What is one-month forecast guidance? Kohshiro DEHARA (dehara@met.kishou.go.jp) Forecast Unit Climate Prediction Division Japan Meteorological Agency
Outline 1. Introduction 2. Purposes of using guidance 3. Regression method Single/Multi regression model Selection of variables Normalization of precipitation data 4. Probability Forecast
1. Introduction Guidance is a statistical downscaling technique based on grid point value (GPV) data predicted using a numerical model. Guidance has a possibility to increase reliability of forecasts. Guidance for 1-month forecasting uses several elements (Tsurf, Z500 etc.) over the targeted area.
2. Purposes of using guidance Observed data Atmospheric and Oceanic conditions Analysis Numerical model Ensembl e forecast Model output GPV data Forecaster Guidance 1-month forecast Area averaged or station s temperature, precipitation. Probability forecasts
3. Regression method Two types of time series data are used to make guidance. variables for forecasts, ex) Temperature, Precipitation (Objective variables, i.e. Predictands) variables predicted by a model, ex) Z500, Wind (Explanatory variables, i.e. Predictors) Our purpose is to predict the future value of predictands using the statistical relationship between predictands and predictors. Past Predictands Predictors Present or Future Predictands Regression equation Predictors
3. Regression method MOS: the Model Output Statistics. MOS is a technique used to objectively interpret numerical model output and produce area-specific guidance. A large data set of observations is compared with the historical model forecast (hind-cast data). The regression model learns the differences and calibrates these errors in future forecasts. Observed data Hind-cast data Regression model Numerical model Predictands Issued Forecast (Tsurf, Rain etc.) Predictors Predicted GPV data (Tsurf, Z500 etc.)
Single regression Single regression is a predictive approach using a single predictor. Single regression model is written as Y = ax + b + ε Y: predictand X: predictor a: regression coefficient b: constant ε: error term
Multiple regression Multiple regression is assumed that predictands are the sum of a linear combination of plural predictors. Multiple regression model is written as Y = a k X k + b + ε k=1,2,,n Y: predictand X: predictors a: regression coefficient b: constant ε: error term Y Predictand will be near this plane. X 1 X 2 Example: two predictors
Selection of variables In JMA s guidance, predictors are selected by the stepwise procedure. The predictors have been investigated in relation to the climate in Japan. In this training, we select predictors based on the correlation coefficient. List of predictors used in JMA s one-month forecast guidance (Initial date : 31 Oct., For eastern Japan) These predictors are anomaly. : in use - : out of use Rain Wind850 Tsurf Wind500 Z500 Temperature - - - - Precipitation - - Sunshine duration -
Frequency Normalization of precipitation data Temperature histogram is generally approximated by a normal distribution, while precipitation histogram is usually approximated by a gamma distribution. The error distribution of regression models is assumed to be approximated by a normal distribution, which is important presumption to make a probabilistic forecast. Precipitation (Raw) 45 40 35 30 25 20 15 10 5 Histogram of observed monthly precipitation have a gap from a normal distribution. Bold line indicates a normal distribution. 0 0 75 150 225 300 375 450 525 600 675 750 825 900 975 1050 1125 1200 mm/month
Frequency Normalization of precipitation data To make guidance, precipitation data need to be normalized. To achieve this, JMA s seasonal forecast guidance uses a power of 1/4 for precipitation (rainfall and snowfall). 35 30 25 20 15 10 Precipitation (power of 1/4) Histogram of observed precipitation after taking power of 1/4 is approximated by a normal distribution. Bold line indicates a normal distribution. 5 0 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 3.25 3.5 3.75 4 4.25 4.5 4.75 5 mm^0.25/month
4. Probability Forecast Long-range forecasting involves the uncertainty due to the chaotic nature of atmospheric flow. It is necessary to take this uncertainty into account, and probabilistic forecasting is essential. Image chart of probabilistic forecast Probability density function corresponding to initial values and errors Predicted probability density function
Probability Forecast The Probability Density Function (PDF) is assumed to be a normal distribution by its mean and standard deviation n. x s The mean is predicted using the regression model and the standard deviation n is assumed to be the root mean square error of the regression model. Predicted PDF 0 xs n root mean square error of regression model predicted using regression model x s
Probability Forecast In this training, let s make guidance for a two-category probability forecast. n Below normal Above normal 30% 70% 0 xs PDF of climatology 50% 0 50%
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