Design Current Profiles Using Empirical Orthogonal Function (EOF) and Inverse FORM Methods
Authors: Forristall George Z. , Cooper Cortis K. 
Published: October 2008

Abstract
In the past, the oil industry has used highly simplified design current profiles. The simplification process produces errors which are typically unimportant in shallow water but the errors can be substantial in deeper water where currents are more complex and some design concepts are sensitive to current. We suggest a new method to develop more accurate current profiles without significantly burdening the design engineer. The method consists of two steps. In the first step, we simplify the current data using Empirical Orthogonal Functions (EOF), a method that accurately expresses complex data with just a few energetic modes. To these modes, we then apply the inverse First Order Reliability Method (FORM) to develop a profile with an n-year recurrence. We describe the EOF and FORM methods and provide some examples of how the analysis applies to real data.

Introduction
Historically the oil industry has based the vertical variation of design current profiles on either simple theoretical formulas or piecewise linear profiles. The latter are usually derived by applying some simplistic vertical averaging to numerical model hindcast results. Figure 1 shows several examples of design profiles given in the codes of API (1993), DOE (1992), and DnV (1991). Note the simple shapes. The magnitudes of the profiles are not important because they reflect local forcing.
These simple design profiles are reasonable for shallowwater and more traditional structures like jackets where waves are a more important load factor then currents. For these cases, the extreme loads occur during extreme storms and the current profiles are relatively simple. Errors in the profiles are of little consequence because the waves dominate the load equation. In deeper water the situation can change, especially for newer concepts like spars and subsystems like risers. In these cases, currents can actually dominate the load equation so simplification of the profile can introduce substantial errors. In addition, the currents tend to be much more complex and less constant with depth. The extreme load may indeed occur during a storm but it may be accompanied by a persistent and strong non-storm generated current. A good example of this condition is found west of Shetlands where there is often a strong (I m/s) current which is largely independent of local wind forcing.
Figure 2 shows some examples of strong, non-storm current profiles measured in various sites around the world. Note the complex profiles.
This paper describes a technique to develop more realistic current profiles with two techniques used in sequence: empirical orthogonal functions (EOF) followed by the inverse First Order Reliability Method (FORM). EOFs are used to reduce a vertical profile into a small number of values, called modes. These are analyzed by the inverse FORM to develop design currents of a specified recurrence interval.
Once the EOF procedure has been used to reduce the data to a few characteristic modes, we apply the inverse FORM to the modal components to derive currents at specified recurrence intervals. The inverse FORM is an elegant way to develop loads from multiple inputs that may be statistically dependent In our case, the inputs correspond to the dominantmodes derived from the EOF.