Water vapor is an active composition of the atmosphere, with extremely uneven distributions and largetemporal and spatial variations in the atmosphere.The phase change of water vapor is directly relatedto precipitation and plays an important role in theatmosphere energy transfer, weather development, radiationbudget of the earth-atmosphere system, and global climate change(Bevis et al., 1992; Rocken et al., 1995; Bi et al., 2006; Falconer et al., 2009; Perler et al., 2011). Low temporal and spatial resolutions of routineatmosphere observations restrict our knowledge on thespatiotemporal variation features of water vapor. As aresult, it leads to low precision of the initial humidityfield in numerical weather prediction(NWP)modelsas well as low accuracy of NWP results(Gutman et al., 2004; Song, 2004; Cao et al., 2005, 2006; Bastin et al., 2007). Ground-based GPS technology provides a newmean for atmospheric water vapor observation, whichcan be made all the time under all weather conditionsat high precision. It supplements the traditional atmosphereobservation methods(Song, 2004; Lutz, 2009).When using path wet delay(PWD)to obtain precipitablewater vapor(PWV)in ground-based GPStechnology, there are three important computation formulasas follows.

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To evaluate the impact of T_m on the PWV, thefirst-order partial derivative is derived as follows:

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Typical values of zenith path hydrostatic delay(PHD)are 2.30 m and 0.00–0.40 m for PWD(Walpersdorf et al., 2001). Assuming the variables of PWD and T_m are constants, substitute the extreme values(e.g., PWD = 400 mm, T_m = 285 K)of all parameters intoEq.(4), the result is as follows:

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Equation(5)shows that the T_m error of 1 K cancause a PWV error of 0.2243 mm in the case of a PWDvalue of 400 mm and T_m of 285 K. Therefore, accuratecalculation of T_m is important. In ground-based GPStechnology, there are several ways to acquire T_m:(1)considering T_m as a constant;(2)computing T_m byuse of a numerical integration method based on Eq.(3)using radiosonde data or numeral prediction products;(3)computing T_m from T_s(Ts denotes surfacetemperature)based on specific local T_m-T_s regressionmodels. In the above methods, considering T_m as aconstant may lead to low precision of T_m and PWV;the numerical integration method has the highest precision and T_m thus derived is often taken as the “true”observation, but it is difficult to apply this method toreal-time acquisition of T_m since the radiosonde dataor numeral prediction products are not available in thereal-time mode. Computing T_m from T_s based on theT_m-T_s regression models is simple and easy with acceptableprecision in the current ground-based GPStechnology.

Most studies use statistical regression models toobtain T_m. Bevis et al.(1992)made an analysisof 8718 radiosonde profiles spanning approximatelya 2-yr interval for the stations in the United Stateswith the latitude range of 27°–65°N and a heightrange of 0–1.6 km, and yielded a linear regressionTm=70.2+0.72T_s. The RMS deviation from this regressionis 4.74 K, which is a relative error of less than2%. The Bevis regression model has been applied tomany studies of T_m in China(Li et al., 1999; Liu et al., 2006; Yue et al., 2008; Li et al., 2009; Yu and Liu, 2009; Wang et al., 2011a, b). However, it is found thatthe errors of the Bevis empirical model distribute unevenlyin China and are generally more than 4 K withthe extreme value of 8 K in some areas(Yu et al., 2011). The impact of the Bevis empirical model errorson the PWV can reach the millimeter level underan extreme weather condition with rich water vapor.

Previous studies focused on the setup of local T_m-Ts regression models for a specific region based onsounding data(Li et al., 1999; Liu et al., 2006; Yue et al., 2008; Li et al., 2009; Wang et al., 2011a). Yu and Liu(2009) and Yu et al.(2011)discussed the errorstatistics of the Bevis model over China and gave thedependence of the errors on the elevation of station.Wang et al.(2011b)investigated the correlation of thecoefficients a and b of the local T_m model with longitude, latitude, and station elevation. Nonetheless, some aspects such as the spatiotemporal distributioncharacteristics of T_m and the associated retrieval errorcomparison between the Bevis model and local modelsover entire China are rarely researched. Yu and Liu(2009)presented a method adding a correction relevantto elevation in the Bevis model to obtain T_m overareas without historical sounding data.

