Modelling and validation of the weighted mean temperature for Turkey

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1 METEOROLOGICAL APPLICATIONS Published online 15 December 2016 in Wiley Online Library (wileyonlinelibrary.com) DOI: /met.1608 Modelling and validation of the weighted mean temperature for Turkey Cetin Mekik* and Ilke Deniz Department of Geomatics Engineering, Faculty of Engineering, Bulent Ecevit University, Zonguldak, Turkey ABSTRACT: Water vapour is involved in many atmospheric processes. Precipitation specifically relies on the amount of precipitable water vapour (PWV) or the water vapour content suspended in the atmosphere. Opportunities with regard to the conversion of existing continuous Global Navigation Satellite System (GNSS) stations to GNSS meteorology stations (GNSS MET) with very little cost and acquisition of near real-time water vapour have become popular in studies of the estimation of water vapour using GNSSs. In order to convert the GNSS observables into meteorological assets, one has to account for the extremely important conversion parameters between zenith wet delay and PWV in GNSS meteorology: T m or Q. They are estimated by analysis of radiosonde profile observations of a radiosonde station (RS). In this study, linear T m models were estimated from 4103 profile observations of eight Turkish RSs for the year The verification of these models was tested by using 1 year of observations at the Ankara and Istanbul RS-GNSS stations. A T m = T s model was computed for Turkey with a root mean square error of ±2.57 K. The accuracies of PWV derived from the developed T m model and the GNSS observations at the Ankara and Istanbul stations in 2013 and 2014 were found to be ±1.7 and ±1.8 mm, respectively. KEY WORDS weighted mean temperature; precipitable water vapour; GNSS meteorology Received 20 January 2016; Revised 30 June 2016; Accepted 30 June Introduction Water vapour is a critical component for many atmospheric processes and also one of the naturally occurring greenhouse gases (Troller, 2004; Perler, 2011). Furthermore, it acts as a thermostat of the global temperature. Even though it can cause overheating in the atmosphere, it can also reduce the amount of solar radiation propagating to ground and form clouds, thereby causing a reduction in global temperatures (Sierk, 2000; Lutz, 2008). Therefore, long term changes in water vapour have become a clear source of information for modelling climate changes (Ning, 2012). Precipitation depends directly on the amount of precipitable water vapour or water vapour content suspended in the atmosphere. Hence, the accuracy of the spatial and temporal distribution of the water vapour affects the accuracy of a weather forecast directly (Sierk, 2000; Lutz, 2008). In industrialized countries, the cost:benefit ratio of national meteorological services is around 1:5. Economic sectors that benefit from these services are agriculture, construction, energy, insurance, communications, transport, logistics and water supply (Perler, 2011). The development and current use of Global Navigation Satellite Systems (GNSSs) is a revolution in the fields of navigation, geodetic surveying, cadastral surveying, engineering surveying and geodynamic applications. Moreover, continuously operating GNSS networks (Continuously Operating Reference Stations) are established in many countries, and continue to be established for the purposes of providing accurate, reliable, continuous and economical spatial data (Bevis et al., 1992; Sierk, 2000; * Correspondence: C. Mekik, Bulent Ecevit University, Faculty of Engineering, Department of Geomatics Engineering, 67100, Zonguldak, Turkey. cmekik@hotmail.com Troller, 2004; Lutz, 2008; Arikan et al., 2011; Mekik et al., 2011; Boutiouta and Lahcene, 2013). In particular, opportunities for conversion of existing continuous GNSS stations to GNSS meteorology stations (GNSS MET) with very little cost and acquisition of near real-time water vapour have become available in studies of the estimation of water vapour using GNSS. In GNSS meteorology, zenith tropospheric delay (ZTD) is an essential parameter which can be converted into water vapour. Mostly, the total ZTD of a station is estimated by using GNSS observations of the station and appropriate stations distributed around it (GNSS MET network), an a priori tropospheric model and a mapping function. The outcome