Model types & tools

A wide variety of catchment modelling software tools is available with a range of structure options and capabilities. A sample of relatively well-used models with some basic descriptors is given in a table below to demonstrate this diversity.

Different catchment model structures and hydrological process algorithms have arisen from differing approaches to model development, as summarised below. Structures and algorithms have been developed and tested with different purposes in mind, in different contexts in terms of the physical environments (cold vs hot, wet vs dry, flat vs steep; or tested across a big range), data availability, and computing power. Modelling software tools have then encoded various approaches, allowing users to build models of catchments by chosing from a specified set of algorithms and structural options included. Different tools include varying degrees of flexibility.

Because of the combinations of algorithm and structural options that they include, most software tools allow models to be built that don't fit cleanly into the various categories that are often used to describe catchment models in theory (e.g. 'physical' vs 'conceptual' or 'distributed' vs 'lumped'). One catchment model can easily include a combination of algorithms that reflect different approaches (e.g. physical, conceptual, and empirical algorithms for different processes) and scales of process representation (e.g. spatially distributed calculation of evapotranspiration and runoff generation with lumped calculation of groundwater). It is useful to understand the simplified categories to help think about structure options and what different modelling tools offer.

Generalised model categories

Model & algorithm development approach

Models are often classified as physical, conceptual, or empirical, which reflect general strategies for trying to describe catchment hydrological behaviour through sets of equations:

• ‘Physical’, ‘mechanistic’, or ‘process-based’ models aim to estimate water flows using physics/biology/chemistry-based understanding of contributing processes developed from field and laboratory experiments. In this approach a catchment-scale model is built from the bottom up by linking representation algorithms for many individual smaller-scale processes (e.g. algorithms describing transpiration of individual plants or how water moves in porous media) together in sequences or iterative loops. These fine-scale process descriptions are linked together to predict the behaviour of the catchment as a whole. As our understanding of individual processes becomes more detailed, so can the models. In a pure form, all the model inputs would be actual measured properties of different parts of the catchment. However, in many settings, measuring these properties in field at the scales that they are modelled is practically infeasible (e.g. obtaining a value of soil saturated hydraulic conductivity that applies to the top 30 cm of soil over many hectares). This can make the algorithms and input parameters more conceptual in practice, with appropriate input value ranges constrained by local physical property data and information, but further narrowed down through model testing and calibration.

• 'Empirical' models, in a pure form, are the opposite end of the strategy spectrum to 'physical' models. The model development starts with observed data of the final outcome, in this case the catchment outlet streamflow, which is the end result of all the internal catchment processes. A structured mathematical search is conducted for equations that best reproduce the output from the available input data (i.e. reproduce streamflow from input rainfall and ET demand). One can think of multiple regression or curve-fitting or machine learning. If the approach is very purely empirical, this mathematical search does not rely on the use of any information or physical understanding about the underlying mechanisms of all the processes that link the inputs to the outputs. However, it can be a way to find out things about these linkages. There is generally the goal of using the least input data possible to achieve acceptable results. For example, looking for the equations that produce the best re-creation of the catchment outflow using only rainfall and catchment size. Then adding temperature data and see if this results in equations with improved predictive capability or not. The forms of the optimised equations that result from this process for one catchment may differ from those found to be optimal for another catchment. There are very local empirical models and others that result from optimising across a variety of conditions, which may come with lower performance at individual sites.

• 'Conceptual' models lie somewhere in-between being purely 'mechanistic' and purely 'empirical'. Often starting from an empirical base, more physically descriptive parameters and compartmentalised representation of parts of the catchment are added to the model structure with the aim of improving prediction. This is guided by a conceptual understanding of hydrological processes in the catchment and observations of patterns in the observed streamflow data (e.g. thresholds for streamflow peak response, regression analyses, etc). Additions to the model structure are tested and kept if they are found improve the model's performance. For example, a catchment could be very simply modelled as two connected water storage units, representing the surface and subsurface. One could then test the impact of adding an additional compartment to separate the subsurface into the vadose zone and an aquifer storage, based on our conceptual understanding that these two have different behaviour. This addition may or may not improve model performance in predicting catchment streamflow. The resulting numerical model is a conceptualisation of dominant and emergent processes. Some parameters and algorithms are not directly linked to individually measured/measurable physical properties and processes in a way that has been physically or mechanistically described. This is because they were not necessarily derived in this way. They may represent amalgamations of multiple processes and properties that tend to co-occur: emergent properties of catchment systems at the scale being modelled, and the scale at which other physical parameters were available for inclusion. Mathematical links between conceptual model parameters and a measurable physical property or a combination of properties may be found post-hoc. This can also be the case for conceptual model equations and measurable catchment processes processes. 
  • NB: This section refers to 'conceptual numerical models', while other text may refer to 'conceptual models' more broadly. The latter describe catchment process understanding without translating this into a full set of algorithms. See the terminology page for clarification.

