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Recycling Rate of Atmospheric Moisture Over the Past Two Decades (1988-2009)
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Liming Li1, Xun Jiang1, Moustafa T. Chahine2, Edward T. Olsen2,
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Eric Fetzer2, Luke Chen2, and Yuk Yung3*
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1 Department of Earth & Atmospheric Sciences, University of Houston, USA
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2 Science Division, Jet Propulsion Laboratory, California Institute of Technology, USA
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3 Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena,
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USA.
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* To whom all correspondence should be addressed. E-mail: yly@gps.caltech.edu
To be submitted to GRL, December 8, 2010
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Abstract
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[1] Numerical models predict that the recycling rate of atmospheric moisture decreases with
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time at the global scale, in response to the global warming. A recent observational study by
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Wentz et al. [2007] did not agree with the result of numerical models. Here, we examine the
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recycling rate by the latest data sets of precipitation and water vapor, and suggest a consistent
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view of recycling rate of atmospheric moisture at the global scale between numerical models and
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observations. In addition, our analyses show that the recycling rate of atmospheric moisture has
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also decreased over the global oceans during the past two decades. However, we find different
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temporal variations of the recycling rate in different regions when exploring the spatial pattern of
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recycling rate. In particular, the recycling rate has increased in the high-precipitation region
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around the equator (i.e., ITCZ) and decreased in the low-precipitation region located in the two
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sides of the equator over the past two decades. Further exploration suggests that the temporal
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variation is stronger in precipitation than in water vapor, which results to the positive trend of
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recycling rate in the high-precipitation region and the negative trend of recycling rate in the low-
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precipitation region.
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1. Introduction
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[2] The hydrological cycle, which involves the atmosphere, surface, and biosphere, has
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enormous impact on human activity. The atmospheric branch of the hydrological cycle, in which
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water vapor leaves the surface by evaporation and returns to the surface by precipitation, is a
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crucial component of weather and climate.
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[3] Exploring the temporal variation of the total mass of water vapor in the global atmosphere is
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straightforward because the total mass of water vapor is related to atmospheric temperature by
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the Clausius-Clapeyron equation under the condition that the relative humidity in the atmosphere
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stays constant. Different datasets display qualitatively consistent increasing trends in the total
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mass of water vapor in the global atmosphere [Trenberth et al., 2005; Wentz et al., 2007; Santer
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et al., 2007]. Such increasing trends are also simulated in the numerical models [Bosilovich et
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al., 2005; Held and Soden, 2006].
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[4] On the other hand, precipitation, which is controlled by the atmospheric circulation and
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cloud microphysics, is more complicated. Consequently, there is no simple relationship between
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precipitation and temperature at the global scale even though surface temperature is correlated to
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local precipitation [Trenberth and Shea, 2005; Adler et al., 2008] and precipitation extremes
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[Allan and Soden, 2008; Liu et al., 2009]. In addition, large discrepancies in the linear trend of
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global precipitation exist among different studies [Allen and Ingram, 2002; Adler et al., 2003;
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Trenbeth et al., 2003; Held and Soden, 2006; Gu et al., 2007; Stephens and Ellis, 2008; Adler et
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al., 2008; Liepert and Previdi, 2009; Trenberth et al., 2010]. A recent paper by Wentz et al.
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[2007] suggests that the increasing trend with time was roughly the same for global precipitation
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(1.4  0.5% per decade) and total water vapor (1.2  0.5% per decade) during the period of 1987-
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2006.
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[5] The study by Wentz et al. [2997] implies that the recycling rate of atmospheric moisture,
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which is defined as the ratio of precipitation to column water vapor, remained constant or
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intensified with time. From the perspective of atmospheric radiative imbalance, it is possible that
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the global precipitation is increasing at a rate of 1.4% per decade [Liepert and Previdi, 2009].
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However, most other observational studies [Adler et al., 2003; Gu et al., 2007; Adler et al.,
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2008;] and climate models [Allen and Ingram, 2002; Held and Soden, 2006; Stephens and Ellis,
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2007] suggest that global precipitation is increasing more slowly than in the total mass of water
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vapor in response to global warming. In this study, we revisit the temporal variation of water
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vapor and precipitation based on the latest version of global data sets with emphasizing the
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variation of the recycling rate of atmospheric moisture in response to global warming during the
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past two decades (1988-2009).
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2. Methodology and Data
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[6] A useful method of estimating the intensity variation of the hydrological cycle in the global
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atmosphere is to use some simple parameters, which include recycling rate [Chahine et al.,
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1997], residence time [Chahine et al., 1992; Trenberth, 1998], and a non-dimensional ratio
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[Stephens and Ellis, 2008]. The purpose of these parameters is to compare the increasing rates
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between the total water vapor and precipitation. Here, we use the recycling rate of atmospheric
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moisture (R) [Chahine et al., 1997] to compare the temporal variation between column water
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vapor (W) and precipitation (P).
RP W
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(1)
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[7] In order to explore
the temporal variation of the recycling rate of atmospheric moisture, we
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convert Equation (1) into
R R  P P  W W
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(2)
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where X and X represent the change and mean value of variable X (i.e., R , P , and W )
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
during a time period.
When the varied percentage of precipitation ( P P ) is larger than the
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

