Hydrological transport model

Last updated
River in Madagascar relatively free of sediment load Anjajavyforestrazorback.jpg
River in Madagascar relatively free of sediment load

An hydrological transport model is a mathematical model used to simulate the flow of rivers, streams, groundwater movement or drainage front displacement, and calculate water quality parameters. These models generally came into use in the 1960s and 1970s when demand for numerical forecasting of water quality and drainage was driven by environmental legislation, and at a similar time widespread access to significant computer power became available. Much of the original model development took place in the United States and United Kingdom, but today these models are refined and used worldwide.


There are dozens of different transport models that can be generally grouped by pollutants addressed, complexity of pollutant sources, whether the model is steady state or dynamic, and time period modeled. Another important designation is whether the model is distributed (i.e. capable of predicting multiple points within a river) or lumped. In a basic model, for example, only one pollutant might be addressed from a simple point discharge into the receiving waters. In the most complex of models, various line source inputs from surface runoff might be added to multiple point sources, treating a variety of chemicals plus sediment in a dynamic environment including vertical river stratification and interactions of pollutants with in-stream biota. In addition watershed groundwater may also be included. The model is termed "physically based" if its parameters can be measured in the field.

Often models have separate modules to address individual steps in the simulation process. The most common module is a subroutine for calculation of surface runoff, allowing variation in land use type, topography, soil type, vegetative cover, precipitation and land management practice (such as the application rate of a fertilizer). The concept of hydrological modeling can be extended to other environments such as the oceans, but most commonly (and in this article) the subject of a river watershed is generally implied.


In 1850, T. J. Mulvany was probably the first investigator to use mathematical modeling in a stream hydrology context, although there was no chemistry involved. [1] By 1892 M.E. Imbeau had conceived an event model to relate runoff to peak rainfall, again still with no chemistry. [2] Robert E. Horton’s seminal work [3] on surface runoff along with his coupling of quantitative treatment of erosion [4] laid the groundwork for modern chemical transport hydrology.


Physically based models

Physically based models (sometimes known as deterministic, comprehensive or process-based models) try to represent the physical processes observed in the real world. Typically, such models contain representations of surface runoff, subsurface flow, evapotranspiration, and channel flow, but they can be far more complicated. "Large scale simulation experiments were begun by the U.S. Army Corps of Engineers in 1953 for reservoir management on the main stem of the Missouri River". This, [5] and other early work that dealt with the River Nile [6] [7] and the Columbia River [8] are discussed, in a wider context, in a book published by the Harvard Water Resources Seminar, that contains the sentence just quoted. [9] Another early model that integrated many submodels for basin chemical hydrology was the Stanford Watershed Model (SWM). [10] The SWMM (Storm Water Management Model), the HSPF (Hydrological Simulation Program – FORTRAN) and other modern American derivatives are successors to this early work.

In Europe a favoured comprehensive model is the Système Hydrologique Européen (SHE), [11] [12] which has been succeeded by MIKE SHE and SHETRAN. MIKE SHE is a watershed-scale physically based, spatially distributed model for water flow and sediment transport. Flow and transport processes are represented by either finite difference representations of partial differential equations or by derived empirical equations. The following principal submodels are involved:

This model can analyze effects of land use and climate changes upon in-stream water quality, with consideration of groundwater interactions.

Worldwide a number of basin models have been developed, among them RORB (Australia), Xinanjiang (China), Tank model (Japan), ARNO (Italy), TOPMODEL (Europe), UBC (Canada) and HBV (Scandinavia), MOHID Land (Portugal). However, not all of these models have a chemistry component. Generally speaking, SWM, SHE and TOPMODEL have the most comprehensive stream chemistry treatment and have evolved to accommodate the latest data sources including remote sensing and geographic information system data.

In the United States, the Corps of Engineers, Engineer Research and Development Center in conjunction with a researchers at a number of universities have developed the Gridded Surface/Subsurface Hydrologic Analysis GSSHA model. [13] [14] [15] GSSHA is widely used in the U.S. for research and analysis by U.S. Army Corps of Engineers districts and larger consulting companies to compute flow, water levels, distributed erosion, and sediment delivery in complex engineering designs. A distributed nutrient and contaminant fate and transport component is undergoing testing. GSSHA input/output processing and interface with GIS is facilitated by the Watershed Modeling System (WMS). [16]

Another model used in the United States and worldwide is Vflo, a physics-based distributed hydrologic model developed by Vieux & Associates, Inc. [17] Vflo employs radar rainfall and GIS data to compute spatially distributed overland flow and channel flow. Evapotranspiration, inundation, infiltration, and snowmelt modeling capabilities are included. Applications include civil infrastructure operations and maintenance, stormwater prediction and emergency management, soil moisture monitoring, land use planning, water quality monitoring, and others.

