- Split View
-
Views
-
Cite
Cite
Yibin Yao, Chaoqian Xu, Bao Zhang, Na Cao, GTm-III: a new global empirical model for mapping zenith wet delays onto precipitable water vapour, Geophysical Journal International, Volume 197, Issue 1, April, 2014, Pages 202–212, https://doi.org/10.1093/gji/ggu008
- Share Icon Share
Abstract
The weighted mean temperature (Tm) is a critical parameter in research of GPS meteorology. Recently, we have established two global Tm models, GTm-I and GTm-Π, using ground-based radiosonde data. These two models, which directly use the location and the day of year to calculate Tm, consider the annual cycle only. In this study, we further take into account the variation characteristics of Tm in semi-annual and diurnal periodicity and estimate the initial phase of each cycle. A more accurate global empirical Tm model called GTm-III is constructed using high-precision Global Geodetic Observing System (GGOS) Atmosphere Tm grid data, and then validated using a new set of Tm grid data, radiosonde data and Constellation Observation System for Meteorology, Ionosphere, and Climate (COSMIC) radio occultation data. Results indicate that compared to the existing global Tm models, GTm-III provides Tm estimates of high accuracy on a global scale and the predicted values are close to the true values in every moment of every day.
1 INTRODUCTION
Previous research of Tm has made substantial achievements worldwide. Using 2-yr radiosonde data from 13 stations in the United States, Bevis et al. (1992) proposed a regression equation for calculating Tm from Ts, which is suitable for mid-latitudes. However, the application of Bevis Tm–Ts relationship has been limited because few GPS stations are equipped with instruments to measure Ts. Ross & Rosenfeld (1997) analysed 23-yr radiosonde data from 53 stations in the world and found that the Tm–Ts relationship changes with station location and season. Li et al. (1999) proposed a regression formula suitable for estimation of Tm in eastern China, and Wang et al. (2011) also established regionally applicable linear models. Yu and Liu (2009) found that the accuracy of Tm calculated using Bevis Tm–Ts relationship has a strong correlation with the altitude. Yao et al. (2012) established a globally applicable empirical Tm model GTm-I, using radiosonde data from 135 stations in 2005–2009, which considered seasonal and geographical variations and was independent of surface temperature. In GTm-I, Ts is expressed by the global pressure and temperature (GPT) model (Boehm et al.2007), and seasonal variations in Tm are considered. To solve the anomalies of GTm-I in some oceanic areas, Yao et al. (2013) simulated Tm in sea areas where observation is unavailable through a combination of GPT model and Bevis Tm–Ts relationship; and the simulated data, together with radiosonde data, were used to recalculate the model coefficients of GTm-I; finally, an improved model GTm-Π was established.
For higher global Tm accuracy, this study built and validated a new global Tm model GTm-III. Compared with the existing Tm models, GTm-III is superior by taking into account the semi-annual and diurnal variation in Tm, in addition to the annual cycle considered in GTm-I and GTm-Π. The proposed GTm-III estimates the initial phase of each cycle and uses high-precision Global Geodetic Observing System (GGOS) Atmosphere Tm (http://ggosatm.hg.tuwien.ac.at/) grid data as data source.
2 METHODS FOR COMPUTING Tm
2.1 Computing Tm based on atmospheric profile information
2.2 Computing Tm based on linear regression formula
2.3 Existing global Tm models: GTm-I and GTm-II
3 CONSTRUCTION OF A NEW GLOBAL Tm MODEL: GTm-III
3.1 Expression of GTm-III
3.2 Data source for constructing GTm-III
GGOS Atmosphere can provide Tm grid data with a time resolution of 6 hr (at UTC 00:00, 06:00, 12:00 and 18:00) and a spatial resolution of 2.5° × 2°; the Tm grid data are obtained based on relevant information provided by ECMWF. Here we first test the accuracy of the above-mentioned products. A total of 341 radiosonde stations uniformly and globally distributed are selected and their Tm at UTC 00:00 and 12:00 of every day in 2010 are taken as the reference values. The Tm at the same station and time is calculated using the bilinear interpolation method with GGOS Atmosphere grid data, and then compared with the reference value. The statistical results of annual average accuracy at all radiosonde stations are shown in Table 1. The histograms of mean bias error (MBE), mean absolute error (MAE) and root mean square (RMS) of Tm gridded data are presented in Fig. 1.