 


varied percentage of column water vapor ( W W ), we have the ratio R R > 0. Otherwise, we
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have the ratio R R  0.


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 (2) shows that the temporal variation of recycling rate is determined by the
[8] Equation
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temporal variations of precipitation and column water vapor. In this study, the latest data sets
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from the Special Sensor Microwave Imager (SSM/I) [Wentz 1997; Wentz and Spencer, 1998] and
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the Global Precipitation Climatology Project (GPCP) [Huffman et al., 2009] are utilized to
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examine the temporal variations of precipitation, column water vapor, and recycling rate over the
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past two decades. The data set of SSM/I (V 6) has oceanic precipitation and water vapor from
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1988 to 2009 with spatial resolution at 0.25º 0.25º (latitude by longitude). The latest version of
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GPCP (V 2.1) has the global precipitation data from 1979 to 2009 with spatial resolution at 2.5º
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2.5º (latitude by longitude). To be consistent with the length of water vapor data from SSM/I, we
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only use the GPCP precipitation between 1988 and 2009. The sea surface temperature (SST)
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with spatial resolution at 2º 2º (latitude by longitude) is also utilized in this study. SST data are
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from the National Oceanic and Atmospheric Administration (NOAA),.
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3. Results
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[9] The temporal variations of precipitation and water vapor at the global scale are shown in
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Figure 1. Figure 1(A) shows two time series of the temporal variations of precipitation based on
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a combined global data from SSM/I and GPCP and the global data from GPCP. The combined
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global data was constructed by combining the precipitation data over ocean from the SSM/I and
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the precipitation data over land from GPCP. Figure 1(B) displays the temporal variation of
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column water vapor over the global oceans, which is based on the oceanic data from SSM/I. We
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calculate the linear trends and the corresponding uncertainties of the time series shown in Fig. 1
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by the least-squares method [Bevington and Robinson, 2003]. The linear trend of global
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precipitation is 0.08  0.43% per decade and 0.26  0.41% per decade for the combined global
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data and the GPCP global data, respectively. The linear trend of column water vapor is 1.01 
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0.39% per decade, which is basically consistent with a recent study [Santer et al., 2007]. We also
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calculate the confidence level of linear trends in Fig. 1 (please refer to Auxiliary Material),
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which shows that the confidence level of linear trend in the global precipitation is less than 90%
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and the confidence level of linear trend in the oceanic water vapor is more than 95%. The weak
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positive trend of global precipitation (0.08  0.43% per decade and 0.26  0.41% per decade) is
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much smaller than the linear trend (1.4  0.5% per decade) in the previous study [Wentz et al.
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2007]. The previous study was also based on a combined global data from SSM/I (ocean) and
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GPCP (land), but a relatively old version of GPCP (V 2) was used [Wentz et al. 2007]. Our study
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(Fig. 1) is based on a recent-released version of GPCP (V2.1) [Huffman et al., 2009]. The new
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dataset of GPCP has been improved by applying a new updated climate anomaly analysis
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method for gauge data [Schneider et al., 2008] and several correction schemes [Huffman et al.,
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2009], so it is better than the old version. Therefore, an exploration of the temporal variation
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based on the latest GPCP (V 2.1) will be more robust than the analyses in the previous study
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based on the relatively old version. The differences of trend between this study (Fig. 1) and the
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previous study [Wentz et al., 2007] are mainly due to the dramatic drop in the rate of increase of
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precipitation over land between the old version (V2) and the new version (V2.1) of the GPCP
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dataset [Huffman et al., 2009].
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[10] The weak positive trend with larger uncertainty in the global precipitation suggests that the
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linear trend of global precipitation is not statistically significant, and the precipitation trend is
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smaller than the significant linear trend in the oceanic water vapor. The comparison of linear
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trends between precipitation and water vapor implies that the recycling rate of global
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atmospheric moisture decreased with time during the past two decades. Therefore, our analysis
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based on the latest and improved precipitation data reconcile the discrepancy of recycling rate of
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global atmospheric moisture between the study by Wentz et al., [2007] and other studies [Allen
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and Ingram, 2002; Adler et al., 2003; Held and Soden, 2006; Gu et al., 2007; Stephens and Ellis,
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2008; Adler et al., 2008]. A consistent view  the slowing in the recycling rate of global
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atmospheric moisture in response to the global warming  now emerges. The slowing of the
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recycling rate of global atmospheric moisture can be explained from the perspective of
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atmospheric energetics [Allen and Ingram, 2002]. The physics behind the slowing is
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complicated, which includes the modification of the tropical Walker Circulation by changing the
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frequency of strong/weak updrafts [Emori and Brown, 2005; Vecchi and Soden, 2007],
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suppression of the surface evaporation [Richter and Xie, 2008], and reduction in the precipitation
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efficiency by a negative feedback through cloud radiative heating [Stephens and Ellis, 2008].
