا ين ان اإلطاقل -طبقت طريقتان ناط طارل ال ا ةفي هذه الدراسة تم تدلناد البنناانا بنساتخدا ن اتتمنيا تلى الطريقاة اخانار .تح ب فالض ن تحلنل ال لدك.المرناة ن طريقة الطرل هي طريقة جدلد لم دلاة تانير ا-تاد،طريقاة تنير-تاد ، طريقاة نع اساتخدا التحاديقا اللدرنريتمناة فنيراك-ثدننسريقة طرل هذه الطرل هي ط أرب ة الم دلة . استخدنت البننانا المدلد لمقنراة النتنئج نع النتنئج المح دبة بنساتخدا البنناانا التنريخناة نفاي ا ا فرا منات ،نطريقة نع استخدا التحديقا اللدرنريتمنةفنيراك -ثدننس ةطريق إ فنمن بننهن ناستنتج لبنناناالدقت لمقنراة اتنئج الطرل اخرب ة لتدلند ا ين ن . لتمثنل التصنريف الداالة لخ ا اخفضلهي التصانريف المدلاد ، حنلاة هذه ال دانل هي طدل سل الة.تلى تخمنط الخ المطلدب تأثنرهن إليجنيثقثة تدانل تم فحصهن سانة 10,000سل لة جرين بحادني إلىهذه الدراسة بأاه يحتنج المقدنة في ا ، نالبدا بشهر نن. أظهرا النتنئج الخ يط اخنلي للخ هذه ال دانل. تأثنرلتقلنل أ ثر أن KEY WORDS: Stream flow data generation, reliability of reservoir, reservoir probability of failure. Introduction Reservoirs are built to supplement future river flows, but no-one can forecast what these will be. It is unlikely that history will repeat itself, yet many procedures use only the historical record. To overcome this dilemma, it is often useful to generate synthetic stream flow data .Stochastic data generation provides designers and analysis of resource systems with alterative sequences of stream flow having the same statistical properties as the historical record. It is then possible to determine the storage capacity (or other design parameter) for each sequence, and thus provide the designer with a AL-Qadisiya Journal For Engineering Sciences ,Vol. 6.No 3 Year 2013 492 distribution of the values .This process gives an idea of the confidence which can be placed on the adopted design value. “Synthetic flows or stochastic data” do not improve poor records but merely improve the quality of designs made with whatever records are available. In the present study, two procedures of capacity-yield are applied to estimate the reliability of Dokan reservoir by using four data generation techniques. The Dokan Reservoir The Dokan dam is located at about 60 km from the northen west of Al-Sulaimania town and at about 300 km from Karkok governorate. The main purposes of the Dokan project are to store and regulate the abundant water of the Lesser Zab river, a tributary of the Tigres river, by creating a large scale reservoir, to supply irrigation water required in the area downstream of the dam, and to control discharges downstream by impounding and regulating floods. In addition to the abovementioned purposes, the discharge and head obtained by the dam are to be utilized for power generation for effective use of hydraulic energy, thereby making this a multi-purpose, for irrigation, flood control, and power generation (Iraqi Ministry of Water Resources,2007). Estimation of Reliability Using Data Generation Techniques A number of generation models are used to evaluate the reliability of a reservoir by behavior analysis and Gould’s procedure. These generation models are designated by the following: TF- log=Thomas-Fiering monthly model with log transformation; TTM=two-tier model using Markovian annual flows; MTTM=modified two-tier model; MFM=modified fragment model;. Before using the generated data in the estimation of Dokan reservoir reliability, it is necessary to make sure that those generated sequences are extracted from the same population of the historical sample. This can be done by verifying the model used in the generation by the following tests: 1. Comparison of the statistical parameters computed from the generated data with the actual values of