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Soil moisture recharges groundwater whenever the soil moisture store exceeds field capacity. Recharge is calculated as a constant percentage of the storage above field capacity. Baseflow from groundwater is simulated using a linear recession of the groundwater store.
Figure 1: Conceptual daily rainfall-runoff model adopted for MUSIC.
Disaggregation Of Modelled Daily Runoff Into Sub-Daily Time Steps
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The temporal distribution of infiltration excess runoff is represented by the rainfall temporal pattern during the period of infiltration excess rainfall conditions. The daily evaporation loss is then removed from the temporal pattern uniformly over the duration of the storm, followed by the soil moisture deficit. The soil moisture deficit is subtracted from the early periods of the rainfall temporal pattern to reflect the progressive increase in soil moisture, leading ultimately to the occurrence of soil saturation excess runoff. The residual rainfall temporal pattern after accounting for the soil moisture deficit corresponds to the saturation excess runoff distribution. The disaggregation procedure is illustrated in Figure 2.
Figure 2: Disaggregation of daily runoff into sub-daily temporal patterns
Disaggregated Runoff Time Series
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The rainfall-runoff model should be calibrated to local conditions whenever possible. Based on information available to date, the following values could serve as a starting point for the calibration process. Remember that MUSIC can estimate the two initial capacities for a given run by using the warm-up option, provided the run duration is twelve months or more.
Impervious threshold | 1 mm |
|---|---|
Initial soil storage | 30% |
Infiltration capacity | 200 mm |
Infiltration exponent | 1 |
Initial groundwater store | 10 mm |
Daily recharge rate | 25% |
Daily drainage rate | 5% |
Daily deep seepage rate | 0% |
The following parameters are more dependent on location.
Location | Soil Store Capacity (mm) | Field Capacity (mm) |
|---|---|---|
Darwin | 300 | 250 |
Brisbane | 120 | 80 |
Sydney | 200 | 170 |
Canberra | 40 | 25 |
Melbourne | 30 | 20 |
Hobart | 30 | 20 |
Adelaide | 40 | 30 |
Perth | 250 | 230 |
The rainfall-runoff model should be calibrated to local conditions whenever possible.
For application in the UK, the MUSIC hydrologic model has been compared to similar UK hydrologic models and methods, in addition to calibration of the model to gauged data for several catchments to assist in deriving suitable parameters.
Similarities to UK Models
There are numerous similarities to existing UK hydrological models. The closest similarity is to the PDM conceptualisation. Fixing values of certain parameters within the PDM model and by making the surface and groundwater stores linear it is possible to almost replicate the response of the pervious fraction of the MUSIC model. The differences are that PDM does not allow for infiltration excess overland flow as it is not perceived to be as commonly observed as saturation excess overland flow in the UK.
As the ReFH model utilises the same soil stores as the PDM model it also shares many similarities with MUSIC, with the added advantage that regression formulae exist for estimating a number of the key parameters.
The key difference in application between the MUSIC hydrological model and existing UK models is that it requires some form of routing to be undertaken on the overland flow in order to replicate observed flows at the event scales whilst both PDM and ReFH have runoff routing functions in built.
It should be clarified that the hydrological model in MUSIC was built for different purposes to both PDM and ReFH which are intended as flood forecasting and flood estimation tools respectively.
The Wallingford Procedure is the primary method for calculating runoff in urban catchments within the UK, although revisions such as the ‘New UK Runoff Model’ have been proposed since its inception.
Another model that has been commonly used in the UK at various times is HYSIM. HYSIM is a hydrological simulation model which uses rainfall and potential evaporation data to simulate the hydrological cycle (surface runoff, percolation to groundwater and river flow) on a continuous basis. Overall the model is similar to the hydrological model in MUSIC, however the model structure is less conceptual and based more on the physical processes. There are a number of soil store layers within HYSIM rather than the two within MUSIC.
This would allow HYSIM to better represent the physical processes but in the absence of observed data the additional parameters make it difficult to calibrate.
Parameterisation of the MUSIC rainfall runoff model in the UK
The majority of the MUSIC parameters can be replicated from existing UK models or literature, a description of this process is given below:
1. Impervious threshold
This is analogous to the depression storage term used in the Wallingford procedure. Depression storage (DS) is calculated from the overland slope (in %) of the catchment using the formula:
DS = 0.71SLOPE-0.48
and the suggestion that for pitched roofs DS should be equal to 0.4mm.
2. Initial Soil Storage
Ideally this should be calibrated from observed data where available but ReFH offers a means for estimating seasonal values based on FEH catchment descriptors:
Cini (Winter) = 298.35BFIHOST0.95PROPWET-0.24(1.20-1.70BFIHOST+0.82PROPWET)
Cini (Summer) = 298.35BFIHOST0.95PROPWET-0.24(0.90-0.82BFIHOST-0.43PROPWET)
It should be noted that these estimators are based on a very small sample set of observed events (Winter, n = 93; Summer, n = 7) and the fit to them is not wonderful (Winter, r2 = 0.53; Summer, r2 = 0.49). The values could also be negative in which case they are set to 0.
