Cn2 Values Research Articles

Quantification of surface layer turbulence using sensible heat values from energy balance versus aerodynamic methods

Surface layer optical turbulence values in the form of the refractive index structure function C n 2 are often calculated from surface layer temperature, moisture, and wind characteristics and compared to measurements from sonic anemometers, differential temperature sensors, and imaging systems. A key derived component needed in the surface layer turbulence calculations is the sensible heat value. Typically, the sensible heat is calculated using the bulk aerodynamic method that assumes a certain surface roughness and a friction velocity that approximates the turbulence drag on temperature and moisture mixing from the change in the average surface layer vertical wind velocity. These assumptions/approximations generally only apply in free convection conditions. To obtain the sensible heat, a more robust method, which applies when free convection conditions are not occurring, is via an energy balance method such as the Bowen ratio method. The use of the Bowen ratio––the ratio of sensible heat flux to latent heat flux––allows a more direct assessment of the optical turbulence-driving surface layer sensible heat flux than do more traditional assessments of surface layer sensible heat flux. This study compares surface layer C n 2 values using sensible heat values from the bulk aerodynamic and energy balance methods to quantifications from sonic anemometers posted at different heights on a sensor tower. The research shows that the sensible heat obtained via the Bowen ratio method provides a simpler, more reliable, and more accurate way to calculate surface layer C n 2 values than what is required to make such calculations from bulk aerodynamic method-obtained sensible heat.

A Multifaceted Exploration of Atmospheric Turbulence and Its Impact on Optical Systems: Structure Constant Profiles and Astronomical Seeing

This study emphasizes the importance of conducting a comprehensive analysis considering the Cn2 atmospheric parameter for a reliable assessment of the seeing value. It highlights the use of the ECMWF ERA5 model to simulate pressure, temperature, and humidity profiles, enabling the evaluation of optical degradation. Accurate modeling and monitoring of temperature and humidity variables are emphasized for precise data in optical communication and astronomical observations. It also discusses the significance of optical turbulence models in understanding the impact of atmospheric turbulence on optical system performance. The validation of the selected Cn2 models is thoroughly analyzed. To evaluate the impact of the boundary layer on seeing conditions, three factors are considered. First, ERA5 data is used to simulate surface Cn2 values using the PAMELA model. Second, typical Cn2 values for specific dates in Redu are obtained. Finally, the thickness of the boundary layer, denoted as hbl, is calculated. This finding highlights the significant influence of the boundary layer on atmospheric seeing conditions and by incorporating Ibl into the models, a more accurate representation of the effects of the boundary layer on seeing quality is achieved.

Water Recharge Variability Across Serayu Watershed Using Soil Water Assessment Tool (SWAT)

Climate change and land use have an influence on the process of groundwater replenishment. Serayu watershed is categorized as one of the critical watersheds in Indonesia due to groundwater conditions. One that affects groundwater is the ability to replenish groundwater. The purpose of the study was to predict groundwater replenishment in the Serayu watershed. The hydrological model approach (SWAT/Soil Water Assessment Tool) was applied. Spatial data is used in SWAT model analysis, namely: Elevation data, stream, soil types, land use land cover, and climate data. Data analysis using QGIS 3.18 and QSWATPlus tools. The model calibration uses cn2 values while NSE and R2 values are used to evaluate the model. Based on cn2 values, SWAT models show performance that can be used for model implementation. Model validation between before and after the calibration process is (R2) 0.86 while the NSE value is 0.66. When viewed from the water equilibrium ratio, the average water recharge value in the Serayu watershed is 49.5 mm.yr-1 from the total precipitation of 2473.6 mm.yr-1. The largest hydrological component occurs in evapotranspiration and surface runoff (1879.9 and 549.2 mm.yr-1, respectively). The high value of surface runoff indicates that the Serayu watershed needs attention regarding the ability of the land in the water recharge process

