Draft Report of the Peer Review Panel of the RSM Theory Manual of the South Florida Water Management District

Contribution by Victor M. Ponce, Panelist

July 1, 2005

1. Determining if proper and sound scientific approaches were used in the development of RSM.

  1. The use of Ponce et al.'s 1978 diffusion-wave applicability criteria [Ponce, V. M. et al., 1978. Applicability of kinematic and diffusion models, Journal of the Hydraulics Division, 104(HY3)] needs to be qualified as an extension to 2-D flow. However, experience suggests that the diffusion flow assumption is a practical one when simulating regional overland flows. Inclusion of the inertia terms is likely to render the model difficult to control and, therefore, defeat the purpose of the modeling.

  2. The RSM's diffusion-flow formulation is not applicable for modeling lake circulation because circulation is not present in models that lack convective inertia [See Ponce, V. M., 1981. Modeling circulation in depth-average flow, ASCE Journal of the Hydraulics Division, 107(HY11)]. The manual should make it clear that lake-circulation modeling is not intended to be part of the RSM.

  3. While the convective and diffusive properties of 1-D surface flow are well known, the same is not true for 2-D surface flows. For instance, how is the diffusivity in one dimension [the channel hydraulic diffusivity, see Ponce V. M., 1989. Engineering Hydrology, Principles and Practices, Prentice Hall, page 290] resolved in two dimensions? There is an urgent need for additional, theoretical work in this area.

  4. There is no need to oversell the capabilities of the implicit scheme used in RSM. While implicit schemes are unconditionally stable, they can be inaccurate if abused. Implicit schemes were oversold in the early years of hydraulic and hydrologic modeling (the 1970's), when the focus was on stability. However, once the model was shown to be stable, the focus shifted to convergence, where the implicit scheme was weak. Experienced numerical modelers will recognize that the objective is to seek a balance between stability and convergence, and not to pursue one or the other by itself. This balance is obtained through the simultaneous minimization of roundoff and truncation errors, in the sense of O'Brien et al. (1950) [A study of the numerical solution of partial differential equations, Journal of Mathematics and Physics, 29(4)].

  5. Contrary to popular opinion, the achievement of grid independence in hydraulic and hydrologic modeling is not an impossible task. In particular, channel routing can benefit from this test of convergence, i.e., of accuracy [For an example of a grid-independent numerical scheme, see Ponce, V. M., 1986. Diffusion wave modeling of catchment dynamics, ASCE Journal of Hydraulic Engineering, 112(8)]. Thus, numerical tests aimed at assessing model errors should focus on grid independence as the ultimate proof of convergence.

  6. The strategy of recovering some of the convective inertia through the use of E instead of H may be unwise (Appendix C.1). In 1-D flow, the full dynamic diffusivity (including all inertia terms) is closer to the kinematic hydraulic diffusivity (neglecting all inertia terms) than the convective-only (partial inertia) model. [See Ponce, V. M., 1990. Generalized diffusion wave equation with inertial effects, Water Resources Research, 26(5)].

  7. At least in 1-D flow (for the canal flow), the use of lookup tables renders the simulation kinematic, i.e., not subject to physical diffusion. Therefore, any hydrograph diffusion manifested in the simulation would necessarily be a function of grid size [See Cunge, J. A. 1969. On the subject of a flood propagation computation method (Muskingum method), Journal of Hydraulic Research, 7(2)]. How is the extensive use of lookup tables reconciled with the diffusion flow assumption, which has built-in physical diffusion through the hysteresis in the rating?

  8. The NRCS runoff curve number method is strictly applicable only to event modeling. However, it is recognized that the method has sometimes been used by default in continuous modeling. There is no such thing as a fixed "curve number" or a constant "maximum potential retention." Thus, a curve number obtained through calibration may not be applicable in the validation phase, unless the two events being used happen to have similar AMC characteristics. The demonstrated discrepancies between simulated and recorded flows may be partly attributed to the variability in AMC within a run [See Ponce, V. M. and R. H. Hakwins, 1996. Runoff curve number: Has it reached maturity? ASCE Journal of Hydrologic Engineering, 1(1)].

  9. The manual needs to give clear guidance on how to estimate Manning's n. The Manning's n is strictly applicable only to fully developed turbulent flow; however, it has been extended, through usage, to the realm of mixed turbulent-laminar and even laminar flow. In practice, the term "effective roughness parameter for overland flow" is often used, and the term N is substituted for n to denote the fact that the flow is not fully turbulent.

