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# Thickness and its uses

## Thickness -- a short explanation!

'Thickness' is a measure of how warm or cold a layer of the atmosphere is, usually a layer in the lowest 5 km of the troposphere; high values mean warm air, and low values mean cold air.

It would be perfectly feasible to define the average temperature of a layer in the atmosphere by calculating its mean value in degrees C (or Kelvin) between two vertical points, but an easier, practical way to measure this same mean temperature between two levels can be gained by subtracting the lower height value of the appropriate isobaric surface from the upper.
Thus one measure of thickness commonly quoted is
= height (500 hPa surface) - height (1000 hPa surface) [ for those of you, like me, too old to catch up with all the changes the world brings, millibars = hPa!, so 500 hPa is exactly the same as 500 mb. ]

In practical meteorology, the most common layers wherein thickness values are analysed and forecast are: 500-1000 hPa [ abbreviated to TT or TTHK] ; 850-1000 hPa; 700-1000 hPa; 700-850 hPa and 500-700 hPa. By subtracting the lower (height) value from the upper value, a positive number is always gained. The 500-1000 hPa value is used to define 'bulk' airmass mean temperature, and can be seen on several products available on the Web. The other 'partial' thicknesses are used for special purposes, for example, the 850-1000 hPa thickness is used for snow probability and maximum day temperature forecasting, as it more accurately defines the mean temperature of the lowest 1500 m (5000 ft) or so of the atmosphere.

Advection is simply the meteorologists word for movement of air in bulk. When we talk about warm advection, we mean that warm air replaces colder air, and vice-versa. These 'bulk' movements of air of differing temperatures can be seen very well on thickness charts, and differential advection, important in studies of stabilisation / de-stabilisation, can also be inferred by considering advection of partial thicknesses.

If you pull up thickness charts from the web, it it useful to highlight the isopleths of thickness, and work out, from either the mslp pattern, or the 500 hPa pattern, whether cold or warm advection is taking place. It should be possible with practice to find warm and cold fronts (tight thickness pattern), and areas where the thermal gradient (spacing of thickness lines) is changing - note particularly areas where developments tend to decrease spacing of thickness lines -->> increased potential for atmospheric development.

Total Thickness (500-1000 hPa) isopleths (when shown in combination with other fields) are conventionally drawn as long-dash lines, with the values either thus [540] or white numerals on a black/solid rectangle. (Where there is no conflict, i.e. the thickness isopleths are the only ones shown, then usually sold/continuous lines are used.) Certain isopleths are considered 'standard', mainly for historical reasons: They are listed hereunder, with the colour code convention used by the UK Met.Office on internal charts.
474 - red 492 - purple 510 - brown 528 - blue 546 - green 564 - red 582 - purple

Operational charts usually show isopleths at 6 dam intervals but some international forecast output will only have the standard isopleths as above: for example the UKMO 2-5 day charts. (If you want to compare forecast values over and near the British Isles with extremes, see here).

Can the 500-1000 hPa patterns be used to infer the snow risk? Well, yes they can, but because the layer is so deep -- some 5 km, or 18000 ft of the lower atmosphere, its not a good indicator. As a VERY rough guide the following may be used:

Rain and snow are equally likely when the 500-1000 hPa thickness is about 5225 gpm (or 522 dam). Rain is rare when the 500-1000 hPa thickness is less than 5190 gpm. Snow is extremely rare when the 500-1000 hPa thickness is greater than 5395 gpm.

## Thickness --- a much longer explanation!

[ Q ] Thickness? ....thickness of what?

[ A ] From time to time in meteorology newsgroups, the word 'thickness' is used, particularly when talking about snow probability, or the prospect of warmer, or colder weather generally. If you simply want to remember that 'Thickness' is a measure of how warm or cold a layer of the atmosphere is, usually a layer in the lowest 5 km of the troposphere, and that high values mean warm air, and low values mean cold air, then you can ignore the rest of this FAQ. If you wish to know a little more, read on!

[ Q ] What is 'Thickness' and how is it measured?

[ A ] Although it would be perfectly feasible to define the average temperature of a layer in the atmosphere by quoting/calculating its mean value in degrees C (or Kelvin) between two vertical points, from the early days of upper air meteorology, it was realised that from the hydrostatic equation, an easy to calculate measure of this same mean temperature between two levels could be gained by subtracting the lower height value of the appropriate isobaric surface from the upper. (** see alternative name below)

The hydrostatic equation, in its simplified form, is -dp/dz = pg/RT ...... Eq(a)

here:
dp being the pressure difference across two defined levels
dz the height difference between those two levels
g the gravitational constant
R specific gas constant for dry air
T average temperature in layer (strictly average virtual temp.)