Reanalysis of multi-decadal series of past observationshas been widely utilized for the studies of atmospheric and oceanic processes and predictability.Since reanalysis data are produced using sophisticated and advanced data assimilation systems developed forNWP, they are more suitable than operational analysisfor use in studies of long-term variability of climate.Reanalysis products are used increasingly in manyfields that require an observational record of the stateof either the atmosphere or its underlying l and and ocean surfaces. So far, ECMWF has produced threereanalysis products including ERA-15, ERA-40, and ERA-interim, among which ERA-interim is a globalreanalysis of the data-rich period since 1989. TheERA-interim data assimilation system uses a 2006release of the Integrated Forecasting System(IFSCy31r2), which contains many improvements in boththe forecasting model and the analysis methodology, compared to those for ERA-40. The ERAinterimreanalysis was put into operation in March2009, and has been running in near real-time tosupport climate monitoring(http://www.ecmwf.int/research/era/do/get/Reanalysis−ECMWF, retrievedon 19 December 2011).

This study adopts the numerical integrationmethod and the sounding data of 87 internationalexchange sounding stations in China to obtain thespatiotemporal distribution characteristics of T_m overChina. Meanwhile, we compare the results of T_m calculatedfrom the Bevis model with those from thelocal regression models based on historical soundingdata, and then evaluate the performance of the Bevismodel and the local T_m-T_s regression models. Whensetting up regression models for areas without soundingdata, the Kriging spatial interpolation method isused to obtain the coefficients of the local T_m-T_s regressionmodels and the results are assessed in comparisonwith the numerical method results using the soundingdata. In addition, the T_m-T_s regression model resultsbased on the ERA-interim reanalysis product are alsocompared with those based on the sounding data ofBeijing and Hong Kong(HK), and the results indicatethat the ERA-interim reanalysis provide anotherdata source for local T_m calculation in areas withoutsounding data.2. Data and method

In this paper, we use local T_m-T_s regression modelsbased on sounding data or the ERA-interim reanalysisproduct to derive T_m, and use the “true” observationcalculated from the sounding data with thenumerical integration formula to validate the regressionresults. The data of 87 international soundingstations in China for 2003–2010 are downloaded fromthe University of Wyoming website http://weather.uwyo.edu/upperair/sounding.html(retrieved on 19December 2011). The ERA-interim data are downloadedfrom http://data-portal.ecmwf.int/data/d/interim−daily(retrieved on 19 December 2011).

The numerical integration method is a discretionform of Eq.(3) and is described below. T_m can be retrievedfrom both sounding data and reanalysis productsas follows(Li et al., 1999; Liu et al., 2006; Yue et al., 2008; Li et al., 2009; Yu and Liu, 2009; Wang et al., 2011a, b).

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For reanalysis product ERA-interim, the temperature, geopotential height(H), and relative humidity(RH)fields have a resolution of 1.5° latitude ×1.5°longitude and 37 vertical levels. The surface temperature(T_s) and surface dew point temperature fields atthe same horizontal resolution are also used. All variablesare available 4 times daily at 0000, 0600, 1200, and 1800 UTC. The water vapor pressure(e)is obtainedfrom RH and saturation water vapor pressure(E)as follows:

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When comparing the T_m values obtained fromsounding with that obtained from ERA-interim basedon Eq.(6), interpolations are conducted as follows. Inthe vertical direction, the level at which the station islocated is determined according to the station’s actualgeopotential height. Linear interpolation is used to obtainthe surface temperature of the station based onthe reanalysis data of two adjacent vertical grids, and exponential interpolation is used to obtain its watervapor pressure. In the horizontal direction, the temperature and water vapor pressure at each level abovethe station are obtained using bi-linear interpolationbased on data of the four adjacent grids at the samelevel.

The T_m-T_s regression model is obtained usingMatlab based on historical T_m and T_s sample pairsas follows. First, T_m is calculated by Eq.(6)twicea day for sounding data and four times a day forERA-interim reanalysis product. Note that T_s canbe directly obtained from the sounding data or ERAinterimreanalysis product. Then, the T_m-T_s regressionmodel based on the total samples in a certain periodof time can be set up with the Matlab software.For example, during a one-year period, there are about730 samples for sounding data and 1460 samples forERA-interim reanalysis product. The precision of theT_m-T_s regression model is evaluated by comparing T_mcalculated by Eq.(6)with T_m calculated by the T_m-T_sregression model.3. Regression of T_m at HK by seasons based on the sounding data

Based on the sounding data of HK(WMO stationID 45004)in 2005, T_m of this station was calculatedby Eq.(6). Figure 1 shows the T_m annual change in2005. T_m varies significantly by season between 275 and 295 K with the highest value in summer and lowestin winter. This gives us a rough idea of how T_mchanges with season. It also raises a question as toif it is better to establish seasonal regression modelsaccording to seasonal sounding data rather than toobtain general/annual regression models according toconsecutive multi-year sounding data time series, i.e., if seasonality of the regression should be considered and could be used to facilitate the regression accuracy?