parameter of this estimation is the difference in the optical and geometric paths in the atmosphere between the satellite and the receiver on the station in the zenith direction of the concerned station plus the effect of the different propagation velocities with respect to the velocity of light in vacuum. ZTD can be separated into two components: the zenith hydrostatic delay (ZHD) and the zenith wet delay (ZWD). The first depends on the atmospheric pressure and is computed with the surface pressure value of the station directly and accurately. The latter is computed by subtracting ZHD from ZTD. Then it is converted to precipitable water vapour (PWV). Once the PWV becomes available, the ZTD can be computed (Hogg et al., 1981). Conversely, when ZWD is known, PWV can be found from the equation of the index of refraction for microwaves in the troposphere (Askne and Nordius, 1987). The fundamental parameter of this formulation is the weighted mean temperature (T m ) of the troposphere in the zenith direction of the station. Values of T m are derived by analysing long term radiosonde profile observations. In addition, a linear relation exists between the values of surface temperature T s and T m of a station: T m = a + bt s where the co-efficients a and b can be estimated

2 Modelling and validation of T m for Turkey 93 Table 1. The linear relation between T s and T m for each station and for all stations. Radiosonde stations Avg. RMSE of T s (K) T m = a + bt s RMSE of T m (K) a RMSE of a b RMSE of b Istanbul ± ± ±2.21 Ankara ± ± ±2.36 Diyarbakır ± ± ±2.26 Samsun ± ± ±2.32 Erzurum ± ± ±2.25 Izmir ± ± ±2.33 Adana ± ± ±2.44 Isparta ± ± ±2.44 All stations ± ± ±0.00 ±2.57 Avg., average; RMSE, root mean square error. 42 N Istanbul Samsun 40 N Ankara Erzurum 38 N Izmir Isparta Adana Diyarbaki r 36 N 26 E 28 E 30 E 32 E 34 E 36 E 38 E 40 E 42 E 44 E Figure 1. Radiosonde stations in Turkey. (Bevis et al., 1992). After determination of the T m model for North America (Bevis et al., 1992), similar local and regional models were developed for Europe (Emardson et al., 1998), Australia (Tregoning et al., 1998), Germany (Solbrig, 2000), Taiwan (Liou et al., 2001), South Korea (Jihyun et al., 2006), North Korea (Dongseob, 2006), India (Suresh Raju et al., 2007), Algeria (Boutiouta and Lahcene, 2013), Canada (Bokoye et al., 2003), the Netherlands and the Baltics (Baltink et al., 2002), Africa (Bock et al., 2008) and Brazil (Sapucci, 2014). These studies revealed that the weighted mean temperature T m depending on T s can be estimated with a root mean square error (RMSE) of ±2 5K (Wang et al., 2005; Pacione et al., 2014). Apart from these local and regional models, there are studies on the determination of a global T m model (Wang et al., 2005). Also, the linear model is assessed by expanding it with surface pressure and surface humidity parameters (Sapucci, 2014). Another approach is the conversion factor Q which is defined as the ratio of ZWD and PWV (ZWD/PWV = Q) (Emardson and Derks, 2000). The conversion factors Q are also derived by analysing long term radiosonde profile observations as is the case in the determination of T m. The conversion factors Q determined at several radiosonde stations are modelled depending on the surface temperature, latitude and day of the year of the station (Emardson and Derks, 2000). Furthermore, they are examined as exponential functions of the latitude and height of the station (Jade and Vijayan, 2008). Also, studies on the conversion factor Q indicate that it can be obtained with ±1% relative precision. To determine PWV with ±1 mm precision, the precision of ZTD is required to be approximately ±7 mm or better. Thus, to minimize errors in the estimation of ZTD, the number of stations to be established in a geodetic network, the distribution of stations, the minimum period of observation and the processing strategies are investigated. Accordingly, it is recommended that the network is formed with International GNSS Service stations, and it is finalized with an experimental optimization of the network which provides high accuracy in ZTD estimation (Schueler, 2001; Dousa, 2004; Jin et al., 2010; Rohm, 2012; Dousa and Bennitt, 2013; Rohm et al., 2014; Rózsa, 2014). Additionally, a comparison of the GNSS derived PWV with the PWV measured by other observation techniques is required in order to evaluate the accuracy of the conversion