Electro-Optical Sensors for Atmospheric Turbulence Strength Characterization with Embedded Edge AI Processing of Scintillation Patterns

This study introduces electro-optical (EO) sensors (TurbNet sensors) that utilize a remote laser beacon (either coherent or incoherent) and an optical receiver with CCD camera and embedded edge AI computer (Jetson Xavier Nx) for in situ evaluation of the path-averaged atmospheric turbulence refractive index structure parameter Cn2 at a high temporal rate. Evaluation of Cn2 values was performed using deep neural network (DNN)-based real-time processing of short-exposure laser-beacon light intensity scintillation patterns (images) captured by a TurbNet sensor optical receiver. Several pre-trained DNN models were loaded onto the AI computer and used for TurbNet sensor performance evaluation in a set of atmospheric propagation inference trials under diverse turbulence and meteorological conditions. DNN model training, validation, and testing were performed using datasets comprised of a large number of instances of scintillation frames and corresponding reference (“true”) Cn2 values that were measured side-by-side with a commercial scintillometer (BLS 2000). Generation of datasets and inference trials was performed at the University of Dayton’s (UD) 7-km atmospheric propagation test range. The results demonstrated a 70–90% correlation between Cn2 values obtained with the TurbNet sensors and those measured side-by-side with the scintillometer.

Analysis of Scintillation Effects on Free Space Optical Communication Links in South Africa

The performance of free space optical communication (FSOC) systems is severely degraded by certain atmospheric conditions prevalent in places where they are deployed, in spite of their numerous advantages. In clear weather conditions, the random fluctuation in the atmosphere’s refractive index causes substantial scintillation losses to transmitted optical signals. It is therefore imperative to estimate the potential losses due to atmospheric turbulence in locations where FSOC links are to be deployed. This will provide the necessary fade margin for FSOC systems so that designed links withstand such atmospheric disturbances. In this paper, statistical analysis of wind speed data collected for various cities of South Africa is used for calculating the corresponding refractive index structure parameter (Cn2). These Cn2 values, as well as the zero inner scale and infinite outer scale model and finite inner and finite outer scale model, are used in computing the scintillation indices not exceeding 50%, 99%, 99.9%, and 99.99% of the time for the investigated locations. The Lognormal and Gamma–gamma distribution models are then employed for the computational analysis of the irradiance fluctuations and channel characteristics while considering the effect of pointing errors for weak and moderate to strong turbulence regimes. Finally, derived mathematical expressions for outage probabilities and bit error rate (BER) performances for FSOC links, employing various intensity modulation and direct detection (IM/DD) schemes, are presented.

Revised runoff curve number for runoff prediction in the Loess Plateau of China

AbstractThe soil conservation service (now Natural Resources Conservation Service) Curve Number (SCS‐CN), one of the most commonly used methods for surface runoff prediction. The runoff calculated by this method was very sensitive to CN values. In this study, CN values were calculated by both arithmetic mean (CN_C) and least square fit method (CN_F) using observed rainfall‐runoff data from 43 sites in the Loess Plateau region, which are considerably different from the CN2 values obtained from the USDA‐SCS handbook table (CN_T). The results showed that using CN_C instead of CN_T for each watershed produce little improvement, while replacing CN_T with CN_F improves the performance of the original SCS‐CN method, but still performs poorly in most study sites. This is mainly due to the SCS‐CN method using a constant CN value and discounting of the temporal variation in rainfall‐runoff process. Therefore, three factors—soil moisture, rainfall depth and intensity—affecting the surface runoff variability are considered to reflect the variation of CN in each watershed, and a new CN value was developed. The reliability of the proposed method was tested with data from 38 watersheds, and then applied to the remaining five typical watersheds using the optimized parameters. The results indicated that the proposed method, which boosted the model efficiencies to 81.83% and 74.23% during calibration and validation cases, respectively, performed better than the original SCS‐CN and the Shi and Wang (2020b) method, a modified SCS‐CN method based on tabulated CN value. Thus, the proposed method incorporating the influence of the temporal variability of soil moisture, rainfall depth, and intensity factors suggests an accurate runoff prediction for general applications under different hydrological and climatic conditions on the Loess Plateau region.