Fig. 1. Annual change of Tm obtained by using the numerical integration method and the 0000 and 1200 UTC sounding data of HK in 2005.

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In this section, the precision of the annual and seasonal T_m-T_s regression models for the HK stationbased on the sounding data are evaluated. There are59 missing records for a total of 4325 valid times forthe period 2003–2008 for HK sounding station. TheHK−annual T_m-T_s model in Table 1 is set up basedon all the sounding data from 2003 to 2008. We classifythe total sounding data of 4325 entries from 2003to 2008 by season, and about 1080(T_m and T_s)samplesare obtained for every season. Based on that, four seasonal T_m-T_s empirical models are set up, calledHK−season(spring, summer, autumn, and winter), asshown in Table 1. Table 1 indicates that the a and bcoefficients of spring and autumn models are close tothat of the annual model, while the a and b coefficientsof summer and winter models differ largely from thatof the annual model.

Table 1. Statistics of the seasonal T_m-T_s empirical models for HK

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We use the sounding data of HK station in 2009to validate the local seasonal T_m-T_s empirical models.The values of T_m in 2009 are calculated using Eq.(6) and taken as real values. With regard to the seasonalregression models in Table 1, there are a total of 730(T_m and T_s)samples in 2009 with averagely 185 samplesin every season. The model values of T_m for thefour seasons in 2009 are calculated from the seasonalT_m-T_s empirical models, respectively, and their statisticresults are shown in Table 2. Although the a and bcoefficients of summer and winter models differ largelyfrom that of the annual model, there is almost no differencewhen replacing any of the seasonal models withthe annual one to calculate T_m. On the contrary, theBevis model has a larger bias than local seasonal modelsbut almost the same RMS.

Table 2. Statistics of the seasonal T_m-T_s empirical models in comparison with the Bevis model for HK

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Why do the a and b coefficients of the summer and winter models differ largely from that of the annualmodel, but the T_m values differ little from thatcalculated from their linear combination? The lineartrends of T_m from the four seasonal models and theannual model are shown in Fig. 2. The summer temperaturein HK varies from 299.15 to 306.15 K(yellowvertical range)with the mean value of 301.15 K, whilethe winter temperature in HK varies from 287.15 to293.15 K(lavender vertical range)with the mean valueof 290.15 K. Figure 2 shows that the trend line of T_mfrom the summer model is very close to that from theannual model within the temperature range of 299.15–306.15 K, so is that with the winter model and annualmodel for the temperature range of 287.15–293.15 K.Thus, T_m calculated from the specific seasonal model and annual model is almost the same.

Fig. 2. Trend lines of the seasonal and annual regression models for HK.

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The average monthly T_m in January, April, July, and October is calculated based on the sounding datafrom 2003 to 2009 by Eq.(6)to reveal the spatial and temporal distribution characteristics of T_m overChina. The results are shown in Fig. 3.

Fig. 3. Spatial distributions of the average monthly Tm(K)calculated by using the sounding data and Eq.(6)overChina in(a)January, (b)April, (c)July, and (d)October.

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Figure 3 shows that the average monthly T_m oversoutheastern China is the highest throughout the year, whereas it is the lowest over northeastern China inJanuary and over the Qinghai-Tibetan Plateau in July.

The general characteristics of spatiotemporal distributionsof the average monthly surface temperatureTs in China are consistent with T_m. The correlationcoefficient between T_m and T_s is 0.848(Wang et al., 2011b), which shows the feasibility of estimating T_mby T_s.

Previous studies(e.g., Li et al., 1999; Liu et al., 2006; Yue et al., 2008; Li et al., 2009; Yu and Liu, 2009; Wang et al., 2011a, b)never investigated theoverall spatiotemporal distribution of T_m over China.Figure 3 shows that the T_m distributions may havesomething to do with the climate pattern, populationdensity, and topography. Southeastern China is underthe influence of the subtropical monsoon climate withhigh population density, and T_m is relatively high inthis region throughout the year. Northeastern Chinais dominated by the temperate monsoon climate, and Tm is comparatively low all the year except in summer.Tm over the Qinghai-Tibetan Plateau is significantlylow compared with other areas in summer because ofits unique topography.4.2 T_m distribution by the regression method based on the sounding data

There are 120 sounding stations in China, amongwhich 87 are international exchange stations. Thedata of the 87 stations from 2009 to 2010 are examined.We use the radiosonde data of 2009 to obtain thelocal T_m-T_s regression model for each station, then usethe sounding data of 2010 to evaluate the local model and compare with the Bevis model.

