Hydrologic Model System

Hydrologic Model System (HMS), a physically-based distributed-parameter model system, was developed to simulate the hydrologic response of large river basins (Yu and Schwartz, 1998; Yu et al., 1998). It comprises pre-processcing, post-preocesscing, and four modules, which are Soil Hydrologic Model (SHM), Terrestrial Hydrologic Model (THM), Ground-water Hydrologic Model (GHM), and Channel Ground-water Interaction (CGI). HMS is designed to model the hydrologic

processces, such as vertical soil moisture flow, evapotranspiration (ET), infiltration, overland flow, channel flow, and ground-water flow within a river basin.

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Soil Hydrologic Model (SHM)

A theoretical partial differential equation for unsaturated flow (referred to as the diffusion equation or Richards equation) was derived to describe the vertical moisture flow by combining Darcy's Law with the continuity equation (Swartzendruber, 1969). The Richard's equation is solved using the Crank-Nicholson numerical scheme (Press at al., 1986; Capehart and Carlson, 1994) and a finite difference scheme of forward in time and backward in space.

SHM receives information from HMS about the available water depth on each grid node at each time step during the simulation. The available water depth is the summation of precipitation and water routed from neighboring grid cells through a kinematic wave approach in THM. The infiltration and evaporation are treated as either sources or sinks in Richards equation rather than incorporated into the upper boundary condition of soil profile. The amount of infiltration and evaporation is distributed over top layers while ET is extracted from the entire root zone according to a weighted function which depends on vegetation type and height. The procedure for the calculation of evaporation on a bare soil and ET on the vegetation canopy follows the Penman-Monteith method (Monteith, 1981). The Green-Ampt technique of infiltration calculation was implemented in SHM (Chow et al., 1988). After computations in SHM, it passes calculated ET back for the water budget calculation for next time step. The modified SHM offers us the potential to simultaneously run multi-storm simulation with mesoscale model (MM). It could provide the spatial distributed soil moisture content to MM in each time step during the simulation. For more detailed information about the processes in SHM, reader should refer to Capehart and Calson (1994) and other sources.

Terrestrial Hydrologic Model (THM)

THM was developed for the simulation of overland and channel flows (Johnson and Miller, 1997). Kinematic wave formulation along with flow-direction algorithm was implemented in THM to account for overland flow delay and storage on each grid cell. The advantage of kinematic wave approach is that it is less complex and it will not be limited in the model predictive ability regarding to the resolution and accuracy of the data sets. Muskingum-Cunge channel routing procedure is used to route the flow through the channel network from one grid cell to another, eventually to the outlet of simulated river basin. The procedure has capability to accommodate spatial parameters to each stream grid cell. The following form of kinematic wave method is used to describe the overland flow (Bedient and Huber, 1988).

In each grid cell, the block is discritized into many segments and the global time step is discritized into many smaller time steps. The finite-difference explicit solution of kinematic wave approximation of overland flow on each grid cell can be formulated as follow.

This formulation is used to derive overland hydrographs on each grid cell, which are added to produce collector hydrographs and, eventually, are routed to the channel or stream hydrographs. The relationship between the storage and discharge due to the routing is shown as follow.

Muskingum-Cunge method (Cunge, 1969; Bedient and Huber, 1988) was implemented in THM for the channel flow routing. The extended finite-difference form of this method can be written as follow.

The outflow hydrograph at the down-stream end of a given grid cell is calculated by the above equation (see Cunge, 1969 and Bedient and Huber, 1988 for detailed calculation). This procedure is applied on each stream grid cell to route the channel flow, through the channel networks derived from Digital Elevation Model (DEM), to the outlet of a river basin.

Ground-water Hydrologic Model (GHM)

The ground-water domain in a watershed is described in above figure. The continuous domain is discretized into a set of small rectangular cells with dimensions z, x, and y. z is the thickness of aquifer (vertical), and x and y are cell dimensions in the x and y coordinate directions. Although the flux can be input to the ground-water domain in GHM, non-flow boundary of the domain is assumed to be corresponded with watershed boundary derived from available DEM or digitized from maps. Non-flow boundary is also assumed at a certain depth in the vertical direction. This distributed depth in each cell is handled in HMS with a similar way as DEMs. This vertical boundary should be the boundary between the local ground-water flow system of the simulated watershed and regional ground-water flow system.

