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Weather Requirements

Wind

The user will specify the pointing errors that they can tolerate in units of the half-power beam-width (HPBW). Let us define f as the two-dimensional pointing error in units of the HPBW given by

f = \sigma_2/\theta

where \sigma_2 is the two-dimensional pointing error and \theta is the HPBW.

The user will define the worst pointing error, f_{max}, that their science can accommodate. Currently since the pointing is dominated by wind these pointing errors correspond to wind speeds and the value of f_{max} will correspond to a maximum wind speed (V_{max}). As a default let us set V_{max} as the wind speed that will produce a two-dimensional pointing error yielding a 10% rms flux error for a point source.

The normalized gain is given by Condon (2003, PTCSSN3)

g = (1 + z)^{-1}

where z = 4ln(2)f^2. A 5% error in flux corresponds to f = 0.14, while a 10% error in flux corresponds to f = 0.20.

Pointing errors due to wind are approximated by (Condon 2003, PTCSPN26) where the two-dimensional pointing error caused by wind is

\sigma_w = \sqrt{2}\sigma_1 = 0.23 (\frac{V}{m s^{-1}})^2 arcsec,

where V is the wind speed and \sigma_1 is the one-dimensional pointing error.

For frequencies below 25GHz, the wind limit corresponds to a wind-induced pointing error which, when added in quadrature to the "benign conditions" tracking error of 2.8", would cause the total tracking error to exceed the respective limit. For frequencies above 25GHz, the wind speed at which the pointing variance contributed by wind is one quarter of the total allowed pointing variance at the specified observing frequency.

Therefore,

\sigma_2^2 = (f\theta)^2 = (2.8)^2 + \sigma_w^2

or

V = (\frac{(f\theta)^2 - (2.8)^2}{(0.23)^2})^{1/4} m/s

\sigma_2^2/4 =(f\theta)^2/4 = \sigma_w^2

or

V = (\frac{(f\theta)^2}{4(0.23)^2})^{1/4} m/s

Note: The telescope is stowed when the wind speed is 25 miles/hr = 11.1 m/s for a sustained period of 1 minute.

Atmosphere

Weather affects the signal-to-noise ratio (S/N) in two ways: (1) it attenuates the signal; and (2) it increases the system temperature and therefore the noise. The signal, S, is proportional to e^{-\tau}, while the noise, N, is proportional to the system temperature T_{sys}. So we define a temperature parameter, T, that is inversely proportional to the S/N ratio as

T = T_{sys}(\nu)e^{\tau(\nu)},

where we have indicated that the system temperature and opacity are frequency dependent. As T increases our observing efficiency decreases. The integration time is inversely proportional to the noise squared. So we can parameterize the observing efficiency as T^2.

N.B., we need to include the receiver temperature, the CMB temperature, and the spillover temperature in Ron's value of the system temperature.

Band Frequency Wavelength Beam FWHM V_{max} 5% V_{max} 10%
PF1-band 340 MHz 88 cm 36' 36.3 m/s 43.3 m/s
PF1-band 415 MHz 72 cm 30' 33.1 m/s 39.6 m/s
PF1-band 680 MHz 44 cm 18' 25.6 m/s 30.6 m/s
PF1-band 770 MHz 39 cm 16' 24.2 m/s 28.9 m/s
PF2-band 970 MHz 31 cm 13' 21.8 m/s 26.0 m/s
L-band 1.4 GHz 21 cm 8.8' 17.9 m/s 21.4 m/s
S-band 2.0 GHz 15 cm 6.2' 15.0 m/s 18.0 m/s
C-band 5.0 GHz 6 cm 2.5' 9.5 m/s 11.4 m/s
X-band 9.0 GHz 3.3 cm 1.4' 7.0 m/s 8.5 m/s
Ku-band 14.0 GHz 2.1 cm 53" 5.5 m/s 6.7 m/s
K-band(l) 21.5 GHz 1.4 cm 33" 4.0 m/s 5.1 m/s
K-band(h) 25.0 GHz 1.2 cm 30" 3.7 m/s 4.8 m/s
Ka-band 32.0 GHz 9 mm 23" 2.6 m/s 4.0 m/s
Q-band 45.0 GHz 7 mm 16" 2.2 m/s 2.6 m/s
W-band(l) 90.0 GHz 3.3 mm 8.0" 1.6 m/s 1.9 m/s
W-band(h) 115.0 GHz 2.6 mm 6.3" 1.4 m/s 1.7 m/s

-- DanaBalser - 06 Dec 2006

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