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The six-hourly forecast data of the ECMWF model initialized at 0000 UTC up to a lead time of 360 hours from January 2012 to November 2016 are used in this paper. The model data are obtained for a grid of 5 × 6 points covering the Beijing area (39°−41°N, 115°−117.5°E) with a horizontal resolution of 0.5°, as well as the grid points on the edge of this area, and thus the model data on this 7 × 8 grid are used. Several predictors (e.g., land−sea mask) have the same value in the Beijing area and do not change with time. In addition to these unnecessary variables, 21 predictors are chosen, broadly based on meteorological intuition. Table 1 shows these predictors and their abbreviations.
Predictor Abbreviation 10-m zonal wind component 10U 10-m meridional wind component 10V 2-m dewpoint temperature 2D 2-m temperature 2T Convective available potential energy CAPE Maximum temperature at 2 m in the last 6 h MX2T6 Mean sea level pressure MSL Minimum temperature at 2 m in the last 6 h MN2T6 Skin temperature SKT Snow depth water equivalent SD Snowfall water equivalent SF Sunshine duration SUND Surface latent heat flux SLHF Surface net solar radiation SSR Surface net thermal radiation STR Surface pressure SP Surface sensible heat flux SSHF Top net thermal radiation TTR Total cloud cover TCC Total column water TCW Total precipitation TP Table 1. The predictors taken from the ECMWF model and their abbreviations.
These model data constitute a part of the original dataset D0, and this part is denoted by X0. A record of meteorological elements on a certain day at a spatial point is called a sample S, and thus there are 1796 samples, i.e., S = 1, 2, …, 1796. Each sample has 61 six-hour time steps TTem with a forecast range of 0−360 hours (TTem= 0, 6, …, 360) and 21 predictors C, as listed in Table 1
$\left( {C \in \{ {\rm{10U}},{\rm{10V}}, \cdots ,{\rm{TP}}\} } \right)$ . The horizontal grid division is 7 × 8, and each spatial point of this region is denoted by (m, n), where m = 1, 2…, 7 and n = 1, 2, …, 8. Therefore, X0 consists of a 5D array, the size of which is 1796 × 61 × 21 × 7 × 8, and it can be written as -
Data assimilation can determine the best possible atmospheric state using observations and short-range forecasts. The weather forecasts produced at the ECMWF use data assimilation and obtain the model analysis (zero-hour forecast) from meteorological observations. Therefore, for this study, the model analysis is used as the label, because not every grid point has an observation station. Furthermore, the model analysis data contain the observational information through data assimilation. The model analysis data used in this paper are the 2-m temperature of the ECMWF analysis in the Beijing area, with a horizontal resolution of 0.5° and recorded every 0000 UTC from 1 January 2012 to 15 December 2016.
These observational data constitute the other part of the original dataset D0, and this part is denoted by Y0, D0 = (X0, Y0). Following the above notation, the samples S = 1, 2, …, 1796 are from January 2012 to November 2016, the predictor C is given the value 2T, 2T stands for 2-m temperature, the horizontal grid division is 5 × 6, and thus m = 2, 3, …, 6 and n = 2, 3, …, 7. Actually, the model analysis data include 1811 days, because, for a sample, the temperatures in the next 15 days are predicted by the model, and the corresponding true values need to be used. Let t be the forecast lead time, t = 24, 48, …, 360 hour, for a fixed (m, n) and S, the temperatures in the next t hours can be aggregated into vectors. Y0 can be written as
where C = 2T was omitted. Y0 consists of a 4D array, of which the size is 1796 × 5 × 6 × 15.
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For this study, the grid temperature forecast is actually a problem of using the predictions from the ECMWF model as the input and obtaining the 2-m grid temperature forecasts as the output. Focusing on the samples from January to November 2016, for each sample, the 2-m grid temperature forecasts in the Beijing area at the forecast lead times of 1−15 days need to be forecast.
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In order to evaluate the forecast results of these methods, the root-mean-square error (RMSE) and temperature prediction accuracy are used to test the results of these algorithms.
The RMSE is one of the most common performance metrics for regression problems, and the RMSE of temperature is denoted by TRMSE,
where f is the machine learning regression function, D is the dataset, K is the total number of samples of dataset D, xk is the input, and yk is the label.
The temperature forecast accuracy (denoted by Fa) in this study is defined as the percentage of absolute deviation of the temperature forecast not being greater than 2°C,
where Nr is the number of samples in which the difference between the forecast temperature and the actual temperature does not exceed ±2°C and Nf is the total number of samples to be forecast.
