Scottish Marine and Freshwater Science Vol 6 No 14: Developing an avian collision risk model to incorporate variability and uncertainty

The report describes the data required, and the methods used, to estimate collision

risk. It is accompanied by a worked example and R code (available at, which enables the collision risk calculations to be

performed in

Part 1: Model Description


As wind energy developments increase globally the potential associated environmental impacts are receiving considerable attention, particularly avian impacts. These potential impacts on bird populations can be grouped into three main types: direct mortality due to collision with turbines/infrastructure; physical habitat modification and/or loss; and behavioural responses of birds to turbines (Fox et al. 2006; Langston 2013). Focussing on avian collision, a variety of methods have been developed to aid the assessment of the risk of collision, including collision risk models.

After extensively reviewing both the peer-reviewed scientific literature and grey literature, 10 distinct collision risk models referring to birds and wind turbines were identified, the earliest dating back to 1996 (Tucker 1996). At their core, most avian collision risk models include a calculation of the probability of a collision occurring (assuming no evasive action or avoidance behaviour) and often also a measure of the number of birds at risk, if an estimate of likely collision events is to be calculated. The probability of collision is generally based on the probability of a turbine blade occupying the same space as the bird during the time that the bird takes to pass through the rotor swept area. This therefore relies upon information on both bird and wind turbine characteristics such as bird morphometrics and flight speed, turbine rotor speed and size, etc.

In the UK, the most frequently used avian collision risk model is commonly known as 'the Band model' (Band, Madders & Whitfield 2007) and was originally conceived in 1995. Since then it has undergone several iterations with the most recent associated with the Strategic Ornithological Support Services ( SOSS) (Band 2012a; b). The Band model (Band 2012b) provides four different options for calculating collision risk.

  • Option 1 - Basic model, i.e. assuming that a uniform distribution of flight heights between the lowest and the highest levels of the rotors and using the proportion of birds at risk height as derived from site survey.
  • Option 2 - Basic model, but using the proportion of birds at risk height as derived from a generic flight height distribution provided.
  • Option 3 - Extended model and using a generic flight height distribution.
  • Option 4 - Extended model and using a flight height distribution generated from site survey.

The most recent update of the Band model guidance also provides an approach under which uncertainty can be expressed. However, this approach is relatively simplistic and can only be applied when the sources of variability are independent of one another. Furthermore, although provided, it is not routinely followed and so could be improved upon. From undertaking interviews with stakeholders (for summary see Appendix 1), it was established that a new collision risk model that was fundamentally different was not required by the industry and the Band model was considered generally fit for purpose. However, although the majority of the stakeholders questioned did not consider major changes necessary, the general opinion was that if it were possible to incorporate uncertainty into the modelling process, it would be beneficial. The main reasoning for this was that expressing collisions as a single number does not sufficiently represent the complexity of the situation. In addition, it is known that the Band model is sensitive to the choice of input parameters (Chamberlain et al. 2006). Variability in input parameters such as bird density, flight speed and turbine rotor speed are likely to contribute uncertainty to the final collision estimates. Sensitivity analyses of both the basic and extended options of the Band model are provided in Appendix 2.

General purpose of model update

The general purpose of this collision risk model update is to further develop the application of the Band model using a simulation approach to incorporate variability and uncertainty. In this report we refer to variability as the inherent heterogeneity of the environment and uncertainty as a lack of data or incomplete knowledge. The simulation model randomly samples from distributions for each of the model parameters and the simulations can then be used to derive average collision estimates, with associated confidence intervals. The model update will therefore allow for a better understanding of the uncertainty associated with the predicted collision impact of a wind farm development and provide confidence limits, something which has previously been absent. In addition, the incorporation of uncertainty would reduce the possibility that a collision estimate was driven by the choice of a single input parameter value. Ultimately, the update should aid streamlining of the planning/consenting stages of a development by providing information not only on the magnitude of collisions i.e. the number of collision events, but also the likelihood of that number of collisions occurring.