The finite-difference numerical method is used to provide a solution to above equation. After the discritization of ground-water domain, sets of tridiagonal matrices can be assembled for x and y direction or for row and column. The iterative alternating direction implicit method (Prickett and Lonnquist, 1971; Yu and Schwartz, 1995) is applied to solve the matrix system. At any given time step, the method reduces a large set of simultaneous equations down to a number of small sets. The node equations of an individual column of the domain are solved while all adjacent related terms are kept constant. This means that the set of column equation is implicit in column direction and explicit in row direction. Two tridiagonal matrix solvers, forward solution and backsubstitution (FB), and reduction and backsubstitution (RB) (Yu and Schwartz, 1995; Yu, 1997), were implemented in GHM. The traditional FB method, is intrinsically data dependent, in the equations at a given grid node depend on values from adjacent grid nodes. This feature effectively prohibits vectorizing and parallelizing the method for solution on a vector and parallel processor. An alternative method of solution, that of reduction and backsubstitution (RB), has no data dependence and was implemented in Fortran for vector and parallel processors to solve a tridiagonal matrix system in GHM. The vectorized code has an overall execution rate of 110 MFLOPs on a Cray Y-MP that is six to 16 times faster than the scalar code. Implementing the code in vector-parallel mode using eight undedicated processors on a Cray Y-MP results in an overall additional speedup of 2.8 times in wall clock time for two-dimensional flow problem and 2.2 times for three-dimensional flow problem (Yu, 1997). In comparison with FB code, RB code requires 26% less of CPU time and 66% less of wall clock time on same flow problem. The implementation of this module is described in detail by Yu and Schwartz (1995), and Yu (1997).

Channel Ground-Water Interaction (CGI)

CGI in HMS is designed to simulate the interaction between the stream and groundwater. The leakage between them, which is treated as either source or sink in GHM, is calculated using Darcy's Law. The approach of CGI is similar to the river package in MODFLOW (McDonald and Harbaugh, 1988). A layer of low permeable material at streambed is assumed to separate water at channel from the ground-water system at each stream cell. Conceptual representation of channel ground-water interaction is shown in above figure. Assuming that all parameters within a cell are constant, the leakage at a given stream cell is sumulated.

The calculated leakage is a function of the hydraulic difference between the ground-water hydraulic head (from GHM) and river stage (from THM) at a given stream cell. When h(i,j) is smaller than B(i,j) and d(i,j) is greater than zero, leakage from stream to the ground water becomes constant (Cd * thickness of the low permeable layer). When h(i,j) is smaller than B(i,j) and d(i,j) is zero, there is no channel ground-water interaction. Often this idealized geometry attributed to the stream differs from the reality. Thus, in practice, Cd usually becomes a calibration parameter.

Publications related to HMS

1.       Yu, Z., Lakhtakia, M., Yarnal, B., White,R., Miller, D., Frakes, B., Barron, E., Duffy, C., and Schwartz, F. 1999.Simulating the river-basin response to atmospheric forcing by linking amesoscale meteorological model and hydrologic model system. Journal ofHydrology, 218(1-2), 72-91. (SCI, IF: 6.708)

2.       Yu, Z., Liu, D., Lü, H., Fu, X., Xiang,L., and Zhu, Y. 2012. A multi-layer soil moisture data assimilation usingsupport vector machines and ensemble particle filter. Journal of Hydrology,475, 53-64. (SCI, IF: 6.708)

3.       Yu, Z., Pollard, D., and Cheng, L. 2006.On continental scale hydrologic simulations with a coupled hydrologic model.Journal of Hydrology, 331(1-2), 110-124. (SCI, IF: 6.708)

4.     Yu, Z., Carlson, T., Barron, E., andSchwartz, F. 2001. On evaluating the spatial-temporal variation of soilmoisture in the Susquehanna River Basin. Water Resources Research, 37(5),1313-1326. (SCI, IF: 6.16)

5.       Yu, Z., White, R., Guo, Y., Voortman, J.,Kolb, P., Miller, D., and Miller, A. 2001. Stormflow simulation using ageographical information system with a distributed approach. Journal of theAmerican Water Resources Association, 37(4), 957-971. (SCI)