In this section, the MOML method with the multiple linear regression algorithm (“lr”) and Random Forest algorithm (“rf”) is used to solve the problem of grid temperature forecasts, mentioned in section 2.3, and datasets 1−3 with two training periods, a year-round training period and running training period, are adopted. It is worth noting that the multiple linear regression algorithm is unsuitable for dataset 2 because it has too many features, and the running training period is unsuitable for Random Forest because of the heavy computation. The univariate linear MOS method is a linear regression method that uses only temperature data and does not require the datasets introduced in the last section. In fact, dataset 1 contains 21 features, dataset 2 contains 2268 features, and multiple linear regression is used on datasets 1 and 2 to obtain models
${\rm{lr}}\_1$ and${\rm{lr}}\_3$ . It can be considered that${\rm{lr}}\_1$ and${\rm{lr}}\_3$ are extensions of multi-feature MOS. The running training period of univariate linear MOS is an optimal training period scheme (Wu et al., 2016). Thus, univariate linear running training period MOS results in the running training period${\rm{mos}}\_{\rm{r}}$ are used as a contrast. The methods used in the problem are listed in Table 2.Method Dataset Training period Notation ECMWF − − ECMWF Univariate linear MOS − Running mos_r MOML (lr) 1 Year-round lr_1_y 3 Year-round lr_3_y 3 Running lr_3_r MOML (rf) 2 Year-round rf_2_y 3 Year-round rf_3_y Table 2. List of methods used and their notation.
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In this subsection, a whole-year comparison of the ECMWF model, univariate linear running training period MOS, and MOML is presented. The results of MOML with the multiple linear regression algorithm,
${\rm{lr}}\_3\_{\rm{r}}$ (Fig. 4), and Random Forest algorithm,${\rm{rf}}\_2\_{\rm{y}}$ , are reported.Figure 4. Results of the
${\rm{lr}}\_3\_{\rm{r}}$ ,${\rm{rf}}\_2\_{\rm{y}}$ and${\rm{mos}}\_{\rm{r}}$ models, using one-year temperature grid data in the Beijing area as the test set. Left: TRMSE (RMSE; units: °C). Right: Fa (forecast accuracy; units: %). (a) shows${\rm{lr}}\_3\_{\rm{r}}$ has obvious advantages when the forecast time is 1−9 days, and (b) shows${\rm{rf}}\_2\_{\rm{y}}$ is superior to other models in the whole forecast period, especially in the longer period.Actually, the better the model data, the better the forecast results. The forecast accuracy is negatively correlated with the RMSE. Generally speaking, the lower the RMSE, the higher the forecast accuracy. The forecast ability of the model decreases linearly in a short time period, and nonlinearly in a long time period.
According to Fig. 4, all of the three methods (
${\rm{mos}}\_{\rm{r}}$ ,${\rm{lr}}\_3\_{\rm{r}}$ and${\rm{rf}}\_2\_{\rm{y}}$ ) can revise the 2-m temperature data of the ECMWF model quite well in the sense of the annual mean. The result of${\rm{lr}}\_3\_{\rm{r}}$ is better than that of${\rm{mos}}\_{\rm{r}}$ when the forecast time is 1−9 days, which also explains why the multiple linear regression model is better than the univariate linear MOS model after extending the features with appropriate feature engineering. In particular, the forecast accuracy of the first day can reach more than 90%, which is 10% higher than that of the ECMWF model. The result of${\rm{rf}}\_2\_{\rm{y}}$ is better than that of${\rm{mos}}\_{\rm{r}}$ in the whole forecast period, especially in the longer period. Because the temperature forecasting problem has strong linearity when the forecast period is short, multiple linear regression produces good results. However, the temperature forecasting problem has nonlinearity when the forecast period is longer, and thus some nonlinear algorithms, such as Random Forest, are more suitable for solving it. Accordingly, the numerical performance of each algorithm in the running and year-round training periods conform to this rule. Therefore,${\rm{lr}}\_3\_{\rm{r}}$ produces the best result, i.e., the highest accuracy and the smallest RMSE, when the forecast time is 1−6 days, while${\rm{rf}}\_2\_{\rm{y}}$ produces the best result when the forecast time is 7−15 days. Thus, a feasible solution (denoted by fMOML) is presented for the grid temperature correction in the Beijing area, which involves using the${\rm{lr}}\_3\_{\rm{r}}$ method for days 1−6 of the forecast lead time and the${\rm{rf}}\_2\_{\rm{y}}$ method for days 7−15 (as shown in Fig. 5).Figure 5. A feasible solution fMOML to the grid temperature correction in the Beijing area. fMOML uses the
${\rm{lr}}\_3\_{\rm{r}}$ method for days 1−6 of the forecast lead time and the${\rm{rf}}\_2\_{\rm{y}}$ method for days 7−15, and it has a lot of advantages in the whole forecast period.The average TRMSE and Fa of the solution fMOML and the ECMWF model (or univariate linear MOS) are calculated respectively, and these values are then used to evaluate the difference between the forecasting abilities of the two methods. In conclusion, the average TRMSE and average Fa of the solution for the fMOML method decreases by 0.605°C and increases by 9.61% compared with that for the ECMWF model, respectively, and by 0.189°C and 3.42% compared with that of the univariate linear running training period MOS, respectively.