Variable . | Average . | Max. . | Min. . |
---|---|---|---|
MBE | −0.45 | 2.90 | −7.82 |
MAE | 1.46 | 7.82 | 0.54 |
RMS | 1.93 | 7.99 | 0.71 |
Variable . | Average . | Max. . | Min. . |
---|---|---|---|
MBE | −0.45 | 2.90 | −7.82 |
MAE | 1.46 | 7.82 | 0.54 |
RMS | 1.93 | 7.99 | 0.71 |
Variable . | Average . | Max. . | Min. . |
---|---|---|---|
MBE | −0.45 | 2.90 | −7.82 |
MAE | 1.46 | 7.82 | 0.54 |
RMS | 1.93 | 7.99 | 0.71 |
Variable . | Average . | Max. . | Min. . |
---|---|---|---|
MBE | −0.45 | 2.90 | −7.82 |
MAE | 1.46 | 7.82 | 0.54 |
RMS | 1.93 | 7.99 | 0.71 |
Table 1 shows that the MBE averages −0.45 K and ranges from −7.82 to 2.9 K; the MAE averages 1.46 K and ranges from 0.54 to 7.82 K; the RMS averages 1.93 K and ranges from 0.71 to 7.99 K. Fig. 1 shows that MBEs between −3 K and 3 K (Tm with such error causes about 0.7 mm error in PWV when ZWD is 400 mm) account for 94 per cent of the total data in consistence with that MAEs below 3 K account for 94 per cent, and RMS below 4 K account for 95 per cent of the total data. Through the above-mentioned analysis and former study experience, Tm grid data provided by GGOS Atmosphere are highly precise and reliable, thus can be used as data source for constructing GTm-III.
3.3 Calculate of GTm-III coefficients
The distributions of α1 in GTm-III and GTm-II are similar. Fig. 2(a) shows that α1 near the equator is relatively larger, and it decreases with the increase of latitude, because annual average Tm decreases with the increase of latitude, and so decreases coefficient α1. Amplitudes of annual periodicity α3 also show similarity between GTm-III and GTm-II. In Fig. 2(b), absolute values of α3 in the Northern Hemisphere seems larger than those in the southern, and the largest value locates in Siberian area, where temperature varies significantly between different years. Because of linear correlation between Tm and temperature, one can infer that Tm in Siberian area changes largely in different years, which explains the largest value of α3 here. In Fig. 2(c), amplitudes of semi-annual periodicity α4 are larger in the polar areas, which caused by phenomena of polar day and night. For amplitudes of diurnal periodicity α5, Fig. 2(d) shows that it is larger in most continental areas, especially in Africa, while smaller in oceanic areas. We believe amplitudes of diurnal periodicity α5 closely relates to temperature difference between day and night.
4 VALIDATION OF GTm-III
A different set of external data including Tm grid data provided by GGOS Atmosphere, radiosonde data and COSMIC occultation data, are used to evaluate the validity and applicability of the GTm-III, to test its accuracy and stability in global scale, and to examine its (dis)advantages compared with the existing models.
Tm from COSMIC should be examined before this validation. As described, 341 radiosonde stations were selected, further all COSMIC occultation events occurred at co-locations with the radiosonde stations in 2010 were selected. The co-location with radiosonde station means that location difference with nearby radiosonde station is less than 1° in longitude and latitude, less than 0.2 km in height at bottom of profiles and less than 1 hr in temporal resolution. Under this qualification, accuracy of Tm from COSMIC was examined by using 1036 selected co-located occultation events and by regarding Tm from radiosonde as the standard. The result shows that MBE between them is 0.7 K, MAE is 1.7 K and RMS is 2.3 K, which indicates that Tm from COSMIC also has high accuracy. Additionally, Yao et al. (2013) show that the GGOS Atmosphere grid data have an MBE of −0.06 K and an RMS of 1.94 K compared with COSMIC data.