6.       Yu, Z., Barron, E., and Schwartz, F. 2000.Retrospective simulation of a storm event: a first step in coupledclimate/hydrologic modeling. Geophysical Research Letters, 27(16), 2561-2565.(SCI, IF: 5.58)

7.       Yu,Z. 2000.Assessing the response of subgrid hydrologic processes to atmospheric forcingwith a hydrologic model system. Global and Planetary Change, 25(1-2), 1-17.(SCI, IF: 4.956)

8.       Yu, Z., Gburek, W., and Schwartz, F. 2000.Evaluating the spatial distribution of water balance in a small watershed,Pennsylvania. Hydrological Processes, 14(5), 941-956. (SCI, IF: 3.784)

9.       Yu, Z., Lakhtakia, M., and Barron, E.1999. Modeling the river basin response to single storm events simulated by amesoscale meteorological model at various resolutions. Journal of GeophysicalResearch, 104(D16), 19675-19690. (SCI, IF: 5.22)

10.     Yu,Z., andSchwartz, F. 1999. Automated calibration applied to constrained ground waterflow modeling. Hydrological Processes, 13, 191-209. (SCI, IF: 3.784)

11.     Yu,Z., andSchwartz, F. 1998. Application of integrated basin-scale hydrologic model tosimulate surface-water and ground-water interactions in Big Darby CreekWatershed, Ohio. Journal of American Water Resources Association, 34(2),409-425. (SCI)

12.     Yu,Z. 1997.Application of vector and parallel supercomputers to ground-water modeling.Computers and Geosciences, 23(9), 917-927. (SCI, IF: 5.168)

13.     Dong, N., Wei, J., Yang, M., Yan,D., Yang, C., Gao, H., Arnault, J., Laux, P., Zhang, X., Liu, Y., Niu, J.,Wang, H., Wang, H., Kunstmann, Harald., Yu, Z.*, 2022. Model estimatesof China's terrestrial water storage variation due to reservoir operation.Water Resources Research, 58(6), e2021WR031787. (SCI, IF:6.16)

14.     Jiang, H., Simonovic, P., Yu, Z.*,and Wang, W. 2020. A system dynamics simulation approach for environmentallyfriendly operation of a reservoir system. Journal of Hydrology, 587, 124971.(SCI, IF: 6.708)

15.     Dong, N., Yu, Z.*, Yang, C., Yang, M., and Wang, W. 2019. Hydrological impactof a reservoir network in the upper Gan River Basin, China, Hydrological Processes,33(12), 1709-1723. (SCI, IF: 3.784)

16.     Jiang, H., Yu, Z.*, and Mo, C. 2017. Ensemble method for reservoir floodseason segmentation. Journal of Water Resources Planning and Management,143(3), 04016079. (SCI, IF: 2.521)

17.     Jiang, H., Simonovic, P., Yu, Z.*, and Wang, W. 2020. Systemdynamics simulation model for flood management of the three gorges reservoir.Journal of Water Resources Planning and Management, 146(7), 05020009. (SCI)

18.     Huang, D., Yu, Z.*, Li, Y., Han, D., Zhao, L., and Chu, Q. 2017. Calculationmethod and application of loss of life caused by dam break in China. NaturalHazards, 85(1), 39-57. (SCI, IF: 3.158)

19.     Dong, N., Yang, M., Yu, Z., Wei, J., Yang, C., Yang, Q.,Liu, X., Lei, X., Wang, H., and Kunstmann, H. 2020. Water resources management ina reservoir-regulated basin: Implications of reservoir network layout onstreamflow and hydrologic alteration. Journal of Hydrology, 586, 124903. (SCI,IF: 6.708)

20.     Wagner, S., Fersch, B., Yuan, F., Yu, Z., and Kunstmann, H. 2016. Fullycoupled atmospheric-hydrological modeling at regional and long-term scales:Development, application, and analysis of WRF-HMS. Water Resources Research,52(4), 3187-3211. (SCI, IF: 6.16)

21.     Liu, X., Sun, H., Zhang, Y., Zheng,C., and Yu, Z. 2019. Simulatingmulti-dimensional anomalous diffusion in nonstationary media usingvariable-order vector fractional-derivative models with Kansa solver. Advancesin Water Resources, 133, 103423. (SCI, IF: 5.361)

