The ability of soil moisture to affect precipitation (SM-P) can be dissected into the ability of soil moisture to affect evapotranspiration (ET; SM-ET) and the ability of ET to affect precipitation (ET-P). SM-ET is a local process that is relatively easy to quantify, but ET-P includes nonlocal atmospheric processes and is more complex. Here, ET-P is quantified both locally and remotely with a back-trajectory method for water vapor transport, using corrected reanalysis data. It is found that, for SM-P and ET-P, local impact is greater than that from remote for most land areas with significant local impacts. By examining the responses of the three metrics (SM-ET, ET-P, and SM-P) to climate variations over different climate regimes, we show that SM-ET is the principal factor that determines the spatial pattern and variation of SM-P. For climatologically wet regions, SM-ET and SM-P are higher during dry periods, and vice versa for climatologically dry regions. All three metrics show highest values over the transitional zones.
 The interaction between soil moisture and precipitation is one of the central issues in climate research because of its importance in the water and energy cycles and the associated weather and climate predictions [e.g., Seneviratne et al., 2010]. The interaction includes a two-way process of precipitation to soil moisture and the other way around. The impact of precipitation on soil moisture is direct, although with regional and seasonal differences in sensitivity [Wei et al., 2008a]. While the impact of soil moisture on precipitation (SM-P) is more complex and harder to observe or quantify. The Global Land-Atmosphere Coupling Experiment (GLACE) was one effort to quantify this impact with model simulations [Koster et al., 2004], but observational studies have been geographically limited and sometimes inconclusive [Findell and Eltahir, 1997; Salvucci et al., 2002; D'Odorico and Porporato, 2004]. For ease of research, SM-P is usually separated into two segments — the impact of soil moisture on surface fluxes (typically latent heat flux or evapotranspiration (ET; SM-ET), and the impact of surface fluxes on atmospheric states and precipitation (ET-P) [Guo et al., 2006; Seneviratne et al., 2010; Wei and Dirmeyer, 2010]. SM-ET is a local process that is relatively easy to quantify as long as the surface data are available, but ET-P is more elusive because of complicated atmospheric processes.
 A main finding of GLACE is that the soil moisture has the strongest impact on precipitation over transitional zones between wet and dry climates, where ET has adequate sensitivity to soil moisture variations and the amount and variability of ET is large enough to affect precipitation. These two requirements cannot be met at the same time over very dry or very wet regions. Also, the Second Phase of GLACE (GLACE-2 [Koster et al., 2011]) shows that anomalous wet and dry soil initializations generates prediction skills for temperature and precipitation over different regions, with dry initializations providing more skill over relatively wet regions and vice versa for wet initializations, both tending to have more skill in the vicinity of the arid-humid transition region over North America. It is evident that past efforts to study SM-P have mainly focused on the land segment (SM-ET), which is easier to identify, but much less is known about ET-P and its role in SM-P. Most past work on this have focused on the atmospheric boundary layer processes [e.g.,Findell and Eltahir, 2003; Santanello et al., 2009], which control the precipitation potential but have less impact on the precipitation amount. In addition, although SM-P includes nonlocal processes (in ET-P), the explanation of the related results was mostly based on the assumption that the impact of soil moisture is predominantly local (e.g., GLACE), which, however, has never been verified.
 In this study, we use a back-trajectory method to estimate the ET sources for land precipitation, thus quantifying and comparing ET-P and SM-P over local and remote grid points. Subsequent analyses focus on local SM-ET, ET-P, and SM-P at different climate conditions and the relative importance of SM-ET and ET-P in SM-P.
2. Data and Method
 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.
 One important issue in the study of SM-P is how strong the local impact is compared to remote impacts. This is mainly due to the fact that ET-P can be nonlocal. Most past studies have assumed that SM-P is predominantly local, but this assumption has never been justified. Here, we calculate SM-P and compare the impacts of local soil moisture with those from surrounding grid points. It is found that, for land grid points that have significant local SM-P (shown inFigure 1), 73%–85% of them (varies with season) show stronger impact from local than from the surrounding grid points (Figure S1). The percentages increase to over 90% for ET-P. Note that the calculations are on the high-resolution MERRA grid, and for lower-resolution grids the local impact should be more predominant. This demonstrates that the impact of local soil moisture has a stronger impact on precipitation than the remote soil moisture if the impact is significant, and the assumption of dominant local impact is basically correct. For simplicity, we focus on the local impacts in the remainder of this paper.
