- Email: [email protected]
Reply to “Comments on ‘STAND, a dynamic model for sediment transport and water quality’ by W. Zeng and M.B. Beck, 2003. Journal of Hydrology 277, 125–133”
Journal of Hydrology 297 (2004) 305–307 www.elsevier.com/locate/jhydrol
Discussion
Reply to “Comments on ‘STAND, a dynamic model for sediment transport and water quality’ by W. Zeng and M.B. Beck, 2003. Journal of Hydrology 277, 125 –133” W. Zenga,*, M.B. Beckb a
b
Georgia Department of Natural Resources, 2 Martin Luther King Jr. Drive, Suite 1058 East, Atlanta, GA 30334, USA Environmental Informatics and Control Program, Warnell School of Forest Resources, University of Georgia, D.W. Brooks Drive, Athens, GA 30602-2152, USA
The authors welcome the critique and thank the discusser for his/her enlightening comments. The discusser has raised a number of questions and asked for more information on the model STAND (Zeng and Beck, 2003). We are pleased to respond accordingly. The discusser questions the authors in not presenting morphological changes and deduces that such changes are totally ignored in STAND. In fact, the equation governing bed changes as presented in Chang (1988), Xie (1990), and Yang et al (1998) and the process of sediment exchange between the bed and the overlying water body, together with the resulting morphological changes, are integral parts of STAND. The authors did not present the bed-deformation equation, however, simply because this equation is mainly used to govern cross-sectional bed changes, and investigating cross-section profile changes is outside the main focus of this model. The authors focused primarily on the model’s capability in capturing time series of the key state variables, which are arguably crucial in determining morphological changes, but not on the resulting bed profile change itself. It is true that the first chapter of Xie (1990), among others, provided continuity and momentum equations * Corresponding author. E-mail address: [email protected] (W. Zeng). 0022-1694/$ - see front matter q 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jhydrol.2004.04.025
for sediment-laden flow. Yet in the third Chapter (One-dimensional Sediment Transport Model) of this same text, governing equations presented for models of various levels of complexity (from the simple noncoupled, steady, capacity-transport model, to the more complicated ones) all include some form of the StVenant equations (some of them simplified). It is indeed desirable to preserve theoretical rigor whenever possible. However, with the complexity of sediment transport and the immaturity of the associated theories, practicalities must often be the priority, just as Xie (1990) presented the theoretical basis and practical solutions to the various problems in his book. Strictly speaking, no sediment transport model should ever start with the equations of mass continuity and momentum only for water. Yet it is a common practice (Chang, 1988; Xie, 1990; Yang et al., 1998), even for studying the Yellow River (Wang, 1992). Parameter ksed has a dimension of [T21], ensuring dimensional homogeneity. Although this method of parameterization (assuming a first-order mechanism) is fairly common in water quality modeling, the authors apologize for any confusion caused by not having specified the dimension of the corresponding parameter. It is the formulations of ksed (Equations 5A and 5B) that the authors hypothesize, not that the processes of scour and deposition are different from
306
W. Zeng, M.B. Beck / Journal of Hydrology 297 (2004) 305–307
each other. Various investigators have employed different ways to represent the process of sediment concentration approaching equilibrium (carrying capacity); the justification of any particular formulation, however, must rest on the basis of a reasonable replication of field observations. The appropriateness of our hypotheses can be checked by comparing the simulation results with the measurements. The value of ksed was not meant to be directly available to a modeler, since it is not the direct parameter. Rather, the processes of entrainment and deposition are controlled by parameters ksedDep and ksedEnt : The values of these parameters are available in Zeng and Beck (2001). Despite what the discusser has described as “quick bed-tearing scour at possibly a rate of ten meters in merely tens of hours” under conditions of high sediment concentration, past investigations have indicated otherwise that the major causes for channel sedimentation are mid- to lower-scale floods with high sediment concentration (See Fig. 4 in Zeng and Zeng, 1996; Yellow River Water Resources Commission, 2001). In the middle reaches of the Yellow River, including the Weihe River, large sheets (or blocks) of bottom sediment can occasionally be scoured under high sediment concentration, like a piece of rug being rolled up (one of the authors was fortunate to see pictures showing these huge blocks surfacing). This is a very special phenomenon. A scour of about 10 m under high sediment concentration (about 800 kg/m3) and mid-magnitude flood (with peak flow rate of about 14,000 m3/s) was indeed documented and analyzed in Zeng and Zeng (1996). Another such occasion with documentation happened near Tongguan in 1977 when sediment concentrations reached 600 –800 kg/m3 and the peak flow reached about 15,000 m3/s. The stage –discharge curve indicated a maximum scour of 3 – 4 m (Zeng and Zeng, 1996). However, the mechanism of this special phenomenon is far from being understood and so far no mathematical model can be used to describe it. The dispersion term in Equation (3) is not negligible, in contrast to the suggestion of the discusser. Trials during calibration indicated a clear and significant effect of the chosen value of the dispersion coefficient. The associated equation is numerically solved using a 4-point implicit scheme. A forward difference is used to replace the time
