This section presents investigation of the effect of tropospheric turbulence
on L-band propagation utilizing RO observations from a GPS to a COSMIC
satellites radio links. We estimated the impact of turbulence strength on
L-band signals in terms of scintillation index. During the time frame
relevant to this study, the COSMIC satellites provide a significant number of
RO profiles (up to about 2000 profiles per day) observed by the six
micro-satellites covering the entire globe.
Utilizing the RO profiles, we were able to estimate the
global distribution of the effect of scintillation on GPS signals. The
technique provides valuable scintillation data especially over the oceans
where ground-based measurements are both difficult and expensive to perform.
RO data were first used to determine the intensity and location of turbulent
regions . Our study differs in that we aim to study the
global climatology of tropospheric turbulence. In addition, we suggest that
amplitude and phase in the impact parameter domain, rather than raw signal
amplitude and phase, provide a more effective observable for measuring
scintillation of interest.
COSMIC signal amplitude measurements
The basic observations of RO soundings on COSMIC are time series of amplitude
(the 1 s voltage signal-to-noise ratio) and phase of L-band signals
transmitted by a GPS satellite (e.g., ). As the radio
signal propagates through the troposphere, the amplitude of the signal (raw
amplitude) suffers from the effects of defocusing, multi-path propagation,
and diffraction effects. Therefore, the raw amplitude fluctuation does not
truly represent the effect of turbulence. To suppress amplitude fluctuations
due to these effects, the canonical transform (CT) has been applied on the
received complex signal to transform it from the time domain to the impact
parameter domain . In RO retrieval processing, the CT
phase is considered the important quantity since it is used to retrieve the
bending angle profile and subsequently the refractivity profile, which are
the primary retrieval variables. In our study, however, the focus is on the
CT amplitude. We assume that CT amplitude fluctuations are dominated by
small-scale irregularities caused by turbulent processes. We note that other
radio-holographic inversion methods can be used such as the full spectrum
inversion and phase matching method .
While these methods might be easier to implement for certain orbital
geometry, studies have shown that all methods yield very similar results in
phase and amplitude .
We note that CT operates under the assumption of a spherically symmetric
atmosphere where each ray is uniquely identified by its impact parameter.
Thus the presence of mesoscale or large-scale horizontal inhomogeneity can
result in fluctuations in the CT amplitudes; however, these tend to occur at
a larger spatial scales than the turbulent effects being considered so that
their contribution to the scintillation estimates is expected to be small.
Scintillation effects on COSMIC RO signals
The scintillation index σI can be viewed as a measure of the effect
of tropospheric turbulence on L-band propagation having signal intensity I.
σI can be described as a normalized standard deviation of intensity
I fluctuation:
σI=〈I2〉-〈I〉2〈I〉212,
where 〈…〉 stands for expected value and I is the CT
intensity, which is the square of the CT amplitude.
The expected value is computed using data in 120 m intervals.
Scintillation index estimates
Figures 1 and 2 show global maps of σI estimated by applying
Eq. (1) on the CT intensity computed from the COSMIC RO measurements.
In the global map of scintillation estimates presented in Fig. 1, the
scintillation index is an altitudinal average of σI between altitudes
1 to 4 km. Figure 2 shows an average of σI between 4 and 8 km. In
this study, we restrict our results to above 1 km due to possible data
quality issues affecting the near-surface retrievals . The
global scintillation maps presented in Figs. 1 and 2 are for the months of
January, April, July, and October of the year 2008. To construct these global
scintillation maps, about 60 000 RO profiles were employed. The results can
be easily extended to other periods.
The scintillation maps (Figs. 1 and 2) contain a wealth of valuable
information. Figures 1 and 2 show similar geographic and seasonal patterns;
however, the values of σI are significantly higher at the lower
altitudes shown in Fig. 1. This is due to the sensitivity of the radio
signals to the water vapor irregularities in the lower troposphere and as a
result signal scintillations are more frequently observed between the top of
the boundary layer and 4 km (cf. Fig. 3 of , and Fig. 2
of , for example). From the scintillation maps, the
followings can be noted.