These general modelling strategy types, used individually or in combination, can lead to different ways of breaking up a catchment into modelled units, representing hydrological processes with algorithms and parameters, and strategies for determining appropriate values for input parameters. In general, more physical models have greater levels of process, spatial, vertical, and time discretisation, require more inputs to set-up, and are more computationally intensive than more conceptual models; however, this is not always the case. There are pros and cons of each type and a rich published literature comparing them. Models of all types may be able to produce similar levels of performance in predicting observed streamflow, depending on the data and information available and the calibration strategy. Depending on the goals of the modelling project, higher levels of discretisation can be required to represent certain scenario types and/or obtain the model outputs needed, as predicting catchment-outlet streamflow is not always the only goal.

In practice, the lines between these essentialised types blur and similar steps are often needed to apply them. Physical algorithms call for more physical data about the catchment as input. Conceptual algorithms use parameters which are often assigned a likely value range based on physical catchment properties and calibrated. If there is no local data with which to calibrate a conceptual model, values are selected based on calibrations in physically comparable sites. When the physical data needed for more physical mechanistic algorithms is lacking, has a mismatched scale, or is otherwise uncertain, then the data and information that is available from the site, and/or comparable sites, is used to determine the likely value ranges for these inputs and they are treated as calibration parameters within these ranges. More conceptual models may call for fewer input parameter values because their algorithms estimate flows that are calculated as multiple finer-scale processes in more physically based models. However, if good physical data exists for a catchment, this can constrain the physical model such that there are a similar number, or fewer, parameters that need calibration. Appropriate strategies will vary by specific case, and even then may be arguable. This is why most modelling software tools include some options in terms of the algorithms, scale, and/or structure so the user can decide what to do in a specific case.

Process discretisation

It is often the case that the flows and processes represented in a catchment model could be described as the result of multiple contributing processes. For example, some models will calculate evapotranspiration (ET) withdrawal from soils from an area using a single process algorithm, while others will calculate direct evaporation of soil moisture and transpiration by plants as two separate processes contributing to the total ET from soils. More physical, mechanistic approaches generally leads to greater levels of process discretisation in a model. This may or may not result in a greater number potentially uncertain inputs to the model, depending on the quality of the available data for the site. A set of somewhat uncertain physical inputs may or may not lead to more output uncertainty than fewer, but potentially more uncertain conceptual parameter inputs. It can be more work to set-up, calibrate, and determine the output uncertainty in the case of a more complex physical model, but the features of the software tools play a large role in determining this.

Discretisation and connectivity between units

Spatial discretisation into modelled units

Catchment models apply different levels of spatial discretization of the catchment area, which are often described using simplified categories, lumped, distributed, and semi-distributed:

• A fully ‘lumped’ model calculates flows and processes at the scale of the entire catchment. Algorithms and parameter values describe to the catchment as a whole and so are necessarily more conceptual. These may still be linked to physically measurable properties, although likely several of these in combination. For example, a catchment-scale model parameter that was describing soil water storage would have correspondence to measurable soil water retention properties averaged over the catchment in combination with geomorphological properties that would influence flow convergence and where saturation would develop.

• A fully 'distributed' model breaks up the catchment into grid cells and calculates inflow, storage, and outflow processes for each grid cell, with reference to the state of surrounding cells (i.e. surface water, soil moisture, groundwater levels in surrounding cells). This can allow each grid cell to have it's own set of input parameter values, although this is not necessarily the case in all distributed models.

• Between these two extremes are 'semi-distributed' models. In these models, the catchment area is generally broken up into subareas that are considered to have relatively homogenous hydrological responses in comparison to other areas, due to similar land cover, soil types, topographic properties and position, etc. These sub-areas typically referred to as hydrological response units (HRUs). Property parameters are assigned and Inflow, storage, and outflow processes are calculated for each HRU. Some models link HRUs and allow some flows between them, while others consider them separately and simply collect the outputs.

Differences can be less distinct in practice. Lumped model structures may be applied at the scale of subcatchments, such that the full catchment model contains many spatial sub-elements that can be given different inputs and parameters. This could be called 'semi-distributed'. It does still differ conceptually from an HRU-based model in that the hillslope from ridge to channel is represented as a consolidated unit rather than multiple units for which different types of connections may be applied. HRUs can be delineated that approach subcatchment scales and likely contain channels. Similarly, distributed, gridded models can have grid cell sizes that are similar to HRU sizes or subcatchment sizes used in other models.