4.1 Tm grid data from GGOS Atmosphere
As mentioned above, GTm-III is constructed using 2005–2011 Tm grid data. Here we validate the model using 2012 Tm grid data. With a spatial resolution of 2.5° × 2°, there are a total of 13 195 Tm gridpoints in the world. The Tm data of all grids directly provided by GGOS Atmosphere at four times (UTC 00:00, 06:00, 12:00 and 18:00) every day are taken as the reference values. The Tm of each gridpoint at the same time is calculated with GTm-III, GTm-II and Bevis Tm–Ts relationship (Ts calculated with GPT model for data unavailable in oceanic areas is referred to as Bevis&GPT). The obtained Tm estimates are compared with the reference values. The MAE and RMS of different models in 2012 are shown in Table 2 and Fig. 3.
Model . | MBE (in K) . | MAE (in K) . | RMS (in K) . | ||||||
---|---|---|---|---|---|---|---|---|---|
. | Mean . | Max. . | Min. . | Mean . | Max. . | Min. . | Mean . | Max. . | Min. . |
GTm-III | 0.11 | 4.7 | −3.8 | 2.5 | 5.5 | 0.8 | 3.2 | 6.5 | 1.0 |
GTm-II | −0.01 | 9.4 | −8.9 | 3.4 | 9.4 | 0.9 | 4.1 | 10.4 | 1.1 |
Bevis&GPT | 1.2 | 14.0 | −5.8 | 4.0 | 14.0 | 0.8 | 4.8 | 14.9 | 1.1 |
Model . | MBE (in K) . | MAE (in K) . | RMS (in K) . | ||||||
---|---|---|---|---|---|---|---|---|---|
. | Mean . | Max. . | Min. . | Mean . | Max. . | Min. . | Mean . | Max. . | Min. . |
GTm-III | 0.11 | 4.7 | −3.8 | 2.5 | 5.5 | 0.8 | 3.2 | 6.5 | 1.0 |
GTm-II | −0.01 | 9.4 | −8.9 | 3.4 | 9.4 | 0.9 | 4.1 | 10.4 | 1.1 |
Bevis&GPT | 1.2 | 14.0 | −5.8 | 4.0 | 14.0 | 0.8 | 4.8 | 14.9 | 1.1 |
Model . | MBE (in K) . | MAE (in K) . | RMS (in K) . | ||||||
---|---|---|---|---|---|---|---|---|---|
. | Mean . | Max. . | Min. . | Mean . | Max. . | Min. . | Mean . | Max. . | Min. . |
GTm-III | 0.11 | 4.7 | −3.8 | 2.5 | 5.5 | 0.8 | 3.2 | 6.5 | 1.0 |
GTm-II | −0.01 | 9.4 | −8.9 | 3.4 | 9.4 | 0.9 | 4.1 | 10.4 | 1.1 |
Bevis&GPT | 1.2 | 14.0 | −5.8 | 4.0 | 14.0 | 0.8 | 4.8 | 14.9 | 1.1 |
Model . | MBE (in K) . | MAE (in K) . | RMS (in K) . | ||||||
---|---|---|---|---|---|---|---|---|---|
. | Mean . | Max. . | Min. . | Mean . | Max. . | Min. . | Mean . | Max. . | Min. . |
GTm-III | 0.11 | 4.7 | −3.8 | 2.5 | 5.5 | 0.8 | 3.2 | 6.5 | 1.0 |
GTm-II | −0.01 | 9.4 | −8.9 | 3.4 | 9.4 | 0.9 | 4.1 | 10.4 | 1.1 |
Bevis&GPT | 1.2 | 14.0 | −5.8 | 4.0 | 14.0 | 0.8 | 4.8 | 14.9 | 1.1 |
Table 2 and Fig. 3 show that for GTm-III, MBE averages 0.11 K and ranges from −3.8 to 4.7 K; MAE averages 2.5 K and ranges from 0.8 to 5.5 K; RMS averages 3.2 K and ranges from 1.0 to 6.5 K. The average MAE and RMS of GTm-III are the smallest, while the average MBE of GTm-II is the smallest. Though the mean of MBE of GTm-II is only −0.01 K, Fig. 3 reflects great positive errors near the South Pole and negative errors in some oceans and on land, resulting in the small average MBE. Therefore, GTm-III improves accuracy globally comparing with GTm-II. The accuracy and stability of GTm-III are slightly higher at mid- and low latitudes than at high latitudes and better in oceanic areas than on land. For Bevis Tm–Ts relationship, large errors exist in parts of the Himalayas and Antarctic regions. Similar errors are observed in the results of GTm-II, which uses the Bevis Tm–Ts relationship as supplemental data source; additionally, large errors are observed in the results of GTm-II in some areas of Chile. Together, the above-mentioned results demonstrate that GTm-III has higher accuracy for estimating Tm with no large errors on a global scale.
