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Reliability Analysis of the GroundwaterConceptual ModelXiankui Zeng a , Dong Wang a , Jichun Wu a & Xi Chen ba Key Laboratory of Surficial Geochemistry, Ministry of Education,Department of Hydrosciences, School of Earth Sciences andEngineering, State Key Laboratory of Pollution Control and ResourceReuse , Nanjing University , Nanjing , P.R. Chinab State Key Laboratory of Hydrology—Water Resources and HydrolicEngineering , Hohai University , Nanjing , P.R. ChinaAccepted author version posted online: 25 Jul 2012.Publishedonline: 08 Feb 2013.

To cite this article: Xiankui Zeng , Dong Wang , Jichun Wu & Xi Chen (2013) Reliability Analysis of theGroundwater Conceptual Model, Human and Ecological Risk Assessment: An International Journal,19:2, 515-525, DOI: 10.1080/10807039.2012.713822

To link to this article: http://dx.doi.org/10.1080/10807039.2012.713822

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Human and Ecological Risk Assessment, 19: 515–525, 2013Copyright C© Taylor & Francis Group, LLCISSN: 1080-7039 print / 1549-7860 onlineDOI: 10.1080/10807039.2012.713822

Reliability Analysis of the Groundwater ConceptualModel

Xiankui Zeng,1 Dong Wang,1 Jichun Wu,1 and Xi Chen2

1Key Laboratory of Surficial Geochemistry, Ministry of Education, Department ofHydrosciences, School of Earth Sciences and Engineering, State Key Laboratory ofPollution Control and Resource Reuse, Nanjing University, Nanjing, P.R. China;2State Key Laboratory of Hydrology—Water Resources and Hydrolic Engineering,Hohai University, Nanjing, P.R. China

ABSTRACTThe hydrologic model is the foundation of water resource management and plan-

ning. Conceptual model is the essential component of groundwater model. Due tolimited understanding of natural hydrogeological conditions, the conceptual modelis always constructed incompletely. Therefore, the uncertainty in the model’s out-put is evitable when natural groundwater field is simulated by a single groundwatermodel. A synthetic groundwater model is built and regarded as the true model, andthree alternative conceptual models are constructed by considering incomplete hy-drogeological conditions. The outputs (groundwater budget terms from boundaryconditions) of these groundwater models are analyzed statistically. The results showthat when the conceptual model is closer to the true hydrogeological conditions, thedistributions of outputs of the groundwater model are more concentrated on thetrue outputs. Therefore, the more reliable the structure of the conceptual model is,the more reliable the output of the groundwater model is. Moreover, the uncertaintycaused by the conceptual model cannot be compensated by parameter uncertainty.

Key Words: reliability analysis, groundwater model, conceptual model, uncer-tainty.

INTRODUCTION

Safety of water resources is the fundamental guarantee for sustainable socioeco-nomic development (Ajami et al . 2008; Wang et al . 2009). Local effects of climatechanges and human activities impact the hydrological cycle and resultant water re-sources (Peugeot et al . 2003; Feng et al . 2009). Therefore, the quantity, quality, anddistribution of water resources should be described precisely for correct decision-making. Hydrologic simulation is an approach that describes hydrological processes

Address correspondence to Dong Wang and Jichun Wu, Key Laboratory of Surficial Geo-chemistry, Ministry of Education, Department of Hydrosciences, School of Earth Sciencesand Engineering, State Key Laboratory of Pollution Control and Resource Reuse, NanjingUniversity, Nanjing 210093, P.R. China. E-mail: wangdong@nju.edu.cn; jcwu@nju.edu.cn

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based on some physical mechanisms and mathematic techniques. With the develop-ment of hydrology, a large number of methods have been developed for hydrologicsimulation, for example, hydrologic statistics methods (Koutsoyiannis 2003; Zenget al . 2012), hydrologic models (McMichael et al . 2006), and stochastic simulation(Salamon and Feyen 2009).

