NOAA's GFS Model vs Barometers

Introduction

In this page we compare atmospheric pressure at the sea's surface (known as MSL pressure) from NOAA's GFS model with the pressure measured by barometers at Frenchman Island, near Marsden Point on the northeast coast of the North Island and at Timaru on the eastern coast of the South Island, as shown to the right.

The comparison is made in three different ways:
(i) statistical moments;
(ii) a typical times series; and
(iii) spectra.

The analyses were carried out on 1 year of data from 15 July 2004 to 15 July 2005.

Statistical Moments

The table below displays the first through fourth statistical moments for each time series. Let us consider each of these moments in turn

Mean (1st Moment)

We would expect the mean pressure to be higher in the north (nearer the equator), than in the south, but the barometers indicate the opposite. This indicates that the barometers have not been calibrated for mean sea level pressure and have an offset. This may be because they are mounted above sea level. Notice that the GFS model correctly shows higher mean pressure in the north.

Standard Deviation (2nd Moment)

The barometers and the GFS model are in close agreement for the 2nd moment, with the southern site having significantly higher standard deviation.

Statistical Moment	Frenchman Island		Timaru
	Barometer	GFS Model	Barometer	GFS Model
Mean	1013.9	1015.5	1014.2	1012.2
Std Dev	7.73	7.83	11.28	10.67
Skewness	-0.213	-0.195	-0.267	-0.302
Kurtosis	-0.203	-0.207	-0.557	-0.493

Skewness (3rd Moment)

Negative skewness tells us that the troughs are generally deeper than the peaks, which is intuitively correct because high-pressure systems generally last longer and are less extreme than low-pressure systems. The more negative skewness for the southern site indicates deeper low-pressure systems than occur in the north. Skewness is quite sensitive to small differences in the extremes of the signal, so the comparison between barometer and the GFS model is essentially as close as could be expected.

Kurtosis (4th Moment)

Kurtosis indicates the flatness of the peaks and troughs relative to what we would get if pressure were distributed normally (when kurtosis would be zero). Negative kurtosis indicates the peaks and troughs are flatter than normal. Kurtosis is also a good indicator of spikes in the data. A single large spike will result in large, positive kurtosis.

Time Series

A typical month of record is shown in the figure below. The slight offset in the mean of the signals is shown quite clearly by this plot. Notice that almost all the fluctuations recorded by the barometers are also present in the GFS model data.

Spectra

The Fourier spectra of the two sets of signals are shown below. For most of the range of each spectrum, the data from the barometers are almost indistinguishable from the data from the GFS model. There appears to be a noise floor (where the spectrum becomes flat) at frequencies higher than 20 deg/h, indicating the limit of validity of the data. Notice the spike at 15 deg/h in the Frenchman Island spectra, appearing in both the barometer spectrum and the GFS model spectrum. This is the diurnal atmospheric tide, S₁. There is no discernable diurnal atmospheric tide at Timaru. This is because the amplitude of the diurnal atmospheric tide varies with latitude as cos³, thus it is highest at the equator and zero at the poles.