between ZWD and PWV estimation (Emardson and Derks, 2000). It has been reported that the precision of GNSS derived PWV is ±1 2mm based on the accuracies of ZTD (network configuration, processing strategies), ZHD and T m (Schueler, 2001; Ning, 2012; Pacione et al., 2014; Pottioux et al., 2014). The purposes of this study were to produce a linear T m T s model using the profile observations of eight Turkish radiosonde stations for the year 2011, to estimate the PWV of two GNSS stations collocated with the Istanbul and Ankara radiosonde stations using the estimated T m T s model, and to validate the model by comparing the GNSS derived PWV to the PWV obtained from the radiosonde stations. 2. Radiosonde temperature profile analysis methodology 2.1. The estimation of the weighted mean temperature T m from radiosonde profiles T m and Q are extremely important conversion parameters between ZWD and PWV in GNSS meteorology. These

3 94 C. Mekik and I. Deniz h All radiosonde stations for Tm = e dh T. h hs 300 (1) e dh T2 where hs is the height of the station, h is the height parameter, e is the water vapour pressure and T is the temperature. Unfortunately, the water vapour pressure e cannot be observed directly from radiosonde stations. Therefore, first the wet bulb temperature (T w ) was derived from the dew point temperature T d and pressure p of the radiosonde profile observations. Then, the water vapour pressure e was computed using T w as well as the saturation vapour pressure (e*). The wet bulb temperature T w is taken as a first approximation value: Tm (K) hs Tw = wt (1 w) Td (2) 260 where the weight w is min(max(210/t, 0.5), 0.98). e*(t w ), the saturation vapour pressure at T w, and the water vapour pressure e are solved with Teten s formula (Nielsen and Petersen, 2003): ) ( ( ) Tw T0 e Tw = a1 exp (3) a2 Tw a3 Tm = Ts r = Ts (K) Istanbul Ankara Diyarbakir Erzurum Izmir Adana Samsun Isparta Figure 2. The linear tendency between T s and T m for all the stations. parameters are derived by analysing the radiosonde profile observations of a radiosonde station: the function of the station s location, meteorological data at the station and time. These conversion parameters to be used for the GNSS MET network should be developed at least for the area covering the network. Therefore, T m and Q parameters estimated over a long time at radiosonde stations are modelled as a function of location of the station (latitude and height of the station), meteorological observations of the station (pressure and temperature of the station) and time. In GNSS MET networks, these models are used to estimate the PWV from GNSS observables. In this study, the estimation methodology of the weighted mean temperature T m is summarized below. The weighted mean temperature T m was computed from the radiosonde profile observations (Askne and Nordius, 1987): where the water freezing temperature T 0 = K; if T > T 0 (above liquid water), a1 = hpa, a2 = hpa, a3 = 7.66 hpa; if T < T 0 (above ice) a1 = hpa, a2 = hpa, a3 = hpa. After the iteration, the water vapour pressure is calculated using the following equation: ( ) e = He Tw 100 (4) where H is the height of the station. In addition, the observed temperatures in a profile were modelled using a polynomial as a function of height to assess the stability of the temperature profile quality. The co-efficients of this model were estimated by the least squares method and tested whether they were statistically significant. All in all, it was found that six co-efficients are sufficient for profile heights up to 8 km while nine co-efficients are sufficient for profile heights up to 30 km. The RMSEs of temperature computed from the model and the temperature profiles were checked against errors in the temperature profiles. Those with errors were identified and were not taken into account in the assessment. After the least Table 2. Seasonal variations of the T m model. Seasons Autumn Winter Spring Summer Avg. RMSE of T s (K) T m = a + bt s ±1.53 ±1.06 ±1.11 ±1.57 RMSE of T m (K) a RMSE of a b RMSE of b ±2.40 ±2.95 ±3.25 ± ±0.02 ±2.53 ±2.17 ±2.28 ±2.75 Avg., average; RMSE, root mean square error. Table 3. Spatial variations coastal and inland of the T m model. Locations Coastal Inland Avg. RMSE of T s (K) ±1.29 ±1.37 T m = a + bt s RMSE of T m (K) a RMSE of a b RMSE of b ±1.88 ± ±0.00 ±2.38 ±2.43 Avg., average; RMSE, root mean square error.

