US H2108 H1 Abstract The structure constant, C
_{n} ^{2}, for optical index of refraction fluctuations is the key to the design of adaptive optical systems that minimize the effects of turbulence on laser beam propagation. This invention uses our model, which converts standard radiosonde data into C_{n} ^{2 }profiles. The results are compared to directly measured in situ values of C_{n} ^{2 }obtained by means of balloon borne thermosondes.Claims(4) 1. An electronic decision aid process to position an electromagnetic emission device in a location which will have a minimum of optical turbulence between it an a target, the process comprising the steps of:
predicting levels of optical turbulence between the target and each location in a set of potential emission locations from which the electromagnetic emission device will project an emission towards the target; and
selecting an optimum emission location which has a lowest level of optical turbulence discovered in the predicting step.
2. An electronic decision and process as defined in
3. An electronic decision aid device, as defined in
C _{n} ^{2}=2.8M ^{2}L^{4/3 } where:
and where T is absolute atmospheric temperature in °K, P is pressure in mb, γ is the dry adiabatic lapse rate of 9.8×10
^{−3 }°K/m, and z is the height above ground.4. A process, as defined in
Description The invention described herein may be manufactured and used by or for the Government for governmental purposes without the payment of any royalty thereon. The present invention relates generally to atmospheric models of optical turbulence and more specifically to an application of a mathematical equation that can be programmed into a computer which converts the usual radiosonde data (weather balloon) to the optical turbulence parameter, C As the acquisition of accurate knowledge of meteorologic conditions in the upper atmosphere has become increasingly important, devices have been developed to satisfy these requirements. As a result of the availability of this data, meteorologists are better able to make their predictions of future weather conditions. One such atmospheric meteorological sensing and telemetering system is described in U.S. Pat. No. 3,781,715 by Poppe et al, the disclosure of which is incorporated herein by reference. The Poppe radiosonde includes a number of meteorological parameter sensors, which are generally of the type having an electrical parameter, e.g., resistance, which is proportional to the sensed meteorological parameters, e.g., temperature. The sensor is connected as part of a meteorological data generator, which produces a signal utilized to modulate a carrier signal. The thus modulated carrier is thereafter transmitted by a suitable antenna carried by the radiosonde and received and processed at a remote, ground-based weather tracking station. For the information transmitted by the weather radiosonde to be most meaningful, it must be correlated to meteorological data. Currently, models are needed to convert standard meteorological data into vertical profiles of C This discussion describes our radiosonde C This invention description describes how the AFGL model was created from very high resolution velocity profiles that we obtained in the stratosphere by means of rocket laid smoke trails; next it will explain how the resulting model is used to convert radiosonde data into C At the end of the discussion some comments will be made about the lessons we learned in this research. Suggestions for future research will also be offered. The present invention is an application of a mathematical equation that can be programmed into a computer, which converts the usual radiosonde data (weather balloon), to the optical turbulence parameter, C The present invention may be defined as a process for estimating optical turbulence C collecting radiosonde data for an area of interest, the radiosonde data including measurements of: absolute temperature in degrees K (°K), pressure (P) in mB, dry adiabatic lapse rate (γ) winds (n/s) and a measure of height above ground in meters(m); (or, alternatively, these data in a weather forecast model) determining an estimate of the largest scale of inertial range turbulence(L); and calculating an estimate for the optical turbulence from the radiosonde data and from L. In the process of the invention the calculating step is performed by
where: and where T is absolute atmospheric temperature in °K, P is pressure in mb, γ is the dry adiabatic lapse rate of 9.8×10 The innovative feature of the invention includes the estimate of L, the scale of inertial range turbulence from radiosonde data or from computer weather forecast data, as discussed below. FIG. 1 is an illustration of how turbulent layers are determined. By means of these computer runs one can estimate the effects of high resolution shears on turbulence given the low resolution shear input data. FIG. 2 is a plot of Y=log <(L) FIG. 3 is a plot of Y=log <(L) FIG. 4 is comparisons between the Thermosonde Derived Profiles and A) the AFGL Model; B) the Van Zandt (NOAA) Model; and C) the Hufnagel model for Flight No. 1 of the CLEAR-1 Program. FIG. 5 is comparisons between the Thermosonde Derived Profiles and A) the AFGL Model; B) the Van Zandt (NOAA) Model; and C) the Hufnagel model for Flight No. 4 of the CLEAR-1 Program. FIG. 6 is comparisons between the Thermosonde Derived Profiles and A) the AFGL Model; B) the Van Zandt (NOAA) Model; and C) the Hufnagel model for Flight No. 10 of the CLEAR-1 Program. FIG. 7 is a plot of Y=log <(L) Basic Concepts The key equation for the AFBL model is:
where: and where T is absolute atmospheric temperature in °K, P is pressure in mb, γ is the dry adiabatic lapse rate of 9.8×10 We now consider the question “How can one estimate L from radiosonde data?” which will occupy us. It is generally known that above the convective boundary layer, atmospheric turbulence occurs in thin layers shaped like pancakes that are miles in width and tens of meters thick (usually). A shear type of instability leads to the formation of the layers, and the shears are generally caused by gravity waves (Dewan and Good, 1986). We used the common rule of thumb.
