Distributed and Physically Based Models

Distributed and physically based models represent hydrological processes spatially across a catchment using the governing equations of flow, resolving how runoff varies from place to place.

Definition

Distributed and physically based models are hydrological models that divide a catchment into spatial units and simulate processes using physically based equations (for infiltration, subsurface and overland flow, and channel routing) with spatially variable parameters and inputs.

Scope

This topic covers spatially distributed hydrological models and physically based formulations that solve the equations for surface and subsurface flow on grids or elements, including the variable-contributing-area approach. It contrasts with lumped conceptual models and connects to calibration and uncertainty challenges.

Core questions

• How do distributed models represent spatial variability of hydrological processes?
• What governing equations underlie physically based models?
• How do approaches like TOPMODEL balance physical basis and parsimony?
• What are the practical limits of physically based distributed modeling?

Key concepts

• Spatial discretization (grids, elements)
• Governing flow equations
• Topographic index (TOPMODEL)
• Variable contributing area
• Coupled surface-subsurface flow
• Parameter and data demands

Key theories

The physically based blueprint

Freeze and Harlan set out the blueprint for coupling the partial differential equations of surface and subsurface flow into a single physically based, spatially distributed model, the template for later distributed models.

TOPMODEL and topographic control

Beven and Kirkby's TOPMODEL uses a topographic index to predict the variable contributing area of saturation, achieving a physically based representation of runoff generation with relatively few parameters.

Fully distributed process models

Models such as the Systeme Hydrologique Europeen (SHE) solve the coupled flow equations on a grid for the whole catchment, exemplifying fully distributed, physically based hydrological modeling.

Clinical relevance

Distributed and physically based models are used where spatial detail matters, such as assessing land-use change, predicting where saturation and erosion occur, simulating ungauged or rapidly changing catchments, and coupling hydrology with water-quality and land-surface models, though their data and parameter demands and equifinality constrain their use.

History

Freeze and Harlan's 1969 blueprint framed physically based distributed modeling; TOPMODEL (1979) offered a parsimonious physically based approach driven by topography, while comprehensive grid-based models such as SHE in the 1980s pursued full process representation, exposing the trade-offs of data demand and parameter identifiability.

Debates

Value of complexity in distributed models

There is ongoing debate over whether fully distributed, physically based models justify their large data and parameter requirements given equifinality and the often comparable performance of simpler conceptual or topographically based models.

Key figures

• R. Allan Freeze
• Keith J. Beven
• Mike J. Kirkby

Seminal works

• freeze1969
• bevenkirkby1979
• abbott1986

Frequently asked questions

What makes a model physically based?

A physically based model represents processes using the governing physical equations (for example for infiltration and subsurface flow) with parameters that, in principle, have physical meaning, rather than relying solely on conceptual stores calibrated to data.

Are distributed models always better than lumped ones?

Not necessarily. They capture spatial variability and can address questions lumped models cannot, but they require much more data, are harder to parameterize, and often do not outperform simpler models for predicting outlet streamflow.