22.     Liu, D., Wang, G., Mei, R., Yu, Z., and Gu, H. 2014. Diagnosing thestrength of land-atmosphere coupling at subseasonal to seasonal time scales inAsia. Journal of Hydrometeorology, 15(1), 320-339. (SCI, IF: 4.871)

23.     Yang, T., Wang, X., Zhao, C., Chen,X., Yu, Z., Shao, Q., Xu, C., Xia,J., and Wang, W. 2011. Changes of climate extremes in a typical arid zone: Observationsand multimodel ensemble projections. Journal of Geophysical Research, 116,D19106. (SCI, IF: 5.22)

24.     Liu, D., Wang, G., Mei, R., Yu, Z., and Gu, H. 2013. Diagnosing thestrength of land-atmosphere coupling at the sub-seasonal to seasonal time scalesin Asia. Journal of Hydrometeorology, 15(1), 320-339. (SCI, IF: 4.871)

25.     Zhang, Y., Papelis, C., Sun, P., andYu, Z. 2013. Evaluation and linkingof effective parameters in particle-based models and continuum models formixing-limited bimolecular reactions. Water Resources Research, 49(8),4845-4865. (SCI, IF: 6.16)

26.     Yao, C., Zhang, K., Yu, Z., Li, Z., and Li, Q. 2014. Improvingthe flood prediction capability of the Xinanjiang model in ungauged nestedcatchments by coupling it with the geomorphologic instantaneous unithydrograph. Journal of Hydrology, 517, 1035-1048. (SCI, IF: 6.708)

27.     Yarnal, B., Lakhtakia, M., Yu, Z., White, R., Pollard, D., Miller,D., and Lapenta, W. 2000. A linked meteorological and hydrological modelsystem: the Susquehanna River Basin Experiment (SRBEX). Global and PlanetaryChange, 25(1-2), 149-161. (SCI, IF: 4.956)

28.     Yang C., Lin, Z., Yu, Z., Hao, Z., and Liu, S. 2010.Analysis and simulation of human activity impact on streamflow in the HuaiheRiver Basin with a large-scale hydrologic model. Journal of Hydrometeorology,11(3), 810-821. (SCI, IF: 4.871)

29.     Yang, T., Shi, P., Yu, Z., Li, Z., Wang, X., and Zhou, X.2015. Probabilistic modeling and uncertainty estimation of urban waterconsumption under an incompletely informational circumstance. StochasticEnvironmental Research and Risk Assessment, 30(2), 725-736. (SCI, IF: 3.821)

30.     Hou, T., Zhu, Y., Lv, H., Sudicky,E., Yu, Z., and Ouyang, F. 2015.Parameter sensitivity analysis and optimization of Noah land surface model withfield measurements from Huaihe River Basin, China. Stochastic EnvironmentalResearch and Risk Assessment, 29(5), 1383-1401. (SCI, IF: 3.821)

31.     Yao, C., Li, Z., Yu, Z., and Zhang, K. 2012. A prioriparameter estimates for a distributed, grid-based Xinanjiang model using geographicallybased information. Journal of Hydrology, 468-469, 47-62. (SCI, IF: 6.708)

32.     Xu, B., Ma, Y., Zhong, P.A., Yu, Z., Zhang, J., and Zhu, F. 2018.Bargaining model of synergistic revenue allocation for the joint operations ofa multi-stakeholder cascade reservoir system. Water Resources Management,32(14), 4625-4642. (SCI, IF: 4.426)

33.     Chen, X., Yang, T., Wang, X., Xu,C., and Yu, Z. 2013. Uncertaintyintercomparison of different hydrological models in simulating extreme flows.Water Resources Management, 27(5), 1393-1409. (SCI, IF: 4.426)

34.     Jia, B., Simonovic, S., Zhong, P.,and Yu, Z. 2016. A multi-objectivebest compromise decision model for real-time flood mitigation operations ofmulti-reservoir system. Water Resources Management, 30(10), 3363-3387. (SCI,IF: 4.426)

35.     Wang, X., Cui, Y., Pan, Y., Li, X., Yu, Z., and Young, M. 2008. Effects ofrainfall characteristics on infiltration and redistribution patterns inrevegetation-stabilized desert ecosystems. Journal of Hydrology, 358(1-2),134-143. (SCI, IF: 6.708)