  10. The sensitivity of the model to variation in Manning's n needs to be documented by examples.

  11. Referring to the 2-D set of governing equations as the St. Venant equations is confusing and inaccurate. The proper name is the "system of depth-integrated two-dimensional equations for unsteady shallow-water flow."
2. Evaluating if the conceptual framework of the model contains all the important hydrological processes necessary to do regional-scale modeling in Florida.

  1. If regional-scale model is the objective, perhaps the calculation of PET should be incorporated into the model itself, rather than considering it to be just another input. PET may vary temporally in a long-term model application, particularly as land-use changes and ecosystem restoration practices are implemented.

3. Determining the appropriate use of the model in South Florida conditions.

  1. Uniform flow (the balance of gravity and friction) is appropriately described by the Manning equation. Steady gradually varied flow (the so-called "backwater computation") is approximately described by the Manning equation. For canals of nearly zero bed slope, such as those of South Florida, the only way to operate them (i.e., convey flows) is to mechanically force a depth gradient (pressure gradient), at which time some inertia may be present. The latter flow is unsteady, meaning "dissipative," in the sense that an unsteady disturbance will dissipate with a finite dissipation rate (the hydraulic diffusivity). By itself, the Manning equation is not able to provide the unsteadiness and associated convection and diffusion properties of a "South Florida" wave, i.e., one governed primarily by friction and the depth-gradient. There is an urgent need to perform theoretical work to identify the convective and diffusive properties of the "South Florida" waves and to eventually build the canal model on these premises. Barring this, an alternative is to implement full dynamic wave modeling in the canals, with all the attendant nonlinearities, instabilities, and extensive data requirements that characterize dynamic wave computations.

4. Making suggestions on modifications and future improvements of the model, including any suggestions for improved computational methods, and future model-expansion ideas.
  1. The use of an implicit, as opposed to an explicit numerical scheme, is a tradeoff that needs to be assessed judiciously. Implicit schemes are usually unconditionally stable, while explicit schemes are not. Therefore, if stability is the issue, an implicit scheme is the preferred choice. However, in numerical modeling, stability is usually achieved at the expense of convergence. Once the focus shifts from stability to convergence (and it eventually must, if the modeling is going to have any semblance of accuracy), an explicit scheme can compete effectively with an implicit scheme. The former (the explicit scheme) will usually achieve convergence at the same time as stability, while the latter (the implicit scheme) may be stable throughout a wide range of grid resolutions, while remaining nonconvergent for some subrange. Therefore, in general, it does not follow that implicit schemes are altogether better than explicit schemes.

  2. The use of a fully implicit model (α = 1) as a norm (default value) is justified only when results of sensitivity analysis clearly show that the tradeoff is an acceptable one (improved stability without unduly sacrificing convergence). I recommend that the manual show explicitly the tradeoffs involved between the use of α = 1 and that of a more convergent value such as α = 0.6.

  3. With such a large number of canals in South Florida, and given the long simulation times, both rainfall and ET should be considered in the canal water balance. This is a simple matter to implement, and it should slightly improve the model accuracy.

5. Making suggestions on the usefulness of the model documentation, including whether the level of detail is sufficient or more is needed, whether the conceptual framework is clear, and so on.

  1. The manual should be reviewed by a competent technical editor to resolve problems with language, grammar and consistency of usage.

  2. Appendix A (Regional Simulation Model Philosophy), particularly A.2 (Scope of the RSM), should be part of Chapter 1 (Introduction). Consider making Appendix B (Governing Equations Using the Traditional Approach) part of Chapter 2 (Hydrologic Simulation Engine Theory and Concepts).

  3. Preferably, the material in Appendix C, Sections C.5 and C.6 should be incorporated into the main body of the manual. The remaining material in Appendix C (Sections C.1 to C.4) should be removed, and references should be made to these papers, as necessary, in the main body of the manual. At the very least, the most important material from Sections C.5 and C.6 should be incorporated into the main body of the manual, and the remainder relabeled as Appendix C and D, respectively.

