HomeHomeUpUpSearchSearchE-mailMail
NEW

Determine the stability class, near surface temperature gradient or lapse rate, ray curvature and refraction constant

Browser should support JavaScript

The stability factor tells something about the low level atmosphere and the average temperature gradient in the boundary layer. The terrestrial refraction more or less depends on the average temperature gradient in the boundary layer, and thus has a relation to this stability class.
Remember that the astronomical refraction is not only related to the overall temperature gradient of the boundary layer, but also on the temperature gradient in lower troposphere, thus it is less determined by the stability class.
Input parameters
Time of dayDayNight (1 hour before sunset to 1 hour after sunrise)
Sun's altitude [°] (only used during Day time)
Total cloud coverClearIsolatedScatteredBrokenOvercast
Ceiling height [m] (only used during Day time)
Windspeed at 10 [m] [m/sec]
the stability factors
Net Radiation Index [-]
Stability class  [-]
Temperature gradient* [°K/km], Avg. temp. gradient*: +/- [°K/km]
Ray curvature (k)  +/- [-]
Refraction constant (K) +/- [-] <K = k/0.0238>
*Lapse rate is the negative of the temperature gradient.

Stability class during the day

To check if the stability classes behave more or less around the sunset and rise times as expected according to the above table, a data collection of some 26,000 hourly measurements (over a period of 3 years) has been evaluated.
The data has been provided by K.Sejkora of the Pilgrim power plant in Plymouth Massachusetts. The data is determined using the temperature gradient method.
Distribution of stability classes on actual hours

To be sure to evaluate the stability class correctly over the day, the above picture has been normalized to sun rise, meridian transit and set using the following method:
The Swiss Ephemeris software (incorporated in the ARCHAEOCOSMO Excel Add-in) has been used to determine the moment of the Sun's rise, meridian transit and set. These three moments were than transformed towards 06:00, 12:00 and 18:00 hour (and not bothering about midnight becoming 0:00; is not important for this study, but its behavior will be comparable to the above picture).
This transformation provided the below picture:
Distribution of stability classes over Hour of day

Looking at the above figure a few things become evident:
  1. The curves are somewhat symmetric around 12:00 (see light blue, stability class B), full symmetry is though not expected (see next bullet)
  2. Due to larger net radiation in the afternoon it is expected that the stability classes will be higher mid afternoon. This can be seen as the peak around 13:00 in stability class A curve (purple).
  3. The typical day-time stability classes (A, B and C) start increasing significantly around 07:00 and stop decreasing significantly around 17:00. This coincides nicely with the rule: 1 hour after sunrise to 1 hour before sunset
  4. The relatively low frequencies of stability class B and C may be an artifact of the way the values are derived. At Pilgrim Station they rely on the vertical temperature gradient method to calculate the stability class. The interval width of the temperature bands for stability classes B and C are the narrowest of all of the stability classes (only 2  [°K/km]), thus reducing the chance of categorizing it as an B or C stability class.
  5. The  D, E, F and G stability classes percolate into daytime, as expected, this happens when the total cloud cover (TC) and ceiling height (CH) are high during day time.
  6. At sunset (06:00) and sunrise (18:00), important for sun related neolithic sites, the D, E, F and G stability factors are as expected predominant (>90% of the cases).
Because of the last observation, I assume that determining the temperature gradient during sun set/rise stability factor can be done by determining the D E, F or G stability factors. If you think differently, let me know.

Comparing Refraction constant determined by stability class and actual measurements

Thom ([1973], page 29-31) did some 500 measurements of the terrestrial refraction in UK. So it would be nice if the resulting Refraction constant (K) values he found were more or less mapping on the Refraction constant values determined from the Stability class.
I am in search for a years worth of stability class in UK (Köppen Class C climate), but in the meantime I used the Pilgrim 3 Plymouth Massachusetts measurements (Köppen Class Dfa climate; a different climate: less clouds, different cloud cover, less wind, higher sun). But at least it shows where I am heading;-).
Here is a comparison between Thom's measured values and the ones of Pilgrim 3:
Refraction during winter

They are not comparable (certainly not near sun rise and sunset moments), but I think this is because Massachusetts is a much warmer and more extreme stability classes (particular Stability class A and G) then UK.

Background how to calculate stability class

Blue-ish text has been edited by me.