derivative term; a central difference is used in place of the spatial derivative; and a central difference is also used to represent the dispersion term. The resulting coefficient matrix for the system of linear equations is tri-diagonal, and the system can be solved easily using standard numerical methods. The discusser is correct in noting that no boundary condition for sediment transport at the downstream end has been arbitrarily imposed, and that is because sediment discharge at a cross-section is under upstream control. However, in order to solve the system of difference equations, an imaginary node is necessary outside the lower boundary. As a result of this, a numerical boundary condition of linearconcentration-gradient has been used. Professionals working with developing river models know from their experience that actual data are scarce and thus valuable in the process of calibrating a model. This has been the case with our own work. When access to the Weihe data was made available, the authors felt almost compelled to test the model with this valuable data set. In presenting the simulation results, rather than to imply that STAND is superior to HEC-6, the authors have merely illustrated how STAND could handle a particular situation where HEC-6 did not perform well. The discusser’s comment that HEC-6 was not designed to handle ‘extreme hydrologic conditions’ is well received. However, it is during these extreme hydrologic conditions that the majority of the sediment is transported through, or deposited into, the channel. Thus, it is crucial for a sediment transport model to be able to simulate such extreme hydrologic events. Consequently, the comparison between the application of the two models in this case is not only relevant, but also important. When a model is being assessed, its capacity in replicating what is observed to happen in reality is paramount. Chinese professionals in hydraulic engineering had an evaluation of different mathematical models (for sediment transport) developed by a variety of research institutions. The result of the evaluation was that the model developed by the Yellow River Commission’s Water Resources Research Institute best reflected the actual situation of the Yellow River, precisely because the researchers summarized empirical equations from a significant number of field observations. What is revealing of this evaluation process is that field observations
W. Zeng, M.B. Beck / Journal of Hydrology 297 (2004) 305–307
and measurements ultimately show a model’s quality in being indeed a ‘model’. Instead of making steady-state assumptions, and instead of STAND being driven by step-functions representing input hydraulic and sediment conditions, the first two levels of our model simulate unsteady flow, and couple this with the resulting non-equilibrium sediment transport (and consequently bed changes) through a variable time step. Though it may not be the first published model to consider ‘noncapacity’ sediment transport, it clearly demonstrated its capability when faced with the rigorous test of high quality field data under transient hydrologic conditions. Instead of testing the model with an aggregate quantity, such as the quantity of deposition between cross-sections over a long period of time, we chose to test the model with some available time series, which, we argue, is a more rigorous approach. The model proves to be up to the test. As stated earlier, it is paramount to see that observations and measurements be well replicated when evaluating a model. Not only did STAND successfully replicate the observed quantities on the Weihe River in the year 1973, the same set of parameters have also generated equally satisfactory replications in the year 1974 (not presented in the paper being discussed). With regard to the wider issues of the role of calibration in model evaluation—and the more philosophical aspects of the subject of modeling— we acknowledge these have been considered only in passing in our paper. We fully agree with the discusser that these are of considerable importance and, by way of supporting this statement, would like to point to work elsewhere on this matter (e.g. Beck, 1987, 2002; Beck et al., 1997). The present exercise in reconciling the constituent hypotheses in STAND with field observations, while based on rudimentary methods of trial and error, makes no claims beyond positions expressed in these other works. Indeed, ‘rudimentary’ though trial-and-error calibration may be, it may still yield useful insights and will, in many instances, act
307
as a prelude to more systematic explorations of the role of uncertainty in matching model performance with the observed record. We welcome, therefore, the discusser’s suggestion (which we believe he is making) that analyses of uncertainty should be much more prominent in the subject of hydraulic modeling.