In this model update, variability and uncertainty are considered together in combination, rather than separately. Some model input parameters will have associated variability, for example bird body length, others may be expected to be point estimates with associated uncertainty, such as turbine rotor radius, and some parameters may have both variability and uncertainty. Ideally it would be possible to differentiate between variability and uncertainty but at present this is not possible due to a lack of data. However, including variability and uncertainty in combination in the model still provides a significant step forward.

The report describes the data required, and the methods used, to estimate collision risk. It is accompanied by a worked example and R code (available at, which enables the collision risk calculations to be performed in a standardised and reproducible way.

Model format

Whereas previous iterations of the Band model have used Microsoft Excel, the collision risk model updated presented uses R Opinions given during stakeholder interviews (for summary see Appendix 1) were that the Excel spreadsheet was difficult to use at times and there was the potential for errors to be easily introduced into calculations, particularly if the spreadsheet did not update correctly when new input parameters were entered. In addition, the Excel spreadsheet does not allow results to be reproduced easily making auditing onerous, as values have to be entered manually for each occasion or scenario. Using R enables reproducible methods and results as code and data are provided along with the computational environment used. This improves understanding and allows verification of results, therefore increasing transparency.

Relationship to previous guidance on collision risk modelling

The model described and presented in this document is an update to the Band collision risk model (Band 2012b) which was most recently updated as part of SOSS. The mechanistic details of the Band model have not been altered and form the core of the model update described below.

The guidance (Band 2012b) states clearly that the collision estimate should be a best-estimate rather than a worst-case scenario.

"This guidance does not recommend use of 'worst case' assumptions at every stage. These can lead to an overly pessimistic result, and one in which the source of the difficulty is often concealed. Rather, it is recommended that 'best estimates' are deployed, and with them an analysis of the uncertainty or variability surrounding each estimate and the range within which the collision risk can be assessed with confidence. In stating such a range, the aspiration should be to pitch that at a 95% confidence level, that is, so that there is 95% likelihood that the collision risk falls within the specified range. However, given the uncertainties and variability in source data, and the limited firm information on bird avoidance behaviour, it seems likely that for many aspects the range of uncertainty may have to be the product of expert judgement, rather than derived from statistical analysis."

The model update presented in this document follows this principle by using ranges of values rather than a single, 'worst-case' scenario.

The previous guidance (Band 2012b) presented a method to express overall uncertainty in collision estimates (stage F), as there are a large number of sources of variability or uncertainty. Cook et al. (2012) and Johnston et al. (2014) are key resources to include in this process as they provide data with confidence limits. However, the uptake of stage F in the collision estimation process appears to have been minimal. There have also been cases of its misapplication with estimates presented with implausible confidence limits such as 40±100 collisions, suggesting that negative numbers of collisions are possible. In addition, the method for expressing uncertainty suggested in stage F does so post hoc, rather than being integrated in to the model itself. Also, combining sources of uncertainty as suggested is only applicable when parameters are independent. The model update described in this document further develops the concepts presented in stage F of the previous guidance.

Before the most recent iteration of the Band model (Band 2012b) was conceived, McAdam (2005) produced a model which incorporated species specific flight height distributions. Variation in flight height has now been incorporated in to the most recent update (Band 2012b), however, the model produced by McAdam (2005) used Monte Carlo simulation to obtain 500 samples. Using Monte Carlo methods allowed for the production of summary statistics rather than single collision estimates, as well as probability distributions of events (numbers of collisions) occurring. It was also executed using R rather than Excel. In the model update presented below, the method of Monte Carlo simulation used by McAdam (2005) has been applied to the most recent version of the Band model to allow the incorporation of uncertain parameter values.