4 95 Modelling and validation of T m for Turkey Table 4. Diurnal variations of the T m model. Time of observation Avg. RMSE of T s (K) Day Night ±1.30 ±1.35 T m = a + bt s RMSE of T m (K) a RMSE of a b RMSE of b ±1.58 ± ±2.51 ±2.31 T m (all RSs) T m (inland) (K) T m (all RSs) T m (day) (K) Avg., average; RMSE, root mean square error. Table 5. The T s differences between T m models. Model differences T s (K) Day night (K) Inland coastal (K) Summer winter (K) T m (all RSs) T m (summer) (K) RS, radiosonde station. METS 60 N ONSA 50 N GOPE BRST BACA IGEO MIKL EVPA MEDI BUCU SRJV DUB2 ZECK ORID YEBE AUT1 40 N ISTA DUTH TUBI GISM ANKR GANM LARM PAT0 NOA1 TUC2 NICO DRAG Radiosonde stations 30 N RAMO GNSS stations 0 10 E 20 E 30 E 40 E Figure 3. The geodetic network utilized in the precipitable water vapour estimation. Table 6. Processing strategies used in Bernese GNSS Software v5.0. Processing parameters Observation data Network design Elevation angle Sampling rate Ionosphere Ambiguities solution A priori model Mapping function ZTD estimation Processing strategies Daily OBS-MAX 3 30 s Ionospheric free linear combination Quazi-ionosphere free strategy and SIGMA strategy Saastamoinen model with the dry Niell mapping function Wet Niell mapping function 1 h interval ZTD, zenith tropospheric delay. squares adjustment, the average of the RMSE was found to be ±1.33 K in the modelling of temperature profiles (Table 1). In parallel with the modelling of temperature using a polynomial, the values of e/t and e/t 2 were modelled as a function of height using the polynomial by the least squares method. The definite integrals in Equation (1) were computed from these polynomials. The radiosonde profile data from eight Turkish radiosonde stations (Figure 1) were downloaded and analysed for the year 2011 (for 0000 and 1200 UTC) (Radiosonde Data, 2014). As can be seen in Figure 1, the distribution of the radiosonde stations largely characterizes the climate zones in Turkey. A total of 4103 radiosonde profiles were analysed after eliminating those with errors Estimation of the T m T s model The T m T s profiles of each radiosonde station indicate that there is a linear tendency between the surface temperature (T s ) and the weighted mean temperature (T m ), which can be seen at all the stations in Figure2.

5 96 C. Mekik and I. Deniz GANM PWV Values (a) PWV (mm) Dec-2014 Nov-2014 Oct-2014 Sep-2014 Aug-2014 Jul-2014 Jun-2014 May-2014 Apr-2014 Mar-2014 Feb-2014 Jan-2014 Dec-2013 Nov Oct GISM PWV Values (b) PWV (mm) Dec-2014 Nov-2014 Oct-2014 Sep-2014 Jun-2014 Jul-2014 Aug-2014 May-2014 Apr-2014 Mar-2014 Feb-2014 Jan-2014 Dec-2013 Nov Oct Figure 4. Global Navigation Satellite System derived precipitable water vapour (PWV) values at (a) GANM station and (b) GISM station. The equation T m = a + bt s can be written for each profile observation. Here, a and b are co-efficients of the linear regression, which were estimated by the least squares method. Furthermore, statistical tests were used for outlier detection in this estimation to increase the reliability of the estimates of the a and b co-efficients. Also, in the linear regression the residuals of the T m values that are greater than ±3 RMSE at 99.7% confidence interval were considered outliers and were removed from the assessment. Table 1 lists the co-efficients of linear regression derived for each radiosonde station and for all stations, and the a posteriori average RMSEs of T m. The correlation between T s and T m was found as Furthermore, to examine the effects of seasonal periodicity on T m, all radiosonde profile observations were evaluated by dividing into seasons: spring (March May), summer (June August), autumn (September November) and winter (December February). The results of this process are given in Table 2.