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[11] Due to the lack of the global long-term continuous data of water vapor, we assume that the
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linear trend of global water vapor is same as that of oceanic water vapor in the above comparison
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between precipitation and water vapor. Such an assumption was also used in the previous study
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[Wentz et al., 2007]. However, it is possible that the linear trend of water vapor is different
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between ocean and land [Simmons et al., 2010] so that the above assumption is not valid. Here,
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we conduct a strict comparison of linear trends between oceanic precipitation and oceanic water
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vapor over the past two decades in Figure 2. The retrieval of water vapor and precipitation near
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coasts is generally not robust due to the complicated meteorological situations there. Therefore,
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the data of water vapor and precipitation close to coasts (i.e., 1 latitude within coasts) are not
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included in this study. The data quality in the polar region is not very good either because there
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are very few in-situ observations available to validate the satellite data. Therefore, only the data
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of precipitation and water vapor over ocean between 60N-60S is used to discuss the recycling
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rate of atmospheric moisture during the past two decades in Figure 2.
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[12] Figure 2 displays the temporal variations of oceanic precipitation, water vapor, and
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recycling rate. Details for the linear trends of the time series in Fig. 2 are written in Table 1. As
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shown in Table 1, the positive linear trend of oceanic precipitation is very weak with large
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uncertainty. The linear trend of oceanic precipitation between 60N and 60S is roughly the same
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as the linear trend of oceanic water vapor from pole to pole (Fig. 1). The recycling rate 1 is
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defined as the ratio of the SSM/I precipitation to the SSM/I water vapor, and the recycling rate 2
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is defined as the ratio of the GPCP precipitation to the SSM/I water vapor. From Table 1, we find
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that the linear trend of recycling rate roughly equates to the difference of linear trends between
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precipitation and water vapor, which is consistent with Eq. (2). The confidence level of linear
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trend in the recycling rate 1 is less than 90%, but the confidence level of linear trend in the
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recycling rate 2 is more than 90%. The qualitatively consistence of oceanic recycling rate
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between the recycling rate 1 and the recycling rate 2 confirms that the previous conclusion based
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on the global precipitation and oceanic water vapor (Fig. 1): the recycling rate of atmospheric
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moisture has decreased during the past two decades.
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[13] In addition to the temporal variation of recycling rate averaging over globe and ocean, we
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also explore the spatial patterns of recycling rate in response to global warming. Figure 3 shows
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the spatial pattern of temporal variation of two recycling rates (recycling rate 1 and recycling rate
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2). As shown in Figure 3, two recycling rates have similar spatial patterns. The temporal
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variation of recycling rate is positive in a narrow band around the equator, which is roughly the
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intertropical convergence zone (ITCZ) identified by the highly reflective clouds [Waliser and
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Gautier, 1993]. The positive temporal variation suggests that the recycling rate of atmospheric
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moisture has intensified in the ITCZ during the past two decades. The recycling rate displays
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strong negative temporal variation at the two sides of the ITCZ in the Pacific Ocean, which
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suggests that the recycling rate of atmospheric moisture has slowed down in these areas. Besides
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the dominant feature in the tropical region, Figure 3 also shows other positive and negative
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centers in the relatively high latitudes.
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[14] The dominant feature of recycling rate in the tropic region shown in Fig. 3 is very
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interesting. Considering that the recycling rate of atmospheric moisture is determined by
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precipitation and water vapor (Eq. (2)), the spatial patterns of temporal variations in precipitation
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and water vapor are also explored. Figure 4 displays the spatial patterns of oceanic precipitation,
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water vapor, and SST. Fig. 4(A) shows that there are positive temporal variations of precipitation
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in the ITCZ, which are high-precipitation area. In addition, negative temporal variations of
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precipitation occur in the two sides of the ITCZ in the tropic region, which are low-precipitation
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area. The opposite temporal variations of precipitation between the high-precipitation and low-
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precipitation areas are consistent with a recent study [Richard et al., 2010]. It suggests that
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extreme weather patterns are intensified during the past two decades. This intensification
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provides a new perspective to examine the amplification of precipitation extremes in response to
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global warming [Allen and Soden, 2008; Liu et al., 2009]. The spatial pattern of temporal
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variation in precipitation also provides an observational evidence for a “rich-get-richer”
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mechanism from numerical simulations [Chou and Neelin, 2004; Neelin et al., 2006], in which
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the tendency of precipitation increasing in the ITCZ and decreasing in the neighboring dry region
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was suggested. The dynamical processes responsible for the “rich-get-richer” mechanism are
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probably associated with the variation of gross moist stability of the atmospheric boundary layer
