This document discusses concepts related to atmospheric climate including: 1. It provides equations for calculating barometric pressure, temperature, and density at different heights above sea level. 2. It explains concepts like water vapor pressure, absolute humidity, mixing ratio, specific humidity, and relative humidity. Formulas are given for calculating each of these. 3. An example calculation is shown that determines values like vapor pressure, dew point temperature, relative humidity, specific humidity, mixing ratio, and vapor pressure deficit based on measurements from a psychrometer.

1. KLIMATOLOGI PERTANIAN
( Kuliah Minggu Ke 7 )
Oleh
Suardy Mandung

4. Barometric formula
Equation 1:
where
P = Static pressure (pascals)
T = Standard temperature (kelvins)
L = Standard temperature lapse rate (kelvins per meter)
h = Height above sea level (meters)
R * = Universal gas constant for air: 8.31432×103 N·m / (kmol·K)
g0 = Gravitational constant (9.80665 m/s²)
M = Molar mass of Earth's air (28.9644 g/mol)

5. where
P = Static pressure (inches of mercury)
T = Standard temperature (kelvins)
L = Standard temperature lapse rate (kelvins per foot)
h = Height above sea level (feet)
R * = Universal gas constant (using feet and kelvins
and gram moles: 8.9494596×104 kg·ft2·s-2·K-
1·kmol-1)
g0 = Gravitational constant (32.17405 ft/s²)
M = Molar mass of Earth's air (28.9644 g/mol)

6. Height
Static Temperature
Above
Pressure Standard Lapse Rate
Subscript Sea Level
Temperature
b
(K)
(m) (pascals) (K/m)
0 0 101325 288.15 -0.0065
1 11,000 22632.1 216.65 0.0
2 20,000 5474.89 216.65 0.001
3 32,000 868.019 228.65 0.0028
4 47,000 110.906 270.65 0.0
5 51,000 66.9389 270.65 -0.0028
6 71,000 3.95642 214.65 -0.002

7. Density Equations
where
ρ = Mass Density (kg/m3)
T = Standard temperature (kelvins)
L = Standard temperature lapse rate (kelvins per meter)
h = Height above sea level (geopotential meters)
R * = Universal gas constant for air: 8.31432×103 N·m / (kmol·K)
g0 = Gravitational constant (9.80665 m/s²)
M = Molar mass of Earth's air (28.9644 g/mol)

8. Or converted to English units:[1]
Where
ρ = Mass Density (slugs/Ft3)
T = Standard Temperature (degrees Kelvin)
L = Standard Temperature Lapse Rate (degrees Celsius per foot)
h = Height above Sea Level (geopotential feet)
R * = Universal Gas Constant (converted to English units: 8.9494596 X
104 Ft2/sec2 K)
go = Gravitational Constant (32.17405 Ft/sec2)
M = Molar Mass of Earth's Air (28.9644 grams per mole)

9. Height Above Sea Mass Density Temperature
Sub Level (h) (ρ) Standard Lapse Rate (L)
scrip Temp.(T)
tb (m) (kg/m3) (K) (K/m)
0 0 1.2250 288.15 -0.0065
1 11,000 0.36391 216.65 0.0
2 20,000 0.08803 216.65 0.001
3 32,000 0.01322 228.65 0.0028
4 47,000 0.00143 270.65 0.0
5 51,000 0.00086 270.65 -0.0028
0.00006
6 71,000 214.65 -0.002
4

10. Derivation ideal gas law:
When density is known:
And assuming that all pressure is hydrostatic:
Substituting the first expression into the second we get:
Integrating this expression from the surface to the altitude z we get:
Assuming constant temperature, molar mass, and gravitational acceleration, we get
the barometric formula:
n this formulation, R is the gas constant, and the term RT / Mg gives the scale height
(approximately equal to 7.4 km for the troposphere).

