This section firstly evaluates the WGTEM model expression using ECMWF ERA-Interim products and NOAA (National Oceanic and Atmospheric Administration) data as the reference, and the external accuracy of the WGTEM is then verified using a comparison with NOAA meteorological measurements and International GNSS Service (IGS) final ZTD products.
3.1. Evaluation of Model Expression
To compare the proposed WGTEM model with existing models, this study utilized the same data sources, ECMWF ERA-Interim products from 2001–2010, to re-build these models. The modeling parameters used were temperature and air pressure, and the ECMWF ERA-Interim products in 2012 were used to validate the performances.
The temperature results of annual global 10,153 grids with respect to the ECMWF data were firstly analyzed, and the statistical results for each model are shown in Table 1
, where the biases of all models are seen to be similar, with a mean value of 0.06 °C. The mean Root Mean Square (RMS) of WGTEM was 2.85°C, which was lower than that of any other model, and the accuracy of RMS accuracy had a percentage superior accuracy compared to the following models of 11% (GPT2), 8% (TropGrid2), and 1% (ITG).
shows the global distribution of WGTEM temperature accuracy and global RMS differences with respect to other models, where a negative value indicates a higher accuracy. The figure shows that the accuracy at low latitudes was superior to that at high latitudes, and the accuracy for marine areas was higher than for land areas. It can also be seen from Figure 1
c that the WGTEM accuracy in land areas was greatly improved compared to GPT2 (by over 2 °C). The most significant RMS improvement is seen in Africa, i.e., the Sahara Desert with a maximum value of 4.16 °C. For marine areas, the WGTEM model results were comparable with those of GPT2, and this was due to the stable diurnal temperature difference in marine areas. WGTEM also considered diurnal variations in temperature, whereas GPT2 did not. Therefore, WGTEM was more accurate than GPT2 for land areas. Although TropGrid2 concerned the diurnal variations and believed that the daily amplitude and the peak time of diurnal variation terms have annual periodic variation, it ignored the semi-annual periodic variation in temperature, which may cause deviations when estimating other periodic item coefficients. It is also evident from Figure 1
d that TropGrid2 was less accurate than WGTEM for certain land areas, including most of the Antarctic region and part of the Arctic region (the RMS difference is 2.90 °C). This fact is mainly due to the obvious semi-annual periodic variation in temperature caused by the polar day and polar night phenomena in the Arctic. Moreover, it is worth mentioning that the TropGrid2 model was less accurate than GPT2 in most of the Arctic and Antarctic areas. In addition, WGTEM was more accurate in some areas than the ITG model.
For the re-established air pressure model, statistical results with respect to the ECMWF reference are shown in Table 2
. The global distribution of WGTEM air pressure accuracy and RMS differences are shown in Figure 2
From Table 2
, it can be revealed that the biases of all models were very similar, while the mean RMS value (6.95 mb) of WGTEM was the smallest and that of TropGrid2 (7.10 mb) was the largest. Figure 2
shows the overall trend in the WGTEM model’s air pressure accuracy, which demonstrates that it decreased with a rise in latitude. WGTEM improved the air pressure accuracy over GPT2 at the equator, with a maximum RMS improvement of 0.97 mb. Since it had the largest solar elevation angle close to the equator, the diurnal variation in air pressure was the most obvious, due to the effect of the sun: Therefore, the highest improvement with the WGTEM model was seen at the equator and its surrounding areas. Figure 2
d displays that the WGTEM not only outperformed the TropGrid2 model at the equator, but also provided improved accuracy in the Arctic and Antarctic regions, with a maximum RMS improvement of 0.85 mb. TropGrid2 was less accurate than the other three models around the globe because it ignored the semi-annual periodic variation. The WGTEM model also had a superior air pressure accuracy over the ITG model at the equator, with a maximum RMS improvement of 0.68 mb. It is worth mentioning that there were two peaks and valleys in the daily variation of air pressure; but, the diurnal variation items of TropGrid2 and ITG can only reflect the changes in peak and valley once. Nonetheless, WGTEM can reflect two peaks and valleys in the daily variation of air pressure, which is consistent with the actual air pressure pattern. Therefore, the WGTEM model was more highly accurate in the term of air pressure.
NOAA provides surface hourly/sub-hourly meteorological data for many stations globally. The air pressure at the meteorological station in Begumpet of day of year (DOY) 250–265 in 2012 was selected for analysis (see Figure 3
), and the air pressure value was calculated for the same location and time using the WGTEM and GPT2 model.
displays the double-peak air pressure pattern during the daytime. The GPT2 model can only reflect the overall trend of this period and ITG can only reflect the single peak and valley. In contrast, WGTEM can show the double peaks and valleys of daily air pressure. Therefore, the performance of the WGTEM model expression was superior to that of GPT2, TropGrid2, and ITG.
3.2. External Accuracy Evaluation of WGTEM
To further analyze the validity, applicability, and superiority of the developed WGTEM model, this section validates the WGTEM’s accuracy using external data sources as references, including NOAA meteorological measurements and IGS final ZTD products. As the ITG model had already been proven to be more accurate than the GPT2 and the TropGrid2 models (Yao et al., 2015), the following section only focuses on a comparison between the WGTEM and ITG models.