those statistics computed from the historical records, for the purpose of simplicity, the relative error (as a percentage) was calculated (Srikanthan and McMahon,1982) from the following equation: %100 )( )(    ValueHistoric ValueHistoricalGenerated Figures (1) to (6) show the relative error of mean, standard deviation, coefficient of variation, coefficient of skewness, correlation coefficient and regression coefficient, respectively. It can be seen that the TF-log,TTM and MTTM models preserved parameters better than the MFM model. However, there was only a small difference between the TF-log and MTTM results, especially for coefficient of variation, coefficient of skewness , correlation coefficient and regression coefficient. There is a worthiness to say here that it is not a condition that the model preserved the statistical parameters to be the best model for reliability, vulnerability and resilience estimation but this will give more trust for this estimation. 2. Comparison of cumulative probability curves for the two series from historical and generated data.Figure (7) shows the cumulative probability curves for Dokan reservoir inflows based on historical and generated data. This figure indicates that all the transformations are not significantly different from that produced from historical data. 3. Comparison of the proportion of negative flows. The model is acceptable so long as the proportion of negative flow is not greater than 5% (McMahon and Mein, 1986). Table (1) shows a comparison between the statistical properties (mean, standard deviation and correlation coefficient) of all generated series by TF-log, TTM, MTTM, MFM, and that of historical Relative Error AL-Qadisiya Journal For Engineering Sciences ,Vol. 6.No 3 Year 2013 492 series. This table indicates that the monthly statistical parameters of TF-Log and MFM generated data are very close to those of historical data. Table (2) shows the comparison between monthly statistical parameters (mean, standard deviation and correlation coefficient) of the generated data by TF-log, TTM, MTTM, MFM and that of historical data. All the monthly means of the generated data pass the t-test and the f-test at 95% significant probability limit. Table (2) shows the results of statistical tests (t-test and f-test) for the monthly means and standard deviations, respectively, for the generated data. It can be seen that the average failure in monthly means and monthly standard deviation is 0% for all generated series. Analysis of the Results Figure (8) shows the effect of the number of years used in the analysis on the estimation of reliability by behavior procedure for the four methods of generation used in this research. It could be seen that the (55) year estimation series of reliability diverges away ,this may be to the longer series. Thus, the use of the longest and longest series will converge the results one to another. Figure (9) shows the same effect of figure (8) but by using the Gould’s procedure. This figure indicates that the sensitivity of results by using Gould’s procedure will be less than of behavior procedure .Also, it could be seen that Gould’s estimation of reliability almost less than the behavior estimation. Figure (10) shows that the estimated vulnerability tends to move on approximately straight line and converge from one model of generation to another under the effect of time series length with increasing the monthly release from the reservoir. Figure (11) also shows that there is a high variation in the estimated value of resilience under the effect of number of years used in the analysis and, as in reliability, the