Global map of altitudinal average (1–4 km altitudes) scintillation
index derived from the COSMIC RO data for January, April, July, and October
2008.
![]()
Global map of altitudinal average (4–8 km altitudes) scintillation
index derived from the COSMIC RO data for January, April, July, and October
2008.
![]()
Histogram of σI2 COSMIC RO averaged over 1–8 km:
(a) tropics, (b) midlatitude, and (c) high
latitude.
![]()
The effects of the tropospheric turbulence on L-band propagation have a very strong seasonal dependence.
Summer hemispheres show significant turbulent activities (measured by
σI) compared to winter hemispheres (Figs. 1a, c and 2a, c).
The magnitude of the global L-band scintillation is relatively large
in the summer hemisphere compared to the winter hemisphere. Increased
turbulence activities due to surface heating could be a reason for higher
scintillation in the summer hemisphere. This property is also consistent with
the global distribution of precipitation content, which has relatively
significant magnitude during summer .
Figures 1 and 2 show that irrespective of seasons, the tropical regions are characterized by a
relatively large σI possibly due to the concentration of significant
amount of water vapor in the lower tropical troposphere.
Using σI as a proxy for turbulence strength, we infer that the northern hemispheric summer
(July 2008, Figs. 1c and 2c) shows relatively large turbulent activities
compared to the southern hemispheric summer (January 2008, Figs. 1a and 2a).
During the respective summer months, the Antarctic region is characterized by
less turbulence strength compared to the Arctic region. This is most
pronounced in the temperate and polar regions. The effect of the Arctic sea
and the high altitude of the Antarctic, make the Arctic polar region
relatively warmer than the Antarctic region. The warm air in the Arctic holds
more moisture than the cold air in the Antarctic. Temperature fluctuations
could also cause the observed differences.
The scintillation estimates for the equinox seasons (April 2008, Figs. 1b and 2b; October 2008, Figs. 1d and 2d)
are symmetrical about the equator. Scintillation estimates in the
tropics are fairly symmetrical for all seasons.
The troposphere over the Sahara region is characterized by low scintillation effects on L-band propagation
compared to the neighboring regions to its east and west. The water vapor content is consistently low and the air is dry
over the Sahara . A close comparison
of the maps (Figs. 1a–d and 2a–d) shows that the strength of scintillation is relatively
enhanced during July (summer) over the Sahara due to relatively hotter air.
Figures 1a–d and 2a–d clearly demonstrate an ocean-continent contrast of the scintillation estimates in
the Southeast Pacific, South America, and South Atlantic regions. Over these
regions, the average σI is
low over the ocean compared to the continent.
These σI oscillations are highly correlated with (i) the convective
available potential energy (CAPE), the values of which are maximum over the continent
, and (ii) atmospheric relative humidity from satellite
data .
The turbulence strength difference between summer and winter seasons over the Antarctica is small compared
to the turbulence strength difference between summer and winter seasons over
the Arctic. Similar results based on radiosonde, satellite, and atmospheric
reanalyses observation were reported .
Compared to other regions, the Arctic and Antarctic have the least
observations available. The RO inferred map presented in Figs. 1 and 2,
therefore, helps to build and enrich the polar region database.
For all seasons, σI changes significantly with season
in the Northeast Pacific compared to Southeast Pacific.
The index of refraction structure parameter Cn2 inferred from CT
signal amplitude of COSMIC RO data.
![]()
The index of refraction structure parameter
The index of refraction structure parameter Cn2 is valuable for
investigating propagation of electromagnetic waves in the atmosphere.
Amplitude and phase of the waves propagating through the atmosphere get
degraded as Cn2 is intensified . Unfortunately,
measuring Cn2 is expensive and difficult to perform, especially over the
oceans. Due to this, Cn2 profiles are available from only a few locations
over the globe ( and the references). RO
offers the possibility of filling these gaps. Here, we present
Cn2 profiles inverted from CT amplitude scintillation incurred on COSMIC RO observations and the Rytov
variance (Eq. 2).