36.     Pan, F., Ye, M., Zhu, J., Wu, Y.,Hu, X., and Yu, Z. 2009.Incorporating layer- and local-scale heterogeneities in numerical simulation ofunsaturated flow and tracer transport. Journal of Contaminant Hydrology,103(3-4), 194-205. (SCI, IF: 4.184)

37.     Zhu, Y., Ren, L., Skaggs, T., Lü,H., Yu, Z., Wu, Y., and Fang, X.2009. Simulation of P. euphratica root uptake from groundwater in an aridwoodland of the Ejina Basin, China. Hydrological Processes, 23(17), 2460-2469.(SCI, IF: 3.784)

38.     Xu, B., Zhong, P, Huang, Q., Wang,J., Yu, Z., and Zhang, J. 2017.Optimal hedging rules for water supply reservoir operations under forecastuncertainty and conditional value-at-risk criterion. Water, 9(8), 568. (SCI,IF: 3.530)

39.     Chen, X., Chen, L., Zhao, J., and Yu, Z. 2015. Modeling the hydrodynamicinteractions between the main channel and the floodplain at McCarran ranch inthe lower Truckee River, Nevada. Natural Hazards and Earth System Sciences,15(9), 2161-2172. (SCI, IF: 4.580)

40.     Huang, Y., Yu, Z., Zhou, Z., Wang, J., and Guo, Q. 2014. Modeling flow andsolute transport in fractured porous media at Jinping I-hydropower station,China. Journal of Hydrologic Engineering, 19(9), 05014007. (SCI)

41.     Pan, F., Ye, M., Zhu, J., Wu, Y.,Hu, X., and Yu, Z. 2009. Numericalevaluation of uncertainty in water retention parameters and effect onpredictive uncertainty. Vadose Zone Journal, 8(1), 158-166. (SCI, IF: 2.945)

42.     Lakhtakia, M., Yarnal, B., Johnson,D., White, R., Miller, D., and Yu, Z.1998. A simulation of river-basin response to mesoscale meteorological forcing:the Susquehanna River Basin Experiment (SRBEX). Journal of American WaterResources Association, 34(4), 921-937. (SCI)

43.     Ju, Q., Yu, Z., Hao, Z., Ou, G., Zhao, J., and Liu, D. 2009. Division-basedrainfall-runoff simulations with BP neural networks and Xinanjiang model.Neurocomputing, 72(13-15), 2873-2883 (SCI, IF: 5.779)

44.     Chen, L., Xiang, L., Young, M.H.,Yin, J., Yu, Z., and van Genuchten,M. 2015. Optimal parameters for the Green-Ampt infiltration model underrainfall conditions. Journal of Hydrology and Hydromechanics, 63(2), 93-101.(SCI)

45.     Wu, X., Xiang, X., Wang, C., Chen,X., Xu, C., and Yu, Z. 2012. Coupledhydraulic and Kalman filter model for real time correction of flood forefast inthe Three Gorges interzone of Yangtze River, China. Journal of HydrologicEngineering, 18(11), 1416-1425. (SCI)

46.     Zhang, X., Bao, W., Qu, S., and Yu, Z. 2012. One-dimensionalhydrodynamic model accounting for tidal effect. Hydrology Research, 43(1-2),113-122. (SCI)

47.     Yuan, F., Ren, L., Yu, Z., and Xu, J. 2008. Computation ofpotential evapotranspiration using a two-source method for the Xin'anjianghydrological model. Journal of Hydrologic Engineering, 13(5), 305-316. (SCI)

48.     Ren, L., Zhang, W., Li, C., Yuan,F., Yu, Z., Wang, J., and Xu, J. 2008.Comparison of runoff parameterization schemes with spatial heterogeneity acrossdifferent temporal scales in semihumid and semiarid Regions. Journal ofHydrologic Engineering, 13(5), 400-409. (SCI)

49.     Yao, C., Li, Z., Bao, H., and Yu, Z. 2009. Application of a developedgrid-Xinanjiang model to Chinese watersheds for flood forecasting purpose.Journal of Hydrologic Engineering, 14 (9), 923-934. (SCI)