1 that the wet-bulb temperature does not lie equidistant from T and T d-a weighted average, with dry-bulb temperature weighted more than dewpoint as in (3), is required. Note that the example chosen for this figure was for a cold-weather situation in which the surface dry-bulb temperature is 0☌. Justification for the one-third rule is provided by the Normand’s rule diagram in Fig. Typical diagrams in textbooks explaining Normand’s rule show T w approximately equidistant from T and T d in such circumstances the arithmetic-mean rule would be a good approximation. There is visual justification for both of these rules. Based on Table 1, the arithmetic-mean rule of Wallace and Hobbs (2006) should become comparatively more accurate than the one-third rule for dry-bulb temperatures between 10° and 20☌, a result broadly consistent with Preston’s (1894) statement quoted earlier in this section. Because T ≥ T w, this suggests that the one-third rule would be especially well suited for relatively moist conditions in which T w is in the vicinity of 0☌. The values of k in Table 1 justify the use of an average that weights temperature twice as much as dewpoint for dry-bulb temperatures between 0° and 5☌. 2013) are inserted into (11), obtaining a range of values for k. Whether this linear combination should be a pure arithmetic mean ( k = 0.5) or a weighted average (for the one-third rule, k = 0.333) is tested in Table 1, in which values of E s, b, and P representative of near–sea level conditions for a range of dry-bulb temperatures and γ (from Sadeghi et al. The form of (10) justifies a linear combination of dry-bulb and dewpoint temperatures as an approximation to wet-bulb temperature, for the assumptions of relatively small wet-bulb depression and relatively moist conditions. Similarly, an Internet search of “wet-bulb temperature and one-third rule” in September 2016 revealed only a handful of mentions aside from Haby’s websites, usually from energy and heating/air conditioning vendors (e.g., Our justification for the possible effectiveness of the both rules follows the following line of reasoning: An Internet search of “wet-bulb temperature and arithmetic mean” in January 2017 revealed only a few relevant links one such link, to a nineteenth-century thermodynamics textbook, includes the statement (without derivation) that “(a)t 53☏ the reading of the wet-bulb thermometer is the arithmetic mean between the dew-point and the temperature of the air…At higher temperatures the reading of the wet-bulb is lower than this mean, and at lower temperatures it is higher” ( Preston 1894, p. For example, the one-third rule seems to have originated empirically, probably with operational meteorologists (J. To our knowledge, no formal and exact derivations exist of either the arithmetic-mean or the one-third rule. ORIGIN AND JUSTIFICATION FOR THE ONE-THIRD RULE AND ARITHMETIC-MEAN RULE. Examples of the application of the one-third rule to precipitation-type forecasting and to agricultural practices to prevent frost damage are presented. The one-third rule is especially useful because its domain of maximum accuracy includes the phase change for water from solid to liquid and vice versa. These two approximations are 1) an arithmetic mean of dry-bulb and dewpoint temperatures and 2) a weighted mean of dry-bulb and dewpoint temperatures known as the “one-third rule.” These approximations are highly accurate in two contiguous temperature and moisture regimes: the arithmetic-mean rule outperforms other approximations for relatively moist (average relative humidity = 61%) situations with dry-bulb temperatures bracketing 13☌, and the one-third rule outperforms other approximations for relatively moist (average relative humidity = 50%) situations with dry-bulb temperatures bracketing 4☌. This article provides theoretical justifications for, and real-life applications of, two different simple linear approximations for the wet-bulb temperature. Most atmospheric thermodynamics textbooks indicate or imply that no simple and accurate approximation relating these three meteorological variables exists. The relationship between the wet-bulb temperature, the dry-bulb temperature, and the dewpoint temperature is nonlinear. The wet-bulb temperature is a widely used moist thermodynamic variable.
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