## 2 Acoustic Propagation Models
### Bellhop-Based Statistical Prediction Model (BH-SPM)  
While the Bellhop model provides an accurate calculation of the acoustic propagation model, network modeling requires near continuous references to propagation delays and signal attenuation values, being computationally infeasible to support this complex model in UWSN simulation frameworks. Thus, it would be of interest to provide an approximation of Bellhop model that supports the time constraints of the network simulation while preserving most of its accuracy.  
In [7] we proposed a statistical model based on the Bellhop approach (BH-SPM) that it is able to produce the acoustic signal attenuation map by means of a statistical prediction model integrated in the simulator tool that significantly reduces complexity. BH-SPM model enables computationally-efficient inclusion of fading and multipath effects into a network simulator. Namely, to assess the average  
Figure 1: Bellhop ray trace.  
system performance, network operation has to be simulated over a large set of channel realizations (e.g., varying surface conditions). Whereas repeated computation of the ray trace for different hops that each of the data packets traverses in a given network may be computationally prohibitive, statistical modeling requires only a single call to the Gaussian random generator for each packet transmission. Thus, the overall simulation time is considerably reduced, allowing a system designer to freely experiment with varying protocols and resource allocation strategies in an efficient manner. The ultimate goal of such computational experiments is to choose the best upper-layer protocol suite and to relate the necessary system resources (power, bandwidth) to the propagation conditions, _i.e._, to the statistical parameters of the transmission loss.  
In Figure 2, the tradeoff between model complexity and accuracy is shown. In this figure, we also define the thresholds for the desirable accuracy and complexity of the sound propagation model. Thus, the shaded area covers those propagation models with the minimum acceptable model propagation accuracy that leads to get reliable results and, at the same time, low computational complexity levels that allow detailed and scalable network simulations.  
In Figure 3 the acoustic attenuation map from the selected propagation models is shown. It was obtained with a specific underwater scenario where a source node, located at 10 m depth, is emitting an acoustic beam of 120 degrees at 10 kHz. The scenario environmental conditions are the same (bathymetry, surface activity, temperature, _etc._). As it can be shown, the waves (at top) and the underwater floor (at bottom) are represented in blue and brown colors, respectively. We can quickly compare the attenuation values for the different models whereas in (a) Thorp, the simple model only shows signal degradation in accordance with the distance without taking into account neither the scenario depth nor the source radiation pattern, in (b) the MMPE model is able to define a more accurate attenuation map taking into account, depth, distance and ocean wave activity. Finally, in Figure 3(c) the acoustic physics are taken into account by using Bellhop model which introduces the ray reflections/absorptions depending on floor sediment composition, the floor shape and the surface wave's geometry. In addition, a different sound speed profile is calculated based on the scenario world location and its bathymetry.  
Figure 2: Tradeoff between model propagation accuracy and computational complexity.  
Once these models are presented, the next step is to determine if the differences appreciated in Figure 3 may be transferred to the upper network layers in such a way that performance of higher layer protocols is affected in a significant way. If so, then it would be necessary to consider the use of complex propagation models that represent as accurate as possible the underwater acoustic propagation in order to obtain simulation results close to the ones obtained in experimental test-beds.