longest and longest series will converge the results. As a result, the use of longest series in the behavior analysis to estimate the reliability, vulnerability and resilience of reservoir will make the results more accurate because of the starting month problem and the assumption of initially full will be overcome by using such series. Figure (12) shows the reliability-yield reservoir relationship depending on Behavior and Gould’s procedure using both historical and generated data .Figure (12-a) indicates that the TF-Log give a smaller reliability estimate than other models where TTM and MTTM results converges to the results based on the historical data which considered to be reasonable one by many researcher in literature. This means that the TTM and MTTM could be considered the best to represent the inflow of Dokan reservoir. Behaviour estimation of reliability is almost more than the case of using Gould's procedure for Dokan reservoir. The 95% reliability, which is considered to be an acceptable limit of reliability(McMahon et. al ,1972), could be obtained with a release of (72-80)% and (75-80)% from the mean flow depending on Behaviour analysis and Gould's procedure ,respectively. Figure (13) shows the vulnerability-yield relationship and indicates that the vulnerability of reservoir increasing and tends to be a straight line with the increasing of the release (decreasing the reliability) by using the historical and generated data. Figure (13) also shows the resilience-yield relationship and indicates that there is a high difference between the historical and generated data estimate. It is also obvious that the reservoir resilience increase with the increasing of the release from the reservoir. Effect of Starting Month on Storage Estimates To examine the effect of starting month on storage size are calculated by starting the analysis in different months for two draft cases (55% and 75% of mean flow) at 95% reliability using both Behavior procedure and Gould analysis with historical data. The storage estimates are plotted for AL-Qadisiya Journal For Engineering Sciences ,Vol. 6.No 3 Year 2013 492 comparison in figure (14). It is observed from the results that the storage size estimated through Behavior analysis vary little with starting month. Figure(15) shows the vulnerability and resilience respectively which were constant with any starting month for both cases .On the other hand Gould’s storage estimates differed markedly for different month . One way to overcome this impact is to use long sequences of synthetic month data in the analysis as shown in figure (16). It can be noted from this figure that the Gould storage estimates varied more than the Behavior estimates which were constant for all cases .However, the Gould estimates based on generated data were considerably less variable than those calculated using historical data. Effect of Inflow Sequence Length on Storage Estimates This section investigates the dependence of estimates of reservoir storage capacity derived using Behaviour analysis and Gould’s proccedure on the length of inflow sequence used for overyear reservoir simulation.For each method of reliability estimation, 20 different sequence lengths are generated varying from 200 to 10,000 years and the required reservoir storage for each sequence is then predicted. It follows from the stochstic theory of storage that the reliability of a reservoir operating on a single realization of the inflow process can theoretically attain steady state only as the sequence length approaches infinity(Moran,1959, quoted in Abdul-Bari,(2006)). The overyear storage estimates as shown