4.2 Radiosonde data
A total of 461 radiosonde stations in the globe are selected; of which, more stations are distributed in the Northern Hemisphere than in the Southern Hemisphere (Fig. 4). As described in Section 2.1, the Tm calculated from radiosonde data at UTC 00:00 and 12:00 every day in 2012 are treated as the reference values. The Tm estimates are calculated using GTm-III, GTm-II and Bevis Tm–Ts relationship (Ts is the actual surface temperature), and are statistically analysed. MAE and RMS of different models are shown in Table 3.
Model . | MBE (in K) . | MAE (in K) . | RMS (in K) . | ||||||
---|---|---|---|---|---|---|---|---|---|
. | Mean . | Max. . | Min. . | Mean . | Max. . | Min. . | Mean . | Max. . | Min. . |
GTm-III | 0.7 | 8.6 | −3.1 | 3.3 | 8.6 | 1.0 | 4.2 | 11.0 | 1.3 |
GTm-II | −0.7 | 6.3 | −7.2 | 3.5 | 7.5 | 1.0 | 4.4 | 10.0 | 1.3 |
Bevis | 0.2 | 9.0 | −8.2 | 3.4 | 9.1 | 1.1 | 4.2 | 11.2 | 1.4 |
Model . | MBE (in K) . | MAE (in K) . | RMS (in K) . | ||||||
---|---|---|---|---|---|---|---|---|---|
. | Mean . | Max. . | Min. . | Mean . | Max. . | Min. . | Mean . | Max. . | Min. . |
GTm-III | 0.7 | 8.6 | −3.1 | 3.3 | 8.6 | 1.0 | 4.2 | 11.0 | 1.3 |
GTm-II | −0.7 | 6.3 | −7.2 | 3.5 | 7.5 | 1.0 | 4.4 | 10.0 | 1.3 |
Bevis | 0.2 | 9.0 | −8.2 | 3.4 | 9.1 | 1.1 | 4.2 | 11.2 | 1.4 |
Model . | MBE (in K) . | MAE (in K) . | RMS (in K) . | ||||||
---|---|---|---|---|---|---|---|---|---|
. | Mean . | Max. . | Min. . | Mean . | Max. . | Min. . | Mean . | Max. . | Min. . |
GTm-III | 0.7 | 8.6 | −3.1 | 3.3 | 8.6 | 1.0 | 4.2 | 11.0 | 1.3 |
GTm-II | −0.7 | 6.3 | −7.2 | 3.5 | 7.5 | 1.0 | 4.4 | 10.0 | 1.3 |
Bevis | 0.2 | 9.0 | −8.2 | 3.4 | 9.1 | 1.1 | 4.2 | 11.2 | 1.4 |
Model . | MBE (in K) . | MAE (in K) . | RMS (in K) . | ||||||
---|---|---|---|---|---|---|---|---|---|
. | Mean . | Max. . | Min. . | Mean . | Max. . | Min. . | Mean . | Max. . | Min. . |
GTm-III | 0.7 | 8.6 | −3.1 | 3.3 | 8.6 | 1.0 | 4.2 | 11.0 | 1.3 |
GTm-II | −0.7 | 6.3 | −7.2 | 3.5 | 7.5 | 1.0 | 4.4 | 10.0 | 1.3 |
Bevis | 0.2 | 9.0 | −8.2 | 3.4 | 9.1 | 1.1 | 4.2 | 11.2 | 1.4 |
Table 3 shows that in terms of the accuracy and stability, GTm-III has the smallest means of MAE (3.3 K) and RMS (4.2 K) among the three models. Bevis Tm–Ts relationship has the smallest mean of MBE of 0.2 K. The mean of MBE is 0.7 K for GTm-III and is −0.7 K for GTm-II, meaning that they have equal absolute value but opposite signs. GTm-II and Bevis Tm–Ts relationship have relatively high accuracy as well, because the radiosonde stations involved in GTm-II modelling basically cover the inspection area; Bevis Tm–Ts relationship uses the North American radiosonde stations and surface temperature measurements. Radiosonde only provides observations at two times with minor changes every day, although GTm-III adds diurnal periodicity, its advantage relative to GTm-II is not obvious in terms of the overall accuracy. Analysis of the accuracy and stability of various models on different DOYs are described later. The daily testing results at all stations of each model were statistically analysed, the MBE, MAE and RMS of different models varying with DOY are shown in Fig. 5.
