**LECTURE 1: Subtlety of statistical applications in climate research (What we must but often forget to do)**

**Vladimir Kryjov**

In general, downscaling from model outputs to a target station (region) climate variable consists of three steps:

1. Assessment of the “relationships” between observed target variable at the target point (region) and model outputs in order to select statistically significant “links”.

2. Development of the “forecasting” equation, which links the target variable with selected model output items, to be used for prediction.

3. Forecast of the target variable at the target point (region) using developed regression equation and selected model output items as predictors.

Let us discuss the dangerous points we may meet.

**Step 1**.

Assessment of the “relationships” between observed target variable at the target point (region) and model outputs in order to select statistically significant “links”.

We may use a correlation analysis (mostly common), composite analysis, etc. In all these methods we perform an analysis of statistical relationships between a series of the target variable and a huge number of the model output series (the number of points in a global map (2.5^{o}x2.5^{o} resolution) exceeds 10000).

Let us use a correlation analysis as an example. As a result of correlation analysis we obtain a set of correlation maps between the series of the target variable at the target station (point) and all the series of the model outputs at all the points. These maps look like the maps shown in Fig. 1.