in figures (17) and (18) are significantly influenced by the length of inflow sequence analyzed. In order to remove the influence of inflow sequence length on the storage estimates by the above methods, the inflow sequence is generated for 10,000 years because of the storage estimates approached a stationary level by about 6,000 years or more for the methodes examined. Effect of Initial Conditions on Storage Estimates The initial reservoir condition (C0) is typically assumed to be full (McMahon and mein,1978), although any initial condition ranging form empty to full could be used.Figure (19,A) showes plots of the behaviour storage estimates againest yield using historical data to explore the influence of the initial full and empty reservoir conditions.To overcom the effectes of the assumed initial conditions, a sequence length of at least 10,000 years would be required because the initially full assumption curve is converged to the initially empty curve for all generated model as shown in figure (19,B-E). Conclusions For this study , the following conclusions are deduced: 1. After using four data generation models, it becomes clear that the Thomas-Fiering with log transformation is the best for generating monthly inflows of Dokan reservoir among the other models. 2. Based on the historical data, the Gould storage estimates vary more widely with starting month than the Behaviour estimates which are approximately constant for all cases as well as AL-Qadisiya Journal For Engineering Sciences ,Vol. 6.No 3 Year 2013 492 the vulnerability and resilience.However, the effect of starting month is relatively substantial in Gould estimates using generated data. 3. The variation in storage estimate becomes neglectable by using sequence length of 6,000 years or more for the methodes examined. 4. The influence of the initial condition (full or empty) in the Behaviour analysis is effectively nullified for inflow sequences longer than about 10,000 years. References Mein, R.G., and McMahon, T.A.(1978):"Reservoir capacity and Yield Procedures.", Development in Water Science9, Elsevier, Amsterdam. Srikanthan, R. and McMahon, T.A.(1985a):"Gould’s Probability Matrix Method .1. The Starting Month Problem.", J. of Hydrology, Vol.77,Pages 125-133. Mein, R.G., and McMahon, T.A.(1986):"River and Reservoir Yield.”, Water Resources Publication, Ft. Collins, Colorado. Madhloom,H.M.(2000): "Probability of Failure of Al-Adhaim Reservoir. ", M.Sc.Thesis, College of Engineering,Babylon University,Iraq. Al-Fatlawi, T.J.(2003): "Evaluation the Probability of Failure of Haditha Reservoir.", M.Sc. Thesis,College of Engineering,Babylon University,Iraq. Hussein, A.K.,(2005):" Probability of Failure to Adhaim Reservoir.", J. of Babylon University, Engineering Sciences Vol.10, No.5, Pages 922-934. Abdul-Bari ,W.H.,(2006): "Reliability of Iraqi Reservoirs. ",M.Sc.Thesis,College of Engineering,Babylon University,Iraq. Ministry of Water Resources.,(2007):" Planning report on Dokan dam Project." Series Model Mean (m 3 /sec.) Standard deviation (m 3 /sec.) Cs R Negative flows (%) Max. flow (m 3 /sec.) Hist. 206 290.84 1.9 0.62 0 5470 Gen. TF-log 203.49 221.57 3.43 0.71 0 2608 TTM 215.84 261.56 2.66 0.67 0 1811 MTTM 199.43 230.91 3.11 0.59 0 1910 MFM 215.89 259.24 2.14 0.99 0 1737 Table 1: Statistical properties of historical and generated data. AL-Qadisiya Journal For Engineering Sciences ,Vol. 6.No 3 Year 2013 499 D e c . 1 5 2 .5 8 1 4 4 .6 4 1 6 3 .8 6 1 5 6 .4 0 2 1 2 .1 2 1 1 0 .3 6 8 6 .7 7 3 1 2 4 .8 7 1 0 0 .6 7 1 0 7 .4 0 0 .7 0 4 0 .5 4 9 0 .7 1 0 0 .6 1 6 1 .0 0 N o v . 