References Beck, M.B., 1987. Water quality modeling: a review of the analysis of uncertainty. Water Resources Research 23(8), 1393–1442. Beck, M.B. (Ed.), 2002. Environmental Foresight and Models: A Manifesto, Elsevier, Oxford. Beck, M.B., Ravetz, J.R., Mulkey, L.A., Barnwell, T.O., 1997. On the problem of model validation for predictive exposure assessments. Stochastic Hydrology and Hydraulics 11(3), 229 –254. Chang, H.H., 1988. Fluvial Processes in River Engineering, Wiley, New York. Wang, S., 1992. One-dimensional Mathematical Model for Morphological Changes at the Lower Reaches of the Yellow River, Proceedings of National Symposium on Basic Theories of Sediment Transport, Beijing (in Chinese). Xie, J., 1990. River Modeling, China Water Resources and Hydropower Press, Beijing (in Chinese). Yang, C.T., Trevin˜o, M.A., Simo˜es, F.J.M., 1998. User’s Manual for GSTARS 2.0 (Generalized Stream Tube Model for Alluvial River Simulation Version 2.0), US Department of the Interior, Bureau of Reclamation, Technical Service Center, Denver. Yellow River Water Resources Commission, 2001. Collection of Studies at the 40th Anniversary of the Operation of the Sanmenxia Reservoir, Yellow River Water Resources Press (in Chinese). Zeng, W., Beck, M.B., 2001. Development and evaluation of a mathematical model for the study of sediment-related water quality issues. Water Science and Technology 43(7), 47 –54. Zeng, W., Beck, M.B., 2003. STAND, a dynamic model for sediment transport and water quality. Journal of Hydrology 277, 125 –133. Zeng, Q., Zeng, W., 1996. Several Important Issues in the Study of Sediment Transport on the Yellow River, Proceedings of the Second Symposium on Water Resources Science and Technology for Professionals on Both Sides of the Taiwan Straight (in Chinese), pp. 455 –485.
Discussion
Reply to “Comments on ‘STAND, a dynamic model for sediment transport and water quality’ by W. Zeng and M.B. Beck, 2003. Journal of Hydrology 277, 125 –133” W. Zenga,*, M.B. Beckb a
b
Georgia Department of Natural Resources, 2 Martin Luther King Jr. Drive, Suite 1058 East, Atlanta, GA 30334, USA Environmental Informatics and Control Program, Warnell School of Forest Resources, University of Georgia, D.W. Brooks Drive, Athens, GA 30602-2152, USA
The authors welcome the critique and thank the discusser for his/her enlightening comments. The discusser has raised a number of questions and asked for more information on the model STAND (Zeng and Beck, 2003). We are pleased to respond accordingly. The discusser questions the authors in not presenting morphological changes and deduces that such changes are totally ignored in STAND. In fact, the equation governing bed changes as presented in Chang (1988), Xie (1990), and Yang et al (1998) and the process of sediment exchange between the bed and the overlying water body, together with the resulting morphological changes, are integral parts of STAND. The authors did not present the bed-deformation equation, however, simply because this equation is mainly used to govern cross-sectional bed changes, and investigating cross-section profile changes is outside the main focus of this model. The authors focused primarily on the model’s capability in capturing time series of the key state variables, which are arguably crucial in determining morphological changes, but not on the resulting bed profile change itself. It is true that the first chapter of Xie (1990), among others, provided continuity and momentum equations * Corresponding author. E-mail address: [email protected] (W. Zeng). 0022-1694/$ - see front matter q 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jhydrol.2004.04.025
for sediment-laden flow. Yet in the third Chapter (One-dimensional Sediment Transport Model) of this same text, governing equations presented for models of various levels of complexity (from the simple noncoupled, steady, capacity-transport model, to the more complicated ones) all include some form of the StVenant equations (some of them simplified). It is indeed desirable to preserve theoretical rigor whenever possible. However, with the complexity of sediment transport and the immaturity of the associated theories, practicalities must often be the priority, just as Xie (1990) presented the theoretical basis and practical solutions to the various problems in his book. Strictly speaking, no sediment transport model should ever start with the equations of mass continuity and momentum only for water. Yet it is a common practice (Chang, 1988; Xie, 1990; Yang et al., 1998), even for studying the Yellow River (Wang, 1992). Parameter ksed has a dimension of [T21], ensuring dimensional homogeneity. Although this method of parameterization (assuming a first-order mechanism) is fairly common in water quality modeling, the authors apologize for any confusion caused by not having specified the dimension of the corresponding parameter. It is the formulations of ksed (Equations 5A and 5B) that the authors hypothesize, not that the processes of scour and deposition are different from
