Infrared signature evolution of a CUBI M. van Iersel 1, A.M.J. van Eijk, H.E.T. Veerman, K.W. Benoist, and L.H. Cohen TNO, Oude Waalsdorperweg 63, 2597 AK the Hague, the Netherlands ABSTRACT A CUBI, a simple geometric metal test-object, is placed in an outdoor environment to monitor the infrared signature. The (daily) temperature evolution of the individual facets is monitored as function of environmental parameters, such as solar irradiance and ambient temperature. This provides insight in the parameters that have the strongest effects on the thermal signature of the CUBI. The CUBI is also imaged by infrared cameras and these recordings are used to estimate the temperature of the CUBI. The recorded images are also used to provide insight in the amount of air turbulence generated by the radiance of the hot CUBI facets. The amount of turbulence is compared with the ambient turbulence as calculated by standard bulk theories. Keywords: CUBI, atmospheric turbulence, IR signatures
1. INTRODUCTION There are different models that predict the infrared (IR) signature of an object in its environment [1 - 6] and calculate the surface temperatures of the object. All these models solve the heat transfer equation, which describes the heat transfer within an object (heat conduction) and between the object and its environment (convection, radiation (of sun, sky, and reflections), evaporation, and condensation). Depending on the model the 1-dimensional or 3-dimensional heat transfer equation is solved. All models take the geometry of the object into account, as well as the physical properties of the material and the environment the object is placed in. Basically all these models are based on steady-state equilibrium conditions and do not predict the evolution of the IR signature and surface temperatures. The real world, however, is far from a steady-state situation and is more dynamic in nature. Constant changes in the environment as well as changes made by the object (i.e., rotation, change of course, etc.) are the reason for a constantly changing IR signature. Modeling the dynamic IR signature is even more complex than the modeling of the steady-state IR signature. To understand the underlying physical processes of the dynamical IR signatures, one would like to simplify things and focus on one aspect of the modeling at the time. To do this, one can try to simplify the physical phenomena which are modeled, or to simplify the object that is modeled. Simplifying the physical phenomena is problematic since several phenomena are dependent upon each other and not all phenomena (e.g. the environmental parameters) can be influenced easily. When simplifying these phenomena, one runs the risk of getting a very simplified picture, which is not a representation of the real world any more. The other option is using a simple geometric (test) object, which can help to understand the underlying physical processes of the dynamic IR signature. A CUBI [4, 7] is such a simple geometric and unclassified test object. It exists of three equal-sized cubes of 0.5 x 0.5 x 0.5 m3. The cubes are arranged in such a way that they form a corner, or L-shape. The CUBI does not have any internal facets, i.e. it is hollow inside. It is used in several experiments [8], mainly to validate or compare IR signature prediction models. To study the dynamical IR signature of the CUBI and to gain insight into the influence of different environmental parameters on the signature and facet temperatures, an experiment was devised. A first analysis of the influence of the meteorological parameters on the facet temperatures of the CUBI is presented in this paper. The CUBI experiment is described in section 2. An analysis of the influence of meteorological parameters on the temperatures of the facets of the CUBI is given in section 3. Section 4 shows the analysis of the IR images and the temperatures of the facets found from these images. The atmospheric turbulence and extra turbulence induced by the hot metal facets of the CUBI are discussed in section 5. In section 6 some conclusions will be presented.
1
[email protected]
2. CUBI EXPERIMENT An experiment was devised to gain better understanding of the dynamic changes of the IR signature and facet temperatures of a CUBI due to environmental changes, as well as changes of the object (change of heading, etc.) itself. In the experimental set up the CUBIs, a meteorological station, two black bodies, and the IR cameras (see Figure 1) are placed on the roof of our laboratory in the Hague, the Netherlands. One CUBI is mounted on a pan-tilt, so it can be turned in an easy way. Both CUBIs are made of 2 mm carbon steel with an insulation of 10 mm low density polyethylene (LDPE) foam and painted in navy grey. The CUBIs are oriented in the standard way of the CUBI; the side with the step is oriented towards the north.
