IHACRES-CMD is a unit hydrograph model that converts time series of rainfall and temperature into a time series of runoff. The version of IHACRES used in Source has six parameters.

## Scale

The model operates at a catchment scale and is typically run at a daily time-step. IHACRES has been used to model catchments that range from 490 m^{2} to 10,000 km^{2} and with time-steps from six minutes to one month (Littlewood* et al.*, 1997).

## Principal developer

The principal developers are the Integrated Catchment Assessment and Management Centre (iCAM), Australian National University, and the Institute for Hydrology, Wallingford, UK.

## Scientific provenance

IHACRES is an acronym for "Identification of unit Hydrographs And Component flows from Rainfall, Evaporation and Streamflow data". IH is also an acronym for the Institute of Hydrology (now the Centre for Ecology and Hydrology, Wallingford, UK) and CRES is an acronym of Centre for Resource and Environmental Studies, Australian National University. The original IHACRES model is described in a paper by authors from these two institutions (Jakeman *et al.*, 1990).

IHACRES model has been used in numerous applications and there are many different versions of the model (see reference list and bibliography). The IHACRES-CMD version currently implemented in Source is described in Croke and Jakeman (2004, 2005) and the references cited therein.

A version of IHACRES was included in Cooperative Research Centre for Catchment Hydrology’s toolkit and is in the eWater toolkit.

## Version

Source version TBA

## Dependencies

Requires rainfall and maximum daily temperature or potential evapotranspiration (PET) as input. Observed streamflow is used for calibration.

## Structures and processes

IHACRES-CMD is a continuous rainfall-runoff model used to generate estimates of runoff from rainfall and temperature (or PET) data. The conceptual layout of the model is shown in Figure 1. The box on the left represents a non-linear loss module that converts rainfall, *P**,* into effective rainfall, *U*. Effective rainfall is the portion of rainfall that will eventually leave the catchment as runoff. Effective rainfall is routed through two parallel stores to produce streamflow.

### Non-linear Loss Module

The non-linear loss module uses a catchment moisture deficit (CMD) accounting scheme, which partitions rainfall into drainage (effective rainfall), evapotranspiration (ET) and changes in catchment moisture. Each time step the CMD is calculated as:

(1) |

where *t* is the time step, *M* is the CMD, *P* is rainfall, *E* is actual evapotranspiration (ET), *U* is drainage (effective rainfall). Units are millimetres per time step. The minimum value of *M* is 0, which means that the catchment is fully saturated, while a value greater than 0 indicates that there is a moisture deficit.

The effective rainfall (drainage) is assumed to be an instantaneous, linear function of the CMD given by:

(2) |

where *d* is a flow threshold. If the CMD is greater than the threshold, no flow is produced. The actual effective rainfall at each time step is given by the integral of equation (2). Other forms for the drainage function could be used (see Croke and Jakeman (2004) for examples) but the linear form only is currently implemented in Source.

Evapotranspiration is calculated as:

(3) |

where *T* is the temperature, *M _{f}* is the value of the CMD before taking into account ET losses,

*e*is a temperature to PET conversion factor, and is a stress threshold. The parameter

*g*represents the value of the CMD above which the ET rate will begin to decline due to insufficient water availability for plant transpiration. To reduce parameter correlation, it is calculated as:

(4) |

where *f* is a multiplication factor on the flow threshold *d*.

### Linear Routing Module

The Linear Routing Module translates effective rainfall into streamflow by routing it through two parallel, linear stores. It is based on the concept of the *instantaneous unit* *hydrograph*,* *which, for a drainage area, is the hydrograph of direct runoff resulting from effective rainfall of infinitely small duration. In the Linear Routing Module, instantaneous unit hydrograph theory is used to describe both direct runoff (quickflow) and baseflow (slowflow). In Figure 1, the top store represents quickflow while the bottom store represents slowflow. The sum of the quick and slow hydrographs gives the total streamflow (Figure 2). Refer to Jakeman *et al.* (1990) for a discussion of instantaneous unit hydrograph theory and Jakeman and Hornberger (1993) for a discussion of the two-store formulation of the Linear Routing Module.

