Comparison of WRF Model Post-Processing Methods for Daily Temperature at Mehrabad Station in Tehran

In last years, different methods for a post-processing the model outputs have been developed which provide a practical tool that combines the observed data and predictions of the model using an algorithm to reduce the systematic errors of the direct model outputs without the need for long historical data archives. It is well known that numerical weather prediction (NWP) models usually exhibit systematic errors in the forecasts of certain meteorological parameters especially near the surface (Galanis et al. , 2006). Direct numerical weather prediction model forecasts of near surface parameters often suffer from systematic errors mainly due to the low resolution of the model topography and inaccuracies in the physical parameterize schemes incorporated in the model. In recent years, the increasing demand for accurate weather forecasts has led to a steady improvement of the skill of numerical weather predictions at both global and regional scales. Despite these improvements, such predictions are still affected by imperfect initial conditions, numerical approximations, and simplification of the physical and chemical processes that govern the evolution of the atmosphere. These imperfections, approximations, and simplifications result in random and systematic errors (e.g., bias) that affect the predictions’ accuracy. Bias here is defined as the ‘‘difference of the central location of the forecasts and the observations” (Monache et al., 2011). In order to reduce the influence of the above mentioned drawbacks in the final output of a NWP model, a variety of approaches based on statistical methods has been used. Most of them are derived from Model Output Statistics (MOS), which are able to account for local effects and seasonal changes. One of the most successful approaches to this problem is the use of Kalman filters (Kalman, 1960; Kalman and Bucy, 1961; Galanis and Anadranistakis, 2002). They consist of a set of mathematical equations that provides an efficient computational solution of the least square method. This paper is organized as follows. In Section 2, we introduce different post-processing method. In Section 3, we show that how the filters are applied on the model outputs for average temperature at Mehrabad meteorological station. In Section 4, statistical results are presented and finally the paper is concluded in section .

In this paper three simple algorithms based on Fourier transform, artificial neural network and Kalman filter have been implemented to correct the average temperature Weather Research and Forecasting (WRF) model forecasts in Tehran Mehrabad station. The WRF forecasting model is a mesoscale atmospheric research as well as environmental forecasts. The first post-processing approach implemented in this study is Fourier transform (FT) which decomposes a function of time (a signal) into its constituent frequencies. The term Fourier transform refers to both the frequency domain representation and the mathematical operation that associates the frequency domain representation to a function of time. The Fourier transform of a function of time is itself a complex-valued function of frequency, whose magnitude (modulus) represents the amount of that frequency present in the original function, and whose argument is the phase offset of the basic sinusoid in that frequency(Bracewell, 1986).Second approach is performed in this study is Artificial Neural Network (ANN) techniques to correct daily average temperature (Hansen and Salamon, 1990) .Generally speaking, data driven processes are governed by systems of linear or non-linear equations, which describe the relationship between the WRF model and observation values of the system's output and the values of inputs. Last approach in this method referred to Kalman Filter. Kalman filtering, also known as linear quadratic estimation (LQE), is an algorithm that uses a series of measurements observed over time, containing statistical noise and other inaccuracies, and produces estimates of unknown variables that tend to be more accurate than those based on a single measurement alone, by estimating a joint probability distribution over the variables for each timeframe. The filter is named after Rudolf E. Kálmán, one of the primary developers of its theory. In practice, the Kalman filter is the statistically optimal sequential estimation procedure for dynamic systems. Any type of Kalman methods aims at eliminating the standard error and, thus, at vanishing the corresponding biases. The fulfillment of this requirement is the main criterion ensuring the credibility of the filter.

In this study, the performances of three post processing methods are tested with the WRF model runs .Statistical results show that the model error varies according to the season at the station and the model forecast is underestimated or overestimated on all days, meaning that the error is positive on all days or negative on all days; While this estimate becomes positive for some days and negative for others after the application of the Kalman refinement, this is evident in the significant reduction in the mean error that measures the bias. From the root mean square of the errors, it measures the scatter of the error, and although its reduction is noticeable after the application of the filter, but it is far from zero and indicates the existence of additional and deficient estimates.

In this paper three simple algorithms based on Fourier transform, artificial neural network and Kalman filter have been implemented to correct the average temperature model forecasts.Results show that all of different methods of predicting average temperature are presented, reduce numerical weather prediction’s systematic and random errors. One of the most successful approaches to this problem is use of Kalman filter. Among the methods, the Kalman refiner was able to modify the WRF model prediction to an acceptable level and greatly reduce the error rate by as much as 90%. The main advantage of this statistical methodology is the easy adaptation to any alteration of the observations as well as the fact that it may utilize short series of back- ground information.