3. Infiltration Capacity
Generally UK models do not consider infiltration excess to be the dominant process in runoff generation and it is not usually physically represented as rainfall intensity rarely exceeds infiltration capacity. For parameterisation purposes this could be set to a sufficiently high value that rainfall will not exceed infiltration or it could be parameterised using literature values (possibly referring back to the HOST soils classification).
4. Infiltration Exponent
This will likely remain as the Australian default value of 1 in the absence of any literature proposing a more suitable value.
5. Initial Groundwater Storage
As with the initial soil storage this can and should be calibrated from observed data when available by using the warm up function. The groundwater store in MUSIC differs to that of the FEH Methods which do not include an explicit store. The PDM does have an explicit store but there are no obvious literature values for calibrating it to.
6. Daily recharge rate
The ReFH model use a daily recharge rate, k defined as:
DK=exp(-kΔt)=0.8 which yields k=0.223
This compares favourably with the MUSIC default of 25%.
7. Daily drainage rate
There is no obvious way of parameterising the daily drainage rate the PDM model is the only UK method that can replicate this. It is evident that higher values should be used for more groundwater dominated catchments (i.e. more permeable catchments). This offers the potential to relate it to HOST class and maybe the BFIHOST catchment descriptor.
8. Daily deep seepage rate
This should probably be set to a default value of zero as there are not many sites where the groundwater can be considered truly lost from the system.
9. Soil store capacity
The ReFH method offers a formula to estimate soil store capacity. Assuming a uniform distribution of soil stores as ReFH does the soil store capacity is half of the value of Cmax. ReFH gives the empirical relationship for Cmax as:
Cmax=596.7BFIHOST0.95PROPWET-0.24 (n=101, r2=0.55, fse=1.61)
Thus,
SMSC=298.35BFIHOST0.95PROPWET-0.24
10. Field Capacity
Again ReFH offers a way to parameterise Field Capacity (FC) from FEH catchment descriptors with the empirical formula:
FC=49.9PROPWET-0.51BFIHOST0.23
Impervious Areas
Arguably the most important parameter to consider is the % of impervious areas within the catchment as this will ultimately dictate the amount of runoff the system generates. Volume 4 of the FEH cites a reference to a paper by Packman (1980) which suggested that 30% of the Urban Area should be considered as impervious. In this reference the urban area is given by the FSR URBAN parameter, which is the area from 1:50,000 Ordnance Survey mapping shown as urban. For use in the more recent FEH methods, an approximate conversion exists:
URBAN=2.05(URBEXT1990).
The value of URBEXT1990 can be updated to the present date using the CPRE urban growth equation.
Another area for discussion is whether impervious areas within the catchment need to be considered as a whole or as disconnected units. This problem is treated in different ways by each method. The Wallingford Procedure denotes the impervious areas as PIMP. There is some disagreement with how this is defined. Some literature defines it as the percentage of impervious areas connected to a storm sewer, whilst others note it as the total impervious area. WaPUG Note 21 give some better (although not definitive) advice on determining the sub-areas with an urban catchment. Within the FEH methodologies the total impervious area is always used.
The decision on whether or not to consider disconnection of impervious areas will have an impact in the calibration of the hydrological model within MUSIC. It should be possible to replicate observed data whichever approach is taken as there should be enough flexibility in parameter values to replicate the effect of disconnection, although there are implications for the identification of parameters. The suggestion of using ReFH to identify a number of parameters would suggest that to be consistent the impervious area should be the total area rather than the connected area.
Calibration of MUSIC to UK Observed Data
Some sets of observed data were collated and a comparison of results from the MUSIC model with default parameters and a MUSIC model with UK derived parameters was made. In order to achieve this several datasets were selected. These were split into three categories:
- Highly urbanised
- Moderately urbanised
- Essentially rural
Highly Urbanised
There were two small gauged catchments with significant urban areas for which a reasonable period of record was available. They were the Eastwood Brook catchment in Southend-on-Sea, Essex and the Ravensbourne East catchment in Bromley, Greater London. Both Catchments are approximately 1000ha in size and have a significant portion of impervious areas.
Eastwood Brook @ Eastwood
The above image is taken from the CEH website. Land-use statistics and map derived from the Land Cover Map 2000, Centre for Ecology and Hydrology. © NERC. Based upon © Crown Copyright 100017897 2005.
