APPENDIX 3 - HUMIDITY CALCULATIONS

Barometric pressure (Pb) from elevation (EL):

 Eq. A3.1

Latent heat of vaporization (l) from air temperature (T):

 Eq. A3.2

Saturation vapour pressure over water is the vapour pressure of the air when the number of water molecules condensing equals the number evaporating from a flat surface of water with both the air and water at some temperature (T). An equation for the saturation vapour pressure (es) over water at temperature (T) is given by:

 Eq. A3.3

When the number of water molecules sublimating equals the number depositing onto a flat surface of ice with both the air and ice at some temperature (T), the saturation vapour pressure (es) over ice at temperature (T) is given by:

 Eq. A3.4

Dew-point temperature (Td) from air temperature (T) and relative humidity (%):

 Eq. A3.5

Ice-point temperature (Ti) from air temperature (T) and relative humidity (%):

 Eq. A3.6

Note that the actual vapour pressure (e) is equal to the saturation vapour pressure (ed) at the dew-point temperature (Td) and, for subzero temperatures, the saturation vapour pressure (ei) at the ice point temperature (Ti).

Dew-point temperature (Td) from vapour pressure (e = ed) over water:

 Eq. A3.7

Ice-point temperature (Ti) from vapour pressure (e = ei) over ice:

 Eq. A3.8

Slope of Saturation Vapour Pressure over liquid water at temperature T:

 Eq. A3.9

Psychrometric Constant (g) as a function of barometric pressure (Pb) and wet-bulb temperature (Tw), from Fritschen and Gay (1979):

 g = 0.000660 (1 + 0.00115 Tw) Pb (g in kPa, Td in C) Eq. 3.10

Saturation vapour pressure (ea) at the air temperature (Ta):

 Eq. A3.11

Vapour pressure (e = ed) at the dew-point temperature (Td):

 Eq. A3.11

Vapour pressure (e = ei) at the subzero ice point temperature (Ti):

 Eq. A3.12

Equivalent temperature (Te) from temperature T, vapour pressure e, and the psychrometric constant g:

 Eq. A3.13

Absolute humidity (c) from vapour pressure (e) and temperature (T):

 Eq. A3.14

Vapour pressure (e) from dry (T) and wet-bulb (Tw) temperature (°C) and barometric pressure (Pb):

 e = ew 0.000660 (1 + 0.00115 Tw) (T - Tw) Pb (e in kPa, Pb in Kpa) Eq. 3.15

where ew is the saturation vapour pressure at the wet-bulb temperature. It is calculated by substituting Tw for Tin Equation A3.3.

Vapour pressure (e) from dry (T) and frost-bulb (Tf) temperature (°C) and barometric pressure (Pb):

 e = ef - 0.000582 (1 + 0.00115 Tf) (T - Tf) Pb (e in kPa, Pb in Kpa) Eq. 3.16

where ef is the saturation vapour pressure at the frost-bulb temperature. It is calculated by substituting Tffor Tin Equation A3.4.

TABLE A3.1
Saturation vapour pressure (kPa) over a flat surface of liquid water calculated using Tetens' formula (Equation A3.3) for air temperature between 0.0 °C and -14.9°C

 TEMPERATURE °C -0.0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8 -0.9 -14 0.207 0.205 0.203 0.202 0.200 0.199 0.197 0.195 0.194 0.192 -13 0.224 0.223 0.221 0.219 0.217 0.216 0.214 0.212 0.210 0.209 -12 0.243 0.241 0.240 0.238 0.236 0.234 0.232 0.230 0.228 0.226 -11 0.264 0.262 0.260 0.258 0.256 0.253 0.251 0.249 0.247 0.245 -10 0.286 0.283 0.281 0.279 0.277 0.275 0.272 0.270 0.268 0.266 -9 0.309 0.307 0.304 0.302 0.300 0.297 0.295 0.293 0.290 0.288 -8 0.334 0.332 0.329 0.327 0.324 0.322 0.319 0.317 0.314 0.312 -7 0.361 0.359 0.356 0.353 0.350 0.348 0.345 0.342 0.340 0.337 -6 0.390 0.387 0.384 0.381 0.378 0.376 0.373 0.370 0.367 0.364 -5 0.421 0.418 0.415 0.412 0.409 0.405 0.402 0.399 0.396 0.393 -4 0.454 0.451 0.447 0.444 0.441 0.437 0.434 0.431 0.428 0.424 -3 0.490 0.486 0.482 0.479 0.475 0.472 0.468 0.465 0.461 0.458 -2 0.527 0.524 0.520 0.516 0.512 0.508 0.504 0.501 0.497 0.493 -1 0.568 0.564 0.559 0.555 0.551 0.547 0.543 0.539 0.535 0.531 0 0.611 0.606 0.602 0.598 0.593 0.589 0.585 0.580 0.576 0.572

