Table 1. East Road construction alternatives

||||Details|
|---|---|---|---|
||Scenario|Comine Sement||
|||g<br>Length(km)|Specifications|
||Status Quo|||
|0|(SQ)<br>(no upgrading)|41.533|Gravel surface with earth drains for all segments|
||Medium Desin|29.546|Gravel surface with earth drains for segments with <9% grade|
|1|g<br>(MD)|7.335<br>4.652|Bituminous sealed surface with lined drains for segments from 9-15% grade<br>Cement concrete surface with lined drains for segments with >15%grade|
||Hih Di|22.355|Gravel surface with earth drains for segments with <6% grade|
|2|g esgn<br>(HD)|14.526|Bituminous sealed surface with lined drains for segments from 6-15% grade|
|||4.652|Cement concrete surface with lined drains with >15%grade|
||Sealed Long,|25.34|Gravel surface with earth drains for shorter or lower-gradient segments|
|3|Steep Sections<br>(SLS)|16.193|Bituminous sealed surface with lined drains for long, steep sections where<br>road segments withgradients of 6% or above extend for 250 meters or more|

# B. Climate Events Likely in Malaita

Rainfall data specifically for Malaita are not currently available but, based on expert input, a set of probable hazard events was selected as a basis for modeling the expected effects on the current road and each of the proposed upgraded road alternatives over the 30-year lifespan of the road. These events include the following three heavy rainfall hazards with varying intensities.

- A high intensity rainfall with a return period<sup>34</sup> of 3 years;

- An extreme intensity rainfall with a return period of 10 years; and

- A catastrophic rainfall with a return period of 30 years.

While these hazards certainly do not capture all the natural risks to which the road would be subject, they represent events that typically render roads unpassable in Malaita.

Note that it would be wrong to assume that a 3-year rain event will occur only once in 3 years. In fact, any of the rainfall events listed above could happen in a single year. The annual probability of occurrence (often referred to as the Annual Exceedance Probability) is simply the inverse of the return period. For example, a rain event with an associated return period of 1 in 3 years has a probability of occurrence, in any given year, of 1/3 or 0.33 (or 33%).<sup>35</sup> The probability (P) of getting (M) rainfall events within a specific (N) years period is described using the binomial probability mass function as it follows a binomial distribution as shown below Table 2 summarizes the calculations for the three type of rain-events over a 30-year time period. Based on these results, if the decision maker adopts a probability threshold of 50%, the number of rain-events likely in the 30-year period would be 10 for 3-year rain-events, 3 for 10-year events and 1 for 30-year events. Alternatively, should a more conservative probability of 30% be utilized, the number of events would be 12, 5 and 2 for the 3-, 10- and 30-year events, respectively. For an illustration purpose, this paper uses a probability threshold of 50%.

> 34 A return period is an estimate of how long it will be between rainfall events of a given magnitude.

> 35 Probability is expressed in mathematical terms and can assume a value of 0, 1 or any value in between. A probability of zero (p=0) indicates that an event has no chance of occurring while a probability of one (p=1) indicates that an event is certain to occur.

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