With the popularity of hydrologic simulation, a hydrologic model has becomethe foundation of water resource management and planning (Koundouri 2004).Plenty of models built with different physical mechanisms and simulation precisionshave been proposed in recent decades. As a result of the complexity and fuzziness ofhydrological conditions, hydrologic models are always built with large uncertaintyin practice (Wang 2009, 2010; Wang et al . 2007). During the past decade, therehas been a surge in the development of techniques for assessing various sources ofuncertainty associated with hydrologic models, such as GLUE (Beven and Binley1992; Beven and Freer 2001) and MCMC (Marshall et al . 2004; Vrugt et al . 2003).

Because of the model’s uncertainty, there is a high risk when the prediction ordecision is made based on an unreliable hydrologic model. A reliable hydrologicmodel with associated uncertainty assessment is able to provide decision-makerswith information that allows them to consider simulation errors in decision-making(Ajami et al . 2008). Therefore, the adverse impacts caused by the unpredictableuncertainty source can be mitigated by constructing a reliable model (Beven andFreer 2001; Draper 1995; Hassan et al . 2008; Huang and Shi 2011).

Groundwater is an important component of available fresh water resources(Koundouri 2004). The groundwater system is influenced by many factors, such asgeological structure, precipitation, and human activities (Fu and Gomez-Hernandez2009). Therefore, when the natural groundwater flow field is simulated by a ground-water model, the uncertainty of the model’s output is inevitable. With the develop-ment of numerical calculation techniques, and the accumulation of knowledge ofhydrologic processes, the uncertainty research of groundwater model is paid moreand more attention in recent decades (Blasone et al . 2008; Hassan et al . 2009;Kuczera and Parent 1998; Vrugt et al . 2003). There is now a general consensus thatthe major difficulty in accurately describing groundwater flow and solute transportprocesses arises from the model’s uncertainty. The uncertainty stems from a numberof factors including the conceptual model (model’s structure), the boundaries andparameters of groundwater model, and the observations errors, and so on (Blasoneet al . 2008; Fu and Gomez-Hernandez 2009; Wu et al . 2011).

A groundwater model is always constructed by three steps: (1) establishing a con-ceptual model that describes the spatial structure of aquifers, boundary conditionsof the groundwater flow field, and so on; (2) constructing a mathematic model todescribe the conceptual model; (3) numerical simulation, and solving the mathe-matic model. How to establish a suitable conceptual model is the most crucial step.A conceptual model is the framework and fundaments of a groundwater model. Theaquifers, boundary conditions, and hydrogeological parameters of a groundwatermodel are determined by the conceptual model. However, due to the restrictionsin economic and technologic conditions, it is hard to obtain a comprehensive un-derstanding of the hydrogeological conditions of a natural groundwater field byfield exploration works, such as topography and landforms, lithology, and geologi-cal structure. As a result, the conceptual model is always constructed incompletelyin practice. The power of the groundwater model is determined by the conceptual

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model. Therefore, for assessing and reducing the risk of the model’s prediction,the reliability analysis of the conceptual model is meaningful and necessary forgroundwater simulation (Poeter and Anderson 2005; Rojas et al . 2008).

In recent years, a number of methods have been proposed to address the prob-lem of the conceptual model’s uncertainty in hydrologic modeling (Rojas et al . 2008,2010a,b,c; Ye et al . 2010). These methods seek to obtain average simulation froma set of plausible models by linearly combining individual model simulation. Insuch methods, such as the Bayesian model averaging (BMA) method, it weights theperformances of proposed models by their corresponding posterior model prob-abilities. Rojas et al . (2008) demonstrated that the BMA method produces moreaccurate and reliable predictions than other existing multi-model techniques. Yeet al . (2010) evaluated alternative groundwater models with different recharge andgeologic components by using an averaging of models method. The study showedthat the contribution of model uncertainty to predictive uncertainty is significantlylarger than that of parametric uncertainty. Nevertheless, these studies emphasizehow to obtain a reasonable description and prediction to the natural groundwaterfield. However, little attention has been devoted to the reliability analysis of the con-ceptual model. In this work, a synthetic groundwater model was constructed, andall the hydrogeological conditions were assumed to be known. The outputs of thesynthetic groundwater model were regarded as true observations. Then, three al-ternative conceptual models were built with incomplete model structure comparedto the true model. Next, the outputs of these groundwater models based on differ-ent conceptual models were collected and compared statistically. Furthermore, thereliability of these conceptual models was analyzed.

