Process representation across tools

The tables below summarise information about different process representation algorithms across the set of modelling tools. They cover the inputs used to model the occurrence and rate (amount per model calculation timestep) of the given hydrological process (e.g. infiltration of water into the soil) as well as some general characteristics of the equations, particularly noting if there are thresholds involved and what these are. The tables can be used to understand what is being considered in the calculation of each process and what inputs each modelling tool needs. Not all the processes listed are represented explicitly by all the tools. This is highlighted in the tables below and an overview is also presented in the capabilities overview table. The nature of the algorithms used and their inputs are linked to the spatial and temporal scale at which the process is being represented in the given tool, described further for each one here.

In these tables thresholds refer to limits that determine when a process would start to occur or would stop occurring. For example, the field capacity soil moisture of a soil is often used as the threshold soil moisture level for percolation of water downwards (to a lower soil layer or to recharge groundwater). If soil moisture is lower than this, no percolation will be calculated in the model. There may be multiple thresholds considered when modelling a process. For example, evapotranspiration of soil moisture may be assumed to stop once the atmospheric demand in the timestep has been met or once the soil moisture has reached wilting point level, even if demand has not yet been met.

The inputs to a process algorithm can include:

• input data (e.g., rainfall, using the rainfall input for a particular modelled unit, for a given timestep),
• property parameter values that the user inputs in the model set-up (e.g., soil moisture content at saturation for a soil layer in a modelled unit)
• states or water storage levels that the model calculated internally for the timestep, so not directly input by the user (e.g., soil moisture content in a certain soil layer at a given timestep)

Different software tools may refer to equivalent inputs using different words and sometimes they require the user to input different specific property values, but end up calculating the same derived property. For example, on software tool may require porosity of soil to be input, another may require bulk density, and another may as for volumetric soil moisture at saturation, any of these, coupled with soil layer depth, can be used to calculate the maximum (or saturation) soil water storage volume. Where possible, similar terms have been used across tools in the tables below to highlight their conceptual similarities where these exist. Details about some of the contrasting terminology used in the interfaces of different tools can be found here.

Canopy interception and evaporation (vs throughfall)

Algorithm description	WRSM-Pitman	SPATSIM-Pitman	ACRU4	SWAT2012	MIKE-SHE, semi-distributed & fully distributed
Algorithm inputs (input data, model calculated states / storages, property parameters)	Rain Cover properties: max interception	Rain Cover properties: max interception	Rain PET Canopy storage (state) Cover properties: max interception (OR LAI)	Canopy interception is not explicitly modelled when using daily timestep modelling. It is implicitly considered in the ‘initial abstraction’, see infiltration & surface runoff below	Rain PET Canopy storage (state) Cover properties: LAI canopy interception coefficient
Function type	exponential & threshold	exponential & threshold	threshold		threshold
Thresholds	yes: timestep interception capacity (calculated)	yes: timestep interception capacity (calculated)	yes: timestep interception capacity (calculated)		yes: timestep interception capacity (calculated)

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Infiltration into soil moisture (vs surface runoff or surface ponding)

Note: This excludes the case of a modelling unit (HRU, grid cell, area within a subcatchment, etc.) is designated as impervious. In this case, rain inputs would become surface runoff, potentially with a portion staying behind as surface storage/ponding if the area has attenuation specified (to represent roughness and flatness).