12. Penyebaran tekan uap air
(dry season)
Penyebaran tekan uap air
(wet season)

13. Water Vapor Pressure
Where
The temperature Tv is in degrees Celsius
The pressure p is in pascals.

14. Absolute humidity
Absolute humidity is the density of water in a particular volume of air. The most
common units are grams per cubic meter,
he amount of vapor in that cube of air is the absolute humidity of that cubic
meter of air. More technically: the mass of water vapor mw, per cubic meter of
air, Va .
volumetric humidity. "absolute humidity." Most humidity charts are given in
g/kg or kg/kg,

15. Mixing ratio / Humidity ratio
Mixing or Humidity ratio is expressed as a ratio of
kilograms of water vapour, mw, per kilogram of dry air,
md, at a given pressure
That ratio can be given as:

16. Specific humidity
Specific humidity is the ratio of water vapor to air (dry air plus water vapor)
in a particular volume of air. Specific humidity ratio is expressed as a ratio
of kilograms of water vapor, mw, per kilogram of air, ma .
That ratio can be given as:
Specific humidity is related to mixing ratio (and vice versa) by:

17. Relative humidity
Relative humidity is defined as the ratio of the partial pressure of water vapor in a
gaseous mixture of air and water vapor to the saturated vapor pressure of water at
a given temperature. Relative humidity is expressed as a percentage and is
calculated in the following manner:
where
is the partial pressure of water vapor in the gas mixture;
is the saturation vapor pressure of water at the temp of the gas mixture
is the relative humidity of the gas mixture being considered.

20. Contoh Perhitungan
Pengamatan suhu udara dengan alat psikrometer
1. TBK = 32,5OC
2. TBB = 27,5OC
3. Tekanan udara = 1 005 mb
4. Tetapan psikometer = 0,000667
Tentukan :
1. Tekanan uap (mb)
2. Suhu Titik embun (OC)
3. Kelembaban Nisbi (%)
4. Kelembaban Spesifik (g/kg)
5. Nisba Campuran (g/kg)
6. Defisit Tekanan Uap (mb)

21. 1. Tekanan Uap Air
TBB ( nilai ini digunakan pada perhitungan RH pad rumus Regnault )
(17,239 T / ( T + 237,3 ))
es * = 6,1078 e
(17,239 x 27,5 / ( 27,5 + 237,3 ))
es * = 6,1078 e
1,7903
es * = 6,1078 e

22. TBB ( nilai ini digunakan pada perhitungan RH pada rumus Regnault )
e = es * - req p ( TBK – TBB)
e = 36,59 – (0,000667) (1 005) ( 32,5 – 27,5 )
e = 36,59 – 3,3351
e = 33,2548 mb (Nilai ini adalah Tekanan Uap air)

23. 2. Suhu Titik Embun
Td = ( 237,3 x Y ) / ( 17,237 – Y )
Y = ln ( e / 6,1078 )
Y = ln ( 33,2548 / 6, 1078 )
Y = 1,6946
Td = ( 237,3 x 1,6948 ) / ( 17,237 – 1,6948 )
Td = 25,88OC

24. 3. Tekanan Uap Air Jenuh
TBK
(17,239 T / ( T + 237,3 ))
es * = 6,1078 e
(17,239 x 32,5 / ( 32,5 + 237,3 ))
es * = 6,1078 e
2,0766
es * = 6,1078 e

25. 4. Kelembaban Nisbi Udara
RH = ( e / es ) x 100%
RH = ( 33,25 mb / 48,72 mb ) x 100%
RH = 68 %

26. 5. Kelembaban Spesifik
SH = ( 622 e ) / (1,622 p )
SH = ( 622 x 33,25 ) / ( 1,622 x 1 005 )
SH = 12,6872 g/kg

27. 6. Nisbi Campuran
SH = 622 ( e / ( p - e ))
SH = 622 ( 33,25 / ( 1005 - 33,25 ))
SH = 21,28 g/kg

28. 7. Defisit Tekanan Uap
DTU = e - es
DTU = 33,25 - 48,72
DTU = 16,47 mb

30. Pan Evaporimeter Class A