The remainder of this article is organized as follows. Following this introduction,the descriptions of a synthetic groundwater model and three conceptual models arepresented. Next, the reliability of three conceptual models is assessed. Finally, themain conclusions drawn from the analysis are presented.

DESCRIPTION TO GROUNDWATER MODELS

The Synthetic Groundwater Model

For assessing the reliability of the conceptual model, a synthetic three-dimensional steady-state groundwater model was constructed. All the hydrogeo-logical conditions of groundwater model were assumed known, including the dis-tribution and location of the aquifers, hydrogeological parameters, and boundaryconditions. The simulation results from this synthetic model (groundwater budgetterms from boundary conditions) are regarded as true observations.

As shown in Figure 1, the spatial size of the synthetic model is 5000 m by 3000 mby 55 m. The platform’s shape is a rectangle (5000 m by 3000 m) and discretizedinto 25 m by 25 m grid cells. The model extends 55 m in the vertical direction (Z),with undisturbed layer thicknesses of 30 m (upper unconfined aquifer), 5 m (thinaquitard as confined bed, neglecting its elastic yield), and 20 m (lower confinedaquifer). All the aquifers were assumed to be horizontal in extension. The hydraulicconductivity of the aquitard was set as 0.1 m/d. The hydraulic conductivity distri-bution within each aquifer is heterogeneous, and the hydraulic conductivity fieldwithin each aquifer was assumed to be statistically stationary.

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Figure 1. The schematic diagram of the synthetic groundwater model.

Two impermeable boundaries are defined at the south and north boundaries. Theeast boundary is bounded by a general head boundary of which the conductance is1180 m2/d, and the water level is 40 m at this boundary. A constant head boundary(water head is 51.4 m) is imposed on the west boundary. Sources and sinks in themodel included precipitation and pumping. The top surface of the unconfinedaquifer receives the precipitation of 5.0∗10−5 m/d uniformly. Five pumping wells arelocated in the confined aquifer, and they pump a total of 1000 m3/d from the lowerlayer.

We assumed a statistically homogeneous deposit with a constant mean hydraulicconductivity K for each aquifer. Smaller scale variability is represented using the the-ory of random space functions, adopting isotropic exponential covariance functionsfor lnK in all layers. The spatial distribution of the hydraulic conductivity in modellayer is generated by the direct Fourier transform method (Robin et al . 1993). Theparameters of the field K are presented in Table 1.

Alternative Conceptual Models

With limited understanding of the true hydrogeological conditions, three alter-native conceptual models were constructed by considering incomplete hydrogeo-logical conditions. One conceptual model (M1) was constructed by considering twolayers as the whole aquifer. Similar to the true model, the thickness of layer 1 is

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Table 1. The mean and the parameters of the covariance functionrepresenting the spatial distribution of hydraulic conductivity K .

Parameter

Layer Mean of K (m/d) Variance of LnK Correlation length of LnK (m)

1 5.0 2.0 60.03 1.0 2.0 60.0

30 m, and the thickness of layer 2 is 25 m, without an aquitard between these twolayers. The hydraulic conductivity fields of the aquifers of M1 are the same as thatof true model. The second conceptual model (M2) was established by consideringthe unconfined aquifer of true model as the whole aquifer. The layer of M2 extends55 m in the vertical direction, and the distribution of hydraulic conductivity is thesame as that of layer 1 of true model. The third conceptual model (M3) includedonly one unconfined aquifer. The thickness of layer of M3 is 55 m, and the hydraulicconductivity field of this layer is the same as that of layer 3 of true model. In addition,the conductance of general head boundary, and the water level of constant headboundaries of three alternative conceptual models are defined in specified ranges(Table 2). The other hydrogeological parameters and boundary conditions were thesame as those of true model.