Eq (a) states that the change of pressure with height (above a point where the total pressure of the column is p), is governed by the mean temperature over the vertical distance involved.
Thus in cold air/low T values, -dp/dz is larger than in warm air/high T. ... or putting it another way, lets start out at 1000 hPa and ascend vertically; in cold air, you would reach the level of 500 hPa sooner (greater rate of change of p) than in warm air. Thus the vertical distance from the level of 1000 hPa to the level of 500 hPa is less in cold air than in warm air
....cold air => low thickness values;
....warm air => high thickness values.
(for a more rigorous treatment/discussion of the hydrostatic equation, see any good textbook on meteorology - there is a list below).

Thickness can be calculated from the heights reported on a radio-sonde ascent, or a thermodynamic diagram can be used to add up the partial thicknesses over successive layers to achieve the net (total) thickness.

An example of the former would be
500 hPa height = 5407 m
1000 hPa height = 23 m
Thickness = 5407-23 = 5384 m (or 538 dam)

Careful note must be made when the height of the 1000 hPa surface is below msl thus: 500 hPa height = 5524 m
1000 hPa height = - 13 m
Thickness = 5524 -(-13) = 5537 m (or 554 dam)

[** NOTE: you will also see 'thickness' charts referred to as 'Relative Topography' charts for this reason - this is especially so on web output from centres in mainland Europe.]

[ Q ] What are the most common layers through which the thickness is analysed / forecast and what are they used for?

[ A ] In practical meteorology, the most common layers wherein thickness values are analysed and forecast are: 500-1000 hPa [ abbreviated to TT or TTHK] ; 850-1000 hPa; 700-1000 hPa; 700-850 hPa and 500-700 hPa.
By subtracting the lower (height) value from the upper value, a positive number is always gained. Some values are quoted in metres, and others dekametres (tens of metres), dependent upon the use to which the value is put. In general, when dealing with the lower atmosphere, metres are used to better refine the output to the inferred surface parameter (e.g. maximum temperature), whilst for the deeper layers, dekametres (10's of metres) are sufficiently accurate.)

500-1000 hPa: (also known by some meteorologists as the 'total' thickness, for historical reasons). This is used to define the broad average temperature for the lower half of the troposphere. From the hydrostatic equation (see Eq(a) and reference (1) below),

Z2 - Z1 = RT/g * ln(p1/p2) ..... Eq(b)

replace p1 and p2 by 1000 hPa and 500 hPa respectively
therefore ln(2) = 0.69
R = universal gas constant for dry air = 2.87 * 10^2 kg^1 K^1
g = 9.81 ms^2
T = mean temperature through layer (K)
Z1, Z2 = heights of isobaric surfaces p1,p2 (in metres)
by substitution, and allowing for the fact that T in the original equation is Kelvin, we have, for the 500/1000 hPa layer....
mean temperature (degC) = (Thickness/20.3) - 273 ..... Eq(c)

thus for 5640 m thickness --- this represents a mean T = +5 degC
5460 m -4
5280 m -13 and so on.
and further, it can be seen that for 10 m (1 dam) change of thickness in this layer, this represents a change in mean temperature through the layer of 0.5 degC. It is useful to remember this when, for example, looking at the Royal Met.Soc 'Weather Log' which shows the deviation from normal of thickness values over a large part of the northern hemisphere ... an anomaly of + 4 dam doesn't mean quite as much as one of + 2 degC!

[ Using this relationship, it is also possible to come up with a crude approximation to the expected surface maximum temperature - for more on this, see here.]

850-1000 hPa: This is useful for defining the temperature structure in the lowest 1500 m or so of the atmosphere, and can therefore be used in such things as rain/snow prediction, maximum temperature forecasting etc.

700-1000 hPa: Similar to 500-1000 hPa but focussed rather more on the lowest 3 km of the atmosphere and therefore an attempt to combine the broader measure of the 500-1000 hPa and the finer details obtained by layers nearer the earth's surface.

500-700 hPa/700-850 hPa: Used in studies of differential thermal advection, particularly when considering possible convection, degrees of instability etc.

[ Q ] What is the historical relevance of 'gridding'?