  4. The name "Theory Manual" may not be the best way to describe the document being reviewed. First, it appears to be a contradiction: If it is a manual (i.e., handbook), it cannot be theoretical at the same time. Second, there is the risk of rendering the document unreadable or unfriendly, solely on the basis of its title. My recommendation is to have two sets of manuals: The first set would be titled "User's Manual," and dwell on the nuts and bolts of how to run the model. The second would be titled "Technical Reference Manual" or simply "Reference Manual." The latter should contain all the information that is necessary to understand the model, but not necessarily to run it. The portions of the theory that are deemed absolutely necessary for understanding should be included in this manual. More esoteric concepts should be left as references to published work [See, for example, the HEC-HMS model's User's Manual and Technical Reference Manual, and the HEC-RAS User's Manual and Hydraulic Reference Manual at http://www.hec.usace.army.mil]

  5. There is a difference between "Bibliography" and "References." "Bibliography" is a list of published works which are related to the topic, but not necessarily quoted in the text. "References" is the list of published works that have been specifically referred to in the text. Most documents of the kind reviewed here will have only a list of references. If a bibliography is deemed necessary, it should be contained in a separate appendix.

  6. The Latex typesetting program is judged to be clearly superior to other programs when used for large, high-technical-content communications such as the manual being reviewed here.

  7. Resolve the question of the usage of English (properly, "U.S. Customary") vs metric (properly, SI) units in the RSM. If both systems are being used, the RSM Facts Sheet should state so. Both systems should be used if the model is going to be applied outside of Florida.

  8. Add a glossary of technical terms as an appendix to improve readability.
6. Suggesting any additional tests that may be desired to fully validate RSM.

  1. It is a well known fact that surface-flow properties are nonlinear, or rather, quasilinear. In practice, this means that the parameters may not remain constant throughout the range of possible flows. A clear example is that of diffusion-wave routing in a natural channel, where the Muskingum-Cunge parameters vary not only with the stage, but also with the rate-of-change in stage. Thus, conventional parameter estimation will miss the peaks and valleys of the flow variability. A three-stage parameter calibration (low, average, and high) may be appropriate to account for the inherent nonlinearity of surface flow.

  2. There are three types of errors in modeling: (1) numerical errors, which are caused by roundoff and/or truncation, (2) physical errors, attributed to inaccurate parameter estimation, and (3) errors that are traceable to poor data quality [e.g., equipment flaws]. A calibration and validation exercise should identify these three sources of errors, and to the extent possible, keep them separate. The numerical errors can be minimized by a judicious choice of grid resolution. The physical errors can be minimized by the proper choice of parameter ranges; the parameters themselves should, preferably, have some physical basis [Example: Manning's n]. The data-quality errors can usually only be assessed in a qualitative way, however, their importance cannot be overemphasized. Full model validation demands the conscious separation of errors; otherwise, one could be calibrating numerical errors against physical and/or data-quality errors. The procedure should be the following: (1) To the extent possible, eliminate the numerical errors; (2) calibrate to the expected values of the physical parameters; and (3) If necessary, assess the quality of the measured data.
7. Suggesting tests for the HPM approach to simulating local hydrology and making recommendations for improvement or expansion of the approach.
  1. There is a need to confirm that the NRCS runoff curve number method is being applied correctly. The Mockus mapping equation (Eq. 50 in Appendix C.5) is valid only for U.S. customary (aka English) units.

  2. While the NRCS runoff curve number method has its limitations, there is still no infiltration method, including the Green and Ampt formula, which has clearly shown its superiority. The advantage of the NRCS runoff curve number is its simplicity and wide usage; its disadvantage is that it is predictive only in a design modeling context. For continuous-modeling applications, there is a need for a local assessment of AMC variability, which leads to a range of curve numbers for a given site.

8. Evaluating whether the model is suitable for meeting client goals.

  1. As documented, the model appears to be suited to evaluating long-term effects of management decisions regarding conflicting uses such as flood control, water supply, water quality, and ecosystem conservation. As such, the 1-d time interval is amply justified on practical grounds. The emphasis on "regional" implies large spatial and temporal scales, i.e., seasonal, annual, or multiannual. The focus should be on "where is the water, when, and for what purpose," and management should seek, through policies and actions, to reconcile ecological and economic (i.e, natural and anthropogenic) demands on the scarce resource. In this context, it should be stated that hydrologic modeling, however limited, is the only feasible alternative.

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