6 Modelling and validation of T m for Turkey 97 Table 7. Statistics of the results for the GISM and GANM stations (PWV RS PWV GNSS ). GNSS station T m model Min. (mm) Max. (mm) Avg. (mm) and RMSE of avg. RMSE of ΔPWV (mm) α = 95% t = avg./rmse of avg. GANM Ankara 743 profiles T m (all RSs) ± 0.06 ± > 1.65, significant T m (all seasons) ± 0.06 ± > 1.65, significant T m (day night) ± 0.06 ± > 1.65, significant GISM Istanbul 671 profiles T m (all RSs) ± 0.07 ± > 1.65, significant T m (all seasons) ± 0.07 ± > 1.65, significant T m (day night) ± 0.07 ± > 1.65, significant α, confidence degree; Avg., average; ΔPWV = PWV RS PWV GNSS ; GNSS, Global Navigation Satellite System; Max., maximum; Min., minimum; PWV, precipitable water vapour; PWV GNSS, GNSS derived PWV; PWV RS, radiosonde computed PWV; RMSE, root mean square error; t f,α, confidence limit. If t > t f,α, average is significant. For the purpose of investigating the effects of different climatic regimes on T m, eight Turkish radiosonde stations were evaluated in two groups: the radiosonde stations located in the coastal climate area (Istanbul, Samsun, Izmir and Adana) and the radiosonde stations located in the inland climate area (Ankara, Diyarbakir, Erzurum and Isparta). The results are given in Table 3. Also, to examine the effect of day and night observations on T m, all radiosonde profile observations were evaluated according to the time of observation. Table 4 shows the results. The ΔT m differences derived from T m models with extreme regional surface temperatures T s = K and T s = K are given in Table 5. The ΔT m values in Table 5 were tested for whether they were statistically significant at the 99.7% confidence interval according to ΔT 3m i. Here, m i is taken as the smallest RMSE of the models compared. Consequently, the differences are not statistically significant. 3. The validation of the T m T s linear equation with GNSS observations Two Continuously Operating Reference Stations (GISM and GANM) were established beside the Istanbul radiosonde station, representing the coastal climate area, and the Ankara radiosonde station, representing the inland climate area, and have been operated since October 2013 (Figure 3). The observation data of these stations are being recorded and transferred to the control centre in Zonguldak, Turkey. They can be downloaded from The geodetic network was designed according to Dousa (2004), Dousa and Bennitt (2013) and Rózsa et al. (2014), and the experimental optimization was performed and is shown in Figure 3. This network was processed by Bernese GNSS Software v5.0. First, the co-ordinates for all stations in the network were derived with high accuracy, and the ZTD estimates were then computed. The processing strategies of Bernese GNSS Software v5.0 used in the estimation of the ZTD values are shown in Table 6. Hereafter, the values of ZHD were computed from the station pressure values, and then the values of ZWD were computed by subtracting the ZHD values from the GNSS derived tropospheric delays. Thus, PWV can be derived as: [ ( ) ] 1 PWV = ZWD 10 6 k3 + k ρ T 2 v R v (5) m Here, ρ v is the density of liquid water, 1000 kg m 3,R v is the original gas constant J K 1 kg 1, k 3 = K 2 hpa and k 2 = 22.1 K hpa 1. The GNSS derived PWV (PWV GNSS ) was computed using the T m model developed not only for all stations (Table 1) and for all seasons (Table 2) but also for day night (Table 4). The precision and reliability of PWV GNSS from the model were tested by comparing PWV GNSS at 0000 and 1200 UTC with the PWV computed from radiosonde (PWV RS ) at 0000 and 1200 UTC. About 1 year of Istanbul and Ankara GNSS observational data for 2013 and 2014 and radiosonde data were processed. PWV GNSS time series of the GISM and GANM stations are depicted in Figure 4. Additionally, the outlier test was performed to remove outliers in the GNSS observations as well as meteorological observations, and the correlation between PWV GNSS and PWV RS was found to be 0.87 for Ankara, 0.90 for Istanbul. Also, the average and RMSE of the average of the differences of PWV GNSS from PWV RS (ΔPWV = PWV RS PWV GNSS )were computed. Statistics of the differences of PWV GNSS from PWV RS are shown in Table 7 and visualized in Figure Results and conclusions Radiosonde temperature profile observations were modelled using a polynomial by the least squares method. As a consequence of this model, the a posteriori RMSE of different radiosonde stations and a posteriori mean RMSE of all stations were obtained as ± K and ±1.33 K, respectively. These results provide a useful quality check for radiosonde temperature profile observations and modelling. The radiosonde temperature values can be taken with equal precision. The effect of ±1.33 K uncertainty in the