Algorithm description	WRSM-Pitman	SPATSIM-Pitman	ACRU4	SWAT2012	MIKE-SHE, semi-distributed, more conceptual	MIKE-SHE, fully-distributed, more physical
Algorithm inputs (input data, model calculated states / storages, property parameters)	Rain Rainfall distribution factor Soil moisture (state) Soil properties: Saturation soil moisture Infiltration rate distribution (min, max)	Rain Rainfall distribution factor Soil moisture (state) Soil properties: Saturation soil moisture Infiltration rate distribution (min, max)	Throughfall (rain-interception) Soil moisture within "infiltration depth"(state) Soil properties: Saturation soil moisture "Infiltration depth" parameter Macropore by-pass (clay cracking)	Throughfall (rain-interception) Soil moisture (state) Soil properties: Saturation soil moisture Curve number (SCS-CN) Macropore by-pass	Throughfall (rain-interception) Soil moisture (state) Soil properties: Saturation soil moisture Saturated hydraulic conductivity (Ksat), Macropore by-pass	Throughfall (rain-interception) Soil moisture (state) Soil properties: Saturation soil moisture Soil moisture retention curve Saturated hydraulic conductivity (Ksat), Macropore by-pass
Function type	non-linear & threshold	non-linear & threshold	power & threshold	power & threshold	linear (rate) & threshold	non-linear & threshold
Thresholds	yes: Max infiltration rate, Saturation soil moisture* *Saturation excess becomes interflow, not surface runoff	yes: Max infiltration rate, Saturation soil moisture* *Saturation excess becomes interflow, not surface runoff	yes: Saturation soil moisture* *Fraction of saturation excess becomes "delayed flow"~interflow, not "quickflow"~surface runoff	yes: Max infiltration rate (calculated), Saturation soil moisture	yes: Max infiltration rate (uses Ksat), Saturation soil moisture	yes: Max infiltration rate (calculated), Saturation soil moisture

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Surface runoff to channel network

Note on surface runoff vs ponding and surface storage: In the Pitman models, all water not calculated to infiltrate in a timestep, which is a month, is assumed to be runoff. For models with shorter timesteps, water reaching the land surface which does not infiltrate into soil in a timestep can become surface runoff or remain as surface ponding/surface storage. In subsequent model timesteps, water still on the land surface can evaporate, infiltrate, and/or become surface runoff in the next timestep. Some models have relatively short timesteps (subdaily, daily) compared to the rate at which water would move all the way across a modelled land unit (which could be large, rough, and/or flat, slowing the flow rate). This is why some water will be 'surface storage' in one timestep and then 'surface runoff' in the next timestep. MIKE-SHE can also consider that land surfaces can be very rough, or have dips that trap water, and so some amount surface water will not be able to run off at all (detention storage). This water will both evaporate and infiltrate over time.
ACRU4 differs notably, assuming the water that does not infiltrate into soil accounts for both surface runoff and interflow runoff.

Algorithm description	WRSM-Pitman	SPATSIM-Pitman	ACRU4	SWAT2012	MIKE-SHE, semi-distributed, more conceptual	MIKE-SHE, fully-distributed, more physical
Algorithm inputs (input data, model calculated states / storages, property parameters)	Surface water present* (state) *Month timestep: all water not infiltrating becomes runoff	Surface water present* (state) *Month timestep: all water not infiltrating becomes runoff	Surface water present* (state) Lag coefficient* *Lag coefficient separates "quickflow"~surface runoff from "delayed-flow"~interflow. Quickflow portion reaches the channel on the same day generated (rain day). The rest is lagged over subsequent days	Surface water present* (state) Surface path properties: Path length Slope Roughness (Manning's n)	Surface water present* (state) Surface path properties: Detention storage Path length Slope Roughness (Manning's n)	Surface water present* (state) Surface path properties: Detention storage Path length (from gridded topography) Slope(from gridded topography) Roughness (Manning's n)
Function type	(no transformation)	(no transformation)	(no transformation)	non-linear	non-linear & threshold	non-linear & threshold
Thresholds	no* *none after infiltration has been calculated	no* *none after infiltration has been calculated	no* *none after infiltration has been calculated	no* *none after infiltration has been calculated	yes: Detention storage	yes: Detention storage

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Evapotranspiration (ET) from soil moisture (SM)

Note: More coverage of evapotranspiration related terminology and inputs across different tools can be found here