Two IGS Station located in Wuhan China and BERBERATI in Africa were selected to analyze the temperature provided by each model in 2012, as shown in Figure 4
As can be seen from Figure 4
, the WGTEM model’s accuracy is 3.3 °C at Wuhan station, which is comparable with that of ITG. Both values are larger than GPT2 by 1 °C. At BERBERATI station, the WGTEM accuracy reaches 1.9 °C, whereas that of ITG is 2.2 °C and GPT2 is 4.1 °C: Therefore, the WGTEM has an 18% and 21% accuracy improvement over ITG and GPT2, respectively.
Next, we verify the WGTEM and ITG temperatures using NOAA data from 698 globally distributed meteorological stations in 2012 as a reference, and the statistical results are summarized in Table 3
. Figure 5
shows the RMS of each station and the global distribution of temperature RMS differences between the WGTEM and ITG models.
shows that the mean RMS of WGTEM at 698 stations was 3.81 °C and the bias was −0.26 °C; therefore, its accuracy was slightly better than that of ITG model. Figure 5
clearly shows that WGTEM temperature accuracy was highly related to latitude: The accuracy in low-latitude areas was evidently higher than that in high-latitude areas. Although the ITG model already considered the various periodic characteristics of temperature, WGTEM provided superior accuracy at some stations, with a maximum improvement of over 0.5 °C.
To analyze the air pressure accuracy, the COTOBATO station in the Philippines and the CHUUKECI station in Pacific Ocean were selected. Their air pressure series changes in 2012 are shown in Figure 6
. The figure shows that the annual WGTEM RMS accuracy was 1.09 hPa at COTOBATO station, whereas that of GPT2 and ITG were 1.55 hPa and 1.63 hPa, respectively. In a word, WGTEM had the highest accuracy at this station. In addition, the ITG model was less accurate than GPT2, which is probably because the ITG did not consider the double-peak characteristics of air pressure. The annual RMS for WGTEM was 1.15 hPa at CHUUKECI station, whereas that of GPT2 and ITG was 1.67 hPa and 1.65 hPa, respectively. WGTEM was therefore still the most accurate model, and the accuracies of the ITG and GPT2 model were similar to each other.
The air pressure comparison results are provided in Table 4
and Figure 7
. The results in Table 4
show that the WGTEM model gave the optimal performance, with a mean/maximum/minimum bias of −0.2/7.8/−8.3 hPa, respectively. As for RMS, the mean value was 5.9 hPa, the maximum was 14.5 hPa, and the minimum was 1.1 hPa. Figure 7
shows the pattern of WGTEM air pressure is the same as that for temperature. To be specific, the accuracy decreased gradually with ascending latitude, and the accuracy at the equator reached 1.1 hPa. In addition, the model’s accuracy decreased significantly to 14.5 hPa in the Arctic owing to the dramatic dynamic change in air pressure. The negative difference between WGTEM and ITG shows that the WGTEM model was more accurate than the ITG. It is also clear that the WGTEM model’s accuracy was better than that of the ITG at some stations in the middle and low latitudes, with a maximum improvement of about 0.5 hPa.
Finally, the accuracy of WGTEM ZTD was analyzed and compared with that of the ITG model. One-year ZTD products for 274 IGS stations with a 1-h time resolution were selected, and the statistical results are listed in Table 5
. Figure 8
depicts the RMS global distribution map for the WGTEM’s ZTDs at all stations as well as the differences between the results and ZTD RMS of the ITG model.
From Table 5
, it is evident that the mean/maximum/minimum bias value of WGTEM ZTDs was 0.18/3.07/1.54 cm, respectively. The mean value of 274 for the RMS was 3.82 cm. In contrast, the mean bias of the ITG model was 0.05 cm, and the mean RMS value was 4.04 cm.
The WGTEM global bias map is shown in Figure 8
a, where a positive bias indicates that the actual value was larger than empirical value and vice versa. It can be clearly seen from the figure that most stations with positive biases were located at the equator. As the highest ZHD accuracy was identified at the equator, it could be inferred that the mean empirical ZWD value is smaller than the actual value in 2012. The WGTEM global RMS map is depicted in Figure 8
b. The WGTEM model had the highest accuracy in Europe, where the RMS of most stations was less than 4 cm. However, the accuracies of stations located in Asia, the east coast of the United States, and northern Australia were relatively low, with RMS values larger than 6 cm. The analysis of the ITG model in 2012 was similar to the RMS global distribution map. The differences were that the ITG model was built on ECWMF ERA-interim data, which have different accuracies in different regions around the world. A comparison between the RMS figures of WGTEM and ITG shows that the accuracy of WGTEM was superior at many stations, by a maximum of 3 cm. The accuracy was also comparatively improved at 20 stations by more than 1 cm, and by more than 0.5 cm at 47 stations. These results indicate that the WGTEM model expression was greatly improved compared to that of the ITG, with respect to ZTD.
In summary, the superiority of the WGTEM model expression makes it more accurate than the other three models described in Section 2
. With the rise in accuracy and temporal resolution of data sources in the future, the WGTEM model’s accuracy will be accordingly improved due to the application of piecewise modeling.