From Fig. 5(a), one can see that biases of Bevis Tm–Ts relationship are generally the smallest, and quantity of positive biases of GTm-III is larger than that of GTm-II. For each model, GTm-III has larger biases in winter, GTm-II has larger biases in spring and Bevis Tm–Ts relationship has larger biases in February, March and April. Figs 5(b) and (c) show that model accuracies are different in different seasons and highest in summer. It also shows that accuracies of Tm calculated by Bevis Tm–Ts relationship are least affected by seasonal differences, and those calculated by GTm-II and GTm-III are lowest in February and in March, which are also lower than that calculated by Bevis Tm–Ts relationship. Because radiosonde stations used in the experiment are mainly located at high latitudes of the Northern Hemisphere, where Tm changes little in summer but greater in winter, and GTm-II and GTm-III are filtered with multiyear Tm observations, one sees larger changes and weak model accuracy in winter. However, the accuracy and stability of each model varies at different time. In DOY 1∼100, accuracies (in terms of RMS) of GTm-III and GTm-II are equivalent, and Bevis Tm–Ts relationship are generally more accurate than them. However, in DOY 100∼300, GTm-III and GTm-II are more accurate than the Bevis Tm–Ts relationship. A statistical comparison shows that during the whole year period, GTm-III is better than GTm-II in 71 per cent cases, and GTm-III is better than the Bevis Tm–Ts relationship in 58 per cent cases.
Further, the accuracy of the models is tested in radiosonde stations at different latitudes by integrating data from the stations at similar latitudes (Fig. 6).
From Fig. 6(a), one can see that GTm-III has relatively smaller biases in each latitude and small differences among biases in different latitudes, verifying general excellence of GTm-III than GTm-II and Bevis Tm–Ts relationship. Figs 6(b) and (c) show that regardless of modelling method, the accuracy and stability of all models are poorer at high latitudes than at low latitudes. For GTm-III, the accuracy and stability are highest in low-latitude regions and slightly better than GTm-II but inferior to Bevis Tm–Ts relationship at high latitudes of the Northern Hemisphere. These results reflect the advantage of Bevis Tm–Ts relationship as a regional model, for it has the highest accuracy and stability in the mid-latitudes of the Northern Hemisphere. Though the Bevis Tm–Ts relationship is better than GTm-III in mid-latitude of the Northern Hemisphere, their differences are small. Moreover, GTm-III is capable of calculating Tm without temperature observations, which also represents its practicality.
4.3 COSMIC occultation data
The existing radiosonde stations cover most of the land areas but rare oceanic areas or polar regions; the number of radiosonde stations is less in the Southern Hemisphere than in the Northern Hemisphere; and low time resolution of radiosonde data leads to flaws in verifying the accuracy and stability of GTm-III on a global scale. In view of the above-mentioned issues related to radiosonde data, later we use the 2012 COSMIC occultation data to test the accuracy and stability of each model. Tm calculated from COSMIC occultation data is taken as the reference value, and Tm estimates obtained with GTm-III, GTm-II and Bevis Tm–Ts relationship are tested. The results in a whole year period are shown in Table 4.