[ A ] Before the advent of super-fast main-frame computers, and the better understanding of the character and physics of the upper air, upper wind forecasts up to 24 hours ahead depended upon a process known as 'gridding' - the arithmetical manipulation of layer thicknesses. A surface/msl pressure chart would be analysed, then the isobaric pattern would be converted to equivalent 1000 hPa height contours, taking into account the temperature if this deviated significantly from the 'standard'; the thickness pattern would be drawn, using thermal wind relationships and known patterns associated with frontal systems, then the 1000 hPa and thickness patterns overlaid, and at the intersection of the 'grid' of such contours, the resultant 500 hPa (or other height, depending upon the thickness used) could be achieved, using the relationship that h(500) = h(1000)+h'(thickness).
This gave better results than just using the poor network of actual 500 hPa heights/winds, and by using thicknesses (i.e. differences), the systematic errors of differing radio-sondes could be effectively ignored .

More importantly, to produce a forecast upper air chart, first the forecast surface pattern was produced using known empirical relationships/rules of thumb etc., then the thickness pattern adjusted to fit around this forecast pattern, keeping the correct relationship found both in analysis and conceptual models in mind, then again by gridding, or graphical addition of the 1000 hPa contours and the thickness pattern, the upper contour pattern could be produced. It was essentially this process that was used to forecast all upper winds until the work could be put on a more rigorous/mathematical basis by the solving of complex equations using the big number- crunching machines from the late 1960's. (Incidentally, you can tell the vintage of someone working in meteorology by whether they refer to the parameter 500-1000 hPa thickness as the Total thickness ... a hangover from these days of gridding charts.)

Further reading: For a useful summary of this method of upper wind forecasting, see Ref:(2) and for a historical perspective, see Ref:(4) "Bomber Command upper air unit" - RAS Ratcliffe.

[ Q ] Does gridding have any relevance today?

[ A ] The reverse of gridding (graphical addition of thickness values to a lower surface height), is de-gridding, and can be a useful technique to master, both to achieve a surface pattern from a 500 hPa/Total Thickness chart, and to attain a simplified conceptual idea of development due to upper air processes.

From the definition of Total Thickness (h') where: h' = h(500) - h(1000) ..... Eq(d)

where h' = total thickness
h(500) = height of the 500 hPa barometric surface
h(1000) = height of the 1000 hPa barometric surface

re-arranging Eq(d), we have h(1000) = h(500) - h' ... Eq(e)

At levels near msl, the approximate relationship [ see cautionary note below # ] holds that a difference of 6 dam = a difference of 8 hPa. ... Eq(f)

Thus, from Eq(e), if at a certain point on a chart, a 500 hPa contour of 540 dam, is crossed by a thickness isopleth of 528 dam, the value of h(1000) = 540-528 = +12 dam. From Eq(f), this relates to an isobaric value of (12/6)*8 = +16 hPa (or 1000+16 = 1016 hPa) All other intersections of the 540 hPa/500 contour, and the 528 thickness isopleth yield the same value. Consideration of other intersections will build up a pattern of 1000 mb (and hence msl) values, and the surface pattern can then be inferred from these two fields.
We can go further, and see that it is clear from Eq(e) that by either decreasing the 500 hPa contour value (trough approaching), or increasing the thickness values (warm advection), the height of the 1000 hPa surface will lower, and because 1000 hPa and mslp are linked, mslp will lower===> development. Where both terms are strong (omega development, whereby an upper short- wave trough engages an area of strong warm advection), then explosive cyclogenesis is possible, all other factors being suitable. This is of course a very simplistic explanation of development, but it is a useful conceptual idea to keep in mind when trying to interpret upper air charts.

[ # The relationship 6 dam=8 mbar is a very approximate one, and was accepted at the time because upper air charts were drawn to 6 dam intervals, surface charts to 8 mbar intervals (or multiples thereof), and accepting the inferred 0.75 dam per millibar (i.e. 6/8) relationship kept things simple. In reality, using the hydrostatic equation (Eq(b) above), for average mean sea level pressure of 1013mbar, average surface temperature of 15degC and taking a narrow 'slice' of the air around mslp, then the true value is 0.83 dam/mbar: other values are 0.80 dam/mbar for mean temperature 0degC and 1000mbar, and at 20degC and 1000mbar, it would be 0.86]

[ Q ] How are thickness isopleths shown on synoptic charts?

[ A ] Total Thickness (500-1000 hPa) isopleths are conventionally drawn as long-dash lines, with the values either thus [540] or white numerals on a black/solid rectangle. Certain isopleths are considered 'standard', mainly for historical reasons, and are coloured (in UK Met.O use) according to the following convention):
474 - red
492 - purple
510 - brown
528 - blue
546 - green
564 - red
582 - purple
Operational charts usually show isopleths at 6 dam intervals but some international forecast output will only have the standard isopleths as above: for example the Bracknell 2-5 day charts.

