V. Krasnopolsky^{1}, R. Campos^{2}, J.H. Alves^{3}, S. Penny^{2}
^{1}NWS/NCEP/EMC, ^{2}AOSC/UMD, ^{3}NCEP/EMC/SRG
Email: vladimir.krasnopolsky@noaa.gov; Phone: 3016833742
In previous works, we demonstrated that neural network (NN) technique can be successfully used for averaging multimodel ensemble for precipitation over the Continental US [1]. Also, we showed [2] that the use of a single NN to calculate nonlinear ensemble mean (NEM) provides better results than conservative ensemble in the NCEP Global Wave Ensemble System (GWES). In this study, we apply an ensemble of NNs to calculate NEM in GWES.
The GWES was implemented in 2005 [3], it is now run with four cycles per day, using a spatial grid with 0.5^{o} resolution, with forecast range to 10 days. A total of 20 perturbed members plus a control member compose the GWES, which consists of an implementation of the WAVEWATCH III model [4], forced by winds from NCEP’s Global Ensemble Forecast System [5].
In the current study, we propose an improvement of the quality of output products from the GWES using an ensemble of NNs to compute nonlinear averages. Currently a conservative ensemble approach is used to calculate the ensemble mean (EM) in the GWES. The conservative EM (CEM) for variable p is calculated as,
(1)
here n is the number of ensemble members and p_{i} is the ith ensemble member.
An improvement upon (1) can be achieved using weighted EM (WEM),
(2)
where W_{i} are weights subscribed to ensemble members. A priori information can be used to select the weights W_{i}. In addition, if observational data are available for the variable p, eq. (2) can be considered as a linear regression. Solving the linear regression equations (2), W_{i} and the linear regression EM (LREM) can be found. Eq. (2) assumes a linear relationship between EM and the ensemble members; however, in reality, this relationship may be significantly nonlinear, and we can use a nonlinear statistical tool like NN to derive a relationship between ensemble members and nonlinear EM (NEM),
(3)
In this study, we selected a “one buoy location” setup. We used 21 GWES ensemble members from a single grid point near the buoy location at 32.501N and 79.099W (buoy #41004 in the North Atlantic Ocean, water depth of 37 meters, distant only 9.7 km to the nearest model grid point was selected). As inputs to our NN we use three model variables related to 5day forecasts: significant wave height, H_{s}, peak period T_{p}, and wind speed at 10 m height, U_{10}, a total of 63 (3 x 21) inputs. Also, two metavariables: sin and cos of the day of the year were used. Thus, each NN in the ensemble of NNs has 65 inputs in total. Each NN has three outputs: H_{s}, T_{p}, and U_{10}. One year of data for buoy #41004 was used for training the NN outputs. For NN validation we used one year of data collected at buoy #41013, located at a distance of about 100 mi from buoy #41004.
Table 1. Performance of three ensemble means (1) to (3) and an NN ensemble for H_{s} on independent validation set (buoy #41013). MAE is mean absolute error, SI – scatter index, CC – correlation coefficient, and Max the largest value of H_{s }in m.

Bias 
RMSE 
MAE 
SI 
CC 
Max 
Conservative EM 
0.03 
0.445 
0.301 
0.334 
0.759 
6.28 
LREM 
0.28 
0.463 
0.313 
0.348 
0.754 
4.46 
NEM (a single NN) 
0.12 
0.424 
0.29 
0.328 
0.782 
4.3 
ENEM( NN Ensemble) 
0.04 
0.373 
0.238 
0.303 
0.807 
4.58 
Figure 1  Scatter plot shows three overlaid scatterplots: blue crosses show wave model ensemble, green diamonds – LREM, and red dots – ENEM.
Table 1 shows comparison of performances for three aforementioned EMs and for ENEM – EM calculated using ensemble of five NNs. All statistics were calculated on an independent validation set (buoy #41013). ENEM outperforms all EMs for all statistics except the max value. Fig. 1 illustrates the reason: there are very few data points with H_{s}.> 3 m. These data are not sufficient for NN (and LR) training in the area of high H_{s}.
As the next step, our investigation will move from one buoy configuration to two regional (Atlantic and Pacific) configurations and, eventually, to a global configuration when one or several ensembles of NNs will provide ENEM over the entire global ocean. In addition, we are going to include the altimeter data in the training process.
References
[1] Krasnopolsky V., and Y. Lin, 2012: "A Neural Network Nonlinear Multimodel Ensemble to Improve Precipitation Forecasts over Continental US", Advances in Meteorology, Volume 2012, Article ID 649450, 11 pages, doi:10.1155/2012/649450
[2] Krasnopolsky V., R. Campos, J.H. Alves, S. Penny 2017: “Using NN for Nonlinear Averaging of NCEP Wave Model Ensemble”, Research activities in Atmospheric and Oceanic Modelling, Edited by E.Astakhova, July 2017,WCRP Report No.12/2017; http://wmc.meteoinfo.ru/bluebook/uploads/2017/docs/08_Krasnopolsky_Vladimir_data_assimilation_for_waves.pdf
[3] Chen, H. S., 2006: Ensemble prediction of ocean waves at NCEP. Proc. 28^{th} Ocean Engineering Conf., Taipei, Taiwan, NSYSU, 25–37.
[4] WAVEWATCH III® Development Group, 2016: User manual and system documentation of WAVEWATCH III® version 5.16. Tech. Note 329, NOAA/NWS/NCEP/MMAB, College Park, MD, USA, 326 pp. + Appendices.
[5] Hou, D., Z. Toth, Y. Zhu, and Y. Yang, 2008: Impact of a Stochastic Perturbation Scheme on NCEP Global Ensemble Forecast System. Proceedings, 19th AMS conference on Probability and Statistics. New Orleans, LA, 2024 Jan. 2008.