The results shown in Table 3 and Fig. 4 revealthat not all the local T_m-T_s models are more precisethan the Bevis model; this is inconsistent with theconclusion of previous studies(Li et al., 1999; Liu et al., 2006; Yue et al., 2008; Li et al., 2009; Yu and Liu, 2009; Wang et al., 2011a, b). In Table 3, dTm meansthe difference between the real value of T_m in 2010 byEq.(6)using sounding data and the model value ofTm by the local T_m-T_s model or the Bevis model usingthe radiosonde data of 2009, where a−l is the a coefficientof the T_m-T_s model and same is for b_l. TheBias_l, RMSe_l, Max_l, and Num_l are respectivelythe mean bias, st and ard deviation, maximum valueof dTm, and the number of samples with dTm greaterthan five degrees based on the local model. Similarly, the Bias_B, RMSe_B, Max_B, and Num_B are thecorresponding statistical variables for the Bevis model.The number of samples is about 730 in 2010.

Table 3. Comparison of the local T_m-T_s model with the Bevis model

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Fig. 4. Distribution of the number of samples with the Tm difference more than 5 K calculated from the Bevis model and the local Tm-Ts model based on the sounding data in China.

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The results indicate that there are 22 soundingstations for which the local T_m-T_s models are not betterthan the Bevis model. Table 3 only lists the statisticalinformation of 9 stations. Table 3 and Fig. 4show that the Bevis model is fit for areas of northeasternChina and the Qinghai-Tibetan Plateau while ithas a large deviation in southeastern and northwesternChina, where the local T_m-T_s model works better.5. Regression of T_m at two stations using the Kriging method based on the sounding data

The Kriging interpolation method provides an unbiasedoptimal estimation for regional variables in alimited area based on variation function spatial analysis.It takes into account the spatial correlation betweenthe data points and is suitable for interpolationof spatial data. Details for Kriging interpolation canbe seen in Zeng and Huang(2007).

The average distance of adjacent sounding stationsis about hundreds of kilometers. For southeastern and northwestern China, the local T_m-T_s modelsare difficult to set up due to the absence of soundingdata. The Kriging spatial interpolation methodis used to obtain the a and b coefficients of the localT_m-T_s models for areas without sounding data. Thismethod is evaluated at two sounding stations, i.e., Pizhou(WMO station ID 57972) and Kuche(WMOstation ID 51644). Pizhou station locates in southeasternChina where a dense network of sounding stationsexists, whereas Kuche station locates in northwesternChina where there is a lack of sounding stations. Selectingthe two stations for test can validate if theKriging interpolation method is able to obtain localT_m-T_s models for areas with both dense and coarsedistributions of sounding stations at acceptable precision.For areas such as southeastern and northwesternChina where the Bevis model fails to perform well, thelocal T_m-T_s models should be set up.

The evaluation for Pizhou station is conducted asfollows: 1)use the Kriging method to generate a and b isosurfaces based on the a and b coefficients of therest of the 86 sounding stations; 2)obtain the interpolatedvalues of the a and b coefficients for this station, and the Kriging T_m-T_s model for this station is thenobtained; 3)use the observed sounding data of 2010to derive a real local T_m-T_s model, compare with theKriging model derived in step 2, and calculate theirdifferences. The same process as described above isapplied to Kuzhe station. The results are shown inTable 4.

Table 4. Comparison of the local T_m-T_s models and the Bevis model for Pizhou and Kuche stations

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In Table 4, a_k is the a coefficient of the T_m-T_smodel based on the Kriging interpolation method and same holds for b_k. The Bias_k, RMSe_k, Max_k, and Num_k are respectively the mean bias, st and arddeviation, maximum value of dTm, and the numberof samples with dTm greater than five degreesbased on the Kriging method. The a_l, b_l, Bias_l, RMSe_l, Max_l, and Num_l are the same as inTable 3.

Table 4 shows that the Kriging spatial interpolationmethod is feasible in setting up the appropriatelocal T_m-T_s model for areas with no historical soundingdata such as southeastern and northwestern China, where the Bevis model performs not well.6. Evaluation of T_m at Beijing and HK calculated by the numerical and regression methods from two data sources6.1 T_m values calculated by the numerical method from both data sources

We used ERA-interim and sounding data of 2003for Beijing and 2007 for HK to derive T_m values byEq.(6). The results are shown in Table 5.