306
W. Zeng, M.B. Beck / Journal of Hydrology 297 (2004) 305–307
each other. Various investigators have employed different ways to represent the process of sediment concentration approaching equilibrium (carrying capacity); the justification of any particular formulation, however, must rest on the basis of a reasonable replication of field observations. The appropriateness of our hypotheses can be checked by comparing the simulation results with the measurements. The value of ksed was not meant to be directly available to a modeler, since it is not the direct parameter. Rather, the processes of entrainment and deposition are controlled by parameters ksedDep and ksedEnt : The values of these parameters are available in Zeng and Beck (2001). Despite what the discusser has described as “quick bed-tearing scour at possibly a rate of ten meters in merely tens of hours” under conditions of high sediment concentration, past investigations have indicated otherwise that the major causes for channel sedimentation are mid- to lower-scale floods with high sediment concentration (See Fig. 4 in Zeng and Zeng, 1996; Yellow River Water Resources Commission, 2001). In the middle reaches of the Yellow River, including the Weihe River, large sheets (or blocks) of bottom sediment can occasionally be scoured under high sediment concentration, like a piece of rug being rolled up (one of the authors was fortunate to see pictures showing these huge blocks surfacing). This is a very special phenomenon. A scour of about 10 m under high sediment concentration (about 800 kg/m3) and mid-magnitude flood (with peak flow rate of about 14,000 m3/s) was indeed documented and analyzed in Zeng and Zeng (1996). Another such occasion with documentation happened near Tongguan in 1977 when sediment concentrations reached 600 –800 kg/m3 and the peak flow reached about 15,000 m3/s. The stage –discharge curve indicated a maximum scour of 3 – 4 m (Zeng and Zeng, 1996). However, the mechanism of this special phenomenon is far from being understood and so far no mathematical model can be used to describe it. The dispersion term in Equation (3) is not negligible, in contrast to the suggestion of the discusser. Trials during calibration indicated a clear and significant effect of the chosen value of the dispersion coefficient. The associated equation is numerically solved using a 4-point implicit scheme. A forward difference is used to replace the time
derivative term; a central difference is used in place of the spatial derivative; and a central difference is also used to represent the dispersion term. The resulting coefficient matrix for the system of linear equations is tri-diagonal, and the system can be solved easily using standard numerical methods. The discusser is correct in noting that no boundary condition for sediment transport at the downstream end has been arbitrarily imposed, and that is because sediment discharge at a cross-section is under upstream control. However, in order to solve the system of difference equations, an imaginary node is necessary outside the lower boundary. As a result of this, a numerical boundary condition of linearconcentration-gradient has been used. Professionals working with developing river models know from their experience that actual data are scarce and thus valuable in the process of calibrating a model. This has been the case with our own work. When access to the Weihe data was made available, the authors felt almost compelled to test the model with this valuable data set. In presenting the simulation results, rather than to imply that STAND is superior to HEC-6, the authors have merely illustrated how STAND could handle a particular situation where HEC-6 did not perform well. The discusser’s comment that HEC-6 was not designed to handle ‘extreme hydrologic conditions’ is well received. However, it is during these extreme hydrologic conditions that the majority of the sediment is transported through, or deposited into, the channel. Thus, it is crucial for a sediment transport model to be able to simulate such extreme hydrologic events. Consequently, the comparison between the application of the two models in this case is not only relevant, but also important. When a model is being assessed, its capacity in replicating what is observed to happen in reality is paramount. Chinese professionals in hydraulic engineering had an evaluation of different mathematical models (for sediment transport) developed by a variety of research institutions. The result of the evaluation was that the model developed by the Yellow River Commission’s Water Resources Research Institute best reflected the actual situation of the Yellow River, precisely because the researchers summarized empirical equations from a significant number of field observations. What is revealing of this evaluation process is that field observations
