# N2 with runlm()

**Dan Kelley Blog/R**, and kindly contributed to R-bloggers]. (You can report issue about the content on this page here)

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# Introduction

The default `swN2()`

calculation in Oce uses a smoothing spline. One disadvantage of this is that few readers will know how it works. A possible alternative is to compute d(rho)/dz using the slope inferred from a running-window linear regression. Such a slope is provided by the new Oce function `runlm()`

, which is tested here. (Note that `runlm()`

is new enough that its argument list may change as a result of tests like the present one.)

# Methods

1 |
library(oce) |

```
## Loading required package: methods
## Loading required package: mapproj
## Loading required package: maps
```

1 2 3 4 5 6 7 8 9 10 11 |
data(ctd) rho <- swRho(ctd) z <- swZ(ctd) drhodz <- runlm(z, rho, deriv = 1) g <- 9.81 rho0 <- mean(rho, na.rm = TRUE) N2 <- -g * drhodz/rho0 plot(ctd, which = "N2") lines(N2, -z, col = "blue") legend("bottomright", lwd = 2, col = c("brown", "blue"), legend = c("spline", "runlm"), bg = "white") |

# Results

The reuults look similar *but* see the question below.

# Conclusions

Quantitative measures could be calculated of course, but this first test suggests that the benefits of `smooth.spline()`

may be had with `runlm()`

.

**Caution.** `runlm()`

is still so young that its argument list and action are likely to change at any time. For example, as I was writing this posting I changes the order of the last two arguments, I made the default `window="hanning"`

, and I changed the auto-selection of `L`

; these changes seemed more sensible for application to things like N2.

# What lengthscale to use?

It may be helpful to determine just how well the two methods can match.

1 2 3 4 5 6 7 |
N2 <- swN2(ctd) N2fromderiv <- function(L) { -g * runlm(z, rho, L = L, deriv = 1)/rho0 } best <- optimize(function(L) sqrt(mean((N2 - N2fromderiv(L))^2)), interval = c(1, 100)) print(best) |

```
## $minimum
## [1] 6.161
##
## $objective
## [1] 7.854e-05
```

1 |
N2best <- N2fromderiv(best$minimum) |

This best-matching estimate is the red line.

1 2 |
plotProfile(ctd, "N2") lines(N2best, ctd[["pressure"]], col = "red") |

# Questions

- Why is there a systematic offset in the last figure?

# Resources

- Source code: 2014-04-07-N2-runlm.R

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**Dan Kelley Blog/R**.

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