Algorithm description	WRSM-Pitman	SPATSIM-Pitman	ACRU4	SWAT2012	MIKE-SHE, semi-distributed, more conceptual	MIKE-SHE, fully-distributed, more physical
Algorithm inputs (input data, model calculated states / storages, property parameters)	S-Pan evaporation Soil moisture (state) Vegetation properties: "Crop" coefficient (vs pan) Pitman ET coefficient* Soil properties: Saturation soil moisture *determines linear decline of ET with soil moisture decline	S-Pan evaporation Soil moisture (state) Vegetation properties: "Crop" coefficient (vs pan) Pitman ET coefficient* Soil properties: Saturation soil moisture *determines linear decline of ET with soil moisture decline	A-Pan evaporation Soil moisture (state) Vegetation properties: "Crop" coefficient (vs pan) Root depth distribution Soil properties: Saturation soil moisture* Field capacity SM Wilting point SM *ET assumed to also decline if soil gets close to saturation, waterlogging, unless wetland plants	Remaining ET demand (PET - Canopy evap.) Soil moisture (state) Vegetation properties: LAI Root depth (max) Root distribution Demand redistribution coefficient Soil properties: Field capacity SM Wilting point SM	Remaining ET demand (PET - Canopy evap. - Ponded evap.) Soil moisture (state) Vegetation properties: "Crop" coefficient ET curtailment SM Root depth (max) Root distribution Soil properties: Field capacity SM Wilting point SM	Remaining ET demand (PET - Canopy evap. - Ponded evap.) Soil moisture (state) Vegetation properties: "Crop" coefficient ET vs SM curve parameter Root depth (max) Root distribution ET demand depth distribution Soil properties: Soil moisture retention curve
Function type	linear & threshold	linear & threshold	multi-part linear & threshold	non-linear & threshold	multi-part linear & threshold	non-linear & threshold
Thresholds	yes: ET demand, Wilting point SM	yes: ET demand, Wilting point SM	yes: ET demand, Wilting point SM	yes: ET demand, Wilting point SM	yes: ET demand, Wilting point SM	yes: ET demand, Wilting point SM

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Evapotranspiration (ET) from groundwater (GW)

Note: More coverage of evapotranspiration related terminology and inputs across different tools can be found here

Algorithm description	WRSM-Pitman (Sami GW)	SPATSIM-Pitman (Hughes GW)	ACRU4	SWAT2012	MIKE-SHE, semi-distributed, more conceptual	MIKE-SHE, fully-distributed, more physical
Algorithm inputs (input data, model calculated states / storages, property parameters)	riparian area only A-Pan evaporation Riparian area Aquifer storage (state) Vegetation properties: "Crop" coefficient (vs pan) Aquifer properties: Storage limit for ET	riparian area only Remaining ET demand (PET - ET from soil) Riparian area Aquifer storage (state) Vegetation properties: "Crop" coefficient (vs pan) Pitman ET coefficient* Aquifer properties: Storage limit for ET	riparian area only Indirect representation: Specified riparian zone HRU can receive a user-specified fraction of the aquifer outflow from connected upslope HRUs. This water is added to riparian HRU soil in the B-horizon, where it can be accessed for ET and can recharge GW. No ET (or capillary rise) is simulated from the GW store of the riparian HRU.	represented through capillary rise into the soil driven by ET demand PET Aquifer storage (state) Soil properties: Capillary rise rate coefficient Aquifer properties: Storage limit for capillary rise + all inputs for ET from soil	riparian area only represented through capillary rise into the soil driven by ET demand Remaining ET demand (PET - Canopy evap. - Ponded evap. - ET from soil) Aquifer storage (state) Aquifer properties: Storage limit for capillary rise + all inputs for ET from soil	capillary rise is calculated, but roots can also extend below the water table and withdraw directly Remaining ET demand (PET - Canopy evap. - Ponded evap. - ET from soil) Water table depth (state) Aquifer properties: Saturated hydraulic conductivity (Ksat) + vegetation property inputs for ET from soil
Function type	non-linear & threshold	non-linear & threshold		non-linear & threshold	non-linear & threshold	non-linear & threshold
Thresholds	yes: ET demand, Aquifer storage limit for ET	yes: ET demand, Aquifer storage limit for ET		yes: ET demand, Aquifer storage limit for capillary rise	yes: ET demand, Aquifer storage limit for capillary rise	yes: ET demand, Water table depth vs root depth

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Interflow generation & routing to channel network