Monte Carlo Simulations

The numerical model of the synthetic groundwater flow field was build based onModflow-2005 (Harbaugh 2005). The Monte Carlo simulation procedure includesthe following steps:

1. Constructing the true groundwater model and running it. Based on the meanand the covariance function of lnK (Table 1), the random fields of K for themodels’ aquifers are generated by the direct Fourier transform method (Robinet al . 1993). Afterward, the outputs of model were collected. In addition, theoutputs of groundwater model include inflow from constant head boundary, andoutput flow from general head boundary leakage.

2. Setting the hydraulic conductivity and boundary conditions for M1. The ran-dom fields K of M1 are also generated by direct Fourier transform method.The parameters of boundary conditions are assigned values by sampling fromcorresponding ranges uniformly.

Table 2. The parameters of constant head boundary (CH) and general headboundary (GHB).

Parameter Minimum Maximum

Water level of CH (m) 48.0 54.0Conductance of GHB (m2/d) 100.0 2000.0

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3. Running the model of M1 and collecting outputs. Then, calculating the likeli-hood values of the parameter set by the following formulas:

L[M(θi |o, si )] = exp(−Q/T) (1)

Q =√√√√

k∑j=1

(si j − o j )2, T =

k∑j=1

o j

k(2)

where L denotes the likelihood value of parameter set θ i; o denotes the observa-tions of water level from the true groundwater model; si denotes the simulatedwater levels of M1; k is the number of observation points. In addition, the waterlevels are observed at the pumping wells.

4. Similar to M1, setting the hydraulic conductivity and boundary conditions of M2and M3. Then the groundwater numerical models of M2 and M3 are built andrun, and the outputs and likelihood values are collected.

5. Repeating step 2–step 4 for 500 times.6. The results from true model, M1, M2, and M3 are analyzed statistically.

Figure 2. The likelihood distributions of inflow from constant head boundary(InCH) and outflow from general head boundary (OutGHB). (A, D),(B, E), and (C, F) denote the outputs generated from M1, M2, and M3,respectively.

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RESULTS AND DISCUSSION

Based on the Monte Carlo technique, the likelihood distributions of groundwateroutputs are shown as Figure 2. The shapes of likelihood distributions of outputsare similar among the three alternative models. However, the distribution rangesare significantly different among the three alternative models. Shown in Figure 3are the means and variances of groundwater outputs with the number of MonteCarlo simulations. The results show that the outputs of the three alternative modelsconverge to stable values with the increase of Monte Carlo simulations. The statisticalpredictive distributions of the outputs of the three alternative models are presentedin Table 3.

As shown in Figure 4A, the distribution range of inflow from constant headboundary (InCH) of M2 is largest among the three alternative conceptual models.

Figure 3. Convergence tests of the mean and variance of the outputs of three alter-native groundwater models with the number of Monte Carlo simulations.(A) Denotes the mean of inflow from constant head boundary (InCH).(B) Denotes the variance of InCH. (C) Denotes the mean of outflowfrom general head boundary (OutGHB). (D) Denotes the variance ofOutGHB.

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Table 3. The probability statistics of the predictive outputs for the threealternative models. The outputs include inflow from constant headboundary (InCH), and outflow from general head boundary(OutGHB).

InCH (m3/d) OutGHB (m3/d)

Model 25% 50% 75% 25% 50% 75%

M1 695.97 804.69 902.78 423.96 552.70 636.53M2 1326.30 1589.39 1798.12 1165.66 1389.35 1514.69M3 386.81 436.32 480.67 137.38 173.22 224.00True model 812.48 572.88

Moreover, the true value of InCH is not contained in the whole range of M2. Thedistribution range of InCH of M3 is smallest among the three models. In addition,the true value of InCH is not contained in the whole range of M3. In contrast, thetrue value of InCH is close to the median of the distribution range of M1, and it iscontained in the confidence interval (25%–75%) of M1. Similar to InCH, for theoutflow of general head boundary (OutGHB), the magnitudes of range of OutGHBfor the three alternative models are: M2 > M1 > M3 (Figure 4B). Moreover, thetrue value of OutGHB is only contained by the confidence interval (25%–75%)of M1.