South Figure 1 Images of the experimental set-up: CUBIs, black bodies, meteorological station, and cameras on top of the roof of the laboratory. There are 21 thermocouples inside the CUBI measuring the temperatures of the different facets (see Figure 2). The meteorological station has all the standard sensors to measure air temperature, relative humidity, wind speed, wind direction, air pressure, rain rate, solar radiance, and sky irradiance. The two black bodies are kept at different temperatures for calibration purposes. The IR cameras are a cooled long-wave infrared (LWIR) camera with a spectral range of 8.0 – 9.4 μm, a cooled mid-wave infrared (MWIR) camera with a spectral range of 3.5 – 5.5 μm, and an uncooled LWIR camera with a spectral range of 7.5 – 14.0 μm. The dynamic changes of the IR signature are captured by an IR camera, while, at the same time, the environmental parameters and temperatures of the CUBI panels are monitored. Data of the meteorological sensors and the thermocouples are recorded every ten seconds and averaged over five minutes. The IR images are recorded once every five minutes. The range between the camera and the CUBIs is 14.5 m. The black bodies are placed at almost the same range as the CUBIs. The sensors on the meteorological station are placed at a height of 2.20 m and the IR cameras are placed at a height of 1.35 m.
North Figure 2 CUBI and the place of the thermocouples (red dots).
South
An example of the recorded meteorological parameters and some of the CUBI facet temperatures are plotted in Figure 3 for 30 June 2015. The plots clearly show the diurnal cycle of air temperature and irradiance. Just past 20.000 s (approximately at 6 a.m.) the air temperature and irradiance start to rise. Also the wind speed starts to grow at this time and the wind direction changes at the same time. Due to the growing amount of irradiance, the facet temperatures start to rise as well.
(a)
(b)
(c)
(d)
Figure 3 Meteorological parameters, air temperature and pressure (a), relative humidity and irradiance (b), and wind speed and direction (c), with the temperatures of the south facets of the CUBI recorded on 30 June 2015.
3. INFLUENCE OF METEOROLOGICAL PARAMETERS ON FACET TEMPERATURES This section addresses the external and internal factors governing the facet temperatures of the CUBI. The external factors represent the impact of the environment, e.g., the amount of (direct) solar irradiance, and often determine the temperature evolution of the CUBI. Internal factors are more subtle and include factors such as facet shadowing, internal heat conduction and facet-to-facet radiation. These effects generally have a minor effect on the temperature evolution of the CUBI. 3.1 Sample day (30 June 2015) The analysis of the facet temperatures is best started with a relatively straightforward case, i.e., a warm and sunny summer day. On 30 June 2015, the sky was cloud-free, and temperatures rose from an overnight low of 13 C to a daytime high of 27 C, obtained in a relative humidity of 40%. During the day, the internal CUBI temperatures rose to typically 10C above the ambient air temperature, and RH dropped accordingly to typically 15% under ambient humidity. Winds were absent during the night, and started to rise at 7.15 a.m., reaching a maximum of 3 m/s at 3.30 p.m. and calming down in the evening. Sunrise and sunset were at 5.23 a.m. and 10.03 p.m., respectively, which implies that the sun reached the due south position at approximately 1.45 p.m.