Algorithm description	WRSM-Pitman	SPATSIM-Pitman	ACRU4	SWAT2012	MIKE-SHE, semi-distributed, more conceptual	MIKE-SHE, fully-distributed, more physical
Algorithm inputs (input data, model calculated states / storages, property parameters)	Interflow from soil layer & from "percolation zone" Soil moisture (state) Percolation zone storage (state) Aquifer storage (state) Soil properties: Saturation soil moisture Field capacity SM Interflow rate power coefficient Max interflow rate Interflow lag coefficient Percolation zone properties Max storage capacity Aquifer properties Max storage capacity	Interflow from soil layer Soil moisture (state) Soil properties: Saturation soil moisture Field capacity SM Interflow rate power coefficient Max interflow rate Interflow lag coefficient	Interflow amount calculated in the same step as surface runoff, not as a separate process: total surface runoff + interflow runoff is calculated in the infiltration vs runoff step, then these are separated through lagging Surface water present* (state) Lag coefficient* *Lag coefficient separates "quickflow"~surface runoff from "delayed-flow"~interflow. The lagged flow that doesn't reach the channel on the rain day, but instead reaches the channel over subsequent days can be considered interflow	Interflow from soil layer Soil moisture (state) Soil properties: Saturation soil moisture Field capacity SM Drainage slope Saturated hydraulic conductivity (Ksat)	Interflow from "interflow zone" (IZ) to calc input into IZ: Macropore flow (Throughfall * by-pass coefficient) Soil moisture (state) Soil properties: Saturation soil moisture Field capacity SM Drainage slope Saturated hydraulic conductivity (Ksat) to calc outflow from IZ: IZ storage (state) IZ properties: Storage threshold for outflow Lateral outflow rate constant	Interflow not modelled as a separate process to "saturated zone" flow. Lateral flow through a "saturated zone" material layer in the model which is not frequently saturated and/or is perched above more permanently saturated layers can be considered as interflow. Flows through different layers can be exported as separate model outputs. See groundwater outflow to channel
Function type	non-linear & threshold	non-linear & threshold		non-linear & threshold	two step: non-linear & threshold, linear reservoir & threshold
Thresholds	yes: Field capacity SM, Percolation zone max storage + Aquifer max storage	yes: Field capacity SM		yes: Field capacity SM	yes: Field capacity SM IZ storage threshold for outflow

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Aquifer recharge

Algorithm description	WRSM-Pitman (Sami GW)	SPATSIM-Pitman (Hughes GW)	ACRU4	SWAT2012	MIKE-SHE, semi-distributed, more conceptual	MIKE-SHE, fully-distributed, more physical
Algorithm inputs (input data, model calculated states / storages, property parameters)	Recharge via "percolation zone" (vadose zone) Soil moisture (state) Vadose zone storage (state) Aquifer storage (state) Soil properties: Saturation soil moisture Field capacity SM Percolation power coefficient Max percolation rate Percolation zone properties: Recharge lag coefficient Max storage capacity Aquifer properties: Max storage capacity	Recharge from soil column Soil moisture (state) Aquifer storage (state) Soil properties: Saturation soil moisture Field capacity SM Percolation power coefficient Max percolation rate Aquifer properties: Max storage capacity	Recharge from soil column* Soil moisture (state) Soil properties: Saturation soil moisture Field capacity SM Percolation rate (~Ksat) *Aquifer storage is unlimited	Recharge via vadose zone Soil moisture (state) Vadose zone storage (state) Aquifer storage (state) Soil properties: Saturation soil moisture Field capacity SM Saturated hydraulic conductivity (Ksat) Vadose zone (VZ) properties: Field capacity Saturated hydraulic conductivity (Ksat) Aquifer properties: Max storage capacity	Recharge via "interflow zone" Soil moisture (state) Interflow zone storage (state) Aquifer storage (state) Soil properties: Saturation soil moisture Field capacity SM Saturated hydraulic conductivity (Ksat) Interflow zone (IZ) properties: Storage threshold for outflow Vertical outflow rate constant Aquifer properties: Max storage capacity	Recharge from soil column Soil moisture (state) Aquifer storage (state) Soil properties: Saturation soil moisture Moisture retention curve Saturated hydraulic conductivity (Ksat) Aquifer properties: Max storage capacity Conductivity (Ksat)
Function type	two step: non-linear & threshold, non-linear	non-linear & threshold	non-linear & threshold	two step: non-linear & threshold, non-linear & threshold	two step: non-linear & threshold, linear reservoir & threshold	non-linear & threshold
Thresholds	yes: Field capacity SM, Vadose zone max storage Aquifer max storage	yes: Field capacity SM, Aquifer max storage	yes: Field capacity SM *Aquifer storage is unlimited	yes: Field capacity SM, Vadose zone field capacity Aquifer max storage	yes: Field capacity SM, Aquifer max storage	yes: Field capacity SM, Aquifer max storage