[ A ] Advection is simply the meteorologists word for movement of air in bulk. When we talk about warm advection, we mean that warm air replaces colder air, and vice-versa. These bulk movements of air of differing temperatures can be seen very well on thickness charts, and differential advection, important in studies of stabilisation/de-stabilisation, can also be inferred by considering advection of partial thicknesses.

Example:

If you pull up thickness charts from the web, it it useful to highlight the isopleths of thickness, and work out, from either the mslp pattern, or the 500 hPa pattern, (or indeed any wind in the layer) whether cold or warm advection is taking place. It should be possible with practice to find warm and cold fronts (tight thickness pattern), and areas where the thermal gradient (spacing of thickness lines) is changing - note particularly areas where developments tend to decrease spacing of thickness lines -->> increased potential for atmospheric development. See also the section relating to thermal winds

Below, is an example of a mslp and thickness chart drawn from the NWS site. Red (warm) and blue (cold) arrows show some areas of significant advection.

[ Q ] What about the various patterns of thickness isopleths?

[ A ] The most obvious patterns that the thickness isopleths can take up look very like those you would see on a surface/isobaric chart: highs, lows, troughs and ridges. A closed high-value contour, usually labelled 'W' is referred to as a warm dome; a closed low-value contour (or series of same), labelled 'K' is a cold pool. The 'W' and 'K' denote WARM and KALT respectively - possibly from the Norwegian/German roots of much of the research into upper air patterns. Cold pools are especially important, being often the first indications that the potential for small/mesoscale deep and vigorous convective activity exists, given a suitable trigger action and sufficient moisture. ( They are sometimes not resolved by NWP suites adequately either, particular those with long grid lengths. ) The horizontal spacing of thickness isopleths is also a useful indicator of the potential for development. Close spacing shows that cold air lies adjacent to warm air -- no doubt with an attendant frontal surface. More importantly, the fact that such a baroclinic zone (surfaces of temperature and pressure intersecting at an angle) exists, means that the potential for development is strong -- a slight displacement, i.e. forcing by a high level jet streak, will lead to substantial falls of pressure and consequent 'weather'.
(Examples of all these features, with further notes, can be found by clicking here.)

Meteorologists will always play close attention to zones of 'tight' thickness contouring for this reason. Troughs and ridges denote tongues of cold and warm air respectively, and, from work by RC Sutcliffe (& others) during and after the Second World War, they can also be used to infer the magnitude and sign of development on the surface. The details of the mathematics are beyond this FAQ, but it is only necessary to recognize the patterns as below:

[ Q ] Can the 500-1000 hPa patterns be used to infer the snow risk?

[ A ] Until the advent of NWP suites capable of using model variables to routinely predict the 850-1000 hPa partial thickness (the one now commonly used in the UK to assess likelihood of snow - see below), the 500-1000 hPa total thickness was used much more extensively than now. In the 1950's and 1960's, some studies were published which attempted to refine the TTHK association with snow/rain prediction ... the results are presented below BUT REMEMBER, better predictors are available and should be used where possible.

(1) Lamb: Q Jnl R.Met.Soc. 1955 Critical value for equal probability of rain and snow(NW Europe)

Average: 527 dam (extremes: 521 to 546)
Established snowfields: 536 dam
Windward edge of snowfields: 528 dam
Seas with SST around 10degC and over windward coasts: 523 dam

Lamb's analysis was undertaken for the whole of NW Europe, including places like Riga and Stockholm, which may explain the difference in the average figure from that in the following section. However, Lamb did make a more detailed analysis for inland stations in the British Isles, where he found that when there was snow lying, the critical values were 5305-5335 gpm, and with no snow lying 5225 gpm, which accords more with Murray below)

(2) Murray: 1959 Using an analysis for the UK only, found the following:

Rain and snow are equally likely when the 500-1000 hPa thickness is about 5225 gpm (or 522 dam)

Rain is rare when the 500-1000 hPa thickness is less than 5190 gpm

Snow is extremely rare when the 500-1000 hPa thickness is greater than 5395 gpm; it is rather uncommon when the value is greater than 5305 gpm.

A personal view here, but I have always regarded the 522 dam isopleth as a better 'first guess' at snow vs rain than the 528 value for frontal precipitation. Indeed, I joined the Met.Office at a time when TTHK were still being extensively used for this purpose, and 522 was regarded as the 'snow-line'

(3) Murray: 1959 Also carried out a more detailed investigation using a combination of predictors, the 500-1000 hPa TTHK, the surface (screen) temperature and the height of the freezing level. (I have only shown the TTHK/screen temp relationship as this is the most useful one for those with access to WWW met.products.) He presented the results in graphical form, but for ease of use, I have converted them to tabular format, using the 'standard' TTHK values. The use of a graph implies greater precision than is usual anyway.