South
East
Top
North
West
Figure 4 Temporal evolution of the facet temperatures of the CUBI on 30 June 2015. Figure 4 shows the temporal evolution of the facet temperatures during the day. The east facets are the first to receive direct solar irradiance, right after sunrise at 5.23 a.m. Consequently, the temperature rises quickly to a maximum temperature of 47 C (well above the ambient air temperature of 21 C at that time) that is reached as early as 9.00 a.m., when the sun is in the due East direction. Shortly afterwards, the temperature starts to drop, which signals, in our opinion, that the incidence of direct solar radiance on the east facets decreases. The east facet temperatures reach a plateau at 1.30 p.m. This time coincides with an abrupt and strong increase in west facet temperatures: one may thus assume that at 1.30 p.m. direct solar irradiance of the east facets ended and that of west facets commenced. This corroborates with the time of passage of the sun through the South. This is also close to the time (2.15 p.m.) that the south and top facets reach their maximum temperature of 45 C. The effect of direct solar irradiance is also visible in the temperature evolution of the lower top facet. This facet is facing upwards, and receives direct solar irradiance once the sun starts climbing in the sky. The facet starts heating up in the morning, closely following the top facet, but the heating is interrupted when the north upper facet casts a shadow on this facet. Later in the afternoon, the shadow recedes and this lower top facet heats up again in the afternoon sun. Figure 4 shows three temperature curves for the lower top facet. The curves correspond to three individual thermocouples: TC16 is located 10 cm from the north upper facet, TC12 exactly at the center of the lower top facet, and TC15 is located in the middle of the positions of the other two thermocouples. Hence, TC16 receives more shadow than TC12 and consequently, as shown by Figure 4, the facet temperature drops more around noon. The temperature drop is at its peak around 2.00 p.m., shortly after the sun reaches the due South position and the shadowing effect is maximal. The temperature evolution of the south and top facets show that direct solar irradiance is not the only factor governing the facet temperature. The south and top facets start heating up immediately after the sun rises at 5.23 a.m., even though these facets do not receive direct solar irradiance at that time. Likewise, the north and west panels start heating up immediately after sunrise. The temperature rise is attributed to the heat exchange between the facets and the air inside and outside the CUBI, although conductive heat flow from the solar lit east panels to the other panels cannot be ruled out. However, we feel that conductive heat flow is a secondary process to heat exchange with the air. The north lower and upper panels, facing sideways, do not receive any direct solar irradiance during the day (except for brief moments in the morning and evening). Figure 4 shows that the temperature of these two north panels tops out at 30 - 33 C, which fits nicely between the external (27 C) and internal (37 C) air temperatures. More evidence of heat exchange with the air is found in the temperature evolution of the south and west facets. The west facets lack direct solar irradiance in the morning, and their temperatures then follow the internal CUBI temperature to a few (2-3 C) degrees; the difference can again be attributed to heat exchange with the colder ambient air. In the afternoon, and with direct solar irradiance, the west facet reaches its maximum temperature of 50 C as late as 5.30 p.m. This is the highest facet temperature of the day, and the combined result of direct solar irradiance and the relatively high internal CUBI temperatures. When turning our attention to the south facets, we note an asymmetry in the heating and cooling cycle. The cooling down is slower than the heating in the morning, and drags behind the solar irradiance curve.
Again, we presume that this reflects the effect of the warm air inside the CUBI, which remains fairly constant at 35 C until 7.45 p.m. Finally, we note the sharp peak in the temperature evolution of the west facet (and to a lesser extent the north and top facets) at 7.45 p.m. This is an artefact caused by the passing shadow of the TNO tower over the CUBI. The analysis presented above was repeated for a total of 17 days spread over all seasons. While seasonal effects caused changes in day length (at our latitude of 52 North the sun is less than 8 hours above the horizon in mid-winter), maximum solar zenith angle, solar irradiant intensity, and ambient temperatures, the overall temperature evolution of the facets could always be explained in terms of direct solar irradiance and heat exchange. These two factors are thus retained as the primary parameters governing the facet temperatures. 3.2 Effect of clouds and rain The presence of clouds reduces the intensity of the solar irradiance, which has an immediate effect on the facet temperatures. These effects are illustrated in Figure 5, which shows the solar irradiance curve (a), air temperature (b) and facet temperature evolutions ((c) and (d)) for 11 July 2013, when a series of clouds passed overhead during the day. Individual cloud passages show up clearly as dips in the solar irradiance curve.