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Groundwater (GW) flow: lateral flow within the saturated zone

Note: This refers to groundwater flow between modelled land units, such as grid cells, HRUs, or subcatchments, depending on the scale that groundwater stores and flows are modelled at (see more on scales of process representation for GW here)
For coverage of groundwater outflow into a river channel, see the table below

Algorithm description	WRSM-Pitman (Sami GW)	SPATSIM-Pitman (Hughes GW)	ACRU4	SWAT2012	MIKE-SHE, semi-distributed, more conceptual	MIKE-SHE, fully-distributed, more physical
Algorithm inputs (input data, model calculated states / storages, property parameters)	GW flow between subcatchments Aquifer storage (state) Aquifer properties: Transmissivity Storage threshold for flow Regional GW slope	GW flow between subcatchments Aquifer storage (state) Aquifer properties: Transmissivity Storage threshold for flow Regional GW slope Max storage capacity	GW flow between HRU aquifers is not modelled Special case, partial exception: upland HRU aquifer outflow routed to riparian HRU soil	GW flow between subcatchment aquifers is not modelled	GW flow between aquifer storage units is not modelled	GW flow between grid cells (Darcy's Law) GW level gradient (state - compare levels in neighboring cells) Aquifer properties: Specific yield Saturated conductivity (Ksat)
Function type	non-linear & threshold	non-linear & threshold				non-linear
Thresholds	yes: Aquifer storage threshold for flow	yes: Aquifer storage threshold for flow				n/a

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Aquifer exchanges with channel: aquifer outflow to channel and channel transmission loss

Algorithm description	WRSM-Pitman (Sami GW)	SPATSIM-Pitman (Hughes GW)	ACRU4	SWAT2012	MIKE-SHE, semi-distributed, more conceptual	MIKE-SHE, fully-distributed, more physical
Algorithm inputs (input data, model calculated states / storages, property parameters)	Dynamic two-way exchange within subcatchment ("runoff module"): aquifer-to-channel or channel-to-aquifer, depending on conditions (calculated state) Additional one-way channel-to-aquifer representation within "channel module" River channel level (input) Subcatchment runoff / area (estimation of local channel store) (state) Aquifer storage/level -> GW slope (state) Aquifer properties: Max flow rate for exchange Exchange flow power coefficient Channel (module) properties: Transmission loss rate	Dynamic two-way exchange: aquifer-to-channel or channel-to-aquifer, depending on conditions (calculated state) River channel level (input) Aquifer storage/level -> GW slope (state) Aquifer properties: Specific yield Conductivity Channel properties: Length of channel Subcatchment drainage density	One-way exchange: aquifer-to-channel (Channel transmission loss not modelled) Aquifer storage (state) Aquifer properties: Outflow proportion	Limited two-way exchange: aquifer-to-channel or channel-to-"bank storage"(separate storage to the subcatchment's aquifer). Bank storage can release water to channel later. Aquifer storage (state) Channel flow (state) Aquifer properties: Storage limit for outflow Specific yield Outflow recession constant Channel properties: Shape - wetted perimeter Bed conductivity	One-way exchange per channel reach unit (can have multiple per subcatchment with different exchange directions): each reach can have either aquifer-to-channel OR channel-to-aquifer, not switch between over time Aquifer storage (state) Aquifer properties: Storage threshold for outflow Specific yield Outflow recession constant Channel properties: Losing vs gaining specification Shape - wetted perimeter Bed conductivity	Dynamic two-way exchange: aquifer-to-channel or channel-to-aquifer, depending on conditions (calculated state) for each riparian grid cell and channel node pair Water table height (state) Channel water level (state) Aquifer properties: Specific yield Conductivity (Ksat) Channel properties: Shape - wetted perimeter Bed conductivity
Function type	non-linear & threshold	non-linear & threshold	rate	non-linear & threshold	linear reservoir & threshold	non-linear & threshold
Thresholds	yes - to switch flow direction: Aquifer water level vs River water level	yes - to switch flow direction: Aquifer water level vs River water level	no	yes - to switch flow direction: Aquifer storage threshold for outflow	yes - for aquifer-to-channel: Aquifer storage threshold for outflow	yes - to switch flow direction: Aquifer water level vs River water level

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