5.4.1                                Streamline analysis

The third style of analysis that has, for example, been in use at the AMC at Casey Station throughout most of the 1990s, involves merging MSLP analyses over the ocean and coastal regions with a streamline analyses of the surface wind over the continent (Figure 5.4.1.1). This style of analysis provides a meaningful assessment of surface conditions as the MSLP analysis provides marine users with a good estimate of likely wind conditions in those areas devoid of observations and the streamline analysis over the continent provides a useful assessment of likely wind conditions inland. The streamline analysis is superior to the MSLP analysis in that it not only defines the wind flow over the continent but centres of anticyclonicity/cyclonicity are also defined by the flow such that weather systems may be tracked across the continent.

The scarcity of surface data inland continues to compromise the accuracy of the analyses. However, the requirements for forecasting in these regions is also quite low. In order to better analyse conditions over data sparse areas of the Southern Hemisphere numerical model data are frequently used. The very short term forecasts from the models provide a good starting point for the analysis, as they are dynamically consistent and the short term nature of the forecast provides a reliable first guess. For the surface wind field the best model data are the first sigma level wind values. These data are typically at around 70 m above the surface and provide a good approximation to the surface 10 m flow. Figure 5.4.1.2 is an example of the surface flow from the high resolution Australian global model (GASP) displayed in the same style as used on the manual analysis.

One deficiency in the numerical models is the poor representation of orography and the synoptic pressure gradients tend to be too weak. However, as may be seen in the following section, these model fields are still of considerable use.

5.4.2                                Use of model sigma surface data

The MSLP chart remains the primary field for analysis although it has limited use in contributing to the forecast process. Pressure as a meteorological parameter provides users with no useful information, per se, but traditionally has been used to infer surface wind fields, frontal positions and associated cloud. The global models from which the MSLP charts are now obtained provide all these data anyway, rendering the MSLP chart somewhat obsolete. The most useful field in Antarctic operations is the surface wind field and the first sigma level wind data out of the numerical models provides the best guess for this. Figure 5.4.2.1 shows an example first sigma level wind forecast from the GASP model where the first sigma level is set at 0.9910. This places the data at each grid point at a pressure of 0.9910 times the surface pressure, resulting in the sigma surface data always remaining above ground. For example, if the surface pressure was 970 hPa then the first sigma level would be at a pressure of 965.15 hPa, which is about 70 m above the surface. In all respects these data provide the most useful guidance for wind forecasting, even over ocean areas where MSLP is typically a reliable field. As the wind is dynamically calculated, strong ageostrophic flows associated with rapidly developing systems, along with corrections for system speed of movement, are fully defined in the model field providing far more accurate wind information than could possibly be inferred by studying an MSLP prognostic chart.

Figure 5.4.1.2     An example of the surface flow from the high resolution Australian  global model (GASP). (Displayed in the same style as used on the manual analysis shown in Figure 5.4.1.1.)

Figure 5.4.2.1     An example of a 0.9910 sigma level wind forecast from the GASP model.

5.4.3                                Estimating 500–hPa or 700–hPa geopotential heights from AWS observations

5.4.3.1                          The Phillpot Technique for 500–hPa heights

Phillpot (1991) argued for the adoption of the 500–hPa level as relevant for Antarctic analysis. In view of the lack of upper–air observations from the interior of Antarctica, he devised a technique for the derivation of 500–hPa height from AWS surface observations in the Antarctic continental interior. This technique employed a calculation of surface to 500‑hPa layer thickness based on a mean virtual temperature of 0ºC and then adding a thickness correction ΔZ(Ts) to allow for the departure of the true layer mean virtual temperature from 0ºC. (Radok and Brown (1996) refer to this as the “thinning” of the surface to 500–hPa layer.) The technique relies upon the correlation between surface temperature and the surface to 500‑hPa layer‑mean temperature, so it is to be expected that the shallower the layer the more accurate the estimated heights. Phillpot described his results as encouraging for stations above 2.5 km, but not below. The basis of the technique is as follows:

·                         Calculate the geopotential height of the 500–hPa level hydrostatically, assuming the surface to 500–hPa layer has a mean virtual temperature of zero. We define this as Z₅₀₀(0).

·                         Apply a surface temperature dependent correction to this height to derive the actual height of the 500–hPa level. We define this correction as ΔZ(T_s) where T_s is the surface temperature.

