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System Index

This page provides a complete index reference for the components of the plans model system, including variables, parameters, initial conditions, and boundary conditions. Each component is presented in tabular form with its symbol, name, description, units, and other relevant details. Together, these tables serve as a comprehensive guide to understanding the building blocks of the model and how they interact.

System overview

The plans model is based on a System Dynamics approach, representing the hillslope system as a column of interconnected storages — like a series of “water buckets” — that fill, spill, drain and dry over time.

plans model column structure

See also

See more details in Model Structure.

Variables

Variables represent the dynamic components of the hydrological system. They hold numerical values for storage levels, as well as the instantaneous flows at each time step of the model simulation. Together, they describe how the system evolves over time.

Name	Symbol	Description	Units	System
c	\(C\)	Canopy storage level	mm	storage
d	\(D\)	Soil saturation deficit (gx - g)	mm	storage
datetime	\(t\)	Date-time label	unitless	time
dv	\(D_{v}\)	Vadose zone saturation deficit (d - v)	mm	storage
ec	\(E_{c}\)	Canopy evaporation flow	mm/{dt}	flow
eg	\(E_{g}\)	Phreatic zone transpiration flow	mm/{dt}	flow
es	\(E_{s}\)	Surface evaporation flow	mm/{dt}	flow
et	\(E\)	Evapotranspiration flow (ET)	mm/{dt}	flow
g	\(G\)	Phreatic zone level	mm	storage
pet	\(E_{\text{pot}}\)	Potential Evapotranspiration	mm/{dt}	flow
ppt	\(P\)	Precipitation	mm/{dt}	flow
ps	\(P_{s}\)	Surface effective precipitation (psf + ptf)	mm/{dt}	flow
psf	\(P_{sf}\)	Canopy stem flow	mm/{dt}	flow
ptf	\(P_{tf}\)	Canopy spill flow (throughfall)	mm/{dt}	flow
q	\(Q\)	Streamflow or discharge at basin outlet	mm/{dt}	flow
qb	\(Q_{b}\)	Groundwater base flow	mm/{dt}	flow
qc	\(Q_{c}\)	Channel flow at basin outlet (routed qh)	mm/{dt}	flow
qh	\(Q_{h}\)	Hillslope flow (qo + qu)	mm/{dt}	flow
qn	\(Q_{n}\)	Infiltration flow (drainage to mineral soil)	mm/{dt}	flow
qo	\(Q_{o}\)	Overland flow (runoff)	mm/{dt}	flow
qobs	\(Q_{\text{obs}}\)	Streamflow observed at basin outlet	mm/{dt}	flow
qu	\(Q_{u}\)	Underland flow (subsurface flow)	mm/{dt}	flow
qv	\(Q_{v}\)	Recharge flow (percolation to phreatic zone)	mm/{dt}	flow
s	\(S\)	Surface storage level	mm	storage
v	\(V\)	Vadose zone storage level	mm	storage

Parameters

Parameters control the behavior of the system. They can influence storage levels and flows, but unlike variables, they remain constant throughout the simulation. Parameters define the conditions under which the model operates and can be adjusted to reproduce observed behavior or to fine-tune the system for a desired outcome.

Name	Symbol	Description	Units	System
ca	\(C_{a}\)	Activation level for canopy flow	mm	storage
ck	\(C_{k}\)	Canopy residence time	d	storage
dea	\(D_{e, a}\)	Deficit activation level for ET (root zone)	mm	flow
dt	\(\Delta t\)	Simulation time step	min	time
gex	\(\hat{G_{e}}\)	ET capacity of capilar zone	mm	storage
gk	\(G_{k}\)	Phreatic zone residence time	d	storage
gx	\(\hat{G}\)	Phreatic zone storage capacity	mm	storage
hw	\(H_{w}\)	Weight for HAND in TSI superposition	unitless	storage
hx	\(\hat{H}\)	HAND upper threshold in TSI superposition	m	storage
kq	\(K_{Q}\)	Channel water celerity	m/d	flow
kv	\(K_{V}\)	Soil hydraulic conductivity	mm/d	flow
sk	\(S_{k}\)	Surface residence time	d	storage
soa	\(S_{o, a}\)	Activation level for overland flow	mm	storage
soc	\(S_{o, c}\)	Fragmentation level for overland flow	mm	storage
sua	\(S_{u, a}\)	Activation level for subsurface flow	mm	storage
suc	\(S_{u, c}\)	Fragmentation level for subsurface flow	mm	storage
sux	\(\hat{S_{u}}\)	Subsurface storage capacity	mm	storage

Initial Conditions

Initial Conditions define the starting values of storage variables at the first time step of the simulation. They serve as the starting point from which the system evolves, allowing the model to compute changes and update states over the entire simulation period.

Name	Symbol	Description	Units	System
c0	\(C_{0}\)	Canopy storage initial conditions	mm	storage
g0	\(G_{0}\)	Phreatic zone initial conditions	mm	storage
s0	\(S_{0}\)	Surface storage initial conditions	mm	storage
v0	\(V_{0}\)	Vadose zone initial conditions	mm	storage

Boundary Conditions

Boundary Conditions define the structural and contextual setup of the system. They determine how the model interacts with its surroundings, such as the configuration of a drainage network for routing procedures. Different boundary arrangements lead to different simulation outcomes, making them a critical input for running the model.

Name	Symbol	Description	Units	System
distance	\(X\)	Distance to basin outlet	m	flow
f_area	\(A\)	Area fraction of basin	unitless	flow