Largely copied from this site

The atmospheric stability is important in determination of lateral and vertical horizontal dispersion parameters. The most commonly used classification is that of Pasquill (1961), later modified by Gifford (1961), and referred to as the Pasquill-Gifford (P-G) stability class. Unstable conditions are represented by the letter ‘A’ (or the number 1), while increasingly more stable conditions are denoted with successive letters of the alphabet, such that extremely stable conditions are represented by ‘F’ and/or ‘G’ (6 and/or 7). Neutral atmospheric conditions are given by the ‘D’ (4) classification. Turner (1964) devised a scheme for determining the stability class of the atmosphere using data customarily collected at NWS sites by considering radiative and wind speed effects. Net radiation calculations require knowledge of total cloud cover, ceiling height and solar altitude (itself a function of the time of day and year, as well as geographic location). The following tables, reproduced from EPA-454/R-99-005 (2000), provide the mechanism for determining the P-G stability classes.

The solar altitude, q, is the angle the sun makes with respect to the earth’s surface. When the sun is directly overhead (i.e. ‘high noon’), q = 90° leading to the strongest insolation, while weak insolation occurs when the sun is near the horizon. This angle is uniquely determined from the latitude and longitude of the location of interest, the time of day, as well as the time of year. Once determined, an insolation class number (IN) is defined, as given in Table A.1.

The Pasquill-Gifford stability categories (A through G) as a function of wind speed and net radiation index (NRI) are shown in Table A.2. Once the solar altitude and insolation class number are known (Table A.1), the procedure shown in Table A.3 requiring the total cloud cover (TC) and ceiling height (CH) is used to determine the NRI. Knowing the NRI and wind speed for a given time yields the P-G stability class (Table A.2).

Table A.1: Insolation class number (IN)
as a function of solar altitude, q.

Solar altitude (°)

Insolation

IN

60 <= q

Strong

4

35 <= q < 60

Moderate

3

15 <= q < 35

Slight

2

q <= 15

Weak

1


Table A.2: Turner’s conversion from NRI to stability class.

Wind speed

Net Radiation Index (NRI)

[m/sec]

[knots]

 [Beaufort]

4

3

2

1

0

-1

-2*

0 to 0.7

0, 1

 0-1

A

A

B

C

D

F

G

0.8 to 1.8

2, 3

 1

A

B

B

C

D

F

G

1.9 to 2.8

4, 5

 2

A

B

C

D

D

E

F

2.9 to 3.3

6

 2

B

B

C

D

D

E

F

3.4 to 3.8

7

 3

B

B

C

D

D

D

E

3.9 to 4.8

8, 9

 3

B

C

C

D

D

D

E

4.9 to 5.4

10

 3

C

C

D

D

D

D

E

5.5 to 5.9

11

 4

C

C

D

D

D

D

D

> 6.0

> 12

 4-12

C

D

D

D

D

D

D
*The NRI=-2 is more likely to be present during clear sun set/rise events

Table A.3: Procedure to determine Net Radiation Index (NRI).
Remark: The conversion from feet to meters seems to be wrong
(using a wrong conversion value 0.3281 instead of 0.3048 [a conversion direction error?])

NRI table

Background how to calculate temperature gradient

Information comes from this site

NRC Regulatory Guide 1.23 indicates the use of temperature differences with height (the lapse rate is the negative of the temperature gradient):

Stability
class
 Temperature
gradient
[°K/km]
 Lapse rate
[°K/km]
Letter
 Number
 smaller
 bigger
 larger
 smaller
A
 1
 -19
19
B
 2
 -17
 -19
 17
 19
C
 3
 -15
 -17
 15
 17
D
 4
 -5
 -15
 5
 15
E
 5
 15
 -5
 -15
 5
F
 6
 40
 15
 -40
 -15
G
 7
40
-40

Temperature gradient is relevant between heights of 10 and 60m.

Descriptive phrase of stability classes (Pasquill index)

Information comes from this site

Stability class
Phrase
A Very unstable
B Moderately unstable
C Slightly unstable
D Neutral
E Slightly stable
F Moderately stable
G Very stable

Total cloud cover

Information coming from this site
Total cloud cover [%]
 Name
 Code
0-10
 Clear
 CLR
10-25
 Isolated
 FEW
25-50
 Scattered
 SCT
50-90
 Broken
 BKN
90-100
 Overcast
 OVC

Disclaimer and Copyright
HomeHomeUpUpSearchSearchE-mailMail
Major content related changes: Nov. 7th, 2004