Converting Standard to Station Pressure for Calculating q

Converting Standard to Station Pressure for Calculating q

What and why?

To calculate q we need vapour pressure (e) and station pressure (P). However, at the hourly station level there are a number of stations where P is not reported but humidity (dewpoint temperature) is and there are a number of times where P is of poor quality and so removed by the QC but humidity is of good quality. To maximise the amount of humidity data we decided not to use the simultaneous P (which would be recorded as sea level pressure and so have to be converted to station level anyway). Instead we choose to estimate and average station P using the standard SLP of 1013 and a correction for height of the station in metres:

                                           Pstation=1013- (Z/10)

As this is constant over time we may be adding small errors to q whereby P is not varying in concert. We estimate these errors in the order of ~-0.1 % of q per 1 hPa increase in P (Willett et al., 2008). We assume that pressure will vary above and below the standard station pressure and so essentially cancel out.

The problem is - this equation is not that accurate. It gives a change in P of 1 hPa per 10m. In fact, this is close to 1.1 hPa. So we need to have a better equation.

Main Conclusions:

                           Pstation=1013 * (((meanT - 0.0065Z)/meanT)^5.265)

where meanT is the station climatological monthly meanT in Kelvin and Z is the station elevation in m.

This would bring the errors closer to zero compared to assuming a static temperature for the globe or the 1 hPa per 10m change. Its computationally a little expensive as this will have to be estimated first and breaking hourly data into discrete months including Leap Years is non-trivial. This would remove the seasonal cycle in the errors but maintain a reasonably systematic error year to year which should not affect the anomalies. Around each month there should be times when the pressure goes above and falls below the estimated station pressure and so these errors should largely cancel out.

In q terms the error introduced at the hourly level remains small. The potential errors for a worst case scenario (station elevations of 2000m) show q up to 0.05 g/kg too low when temperatures are below zero and humidities are high, and up to 0.20 g/kg too high when temperatures and humidities are high. In percentage terms this equates to 2.3% too low when temperatures are below zero and humidity is high and to 1.3% too low when temperatures and humidities are high. For the vast majority of stations this will be much smaller as most stations are below 1000m. This should average out over the month as there will be times when the estimated station P will be too high and too low.

Remaining Questions?

Should this be accounted for in an uncertainty model for the absolute values? The current uncertainty model expressed is built upon the anomalies and so does not need to take this in.

Working:

The Smithsonian Meteorological Tables (List 1963) show that at 15 deg C the pressure difference with elevation is as follows:

                      Pstation/Psea=(((288 - 0.0065Z)/288)^5.265) 

To explore this further Table 1 shows changes in station P (Pst) given different station temperatures (stationT) and station elevations (stationZ) in metres. This gives a range of changes in hPa for a 10m change in height from 1.5 at very low temperatures to 1.0 at very high temperatures. There is also a range across elevations for each temperature band. This is 0.16 at very low temperatures reducing to 0.09 at very high temperatures.

Table 1: Change in station pressure (hPa) from standard sea level pressure at different temperature and elevation.