Stochastic models

These models based on data are black box systems, using mathematical and statistical concepts to link a certain input (for instance rainfall) to the model output (for instance runoff). Commonly used techniques are regression, transfer functions, neural networks and system identification. These models are known as stochastic hydrology models. Data based models have been used within hydrology to simulate the rainfall-runoff relationship, represent the impacts of antecedent moisture and perform real-time control on systems.

Model components

Surface runoff modelling

Columbia River, which has surface runoff from agriculture and logging ColumbiarivergorgeJRH.jpg
Columbia River, which has surface runoff from agriculture and logging

A key component of a hydrological transport model is the surface runoff element, which allows assessment of sediment, fertilizer, pesticide and other chemical contaminants. Building on the work of Horton, the unit hydrograph theory was developed by Dooge in 1959. [18] It required the presence of the National Environmental Policy Act and kindred other national legislation to provide the impetus to integrate water chemistry to hydrology model protocols. In the early 1970s the U.S. Environmental Protection Agency (EPA) began sponsoring a series of water quality models in response to the Clean Water Act. An example of these efforts was developed at the Southeast Water Laboratory, [19] one of the first attempts to calibrate a surface runoff model with field data for a variety of chemical contaminants.

The attention given to surface runoff contaminant models has not matched the emphasis on pure hydrology models, in spite of their role in the generation of stream loading contaminant data. In the United States the EPA has had difficulty interpreting [20] diverse proprietary contaminant models and has to develop its own models more often than conventional resource agencies, who, focused on flood forecasting, have had more of a centroid of common basin models.

Example applications

Liden applied the HBV model to estimate the riverine transport of three different substances, nitrogen, phosphorus and suspended sediment [21] in four different countries: Sweden, Estonia, Bolivia and Zimbabwe. The relation between internal hydrological model variables and nutrient transport was assessed. A model for nitrogen sources was developed and analysed in comparison with a statistical method. A model for suspended sediment transport in tropical and semi-arid regions was developed and tested. It was shown that riverine total nitrogen could be well simulated in the Nordic climate and riverine suspended sediment load could be estimated fairly well in tropical and semi-arid climates. The HBV model for material transport generally estimated material transport loads well. The main conclusion of the study was that the HBV model can be used to predict material transport on the scale of the drainage basin during stationary conditions, but cannot be easily generalised to areas not specifically calibrated. In a different work, Castanedo et al. applied an evolutionary algorithm to automated watershed model calibration. [22]

Lake Tahoe, headwater sub-basin of the Truckee River watershed Lake-tahoe.jpg
Lake Tahoe, headwater sub-basin of the Truckee River watershed

The United States EPA developed the DSSAM Model to analyze water quality impacts from land use and wastewater management decisions in the Truckee River basin, an area which include the cities of Reno and Sparks, Nevada as well as the Lake Tahoe basin. The model [23] satisfactorily predicted nutrient, sediment and dissolved oxygen parameters in the river. It is based on a pollutant loading metric called "Total Daily Maximum Load" (TDML). The success of this model contributed to the EPA's commitment to the use of the underlying TDML protocol in EPA's national policy for management of many river systems in the United States. [24]

The DSSAM Model is constructed to allow dynamic decay of most pollutants; for example, total nitrogen and phosphorus are allowed to be consumed by benthic algae in each time step, and the algal communities are given a separate population dynamic in each river reach (e.g. based upon river temperature). Regarding stormwater runoff in Washoe County, the specific elements within a new xeriscape ordinance were analyzed for efficacy using the model. For the varied agricultural uses in the watershed, the model was run to understand the principal sources of impact, and management practices were developed to reduce in-river pollution. Use of the model has specifically been conducted to analyze survival of two endangered species found in the Truckee River and Pyramid Lake: the Cui-ui sucker fish (endangered 1967) and the Lahontan cutthroat trout (threatened 1970).

See also

Related Research Articles

Hydrology The science of the movement, distribution, and quality of water on Earth and other planets

Hydrology is the scientific study of the movement, distribution and management of water on Earth and other planets, including the water cycle, water resources and environmental watershed sustainability. A practitioner of hydrology is called a hydrologist. Hydrologists are scientists studying earth or environmental science, civil or environmental engineering and physical geography. Using various analytical methods and scientific techniques, they collect and analyze data to help solve water related problems such as environmental preservation, natural disasters, and water management.

