## Estimating the dewpoint

 E. Linacre 6/'99

Table 6.1 in the text (1) was derived from a diagram in a previous book (2, Fig 3.10). That in turn was contrived from a collection of longterm average monthly mean values of daily extreme temperatures and dewpoint from 127 places around the world. This empirical relationship was tested at 46 other places, and estimated values were, on average, very close to the actual values. The mean error in dewpoint was a mere 0.8 K, however the standard deviation was 3.8 K. So this relationship does yield normative values.

The relationship is based on the fact that today's minimum temperature is governed by the rate of cooling from the maximum temperature in the afternoon until sunrise the next morning. That rate is governed chiefly by the value of the longwave radiation flux from the ground at the maximum and subsequent temperatures, and by the longwave radiation to the ground from the clouds and the air, i.e. the sky radiation. The latter depends on the air's humidity in the case of a clear sky (3), or otherwise on the amount of cloudiness (2, p.96). The latter is also assumed related to the humidity measured at the surface. The most significant radiators, low clouds, also relate best to surface humidity. So the minimum depends on the maximum and the humidity. This can be rearranged as an association of the humidity with the two daily extreme temperatures.

The relation between surface dewpoint temperature and cloudiness is only approximate. For instance, it is less invalid near the coast, where sea breezes affect surface conditions alone. At Sydney, for example, there is indeed a relationship between the cloudiness and the difference between the daily maximum Tx and the dewpoint Td, but the correlation is not high (2, p.142). A large estimation error at a particular place or time signals another process, in particular advection (e.g. a sea breeze), and is worth investigating.

The values in Table 6.1 may be represented by the following equation -

 Td = 0.38 Tx - 0.018 Tx2 + 1.4 Tn - 5 ° C

where Tn is the minimum. The standard error between the data and this quadratic equation is only 0.57 K, which is reasonable since values in the Table were adjusted to the nearest integer and hence may be wrong by half a degree. The equation means that a Tx of 25 ° C and a minimum of 20 ° C imply a dewpoint of 22 ° C, for instance.

Similar equations have been derived, but not specified for places in Spain (4).

References

1. Linacre, E.T. and B. Geerts 1997. Climates and Weather Explained (Routledge) 432pp.
2. Linacre, E.T. 1992. Climate Data and Resources (Routledge) 366pp.
3. Brunt, D. 1932. Notes on the radiation in the atmosphere. Quart. J. Roy. Meteor. Soc., 58, 389-418.
4. Castellvi, F., P.J. Perez, C.O. Stockle and M. Ibanez 1997. Methods for estimating vapour pressure deficit on a regional scale, depending on data availability. Agric. Forest Meteor., 87, 243-52.