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stationT	Psea	stationZ	Xconstant	powerfactor	Pst/Psea	Pst	delta hPa/10m
-50	1013.25	10	0.0065	5.256	1.00	1011.70	-1.55
-50	1013.25	100	0.0065	5.256	0.98	997.83	-1.54
-50	1013.25	500	0.0065	5.256	0.93	938.05	-1.5
-50	1013.25	1000	0.0065	5.256	0.86	867.44	-1.46
-50	1013.25	2000	0.0065	5.256	0.73	739.10	-1.37
-40	1013.25	10	0.0065	5.256	1.00	1011.77	-1.48
-40	1013.25	100	0.0065	5.256	0.99	998.49	-1.48
-40	1013.25	500	0.0065	5.256	0.93	941.18	-1.44
-40	1013.25	1000	0.0065	5.256	0.86	873.32	-1.4
-40	1013.25	2000	0.0065	5.256	0.74	749.47	-1.32
-30	1013.25	10	0.0065	5.256	1.00	1011.83	-1.42
-30	1013.25	100	0.0065	5.256	0.99	999.09	-1.42
-30	1013.25	500	0.0065	5.256	0.93	944.06	-1.38
-30	1013.25	1000	0.0065	5.256	0.87	878.75	-1.35
-30	1013.25	2000	0.0065	5.256	0.75	759.09	-1.27
-20	1013.25	10	0.0065	5.256	1.00	1011.88	-1.37
-20	1013.25	100	0.0065	5.256	0.99	999.65	-1.36
-20	1013.25	500	0.0065	5.256	0.93	946.72	-1.33
-20	1013.25	1000	0.0065	5.256	0.87	883.77	-1.29
-20	1013.25	2000	0.0065	5.256	0.76	768.03	-1.23
-10	1013.25	10	0.0065	5.256	1.00	1011.94	-1.31
-10	1013.25	100	0.0065	5.256	0.99	1000.16	-1.31
-10	1013.25	500	0.0065	5.256	0.94	949.18	-1.28
-10	1013.25	1000	0.0065	5.256	0.88	888.43	-1.25
-10	1013.25	2000	0.0065	5.256	0.77	776.37	-1.18
0	1013.25	10	0.0065	5.256	1.00	1011.98	-1.27
0	1013.25	100	0.0065	5.256	0.99	1000.64	-1.26
0	1013.25	500	0.0065	5.256	0.94	951.47	-1.24
0	1013.25	1000	0.0065	5.256	0.88	892.77	-1.2
0	1013.25	2000	0.0065	5.256	0.77	784.17	-1.15
10	1013.25	10	0.0065	5.256	1.00	1012.03	-1.22
10	1013.25	100	0.0065	5.256	0.99	1001.08	-1.22
10	1013.25	500	0.0065	5.256	0.94	953.60	-1.19
10	1013.25	1000	0.0065	5.256	0.89	896.82	-1.16
10	1013.25	2000	0.0065	5.256	0.78	791.47	-1.11
20	1013.25	10	0.0065	5.256	1.00	1012.07	-1.18
20	1013.25	100	0.0065	5.256	0.99	1001.50	-1.18
20	1013.25	500	0.0065	5.256	0.94	955.58	-1.15
20	1013.25	1000	0.0065	5.256	0.89	900.60	-1.13
20	1013.25	2000	0.0065	5.256	0.79	798.32	-1.07
30	1013.25	10	0.0065	5.256	1.00	1012.11	-1.14
30	1013.25	100	0.0065	5.256	0.99	1001.88	-1.14
30	1013.25	500	0.0065	5.256	0.94	957.44	-1.12
30	1013.25	1000	0.0065	5.256	0.89	904.15	-1.09
30	1013.25	2000	0.0065	5.256	0.79	804.76	-1.04
40	1013.25	10	0.0065	5.256	1.00	1012.15	-1.1
40	1013.25	100	0.0065	5.256	0.99	1002.24	-1.1
40	1013.25	500	0.0065	5.256	0.95	959.19	-1.08
40	1013.25	1000	0.0065	5.256	0.90	907.48	-1.06
40	1013.25	2000	0.0065	5.256	0.80	810.83	-1.01
50	1013.25	10	0.0065	5.256	1.00	1012.18	-1.07
50	1013.25	100	0.0065	5.256	0.99	1002.58	-1.07
50	1013.25	500	0.0065	5.256	0.95	960.82	-1.05
50	1013.25	1000	0.0065	5.256	0.90	910.61	-1.03
50	1013.25	2000	0.0065	5.256	0.81	816.56	-0.98

So we have a few options:

Use global average temperature (14.5 deg C): this will give a range change in hPa of 1.2 to 1.09 per 10m across the elevations of 10 to 2000m (Table 2). The realistic potential error here in station P from not using actual temperatures could be: -21.96 hPa compared to station pressure at 50 deg and 2000m; -0.13 hPa compared to station pressure at 50 deg an 10m; 55 hPa compared to station pressure at -50 deg and 2000m; and 0.35 hPa compared to station pressure -50 deg and 10m. So, differences are largest at height and for cooler temperatures (obviously). 