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and the related adjusting of convection and precipitation [Held and Soden, 2006; Chou et al.,
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2009].
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[15] The spatial pattern of temporal variation is similar between recycling rate (Fig. 3) and
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precipitation (Fig. 4(A)). In addition, the magnitude of temporal variation is much stronger in
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precipitation than in water vapor (Fig. 4). Therefore, we think that the temporal variation of
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precipitation is dominant in the temporal variation of recycling rate of atmospheric moisture.
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Figure 4 also shows that the spatial patterns of temporal variations are similar between
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precipitation and water vapor, which implies that the temporal variations of precipitation are
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related to the temporal variations of water vapor even though the magnitudes of their temporal
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variations are different. The exploration of SST (Fig. 4(C)) shows that the temporal variations
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are similar in some regions but different in other regions between SST and water vapor. The
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comparison of spatial patterns between water vapor and SST suggests that the relationship of
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temporal variations between them is complicated.
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4. Conclusions
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[16] In this study, we explore the temporal variations of global and oceanic precipitation, water
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vapor, and recycling rate of atmospheric moisture during the past two decades. Our analyses
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suggest that a consistent view between observation and numerical modeling  the global or
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oceanic recycling rate of atmospheric moisture has decreased over the past two decades in
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response to the global warming. Considering that the linear trend of global precipitation is
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sensitive to different datasets and different versions of datasets, we suggest caution in
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interpreting the linear trends of time series at the global scale, as pointed out by some previous
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studies [Gu et al., 2007; Lambert et al., 2008; John et al., 2009; Huffman et al., 2009]. We urge
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further examination of this important trend when longer and better global precipitation datasets
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become available.
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[17] We also explore the spatial pattern of temporal variations in the recycling rate of
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atmospheric moisture. Recycling rate has increased in the ITCZ and decreased in the neighboring
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region over the past two decades. Our exploration shows that the spatial pattern of temporal
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variations in the recycling rate is mainly controlled by the spatial pattern of temporal variations
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in the precipitation whose magnitude is much stronger than the magnitude of the temporal
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variations in the water vapor. The spatial patterns of temporal variations in precipitation, water
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vapor, and recycling rate enrich our knowledge of the hydrological cycle, which further provide
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constraints for climate models. Correct simulation of these important features by the climate
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models will help elucidate the physics behind the different temporal variations in the wet and dry
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areas, paving the way for more accurate prediction of future climate change driven by
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anthropogenic activities.
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[18] Acknowledgments. We thank S. Newman, N. Heavens, R. Shia, D. Waliser, L. Kuai, M.
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Line, X. Zhang, and M. Gerstell for helpful comments. This work was partly supported by the Jet
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Propulsion Laboratory, California Institute of Technology, under contract with the National
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Aeronautics and Space Administration.
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bring? Science, 317, 233-235, doi:10.1126/science.1140746.
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Wentz F. J. (1997), A well-calibrated ocean algorithm for SSM/I, J. Geophys. Res., 102, 87038718.
Wentz, F. J., and R. W. Spencer (1998), SSM/I Rain Retrievals within a Unified All-Weather
Ocean Algorithm, J. Atmos. Sci., 55, 1613-1627.
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1
Figure Captions
2
3
Figure 1. Temporal variations of global-mean precipitation and oceanic-mean water vapor. (A)
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Precipitation (P). (B) Column water vapor (W). The red line in panel A is based on the combined
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global data from the latest version of GPCP (V 2.1) (land) and SSM/I (V 6) (ocean), and the blue
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line in panel A is based on the global data from the latest version of GPCP (V2.1).
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Deseasonalization and low-pass filter were applied to the time series. Seasonal cycle was
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removed by subtracting the monthly mean data. Low-pass filter was constructed so that only
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signals with periods longer than 6 months were kept.
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Figure 2. Temporal variations of precipitation, water vapor, and recycling rate averaged over
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ocean between 60N and 60S. (A) Precipitation (P). (B) Water vapor (W). (C) Recycling rate
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(R). El Niño-Southern Oscillation (ENSO) signals have been removed from time series by a
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regression method based on the Niño3.4 index. Note: the linear trend of time series is basically
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consistent between the data with the ENSO signals and the data without the ENSO signals. The
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recycling rate 1 is defined as the ratio of SSM/I precipitation to SSM/I water vapor, and the
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recycling rate 2 is defined as the ratio of GPCP precipitation to SSM/I water vapor.
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Figure 3. Spatial pattern of temporal variation of recycling rate ( R R ) over the time period of
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1988-2009. Color represents the ratio of temporal variation to time mean during one decade. For
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of recycling rate ( R ) over one decade
each grid point of the global maps, the temporal variation
22
is estimated by the production of linear trend and time span (one decade). Time mean value ( R )