(a)
(b)
(c) (d) Figure 5 Temporal evolution on 11 July 2013: (a) solar irradiance, (b) internal and external air temperatures, (c) east facets, and (d) north facets. Figure 5 (c) shows data for the east facets of the CUBI. A comparison with Figure 4 reveals that the temperature evolution follows the same general pattern, but that each cloud passage leads to an instantaneous drop in facet temperature. Likewise, the end of cloud passage leads to an instantaneous rise in facet temperature. The fall and rise in temperature are well-correlated with the dips in (direct) solar irradiance. However, the cloud passages also provoke (small) changes in the ambient and internal temperatures (see Figure 5 (b)). In this graph the curves labeled CS T1, CS T2 and CS T3 represent internal temperatures and the curves labeled CS T4 and CS T5 represent temperatures measured at the meteorological mast. This is reflected in the temperature evolution of the north upper and lower facets, which do not receive direct solar irradiance. The north facet temperatures exhibit a pattern
of small dips correlated with the cloud passage. These dips are thought to reflect the changed conditions in the heat balance between the metal facet and the internal / external air. When clouds thicken, the pattern of dips becomes less clear and overcast conditions generally result in a more or less smooth reduction of the solar irradiant intensity over the day. The CUBI then reflects the effects of the reduced solar irradiance. However, the CUBI’s behavior changes when rain comes into play. Since heat exchange with water is more efficient than with air, the deposit of the water on the facets causes these facets to assume the temperature of the rain droplets (ambient air). This leads to more cooling than induced by passing clouds. 3.3 Additional effects A close inspection of the data reveals additional, but secondary effects on the facet temperatures. Rather than engaging in elaborate discussions about small but significant changes in facet temperatures, we will point out a few of these secondary effects in the figures that were already presented. Note that these effects have been confirmed by the analysis of additional days. Returning to Figure 4, it can be seen that the temperature rise of the east facets in not constant. The facet starts to warm up at 5.30 a.m. when the sun rises above the horizon and starts irradiating the facet, but the heating clearly slows down after 7.40 a.m. when the sun still fully illuminates the facet. The time of 7.40 a.m. coincides with the arrival of an easterly wind, which was completely absent at night, and rose to a maximum of 3 m/s during the day. We thus presume that the slower heating of the facet reflects the cooling effect of the wind. Also in Figure 4, a close inspection of the north lower and upper facet temperatures reveals that the lower facet is initially cooler than the upper facet, but this situation is reversed after 11.15 a.m. The reversal may be explained by radiation of the stone underground onto the lower facet. Early morning, the stone underground is cold and prevents the lower facet from heating up. During the day, the stone underground heats up and starts radiating onto the north lower facet, which then catches up with the north upper facet. Furthermore, Figure 4 shows that the north upper facet has three thermocouples (one in the middle and two lower down, closer to the north middle facet) and that these three temperatures differ in their evolution. The CUBI design is such that these differences could provide information about radiation of heat through the air of the middle facet onto the upper facet. While we found some indications for this process, no unequivocal data can be presented at this time. Finally, a close inspection of the east and west facet temperatures in Figure 4 reveals that the east single facet cools down a little bit more rapidly than the low and high facets, and the low facet again a bit more rapidly than the high facet. Likewise, the west single facet heats up less quickly than the low facet, which again heats up slower than the high facet. We hypothesize that this behavior reflects internal heat conduction from the south facets to the west and east side of the CUBI, which thus impacts the low and high facets more than the single facet. Likewise, heat conduction from the top facet would explain the difference in low and high facets.
4. ANALYSIS OF INFRARED IMAGES The meteorological parameters and facet temperatures are recorded continuously. This is not feasible for the IR images and only during specific times the IR images were recorded. An example of such recorded images in the MWIR and LWIR bands are shown in Figure 6. These images were recorded on 30 June 2015 at 3.35 p.m. The grey values of the images need to be converted into radiance levels. The two black bodies, which are kept at fixed temperatures (and fixed radiance), are shown in the image as well and hence it is known which grey level corresponds to which temperature of the black body. The corresponding radiance levels can be calculated from these temperatures using Planck’s law. Using these two points and assuming that the cameras have a linear response to the received irradiance, a two-point calibration will suffice to determine the relationship between the grey values in the image and the radiance levels. Here the radiance levels are calculated using Planck’s law integrated over the wavelength band of the camera.