The quickflow and slowflow equations are:

(5) |

where:

*t* is the time step

*Q _{q}* and

*Q*are quickflow and slowflow, respectively. They are subject to the initial conditions

_{s}*Q*[

_{q}*t*

_{0}] = 0 and

*Q*[

_{s}*t*

_{0}] = 0

*U* is effective rainfall

α* _{q}* and α

*are calibration parameters, 0 < -α*

_{s}*< 1 and 0 < -α*

_{q}_{s}< 1

*v _{q}* and

*v*are the proportions of effective rainfall diverted to quickflow and slowflow, respectively,

_{s}*v*+

_{q}*v*= 1 and

_{s}*v*,

_{q}*v*> 0

_{s}Total streamflow *Q* is the sum of quickflow and slowflow:

(6) |

It is more intuitive to express the parameters α* _{q}* and α

*in terms of the time constants τ*

_{s}*and τ*

_{q}*, respectively:*

_{s}(7) |

where Δ*t* is the time step size.

The time constants τ* _{q}* and τ

*represent the time required for the quickflow and slowflow responses to fall to 1/*

_{s}*e*of their initial values after an impulse of rainfall. They are subject to the condition τ

*< τ*

_{q}*, which says that that quickflow should receed more quickfly than slowflow (Figure 2).*

_{s}###### Figure 2. Linear Routing, example

## Limitations

IHACRES-CMD is designed to represent the large-scale, conceptual rainfall-runoff processes occurring in a catchment. The model parameters may not be directly related to physical properties that can be measured in the field.

## Input data

IHACRES-CMD requires three sets of time series data. These are:

- Observed rainfall (expressed as a depth, e.g. mm)
- Temperature (daily maximum) in degrees Celsius or potential evapotranspiration (PET) depth (e.g. mm)
- Observed streamflow for calibration

## Parameters or settings

IHACRES-CMD has six parameters requiring calibration as described in Table 1.

###### Table 1. IHACRES-CMD model parameters. Feasible values are the range of theoretically possible values. Typical ranges are parameter upper and lower bounds typically used for model calibration via automatic optimisation algorithms.

Parameter | Description | Units | Default | Feasible Values | Typical Range |
---|---|---|---|---|---|

| Time constant governing the rate of recession of quickflow | Day | 1 | > 0 | 0.5 - 10 |

| Time constant governing rate of recession of slowflow. The slowflow time constant must always be greater than the quickflow time constant: | Day | 10 | > 0 | 10 - 350 |

| The proportion of slow flow to total flow | Proportion | 0.5 | [0, 1] | 0 - 1 |

| Flow threshold | mm | 200 | > 0 | 50 - 550 |

| Temperature to PET conversion factor | Dimensionless | 0.1 | > 0 | 0.01 - 1.5 |

| Plant stress threshold factor (expressed as a multiplicative factor of | Dimensionless | 0.5 | > 0 | 0.01 - 3 |

## Output data

The primary output of the IHACRES-CMD model is a time series of total streamflow. It also outputs time series of quickflow and slowflow, the sum of which gives total streamflow.

In addition, the internal state variables listed in Table 2 can be recorded.

###### Table 2. Recorded state variables.

State Variable | Symbol | Frequency |
---|---|---|

Catchment moisture deficit (CMD) | M | time step |

Effective rainfall | U | time step |

Evapotranspiration (ET) | E | time step |

References

Croke, B.F.W., and A.J. Jakeman (2004) A catchment moisture deficit module for the IHACRES rainfall-runoff model.* Environmental Modelling and Software* 19:1-5.

Croke, B.F.W., and A.J. Jakeman (2005). Corrigendum to "A Catchment Moisture Deficit module for the IHACRES rainfall-runoff model" [Environ. Model. Softw. 19 (1) (2004) 1-5], *Environmental Modelling and Software* 20(7): 977.

