The Revision of Intensity-Duration-Frequency Curves for Barbados

The application of frequency analysis to rainfall data allows for the estimation of rainfall depths and intensities along with their associated return periods. These estimated rainfall depths or intensities and their probabilities of exceedance are important for flood hazard assessments, and the design of drainage infrastructure amongst other water resources management applications.

The Caribbean Institute for Meteorology and Hydrology (CIMH) manages several rainfall stations across the Caribbean inclusive of Barbados with data from these stations being transferred to the CIMH in near real-time to support impact-based forecasting and decision-making - current focus being the disaster management community although other sectoral applications are possible and will be explored in the coming years

This study utilizes the stations on Barbados with supporting data to revise the IntensityDuration-Frequency (IDF) data for Barbados This article (i) outlines the methodology for the development of IDF curves, (ii) demonstrates the application of the methodology at a location of interest, (iii) provides a revision to IDF data for Barbados and (iv) shares limitations with regards to their current application

Data and Methods

Table 1 presents metadata for the rainfall station located at Apes Hill, St James that were used to demonstrate the procedure for IDF data generation. The methodology is outlined below:

Obtain sub-daily rainfall data from target station; Extract annual rainfall maxima corresponding to 5, 10, 15 and 30 minute and 1, 2, 6, 12 and 24 hour durations; Test the extracted rainfall series for outliers, homogeneity and independence and reject unsuitable data series; Rank the data series (lowest to highest) for each duration of interest and calculate the probabilities of exceedance;.

Fit a suitable extreme value distribution (Generalised Extreme Value) distribution to the plotted data points;

Estimate for each duration the annual maximum rainfall depths for the return periods of interest (e.g. 2, 5, 10, 25 and 50 yr);

Fit an appropriate Depth-DurationFrequency (DDF) function to the depthduration data;

Convert the DDF data to Intensity-DurationFrequency (IDF) data if required

In the absence of adequate sub-daily rainfall data, scaling techniques and disaggregation factors may be applied to generate IDF information (Nguyen et al 1998 and Lumbroso et al 2011)

Results

Table 2 presents the annual maxima series for the durations of interest that were extracted from the Apes Hill rainfall data

The maximum 24 hour duration rainfall of 125.5 mm was reported in 2016 while the maximum 1 hour duration rainfall of 56.5 mm was reported in 2017 This highlights the variations of intensity within rainfall events and demonstrates the importance of considering intensities rather than daily rainfall accumulations for design purposes.

Note the 2015 data series shows lower rainfall accumulations for the various durations than is expected due to an incomplete data series As such, the data series failed outlier statistical tests and was removed from the IDF curve development process.

Figure 1 illustrates the fitted GEV distribution for each extreme value rainfall series (see Nguyen et al 1998) on Gumbel plots which are a standard method of representing annual maxima data. The magnitude of the event is plotted on the y-axis and the frequency (return period) plotted on the x-axis using a Gumbel reduced variate scale

The DDF data was extracted from the GEV distribution fits and converted to IDF data.

Table 3 presents the IDF table for the station at Apes Hill The corresponding IDF curves are presented as Figure 2 Each line on the graph represents the likelihood of an event occurring The green line at the top, for example, shows events that have a 1/50 or 2 percent chance of occurring. The red line to the bottom represents events that have a higher percentage chance of occurring , at 1/2 or 50 percent.

Application

IDF curves for Barbados were first published in Lirios (1971) who used nine (9) recording rainfall stations, seven (7) of which had less than ten (10) years of data. Eight (8) of the recording rainfall stations used in Lirios’ study went into disrepair some time ago, hence, updates at these locations are no longer possible.

The procedure showcased above was used by the CIMH to develop revised IDF curves for ten (10) selected locations in Barbados - Halfmoon Fort (St Lucy), Apes Hill (St James), Springvale (St. Thomas), Holetown (St. James), Zhores (St. John), Crab Hill (St. Lucy), Canefield (St. Thomas), Orange Hill (St. Peter), Husbands (St. James) and the Grantley Adams International Airport (Christ Church).

The IDF data produced may be used to generate IDF grid and contour maps for return periods of interest for the varying durations through the application of spatial interpolation techniques The grid demonstrated in Figure 3 was created using a b-spline interpolation technique. Other interpolation strategies such as kriging which preserves values at station locations will be investigated.

Utilizing IDF grids within a GIS environment allows for IDF estimates to be obtained at the locations of interest between station locations to (i) support the estimation of peak flows for engineering design, (ii) provide intensity data for modeling applications and (iii) support flood hazard mapping assessments Notwithstanding, users of the information provided need to be aware of data quality concerns and uncertainties before integrating such data into their applications.

Discussion and Limitations

Ideally, the number of station years required for meaningful frequency analysis should be at least ten (10) years and should be more than or equal to half the return period being estimated. For example, 25 or more years of data would be required to estimate values corresponding to a 50 year return period. Therefore, extrapolating curves beyond their useful range significantly increases uncertainties Currently, the majority of current high-temporal resolution recording rainfall stations across the Caribbean including Barbados have not yet reached this minimum standard With historic stations in a state of disrepair due to a combination of natural hazards and limited resourcing, suitable data availability is limited Further, spatial interpolation of rainfall data is often challenging given the spatial variability resulting from elevation differences and local climatic profiles. Hence, application of any data presented above should be done with due caution in consideration of such limitations especially considering the potential impact on effectiveness and cost of drainage design works

Over the last 1-2 decades, there has been significant improvements regarding the maintenance of local and regional monitoring networks through the work of the CIMH, local stakeholders and the donor community. Continued investments will support the continuous update of IDF data for Barbados and the Caribbean region The CIMH has developed and implemented a procedure that consults its hydrological database, extracts the required data for IDF curve development, performs the requisite statistical tests (e.g. Grubbs, Mann-Kendell), fits the GEV distribution for frequency analysis, calculates DDF data and publishes IDF curve data.

The procedure will be used in the future to generate design rainfall data for flood hazard assessments to minimise the impact of extreme rainfall events on critical infrastructure provided that the stations continue to be maintained through adequate resourcing.

Research continues on the impact of climate change on rainfall intensities in the Caribbean with no definitive trends identified Notwithstanding, the application of IDF data, which is based on an analysis of historical data, for "climate smart" design raises some interesting questions given the likely nonstationarity.

References

Lumbroso, D M , S A Boyce, H Bast, N Walmsley (2011), The challenges of developing rainfall intensity curves and national flood hazard maps for the Caribbean, Journal of Flood Risk Management, Vol 4 (1), 42-52

Nguyen, V. T. V., T. D. Nguyen, H. Wang (1998), Regional estimation of short duration rainfall extremes, Water Science Technology, Vol. 37 (11) 15-19

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