Vaisala RVP900, Руководство пользователя

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7.4.5 Spectrum Width Algorithms
The spectrum width is a measure of the combined effects of shear and turbulence.
To a lesser extent, the antenna rotation rate can also effect the spectrum width. At high
elevation angles, the fall speed dispersion of the scatterers also effects spectrum width.
There are two choices for the spectrum width algorithm used in the RVP900, depending on
the speed and accuracy that are required for the application:
•
R
0
,
R
1
"fast" algorithm valid when SNR >> 10 dB
•
R
0
,
R
1
,
R
2
"accurate" algorithm for SNR >> 0 ... 5 dB
Use the SOPRM command to select the approach.
7.4.5.1 R0, R1 Width Algorithm
Given samples of the Doppler autocorrelation function, numerous estimates of spectral
variance can be computed (Passarelli & Siggia, 1983). The particular estimator used by the
RVP900 employs the magnitudes of R
0
and R
1
and assumes that the Doppler spectrum is
Gaussian (usually an acceptable assumption) and that the signal-to-noise ratio is large.
Specifically we have (similar to Srivastava, et al 1979):
�������� = 2ln
�
0
�
1
= − 2ln ���
where ln represents the natural logarithm. This can be compared to the expression in the
preceding section for SQI to illustrate that this expression for the variance is only valid when:
���
��� + 1 ≈ 1
which occurs when the SNR is large.
This variance estimator is normalized to the Nyquist interval in units of [-π, π]. For example,
a variance of Π
2
/25 would be obtained from a Gaussian spectrum having a standard
deviation equal to one fifth of the total width of the plotted spectral distribution. For
scientific purposes, the spectrum width (standard deviation) is more physically meaningful
than the variance, since it scales linearly with the severity of wind shear and turbulence. For
these reasons, the width
W is output by RVP900:
� = ��������
�
For efficient packing in 8-bits, width is normalized to the Nyquist interval [-1, 1 ]. For the
example given above, the output width
W
would be (1/5). To obtain the width in meters per
second, one multiplies the output width by
V
u
.
7.4.5.2 R0, R1, R2 Width Algorithm
The width algorithm in this case is similar except that the addition of
R
2
extends the validity
of the width estimates to weak signals. In this case the variance is:
�������� = 23ln
�
1
�
2
RVP900 User Guide M211322EN-J
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