Table 2: Change in station pressure (hPa) from standard sea level pressure at 14.5 deg C and a range of elevations.

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stationT	Psea	stationZ	Xconstant	powerfactor	Pst/Psea	Pst	delta hPa/10m
14.5	1013.25	10	0.0065	5.256	1.00	1012.05	-1.20
14.5	1013.25	100	0.0065	5.256	0.99	1001.27	-1.20
14.5	1013.25	500	0.0065	5.256	0.94	954.51	-1.17
14.5	1013.25	1000	0.0065	5.256	0.89	898.55	-1.15
14.5	1013.25	2000	0.0065	5.256	0.78	794.60	-1.09

However, in terms of the error introduced into q, this remains small. Not all ranges of temperature (-50 to 50 deg) are plausible at all elevations. I've limited analysis here from -10 to 30 deg. I've also explored a range of humidities from a vapour pressure of 1 to 30 - again, only plausible points are shown so there are no points for a vapour pressure of 5 hPa or above when the temperature is -10 deg. Specific humidity calculated using station pressure converted using a temperature of 14.5 deg (global mean) as opposed to the actual temperature is shown in Figure 1 (g/kg) and Figure 2 (%) for a plausible range of points. This shows that the potential errors are small - up to 0.05 g/kg too low when temperatures are below zero and humidities are high, and up to 0.20 g/kg too high when temperatures and humidities are high. In percentage terms this equates to 2.3% too low when temperatures are below zero and humidity is high and to 1.3% too low when temperatures and humidities are high.

Figure 1: Error in specific humidity (in g/kg) from calculating using station P converted from standard P (1013.25) assuming mean temperature of 14.5 deg compared to -10 deg, 0 deg and 30 deg at a range of vapour pressures (1 to 30) and station elevations (10 to 2000m). Only plausible points are shown e.g., there is no value for 30 deg - 14.5 deg at 30 hPa vapour pressure at 2000m elevation as 30 degrees with very high humidity would never occur at such high elevation. Similarly, at very low temperatures the humidity would never reach above 10 hPa and so these are not shown.

Figure 2: Error in specific humidity (as a percentage) from calculating using station P converted from standard P (1013.25) assuming mean temperature of 14.5 deg compared to -10 deg, 0 deg and 30 deg at a range of vapour pressures (1 to 30) and station elevations (10 to 2000m). Only plausible points are shown e.g., there is no value for 30 deg - 14.5 deg at 30 hPa vapour pressure at 2000m elevation as 30 degrees with very high humidity would never occur at such high elevation. Similarly, at very low temperatures the humidity would never reach above 10 hPa and so these are not shown.

Errors would be fairly systematic should station temperatures be constantly above or below 14.5 degrees. If they move around then over the year these may cancel out but even on the monthly scale these may introduce an annual cycle in the errors. This shouldn't affect the anomalies too much.

Use climatological station mean temperature:

This would bring the errors closer to zero but would take a fair bit more computation. There will likely be errors in the climatological temperature but its probably still better than using a single value for the globe. Errors would be fairly systematic, especially in terms of the anomalies and possibly have a strong annual cycle.

Use climatological station mean temperature for the month:

This would bring the errors even close to zero but would be computationally quite expensive. This would remove the seasonal cycle in the errors but maintain a reasonably systematic error which should not affect the anomalies. Around each month there should be times when the pressure goes above and falls below the estimated station pressure and so these errors should largely cancel out.

Use actual station mean temperature for the month:

This would be very slow computationally as each individual month would have to be treated separately. This would also remove the systematic nature of this error which may make it harder to disentangle at a later date.

References:

Willett, K. M., Jones, P. D, Gillett, N. P. and Thorne, P. W., 2008: Recent changes in surface humidity: development of the HadCRUH dataset. Journal of Climate, 21, 5364-5383.

List, R. J., 1963: Smithsonian Meteorological Tables. Vol 114. 6th Ed. Smithsonian Institution, Washington DC. pp268