Table 5. Comparison of T_m computed by Eq.(6)from the ERA-interim data and from the soundingdata for Beijing and HK

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There are 1460 samples for the ERA-interim datain both 2003 and 2007, from which 730 samples matchthe time of the sounding data for 2003 and 719 samplesfor 2007. Table 5 shows that there is little differencebetween the T_m values calculated by Eq.(6)fromthese two different datasets.

Statistical analysis in Table 5 is performed in thefollowing way:

Difference: di = T_m(ERA interim)− T_m(sounding);

Systematic error: Bias=, where n is numberof samples;

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Once the local T_m-T_s empirical formula has beenset up, T_m can be calculated by T_s with high precision, and it can then be used to obtain PWV using PWDin ground-based GPS. We set up a T_m-T_s empiricalformula using the ERA-interim data of 2003 for Beijing and 2007 for HK. The accuracy of this empiricalformula is evaluated by the ERA-interim data of 2004for Beijing and 2008 for HK. The statistical results arelisted in Table 6.

Table 6. Statistics of the T_m-T_s regression models for Beijing and HK based on the ERA-interim data

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How the statistical analysis in Table 6 was performedis detailed in Table 7 for both Beijing and HK.

Table 7. Statistical method used to obtain Table 6

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To further underst and the regressed T_m valuesfrom the ERA-interim data, the corresponding soundingdata were also processed. Comparisons of T_m bythe ERA-interim and sounding data are shown in Table 8. Table 8 shows that the local T_m-T_s empiricalmodel(T_m-T_s)EAR-interim based on the EAR-interimreanalysis data coincides well with that based on thesounding data.

Table 8. Comparisons of the T_m-T_s empirical formulas derived from ERA-interim data and sounding data

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To sum up, the above comparisons demonstratea good agreement between ERA-interim reanalysisproduct and sounding data when calculating T_m basedon the numerical integration method and when settingup T_m-T_s regression models in Beijing and HK. This iseasy to underst and since radiosonde data are the key and main data source for the assimilation of reanalysisproducts. For areas with rich sounding data, the reanalysisproduct in general has good quality too. Itis also proved that the ECMWF reanalysis productERA-interim can be applied to the acquisition of T_mfor Beijing and HK areas.7. Conclusions

This paper first compares the difference betweenthe annual and seasonal T_m-T_s regression models forHK in detail and then examines the applicability of theBevis T_m-T_s regression model over China. For areaslack of historical sounding data, the Kriging interpolationmethod and the ECMWF reanalysis productERA-interim are used to set up local T_m-T_s models.We draw the following conclusions:

(1)The annual and seasonal T_m models have considerableaccuracy, T_m can be calculated precisely byannual T_m model for all seasons, and it is not necessaryto set up local seasonal T_m models for HK soundingstation.

(2)The Bevis model is fit for areas of northeasternChina and the Qinghai-Tibetan Plateau, butit produces a large deviation of T_m in southeastern and northwestern China, where the local T_m-T_s modelshould be set up.

(3)The Kriging spatial interpolation method canbe used to set up the local T_m-T_s model for areas withno historical sounding data such as southeastern and northwestern China, where the Bevis model performsnot well.

(4)Acquisition of the local T_m based on ERAinterimreanalysis data coincides well with that basedon the sounding data for Beijing and HK, which mightprovide a substitute available data source to set uplocal T_m-T_s models for areas lack of sounding data.

For areas lack of historical sounding data, theKriging interpolation method and the ECMWF reanalysisproduct ERA-interim were both employed toset up the local T_m-T_s model. The ECMWF reanalysisproduct has wide data coverage and long data spanon acceptable grid resolutions, whereas for the Krigingmethod in Section 5, there are only 120 soundingstations in China. Future research may focus on thevalidation of the ECMWF reanalysis product ERAinterimin setting up local T_m-T_s models in comparisonwith the Kriging method. If the result is encouraging, the ECMWF reanalysis product can be used to set upthe local T_m-T_s models on the grid scale. Meanwhile, the Kriging method may also be used to interpolatedthe a and b coefficients of the local T_m-T_s models formore homogeneously and rich distributed grids.

It should be pointed out that because the qualityof the reanalysis product strongly depends on thequality and richness of the sounding data, for areaswith no or few sounding data, the quality of the reanalysisproduct may not be good. It is difficult to saywhether the reanalysis product is fit for T_m calculationfor areas without sounding data. Nevertheless, it willbe the direction of further research about whether thereanalysis product might serve as an effective and richdata source for the acquisition and localization of T_mfor areas with no sounding data.

Acknowledgments. The ECMWF ERAinterimdata used in this study are provided by theECMWF, and sounding data are provided by the Universityof Wyoming.