Vertical discretisation into modelled units and/or layers within spatial units

Models also vary in their vertical discretisation of surface, soil, and rock layers. The terms ‘lumped’ and ‘distributed’ typically refer to horizontal/surface discretization, as terminology that emerged when catchment models were more predominantly surface-water focused in their process descriptions. What is called a ‘lumped’ catchment model, based on its horizontal discetisation, can have multiple vertical compartments/storages. As an inverse, model that is ‘distributed’ spatially, in the sense of breaking up the space into grid cells, could use fewer different vertical layers than a spatially lumped model. Often saying 'fully distributed' does imply that both the land surface and the subsurface are represented using regular horizontal and vertical grids, creating a 3D grid for the sub-surface in which every subsurface cube (or rectangular volume if not cubic) has individually calculated inputs, storage, and outputs, and could theoretically have its own property parameters assigned.

Models can also use different spatial discretisation across their different vertical layers. For example the vegetation canopy, land surface, and soils may be represented using HRUs (semi-distributed), while the groundwater flows may be represented as a lumped unit at the subcatchment scale (the general strategy in SWAT). In other cases, the spatial discetisation will be the same for all vertical layers included in the model, such that each vertical layer included effectively makes a sub-unit with an HRU for example.

Discretisation & modelling approach

There is a correspondence with more physically-based algorithms, more process discretisation, and higher levels of spatial and vertical discretisation, but this is not always the case. Conceptual process algorithms can be applied to grid cells for example (i.e. a distributed conceptual model). More discretisation allows the opportunity for more localised definition of property parameters, but this does not always need to be the case in practice. There can still be a reason to use a more discretised model structure even when there isn't detailed spatial data on physical properties. For example, if there is information about the spatial distribution of rainfall across a catchment, but little information with which to parameterise soil and vegetation properties, uniform parameters could be assigned to all the spatial units in the model, but units will differ in the rainfall inputs they receive. This can result in performance improvement over a more spatially lumped model depending on the case.

It should be noted that algorithms used to calculate different flows (e.g. infiltration into soil, surface runoff across a hillslope, transpiration) are often developed and tested at particular spatial-scales. The relationship they describe, between inputs, parameters, and outputs, may not take the same form at a very different spatial scale and/or the parameter value ranges typically used at one scale may not be appropriate when the equations are applied a very different scale.

Surface & subsurface flow connectivity between discretised model units

An important structural difference between models, that may be quite similar otherwise, can be the surface and subsurface connectivity between discretised model units. Distributed models have to explicitly calculate exchanges of water between neighboring grid cells to be sensical. Gridded models differ in the algorithms used for these exchanges and also whether or not they include flow soil moisture between grid cells in unsaturated conditions. Semi-distributed HRU models, and models with many lumped subcatchments, can vary more notably from case to case in the surface and subsurface flow connections that are calculated between these units. For example surface runoff calculated for an individual HRU may be routed directly to the stream channel or may be routed across a sequence of HRUs, allowing for infiltration along the flowpath. Different cases can physically justify either approach. HRUs may be at a scale that would include channelised flows when surface runoff is generated and/or the landscape flow path is generally relatively saturated when surface runoff is produced anywhere such that little flow path infiltration would occur overall. In theses case little if anything would be gained from the extra effort of routing the water across a series of HRUs. In other cases, a potential flow buffering impact of other parts of the landscape along a flow path may be critical to model explicitly. Similarly, subsurface flow connections between separately modelled units can differ and have big impacts. There may be significant regional groundwater flow that moves groundwater between subcatchments. A model that does not include this subsurface connection between subcatchments may need to be adjusted in other ways to implicitly account for this and produce reasonable output.

Temporal discretisation (calculation time-steps)

Different models use different timesteps for the calculation of flows into and out of modelled units, ranging from monthly all the way to minutes and seconds. As data collection technologies have developed, input data at increasingly small timesteps has become available (in some areas and for some data types), and daily timestep catchment models are perhaps the most common. Process algorithm equations are timestep specific to some degree: the relationship between monthly rainfall, monthly averaged soil moisture, and monthly runoff generation would be very different to the relationship between hourly rainfall, hourly averaged soil moisture, and hourly runoff generation. In general higher levels of process discretisation and spatial discretisation require smaller timesteps, while doing lumped calculations for large areas in a step can more appropriate when done for longer timesteps, daily or longer. Some processes, like groundwater flow, occur more slowly at the scale that we are interested in them, and so there isn't a great benefit to calculating them for small timesteps. Some model structures can use different timesteps for calculating different processes in a single model and some can change the timestep length when specific processes are occurring (i.e. when surface runoff is present right after a storm), a feature available in some software tools (e.g. MIKE-SHE). Some software tools produce outputs at different time-steps than are used for process calculation. For example the Ptiman models break months into four equal steps for process calculation, but output stores and flow monthly. MIKE-SHE process calculations can use a range of time-steps, but the user can set the tool to save daily results timeseries.