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Considering that the change in temperature is seasonal within a year and fierce in some months in the Beijing area, a month-by-month comparison of the ECMWF model, univariate linear running training period MOS (
${\rm{mos}}\_{\rm{r}}$ ) and MOML method (${\rm{lr}}\_3\_{\rm{r}},{\rm{rf}}\_2\_{\rm{y}},{\rm{rf}}\_3\_{\rm{y}},{\rm{ }}{\rm{lr}}\_3\_{\rm{y}},{\rm{ }}{\rm{lr}}\_1\_{\rm{y}}$ ) is presented in this subsection. -
It is more important to improve the accuracy of temperature forecasts in winter, because the forecast results of the ECMWF model do not work well in winter months. The forecast data in winter months are revised by the six methods listed in Table 2. Figure 6 shows the correction results of the grid temperature data in the Beijing area in November, December, January and February.
Figure 6. Results of grid temperature forecasts in the Beijing area in November (a), December (b), January (c) and February (d). In these months, the forecast results of the ECMWF model do not work well, and the linear methods
${\rm{lr}}\_3\_{\rm{r}}$ are better than other methods.From December to February, the average TRMSE and average Fa of the
${\rm{lr}}\_3\_{\rm{r}}$ method decreases by 1.267°C and increases by 27.91%, respectively, compared with that of the ECMWF model, and by 0.652°C and 15.52% compared with that of the univariate linear running training period MOS, respectively. As shown in the figures, the forecast results of the ECMWF model do not work well in these four months, while the results of the MOML methods are all better than those of the ECMWF model. On the whole, in these months, the results of linear methods are better than other methods when the forecast lead time is relatively short, and the results of MOML with Random Forest are better when the forecast lead time is relatively long. The results of the running training period are better than those of the year-round training period when applying a linear method. On the whole,${\rm{lr}}\_3\_{\rm{r}}$ method is the best method in winter months. -
Figure 7 shows the results of the grid temperature data in the Beijing area in March, June, July, August and October. In these five months, the forecast result of the ECMWF model are better than those in winter months, and the results of some MOML methods do not work better than the ECMWF model. On the whole, in these months, the results of MOML with the multiple linear regression algorithm are better than those of other methods in the first few days of the forecast period, and those with Random Forest are better than other methods when the forecast time is relatively long. Also, the results of the running training period are better than those of the year-round training period when applying a linear method.
Figure 7. Results of grid temperature forecasts in the Beijing area in March (a), June (b), July (c), August (d) and October (e). In these five months, the forecast results of the ECMWF model are better than those in winter months. The linear methods are better than other methods when the forecast lead time is short, and Random Forest algorithm are better when the forecast lead time is relatively long.
Figure 8 shows the correction results of the grid temperature data in Beijing in April, May and September. The forecast results of the ECMWF model in these three months are better than those in the other months, and there is no need for revision in selected times of the forecast period. On the whole, in these three months, the results of MOML with the multiple linear regression algorithm are best in the first few days of the forecast period, and those with the Random Forest algorithm are better than for other methods in the next few days. Also, the results of the running training period are close to those of the year-round training period when applying a linear method.
Figure 8. Results of grid temperature forecasts in the Beijing area in April (a), May (b) and September (c). In these three months, the forecast results of the ECMWF model in these three months are better than those in the other months. The multiple linear regression algorithm is best in the first few days of the forecast period, and the Random Forest algorithm is better than for other methods in the next few days.
Predictor | Abbreviation |
10-m zonal wind component | 10U |
10-m meridional wind component | 10V |
2-m dewpoint temperature | 2D |
2-m temperature | 2T |
Convective available potential energy | CAPE |
Maximum temperature at 2 m in the last 6 h | MX2T6 |
Mean sea level pressure | MSL |
Minimum temperature at 2 m in the last 6 h | MN2T6 |
Skin temperature | SKT |
Snow depth water equivalent | SD |
Snowfall water equivalent | SF |
Sunshine duration | SUND |
Surface latent heat flux | SLHF |
Surface net solar radiation | SSR |
Surface net thermal radiation | STR |
Surface pressure | SP |
Surface sensible heat flux | SSHF |
Top net thermal radiation | TTR |
Total cloud cover | TCC |
Total column water | TCW |
Total precipitation | TP |