The RSS version 7.0 ocean products are available for SSM/I, SSMIS, AMSR-E, WindSat, and TMI. The inversion algorithm is mainly based on Wentz and Spencer (1998), in which above a cutoff in the liquid water column (2.45 mm), water vapor is no longer retrieved. The various radiometers from the different satellites have been precisely intercalibrated at the radiance level by analyzing the measurements made by pairs of satellites operating at the same time. This was done for the explicit purpose of producing versions of the data sets that can be used to study decadal-scale changes in TPW, wind, clouds, and precipitation; thus, special attention was focused on interannual variability in instrument calibration. The calibration procedures and physical inversion algorithm used to simultaneously retrieve TPW, surface wind speed (and thereby surface wind stress and surface roughness), and the total liquid water content are summarized in Wentz (2013, 1997). This allows the algorithm to minimize the effect of wind speed, clouds, and rain on the TPW measurement.

The RSS version 7.0 daily data are available on a 0.25∘ latitude × 0.25∘ longitude grid for daytime and nighttime (i.e., 1440 × 720 × 2 per day). Figure 1a–d show the RSS v7.0 monthly mean F16 SSMIS TPW (in millimeters), surface skin temperature (in Kelvin), liquid water path (LWP, in millimeters), and rain rate (RR, in millimeters per hour), respectively, in 2007. Figure 1 shows that the variation in and distribution of TPW over oceans (Fig. 1a) is, in general, closely linked to surface skin temperature variations over the Intertropical Convergence Zone (ITCZ) (Fig. 1b), which is modulated by clouds and the hydrological cycle (Soden et al., 2002). The distribution of monthly TPW is consistent with that of cloud water, where the highest TPW values (and LWP and RR) occur in persistent cloudy and strong convective regions over the tropical western Pacific Ocean near Indonesia.

Because COSMIC reprocessed TPW data are only available from June 2006 to December 2013 (i.e., COSMIC2013), the SSM/I F15, SSMIS F16, SSMIS F17, and WindSat RSS version 7.01 ocean products covering the same time period are used in this study. Table 1 summarizes the starting date and end date for RSS SSM/I F15, SSMIS F16, SSMIS F17, and WindSat data. The all sky daily RSS ocean products for F15, F16, F17, and WindSat are downloaded from http://www.remss.com/missions/ssmi.

The atmospheric refractivity N is a function of pressure P, temperature T, water vapor pressure Pw, and water content W through the following relationship (Kursinski et al., 1997; Zou et al., 2012): N=77.6PT+3.73×105PwT2+1.4Wwater+0.61Wice, where P is the pressure in hectopascals, T is the temperature in Kelvin, Pw is the water vapor pressure in hectopascals, Wwater is the liquid water content in grams per cubic meter, and Wice is the ice water content in grams per cubic meter. The last two terms generally contribute less than 1 % to the refractivity and may be ignored (Zou et al., 2012). However, they can be significant for some applications under conditions of high cloud liquid or ice water content, as shown by Lin et al. (2010), Yang and Zou (2012), and Zou et al. (2012). We will neglect these terms in this study, but because we are looking at small differences between MW and RO TPW in cloudy and precipitating conditions in this paper, we estimate the possible contribution of these terms to RO TPW and the consequences of neglecting them here. Since both of these terms increase N, neglecting them in an atmosphere in which they are present will produce a small positive bias in water vapor pressure Pw and therefore total precipitable water when integrated throughout the entire depth of the atmosphere.

Typical values of cloud liquid water content range from ∼ 0.2 g m-3 in stratiform clouds to 1 g m-3 in convective clouds (Cober et al., 2001). Extreme values may reach ∼ 2 g m-3 in deep tropical convective clouds (i.e., cumulonimbus). Ice water content values are smaller, typically 0.01–0.03 g m-3. Heymsfield et al. (2002) reported high ice water content values ranging from 0.1 to 0.5 g m-3 in tropical cirrus and stratiform precipitating clouds, although values rarely reach as high as 1.5 g m-3 in deep tropical convective clouds (Leroy et al., 2017).

For extremely high values of Wwater and Wice of 2.0 and 0.5 g m-3, the contributions to N are 2.8 and 0.3, respectively. The values of N in the atmosphere decrease exponentially upward, from ∼ 300 near the surface to ∼ 150 at P = 500 hPa. Using the extreme values above at 500 hPa, Wwater may contribute from up to 1.6 % of N and Wice up to 0.2 %. Thus, we may assume that in most cases the error in N due to neglecting these terms will be less than 1 %. The effect on TPW will be even less since clouds do not generally extend through the full depth of the atmosphere. Finally, the ∼ 200 km horizontal averaging scale of the RO observation footprint makes it unlikely that such extremely high values of water and ice content will be present over this scale. We conclude that the small positive bias in RO TPW introduced by neglecting the liquid and water terms in Eq. (1) will be less than 1 %.