18
1
is computed for the time period of 1988-2009. (A) Recycling rate based on SSM/I precipitation
2
and SSM/I water vapor. (B) Recycling rate based on GPCP precipitation and SSM/I water vapor.
3
4
Figure 4. Same as Fig. 3 except for the temporal variations of precipitation, water vapor, and sea
5
surface temperature. (A) Precipitation (P). (B) Column water vapor (W). (C) Sea surface
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temperature (SST). The precipitation data in panel A is from SSM/I. The spatial pattern of
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precipitation from GPCP, which is basically the same as the pattern from SSM/I, is not shown.
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1
Table 1. The linear trends of ocean-mean precipitation (P), column water vapor (W), and recycle
2
rate (R) shown in Figure 2 (1988-2009).
3
Precipitation ( P )
Water Vapor ( W )
Recycling Rate ( R )
4
SSM/I
GPCP
SSM/I
Rate 1
Rate 2
Units
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Linear Trend

0.13
0.33

0.97
0.82

0.65
%/decade
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Uncertainty
0.63
0.54
0.37
1.11
0.51
%/decade
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1
Figure 1
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1
Figure 2
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1
Figure 3
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Figure 4
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1
Auxiliary Material for
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Recycling Rate of Atmospheric Moisture
3
Over the Past Two Decades (1988-2009)
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5
Confidence Level of Linear Trend
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The confidence levels on the linear trends of the time series of the precipitation are
7
estimated by the t-statistics. For the linear trend coefficient b calculated from the least-square
8
fitting, the t-statistics is defined by t  b / SE (b) [Box et al., 2005]. SE(b) is the standard error of
11

2
the linear trend b , which is estimated by SE(b)  ( / N1 ) (1/N 2 ) x i [Bevington and


Robinson, 2003], where  is the standard deviation of the data, N1 is the number of degrees of


freedom of the data, N 2 is the length of the data set, and x i is the time series corresponding to a
12

number of measurements with
13


formula suggested by N1  N2 1 r(x)2  1 r(x)2  [Bretherton et al., 1999], where r(x) is
14


the autocorrelation corresponding to a lag of time interval x . The linear trend is statistically
15
 t is larger than a certain value t , which can be found from
significant when
the t-distribution
0
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table [Box et al., 2005].
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
x
i

 0. The number of degrees of freedom N1 is estimated by a


References
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20
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Box, G. E. P., J. S. Hunter, and W. G. Hunter (2005), Statistical for experiments, Second Edition,
John Wiley & Sons Inc., pp. 370-371.
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1
2
3
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Bretherton, C. S., M. Widmann, V. P. Dymnikov, J. M. Wallace, and I. Blade (1999), The
effective number of spatial degrees of a time varying field, J. Clim., 12, 1990-2009.
Bevington, P. R., and D. K. Robinson (2003), Data Reduction and Error Analysis for the
Physical Sciences, Third Edition, McGraw-Hill, New York.
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