After calibration, the recorded images can be converted to the target radiance, LCUBI, (at source), which is given by: 𝐿𝐶𝑈𝐵𝐼,𝑟𝑒𝑐𝑒𝑖𝑣𝑒𝑑 = 𝜏 𝐿𝐶𝑈𝐵𝐼 + 𝐿𝑝𝑎𝑡ℎ .
(1)
Here, LCUBI,received is the radiance at lens (from the calibrated images), τ is the atmospheric transmission over the path between the lens and the CUBI, and Lpath is the atmospheric path radiance. In this case it is not necessary to correct the radiance for transmission and path radiance, since the CUBIs and the black bodies are placed at the same range and, hence, the light travels the same length through the same atmosphere. From this it follows that: 𝐿𝐶𝑈𝐵𝐼,𝑟𝑒𝑐𝑐𝑒𝑖𝑣𝑒𝑑 = 𝐿𝐶𝑈𝐵𝐼 .
(2)
Figure 6 MWIR (left) and LWIR (right) images recorded at 30 June 2015 at 3.35 p.m.
The next step is to use Plank’s law to calculate the target equivalent temperature, i.e. the temperature a black body would have when it is placed at the same range as the CUBI. From this target equivalent temperature it is possible to calculate the target real temperature, TCUBI. To do this calculation, the target radiance values, LCUBI, need to be corrected for reflections of the surrounding environment: 𝐿𝐵𝐵 (𝑇𝐶𝑈𝐵𝐼 ) =
𝐿𝐶𝑈𝐵𝐼 − (1− 𝜀)𝐿𝑠𝑢𝑟𝑟𝑜𝑢𝑛𝑑𝑖𝑛𝑔𝑠 𝜀
.
(3)
Here LBB(TCUBI) is the radiance of a black body at same temperature of the CUBI, Lsurroundings is the radiance of the direct surroundings of the CUBI, and ε is the emissivity coefficient. The radiance of the direct surroundings, Lsurroundings, can be found when the assumption is made that the CUBI reflects mainly the sky radiance, Lair, which can be approximated using Planck’s law to calculate the radiance of a black body at air temperature, LBB(Tair). Further it is assumed that the CUBI has an emissivity coefficient of 0.98 in both MWIR and LWIR bands. Using the method described above, the target equivalent temperature and the target real temperature of the CUBI are calculated from the images recorded on 30 June 2015. Figure 7 shows the results from the images recorded with the MWIR and LWIR cameras. The south facets of the CUBI are shown on the images and one should compare the calculated target real temperature with the temperature measured by the thermocouples on the south facets. The temperature measured on the south facets are shown in Figure 3(d), but for ease of convenience they are also plotted in Figure 7. Comparing these temperature curves shows that the curves have the same shape and reach approximately the same maximum temperature, just over 46 °C. One should note that the time in Figure 7 does not cover a full day, since the IR cameras are not running continuously. It starts at 33.000 s (9.10 a.m.) and stops at 85.800 s (11.05 p.m.). The comparison was made for other days and a similar trend is seen on these days.
Figure 7 Target real temperature (red) and target equivalent temperature (blue) calculated from the MWIR (left) and LWIR (right) images recorded at 30 June 2015 as well as the thermocouple data from the south facet (green).