Jakeman, A.J., and G.M. Hornberger (1993). How much complexity is warranted in a rainfall-runoff model?, *Water Resources. Research* 29:2637-2649

Jakeman, A.J., I.G. Littlewood and P.G. Whitehead (1990). Computation of the instantaneous unit hydrograph and identifiable component flows with application to two small upland catchments.*Journal of Hydrology* 117: 275-300.

## Bibliography

Chiew, F.H.S., M.J. Stewardson and T.A. Mc Mahon (1993). Comparison of six rainfall-runoff modelling approaches. Journal of Hydrology 147: 1-36.

Croke, B.F.W., F. Andrews, A.J. Jakeman, S.M. Cuddy and A. Luddy (2005). Redesign of the IHACRES rainfall-runoff model, 29th Hydrology and Water Resources Symposium, Water Capital, Engineers Australia, 21-23 February, 2005

Croke, B.F.W., F. Andrews, A.J. Jakeman, S.M. Cuddy and A. Luddy (2006). IHACRES Classic Plus: A redesign of the IHACRES rainfall-runoff model, *Environmental Modelling and Software* 21:426-427

Dye, P.J., and B.F.W. Croke (2003). Evaluation of streamflow predictions by the IHACRES rainfall-runoff model in two South African catchments, *Environmental Modelling and Software* 18:705-712.

Hansen, D.P., W. Ye, A.J. Jakeman, R. Cooke, P. Sharma, Analysis of the effect of rainfall and streamflow data quality and catchment dynamics on streamflow prediction using the rainfall-runoff model IHACRES, *Environmental Software*, 11:193-202

Jakeman, A.J., and G.M. Hornberger (1993). How much complexity is warranted in a rainfall-runoff model?, *Water Resources Research*, 29:2637-2649

Letcher, R.A., S.Y. Schreider, A.J. Jakeman, B.P. Neal and R.J. Nathan (2001). Methods for the analysis of trends in streamflow response due to changes in catchment condition. *Environmetrics*12(7): 613-630.

Littlewood, I.G., K. Down, J.R. Parker and D.A. Post (1997) IHACRES: Catchment-scale rainfall-streamflow modelling (PC version) Version 1.0 - April 1997 (with revisions for release of downloadable v1.02, September 2003). Institute of Hydrology, Centre for Ecology and Hydrology, Wallingford, Oxon, UK. http://www.ceh.ac.uk/products/software/ihacre/download.asp

Neil McIntyre, Aisha Al-Qurashi, Performance of ten rainfall-runoff models applied to an arid catchment in Oman, *Environmental Modelling and Software* 24(6): 726-738

Merritt, W.S., B.F.W. Croke and P. Perez (2001). Predicting flows in ungauged catchments and catchments subject to forest cover changes. MODSIM, Canberra, International congress on modelling and simulation.

Post, D.A. (2009). Regionalizing rainfall-runoff model parameters to predict the daily streamflow of ungauged catchments in the dry tropics. *Hydrology Research* 40 (5): 433-444.

Post, D.A. and Jakeman, A. J. (1996). Relationships between physical descriptors and hydrologic response characteristics in small Australian mountain ash catchments. Hydrological Processes 10: 877-892.

Post, D.A. and Jakeman, A. J. (1999). Predicting the daily streamflow of ungauged catchments in S. E. Australia by regionalising the parameters of a lumped conceptual rainfall-runoff model. Ecological Modelling 123: 91-104.

Schreider, S.Y., A.J. Jakeman, R.A. Letcherb, R.J. Nathan, B.P. Neal and S.G. Beavis (2002). Detecting changes in streamflow response to changes in non-climatic catchment conditions: farm dam development in the Murray¯Darling basin, Australia. Journal of Hydrology 262: 84-98.

Ye, W., B.C. Bates, N.R. Viney, M. Sivapalan and A.J. Jakeman (1997). Performance of conceptual rainfall-runoff models in low-yielding ephemeral catchments. *Water Resources Research* 33(1): 153-166.