To resolve the ambiguity of COSMIC refractivity associated with both temperature and water vapor in the lower troposphere, a 1D-Var algorithm (http://cdaac-www.cosmic.ucar.edu/cdaac/doc/documents/1dvar.pdf) is used to derive optimal temperature and water vapor profiles while temperatures and water vapor profiles from the ERA-Interim reanalysis are used as a priori estimates (Neiman et al., 2008; Zeng et al., 2012).

Note that because RO refractivity is very sensitive to water vapor variations in the troposphere (Ho et al., 2007), and is less sensitive to temperature errors, the RO-derived water vapor product is of high accuracy (Ho et al., 2010a, b). It is estimated that 1 K of temperature error will introduce less than 0.25 g kg-1 of water vapor bias in the troposphere in the 1D-Var retrievals. Although the first-guess temperature and moisture are needed for the 1D-Var algorithm, the retrieved water vapor profiles are weakly dependent on the first-guess water vapor profiles (Neiman et al., 2008).

The horizontal footprint of a COSMIC observation is about 200 km in the lower troposphere and its vertical resolution is about 100 m near the surface and 1.5 at 40 km. The COSMIC post-processed water vapor profiles version 2010.2640 collected from the COSMIC Data Analysis and Archive Center (CDAAC) (http://www.cosmic.ucar.edu/) are used to construct the COSMIC TPW data. To further validate the accuracy of COSMIC-derived water vapor, we have compared COSMIC TPW values with those derived from ground-based GPS (i.e., International Global Navigation Satellite Systems–IGS; Wang et al., 2007), which are assumed to be independent of location. Only those COSMIC profiles whose lowest penetration heights are within 200 m of the height of ground-based GPS stations are included. Results showed that the mean global difference between IGS and COSMIC TPW is about -0.2 mm with a standard deviation of 2.7 mm (Ho et al., 2010a). Similar comparisons were found by Teng et al. (2013) and Huang et al. (2013).

In this study, only those COSMIC water vapor profiles penetrating lower than 0.1 km are integrated to compute TPW. Approximately 70 to 90 % of COSMIC profiles reach to within 1 km of the surface (Anthes et al., 2008). Usually more than 30 % of COSMIC water vapor profiles reach below 0.1 km in the midlatitudes and higher latitudes and a little bit less than 10 % in the tropical regions. To compensate for the water vapor amount below the penetration height, we follow the following procedure: i.

We assume that the relative humidity below the penetration height is equal to 80 %. This is a good assumption, especially over oceans near the sea surface (Mears et al., 2015).

The COSMIC TPW estimates are not very sensitive to the assumption of 80 % relative humidity below 0.1 km (step i above). The assumption of 80 % ± 10 % (i.e., 90 and 70 %) relative humidity below 0.1 km introduces an uncertainty of about ±0.03 mm in the water vapor–COSMIC comparisons for all conditions. As shown in Sect. 4, this uncertainty is small compared to the observed differences between the RO and MW estimates.

Pairs of MW and RO TPW estimates collocated within 50 km and 1 h are collected. The location of RO observation is defined by the RO tangent point at 4–5 km altitude. Wick2008 used MW–RO pairs within 25 km and 1 h in time. To evaluate the effect of the spatial difference on the TPW difference, we also computed TPW differences for MW–RO pairs within 75, 100, 150, and 200 km. We found that the larger spatial difference increases the mean TPW biases slightly to ±0.25 mm and the standard deviations to ±1.91 mm, which is likely because of the high spatial variability in water vapor. Note that, although not shown, the mean biases and standard deviations of the mean biases are slightly larger over the tropics than over midlatitudes. This could be because of the combined effect of the larger spatial TPW variation in the tropical region than that in the midlatitudes (see Fig. 1a and Neiman et al., 2008; Teng et al., 2013; Mears et al., 2015) and the fact that the MW TPW retrieval uncertainty is also larger over stronger convection regions. More results are detailed in Sect. 4.

With a 0.25∘ × 0.25∘ grid, there are about 20 to 60 MW pixels matching one COSMIC observation. The number of pixels varies at different latitudes. A clear MW–RO pair is defined as instances when all the TCW values for the collocated MW pixels are equal to zero. A cloudy MW–RO ensemble is defined as instances when all the TCW values from the collocated MW pixels are larger than zero. Partly cloudy conditions (some of pixels zero and some nonzero) are excluded from this study. The cloudy ensembles are further divided into precipitating and non-precipitating conditions. MW–RO pairs are defined as cloudy non-precipitating when less than 20 % of MW pixels have rainfall rates larger than 0 mm h-1. Cloudy precipitating MW–RO pairs are defined when more than 20 % of the pixels have rainfall rates larger than zero. Because microwave radiances are not sensitive to ice, we treat cloudy pixels of low density like cirrus clouds as clear pixels.