As stated above, for both InCH and OutGHB, the conceptual model of M1 issignificantly more reliable than that of M2 and M3. Furthermore, the conceptualmodel of M1 is constructed by two layers, which is similar to the structure of the truemodel. In contrast, the conceptual models of M2 and M3 are both constructed byonly one layer (unconfined or confined layer of true model). Therefore, the morereliable the structure of the conceptual model is, the more reliable the output of

Figure 4. Cumulative probability curves of the groundwater outputs of M1, M2,and M3. (A) Denotes inflow from constant head boundary (InCH).(B) Denotes outflow from general head boundary (OutGHB). The hori-zontal lines represent the values obtained from true groundwater model.

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the groundwater model is. Furthermore, the parameter uncertainty of each alter-native conceptual model is estimated. However, the groundwater model outputs’predictive distributions produced by model M1 and M2 seriously deviate from thecorresponding true values. Thus, the uncertainty derived from the model’s structurecannot be compensated by the calibration of the input parameter of groundwatermodel. In addition, the Bayesian model averaging method is an effective frame-work for treating conceptual mode uncertainty, which combines the results of themultiple alternative models by weighted linear addition.

CONCLUSIONS

The output uncertainty is inevitable when a natural groundwater field is simu-lated by a groundwater model. Moreover, the power of a groundwater model is deter-mined by the reliability of its conceptual model. Based on a synthetic groundwatermodel that is regarded as a true model, three alternative conceptual models weredeveloped. The outputs of these groundwater models were analyzed and compared.The results show that when the conceptual model is closer to the true hydrogeolog-ical conditions, the predictive distribution of the output of groundwater model ismore concentrated on true output. In addition, the uncertainty derived from themodel’s structure cannot be compensated by the calibration of the input parame-ter of groundwater model. Thus, the more reliable the structure of the conceptualmodel is, the more reliable the output of groundwater model is.

ACKNOWLEDGMENTS

This study was supported by the National Natural Science Fund of China(Nos. 41172207, 41030746, 40725010, 41071018, and 40730635), Water ResourcesPublic-welfare Project (No. 200701024), the Skeleton Young Teachers Program andExcellent Disciplines Leaders in Midlife-Youth Program of Nanjing University.

REFERENCES

Ajami NK, Hornberger GM, and Sunding DL. 2008. Sustainable water resource managementunder hydrological uncertainty. Water Resour Res 44:W11406

Beven K and Binley A. 1992. The future of distributed models—Model calibration and un-certainty prediction. Hydrol Process 6:279–98

Beven K and Freer J. 2001. Equifinality, data assimilation, and uncertainty estimation inmechanistic modelling of complex environmental systems using the GLUE methodology.J Hydrol 249:11–29

Blasone RS, Vrugt JA, Madsen H, et al. 2008. Generalized likelihood uncertainty estimation(GLUE) using adaptive Markov chain Monte Carlo sampling. Adv Water Resour 31:630–48

Draper D. 1995. Assessment and propagation of model uncertainty. J Roy Stat Soc B Met57:45–97

Feng LH, Zhang XC, and Luo GY. 2009. Research on the risk of water shortages and thecarrying capacity of water resources in Yiwu, China. Hum Ecol Risk Assess 15:714–26

Hum. Ecol. Risk Assess. Vol. 19, No. 2, 2013 523

Dow

nloa

ded

by [

Um

eå U

nive

rsity

Lib

rary

] at

23:

19 2

3 N

ovem

ber

2014

X. Zeng et al.

Fu JL and Gomez-Hernandez JJ. 2009. Uncertainty assessment and data worth in groundwaterflow and mass transport modeling using a blocking Markov chain Monte Carlo method. JHydrol 364:328–41

Harbaugh AW. 2005. The U.S. Geological Survey modular ground-water model—The ground-water flow process: U.S. Geological Survey Techniques and Methods 6-A16. US GeologicalSurvey, Washington, DC, USA

Hassan AE, Bekhit HM, and Chapman JB. 2008. Uncertainty assessment of a stochastic ground-water flow model using GLUE analysis. J Hydrol 362:89–109

Hassan AE, Bekhit HM, and Chapman JB. 2009. Using Markov Chain Monte Carlo to quantifyparameter uncertainty and its effect on predictions of a groundwater flow model. EnvironModell Softw 24:749–63