W. Zeng, M.B. Beck / Journal of Hydrology 297 (2004) 305–307
and measurements ultimately show a model’s quality in being indeed a ‘model’. Instead of making steady-state assumptions, and instead of STAND being driven by step-functions representing input hydraulic and sediment conditions, the first two levels of our model simulate unsteady flow, and couple this with the resulting non-equilibrium sediment transport (and consequently bed changes) through a variable time step. Though it may not be the first published model to consider ‘noncapacity’ sediment transport, it clearly demonstrated its capability when faced with the rigorous test of high quality field data under transient hydrologic conditions. Instead of testing the model with an aggregate quantity, such as the quantity of deposition between cross-sections over a long period of time, we chose to test the model with some available time series, which, we argue, is a more rigorous approach. The model proves to be up to the test. As stated earlier, it is paramount to see that observations and measurements be well replicated when evaluating a model. Not only did STAND successfully replicate the observed quantities on the Weihe River in the year 1973, the same set of parameters have also generated equally satisfactory replications in the year 1974 (not presented in the paper being discussed). With regard to the wider issues of the role of calibration in model evaluation—and the more philosophical aspects of the subject of modeling— we acknowledge these have been considered only in passing in our paper. We fully agree with the discusser that these are of considerable importance and, by way of supporting this statement, would like to point to work elsewhere on this matter (e.g. Beck, 1987, 2002; Beck et al., 1997). The present exercise in reconciling the constituent hypotheses in STAND with field observations, while based on rudimentary methods of trial and error, makes no claims beyond positions expressed in these other works. Indeed, ‘rudimentary’ though trial-and-error calibration may be, it may still yield useful insights and will, in many instances, act
307
as a prelude to more systematic explorations of the role of uncertainty in matching model performance with the observed record. We welcome, therefore, the discusser’s suggestion (which we believe he is making) that analyses of uncertainty should be much more prominent in the subject of hydraulic modeling.
References Beck, M.B., 1987. Water quality modeling: a review of the analysis of uncertainty. Water Resources Research 23(8), 1393–1442. Beck, M.B. (Ed.), 2002. Environmental Foresight and Models: A Manifesto, Elsevier, Oxford. Beck, M.B., Ravetz, J.R., Mulkey, L.A., Barnwell, T.O., 1997. On the problem of model validation for predictive exposure assessments. Stochastic Hydrology and Hydraulics 11(3), 229 –254. Chang, H.H., 1988. Fluvial Processes in River Engineering, Wiley, New York. Wang, S., 1992. One-dimensional Mathematical Model for Morphological Changes at the Lower Reaches of the Yellow River, Proceedings of National Symposium on Basic Theories of Sediment Transport, Beijing (in Chinese). Xie, J., 1990. River Modeling, China Water Resources and Hydropower Press, Beijing (in Chinese). Yang, C.T., Trevin˜o, M.A., Simo˜es, F.J.M., 1998. User’s Manual for GSTARS 2.0 (Generalized Stream Tube Model for Alluvial River Simulation Version 2.0), US Department of the Interior, Bureau of Reclamation, Technical Service Center, Denver. Yellow River Water Resources Commission, 2001. Collection of Studies at the 40th Anniversary of the Operation of the Sanmenxia Reservoir, Yellow River Water Resources Press (in Chinese). Zeng, W., Beck, M.B., 2001. Development and evaluation of a mathematical model for the study of sediment-related water quality issues. Water Science and Technology 43(7), 47 –54. Zeng, W., Beck, M.B., 2003. STAND, a dynamic model for sediment transport and water quality. Journal of Hydrology 277, 125 –133. Zeng, Q., Zeng, W., 1996. Several Important Issues in the Study of Sediment Transport on the Yellow River, Proceedings of the Second Symposium on Water Resources Science and Technology for Professionals on Both Sides of the Taiwan Straight (in Chinese), pp. 455 –485.