5. CALCULATING THE REFRACTIVE INDEX STRUCTURE PARAMETER It is possible to calculate the refractive index structure parameter, Cn2, from the recorded meteorological data using standard Monin-Obhukov similarity theory [9, 11]. The micro-meteorological model TARMOS [11] was used to do this calculation. TARMOS offers two modes: with an assumed relation for the roughness length for momentum, z0m [12], or with an assumed relation for the drag coefficient under neutral conditions, CDN [13]. On the roof of our laboratory lie some tiles and a roughness length of 0.03 m for stone was used in the calculation of the refractive index structure parameter. Using the meteorological data of 30 June 2015 the refractive index structure parameter, Cn2, was calculated. Figure 8 shows the results of this calculation as the blue line. It clearly shows that Cn2 fluctuates strongly in the beginning, reflecting the neutral conditions in the morning. Just past 40.000 s (just past 11.05 a.m.) the refractive index structure parameter starts to rise, reaching a maximum value of 1.8 * 10-13 m-2/3 at approximately 57.600 s (4 p.m.). When one looks at the cars parked in a parking lot on a hot summer day, one can see the air simmering just above the roofs of the cars. The metal of the car roof heats up by the sun and starts radiating and heating up the air in a small layer above the roof and hence creating some turbulence in this small layer of air just above the roof. As was shown above, the CUBI facets reach a higher temperature than the surrounding air temperature. Just like the cars, the CUBI shows some turbulence in a small layer of air above it. The amount of turbulence created by the CUBI in the first few centimeters above it, was calculated using the Monin-Obhukov similarity theory. Instead of the air temperature, the temperature of the CUBI facet, as measured by the thermocouples, was used. Further a roughness length of 0.0002 m for steel was used. Again, Tarmos was used to calculate the refractive index structure parameter in the first few centimeters just above the metal surface. The results for 30 June 2015 are shown in Figure 8 by the red line. It clearly shows that the refractive index structure parameter starts to rise around 26.000 s (7.13 a.m.). This corresponds with the rise of air temperature and irradiance as shown in Figure 3. This happens after sun rise and only then the CUBI starts to heat up. A maximum of value of Cn2 of 2.8*10-12 m-2/3 is reached around 51.000 s (2.11 p.m.). This maximum coincides with the maximum of solar irradiance as is shown in Figure 3(b). The maximum value of the refractive index structure parameter for the CUBI is an order of magnitude higher than the maximum value calculated for the air temperature.
Figure 8 Refractive index structure parameter Cn2 calculated using the air temperature (blue) and the CUBI facet temperature (red).
The IR images recorded on the same day, 30 June 2015, can be used to estimate the blur in the image. As is shown in [14] the estimated blur can be used to calculate the refractive index structure parameter by: 𝑏𝑙𝑢𝑟 =
𝜆𝑓 2.3548 𝐷
−1/2 𝐷 5/3
⌊1 − 0.268 ( ) 𝑟0
⌋
,
(4)
where λ is the wavelength, f is the focal length, D the aperture size, and r0 is the Fried parameter which is given by: 𝑟0 = (1.325 𝑘 2 𝐶𝑛2 𝐿)−3/5 .
(5)
Here k is the wave number (2π/λ), Cn2 is the refractive index structure parameter, and L is the path length between the CUBI and the camera. Equation (4) is plotted as the blue line in Figure 9. The technique described in [15] is used to estimate the blur in the MWIR and LWIR images recorded on 30 June 2015 at 2.10 p.m. This time coincides with the maximum irradiance as shown in Figure 3(b). The blur estimated in the MWIR image is 3.72 pixels and for the LWIR image it is 3.88 pixels. These values are shown in Figure 9 as the black dashed line for the MWIR image and as the black dash-dotted line for the LWIR image. The corresponding refractive index structure parameter values are 1.9 * 10-11 m-2/3 for the MWIR image and 2.0 * 10-11 m-2/3 for the LWIR image. This is about an order of magnitude larger than the value we calculated for the facet temperatures of the CUBI.
6. CONCLUSIONS A data set was recorded existing of the CUBI facet temperatures, the meteorological data, and on occasion MWIR and LWIR images. An analysis of the influence of the meteorological parameters on the facet temperatures showed that the temperature evolution of the facets can be explained in terms of the solar irradiance and the heat exchange with the surrounding air. The effects of clouds and rain on the CUBI temperature were illustrated. From the recorded images the temperature of the CUBI was estimated and this calculated temperature corresponds very well to the recorded temperatures of the thermocouples. The refractive index structure parameter for air was calculated from the meteorological parameters using standard Monin-Obhukov similarity theory. The same theory was used to calculate the refractive index structure parameter in the
first few centimeters above the CUBI. This parameter was also calculated using Eqn. (4) and (5) and the estimated blur from the images. These values show an order of magnitude difference.
