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1.1
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

Regular (linear) multi-model ensemble (LENS) is calculated as an average of the eight models: _{ }*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:

_{ }

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:

_{ }

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

_{ }

_{ }

*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

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.