SWAT模型参数对土地利用变化的响应及其对不同时间尺度径流模拟的影响

SWAT模型广泛应用于土地利用变化的水文效应评估研究，但土地利用变化是否对模型参数产生影响，进而影响径流模拟效果还有待于进一步分析。以东南沿海福建省山美水库流域为研究区，基于SWAT模型，分别模拟1995年、2005年、2015年土地利用条件下的年、月、日尺度径流过程，采用SWAT-CUP进行参数敏感性分析与自动率定，分别获取1995年、2005年、2015年3种土地利用条件下径流过程模拟的最优参数集，比较参数差异；将3组参数集分别应用到不同土地利用条件，分析参数变化对不同时间尺度径流模拟的影响。结果表明：（1）1995-2015年间，研究区土地利用格局发生了较大变化，主要表现为林地转向园地和建设用地；3期土地利用条件下率定的SWAT模型都能较好地模拟山美水库流域年、月、日尺度径流，其效率系数NS和决定系数R²分别大于0.62和0.78。（2）不同土地利用条件下敏感参数基本一致，敏感参数分别为CN2、SOL_AWC、SOL_K、CANMX、ESCO、GW_DELAY、OV_N，但敏感参数取值随着土地利用变化而变化，其变化规律符合敏感参数的物理意义，变化率基本与土地利用变化强度正相关。（3）由土地利用变化引起的参数变化，对年、月径流模拟的影响较小，对日径流影响显著，且随着土地利用变化强度的增加而增加。;The distributed hydrological model provides an effective means for runoff simulation and hydrological response to land use change. SWAT model is widely used to evaluate the hydrological response of land use change. However, the response of model's parameters to land use change and its effects on the simulation of runoff have not been well investigated. In this study, Shanmei Reservoir watershed located in the southeastern China was took as a research area and SWAT models for the simulation of the annual, monthly, daily runoff were constructed under the land use conditions of 1995, 2005 and 2015, respectively. The optimal values set for the sensitive parameters under three land use conditions were determined with the method of SWAT-CUP, respectively. The three optimal values sets of parameters then were applied to analyze the effects of land use change on the simulation of different time scales runoff. The results showed that:(1) the land use pattern in the study area changed greatly from 1995 to 2015. The garden and urban land were increased while the forest was reduced significantly. The SWAT models well simulated the different time scales runoff process for the three land use conditions of 1995, 2005 and 2015 with the Nash-Suttcliffe (NS) was above 0.62 and the coefficient of determination (R²) above 0.78. (2) The sensitive parameters were same for the three land use conditions which included CN2, SOL_AWC, SOL_K, CANMX, ESCO,GW_DELAY and OV_N. The values of the sensitive parameters were varied with the change of land use and the variation was coincident with the physical meaning of sensitive parameters. The values of CN2, SOL_K, CANMX, ESCO and OV_N in the study area were gradually increased from 1995 to 2015, while the values of SOL_AWC and GW_DELAY gradually decreased. The reason for the changing trend of sensitive parameters was that the land use in the study area was changed partly from forest to garden, pasture, orchard and urban land from 1995 to 2015, resulting in the decrease of the forest area. (3) The change of the value of sensitive parameters, caused by land use change, had little influence on the simulation of the annual and monthly runoff but significantly on the daily runoff. The influences on the daily runoff increased with the increase of the amplitude of land use change.