·                         Thus the actual height of the 500–hPa level, here defined as Z₅₀₀(T), is estimated from the equation:

Z₅₀₀(T) = Z₅₀₀ (0) – ΔZ(T_s)                                                         Equation 5.4.3.1.1

where Figure 5.4.3.1.1 shows the simple relationship between these variables.

Phillpot used IGY data to develop regression equations for individual sites, relating the surface temperature T_s to ΔZ(T_s). He found a relationship of the form:

ΔZ(T_s) = mT_s + c                                                                                   Equation 5.4.3.1.2

where T_s is in °C, m is given in gpdm °C^–1 and c is given in gpdm.

Phillpot tabulated values of m and c for Byrd, Pionerskaya, Amundsen–Scott, Vostok and Sovietskaya, and appears to have used stations Byrd and Sovietskaya to estimate the variation of m and c with height. (His Figure 3 shows a straight line connecting plots for these two stations and Phillpot reported that he estimated his best fit for the stations available “by eye”.) Assuming a linear variation of m and c between Byrd and Sovietskaya, the following relationship is found:

m = –0.00015h + 0.739                                                                         Equation 5.4.3.1.3

c = 0.052h – 33.8                                                                                               Equation 5.4.3.1.4

where h is in gpdm.

This relationship (Equation 5.4.3.1.3) does not quite yield the results shown in Phillpot's Table 2, since Phillpot appears to have quoted the original values derived from his study where available and the values derived from his best–fit line otherwise. It might also be acceptable to use a line of best fit for stations above 2.5 km, since Phillpot believes his results to be accurate to 4 gpdm only above that level. Using the method of least squares, this yields the following values:

m = –0.0014h + 0.7                                                                               Equation 5.4.3.1.5

c = 0.058h – 35.5                                                                                               Equation 5.4.3.1.6

where h is once again in gpdm. Given the limitations in accuracy of the technique, it is unclear that such a refinement would provide any improvement.

Thus to employ Phillpot's technique for a given AWS, the equations for m and c are solved using the elevation of the AWS. This needs to be done only once for any given AWS or surface observation station, of course. An estimation of Z₅₀₀(T) then follows routinely as:

Z₅₀₀(T) = Z₅₀₀ (0) – ΔZ(T_s) = Z₅₀₀(0) – (mT_s + c)                       Equation 5.4.3.1.7

where Z₅₀₀ (0) is calculated via the usual hypsometric equation:

Z₅₀₀(0) = (RT/g)(ln(Psfc/500))                                                   Equation 5.4.3.1.8

in which: Psfc is the surface pressure; R is the universal gas constant 287.05; T is 273.16K; and g is 9.80665 m s^–1.

5.4.3.2                          Radok and Brown's technique for 500–hPa heights

Radok and Brown (1996) used Phillpot’s IGY data to devise a similar technique for the estimation of 500–hPa heights, although their technique estimates the layer mean temperature rather than the ‘thinning’ of the surface to 500–hPa layer due to departure of the layer mean temperature from 0ºC. Radok and Brown’s approach yields regression equations for all stations used by Phillpot but, as they show in their Figure 1, these equations can be replaced by a single equation with little loss of accuracy. Radok and Brown suggest that their approach should yield more accurate 500–hPa heights. Radok and Brown analysed 3,494 soundings taken from stations ranging in elevation from near mean sea level (e.g. McMurdo) to over 3 km (Vostok) to yield a regression equation for the surface to 500–hPa layer mean temperature:

                                                                       Equation 5.4.3.2.1

where Ts is the surface temperature. In order to estimate Z₅₀₀ it is necessary only to use T_s to estimate the mean virtual temperature between the surface and 500 hPa, then employ that temperature in the hypsometric equation.

Regardless of the method chosen to estimate Z₅₀₀, the estimate is only as good as the knowledge of the AWS elevation. Errors caused by incorrectly specified temperature become small compared to errors in AWS elevation as the elevation of the AWS increases.

The techniques related above are used only in manual analyses of the 500–hPa level, as for numerical analysis the surface conditions may be ingested directly.