Figure 9 Refractive index structure parameter Cn2 vs. blur calculated using Eqn. (4) (blue) and the estimated value in the MWIR image (dashed line) and LWIR image (dash-dotted line).
ACKNOWLEDGEMENTS The work in this paper was performed as part of the TNO research programme V1303 – Above Water Signatures sponsored by the Ministry of Defence of the Netherlands.
REFERENCES 1.
Kunz, G.J. , Moerman, M.M., van Eijk, A.M.J., Doss-Hammel, S.M., and Tsintikidis, D., “EOSTAR : An electro-optical sensor performance model for predicting atmospheric refraction, turbulence and transmission in the marine surface layer”, Proc. SPIE 5237, 81-92 (2003).
2.
Van Eijk, A.M.J., Degache, M.A.C., Tsintikidis, D., and Hammel, S., “EOSTAR Pro: a flexible extensive library to assess EO sensor performance”, Proc. SPIE 7828 (2010).
3.
Van Eijk, A.M.J., Degache, M.A.C, and de Lange, D.J.J., “The EOSTAR model suite” in International Symposium on Optronics in Defense and Security, OPTRO 2010, 3-5 February, Paris, France. (2010).
4.
Malaplate, A., Grossmann, P., and Schwenger, F., “CUBI – a Test Body for thermal Object Model Validation”, Proc. SPIE 6543(2007).
5.
F.D. Lapierre, Dumont, R., Borghgraef, A., Marcel, J-P, and Acheroy, M., “OSMOSIS: An Open-Source Software for Modelling of Ship Infrared Signature”, in Proceedings of the 3rd International IR Target, Background Modelling & Simulation (ITBMS) Workshop, 25-29 June 2007, Toulouse, France.
6.
Vaitekunas, D.A., Sideroff, Ch., and Moussa, Ch., “Improved signature prediction through coupling of ShipIR and CFD”, Proc. SPIE 8014 (2011).
7.
Bushlin, Y., Lessin, A., and Reinov, A., “Comparison of thermal modeling and experimental results of a generic model for ground vehicle”, Proc. SPIE 62390P (2006).
8.
CUBI forum website: http://www.iard.co.il/cubi/
9.
Monin, A.S. and Obukhov, A.M., “Basic laws of turbulent mixing in the atmosphere near the ground”, Tr. Inst. Acad. Nauk. Sci., SSR. Inst. Geophiz., 24, 1963-1987 (1954).
10. Frederickson, P.A., Davidson, K.L., Zeisse, C.R., and Bendall, C.S., “Estimating the Refractive Index Structure Parameters (Cn2) over the Ocean Using Bulk Methods”, Journal of Applied Meteorology, Vol. 39, pp. 1770 – 1783 (2000). 11. Kunz, G.J., “A bulk model to predict optical turbulence in the marine surface layer”, TNO Physics and Electronics Laboratory, The Hague, the Netherlands, report FEL-96-A053 (1996). 12. Smith, S.D., “Coefficients for sea surface wind stress, heat flux, and wind profiles as a function of wind speed and temperature”, J. Geophys. Res, 93, no C12, 15.467-15.472 (1988). 13. Davidson, K.L., Schacher, G.E., Fairall, C.W., and Goroch, A.K., “Verification of the bulk method for calculating over water optical turbulence”, Appl. Opt., 20, 17, pp. 498-502 (1981). 14. Repassi, E. and Weiss, R., “Computer Simulation of Image Degradations by Atmospheric Turbulence for Horizontal Views”, Proc. SPIE 8014 (2011). 15. Bouma, H., Dijk, J., and van Eekeren, A., “Precise local blur estimation based on the first-order derivative”, Proc. SPIE 8399 (2012).
