Present Value Damages (PVD)

Select additional settings

Settings to be specified for PVD calculation are:

• Appraisal Period – this should be set to the required appraisal period length. This can be shorter or longer than the number of years between the earliest and latest specified scenarios.  If an appraisal period is set which ends later in a later year than the latest specified scenario, Damage Calculator will extrapolate AADs from the last two scenarios.  

• Select an interpolation method.  Three interpolation methods (for calculating AADs between specified epochs) are provided.  

• Apply capping – tick box to compare calculated PVDs against market value for each property. If PVD for a property exceeds its market value, then PVD is capped to market value.  

• Apply Writeoff – tick box to check onset of flooding at each scenario and compare with specified writeoff %AEP.  If flooding of a property is more frequent than the specified writeoff %AEP, the property will be ‘written off’ – i.e. it is assumed that the property is abandoned.  If a property is written off, the discounted market value is added to the total damages in the year of writeoff, and accumulation of all damages ends at the year of writeoff. 

Calculating Present Value Damages   

Damage calculator produces economic damages for each return period that is loaded in.  For example, if the following are loaded in:

then damage calculator will produce eight sets of damage columns – one for each return period.  

It should be noted that Damage Calculator can help reduce the number of flood depth grids required for  analysis as it allows the same grid to be re-used in multiple scenarios.

Damage calculator is also able to average and aggregate these results into a single Present Value Damage (PVD) figure, via an Annual Average Damage (AAD) ->  PVD calculation process.  The following limitations apply to this process:

• For annual average damages to be calculated for a scenario year, at least two return periods must be input.

• For present value damages to be calculated, at least two scenario years must be input. 

User Method    

Present value damage results are undertaken if the ‘Calculate PVD’ checkbox on the ‘Calculation Information’ tab is ticked.  It should be noted that the ‘Calculation PVD’ checkbox is only enabled if a minimum of two scenario years are present in ‘Scenario’ column of the ‘Events’ box at the bottom of the ‘Calculation Information’ tab. 

Once the ‘Calculate PVD’ checkbox is ticked, the user then needs to:

• Select an interpolation method from the ‘Interpolation Method’ group box

• Input an appraisal period to the ‘Appraisal Period (years)’ text box 

• Choose whether to apply capping and / or writeoff

Theory of Annual Average Damages (AAD)

To calculate annual average damage (AAD) values, damage calculator requires at least two flood model results for a given scenario year / epoch.

The AAD calculation process plots this data on a chart of damage verses probability (i.e. return period). It then calculates the area under this chart as the AAD value, as shown in Figure 1 below:

Some extrapolations are required to calculate a full area (and therefore full AAD value).  Different extrapolations are required for each ‘end’ of the polygon on the X-axis.

1.    An extrapolation from the two highest return periods (lowest probabilities) input is used to calculate the area between the highest RP (lowest probability) input and the ‘infinite’ RP (zero probability) event.  Damage calculator undertakes this extrapolation automatically with no user intervention.  The theory of this extrapolation is shown in the Figure 2 below:

2.    An additional extrapolation may be required if model results are not available with a sufficiently low return period (high probability) that one or more results grids are available with zero flooding and damages.  Illustrations of AAD calculations with and without a ‘zero flooding’ grid are provided in Figures 3 and 4.  It is noted that in Figure 4 (the ‘without zero flooding’ example) that an area of the AAD polygon at the low probability (right hand) end is ‘missing’ when compared with Figure 3.  Unlike the extrapolation shown in Figure 2, damage calculator does not undertake this extrapolation automatically, and further user input is required.  The input required is a dummy ‘blank’ grid which contains no flooding.  Such a grid can be generated either within the Flood Modeller Grid Calculator, or using independent GIS software, either by changing all depth in an existing model grid to ‘-9999’, or by deleting all depth values where properties are present.  Once a ‘dummy blank’ grid is available, this can be input to damage calculator as normal.  Example AAD calculations with a blank grid included for ‘zero flooding’ are shown in Figure 5.

Theory of Present Value Damages (PVD)

Calculated AADs for each year of the appraisal period are discounted to present day values using user specified discount rates.  All yearly values are the summed to calculate the total PVD value.  The user can choose to subject this value to capping or writeoff.

Interpolation Methods  

Interpolation Method – PVD is calculated by interpolating AAD values calculated for each specified scenario to give AAD values for every year of the appraisal period.  An interpolation method is required for this calculation.  Options are:

• Linear – assumes straight lines joining modelled scenario AAD points leading to varying AAD values throughout appraisal period.

• Stepped – assumes constant AAD between modelled AAD points, with a step in distribution occurring at each scenario within appraisal period.

• Combined – assumes a linear distribution between the first and second scenario, followed by a stepped distribution between subsequent scenarios.

These interpolation methods are illustrated in Figures 6 to 8 below:

It should be noted that the interpolation method selected will also affect the extrapolation which occurs at the end of the appraisal period, if the appraisal period is set to a longer period than the time between the first and last scenarios.  

• For linear interpolation, AADs are extrapolated based on the gradient between the final two scenarios specified.  This is illustrated in Figure 9.

• For stepped and combined interpolation, AADs are extrapolated from the final scenario specified.  This is illustrated in Figure 10.