The recycling rate of atmospheric moisture over the past two decades (1988–2009)

Numerical models predict that the recycling rate of atmospheric moisture decreases with time at the global scale, in response to global warming. A recent observational study (Wentz et al 2007 Science 317 233–5) did not agree with the results from numerical models. Here, we examine the recycling rate by using the latest data sets for precipitation and water vapor, and suggest a consistent view of the global recycling rate of atmospheric moisture between numerical models and observations. Our analyses show that the recycling rate of atmospheric moisture has also decreased over the global oceans during the past two decades. In addition, we find different temporal variations of the recycling rate in different regions when exploring the spatial pattern of the recycling rate. In particular, the recycling rate has increased in the high-precipitation region around the equator (i.e., the intertropical convergence zone) and decreased in the low-precipitation region located either side of the equator over the past two decades. Further exploration suggests that the temporal variation of precipitation is stronger than that of water vapor, which results in the positive trend of the recycling rate in the high-precipitation region and the negative trend of the recycling rate in the low-precipitation region.


Introduction
The hydrological cycle, which involves the atmosphere, surface and biosphere, has enormous impact on human activity. The atmospheric branch of the hydrological cycle, in which water vapor leaves the surface by evaporation and returns to the surface by precipitation, is a crucial component of weather and climate.
Besides the effects of regional meteorology (Ye and Fetzer 2009), the temporal variation of the total mass of water vapor in the global atmosphere is related to atmospheric temperature by the Clausius-Clapeyron equation under the approximation that the relative humidity in the atmosphere stays constant. Different datasets display qualitatively consistent increasing 4 Author to whom any correspondence should be addressed. trends in the total mass of water vapor in the global atmosphere , Wentz et al 2007, Santer et al 2007. Such increasing trends in water vapor are also simulated in the numerical models (Bosilovich et al 2005, Held andSoden 2006) even though the mechanism of how water vapor affects climate change is still not very clear (Held andSoden 2006, Ingram 2010).
On the other hand, precipitation, which is controlled by the atmospheric circulation and cloud microphysics, is more complicated. Consequently, there is no simple relationship between precipitation and temperature at the global scale even though surface temperature is correlated with local precipitation Shea 2005, Adler et al 2008) and precipitation extremes Soden 2008, Liu et al 2009). Large discrepancies in the linear trend of global precipitation exist among different studies (Allen and Ingram 2002, Adler et al 2003, Trenberth et al 2003, Held and Soden 2006, Gu et al 2007, Stephens and Ellis 2008, Adler et al 2008, Liepert and Previdi 2009, Trenberth 2011, Zhou 2011. A recent letter by Wentz et al (2007) suggests that the increasing trend with time was roughly the same for global precipitation (1.4 ± 0.5% per decade) and total water vapor (1.2 ± 0.5% per decade) during the period 1987-2006.
The study by Wentz et al (2007) implies that the recycling rate of atmospheric moisture, which is defined as the ratio of precipitation to column water vapor, remained constant or intensified with time. From the perspective of atmospheric radiative imbalance, it is possible that global precipitation is increasing at a rate of 1.4% per decade (Liepert and Previdi 2009). However, most other observational studies (Adler et al 2003, Gu et al 2007, Adler et al 2008 and climate models (Allen and Ingram 2002, Held and Soden 2006, Stephens and Ellis 2008 suggest that global precipitation is increasing (∼0.2-0.7% per decade) more slowly than in the total mass of water vapor (∼1.4-1.5% per decade) in response to global warming. In this study, we revisit the temporal variation of water vapor and precipitation based on the latest version of global data sets with emphasis on the variation of the recycling rate of atmospheric moisture that accompanies global warming during the past two decades ).

Methodology and data
A useful method of estimating the intensity of the hydrological cycle in the global atmosphere is to use some simple parameters, which include recycling rate (Chahine et al 1997), residence time (Chahine et al 1992, Trenberth 1998, and a non-dimensional ratio between the precipitation sensitivity and the water vapor sensitivity (Stephens and Ellis 2008). The purpose of these parameters is to compare the increasing rates between the total water vapor and precipitation. Here, we use the recycling rate of atmospheric moisture (R) (Chahine et al 1997) to compare the temporal variation between column water vapor (W ) and precipitation (P).