General data requirements

The model update is based on the Band model (Band 2012b) therefore the types of data required are the same:

  • Bird survey - data on the number of birds flying through or around the site, and their flight height
  • Bird specification - details on bird morphology and flight speed
  • Turbine specification - details on the number, size and rotation speed of turbine blades
  • Bird behaviour - prediction of likely change due to wind farm, e.g. avoidance

The crucial difference from previous iterations of the Band model is that rather than using a single value for a given input parameter, for example bird flight speed, this update of the model randomly samples from a distribution of values. Using the randomly sampled parameter values, a collision risk estimate is calculated. This process is then repeated numerous times to produce a distribution of collision estimate for which summary statistics i.e. average and spread, can be calculated. Whereas the previous guidance and methods provided a measure of uncertainty post hoc, uncertainty is now incorporated in the modelling procedure itself with this update. Therefore, information regarding uncertainty in the data is required to be entered into the model.

Where possible, and when suitable, a mean and standard deviation should be provided for input parameters. These should capture the uncertainty within the data. For example, if the maximum turbine blade width has not been decided upon but is likely to be 5 metres then a mean = 5 should be provided with a standard deviation which describes the uncertainty and possible values. For this example, a mean of 5 and standard deviation of 0.3 would give a minimum of approximately 4 metres, and a maximum of approximately 6 metres. If there is no uncertainty and it is definite that the maximum blade width is to be 5 metres then a value of 5 should be entered as the mean and either 0 entered as the standard deviation or it left blank.

To incorporate uncertainty into the collision risk estimate, a mean and standard deviation will be required for the following parameters. Attention should be paid to the units of measure.

Table 1: Bird-related parameters

Parameter Units Description/Notes
Length m (metres)
Wingspan m (metres)
Flight speed m/sec Available from telemetry data or wind tunnel experiments
Flight type Flapping or gliding
Nocturnal activity Proportion e.g. 0.5 for 50% Available from telemetry data or visual observations
Proportion at collision risk height Proportion e.g. 0.5 for 50%
Flight height distribution Proportion e.g. 0.5 for 50% Distribution curves from which the
proportion of birds flying within 1 metre
height bands are calculated. Data provided
by BTO (Johnston et al. 2014). (See below)
Avoidance rate Proportion e.g. 0.5 for 50% Suggested values available from MSS avoidance report
Bird density Birds/km 2 Birds in flight in daytime, taken from survey data

Table 2: Turbine-related parameters

Parameter Units Description/Notes
Rotor radius m (metres) Measured from the axis of rotation to blade tip.
Hub height m (metres) Sum of rotor radius and minimum blade
clearance above HAT. (See below)
Max. blade chord width m (metres)
Rotation speed rpm See below
Blade pitch Degrees relative to rotor plane See below
Turbine operation time Proportion e.g. 0.5 for 50% Requires both information on wind availability
and maintenance down time.

This model requires information on flight height distributions, if options 2, 3 or 4 are to be used. A generic flight height distribution is presented with the SOSS guidance (Band 2012a; b; Cook et al. 2012), however this does not provide information on the uncertainty associated with the distribution. Johnston et al. (2014) used a bootstrapping technique to provide confidence limits associated with the generic flight distribution and these bootstraps can be used within this model update to provide uncertainty associated with the flight height distribution curve. For each iteration of the model, a curve produced from a bootstrap sample is re-sampled and used. It is possible to use this update to calculate a collision risk estimate using option 4, should site-specific data on flight height distributions be available.

The model also requires information on wind speed (m.s -1) at the proposed site as well as the relationship between rotor speed and wind speed and turbine pitch and wind speed. This allows rotor speed and pitch to be linked both to the wind speed and also to each other. This is achieved through the provision of data similar to that in table 3 (below), describing the relationship between wind speed and rotor speed and pitch, as well as information on wind speed at the site.

Table 3: Example data describing relationship between wind speed, rotor speed and blade pitch.