The matching pairs of RO and MW observations are not distributed uniformly over the world's oceans. In fact, they are heavily concentrated in middle latitudes, as shown in Fig. 1e. This biased distribution is caused by several factors, including the polar orbits of the satellites, which produce more observations in higher latitudes, and also the failure of many COSMIC RO soundings to penetrate to 0.1 km in the subtropics and tropics (due to super-refraction, which is often present in these regions). Thus, the results presented here, especially the trends, are not representative of global averages. However, the main purpose of this paper is to compare two independent satellite systems for obtaining TPW under varying sky conditions. If the agreement is good, one has confidence in both systems. In this case, SSM/I and WindSat estimates of TPW will be verified and can then be used with confidence globally, including where RO observations are sparse or do not exist.

Figure 3a–c depict the scatter plots for F16–COSMIC pairs under cloudy, cloudy non-precipitating, and precipitating conditions from June 2006 to December 2013 over oceans. While there is a very small bias (0.031 mm) for clear pixels (Fig. 2b), there is a significant positive TPW bias (0.794 mm) under cloudy conditions (Fig. 3a). This may explain the close to 0.45 mm mean TMI gb-GPS TPW biases found by Wentz (2015) in which close to 7 years of data were used. Figure 3c depicts that the large SSM/I TPW biases under cloudy skies are mainly from the pixels with precipitation (mean bias is equal to 1.825 mm) although precipitation pixels are of about less than 6 % of the total F16–COSMIC pairs. Because RO measurements are not significantly affected by clouds and precipitation, the biases mainly result from MW retrieval uncertainty under cloudy conditions. The fact that the MW–COSMIC biases for precipitating conditions (1.825 mm, Fig. 3c, and 1.64–1.88 mm in Table 2) are much larger than those for cloudy but non-precipitating conditions indicates that significant scattering and absorbing effects are present in the passive MW measurements when it rains. The correlation coefficients for F15–RO, F16–RO, F17–RO, and WindSat–RO pairs for all sky conditions are all larger than 0.96 (not shown).

MW and gb-GPS TPW comparisons show differences similar to the MW–RO differences under different sky conditions. We compared F16 pixels with those from gb-GPS within 50 km and 1 h over the 33 stations studied by Mears et al. (2015) from 2002 to 2013. Figure 4a–d depict the scatter plots for F16 gb-GPS TPW under clear, cloudy, cloudy non-precipitating, and cloudy precipitating conditions, respectively. The F16-gb-GPS mean biases are equal to 0.241 mm (clear skies), 0.614 mm (cloudy skies), 0.543 mm (cloudy non-precipitating), and 1.197 mm (precipitating), which are similar to those estimated from MW–RO comparisons (Table 2).

The results above show that the MW estimates of TPW are biased positively compared to both the RO and the ground-based GPS estimates, which are independent measurements. The biases are smallest for clear skies and largest for precipitating conditions, with cloudy, non-precipitating biases in between. Overall, the results suggest that clouds and especially precipitation contaminate the MW radiometer measurements, which in turn affect the MW TPW retrievals.

To further examine how rain and cloud droplets affect the MW TPW retrievals, we show how the F16–RO TPW biases vary under different meteorological conditions in Fig. 5. The bias dependence on wind speed (Fig. 5a) is small. Unlike the results from Mears et al. (2015), the mean TPW biases between F16 and COSMIC are within 0.5 mm with high winds (wind speed larger than 20 m s-1). Figure 5b indicates that the F16–COSMIC bias is larger, with a TPW greater than about 10 mm, which usually occurs under cloudy conditions. The F16–COSMIC biases can be as large as 2.0 mm when the rainfall rate is larger than 1 mm h-1 (Fig. 5c), which usually occurs with high total liquid cloud water conditions. The F16 TPW biases can be as large as 2 mm when total cloud water is larger than 0.3 mm (Fig. 5d). Figure 5e shows that the larger F16–COSMIC TPW biases (2–3 mm) mainly occur over regions with a surface skin temperature less than 270 K (higher latitudes; see Fig. 1b). The F15, F17, and WindSat TPW biases under different meteorological conditions are very similar to those of F16 (not shown).

In Fig. 6 we compare RSS v7.0 F16 MW TPW to the gb-GPS TPW over various meteorological conditions. The magnitudes of the MW gb-GPS TPW differences under high rain rate and high total cloud water conditions are somewhat smaller than those of MW–RO pairs (varying from about 0.5 to 2.0 mm), which may be because most of the MW gb-GPS samples are collected under low rain rates (less than 1 mm h-1).