So we have Therefore, during a time period we can approximate equation (2) as below where X andX represent the change and mean value of variable X (i.e., R, P, and W ) during the time period. When the varied percentage of precipitation ( P/P) is larger than the varied percentage of column water vapor ( W/W ), we have the ratio R/R > 0. Otherwise, we have the ratio R/R 0. In physics, the parameter R/R is the same as another non-dimensional ratio ε = ( P/P)/( W/W ), which is developed by Stephens and Ellis (2008). It should be mentioned that the balance described in equation (3) probably does not hold except for the global mean where the flux divergence term drops out. Equation (2) shows that the temporal variation of recycling rate is determined by the temporal variations of precipitation and column water vapor. In this study, the latest data sets from the Special Sensor Microwave Imager (SSM/I) (Wentz 1997, Wentz andSpencer 1998) and the Global Precipitation Climatology Project (GPCP) (Huffman et al 2009) are utilized to examine the temporal variations of precipitation, column water vapor, and recycling rate over the past two decades. The data set of SSM/I (V 6) has oceanic precipitation and water vapor from 1988 to 2009 with spatial resolution at 0.25 • × 0.25 • (latitude by longitude) (SSM/I data are provided by Remote Sensing Systems from the website: www.ssmi.com/ ssmi/ssmi browse.html). The latest version of GPCP (V 2.1) has the global precipitation data from 1979 to 2009 with spatial resolution at 2.5 • × 2.5 • (latitude by longitude) (GPCP V 2.1 data are provided by the Earth System Research Laboratory from the website www.esrl.noaa.gov/psd/data/gridded/data. gpcp.html). To be consistent with the length of water vapor data from SSM/I, we only use the GPCP precipitation between 1988 and 2009.

Results
The temporal variations of precipitation and water vapor at the global scale are shown in figure 1. Figure 1(A) shows two time series of the temporal variations of precipitation based on a combined global data from SSM/I and GPCP and the global data from GPCP. The combined global data was constructed by combining the precipitation data over ocean from the SSM/I and the precipitation data over land from GPCP. Figure 1(B) displays the temporal variation of column water vapor over the global oceans, which is based on the oceanic data from SSM/I. We calculate the linear trends and corresponding uncertainties of the time series shown in figure 1 by the least-squares method (Bevington and Robinson 2003). The linear trend of global precipitation is 0.08 ± 0.43% per decade and 0.26 ± 0.41% per decade for the combined global data and the GPCP global data, respectively. The linear trend of column water vapor is 1.01 ± 0.39% per decade, which is basically consistent with the value of 1.37 ± 0.72% per decade from a recent study (Santer et al 2007). We also calculate the confidence level of linear trends in figure 1 (please refer to the appendix), which shows that the confidence level of linear trend in the global precipitation is less than 90% and the confidence level of linear trend in the oceanic water vapor is more than 95%. The weak positive trend of global precipitation (0.08 ± 0.43% per decade and 0.26 ± 0.41% per decade) is much smaller than the linear trend (1.4 ± 0.5% per decade) in the previous study (Wentz et al 2007). The previous study was also based on a combined global data from SSM/I (ocean) and GPCP (land), but a relatively old version of GPCP (V 2) was used (Wentz et al 2007). Our study (figure 1) (A) is based on the global data from the latest version of GPCP (V 2.1). Deseasonalization and low-pass filter were applied to the time series. Seasonal cycle was removed by subtracting the monthly mean data. Low-pass filter was constructed so that only signals with periods longer than six months were kept.
The new dataset of GPCP has been improved by applying a new updated climate anomaly analysis method for gauge data (Schneider et al 2008) and several correction schemes (Huffman et al 2009). GPCP V 2.1 has better data quality and more continuous coverage than the old version (Huffman et al 2009). Therefore, an exploration of the temporal variation based on the latest GPCP (V 2.1) will be more robust than the analyses in the previous study based on the relatively old version. The differences of trend between this study (figure 1) and the previous study (Wentz et al 2007) are mainly due to the dramatic drop in the rate of increase of precipitation over land between the old version (V 2) and the new version (V 2.1) of the GPCP dataset (Huffman et al 2009).