Parameter | MUSIC Default | UK parameter estimate |
|---|---|---|
Impervious threshold | 1 mm | 0.4 mm |
Initial soil storage | 30% (or calibration) | 53% [Summer], 79% [Winter] (or calibration) |
Infiltration capacity | 200 mm | 200 mm |
Infiltration exponent | 1 | 0 |
Initial groundwater store | 10 mm (or calibration) | 10 mm (or calibration) |
Daily recharge rate | 25% | 22.3% |
Daily drainage rate | 5% | 5% |
Daily deep seepage rate | 0% | 0% |
Soil Store Capacity | ? mm | 156 mm |
Field Capacity | ? mm | 86 mm |
Impervious Area | ? % | 20% |
Muskingham Cunge Routing - K | 150 mins | 66 mins |
Muskingham Cunge Routing - θ | 0.25 | 0.25 |
A number of parameters in MUSIC do not have default parameters so the same values were used in both simulations. As the simulation was being carried out at a 30min time-step the use of routing was required in order to come close to matching the observed flows. The theta parameter of Muskingham Cunge routing was assumed to be the default of 0.25 in the absence of better information whilst the K parameter was estimated from observed level data (or assuming a wave celerity of 1m/s) and the FEH parameter DPLBAR.
K=L/c=L/√(g(ybar))
K≈DPLBAR/1 or K≈DPLBAR/√(g•Average Flow Depth)
Calibration statistics and time series graphs for the Eastwood Catchment are shown below.
MUSIC default values – NSE = -0.08
UK Values – NSE = 0.11
The use of UK default values did increase the performance of the simulation as evidenced by the increase in NSE values. Overall the NSE values were poor, however on a visual inspection the models appearance appeared to be satisfactory, with a good match of peak heights and timing of flows. NSE and other objective functions are very susceptible to timing errors and as such the model could be greatly improved by an improved calibration of the routing parameters to ensure that the timing of simulated events is improved. Given also that the NSE was calculated on the 30 minute time-step data, it was expected that low values would be obtained as the disaggregation process used in MUSIC does not adequately simulate baseflow recession due to the daily flow being effectively sub-divided through the day according to the process outlined previously in this Appendix, rather than the flow being dynamically calculated at each 30 minute time-step.
Both parameter sets performed poorly at simulating the baseflow which may be due to the MUSIC hydrological model assuming a constant baseflow over each 24 hour period. The model performance could be improved by reducing the daily baseflow rate.
MUSIC Hydrologic Model Calibration using the Rainfall Runoff Library (RRL)
MUSIC has been calibrated to a broad range of regions across Australia and in several other countries. Typically, this calibration has focussed on obtaining satisfactory daily flow results through the comparison of observed and predicted daily flows. In terms of ensuring the appropriateness of the hydrologic model in MUSIC for UK applications, a calibration process was undertaken for several catchments with a range of climatic and catchment (land use, soil, slope etc) factors. The results of these calibration tasks are shown below.
MUSIC has been calibrated to a broad range of regions across Australia and in several other countries. Typically, this calibration has focussed on obtaining satisfactory daily flow results through the comparison of observed and predicted daily flows. In terms of ensuring the appropriateness of the hydrologic model in MUSIC for UK applications, a calibration process was undertaken for several catchments with a range of climatic and catchment (land use, soil, slope etc) factors. The results of these calibration tasks are shown below.
Calibration Catchments
Four calibration catchments were assessed as part of this task and further details are provided above. A summary of the catchments used is shown below:
- Ravensbourne – 1030 ha mixed land use catchment
- Eastwood Brook – 1040 ha urbanised catchment – 67.8% Built up areas
- Costa Beck – 780 ha rural catchment – 7.9% Built up areas
- Coal Burn – 150 ha rural catchment – 5.9% Built up areas
Both rural and urban catchments were selected for calibration to demonstrate the suitability of the model to assess both existing urban areas and undeveloped catchments prior to greenfield development.
Calibration Methodology
Each catchment was established in the Rainfall Runoff Library (RRL) tool (see
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org.au/Tools/RRL) developed by the Cooperative Research Centre for Catchment Hydrology. This tool allows the user to evaluate and calibrate several rainfall runoff models for a particular catchment and review model results. The SimHyd rainfall-runoff model is very similar to the rainfall-runoff model in MUSIC as the latter was derived from SimHyd and uses similar parameters, so is a useful starting point to calibrate the MUSIC model.
Similar parameters derived from calibrating the catchments in RRL were then transferred to the MUSIC rainfall runoff parameterisation page in one source node to represent the whole catchment. This simplistic catchment representation was suitable in this case though complex routing is lumped into one routing parameter set included in a link between the source node and a receiving node as shown below.
Figure 1. Simplified Catchment Representation
Subdaily observed data was then imported into MUSIC at the receiving node and the observed and predicted runoff time series were then examined.
Qualitative Model Performance Analysis
A qualitative model performance assessment was undertaken on the resulting flows and is considered a subjective assessment of the goodness of fit between the observed and modelled results. A qualitative assessment is advantageous in that it provides an unambiguous performance measure that can be used to assess how well the model has been calibrated. A number of differing qualitative measures are provided through a series of graphs as described below:
- Time series (hydrograph) comparison of 30 minute and daily flows to assess the general response and pattern of predicted flows; and
- Scatter plots for monthly and daily volumes to provide a visual observation of the scatter around the line of perfect fit (i.e. a 45° line through the origin representing a perfect calibration).
Examples of these are provided below:
Figure 2. Observed and Modelled Daily Hydrograph (Coalburn – 1992-2003 excerpt)
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