Model . | Bias (in K) . | MAE (in K) . | RMS (in K) . |
---|---|---|---|
GTm-III | −0.5 | 2.9 | 3.9 |
GTm-II | −1.4 | 3.9 | 5.0 |
Bevis | 0.9 | 3.4 | 4.4 |
Model . | Bias (in K) . | MAE (in K) . | RMS (in K) . |
---|---|---|---|
GTm-III | −0.5 | 2.9 | 3.9 |
GTm-II | −1.4 | 3.9 | 5.0 |
Bevis | 0.9 | 3.4 | 4.4 |
Model . | Bias (in K) . | MAE (in K) . | RMS (in K) . |
---|---|---|---|
GTm-III | −0.5 | 2.9 | 3.9 |
GTm-II | −1.4 | 3.9 | 5.0 |
Bevis | 0.9 | 3.4 | 4.4 |
Model . | Bias (in K) . | MAE (in K) . | RMS (in K) . |
---|---|---|---|
GTm-III | −0.5 | 2.9 | 3.9 |
GTm-II | −1.4 | 3.9 | 5.0 |
Bevis | 0.9 | 3.4 | 4.4 |
Table 4 shows that the accuracy and stability of GTm-III are the highest globally (Bias, −0.5 K; MAE, 2.9 K; RMS, 3.9 K), obviously better than those of GTm-II and Bevis Tm–Ts relationship (Ts is the measured surface temperature). This is because GTm-III takes into account the characteristics of Tm of semi-annual and diurnal periodicity, and uses globally high-accuracy Tm gird data for modelling.
To test the accuracy of the models at different time points, we make daily statistics. The MAE and RMS of each model varying with DOY are shown in Fig. 7.
Fig. 7 shows that the accuracy and stability of each model have no obvious changes with season, there are minor differences between results from radiosonde data and those from COSMIC occultation data, because COSMIC data can reflect comprehensive global changes at every moment of every day while radiosonde data only reflect the changes at two moments of every day on the continent of the Northern Hemisphere. As a result, the test with radiosonde data shows significant seasonal differences, but this phenomenon does not appear in the test with COSMIC data. When compared with GTm-II, GTm-III has high accuracy and stability on a daily scale. This observation reflects that the Tm estimated by GTm-III at each time of every day is closer to the reference value, proving the advantages of GTm-III in model and data source. Similar results are obtained when comparing GTm-III with the Bevis Tm–Ts relationship. Though, the Bevis Tm–Ts relationship considers changes of Tm in 1 d by using observed temperatures it is a locally applicable formula, which cannot represent global relationships between Tm and the Earth's surface temperature.
Finally, the accuracy of the models at different latitudes is tested by integrating data from stations at similar latitudes (Fig. 8).
Fig. 8 shows that among the three models, GTm-III provides Tm estimates with the highest precision; the accuracy and stability of GTm-III are best at low latitudes and better in the Southern Hemisphere than in the Northern Hemisphere. The precision of Tm estimated by GTm-III is higher than that of GTm-II at all latitudes. Compared with Bevis, GTm-III has relative low precision in the north of N40º, relative high precision between N40º and S35º, and highest in the south of S55º. In the south of 66ºS, the precision of Tm estimated by Bevis decreases with increasing latitude, with the maximal MAE close to 10 K and maximal RMS greater than 10 K. Tm–Ts relationship changes with station locations and seasons, and climate in the Arctic and Antarctic regions are significantly different, so precisions of Tm estimated by the Bevis Tm–Ts relationship in the two regions are quite different.
5 CONCLUSIONS
By considering the actual variation characteristics of Tm, an accurate global empirical Tm model, GTm-III, is constructed using high-precision GGOS Atmosphere Tm grid data. The characteristics of Tm in semi-annual and diurnal periodicity are added into GTm-III based on the existing conventional model, and the initial phase of each cycle is estimated. The GTm-III, which can obtain Tm at any time and place without measured Ts data, is validated with a complete set of external data: Tm grids data for testing the accuracy and stability of a model at four moments of the day on a global scale; radiosonde data for testing the accuracy and stability of a model at two moments of the day in partial land areas; and COSMIC occultation data for testing the accuracy and stability of a model at most times of the day worldwide. Results show that GTm-III is superior to GTm-II and the former represents the most stable and a truly globally applicable model for estimating Tm.
The authors would like to thank ‘GGOS Atmosphere’ for providing grids of Tm and COSMIC for the occultation data. This research was supported by the National Natural Science Foundation of China (41174012 and 41274022) and The National High Technology Research and Development Program of China (2013AA122502).
REFERENCES
SUPPORTING INFORMATION
Additional Supporting Information may be found in the online version of this article:
Appendix (Supplementary Data).
Please note: Oxford University Press is not responsible for the content or functionality of any supporting materials supplied by the authors. Any queries (other than missing material) should be directed to the corresponding author for the article.