Stormwater water that originates during precipitation events and snow/ice melt

Stormwater, also spelled storm water, is water that originates from rain, including snow and ice melt. Stormwater can soak into the soil (infiltrate), be stored on the land surface in ponds and puddles, evaporate, or runoff. Most runoff is conveyed directly to nearby streams, rivers, or other water bodies without treatment.

Water pollution Contamination of water bodies

Water pollution is the contamination of water bodies, usually as a result of human activities. Water bodies include for example lakes, rivers, oceans, aquifers and groundwater. Water pollution results when contaminants are introduced into the natural environment. For example, releasing inadequately treated wastewater into natural water bodies can lead to degradation of aquatic ecosystems. In turn, this can lead to public health problems for people living downstream. They may use the same polluted river water for drinking or bathing or irrigation. Water pollution is the leading worldwide cause of death and disease, e.g. due to water-borne diseases.

Hydrogeology The study of the distribution and movement of groundwater

Hydrogeology is the area of geology that deals with the distribution and movement of groundwater in the soil and rocks of the Earth's crust. The terms groundwater hydrology, geohydrology, and hydrogeology are often used interchangeably.

The United States Environmental Protection Agency (EPA) Storm Water Management Model is a dynamic rainfall–runoff–subsurface runoff simulation model used for single-event to long-term (continuous) simulation of the surface/subsurface hydrology quantity and quality from primarily urban/suburban areas. It can simulate the Rainfall- runoff, runoff, evaporation, infiltration and groundwater connection for roots, streets, grassed areas, rain gardens and ditches and pipes, for example. The hydrology component of SWMM operates on a collection of subcatchment areas divided into impervious and pervious areas with and without depression storage to predict runoff and pollutant loads from precipitation, evaporation and infiltration losses from each of the subcatchment. Besides, low impact development (LID) and best management practice areas on the subcatchment can be modeled to reduce the impervious and pervious runoff. The routing or hydraulics section of SWMM transports this water and possible associated water quality constituents through a system of closed pipes, open channels, storage/treatment devices, ponds, storages, pumps, orifices, weirs, outlets, outfalls and other regulators. SWMM tracks the quantity and quality of the flow generated within each subcatchment, and the flow rate, flow depth, and quality of water in each pipe and channel during a simulation period composed of multiple fixed or variable time steps. The water quality constituents such as water quality constituents can be simulated from buildup on the subcatchments through washoff to a hydraulic network with optional first order decay and linked pollutant removal, best management practice and low-impact development removal and treatment can be simulated at selected storage nodes. SWMM is one of the hydrology transport models which the EPA and other agencies have applied widely throughout North America and through consultants and universities throughout the world. The latest update notes and new features can be found on the EPA website in the download section. Recently added in November 2015 were the EPA SWMM 5.1 Hydrology Manual and in 2016 the EPA SWMM 5.1 Hydraulic Manual and EPA SWMM 5.1 Water Quality Volume (III) + Errata

Surface runoff The flow of excess stormwater, meltwater, or water from other sources over the Earths surface

Surface runoff is the flow of water that occurs when excess stormwater, meltwater, or other sources flow over the Earth's surface. This can occur when the soil is saturated to full capacity, and rain arrives more quickly than soil can absorb it. Surface runoff often occurs because impervious areas do not allow water to soak into the ground. Surface runoff is a major component of the water cycle. It is the primary agent of soil erosion by water. The land area producing runoff that drains to a common point is called a drainage basin.

Water balance

In hydrology, a water balance equation can be used to describe the flow of water in and out of a system. A system can be one of several hydrological domains, such as a column of soil or a drainage basin. Water balance can also refer to the ways in which an organism maintains water in dry or hot conditions. It is often discussed in reference to plants or arthropods, which have a variety of water retention mechanisms, including a lipid waxy coating that has limited permeability.


The DSSAM Model is a computer simulation developed for the Truckee River to analyze water quality impacts from land use and wastewater management decisions in the Truckee River Basin. This area includes the cities of Reno and Sparks, Nevada as well as the Lake Tahoe Basin. The model is historically and alternatively called the Earth Metrics Truckee River Model. Since original development in 1984-1986 under contract to the U.S. Environmental Protection Agency (EPA), the model has been refined and successive versions have been dubbed DSSAM II and DSSAM III. This hydrology transport model is based upon a pollutant loading metric called Total maximum daily load (TMDL). The success of this flagship model contributed to the Agency’s broadened commitment to the use of the underlying TMDL protocol in its national policy for management of most river systems in the United States.

HBV hydrology model

The HBV hydrology model, or Hydrologiska Byråns Vattenbalansavdelning model, is a computer simulation used to analyze river discharge and water pollution. Developed originally for use in Scandinavia, this hydrological transport model has also been applied in a large number of catchments on most continents.