Wind speed (m/s) Rotor Speed (rpm) Pitch (degrees)
0 0 90
1 0 90
2 0 90
3 6 0
4 6 0
5 6 2
6 8 4

The turbine operation time is wind availability minus maintenance down time. Wind availability should be provided as a constant i.e. proportion of time the wind conditions allow for turbine operation and should be available from meteorological data. Maintenance time should be provided as a monthly mean and standard variation as it is expected that there will be uncertainty and variability surrounding maintenance.

Hub height is the distance from highest astronomical tide ( HAT) to the axis of rotation of the turbine. This distance comprises the rotor radius and the distance between the minimum rotor tip height and HAT. Therefore, as rotor radius is already entered into the model, it is importantly only the distance component from HAT to the minimum rotor height that is required here and not the total hub height.

Calculating collision risk

As stated previously, this model is an update of the Band model. For more information on the Band model refer to (Band 2012a; b) and associated information on the SOSS website

Monte Carlo simulation

The model update presented herein uses Monte Carlo simulation. Monte Carlo simulation is a computational technique that uses random sampling to produce numerical results, and in this model update, is used to obtain values for uncertain input parameters, for example flight speed or bird length. These values are then used in the Band model. For each set of random samples, a collision estimate is calculated. Therefore if the simulation is run for 100 iterations, 100 sets of random input parameters will be sampled and 100 collision risk estimates calculated, instead of a single value. Monte Carlo simulation therefore allows for the presentation of a range of possible outcomes, when there is uncertainty surrounding the input data, and produces distributions of possible collision estimates. The distribution data can then be further re-sampled and used in stochastic population models, should this be required.

Sampling distributions

With the exception of rotor speed, pitch and flight height distributions, input values for the Band model are sampled from probability distributions. These distributions are parameterised using data provided by the user and have been constrained to the Normal distribution, or in cases where negative values are not plausible, the truncated Normal distribution. The user defines the mean or expected value and a standard deviation to describe the variation about the mean. Values in the middle near the mean are most likely to occur. The decision to use the Normal distribution was made on the basis of ease of parameterisation for the user as well as suitability. The Normal distribution was considered more suitable that a uniform distribution because in most cases it is expected that there will be a more likely value, and the uniform distribution, where all values are equally likely, would therefore enter more uncertainty than realistic into the model. It is however accepted that in all cases, the Normal distribution may not be the most suitable distribution, but there is a balance to be achieved between suitability and ease of use.

Collision risk options

The Band model provides four different options for calculating collision risk (Band 2012b). Options 1, 2 and 3 are the most frequently used. The model update calculates estimates for both the basic (options 1 and 2) and extended (option 3) versions of the Band model. It is possible to use this update to calculate a collision risk estimate using option 4, should site-specific data on flight height distributions be available. However, this would require a large amount of data collection, to provide information on variation in flight height distribution therefore the default option does not include option 4.

Running the model

As well as being designed to run numerous simulations of the Band model, this update is designed to loop through multiple species and multiple turbine designs automatically. Therefore once the initial user information is entered and the model begins, the user is not required to enter any further information and the results will be saved automatically to the location specified by the user. The number of results obtained will depend on the number of different turbine designs and species entered.

Model Output

The model outputs information on the expected numbers of collisions. The information is provided both as tables and figures. Descriptions of the outputs are listed below and illustrated examples are provided in the worked example.


1. Overall summary table of collisions by species, turbine and model option. Results are presented as mean, standard deviation ( SD) and coefficient of variation ( CV), and median and inter quartile range ( IQR).

2. Monthly summaries of collisions. Separate tables are produced according to species, turbine and model option for example 6_Black_legged_Kittiwake_monthlySummaryOpt3.csv. Results are presented as mean, standard deviation ( SD) and coefficient of variation ( CV), and median and inter quartile range ( IQR).

3. Summary of sampled bird parameters by species, turbine and model option presented as mean and standard deviation ( SD), and median and inter quartile range ( IQR).