1 0 2 .0 6 9 7 .3 6 1 1 0 .9 6 1 0 3 .2 5 7 3 .1 5 6 3 .9 1 5 8 .8 3 1 0 5 .4 6 7 3 .5 6 3 7 .0 4 0 .4 6 2 0 .5 9 8 0 .7 2 1 0 .6 4 2 0 .9 9 9 O c t. 5 8 .8 9 5 8 .7 4 7 2 .7 2 6 1 .0 4 4 7 .5 5 2 2 .7 8 2 5 .6 3 6 8 .2 8 3 2 .5 1 2 4 .0 7 0 .5 4 1 0 .7 2 1 0 .8 3 1 0 .5 9 0 1 .0 0 S e p . 5 4 .7 8 5 4 .6 6 6 0 .2 9 5 4 .7 9 4 3 .8 9 2 4 .0 6 2 5 .3 0 5 1 .0 4 2 9 .7 1 2 2 2 .2 2 0 .6 3 2 0 .5 7 2 0 .3 7 7 0 .3 1 1 1 .0 0 A u g . 6 1 .2 7 6 3 .6 0 6 4 .0 4 5 7 .7 3 4 3 .8 9 3 7 .5 5 3 6 .5 7 6 9 .2 0 5 0 .8 6 2 2 .2 2 0 .7 9 5 0 .9 1 3 0 .8 3 0 0 .8 6 5 1 .0 0 Ju l. 7 6 .1 8 8 1 .6 9 9 6 .4 8 8 3 .1 4 5 4 .8 6 3 8 .5 0 3 8 .9 6 8 3 .3 8 4 6 .5 8 2 7 .7 7 0 .7 7 8 0 .8 5 1 0 .8 0 8 0 .4 7 1 1 .0 0 Ju n . 1 3 6 .0 9 1 4 2 .7 3 1 5 8 .7 7 1 5 1 .9 1 9 8 .0 3 6 7 .8 0 7 1 .0 1 1 1 5 .1 5 9 3 .4 2 5 1 .1 2 0 .8 5 9 0 .9 2 0 0 .9 0 0 0 .7 9 6 0 .9 1 7 M a y 2 9 5 .7 1 2 8 7 .6 5 3 0 2 .7 4 2 8 9 .7 8 2 3 7 .7 3 1 5 9 .6 8 1 4 7 .0 2 2 2 3 .1 2 1 8 3 .6 0 1 2 0 .3 7 0 .9 2 0 0 .9 2 4 0 .9 2 2 0 .8 1 5 0 .9 1 7 A p r. 5 7 0 .8 9 5 7 9 .3 7 4 5 3 .0 8 4 2 9 .9 1 4 7 3 .0 2 7 2 4 .4 2 3 9 3 .0 0 4 7 9 .4 9 4 7 9 .6 9 2 4 2 .3 1 0 .2 8 4 0 .5 0 4 0 .1 8 8 0 .2 0 5 0 .9 9 9 M a r. 4 6 2 .1 5 4 3 5 .5 8 5 0 8 .3 0 4 6 0 .5 1 7 4 2 .4 4 3 1 2 .9 8 2 2 0 .4 5 3 4 9 .8 1 2 5 8 .8 1 3 7 5 .9 1 0 .3 7 9 0 .5 9 0 0 .3 4 8 0 .3 8 8 0 .9 9 9 F e b . 3 0 9 .1 1 2 9 8 .4 7 3 5 4 .4 5 3 2 7 .5 6 4 0 2 .3 0 1 5 5 .0 1 1 7 1 .5 5 2 5 7 .7 4 1 8 2 .8 3 2 0 3 .7 0 0 .4 7 7 0 .6 4 2 0 .6 4 6 0 .6 0 0 1 .0 0 Ja n . 1 9 2 .4 6 1 9 6 .7 8 2 4 3 .0 2 2 2 1 .8 9 1 6 0 .9 2 1 0 5 .6 3 1 0 9 .7 4 1 8 5 .2 9 1 3 8 .4 6 8 1 .4 8 0 .6 6 7 0 .7 6 7 0 .8 0 2 0 .7 4 5 1 .0 0 S e ri e s H is t. T F -l o g T T M M T T M M F M H is t. T F -l o g T T M M T T M M F M H is t. T F -l o g T T M M T T M M F M M e a n (m 3 /s e c .) S ta n d a rd d e v ia ti o n (m 3 /s e c .) C o rr e la ti o n c o e ff ic ie n t T a b le 2 : M o n th ly S ta ti st ic a l P a ra m e te rs o f H is to ri c a l a n d G e n e ra te d M o n th ly D a ta . AL-Qadisiya Journal For Engineering Sciences ,Vol. 6.No 3 Year 2013 033 Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Time (month) -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 R e la ti v e E r r o r (% ) TF-log TTM MTTM MFM Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Time (month) -0.8 -0.4 0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 R e la ti v e E r r o r (% ) TF-log TTM MTTM MFM Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Time (month) -0.8 -0.4 0.0 0.4 0.8 1.2 1.6 2.0 2.4 R e la ti v e E r r o r (% ) TF-log TTM MTTM MFM Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Time (month) -2.0 0.0 2.0 4.0 6.0 8.0 10.0 12.0 R e la ti v e E r r o r (% ) TF-log TTM MTTM MFM Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Time (month) -0.8 -0.4 0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 R e la ti v e E r r o r (% ) TF-log TTM MTTM MFM Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Time (month) -0.8 -0.4 0.0 0.4 0.8 1.2 1.6 2.0 2.4 R e la ti v e E r r o r (% ) TF-log TTM MTTM MFM Figure 1: Relative error of the mean. Figure 2: Relative error of the standard deviation. Figure 3: Relative error of the coefficient of variation. Figure 4: Relative error of the coefficient of skewness. Figure 5: Relative error of the correlation coefficient. Figure 6: Relative error of the regression coefficient. AL-Qadisiya Journal For Engineering Sciences ,Vol. 6.No 3 Year 2013 033 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 Inflow (cumecs) 0 10 20 30 40 50 60 70 80 90 100 P r o b a b il it y o f fl o w l e ss t h a n ( % ) His TFM 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 Inflow (cumecs) 0 