Numerical Studies On Forecast Error Correction Of GRAPES Model With Variational Method

The forecast error still occurs in numerical weather prediction for the imperfect initial state of atmosphere and inaccuracy description of the atmospheric equations. In this paper, forecast error is split into two components, systematic forecast error and non-systematic forecast error. After the correction of systematic forecast error, variational method is used to estimate and correct the non-systematic forecast error in the following two ways. (1) The mapping relationship between the state variable and non-systematic forecast error is built by variational method (DEM), based on the state-dependent characteristics of non-systematic forecast error. (2) The mapping relationship between the non-systematic forecast error of a certain time and the non-systematic forecast error a day before is built by variational method (TEM), based on the time dependency of non-systematic forecast error. The mapping relationship also can be built through "similarity samples" (SEM), and a stable result is expected. The hindcast data of 500hPa height field generated by GRAPES model in January and July from 2001 to 2010 is used to test the effectiveness of the above three methods. The analysis data from NCEP FNL is used as criterion to assess the result of the methods. Prior the estimation of non-systematic, the space distribution of forecast error in East Asia is analyzed preliminarily. The main conclusions are as follows:(1) The space distribution of systematic forecast error shows that they have seasonal characteristics and regional characteristics, and reflects the overall feature of GRAPES forecast. The forecast of GRAPES model is positive deviation to the analysis data at winter in the north of 20°N and west of 120°E, and the maximum deviation is in the northeast of Tibet Plateau. The forecast of GRAPES model is negative deviation to the analysis data at summer in the south of 40°N, especially in the Tibet Plateau. Systematic forecast error grows with the length of period of validity. GRAPES model has deficiency in dynamic and thermodynamic process in big scale.(2) Non-systematic forecast error is state-dependent, and changes with the season and the state of weather. No matter winter or summer, the weight of 24h non-systematic forecast error in total forecast error is over 50%, which of 48h is over 45%. Therefore, it’s very important to estimate the non-systematic forecast error and correct the forecast.(3)The estimation of non-systematic forecast error at 500hPa height field of January and July from 2008 to 2010 shows that DEM method has certain capability to estimate the non-systematic forecast error. To most of the test samples, the estimation of non-systematic forecast error consistent with the real one, and a little less than the real one. The forecast of 168 samples corrected by systematic forecast error improves. After the non-systematic forecast error correction, 127 samples’forecast gets improved further. After the systematic forecast error correction and non-systematic forecast error correction, the effective rate of forecast is improved from 91.8% to 96.7%.(4) The common similarity method describes the difference of data samples in terms of an average. It can suffer from the effect of several extreme sample factors. For this reason, a new similarity method called similarity area ratio is developed to determine the similarity in a global view. The data including temperature, height, and wind at 00:00 UTC in the winter from 2001 to 2011 is used to test the validity and efficiency of the similarity-area-ratio method. The results show the similarity area ratio is better than Hamming distance and correlation coefficient. The long-term predictions based on these above three similarity methods are performed with monthly mean temperature data from 1948 to 2013 to further test their efficiency. The results show that the similar sample selected by these methods is same for some references. The frequency of the best forecasts with similarity-area-ratio method is higher than that with the other similarity methods.(5) Similar samples are chosen by similarity-area-ratio method as training samples for the 93 test samples. The result shows that both the DEM method and SEM method has certain capability to estimate the non-systematic forecast error.90 samples’forecast is improved after non-systematic forecast error correction.62 and 57 samples’ forecast get improved after DEM and SEM, respectively. The experimental result of 2008 and 2010 shows that SEM method is better than Dem method and the experimental result of 2009 shows that SEM method is worse than SEM method, which means that SEM method is not very stable, and may relate to the selection of similar samples.(6) The non-systematic forecast error of 24h and 48h forecast of January and July from 2008 to 2010 is estimated by TEM method, and compared to DEM and SEM method. The experimental result of 180 test samples shows that TEM method has the ability to estimate the non-systematic forecast error, and can improve the forecast based on the systematic forecast error correction. Compare the forecast error correction effect and the result shows that the TEM method is more efficiency at correct forecast error than the other two methods.61 samples’RMS of forecast corrected by TEM method is less than the RMS of forecast corrected DEM method, and 59 samples’ RMS of forecast corrected by Tem method is less than the RMS of forecast corrected SEM method. The TEM method can estimate the non-systematic forecast error and correct forecast more efficiency.