# Optical Turbulence Profile Forecasting and Verification in the Offshore Atmospheric Boundary Layer
###### Abstract  
A backpropagation neural network (BPNN) approach is proposed for the forecasting and verification of optical turbulence profiles in the offshore atmospheric boundary layer. To better evaluate the performance of the BPNN approach, the Holloman Spring 1999 thermosonde campaigns (HMNSP99) model for outer scale, and the Hufnagel/Andrew/Phillips (HAP) model for a single parameter are selected here to estimate profiles. The results have shown that the agreement between the BPNN approach and the measurement is very close. Additionally, statistical operators are used to quantify the performance of the BPNN approach, and the statistical results also show that the BPNN approach and measured profiles are consistent. Furthermore, we focus our attention on the ability of the BPNN approach to rebuild integrated parameters, and calculations show that the BPNN approach is reliable. Therefore, the BPNN approach is reasonable and remarkable for reconstructing the strength of optical turbulence of the offshore atmospheric boundary layer. optical turbulence; backpropagation neural network; Holloman Spring 1999 thermosonde campaigns model; Hufnagel/Andrew/Phillips model +
Footnote †: journal: Applied Sciences  
0000-0001-8823-2222-22222-  
boundary layer research. A sonic anemometer and a platinum wire sensor were installed on a 32 m tower [10]. A second experiment, known as the Minnesota experiment, was performed near Donaldson, Minnesota, USA, in 1973, where a 32 m tower was also installed and a large balloon with turbulence probes was attached to a flying cable. Since the 1970s, many investigations have been performed to determine turbulence height profiles [11]. [PERSON] analyzed temperature fluctuations in the lowest 200 m of the atmosphere in Culgoora, Australia, in January 1972 with the aid of resistance thermometers and anemometers used at different heights under a captive balloon [12; 13]. [PERSON], [PERSON] et al., and [PERSON] et al. employed two micro-thermal probes placed 1 m apart under a balloon to measure temperature fluctuations up to more than 20 km above the ground [14; 15; 16; 17]. Over the years, several models have been developed that calculate the \(C_{n}^{2}\) profile. Firstly, the simplest empirical model can be derived from the use of segmented fitting on experimental data, requiring only the input of an altitude variable. For example, the submission laser communication (SLC) model, the Air Force Geophysics Laboratory (AFGL) and Air Force Maui Optical Station (AMOS) model, and the Critical Laser Enhancing Atmospheric Research (CLEAR I) model [18; 19; 20; 21]. Secondly, a parameterization model can be used, based on the basic theory of turbulence to establish the relationship between conventional meteorological parameters and the profiles of \(C_{n}^{2}\) through the outer scale, such as with the Hufnagel model and Tatarski model [22; 23]. Furthermore, another method to forecast the \(C_{n}^{2}\) profile is given by [PERSON] and [PERSON] [24], who estimate \(C_{n}^{2}\) with the use of the weather research and forecast (WRF) numerical weather prediction (NWP) model. However, due to uncertain parameters of this model, the profiles offered by such a model are unsatisfactory. Meanwhile, based on the baroclinic energy of the atmosphere, [PERSON] and [PERSON] obtained \(C_{n}^{2}\) profiles of the atmospheric boundary layer using the energy spectrum of the turbulence, ranging from large-scale atmospheric fluctuations to small-scale turbulent fluctuations [25]. Each the conventional method has its own advantages and limitations, and no method is known to be superior [26]. With the development of machine learning theory, neural networks have been gaining interest [27; 28; 29]. [PERSON] and [PERSON] employed a neural network to attempt to learn the Spalart-Allmaras turbulence model [30]. This work represents an important step in the use of machine learning algorithms for generalization.