The main idea of proposed method is to establish statistical relationship between NWP (Numerical Weather Prediction) forecast  models and weather observations at an individual wireless sensor node or weather station. This approach is also known as Model Output Statistics or MOS. By using archived model forecast output along with surface observations, the resulting model implicitly takes into account physical effects which the underlying NWP model cannot explicitly resolve, resulting in better forecasts.

A multiple linear regression model was developed for the prediction of temperature, air pressure and relative humidity in Helsinki Kumpula region. Each parameter is expressed as a linear function of values from NWP model. Coefficients of linear functions are calculated by minimizing the sum of the squares of the distances from each data point to the plane in multidimensional space.  Proposed model allows to reduce forecast error in Helsinki Kumpula region.  Mean relative reduction of RMSE (Root Mean Square Error) of temperature is 15.29%, mean relative reduction of RMSE of air pressure is 84.7% , mean relative reduction of RMSE of relative humidity is 3.87%

Weather observations

We used 2 years of weather observations that are accessible through the FMI's open data web services : http://en.ilmatieteenlaitos.fi/open-data-manual

FMI's open data web services provides observations of temperature, air pressure, humidity, wind direction, wind speed and gust speed with 10 minutes interval.

NWP output history

We used output of Global Forecast System or GFS (0.5° grid) for 2 years. The GFS is a global numerical weather prediction system containing a global computer model and variational analysis run by the US National Weather Service. The mathematical model is run four times a day, and produces forecasts for up to 16 days in advance with 3 hours interval. It is one of the predominant synoptic scale medium-range models in general use.

Multiple linear regression

One of the easies ways to establish relationship between NWP output and real-world   observations at specific weather station is a multiple linear regression. Multiple linear regression attempts to model the relationship between two or more explanatory variables (predictors) and a response variable (predicant) by fitting a linear equation to observed data. 

Graphs

Temperature

Horizontal axis - days.

Top graph : blue dots - RMSE of GFS temperature forecast, red crosses - RMSE of corrected GFS temperature forecast.

Middle graph : blue dots - RMSE of corrected GFS temperature forecast.

(click to enlarge)

Air pressure

Horizontal axis - days.

Top graph : blue dots - RMSE of GFS air pressure forecast, red crosses - RMSE of corrected GFS air pressure forecast.

Middle graph : blue dots - RMSE of corrected GFS air pressure forecast.

(click to enlarge)

Relative humidity

Horizontal axis - days.

Top graph : blue dots - RMSE of GFS relative humidity forecast, red crosses - RMSE of corrected GFS relative humidity forecast.

Middle graph : blue dots - RMSE of corrected GFS relative humidity forecast.

(click to enlarge)