To further examine MW TPW long-term stability and trend uncertainty due to rain and water droplets for different instruments, we compared time series of the MW and COSMIC monthly mean TPW differences from June 2006 to December 2013. Figure 7a–d show the monthly mean F16–COSMIC TPW differences from June 2006 to December 2013 for clear, cloudy, cloudy non-precipitating, and precipitating conditions. In general, the microwave TPW biases under different atmospheric conditions are positive and stable from June 2006 to December 2013, as reflected in relatively small standard deviation values (Table 3). Except for F15, the standard deviations of the monthly mean TPW anomaly range are less than 0.38 mm (Table 3). In contrast, the F15–COSMIC monthly mean σ values range from 0.48 to 0.69 mm with different conditions.

Table 3 also shows the trend in the RO estimates of TPW differences over the 8-year period of study. The trends range from -0.12 mm decade-1 (WindSat, clear skies) to 2.52 mm decade-1 (F15, precipitating conditions). The overall trend of TPW as estimated by RO (second line in each row of Table 3) is positive, as discussed in the next section. Table 3 shows that in general the trends are more strongly positive under cloudy and precipitating conditions compared to clear conditions.

Figure 8 depicts the deseasonalized trends of the MW–RO TPW differences for F15 (Fig. 8a), F16 (Fig. 8b), F17 (Fig. 8c), and WindSat (Fig. 8d) under cloudy skies. Except for F15, the deseasonalized trends of the MW–RO TPW differences for the MW radiometers are close to zero, indicating little change over these 8 years. The trends of the biases associated with F15, F16, F17, and WindSat under all sky conditions range from -0.09 to 0.27 mm decade-1 (details not shown).

The reason for larger standard deviations of the MW minus RO differences for F15 (Tables 2 and 3 and Fig. 8a) is very likely because the F15 data after August 2006 were corrupted by the rad-cal beacon that was turned on at this time. Adjustments were derived and applied to reduce the effects of the beacon, but the final results still show excess noise relative to uncorrupted measurements (Hilburn and Wentz, 2008). RSS does not recommend using these measurements for studies of long-term change. Thus, we consider the F15 data less reliable during the period of our study.

Figure 9 shows the deseasonalized time series of the monthly mean TPW for all MW and RO pairs under all sky conditions. The nearly 8-year trends for TPW estimated from both passive MW radiometers and active COSMIC RO sensors are positive and very similar in magnitude. The mean trend of all COSMIC RO TPW is 1.79 mm decade-1 with a 95 % confidence interval of [0.96, 2.63] mm decade-1 while the mean trend from all the MW estimates is 1.78 mm decade-1 with a 95 % confidence interval of [0.94, 2.62]. This close agreement between completely independent measurements lends credence to both estimates. The mean TPW over this period, calculated from all MW data in our data set was 26.04 mm; thus, the trend of 1.78 mm decade-1 represents a trend of approximately 6.9 % per decade for our data set.

As discussed earlier, the trend of 1.78 mm decade-1 is heavily biased toward middle latitudes (40–60∘ N and 40–65∘ S) and is not representative of a global average. In fact, it is four to six times larger than previous estimates over earlier time periods. For example, Durre et al. (2009) estimated a trend of 0.45 mm decade-1 for the Northern Hemisphere over the period 1973–2006. Trenberth et al. (2005) estimated a global trend of 0.40 ± 0.09 mm decade-1 for the period 1988 to 2001. Using SSM/I data, Wentz et al. (2007) estimated an increase of 0.354 mm decade-1 over the period 1997–2006. The 100-year trend in global climate models is variable, ranging from 0.55 to 0.72 mm decade-1 (Roman et al., 2014).

The very close agreement between RO and MW observations where they coexist gives credibility to both observing systems and allows us to use global MW data to compute global TPW trends over all oceanic regions, including where RO observations are sparse or absent. Figure 10 shows the global map of TPW trends over oceans using all F16, F17, and WindSat data from 2006 to 2013. Figure 10 shows that the positive trends in TPW occur mainly over the central and northern Pacific, south of China and west of Australia, southeast of South America, and east of America. Positive trends also exist in general over the middle latitudes (40–60∘ N and 40–65∘ S) where most of our matching RO and MW data pairs occur.

Mears et al. (2017) computed global average (60∘ S to 60∘ N) TPW using a number of data sets from 1979 to 2014. Figure 11 shows the data from the ERA-Interim reanalysis (Dee et al., 2011), RSS MW, and COSMIC. (This figure was obtained using the same data used to construct Fig. 2.16 in Mears et al., 2017). Figure 11 shows close agreement between RSS MW and COSMIC. The global mean trend from June 2006 to December 2013 from the COSMIC observations is 0.32 mm decade-1 and for RSS MW it is 0.31 mm decade-1.