# BMT UK Ltd

## Storm and Calm Persistence

### Persistence Table

Persistence statistics show the likelihood of continuous periods of stormy or calm weather. The probability of the weather remaining calm for a period of time is of vital interest to those planning lengthy marine operations requiring calm weather.

In terms of persistence statistics:

A Storm
A continuous period of time during which the significant wave height is above a defined threshold. The duration of the storm is the time between the wave height rising above the threshold, and it dropping back below the threshold again.
A Calm
A continuous period of time during which the significant wave height is below a defined threshold. The duration of the calm is the time between the wave height dropping below the threshold, and it rising back above the threshold again.

For any chosen threshold wave height, the weather is regarded as an alternation of "storms" and "calms". Persistence statistics are the statistics of the durations of these alternating periods of storm and calm. These statistics can  be presented in one of three ways:

1. Cumulative Probability: This option gives the probability of an existing storm (or calm) persisting for a given period of time. It is important to note that this refers to an existing storm, and does not include the probability of meeting a given wave height at any one time. Thus, for example, if the significant height is at present 5m, and a cumulative probability of 0.32 is marked in the storm persistence matrix against the duration of 10 hours in the 5m column, then this means that there is a 32% probability that the storm will persist at this level (or higher) for a duration of 10 hours. If the same figure was in the calms matrix it would indicate that there is a 32% probability that the sea state will remain at this level (or lower) for a total duration of 10 hours.

2. Number of Occurrences: This option gives the number of times a storm (greater than the threshold wave height) or calm (less than the threshold wave height), and lasting at least the specified duration will occur during a given period of time. Note that in accordance with the usual convention for persistence statistics, the number of occurrences do not include sequences of short durations combining to form longer durations. Thus the numbers for 3 hour durations do not, for example, include the sequence of 4x3 hour durations in one 12 hour duration.

3. Proportion of the Time: This option gives the proportion of the time the total time that is occupied by storms (or calms) with at least the specified duration. For example, if you wished to perform an offshore operation which required a wave height less than 2m,  for a duration equal or greater than 10 hours, and the percentage of time for calms of this threshold and duration was given as 0.34, this would indicate that you would have a 34% chance of arriving in the field during a suitable calm (although part of your required calm period may have already passed).

Any one persistence page shows statistics for either storms or calms in one of these three presentations. The top of the page has a table which has columns for different wave height thresholds, and rows for different durations of storm or calm. The body of the table contains the chosen persistence statistic. The bottom row of the table gives the mean duration of storms or calms for each threshold wave height.

### Persistence Plot

The persistence table is followed by a persistence plot, which shows some of the data from the persistence table. For each table, three plot formats are possible:

1. Matrix: This is is a plot of the body of the persistence table. It has a number of curves for different wave height thresholds, and shows the specified persistence statistic as a function of storm or calm duration.

2. Linear Mean Duration: This shows the variation of mean storm or calm duration as a function of threshold wave height. The mean duration is plotted on a linear axis.

3. Log Mean Duration: This shows the variation of mean storm or calm duration as a function of threshold wave height. The mean duration is plotted on a logarithmic axis.

### Presentation Form

The persistence plot is followed by a form which is used to select different presentations of the persistence data.

The first item is a pulldown menu to select on of the three forms of persistence statistics:

• Cumulative Probability.
• Number of Occurrences.
• Proportion of the Time.

Alongside this menu is a box to enter (in years) the duration to use for the "Number of Occurrences" option. The default value is 10 years. This value is ignored for the other two forms of statistic.

The next item on the form is a second pulldown menu to select statistics for either storms or calms.

This is followed by another pulldown menu to select the format of the persistence plot.

Clicking on the "Show Persistence" button will refresh the page to show the selected statistics.