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#2585 (Error in formula in Cdn10_Lupkes2012 in sbcblk.F90) – NEMO

Opened 3 years ago

Closed 3 years ago

# Error in formula in Cdn10_Lupkes2012 in sbcblk.F90

Reported by: Owned by: dlivings systeam low SBC trunk minor trunk SBC ice drag SI3

### Description

In the current version of NEMO/trunk/src/OCE/SBC/sbcblk.F90 (last changed at [13501]), in subroutine Cdn10_Lupkes2012, there is an error at L1346 in the formula for air-ice drag, or at least an inconsistency with the formula in the comment at L1313 and in the original paper. The exponent (zmu-1._wp) should be just zmu.

(No commits)

### comment:1 follow-up: ↓ 2 Changed 3 years ago by clem

This is not a bug. There is a misunderstanding in the way air-ice drag is used in the code. Wrt Lupkes formulation, we divide the drag by A, hence the factor (mu-1). I describe it in more details hereafter:

The generic air-(ice/ocean) drag described by Lupkes is this one:

```Cd = Cdw * (1-A) + Cdi * A + Ce * (1-A)**(nu+1/(10*beta)) * A**mu
```

Extracting the air-ice drag from it, you find:

```Cd_ice * A = Cdi * A + Ce * (1-A)**(nu+1/(10*beta)) * A**mu
```

The way we use it in the code is without the ice concentration A (because we do not want it to be a cell-average drag). Hence:

```Cd_ice = Cdi + Ce * (1-A)**(nu+1/(10*beta)) * A**(mu-1)
```

### comment:2 in reply to: ↑ 1 Changed 3 years ago by gsamson

• Resolution set to fixed
• Status changed from new to closed

Thanks for explaining it Clément ! I close the ticket

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