Huang CF and Shi X. 2011. A discrete model of the expected loss for catastrophe insurancein natural disasters. J Risk Anal Crisis Response 1:48–58

Koundouri P. 2004. Current issues in the economics of groundwater resource management.J Econ Surv 18:703–40

Koutsoyiannis D. 2003. Climate change, the Hurst phenomenon, and hydrological statistics.Hydrolog Sci J 48:3–24

Kuczera G and Parent E. 1998. Monte Carlo assessment of parameter uncertainty in concep-tual catchment models: The Metropolis algorithm. J Hydrol 211:69–85

Marshall L, Nott D, and Sharma A. 2004. A comparative study of Markov chain Monte Carlomethods for conceptual rainfall-runoff modeling. Water Resour Res 40:Artn W02501

McMichael CE, Hope AS, and Loaiciga HA. 2006. Distributed hydrological modelling inCalifornia semi-arid shrublands: MIKE SHE model calibration and uncertainty estimation.J Hydrol 317:307–24

Peugeot C, Cappelaere B, Vieux BE, et al. 2003. Hydrologic process simulation of a semiarid,endoreic catchment in Sahelian West Niger. 1. Model-aided data analysis and screening. JHydrol 279:224–43

Poeter E and Anderson D. 2005. Multimodel ranking and inference in ground water model-ing. Ground Water 43:597–605

Robin MJL, Gutjahr AL, Sudicky EA, et al. 1993. Cross-correlated random-field generationwith the direct fourier-transform method. Water Resour Res 29:2385–97

Rojas R, Feyen L, and Dassargues A. 2008. Conceptual model uncertainty in groundwatermodeling: Combining generalized likelihood uncertainty estimation and Bayesian modelaveraging. Water Resour Res 44:W12418

Rojas R, Batelaan O, Feyen L, et al. 2010a. Assessment of conceptual model uncertainty forthe regional aquifer Pampa del Tamarugal—North Chile. Hydrol Earth Syst Sc 14:171–92

Rojas R, Feyen L, Batelaan O, et al. 2010b. On the value of conditioning data to reduceconceptual model uncertainty in groundwater modeling. Water Resour Res 46:W08520

Rojas R, Kahunde S, Peeters L, et al. 2010c. Application of a multimodel approach to accountfor conceptual model and scenario uncertainties in groundwater modelling. J Hydrol394:416–35

Salamon P and Feyen L. 2009. Assessing parameter, precipitation, and predictive uncertaintyin a distributed hydrological model using sequential data assimilation with the particlefilter. J Hydrol 376:428–42

Vrugt JA, Gupta HV, Bouten W, et al. 2003. A Shuffled Complex Evolution Metropolisalgorithm for optimization and uncertainty assessment of hydrologic model parameters.Water Resour Res 39:Artn 1201

Wang D. 2009. Rethinking risk analysis: The risks of risk analysis in water issues as the case.Hum Ecol Risk Assess 15:1079–83

Wang D, Singh VP, and Zhu YS. 2007. Hybrid fuzzy and optimal modeling for water qualityevaluation. Water Resour Res 43:W05415

524 Hum. Ecol. Risk Assess. Vol. 19, No. 2, 2013

Dow

nloa

ded

by [

Um

eå U

nive

rsity

Lib

rary

] at

23:

19 2

3 N

ovem

ber

2014

Analysis of Groundwater Conceptual Model

Wang D, Singh VP, Zhu YS, et al. 2009. Stochastic observation error and uncertainty in waterquality evaluation. Adv Water Resour 32:1526–34

Wu JC, Lu L, and Tang T. 2011. Bayesian analysis for uncertainty and risk in a groundwaternumerical model’s predictions. Hum Ecol Risk Assess 17:1310–31

Ye M, Pohlmann KF, Chapman JB, et al. 2010. A model-averaging method for assessinggroundwater conceptual model uncertainty. Ground Water 48:716–28

Zeng XK, Wang D, and Wu JC. 2012. Sensitivity analysis of the probability distributionof groundwater level series based on information entropy. Stoch Env Res Risk A.doi:10.1007/s00477-012-0556-2

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