An Improved SCS-CN Method Incorporating Slope, Soil Moisture, and Storm Duration Factors for Runoff Prediction

Soil Conservation Service Curve Number (SCS-CN) is a popular surface runoff prediction method because it is simple in principle, convenient in application, and easy to accept. However, the method still has several limitations, such as lack of a land slope factor, discounting the storm duration, and the absence of guidance on antecedent moisture conditions. In this study, an equation was developed to improve the SCS-CN method by combining the CN value with the tabulated CN2 value and three introduced factors (slope gradient, soil moisture, and storm duration). The proposed method was tested for calibration and validation with a dataset from three runoff plots in a watershed of the Loess Plateau. The results showed the model efficiencies of the proposed method were improved to 80.58% and 80.44% during the calibration and validation period, respectively, which was better than the standard SCS-CN and the other two modified SCS-CN methods where only a single factor of soil moisture or slope gradient was considered, respectively. Using the parameters calibrated and validated by dataset of the initial three runoff plots, the proposed method was then applied to runoff estimation of the remaining three runoff plots in another watershed. The proposed method reduced the root-mean-square error between the observed and estimated runoff values from 5.53 to 2.01 mm. Furthermore, the parameters of soil moisture (b1 and b2) is the most sensitive, followed by parameters in storm duration (c) and slope equations (a1 and a2), and the least sensitive parameter is the initial abstraction ratio λ on the basis of the proposed method sensitivity analysis. Conclusions can be drawn from the above results that the proposed method incorporating the three factors in the SCS method may estimate runoff more accurately in the Loess Plateau of China.

Measurement and analysis of atmospheric optical turbulence in Lhasa based on thermosonde

In this paper, we have analyzed the wind, temperature and optical turbulence index structure constant (Cn2) that are directly measured for the first time at Lhasa, Tibet. Unlike other mid-or-low latitude regions, the wind speed in Lhasa increases with the altitude according to the wind profiles, besides a strong wind speed near the tropopause. The temperature profiles indicate a large temperature change near the tropopause. The optical turbulence profiles show daily variation. When the altitude is below 12 km, except for individual points, the Cn2 values during morning and evening are basically in the same range of 10−17-10−15 m-2/3. When altitude is above 12 km, the intensity of turbulence during the morning in Lhasa is 1–2 orders of magnitude larger than that of the evening. In addition, we propose a turbulence profile model on the basis of Hufnagel-valley model to calculate the integrated values of the refractive index structure constants of the entire atmosphere, such as the Fried parameter, the seeing, the coherence time and the isoplanatic angle. The mean atmospheric coherence length r0 is 5.77 cm. Differences in these parameters between morning and evening also illustrate the stronger turbulence in the morning than evening.

Strategies to enhance the reliability of flow quantile prediction in the gauged and ungauged basins

AbstractThe precise reproduction of different flow regimes in both gauged and ungauged watersheds is crucial for managing environmental flow and water quality requirements. However, the ability of hydrological models to reproduce flow quantiles (FQs) is often influenced by the process of calibrating the most dominant parameters through traditional parameter estimation methods. This research proposes a systematic parameter estimation approach to improve the credibility of the hydrologic model in reproducing FQs in gauged and ungauged watersheds through the following steps: (a) implementation of parameter sensitivity analysis to identify the dominant parameters, (b) initial estimation of the sensitive parameter values, (c) an iterative search for the optimal value of the dominant parameter in reproducing FQs and (d) regionalization of parameters to estimate FQs in the ungauged watersheds. The analysis shows the highest sensitivity of the runoff curve number (CN2) in simulating the hydrologic process in all test watersheds. Moreover, the best value of CN2 was found to be different for each flow quantile. Therefore, CN2 was updated for reproduction of FQs, which resulted in an overall average improvement of the regionalized model accuracy (across all test watersheds and flow quantiles) by 37 and 46% during the calibration and validation periods, respectively. The spatiotemporal dynamics of the water balance components that often control the behaviours of FQs in both the gauged and ungauged watersheds were also quantified. The results show a wide range of spatiotemporal variations for the majority of the water balance components.