In hydrology and sewage collection and disposal, antecedent moisture is the relative wetness or dryness of a watershed or sanitary sewershed. Antecedent moisture conditions change continuously and can have a very significant effect on the flow responses in these systems during wet weather. The effect is evident in most hydrologic systems including stormwater runoff and sanitary sewers with inflow and infiltration. Many modeling and analysis challenges that are created by antecedent moisture conditions are evident within combined sewers and separate sanitary sewer systems.

WMS (hydrology software) hydrology software

WMS is a watershed computer simulation and modeling software application from Aquaveo. It was originally created in the early 1990s at the Engineering Computer Graphics Laboratory at Brigham Young University.

The Hydrologic Modeling System (HEC-HMS) is designed to simulate the precipitation-runoff processes of dendritic drainage basins. It is designed to be applicable in a wide range of geographic areas for solving the widest possible range of problems. This includes large river basin water supply and flood hydrology, and small urban or natural watershed runoff. Hydrographs produced by the program are used directly or in conjunction with other software for studies of water availability, urban drainage, flow forecasting, future urbanization impact, reservoir spillway design, flood damage reduction, floodplain regulation, and systems operation.

GSSHA is a two-dimensional, physically based watershed model developed by the Engineer Research and Development Center of the United States Army Corps of Engineers. It simulates surface water and groundwater hydrology, erosion and sediment transport. The GSSHA model is used for hydraulic engineering and research, and is on the Federal Emergency Management Agency (FEMA) list of hydrologic models accepted for use in the national flood insurance program for flood hydrograph estimation. Input is best prepared by the Watershed Modeling System interface, which effectively links the model with geographic information systems (GIS).

Hydrological optimization applies mathematical optimization techniques to water-related problems. These problems may be for surface water, groundwater, or the combination. The work is interdisciplinary, and may be done by hydrologists, civil engineers, environmental engineers, and operations researchers.

The following outline is provided as an overview of and topical guide to hydrology:


Vflo is a commercially available, physics-based distributed hydrologic model generated by Vieux & Associates, Inc. Vflo uses radar rainfall data for hydrologic input to simulate distributed runoff. Vflo employs GIS maps for parameterization via a desktop interface. The model is suited for distributed hydrologic forecasting in post-analysis and in continuous operations. Vflo output is in the form of hydrographs at selected drainage network grids, as well as distributed runoff maps covering the watershed. Model applications include civil infrastructure operations and maintenance, stormwater prediction and emergency management, continuous and short-term surface water runoff, recharge estimation, soil moisture monitoring, land use planning, water quality monitoring, and water resources management.

The Water Erosion Prediction Project (WEPP) Model is a physically based erosion simulation model built on the fundamentals of hydrology, plant science, hydraulics, and erosion mechanics. The model was developed by an interagency team of scientists to replace the Universal Soil Loss Equation (USLE) and has been widely used in the United States and the world. WEPP requires four inputs, i.e., climate, topography, soil, and management (vegetation); and provides various types of outputs, including water balance, soil detachment and deposition at points along the slope, sediment delivery, and vegetation growth. The WEPP model has been improved continuously since its public delivery in 1995, and is applicable for a variety of areas.

Water quality modeling involves the prediction of water pollution using mathematical simulation techniques. A typical water quality model consists of a collection of formulations representing physical mechanisms that determine position and momentum of pollutants in a water body. Models are available for individual components of the hydrological system such as surface runoff; there also exist basinwide models addressing hydrologic transport and for ocean and estuarine applications. Often finite difference methods are used to analyse these phenomena, and, almost always, large complex computer models are required.

In hydrology, routing is a technique used to predict the changes in shape of a hydrograph as water moves through a river channel or a reservoir. In flood forecasting, hydrologists may want to know how a short burst of intense rain in an area upstream of a city will change as it reaches the city. Routing can be used to determine whether the pulse of rain reaches the city as a deluge or a trickle.

Aquaveo is a modeling software company based in Provo, Utah that develops software used to model and simulate groundwater, watershed, and surface water resources. Its main software products include SMS, GMS, WMS, and Arc Hydro Groundwater.