Examples of modelling software tools

Examples of catchment hydrological modelling tools showing a range of temporal and spatial discretisation structure options.
Note: Proprietary = permission required for use, often with a fee ; HRU = hydrologic response unit; 'catena' routing = routing of water from one unit to the next in a downslope sequence

Modelling tool	Current curator / developer / owner	Proprietary	Time step	Spatial discretisation options	Documentation references
ACRU (Agricultural Catchment Research Unit model)	University of KwaZulu Natal (UKZN) Centre for Water Resources Research (CWRR)	no	Daily	Semi-distributed: HRUs (not catena) in subcatchments	(Schulze, 1986, 1995; Schulze and Davis, 2018)
FLEX- Topo	Delft University of Technology, Water Resources (TU-Deft)	no	Daily & sub-daily	Semi-distributed: HRUs (catena or not) in subcatchments	(Savenije, 2010)
HBV (Hydrologiska Byråns Vattenbalansavdelning)	Swedish Meteorological and Hydrological Institute (SMHI)	no	Daily & sub-daily	Lumped/semi-distributed: Subcatchment (zone option for snow & soil moisture)	(Bergström, 1976, 1995)
HEC-HMS + HEC-RAS (Hydrologic Engineering Center - Hydrologic Modelling System & River Analyses System)	US Army Corps of Engineers (USACE)	no	Daily & sub-daily	Semi-distributed: HRUs (not catena) in subcatchments	(USACE-HEC, 2000, 2010, 2018)
HPSF (Hydrological Simulation Program – FORTRAN)	U.S. Environmental Protection Agency (EPA) & U.S. Geological Survey (USGS)	no	Daily & sub-daily	Lumped/semi-distributed: Subcatchment OR HRUs in subcatchments	(Bicknell et al., 1993; Johanson et al., 1980)
HYPE (Hydrological Predictions for the Environment)	Swedish Meteorological and Hydrological Institute (SMHI)	no	Daily	Semi-distributed: HRUs (not catena) in subcatchments	(Arheimer et al., 2008; Lindström et al., 2010)
MIKE-SHE + MIKE-11 (Système Hydrologique Européen)	Danish Hydrologic Institute (DHI)	yes	Daily & sub-daily	Distributed/semi-distributed: Gridded OR HRUs (catena or not) in subcatchments	(Abbott et al., 1986; DHI, 2014; Refsgaard and Storm, 1995)
Pitman : WRSM-Pitman (Water Resources System Model) & SPATSIM-Pitman (Spatial and Time Series Information Modelling)	Water Research Commission (WRC); WRSM: Bailey & Pitman Water Resources Ltd SPATSIM: Rhodes University Institute of Water Resources (IWR)	no	Monthly (daily version exists)	Lumped/semi-distributed: Subcatchments (internal subdivision options: irrigated, afforestation/invasive alien plants, wetland, impervious)	(Bailey and Pitman, 2015; Hughes, 2004, 2013; Pitman, 1973)
RHESSys (Regional Hydro-Ecological Simulation System)	University of California Santa Barbara, Bren School of Environmental Science & Management	no	Daily	Semi-distributed: HRUs (catena routing) in subcatchments (‘patches’ along ‘hillslopes’ in ‘basins’)	(Running and Coughlan, 1988; Tague and Band, 2004)
SWAT (Soil and Water Assessment Tool)	Texas A&M University & US Department of Agriculture (USDA-ARS)	no	Daily & sub-daily	Semi-distributed: HRUs (not catena) in subcatchments	(Arnold et al., 1998; Neitsch et al., 2011)
TOPMODEL	Lancaster University, Department of Environmental Science	no	Daily & sub-daily	Distributed: Gridded	(Beven and Kirkby, 1979)
VIC (Variable Infiltration Capacity model)	University of Washington, Department of Civil and Environmental Engineering	no	Daily & sub-daily	Distributed: Gridded	(Liang et al., 1994)
WEAP (Water Evaluation and Planning System)	Stockholm Environment Institute's U.S. Center	no	Month	Semi-distributed: HRUs (not catena) in subcatchments	(Sieber, 2019; Yates et al., 2005)
3Di	3Di Foundation (Delft University of Technology, Deltares, Nelen & Schuurmans consulting)	yes	Daily & sub-daily	Distributed: Gridded	(3Di Foundation 2015)