where Ri is the Richardson number, N is the buoyancy frequency, and S is the vector vertical shear of the horizontal velocity defined as Where V
and, in the present report we shall use Eq. (5). Standard radiosondes report data, such as velocity, at intervals of 300 m and larger. When such velocities are used in Eq. (4), only rarely will condition (5) hold. Presumably, since one expects that the layers are of order 1/10 the resolution of the radiosondes, the shears responsible must be on that same scale. Van Zandt et al (1981) pointed this out and indicated the resultant need for a statistical model to estimate small scale wind structure. We must use a statistical association between the large scale shears, called S The Small Scale L-Model To obtain the statistical association mentioned above we used our high resolution (10 m) stratospheric velocity profiles described in Dewan et al (1984). In all, these data consisted of 55.3 km of velocity profile information. The choice of 300 m for “radiosonde scale”, is not as arbitrary as might appear. It is based in part on subsequent model performance. Our procedure is described with reference to FIG.
but the 1/10 factor is not taken into account until the model is actually applied to the radiosonde data. Next, we obtained a weighted average of (
Occasionally a layer L Several methods to obtain S
This is to be used in Eq. (10) below. These regressions were obtained from data analyzed for every 10 m (that is, the 300 m region was shifted by 10 m for each output pair of <L
These are based on (Bevington (1969))
Using a representative value of S FIGS. 2 and 3 show a large scatter of data points about the lines. In spite of this we will see that the model performs well. The explanation lies in the fact that the standard deviation of a linear regression is like that of a mean quantity: an additional factor of the square root of a number of independent cases is involved in the “standard error” of the mean. While Eq. (8) is the model of choice, a slightly different model was employed below, namely:
but the difference is not important to model performance. An additional point must be made regarding the application of our model to the troposphere. As has been mentioned, all of the velocities in our statistical database are from the stratosphere. For this reason we must assume that this database does not differ significantly in shear statistics from actual tropospheric statistical characteristics. (Hopefully future modifications of this basic patent will be based on actual tropospheric statistics.) Model Application to Radiosonde Data Our model consists essentially of Eq. (1). Equation (2) is evaluated directly from raw radiosonde information. When we used high resolution pressure and temperature sensors, we preprocessed the data in a manner to be described. Using Eq. (4), the velocity information was converted into shears, which were then inserted in to Eq. (9) to obtain Y≡log
where the factor (0.1) comes from Eq. (6). Note that Eq. (9) contains in effect two independent pieces of the model that are applied to the stratosphere and troposphere separately. Thus, to apply this AFGL model one must first ascertain the altitude of the tropopause. In all the cases we studied this was unambiguous; but this may or may not be a problem when the model is applied to a larger volume of data, since tropopause height can be ambiguous, as is known from published data. In connecting the tropospheric model to the stratospheric model we used linear interpolation. Finally, it should be mentioned that it was necessary to build certain upper limits into the model. If the raw shear is greater than 0.04, the model assigns the value 0.04 to the shear. This was necessary because a single outlier shear due to an artifact could totally dominate the effects of the entire C Similarly, we also placed an upper limit on dT/dz in the tropospheric model. We never allowed it to exceed zero and all gradients which did were set equal to 10 Model Tests As was mentioned in the introduction, we compared the model C where k is the optical wave number≡2π/λ, and
We thus use, for figures of merit, The lower limits on these integrals were chosen to avoid the boundary layer, and all altitudes, z, are distances above ground as opposed to “above sea level”. Comparisons: Clear-1 Data During the CLEAR-1 program we obtained data from 49 thermosonde flights. To compare results from standard radiosondes we used the routine meteorological flights from El Paso located about 50 miles from the thermosonde launch site. Only those thermosonde flights nearest in time to radiosonde launches were used in our comparisons. Table 1 lists the flight information. FIGS. 4,
Up until this point our conclusions (based on Tables 1-4) are that (a) the VanZandt model gave the closest values to the thermosonde the largest number of times, and (b) it also came the closest in value if one eliminates the two worst cases in all of them. Tables 2-4 were supplemented by Tables 5 and 6, which used an alternative model as indicated. Despite the large apparent difference in these regressions, as seen in FIGS. 2 and 3 in comparison to FIG. Tables 2, 3, and 4, which compare the three models (AFGL, HUF, VZ), while showing a modest advantage to the VZ model do not compare the computational prices or loads of these models. The HUF model is clearly the simplest model, but it is significantly inferior in performance. The AFGL model (called the “Dewan Model” by the scientists at AFRL currently doing research on it) is extremely simple in comparison to the VZ model. In fact the complexity of the VZ model is so great that the computational burden it would impose makes it useless for the purpose of using it as an electronic decision aid (i.e., by imbedding it into a weather forecasting program). For this reason the AFGL model is unique for turbulence forecasting and it is this which gives this invention its advantage over other approaches. It is the most simple model with ability to forecast optical turbulence to the degree of accuracy needed.
NOTE: In Tables 5 and 6, flight number 6 was omitted. While the invention has been described in its presently preferred embodiment it is understood that the words which have been used are words of description rather than words of limitation and that changes within the purview of the appended claims may be made without departing from the scope and spirit of the invention in its broader aspects. Patent Citations
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