temperature profiles of T m will be approximately ±1 K under normal meteorological conditions (for t = 18 C, T m = K). It is apparent from Table 1 that the a posteriori RMSE of the linear T m models is ± K. Moreover, the a posteriori RMSE of the T m model for all stations which are assumed to have equal precision is obtained as ±2.57 K. Compared with the individual stations, there is an increase in the RMSE of T m due to the fact that it is connected with the areal size occupied by the stations. Furthermore, the maximum difference between the RMSE of T m for each station is ±0.37 K. The proportional effect of this difference under normal meteorological conditions is at the level of 0.1%. As can be seen in Table 2, the RMSE values of the seasonal variations in the T m linear model indicate that the minimum RMSE is ±2.17 K for winter and the maximum RMSE is ±2.75 K for summer. The difference between RMSE values for winter and summer is about ±0.58 K. The proportional effect of this difference on PWV is 0.2% under normal meteorological conditions and can be neglected. Also, the results presented in Table 6 demonstrate that differences between a posteriori RMSE of summer winter, all seasons and day night are statistically significant. On the other hand, the results show that the differences between a posteriori RMSE of coastal inland are not statistically significant. The effects of seasonal and diurnal

7 98 C. Mekik and I. Deniz (a) GANM PWV Differences (PWVRS-PWVGNSS) ΔPWV (mm) (b) Dec-2014 Nov-2014 Oct-2014 Sep-2014 Aug-2014 Jul-2014 Jun-2014 May-2014 Apr-2014 Mar-2014 Feb-2014 Jan-2014 Dec-2013 Nov Oct GISM PWV Differences (PWVRS-PWVGNSS) ΔPWV (mm) Dec-2014 Nov-2014 Oct-2014 Sep-2014 Jun-2014 Jul-2014 Aug-2014 May-2014 Apr-2014 Mar-2014 Feb-2014 Jan-2014 Dec-2013 Nov Oct Figure 5. The differences between Global Navigation Satellite System (GNSS) derived precipitable water vapour (PWVGNSS ) and radiosonde computed PWV (PWVRS ) (ΔPWV) at (a) GANM station and (b) GISM station. variations are in agreement with the results given by Liou et al. (2001), Suresh Raju et al. (2007) and Wang et al. (2005). Furthermore, the precision differences in modelling can be attributed to the model error and the inhomogeneity of meteorological parameters. The influence of seasonal, diurnal and spatial variations on the PWV can be tested by comparing PWVGNSS with PWVRS in a more reliable way. For that purpose, the comparisons performed are given in Table 7. As demonstrated in Table 7, the statistics of the differences of PWVGNSS from PWVRS reveal that a posteriori RMSE values of the models are close to each other. They also indicate that the seasonal and diurnal effects on T m tend to have an insignificant influence on PWV. Moreover, the T m model developed for all stations

8 Modelling and validation of T m for Turkey 99 must have a minimal systematic component. The minimum bias RMSE values for Ankara and Istanbul were obtained using the T m model for all stations. Thus, the average values and RMSE of ΔPWV obtained for Ankara and Istanbul are 2.0 ± 1.6 and 2.3 ± 1.7 mm, respectively. Rózsa (2014) suggests that the precision of this difference is the sum of the precision of PWV GNSS and PWV RS and determines the precision of different radiosonde models as ± mm for PWV = 50 mm. This finally corresponds to 1.0 mm for Turkey with an average annual rainfall of approximately 65 mm. In the present study, the precision of PWV GNSS at the Ankara and Istanbul stations is found to be ±1.2 and ±1.4 mm respectively which roughly coincides with the findings of Rózsa (2014). The contribution of seasonal and diurnal variations to the estimation of PWV using the T m model can also be analysed with the average and RMSE of difference values in Table 7. This indicates that the maximum average difference is 0.02 mm for Ankara whereas it is 0.06 mm for Istanbul. On the other hand, the RMSEs of the three T m models are equal for Ankara and the differences between the RMSEs of the models are mm for Istanbul. These results reveal that seasonal and diurnal variations do not affect PWV estimation from T m significantly. On the grounds that radiosonde data are considered as the reference, the PWV GNSS values derived using the same geodetic networks and assessment strategies should be corrected by mm. Thus, the systematic component between PWV GNSS and PWV RS can be eliminated. Consequently, the linear model T m = T s ± 2.57 K can be used for the area covering all Turkish radiosonde stations in the conversion between ZWD and PWV. Also, the precision of PWV GNSS obtained from this model can be expected to be between ±1.2 and ±1.4 mm if the systematic component of PWV GNSS is to be corrected by an average of mm. 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