In this study, data from the Modern Era Retrospective-analysis for Research and Applications (MERRA) [Rienecker et al., 2011] are used. For the land variables, we use an ancillary product called “MERRA-Land” [Reichle et al., 2011] instead of the original MERRA output. MERRA-Land is produced with the same land model as MERRA but driven uncoupled from the atmospheric model with revision of parameter values in the original canopy interception model, which caused large biases. The atmospheric forcing for the offline simulation is the same as MERRA except the MERRA precipitation is corrected with the observational based Global Precipitation Climatology Project (GPCP) pentad product [Huffman et al., 2009; Xie et al., 2003]. For the calculation of ET-P, which needs precipitation data, the MERRA precipitation has been corrected by the daily gauge-based CPC Unified precipitation at a resolution of 0.5° × 0.5° [Xie et al., 2007; Chen et al., 2008]. The data from 1979 to 2005 are used. The horizontal resolution for MERRA is 2/3° longitude by 1/2° latitude.
2.2. Calculation of SM-ET, ET-P, and SM-P
 SM-P can be simply expressed as (∂p/∂w) · σ(w), where ∂p/∂w is a derivative (sensitivity) of precipitation (p) with respect to soil moisture (w), and σ(w) is the standard deviation (characteristic variability) of soil moisture. The product describes the characteristic impact that soil moisture variations may have on precipitation, and is denoted by SM-P here. However, this simple expression does not make the calculation of SM-P easy because precipitation itself has a direct impact on soil moisture and their causal relationship cannot be easily identified by a derivative or correlation coefficient [e.g.,Wei et al., 2008b]. In other words, ∂p/∂w describes not only the sensitivity of p to w but also the (reciprocal of) sensitivity of w to p.Thus we further expand SM-P to a product of SM-ET and ET-P as
This expansion follows Dirmeyer to quantify SM-ET as a product of the sensitivity of ET to soil moisture (∂E/∂w) and σ(w), showing the characteristic impact of soil moisture variation on ET. ET-P is symbolically shown as a derivative of precipitation with respect to ET (∂p/∂E) but faces the same problem as ∂p/∂w, so also cannot be directly calculated. Note that ET-P is shown here as the sensitivity of precipitation to ET but not the characteristic impact of ET on precipitation (∂p/∂E · σ(E)). This is restricted by the balance of the equation. Thus, ET-P shown in this study is the sensitivity of precipitation to ET, but it may not in other studies. It can be found that SM-ET has the same unit as ET, and ET-P has no unit when precipitation and ET are in the same unit.
 Mathematically, the formulation of SM-ET is equivalent to the correlation between soil moisture and ET multiplied by the standard deviation of ET (see Text S1 in theauxiliary material). Different from ∂p/∂w, the derivative ∂E/∂w or correlation can be used to identify the causal relationship between soil moisture and ET because there is a unique relationship between them. A positive derivative or correlation, usually happens when there is soil moisture deficit, means the variation of soil moisture has some impact on ET. While a negative derivative or correlation means the variation of soil moisture is driven by ET variations, occurring when the soil moisture is sufficient and its variation does not affect ET but the available energy for ET is limited.
 ET-P depends not only on the local boundary layer process, which controls the triggering of convection, but also on the moisture transport, which is important for the precipitation amount. It is, therefore, difficult to attribute precipitation to the ET that contributes to it.Guo et al. quantified ET-P within the GLACE framework, using ensemble model simulations, and there have been some other efforts to roughly quantify it based on precipitation types [Koster and Suarez, 2003] or the precipitation recycling [Dirmeyer et al., 2009]. Here, we estimate ET-P based on the Quasi-isentropic back-trajectory (QIBT) method [Dirmeyer and Brubaker, 1999, 2007; Brubaker et al., 2001]. The method tracks the evaporative water vapor sources for each precipitation event (each grid point with precipitation) backward in time along the isentropic surfaces, assuming precipitated water is drawn from the atmospheric column in a distribution that follows the vertical profile of specific humidity. Traces start from the grid box and time step with precipitation, backward in time and space until all of its original precipitation is attributed to ET, but no longer than 15 days. The time step for the calculation is 45 min, and the outputs are aggregated into pentads. The output of this calculation is a two-dimensional evaporative source field around each grid point with precipitation. Please see the reference papers above for a detailed description of the QIBT method. The QIBT method can calculate both local and remote moisture sources for precipitation, thus quantifying ET-P over these sources.
 Our approach is similar to that used by Wei et al. [2012a] but has slight modifications. Three factors are considered: the correlation between precipitation at a grid point and its moisture sources over different grid points, the percentage contribution of the moisture sources to the precipitation at each grid point (where the source and sink areas match, this is recycling ratio), and the correlation between the moisture sources over each grid point and the total ET for the same grid point. The first two factors identify the dominant moisture sources, and Wei et al. [2012a] have shown that the pattern of their product is similar to the first principal component of the moisture sources. But being a dominant moisture source does not guarantee that the ET there has a strong impact on precipitation; the evaporative moisture contribution could also respond passively to precipitation variations [Wei et al., 2012a]. Therefore, the third factor measures the connection between the total ET at each grid point and its portion that contributes to precipitation, which must be strong to identify the controlling effect of total ET on precipitation, and it is a crucial factor for quantifying the sensitivity. As all three factors are essential, their product is used as a metric for ET-P. In order to make the scale consistent, the second factor (a percentage) is taken a square root before calculating the product. As the QIBT method tracks the water vapor sources for up to past 15 days, it considers the impact of previous soil moisture and ET anomalies. In addition, the method considers not only water vapor transport but also indirectly the related change of convective instability and triggering of precipitation [Wei et al., 2012b]. Therefore, this method considers both triggering and amplification of rainfall by ET, as defined by Findell et al. .
 ET and top 1-meter soil wetness data from MERRA-Land are used for the calculation of SM-ET, and the calculations are made at the pentad time scale to reduce the impact of synoptic storms. The 31-day running means of the data are removed before calculation, in order to filter out monthly and longer time scale variations that may distort the signal. The significance of SM-ET is contingent on the significance of the correlation between soil moisture and ET, which is tested using Fisher's Z transformation and the impact of autocorrelation on the degree of freedom is considered [Zwiers and von Storch, 1995]. The aggregated monthly data of the QIBT analysis are used for the calculation of ET-P. It is significant only when all of its three factors are significant (tested using t-test). Sample results of ET-P and its components over the Southern Great Plains, India, and the Yangtze River Valley are shown in theauxiliary material(Text S2). SM-P at each grid point is simply calculated as the product of SM-ET and ET-P, and it is significant only when both SM-ET and ET-P are significant.
2.3. Separation for Different Time Periods and Different Climate Conditions
 In order to investigate the impact of different climates, different time periods and different climate conditions are separated for study. First, the three metrics SM-ET, ET-P, and SM-P are calculated for four different seasons: March–April–May (MAM), June–July–August (JJA), September–October–November (SON), and December–January–February (DJF). Then further analyses are performed for JJA. There are 27 years (1979–2005) of data available, so there are a total of 81 JJA months. According to the monthly top 1-meter soil wetness, the 81 months are separated into three groups from wet to dry at each grid point: wet, medium, and dry. Each group has 27 months, and they are different for each grid point. The three metrics are calculated for each group.