Performance analysis of weather research and forecasting model for simulating near-surface optical turbulence over land

Accurate knowledge of the optical turbulence (Cn2) in the atmospheric surface layer is of great significance for the applications of various ground-based optical systems (e.g., astronomical observation, laser communication and target detection), however, many methods using instruments to measure Cn2 are limited spatially and temporally and they are more difficult and expensive in severe environments, which makes estimations a less expensive and convenient alternative. This study introduces a method where the products of Weather Research and Forecasting (WRF) model coupled with Monin–Obukhov similarity (MOS) theory is used to estimate the value of Cn2 in the surface layer, and the performance of this method is evaluated against the corresponding Cn2 dataset from the in-situ micro-thermometer during a campaign over south-west China. The variance between the estimated Cn2 and measured Cn2 is found to be comparable to the observed variance of the temporal due to temporal and spatial variations of the atmospheric turbulence. Evaluation against direct observations shows that this approach can well estimate Cn2 time series with some error in some time periods, and both the estimated Cn2 and the measured Cn2 are more consistent in trend and magnitude in general. Given these validated results, this method has the potential to be a useful tool in a wide range of ground-based optical applications.

A new model for the profiles of optical turbulence outer scale and Cn2 on the coast

Atmospheric optical turbulence severely restricts the performances of electro-optical systems. The turbulent atmosphere causes the intensity of a light beam to fluctuate or scintillate, leads the light beam to wander and makes the images randomly displace, which directly relates to the refractive index structure parameter Cn2. Therefore the knowledge of Cn2 is essential to evaluate and to predict the effects of optical turbulence on electro-optical imagery systems. During the period from December 13, 2016 to January 2, 2017, 30 sets of sounding data, which include temperatures, humidities, pressures, wind speeds, wind directions and atmospheric refractive index structure parameters, are obtained by using a self-developed meteorological radiosonde for turbulence at Marine Meteorological Science Experiment Base at Bohe of Maoming. On the basis of the HMNSP99 outer scale model, an atmospheric optical turbulence outer scale formula of Maoming is obtained by fitting the sounding data. At the same time, the experimental data of the turbulence profiles are statistically averaged, and then based on the Hufnagel-Valley model, a statistical model is obtained, which is appropriate to the variation of the turbulence profile on the coast. According to Tatarski turbulence parameterization and the Maoming outer scale formula, the new estimated Cn2 values are compared with their experimental observations and the results from other already defined models, respectively. Statistical analysis shows that the overall correlation coefficients of log10(Cn2) between observed values and estimated values by using the new fitting Maoming outer scale formula, the HMNSP99 model, the Dewan model and the Coulman model are 0.924, 0.848, 0.763 and 0.651, respectively. Also, both the trends and magnitudes for these four outer scale models are consistent with each other. The errors of the above four outer scale models are very small:their overall average absolute errors and average relative errors are 0.514 and 2.963%, 0.627 and 3.612%, 0.943 and 5.439%, 0.766 and 4.417%, respectively, and the error of the Maoming outer scale model is smallest. The reliabilities and validities of the new outer scale and Cn2 models are further verified. In addition, it is found that the occurrence of upper air optical turbulence is closely related to wind shear and temperature gradient. The results support the prediction of the atmospheric optical turbulence profile required for electro-optical engineering on the coast.

Real Measurements and Evaluation of the Influence of Atmospheric Phenomena on FSO Combined with Modulation Formats

The influence of atmospheric environment is fundamental for Free-Space Optical link (FSO). The atmosphere can significantly degrade the communication quality of FSO up to so low received power/RSSI level that it can lead to the loss of communication. For this reason, authors used a professional weather station built on site of FSO link for measurement of real atmospheric conditions such as wind speed, temperature, relative air humidity, air pressure and solar radiation. Random changing of these atmosphere parameters creates atmospheric turbulences, absorption and dispersion centers. It is necessary to specify the value of refractive index structure parameter Cn2 because it determines the influence of atmosphere on the FSO. The first part of this article includes the theoretical calculation of Cn2, there are used two models PAMELA and Macroscale-Meteorological model. The evaluation of the atmospheric influences and the RSSI value of received power level and also simulation of different types of modulation formats OOK-RZ, OOK-NRZ and BPSK in Optiwave is in tegral part of this article.