10 20 30 40 50 60 70 80 90 100 P r o b a b il it y o f fl o w l e ss t h a n ( % ) His TTM 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 Inflow (cumecs) 0 10 20 30 40 50 60 70 80 90 100 P r o b a b il it y o f fl o w l e ss t h a n ( % ) His MTTM 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 Inflow (cumecs) 0 10 20 30 40 50 60 70 80 90 100 P r o b a b il it y o f fl o w l e ss t h a n ( % ) His MFM 50 60 70 80 90 100 Yield (% mean flow) 80 85 90 95 100 R e li a b il it y ( % ) Thomas-Fiering Model 55 year 220 year 550 year 770 year 50 60 70 80 90 100 Yield (% mean flow) 80 85 90 95 100 R e li a b il it y ( % ) Two-Tier Model 55 year 220 year 550 year 770 year Figure 7: Cumulative probability function for Dokan reservoir inflow using both historical and generated data. AL-Qadisiya Journal For Engineering Sciences ,Vol. 6.No 3 Year 2013 034 50 60 70 80 90 100 Yield (% mean flow) 75 80 85 90 95 100 R e li a b il it y ( % ) Modified Two-Tier Model 55 year 220 year 550 year 770 year 50 60 70 80 90 100 Yield (% mean flow) 80 85 90 95 100 R e li a b il it y ( % ) Modified Fragment Model 55 year 220 year 550 year 770 year 50 60 70 80 90 100 Yield (% mean flow) 80 85 90 95 100 R e li a b il it y ( % ) Thomas-Fiering Model 55 year 220 year 550 year 770 year 50 60 70 80 90 100 Yield (% mean flow) 80 85 90 95 100 R e li a b il it y ( % ) Two-Tier Model 55 year 220 year 550 year 770 year 50 60 70 80 90 100 Yield (% mean flow) 75 80 85 90 95 100 R e li a b il it y ( % ) Modified Two-Tier Model 55 year 220 year 550 year 770 year 50 60 70 80 90 100 Yield (% mean flow) 80 85 90 95 100 R e li a b il it y ( % ) Modified Fragment Model 55 year 220 year 550 year 770 year Figure 8: Effect of number of years used in generation on the estimation of reliability by Behavior procedure. Figure 9:Effect of number of years used in generation on the estimation of reliability by Gould’s procedure. AL-Qadisiya Journal For Engineering Sciences ,Vol. 6.No 3 Year 2013 030 50 60 70 80 90 100 Yield (% mean flow) 0 100 200 300 400 500 600 V u ln e r a b il it y ( m il li a r d c m ) Thomas-Fiering Model 55 year 220 year 550 year 770 year 50 60 70 80 90 100 Yield (% mean flow) 0 100 200 300 400 500 600 V u ln e r a b il it y ( m il li a r d c m ) Two-Tier Model 55 year 220 year 550 year 770 year 50 60 70 80 90 100 Yield (% mean flow) 200 300 400 500 600 V u ln e r a b il it y ( m il li a r d c m ) Modified Two-Tier Model 55 year 220 year 550 year 770 year 50 60 70 80 90 100 Yield (% mean flow) 100 200 300 400 500 600 V u ln e r a b il it y ( m il li a r d c m ) Modified Fragment Model 55 year 220 year 550 year 770 year 50 60 70 80 90 100 Yield (% mean flow) 0 5 10 15 20 25 30 R e si li e n c e ( m o n th ) Thomas-Fiering Model 55 year 220 year 550 year 770 year 50 60 70 80 90 100 Yield (% mean flow) 0 5 10 15 20 25 30 35 40 R e si li e n c e ( m o n th ) Two-Tier Model 55 year 220 year 550 year 770 year Figure (10): Effect of number of years used in generation on the estimation of vulnerability. AL-Qadisiya Journal For Engineering Sciences ,Vol. 6.No 3 Year 2013 032 50 60 70 80 90 100 Yield (% mean flow) 0 40 R e si li e n c e ( m o n th ) Modified Two-Tier Model 55 year 220 year 550 year 770 year 50 60 70 80 90 100 Yield (% mean flow) 0 5 10 15 20 25 30 R e si li e n c e ( m o n th ) Modified Fragment Model 55 year 220 year 550 year 770 year 50 60 70 80 90 100 Yield (% mean flow) a. Behavior procedure 75 80 85 90 95 100 R e li a b il it y ( % ) TF-log TTM MTTM MFM His. 50 60 70 80 90 100 Yield (% mean flow) b. Gould's procedure 75 80 85 90 95 100 R e li a b il it y ( % ) TF-log TTM MTTM MFM His. 50 60 70 80 