The weak positive trend with larger uncertainty in the global precipitation suggests that the linear trend of global precipitation is not statistically significant, and the precipitation trend is smaller than the significant linear trend in the oceanic water vapor. The comparison of linear trends between precipitation and water vapor implies that the recycling rate of global atmospheric moisture decreased with time during the past two decades. Therefore, the linear trends of precipitation (0.08 ± 0.43% per decade or 0.26 ± 0.41% per decade) based on the latest and improved precipitation data are basically consistent with the estimated trends for precipitation (∼0.2-0.7% per decade) from the numerical simulations (Allen and Ingram 2002, Held and Soden 2006, Stephens and Ellis 2008, which reconcile the discrepancy of recycling rate of global atmospheric moisture between the study by Wentz et al (2007) and the other studies (Allen and Ingram 2002, Held and Soden 2006, Stephens and Ellis 2008. A consistent view-the slowing in the recycling rate of Note: the linear trend of time series is basically consistent between the data with the ENSO signals and the data without the ENSO signals. The recycling rate 1 is defined as the ratio of SSM/I precipitation to SSM/I water vapor, and the recycling rate 2 is defined as the ratio of GPCP precipitation to SSM/I water vapor. global atmospheric moisture in response to global warmingnow emerges. The slowing of the recycling rate of global atmospheric moisture can be explained from the perspective of atmospheric energetics (Allen and Ingram 2002). The physics behind the slowing is complicated, which includes the modification of the tropical Walker Circulation by changing the frequency of strong/weak updrafts (Emori andBrown 2005, Vecchi andSoden 2007), suppression of the surface evaporation (Richter and Xie 2008), and reduction in the precipitation efficiency by a negative feedback through cloud radiative heating (Stephens and Ellis 2008).
Due to the lack of global long-term continuous data of water vapor, we assume that the linear trend of global water vapor is same as that of oceanic water vapor in the above comparison between precipitation and water vapor. Such an assumption was also used in the previous study (Wentz et al 2007). However, it is possible that the linear trend of water vapor is different between ocean and land (Simmons et al 2010) so that the above assumption is not valid. Here, we conduct a strict comparison of linear trends between oceanic precipitation and oceanic water vapor over the past two decades in figure 2. The retrieval of water vapor and precipitation near coasts is generally not robust due to the complicated meteorological situations there. Therefore, the data of water vapor and precipitation close to coasts (i.e., 1 • latitude within coasts) are not included in this study. The data quality in the polar region is not very good either because there are very few in situ observations available to validate the satellite data. Therefore, only the data of precipitation and water vapor over ocean between 60 • N-60 • S are used to discuss the recycling  figure 2. Figure 2 displays the temporal variations of oceanic precipitation, water vapor, and recycling rate. Details for the linear trends of the time series in figure 2 are written in table 1. As shown in table 1, the positive linear trend of oceanic precipitation is very weak with large uncertainty. The linear trend of oceanic water vapor between 60 • N and 60 • S is roughly the same as the linear trend of oceanic water vapor from pole to pole (figures 1(B) and 2(B)). The recycling rate 1 is defined as the ratio of the SSM/I precipitation to the SSM/I water vapor, and the recycling rate 2 is defined as the ratio of the GPCP precipitation to the SSM/I water vapor. From table 1, we find that the linear trend of recycling rate roughly equates to the difference of linear trends between precipitation and water vapor, which is consistent with equation (2). The confidence level of linear trend in the recycling rate 1 is less than 90%, but the confidence level of linear trend in the recycling rate 2 is more than 90%. The qualitatively consistent oceanic recycling rate between the recycling rate 1 and recycling rate 2 confirms that the previous conclusion based on the global precipitation and oceanic water vapor (figure 1): the recycling rate of atmospheric moisture has decreased during the past two decades.