Estimating optical turbulence of atmospheric surface layer at Antarctic Taishan station from meteorological data

Turbulence intensity in the near-surface layer and its decrease rate with height are closely related to the quality of potential sites. Astronomers have been pursuing a perfect astronomical site to place the large-aperture telescopes. Compared with the best mid-latitude sites, Antarctic plateau inevitably becomes an ideal site for building the next-generation large optical and infrared telescopes, which is because of its low infrared sky emission, low atmospheric precipitable water vapour content, low aerosol and dust content of the atmosphere, and light pollution. In this paper, we establish a model of the atmospheric optical turbulence in surface layer, and use it to estimate Cn2 at Antarctic Taishan station for the first time. The meteorological parameters of the model input are the data measured by a mobile atmospheric parameter measurement system at Antarctic Taishan station from 30 December 2013 to 10 February 2014. The values of Cn2, estimated by the model and measured by a micro-thermometer, are compared. Sensitivity analysis of the estimation method is also carried out. The measurement results and analyses show that Cn2 obtained at Taishan station has obvious diurnal variation characteristics, with well-behaved peaks in the daytime and nighttime, and minima near sunrise and sunset. Cn2 obtained in the nighttime is stronger than that in daytime, more specifically, it is on the order of 210-14 m-2/3. The comparison between model predictions and experimental data demonstrates that it is feasible to estimate Cn2 in Antarctic by using this model. The biggest differences between Cn2 values obtained from the model and measurement usually emerge at sunrise and sunset, respectively. Considering the fact that Antarctic atmosphere is in a stable state most of the time, the values of Cn2 estimated by different nondimensional structure parameter functions are nearly the same. Thus, the measurement accuracy of air temperature difference from one height to another is the main factor that affects the estimated value of Cn2.

Quantification of optical turbulence in the ocean and its effects on beam propagation.

The influence of optically active turbulence on the propagation of laser beams is investigated in clear ocean water over a path length of 8.75 m. The measurement apparatus is described and the effects of optical turbulence on the laser beam are presented. The index of refraction structure constant is extracted from the beam deflection and the results are compared to independently made measures of the turbulence strength (Cn2) by a vertical microstructure profiler. Here we present values of Cn2 taken from aboard the R/V Walton Smith during the Bahamas optical turbulence exercise (BOTEX) in the Tongue of the Ocean between June 30 and July 12, 2011, spanning a range from 10-14 to 10-10 m-2/3. To the best of our knowledge, this is the first time such measurements are reported for the ocean.

Estimating the surface layer refractive index structure constant over snow and sea ice using Monin-Obukhov similarity theory with a mesoscale atmospheric model

Since systematic direct measurements of refractive index structure constant ( Cn2) for many climates and seasons are not available, an indirect approach is developed in which Cn2 is estimated from the mesoscale atmospheric model outputs. In previous work, we have presented an approach that a state-of-the-art mesoscale atmospheric model called Weather Research and Forecasting (WRF) model coupled with Monin-Obukhov Similarity (MOS) theory which can be used to estimate surface layer Cn2 over the ocean. Here this paper is focused on surface layer Cn2 over snow and sea ice, which is the extending of estimating surface layer Cn2 utilizing WRF model for ground-based optical application requirements. This powerful approach is validated against the corresponding 9-day Cn2 data from a field campaign of the 30th Chinese National Antarctic Research Expedition (CHINARE). We employ several statistical operators to assess how this approach performs. Besides, we present an independent analysis of this approach performance using the contingency tables. Such a method permits us to provide supplementary key information with respect to statistical operators. These methods make our analysis more robust and permit us to confirm the excellent performances of this approach. The reasonably good agreement in trend and magnitude is found between estimated values and measurements overall, and the estimated Cn2 values are even better than the ones obtained by this approach over the ocean surface layer. The encouraging performance of this approach has a concrete practical implementation of ground-based optical applications over snow and sea ice.