90 100 Yield (% mean flow) 0 100 200 300 400 500 600 V u ln e r a b il it y ( m il ia r d c u .m ) TF-log TTM MTTM MFM His. 50 60 70 80 90 100 Yield (% mean flow) 0 5 10 15 20 25 30 35 40 R e si li n c e ( m o n th ) TF-log TTM MTTM MFM His. Figure 11: Effect of number of years used in generation on the estimation of resilience. Figure 12: Reliability-yield relationship depending on Behavior and Gould’s procedure using both historical and generated data (770 years of generation). Figure 13:Vulnerability-yield and Resilience-yield relationships depending on both historical and generated data (770 years of generation). AL-Qadisiya Journal For Engineering Sciences ,Vol. 6.No 3 Year 2013 032 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Starting month 800 900 1000 1100 1200 1300 1400 1500 S to r a g e ( m il li o n c u .m ) Yield =55 % Behavior Gould Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Starting month 1000 2000 3000 4000 5000 6000 7000 8000 S to r a g e ( m il li o n c u .m ) Yield =75 % Behavior Gould Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Starting month 240 260 280 300 320 340 360 380 400 420 V u ln e r a b il it y ( m il li o n c u .m ) Yield=75% Yield=55% Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Starting month 8.0 8.5 9.0 9.5 10.0 10.5 11.0 R r si li e n c e ( m o n th ) Yield=75% Yield=55% Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Starting month 1000 1500 2000 2500 3000 3500 4000 S to r a g e ( m il li o n c u .m ) Yield =55 % Behavior Gould Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Starting month 10000 20000 30000 40000 50000 60000 S to r a g e ( m il li o n c u .m ) Yield =75 % Behavior Gould Figure 16:Effect of starting month on Storage estimates using generated data. Figure 15:Effect of starting month on Vulnerability and Resilience estimates using historical data. Figure 14:Effect of starting month on Storage estimates using historical data. AL-Qadisiya Journal For Engineering Sciences ,Vol. 6.No 3 Year 2013 032 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 Length of generated sequence (year) 0 1000 2000 3000 4000 5000 6000 7000 8000 S to r a g e ( m il li o n c u . m ) TF-log TTM MTTM FM 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 Length of generated sequence (year) 800 1600 2400 3200 4000 4800 5600 6400 S to r a g e ( m il li o n c u . m ) TF-log TTM MTTM TRM Figure 17:Effect of inflow sequence length on storage estimates by Behavior analysis (yield=75% of mean monthly flow). Figure 18:Effect of inflow sequence length on storage estimates by Gould’s procedure analysis (yield=75% of mean monthly flow). AL-Qadisiya Journal For Engineering Sciences ,Vol. 6.No 3 Year 2013 032 50 55 60 65 70 75 80 85 90 Yield (%) 0 2000 4000 6000 8000 10000 S to r a g e ( m il li o n c u .m ) A. Using historical data Initially full Initially empty 50 55 60 65 70 75 80 85 90 Yield (%) 0 1000 2000 3000 4000 5000 6000 7000 S to r a g e ( m il li o n c u .m ) B. Using generated data (TF-log) Initially full Initially empty 50 55 60 65 70 75 80 85 90 Yield (%) 2000 4000 6000 8000 10000 12000 14000 16000 S to r a g e ( m il li o n c u .m ) C. Using generated data (TTM) Initially full Initially empty 50 55 60 65 70 75 80 85 90 Yield (%) 0 4000 8000 12000 16000 20000 24000 S to r a g e ( m il li o n c u .m ) D. Using generated data (M TTM ) Initially full Initially empty 50 55 60 65 70 75 80 85 90 Yield (%) 2000 4000 6000 8000 10000 12000 14000 S to r a g e ( m il li o n c u .m ) E. Using generated data (FRM) Initially full Initially empty Figure 19:Effect of initial conditions on storage estimates using Behaviour analysis.