5.4.3.3                          700–hPa heights

The limitation of Phillpot's technique to stations above 2.5 km is particularly serious for the case of West Antarctic AWSs, most of which are below 2 km, which lead Phillpot to apply his technique to the estimation of 700–hPa heights (Phillpot, undated, unpublished). In this case, Phillpot used data from Byrd and Little America Stations, collected during the IGY. Phillpot followed the same approach as for his 500–hPa study, thus:

Z₇₀₀(T) = Z₇₀₀ (0) – ΔZ(T_s)                                                                     Equation 5.4.3.3.1

where the correction ΔZ(T_s) is once again estimated as:

ΔZ(T_s) = mT + c                                                                                                Equation 5.4.3.3.2

Two sets of regression equations were derived, each including coefficients for winter, summer, intermediate seasons and for the whole year. His conclusion was that since the estimated height corrections vary little from season to season, sufficient accuracy would result from the use of whole year data. He also suggested that, while root mean square (RMS) errors in the Little America data precluded the use of his technique near sea level, a linear interpolation of his coefficients between the elevations of Byrd and Little America should lead to a reasonable estimate near 1,000 m (~3,300 ft). Phillpot's results are shown in Table 5.4.3.2.1.

Table 5.4.3.2.1     Regression coefficients for use in Equations 5.4.3.3.1 and 5.4.3.3.2.

	Elevation (gpdm)	m	c	RMS error (gpdm)
Little America	4	0.37	–10.70	1.65
Byrd	153	0.18	–4.90	3.70

Phillpot comments that because of the large RMS error in the Little America estimations, use of his technique is not advisable at low elevations. He suggests that a linear interpolation between the m, c and RMS errors at Little America and Byrd should give acceptable estimates of 700–hPa heights at or above 1 km elevation.

The linear relationships between m, c, rms error and height implied by Table 5.3.3.2.1 are:

m = 0.00128h + 0.375                                                                                       Equation 5.4.3.3.3.

c = 0.0389h – 10.86                                                                                           Equation 5.4.3.3.4

rms = 0.0138h + 1.6                                                                                          Equation 5.4.3.3.5

where h is given in gpdm.

700–hPa Height Estimation via Radok and Brown’s Technique in the FROST project

In view of the simplicity of Radok and Brown's technique using a single regression equation for 500–hPa height over a range of elevations it would seem that their technique should be adapted for 700–hPa height estimations. Unfortunately, this is not straightforward because their regression estimated the surface to 500–hPa mean virtual temperature, which is not simply related to the surface to 700–hPa mean virtual temperature. It is simpler to use the Phillpot technique, but one possible approach (rather circuitous) is that used during the FROST project, sketched as follows:

In order to estimate the surface to 700–hPa layer thickness from the surface to 500–hPa mean layer temperature available via the Radok and Brown formula, a constant lapse rate in the two layer surface to 700–hPa and 700–500–hPa was assumed, i.e. lapse rate Γ was defined as:

where K is some constant. After examining mean temperatures and pressures of the surface, 700 and 500–hPa levels from the UCAR RAOB data set, K was assigned the value 1.3. Different values were found for the stations Halley (1.2), Marambio (1.4) and McMurdo (0.8). Since each of the AWS sites of interest for 700–hPa height estimations was over the ice sheets near Byrd, the figure for Byrd was used in the FROST project because there was no basis on which to estimate the variation of K with distance from Byrd.

In order to calculate Z₇₀₀ for each T_sfc and P_sfc, a half interval search technique was then used to find the value of Γ7 required to minimise the difference:

                                                                                     Equation 5.4.3.3.7

between the 500–hPa height obtained assuming a layer mean temperature from the hypsometric equation :

                                                                     Equation 5.4.3.3.8

and that obtained with the assumption of constant lapse rate :

                                                                       Equation 5.4.3.3.9

where the thickness ΔZ of a layer with p0 > p > p1, temperature T₀ at the lower boundary and constant lapse rate Γ within the layer is given by :

                                                                                       Equation 5.4.3.3.10

where R is the gas constant for dry air and g is the standard acceleration due to gravity.

Thus the final value of Γ₇ was used to calculate the 700–hPa height using the surface pressure and temperature and assuming constant lapse rate.

Generally, the results for both the Phillpot or Radok and Brown techniques were close to each other above 1 km elevation, where the Phillpot technique would be expected to be acceptable It would be simpler to use Phillpot's technique in the absence of a study similar to Radok and Brown and focusing on the 700–hPa level.

Regardless of whether the Phillpot technique or a modification of the Radok and Brown technique is used, however, results are dependent on the quality of the AWS data and especially on knowledge of the elevation of the AWS site.