  1. Mulvany, T.J. (1850). "On the use of self registering rain and flow gauges". Proc. Institute Civ. Eng. 4 (2): 1–8.
  2. M.E. Imbeau, (1892) La Durance: Regime. Crues et inundations, Ann. Ponts Chausses Mem. Doc. Ser. 3(I) 5–18
  3. Horton, R.E. (1933). "The role of infiltration on the hydrologic cycle". Trans. Am. Geophys. Union. 145: 446–460. doi:10.1029/TR014i001p00446.
  4. Horton, R.E. (1945). "Erosional development of streams and their drainage basins: Hydrological approach to quantitative geomorphology". Bull. Geol. Soc. Am. 56 (3): 275–330. doi:10.1130/0016-7606(1945)56[275:edosat]2.0.co;2.
  5. Report on use of electronic computers for integrating reservoir operations, vol.1 DATAmatic Corporation technical reports, prepared in cooperation with Raytheon Manufacturing Company for the Missouri River Division, Corps of Engineers, U.S. Army, January, 1957
  6. M.P.Barnett, Comment on the Nile Valley Calculations, Journal of the Royal Statistical Society, Series B, vol. 19, 223, 1957
  7. H.A.W. Morrice and W.N. Allan, Planning for the ultimate hydraulic development of the Nile Valley, Proceedings of the Institute of Civil Engineers, 14, 101, 1959,
  8. F.S. Brown, Water Resource Development – Columbia River Basin, in Report of Meeting of Columbia Basin Inter-Agency Committee, Portland, OR, Dec. 1958
  9. D.F. Manzer and M.P. Barnett, Analysis by Simulation: Programming techniques for a High-Speed Digital Computer, in Arthur Maas et al, Design of Water Resource Systems, pp. 324–390, Harvard University Press, Cambridge, MA, 1962.
  10. N.H. Crawford and R.K. Linsley. Digital simulation in hydrology: Stanford Watershed Model IV, Technical Report No.39 Stanford University, Palo Alto, Ca. (1966)
  11. Abbott, P.E.O'Connell; Bathurst, J.C.; Cunge, J.A.; Rasmussen, J. (1986). "An Introduction to the European System: Systeme Hydrologique Europeen (SHE)". Journal of Hydrology . 87 (1–2): 61–77. doi:10.1016/0022-1694(86)90115-0.
  12. Vijay P. Singh,, Computer Models of Watershed Hydrology, Water Resource Publications, pgs. 563-594 (1995)
  13. Downer, C.W., and F.L. Ogden, 2006, Gridded Surface Subsurface Hydrologic Analysis (GSSHA) User's Manual, Version 1.43 for Watershed Modeling System 6.1, System Wide Water Resources Program, Coastal and Hydraulics Laboratory, U.S. Army Corps of Engineers, Engineer Research and Development Center, ERDC/CHL SR-06-1, 207 pp.
  14. Downer, C.W.; Ogden, F.L. (2004). "GSSHA: A model for simulating diverse streamflow generating processes". Journal of Hydraulic Engineering. 9 (3): 161–174. doi:10.1061/(ASCE)1084-0699(2004)9:3(161).
  15. Downer, C.W., F.L. Ogden, J. M. Niedzialek, and S. Liu, 2006, Gridded Surface/Subsurface Hydrologic Analysis (GSSHA) Model: A Model for Simulating Diverse Streamflow Producing Processes, pp. 131–159, in Watershed Models, V.P. Singh, and D. Frevert, eds., Taylor and Francis Group, CRC Press, 637 pp.
  16. "Watershed Modeling System". Aquaveo . Retrieved 19 February 2016.
  17. Vieuxinc.com
  18. J.C.I. Dooge, Parameterization of hydrologic processes, JSC Study Conference on Land Surface Processes in Atmospheric General Circulation Models, 243–284 (1959)
  19. C.M. Hogan, Leda Patmore, Gary Latshaw, Harry Seidman et al. Computer modeling of pesticide transport in soil for five instrumented watersheds, U.S. Environmental Protection Agency Southeast Water Laboratory, Athens, Ga. by ESL Inc., Sunnyvale, California (1973)
  20. Steven Grant, I K Iskandar , Contaminant Hydrology, CRC Press (2000) ISBN   1-56670-476-6
  21. Rikard Liden, Conceptual Runoff Models for Material Transport Estimations, PhD dissertation, Lund University, Lund, Sweden (2000)
  22. Castanedo, F.; Patricio, M.A.; Molina, J.M. (2006). Evolutionary Computation Technique Applied to HSPF Model Calibration of a Spanish Watershed. IDEAL. Lecture Notes in Computer Science. 2006. pp. 216–223. CiteSeerX . doi:10.1007/11875581_26. ISBN   978-3-540-45485-4.
  23. Development of a dynamic water quality simulation model for the Truckee River, Earth Metrics Inc., Environmental Protection Agency Technology Series, Washington D.C. (1987)
  24. USEPA. 1991. Guidance for water quality-based decisions: The TMDL process, EPA 440/4-91-001. U.S. Environmental Protection Agency, Office of Water, Washington, DC.