4. Summary of sampled turbine parameters by species, turbine and model option presented as mean and standard deviation ( SD), and median and inter quartile range ( IQR).


1. 3-panel boxplots of monthly collisions for model options 1, 2 and 3 by species, and turbine type.

2. Density plots of numbers of collisions by species, and turbine type. A density curve is plotted for each of the 3 model options.

3. If 2 or more turbine models are included, then a 3-panel figure will be produced for each species, with the panels representing model options 1, 2 and 3 and each panel containing density plots for the different turbines included.

In addition to the collision estimates, the model also saves a copy of the input files which were entered into the model, as well as a summary of the randomly sampled input parameter values. This would therefore allow for the model to be re-run and results verified (if required). It also outputs a text file stating the time elapsed between the start and the end of the model, the number of iterations, the species for which the model was run and also the different turbines i.e. 6 MW, 8 MW, etc. if more than one turbine type was specified.

Future work

During this project, an update to the Band collision risk model (Band 2012b) has been developed, however it is accepted that there are still aspects which could be improved further in the future with additional updates, particularly with improved data collection methods and understanding of the interactions between birds and wind farms. These are listed below.

1. Wind speed data: This model update has taken a step forward from previous iterations of the Band model by including the relationship between wind speed data and both rotor speed and rotor pitch, however there are still improvements which could be made. Due to a lack of clarity in the availability and format of site-specific wind speed data which is available to developers it was decided that in this model update, wind speed would be sampled from a truncated Normal distribution, parameterised by a mean and standard deviation set by the user. In the future, if consensus could be reached on wind data availability and format, a summary of the raw wind speed data could be used, rather than using it to parameterise a sampling distribution. If this were the case, then it would also be possible to programme the model to automatically calculate wind availability from the wind speed data, rather than this being entered manually.

2. Monthly vs. annual input parameters: The current model uses annual estimates for the majority of input parameters such as bird flight speed and percentage of nocturnal activity. It is possible that these may differ between the breeding and non-breeding season, and vary monthly, and in response to wind speed. However, at present it was considered that data of sufficient quality were not available for enough parameters on a monthly basis to warrant including this in the model for all. Should this be the case, including monthly values for all parameters could introduce unrealistic precision into the model; therefore only monthly values were included for bird density and turbine operation time. In the future it might be more appropriate to consider all input parameters on a monthly basis.

3. Linking wind speed and flight speed: Within this model update bird flight speed was not linked to wind speed. This alteration could improve the model, however little data is available regarding bird flight speeds, especially in relation to wind speed, though more flight speed data are becoming available as the number of projects using telemetry e.g. GPS tags, increases . The link between flight speed and wind speed was however included in the model produced by McAdam (2005), therefore it would be possible to include this relationship in future updates, should sufficient data become available.

4. Validate the model: Due to the difficulties associated with collecting collision data offshore, as yet, it has not been possible to validate this model update. This is the case for previous versions of the Band model and also collision risk models in general. In the guidance supplied alongside the 2012 update to the Band model, Band (2012b) highlights that there is likely to be uncertainty as a result of simplifications in the model itself. As an estimate, it is suggested that this may be in the region of 20%. By using the results of projects, such as the bird collision avoidance component of the Offshore Renewables Joint Industry Programme ( ORJIP) in the UK, to validate the model, it may be possible to quantify this uncertainty more accurately and reduce it through further refinements to the model.

5. Sensitivity analysis: Whilst it is possible to perform a manual sensitivity analysis on the model update (results available in Appendix 2), it would be useful in the future to have the utility to perform a sensitivity analysis as a matter of course during the assessment of collision risk. This would offer users the ability to highlight which parameters had the strongest influence on the final collision estimates and consider how best to target data collection in order to reduce uncertainty. It may also enable developers to plan mitigation strategies, for example by demonstrating how using fewer, larger turbines may reduce collision risk.


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