Application of the neural network technique to develop a nonlinear multi-model ensemble for precipitation over ConUS

            The neural network (NN) technique is used for development of novel nonlinear multi-model ensemble for calculating precipitations over the US territory.  24-hour precipitation forecasts over ConUS are available from 8 operational models, including NCEP's own mesoscale and global models (NAM and GFS), the regional and global models from the Canadian Meteorological Center (CMC and CMCGLB), global models from the Deutscher Wetterdienst (DWD), the European Centre for Medium-Range Weather Forecasts (ECMWF), the Japan Meteorological Agency (JMA) and the UK Met Office (UKMO).  Also NCEP Climate Prediction Center (CPC) precipitation analysis is available.  CPC analysis is used for the verification of model predictions.  Actually all models demonstrate similar behavior: at lower levels of precipitation they are slightly wetter than the CPC analysis and at the higher levels (> 50-60 mm/day) they are dryer than the CPC analysis (for detailed discussion, see Lin and Krasnopoolsky 2011).  The model results are shown in Fig.1.   

            Regular (linear) multi-model ensemble (LENS) is calculated as an average of the eight models: , where N = 8 and P_i is precipitation predicted by the model number i.  As can be seen in Fig. 1, the regular linear multi-model ensemble goes inside (in the middle of) the envelop created by the models and does not improve the situation significantly. 

We introduced and investigated two improvements: (1) created a multiple linear regression ensemble using the available eight models and (2) created a nonlinear NN ensemble.  The multiple linear regression ensemble was created in the following way:

                              (1)

where a_i are regression parameters, , , jday is the Julian day, lat is the latitude, and lon is the longitude.

            The NN ensemble is defined following Krasnopolsky (2007); it is an analytical nonlinear regression that can be written as:

                                                (2)

where x_i are components of the input vector X composed of the same inputs as those used for MLRE (1), a and b are fitting parameters, and  is a “neuron”.  The activation function  is usually a hyperbolic tangent, n is the numbers of inputs, and k is the number of neurons in (2).  Definitions of NN terminology can be found in many places, for example in the review paper by Krasnopolsky (2007). 

Fig. 1.  Binned scatter plot for eight models (ensemble members): CMC – blue solid, CMCGLB – blue dashed, DWD – blue dotted, ECMWF – blue dot dashed, JMA – double dot dashed, GFS – green solid, NAM – green dashed, UKMO – brown solid; and for ensembles: LENS – red dashed, MLRE – red dot dashed, and NNENS – red solid.

            Fig. 1 shows the binned scatter plot for the amount of precipitation over the US territory during the first seven months of 2010.  It shows the model and ensemble results vs. CPC analysis.  The MLRE and NNENS have been developed using 2009 data.  As can be seen from the figure, all models are significantly dryer than the CPC analysis at higher precipitation amounts.  The linear ensemble, LNENS (red dashed line), does not change the situation.  The multiple linear regression ensemble, MLRE (red dot dashed line), does not introduce a significant improvement upon LNENS.  The NN ensemble, NNENS (red solid line) significantly improves model results at higher precipitation amounts.

            Many different NN ensembles (2) can be trained; only one of them is shown in Fig. 1.  They are flexible enough to negotiate the wetness at lower amounts of precipitations with the dryness at the higher amounts.  We are working on polishing NN ensemble technique to produce new operational products.