Assuming that the wavelength of propagation is small compared to the scale of
index of refraction fluctuations, σI can be expressed in terms of
turbulence properties (Cn2) of the medium by the Rytov variance. The
Rytov variance assumes wave propagation in weak fluctuation regimes
(σI2< 1) caused by turbulence processes having characteristics of
Kolmogorov spectra. Since the amplitude of fluctuations of the RO signals
considered are characterized by σI2<1, the Rytov variance is valid
for the present analysis. Note that the Rytov variance was used to describe
characteristics of weak scintillation of radio and microwave propagation in
the atmosphere
. For
plane waves, σI2 is proportional to Cn2 :
σI2=1.23Cn2κ∘76L116,Cn2=0.813σI2κ∘-76L-116,κ∘=2πλ.
κ∘ is a wavenumber of the electromagnetic wave, λ is
wavelength, and L is the propagation path length between a transmitter and
a receiver through the turbulent medium.
The Cn2 profile can be calculated from σI2 profile for each
occultation by making use of Eq. (2) with λ=0.2 m and
κo=31.4 m-1. Figure 3a, b, and c show the distribution of
σI2 averaged over 1–8 km in the tropics, midlatitude, and
high-latitude troposphere, respectively. The histograms reveal that about
95 % of the σI2 values are less than 1 in Fig. 3a. The
distribution of σI2 shows values less than 1 for more than 95 % of
the cases. Since measured σI2<1 in Figs. 1 and 2 predominantly,
the application of the Rytov variance is justified for estimating Cn2
profile. To compute Cn2 profiles from σI2 profiles, we still
have to know the value of an effective signal propagation length L in the
lower troposphere corresponding to RO geometry. For that purpose, L has
been estimated using an MPS model simulation technique
described in Sect. 3. We use the MPS model to calculate the scintillation
index σI2model by varying the value of Cn2 (the MPS model
runs use index of refraction as input derived from Kolmogorov spectra,
Eqs. 3 and 4). We used the following procedures in the MPS model to
estimate L. The relationship between the scintillation index
σI2model and Cn2 is linear (Eq. 2). Using linear
regression, we determine the slope in the σI2model and Cn2
relationship. The propagation path length L is estimated from the slope
and has an average value of L=650 km in the lower troposphere. We
recognize that L is not exactly a constant and would vary with altitudes
and differ from sounding to sounding; however, we expect using a single
average L to estimate Cn2 for all occultations to be a good
approximation to first order.
(a, b) Example refractivity profile employed as an input
for the multi phase screen (MPS) simulation runs; (c) scintillation
index σI2 profiles inferred from MPS model runs;
(d) σI2 inferred from COSMIC RO observations (averages over
Central Pacific, New Mexico, and Arctic, north of Alaska); and
(e) Cn2 derived from σI2 MPS model.
![]()
Figure 4 depicts representative Cn2 profiles calculated utilizing COSMIC
RO signal amplitudes received over the Central Pacific, New Mexico, Southeast
Pacific, and Arctic (north of Alaska) in January and July 2008. The Cn2
profiles are averaged over 5∘ latitude and 5∘ longitude. The
Cn2 profiles shown in Fig. 4, estimated from COSMIC RO, decrease with
altitude in the lower troposphere in agreement with measured Cn2 profiles
(, for example). Specifically, in Fig. 4a,
b, and d (Central Pacific, New Mexico, and Arctic (north of Alaska)), the
Cn2 profiles show clear seasonal behavior (summer–winter contrast).
Cn2 is larger in the July compared to January (New Mexico and Arctic
(north of Alaska), Fig. 4b and d). It is larger in January compared to July
(Southeast Pacific, Fig. 4c). In contrast, Cn2 is only a little larger in
July compared to January (Central Pacific, Fig. 4a). The mean Cn2 value
(0.25×10-14 m-2/3), reported in and the references
therein, agrees with an approximate mean summer values of
Cn2 displayed in Fig. 4b and d.