(a) percentage probability (P) of type of precipitation in relation to surface temperature and 500-1000 hPa thickness.

 SCREEN TEMPERATURE (degC) >> -1 0 1 2 3 4 TTHK (dam) 516 A A A A A A 522 A A B C C C 528 A B C C D D 534 A B C D D D

A is P >90%
B is 90% >P> 50%
C is 50% >P> 10%
D is P< 10%

In critical rain/snow situations, one of the variables that is difficult to forecast is the screen temperature. Therefore this method is not the answer it may at first sight seem.

(4) Boyden .

In the course of work to compare various predictors, Boyden gave the following figures. 500-1000 hPa TTHK

5180 gpm: 90%
5238 gpm: 70%
5258 gpm: 50%
5292 gpm: 30%
5334 gpm: 10%

In the course of this work, Boyden confirmed what others have already pointed out, that the 500-1000 hPa thickness parameter is the poorest discriminator for rain/snow. The best was height of freezing level and surface temperature, both difficult to forecast in 'critical' situations, and the next best/least worst was the 850-1000 hPa value, though Boyden devised the correction 'factor' that we all now use to take account of mean sea level pressure and local height.

[ Q ] So, how are the 850-1000 hPa values used.

[ A ] This parameter can be used in several ways, the two of most use to the 'bench' forecaster are: (1) calculation of the risk of rain vs. snow, and (2) forecasting the daytime maximum temperature.

(1). Because the layer from 1000 hPa to 850 hPa covers the lowest 1500 metres or so of the atmosphere, it is better suited to deciding on which phase precipitation will reach the ground ( i.e. whether snow will melt to sleet or rain), than the 'total' thickness layer 500-1000 hPa. Statistical relationships have been produced:

The following are un-adjusted critical values and adjusted values for the 850-1000 hPa partial thickness found by statistical analysis: snow probability:
Probability:............................90%.....70%.....50%.....30%.....10%

It is important to remember that when mslp values differ markedly from 1000 hPa, or the height of a station/area differs greatly from msl, a correction has to be made to the partial thickness before assessing the snow risk. Also, the partial thickness only takes into account the mean temperature of the lowest 250 hPa or so of the atmosphere and not the humidity, which is of vital importance for accurate snow prediction. Downward penetration of snow is greatly aided when precipitation falls into dry air.

Boyden found that the following correction should be made to the partial thickness (850-1000 hPa): (Z - h)/30

where Z: height in metres of the 1000 hPa surface above msl
h: height in metres of the ground asl.
... and then the second line of critical values used in the table above.

(2). The 850-1000 hPa is a very good layer within which to determine the air mass likely to affect your station and therefore its use to work out the potential daytime maximum temperature has long been recognised. One such, after Callen and Prescott, relates the partial thickness values.... to the cloud classification for the day ahead.

The relationship between 850-1000 hPa thickness (h*) and the unadjusted maximum temperature (Tu) is given by: Tu = -192.65 + 0.156h* ... Eq(g)

An adjustment is then added to this figure, depending upon forecast 'cloud class' and the time of the year.

The four cloud classes are:(simplified)
Class 0: Low and medium cloud generally less than half cover. High cloud not overcast. Fog only around dawn, if at all.
Class 1: Roughly 50% cloudiness. If fog occurs, it clears slowly during the morning.
Class 2: Mainly cloudy. If fog occurs, clears by midday, but slowly.
Class 3: Overcast with rain/snow etc. Persistent Fog.

Then the following matrix can be used to find the adjustment to be added to Tu. (Whole values degrees C only)

 MONTH CLASS
 0 1 2 3 JAN -4 -4 -5 -5 FEB -3 -3 -4 -5 MAR -1 -2 -3 -4 APR +1 0 -1 -2 MAY +2 +1 0 -1 JUN +4 +3 +1 0 JUL +4 +3 +1 0 AUG +3 +2 +1 0 SEP +1 0 -1 -1 OCT -1 -1 -2 -3 NOV -2 -3 -4 -4 DEC -4 -4 -5 -5

The original work was based on maxima recorded at Gatwick airport, using upper air ascents (12Z) from nearby Crawley radio-sonde .. both sites now no longer providing the appropriate data. They should NOT be used for latitudes well away from the south of England, particularly in the 'winter half-year', when insolation values (due to differing sun angle and daylength parameters) will differ markedly with latitude.
Also, where marine influence is strong then the values will be highly modulated by local sea surface temperatures.
There are a series of graphs, from which it is technically possible to read off the correction to decimals of a degree, and to refine the correction dependent upon the position in the month, but for practical meteorology, these will do!