Use of weather research and forecasting model outputs to obtain near-surface refractive index structure constant over the ocean.

The methods to obtain atmospheric refractive index structure constant (Cn2) by instrument measurement are limited spatially and temporally and they are more difficult and expensive over the ocean. It is useful to forecast Cn2 effectively from Weather Research and Forecasting Model (WRF) outputs. This paper introduces a method that WRF Model is used to forecast the routine meteorological parameters firstly, and then Cn2 is calculated based on these parameters by the Bulk model from the Monin-Obukhov similarity theory (MOST) over the ocean near-surface. The corresponding Cn2 values measured by the micro-thermometer which is placed on the ship are compared with the ones forecasted by WRF model to determine how this method performs. The result shows that the forecasted Cn2 is consistent with the measured Cn2 in trend and the order of magnitude as a whole, as well as the correlation coefficient is up to 77.57%. This method can forecast some essential aspects of Cn2 and almost always captures the correct magnitude of Cn2, which experiences fluctuations of two orders of magnitude. Thus, it seems to be a feasible and meaningful method that using WRF model to forecast near-surface Cn2 value over the ocean.

Effects of biological tissues on the propagation properties of anomalous hollow beams

We derived analytical formulae of anomalous hollow beams (AHBs) passing through the turbulent biological tissues based on the extended Huygens–Fresnel integral formula. With the help of these formulae, we investigate the propagation properties of AHBs in turbulent biological tissues, the irradiance and spreading properties of AHBs in turbulent biological tissues are studied numerically. It is found that the circular and elliptical AHBs eventually become Gaussian beams in the far field and the central irradiance of the AHB rises more rapidly as the value of Cn2 grows. We also calculate the formulae of the effective beam size of AHB and find that finally Wxz becomes equal to Wyz in turbulent biological tissues which can be used to explain the beam spot eventually becomes circular under the influence of turbulence of biological tissues.

Wavelength correction of refractivity variation measurements

The index of refraction structure constant, Cn2 indicates how strongly the index of refraction varies in a region of the atmosphere. These variations usually arise through turbulent motions, creating an inhomogeneous distribution of species, density, temperature and pressure. Because the index of refraction also depends on wavelength, the measured value of Cn2 will depend on wavelength. This Cn2 difference generally becomes more pronounced as the difference in wavelength increases. This paper describes a technique for converting between measurements of Cn2 at different wavelengths, and gives an example for converting from centimeter to visible and near IR wavelengths.

Direct evaluation of refractive-index structure functions from large-eddy simulation output for atmospheric convective boundary layers

Fluctuations of the refractive index associated with atmospheric turbulence affect the propagation of electromagnetic and acoustic waves in the atmosphere. In the reported study, the effects of turbulence on wave propagation in the atmospheric convective boundary layer (CBL) are considered in terms of the second-order refractive index structure function and related to its structure-function parameter Cn2. Two structure-function evaluation methods are compared. The direct evaluation method involves calculating the refractive index at each point in the simulation domain with subsequent calculation of the structure function. The second method is based on a parameterized linear relationship between the refractive-index structure function and temperature/humidity structure functions. For each evaluation method, vertical profiles of Cn2 computed for separations along the three coordinate directions collapse together over a significant portion of the CBL. Near-surface divergence of Cn2 values along the horizontal directions was noted and attributed to the influence of surface wind shear on the turbulent fluctuations of temperature and humidity. The behavior of Cn2 near the surface was shown to agree favorably with similarity-theory predictions.