## TOPMODEL (Topography based Hydrological Model)

TOPMODEL is a physically-based, semi-distributed, variable-source area rainfall-runoff model, and is based on the Topographic Wetness Index (TWI).

physically-basedsemi-distributedvariable-sourcerainfall-runoffTopographic Wetness Index
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#### Authorship

Affiliation:
Centre for Research on Environmental Systems, Lancaster University, Lancaster, U.K.
Affiliation:
Centre for Research on Environmental Systems, Lancaster University, Lancaster, U.K.
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Application-focused categoriesNatural-perspectiveLand regions

#### Model Description

English {{currentDetailLanguage}} English

Quoted from: USGS. "TOPMODEL Simulations of Streamflow and Depth to Water Table in Fishing Brook Watershed, New York, 2007–09", National Water-Quality Assessment Program. https://pubs.usgs.gov/sir/2011/5190/pdf/sir2011-5190_nystrom_508.pdf

TOPMODEL, first proposed by Beven and Kirkby (1979), is a physically based, semi-distributed, variable-source area rainfall-runoff model, and is based on the TWI proposed by Kirkby (1975). Three main assumptions underlie most formulations of TOPMODEL (Beven and others, 1995): 1. The hydraulic gradient of the water table can be approximated by the land-surface slope. 2. Dynamic conditions can be adequately represented by a steady-state approximation. 3. The saturated hydraulic conductivity decreases exponentially with depth. TOPMODEL is expected to be best applied in watersheds where these assumptions hold, for example, humid watersheds with shallow soils, which are likely to have topographic controls on water-table depth (Beven and others, 1995). TOPMODEL groups areas of hydrological similarity using a topographically based wetness index and simulates runoff generation from several sources based on calculated watershed storage and storage deficits.

Topographic Wetness Index and Saturation Deficit

The TWI represents the local subsurface hydraulic conditions by combining the local hydraulic gradient (approximated by the local surface slope) and the volume of water draining through a point (proportionate to the upslope contributing area). The TWI is defined as

where

TWI is the topographic wetness index, in ln(meters);

ln is the natural logarithm;

α is the upslope contributing area per unit contour length, in meters, and

tan β is the local slope.

and is typically calculated on a spatially distributed basis using DEMs. High values of the TWI indicate locations that have large contributing areas and low slopes and that are likely to be saturated; areas with high TWI values often are found along streams, in areas of groundwater discharge, and wetlands (fig. 3) (Wolock and Price, 1994). Low values of TWI indicate areas unlikely to be saturated, with small contributing areas and high slopes; areas with low TWI values typically are found at the top of hillslopes and in areas of groundwater recharge. In many versions of TOPMODEL (including the version used in this investigation), the TWI is used to group hydrologically similar areas in the watershed; calculations then are performed in a semi-distributed manner on the groups rather than on a fully distributed basis. In TOPMODEL, the vertical profile of hydraulic conductivity is assumed to follow an exponential decay of the form:

where

Kz is the hydraulic conductivity at depth z, in millimeters per hour;

K0 is the hydraulic conductivity at the surface, in millimeters per hour;

m is a scaling parameter, in millimeters;

ndrain is the readily drained soil porosity; and,

z is the depth from the surface, in millimeters.

A steady-state approximation of conservation of mass (continuity) and Darcy’s law is applied using the TWI and the exponential conductivity profile to calculate subsurface flow and storage. TOPMODEL equations generally are defined in terms of the saturation deficit, a measure related to depth to the saturated zone; the saturation deficit is equal to the depth to water table multiplied by the readily drained soil porosity. The saturation deficit at a specific location is related to, and can be calculated from, the watershed-average saturation deficit:

where

Sx is the local saturation deficit, in millimeters;

S is the watershed-average saturation deficit, in millimeters;

m is a scaling parameter, in millimeters;

Λ is the watershed average topographic wetness index, in ln(meters); and

TWIx is the local topographic wetness index, in ln(meters).

TOPMODEL Streamflow-Generation Concepts

The main forcing mechanism for streamflow generation in TOPMODEL is precipitation, and an accurate precipitation record is required as input to TOPMODEL for accurate runoff prediction (Beven, 2001). TOPMODEL uses variable-source area runoff-generation mechanisms to model streamflow, including base flow, return flow, runoff generated from precipitation on saturated areas, and direct precipitation on open water. TOPMODEL uses two main conceptual subsurface stores of water: an unsaturated zone and a saturated zone; runoff is generated only from the saturated zone. The location of the interface between the two zones corresponds to the saturation deficit and controls the types and amounts of flow generated by the model.

Potential evapotranspiration is calculated using the Hamon method (Hamon, 1961). Precipitation that falls is first used to satisfy potential evapotranspiration, and then infiltrates into the unsaturated zone and may drain to the saturated zone; a macropore-flow term allows a percentage of precipitation to infiltrate directly to the saturated zone. Evapotranspiration, when not satisfied from precipitation, is taken from the root zone at a rate proportional to the root-zone storage (Beven and others, 1995). Precipitation that falls on open water areas (including lakes and streams) immediately becomes streamflow. To account for attenuation in lakes, an exponential decay function is applied to the portion of flow in the watershed that drains through lakes.

Water from the saturated zone drains to streams as base flow based on the steady-state application of continuity and Darcy’s law. The saturation deficit is calculated for each TWI value; when the saturation deficit is less than zero for a given TWI, the saturated zone reaches the land surface, and the portion of flow in the saturated zone equivalently “above” the land surface becomes return flow. If precipitation falls on areas with a saturation deficit equal to or less than zero, the precipitation becomes saturation overland flow. Runoff generated by infiltration excess occurs when the precipitation intensity exceeds the infiltration capacity.

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#### How to Cite

Keith Beven, Andrew Binley (2019). TOPMODEL (Topography based Hydrological Model), Model Item, OpenGMS, https://geomodeling.njnu.edu.cn/modelItem/5ee7cd6a-c71d-45a8-b7d6-060c07978be9

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#### Authorship

Affiliation:
Centre for Research on Environmental Systems, Lancaster University, Lancaster, U.K.
Affiliation:
Centre for Research on Environmental Systems, Lancaster University, Lancaster, U.K.
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#### History

Last modifier :
zhangshuo
Last modify time :
2020-12-30
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