TABLE A3.2
Saturation vapour pressure (kPa) over a flat surface of liquid water calculated using Tetens' formula (Equation A3.3) for air temperature between0 °C and 14.9 °C

 TEMPER 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0 0.611 0.615 0.620 0.624 0.629 0.633 0.638 0.643 0.647 0.652 1 0.657 0.661 0.666 0.671 0.676 0.681 0.686 0.691 0.696 0.701 2 0.706 0.711 0.716 0.721 0.726 0.731 0.737 0.742 0.747 0.752 3 0.758 0.763 0.769 0.774 0.780 0.785 0.791 0.796 0.802 0.808 4 0.813 0.819 0.825 0.831 0.836 0.842 0.848 0.854 0.860 0.866 5 0.872 0.878 0.885 0.891 0.897 0.903 0.910 0.916 0.922 0.929 6 0.935 0.942 0.948 0.955 0.961 0.968 0.975 0.981 0.988 0.995 7 1.002 1.009 1.016 1.023 1.030 1.037 1.044 1.051 1.058 1.065 8 1.073 1.080 1.087 1.095 1.102 1.110 1.117 1.125 1.133 1.140 9 1.148 1.156 1.164 1.172 1.179 1.187 1.195 1.203 1.212 1.220 10 1.228 1.236 1.245 1.253 1.261 1.270 1.278 1.287 1.295 1.304 11 1.313 1.321 1.330 1.339 1.348 1.357 1.366 1.375 1.384 1.393 12 1.403 1.412 1.421 1.431 1.440 1.449 1.459 1.469 1.478 1.488 13 1.498 1.508 1.517 1.527 1.537 1.547 1.558 1.568 1.578 1.588 14 1.599 1.609 1.619 1.630 1.641 1.651 1.662 1.673 1.684 1.694

TABLE A3.3
Saturation vapour pressure (kPa) over a flat surface of ice calculated using Tetens' formula (Equation A3.4) for air temperature between 0.0 °C and -14.9 °C

 TEMPERATURE °C -0.0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8 -0.9 -14 0.181 0.179 0.177 0.176 0.174 0.173 0.171 0.169 0.168 0.166 -13 0.198 0.196 0.194 0.193 0.191 0.189 0.187 0.186 0.184 0.182 -12 0.217 0.215 0.213 0.211 0.209 0.207 0.205 0.204 0.202 0.200 -11 0.237 0.235 0.233 0.231 0.229 0.227 0.225 0.223 0.221 0.219 -10 0.259 0.257 0.255 0.253 0.250 0.248 0.246 0.244 0.242 0.239 -9 0.284 0.281 0.279 0.276 0.274 0.271 0.269 0.266 0.264 0.262 -8 0.310 0.307 0.304 0.302 0.299 0.296 0.294 0.291 0.289 0.286 -7 0.338 0.335 0.332 0.329 0.326 0.323 0.321 0.318 0.315 0.312 -6 0.368 0.365 0.362 0.359 0.356 0.353 0.350 0.347 0.344 0.341 -5 0.401 0.398 0.395 0.391 0.388 0.385 0.381 0.378 0.375 0.372 -4 0.437 0.433 0.430 0.426 0.422 0.419 0.415 0.412 0.408 0.405 -3 0.476 0.472 0.468 0.464 0.460 0.456 0.452 0.448 0.445 0.441 -2 0.517 0.513 0.509 0.505 0.500 0.496 0.492 0.488 0.484 0.480 -1 0.562 0.558 0.553 0.548 0.544 0.539 0.535 0.530 0.526 0.522 0 0.611 0.606 0.601 0.596 0.591 0.586 0.581 0.576 0.572 0.567