In addition to the temporal variation of recycling rate averaging over globe and ocean, we also explore the spatial patterns of recycling rate in response to global warming. Figure 3 shows the spatial pattern of temporal variation of two recycling rates (recycling rate 1 and recycling rate 2). As shown in figure 3, the two recycling rates have similar spatial patterns. The temporal variation of recycling rate is positive in a narrow band around the equator, which is roughly the intertropical convergence zone (ITCZ) identified by highly reflective clouds (Waliser and Gautier 1993). Even though the confidence level of the linear trend of precipitation in the narrow band is less than 90%, the positive temporal variation suggests that the recycling rate of atmospheric moisture has intensified in the ITCZ during the past two decades. The recycling rate displays strong negative temporal variation at the two sides of the ITCZ in the Pacific Ocean with the confidence level of the linear trend larger than 90%, which suggests that the recycling rate of atmospheric moisture has slowed down in these areas. Besides the dominant feature in the tropical region, figure 3 also shows other positive and negative centers in the relatively high latitudes. Since the global average of recycling rate is decreased, it implies that the negative recycling is stronger (or spatially larger) than the positive recycling rate.
The dominant feature of recycling rate in the tropic region shown in figure 3 is very interesting. Considering that the recycling rate of atmospheric moisture is determined by precipitation and water vapor (equation (2)), the spatial patterns of temporal variations in precipitation and water vapor are also explored. Figure 4 displays the spatial patterns of oceanic precipitation and water vapor. Figure 4(A) shows that there are positive temporal variations of precipitation in the ITCZ, which is a high-precipitation area. In addition, negative temporal variations of precipitation occur in the two sides of the ITCZ in the tropic region, which are is a low-precipitation area. The opposite temporal variations of precipitation between the high-precipitation and lowprecipitation areas are consistent with a recent study (Allan et al 2010). It suggests that the precipitation over highprecipitation areas has intensified during the past two decades. This intensification provides a new perspective to examine the amplification of precipitation extremes in response to global warming Soden 2008, Liu et al 2009). The spatial pattern of temporal variation in precipitation also provides an observational evidence for a 'rich-get-richer' mechanism from numerical simulations Neelin 2004, Neelin et al 2006), in which the tendency of precipitation increasing in the ITCZ and decreasing in the neighboring dry region was suggested. The dynamical processes responsible for the 'rich-get-richer' mechanism are probably associated with the variation of gross moist stability of the atmospheric boundary layer and the related adjusting of convection and precipitation (Held andSoden 2006, Chou et al 2009).
The spatial pattern of temporal variation is similar between recycling rate (figure 3) and precipitation ( figure 4(A)). In addition, the magnitude of temporal variation is much stronger in precipitation than in water vapor (figure 4). Globally the trend in precipitation is smaller than that of water vapor, but regionally the trend in precipitation appears to dominate in the temporal variation of the recycling rate of atmospheric moisture (figures 4(A) and (B)). Figure 4 also shows that the spatial patterns of temporal variations are similar between precipitation and water vapor, which implies that the temporal variations of precipitation are related to the temporal variations of water vapor even though the magnitudes of their temporal variations are different.

Conclusions
In this study, we explore the temporal variations of global and oceanic precipitation, water vapor, and recycling rate of atmospheric moisture during the past two decades. Our analyses suggest that a consistent view between observation and numerical modeling-the global or oceanic recycling rate of atmospheric moisture has decreased over the past two decades. Considering that the linear trend of global precipitation is sensitive to different datasets and different versions of datasets, we suggest caution in interpreting the linear trends of time series at the global scale, as pointed out by some previous studies (Gu et al 2007, Lambert et al 2008, John et al 2009, Huffman et al 2009. We urge further examination of this important trend at the global and regional scales when longer and better global precipitation datasets become available. We also explore the spatial pattern of temporal variations in the recycling rate of atmospheric moisture. Recycling rate has increased in the ITCZ and decreased in the neighboring region over the past two decades. Our exploration shows that the spatial pattern of temporal variations in the recycling rate is mainly controlled by the spatial pattern of temporal variations in precipitation whose magnitude is much stronger than the magnitude of the temporal variations in water vapor. The spatial patterns of temporal variations in precipitation, water vapor, and recycling rate enrich our knowledge of the hydrological cycle, which further provide constraints for climate models. Correct simulation of these important features by the climate models will help elucidate the physics behind the different temporal variations in the wet and dry areas, paving the way for more accurate prediction of future climate change driven by anthropogenic activities. (Bretherton et al 1999), where r ( x) is the autocorrelation corresponding to a lag of time interval x. The linear trend is statistically significant when t is larger than a certain value t 0 , which can be found from the t-distribution table (Box et al 2005).