Figure 1shows the results of local SM-P for four different seasons. SM-ET and ET-P are shown in theauxiliary material(Figures S2 and S3). SM-P displays a strong seasonal cycle that partly follows the swing of monsoon rain belts, with high values mainly over the transitional zones between humid and arid regions and mainly in the warm climate zones. This is caused by the constraints of considered factors: high sensitivity of ET to soil moisture, sufficient ET variability, and enough moisture in the atmosphere for the instigation of precipitation. The pattern for JJA shows strong similarity to that of the land-atmosphere coupling strength found for boreal summer in GLACE. The patterns of SM-P are more similar to those of SM-ET than to ET-P (more discussion next).
Figure 2shows SM-ET, ET-P, and SM-P during locally-defined dry and wet months for JJA. Overall, SM-ET is much stronger during dry months than wet months, mainly because of the variation of the sensitivity of ET to soil moisture (∂E/∂w), while ET-P is comparable for the two periods. This leads to a much stronger SM-P during dry months than wet months. In addition to the amplitude, the spatial distribution of SM-P is also closer to SM-ET than to ET-P, as can be seen from the spatial correlations. ET-P depends more on atmospheric characteristics, so it has relatively less spatial variations than those of SM-ET and SM-P. In addition to the global features, the three coupling metrics also show some regional differences between the dry and wet months. For example, in the very dry regions of North Africa, the Middle East, and the Gobi desert, SM-ET is stronger during wet months rather than the dry months as for the global average. This is more clearly shown inFigure 3.
Figure 3shows the average of the three metrics as a function of the climatological soil wetness sorted by dry, medium, and wet months. All ice-free land points over the globe are included. It can be seen that all three metrics peak at an intermediate soil wetness, consistent with the findings from GLACE and GLACE-2, although ET-P has a flatter distribution than the other two. Both SM-ET and SM-P show a seesaw structure with climatologically wet regions having higher values during dry months and vice versa for dry regions. ET-P is consistently higher during wet months than dry months, probably because precipitation is more easily triggered in a wetter climate, but the difference is relatively small. It is evident that the seesaw structure of SM-P comes from SM-ET, showing that the temporal variability of SM-P is mainly controlled by SM-ET, even at the regional scale. Therefore, SM-P is similar to SM-ET not only in spatial pattern but also in temporal variability. As SM-ET is easier to calculate and observe than ET-P, it may be used as a surrogate for SM-P.
 SM-ET has higher values over transitional zones because of the compromise between the high sensitivity of ET to soil moisture and high ET variability (Figure S4). But why does ET-P also have higher values over transitional zones? Over very dry regions, precipitation is difficult to trigger by ET variations, so ET-P is very low. Over very wet regions, precipitation is easily triggered by ET [e.g.,Findell et al., 2011] (Text S3), but the precipitation variation is mostly controlled by the large-scale moisture transport rather than ET variations, which leads to a weak ET-P (seeWei et al. [2012a] for an example in the Yangtze River Valley). Only over transitional zones can the surface ET exert enough control on precipitation.
4. Summary and Discussion
 By separating SM-P into a land segment (SM-ET) and an atmospheric segment (ET-P), we studied the different roles of the two segments in SM-P and the variations of each of these three metrics with climate. Although ET-P and so SM-P could be nonlocal, we find that the local impacts dominate for a vast majority of the land area that has significant local impacts. It is found that, over climatologically wet regions, both SM-ET and SM-P are higher during dry months than wet months, and vice versa over climatologically dry regions. This shows that the impact of soil moisture is stronger when the climate changes towards a transitional state between dry and wet, similar to the finding from previous studies [Seneviratne et al., 2006; Koster et al., 2011]. Although all the three metrics show highest values over the transitional zones, the spatial pattern and temporal variability of SM-P are largely determined by SM-ET. ET-P has much less spatial and temporal variabilities so it is less determinant. This result is consistent with that found byGuo et al. , which used a similar definition of SM-ET based on the GLACE framework. This result also explains why SM-P can be explained in past studies by its land segment only [e.g.,Koster et al., 2004], and suggests that, in most cases, SM-ET may be used as a surrogate for SM-P.
 In fact, it can be found in equation (1)that it is an “unfair competition” between SM-ET and ET-P. SM-ET quantifies the characteristic impact of soil moisture on ET, while ET-P here only estimates the sensitivity of precipitation to ET without considering the variability of ET, which, as can be seen fromequation (1), only needs to be considered once in the process from soil moisture to precipitation. The variability of soil moisture and ET, which is related to atmospheric, especially precipitation, variability, could be an important factor affecting soil moisture-precipitation coupling [Wei et al., 2010, 2012c; Wei and Dirmeyer, 2010; Dirmeyer, 2011]. However, it is found that the spatial distribution and temporal variability of ET-P do not change much even when ET variability is considered in ET-P (ET-P becomes characteristic impact of ET on precipitation;Figure S4).
 Although this study uses reanalysis data, which is better constrained than model-only simulations, there are still many biases and uncertainties in it. Therefore, the results may be somewhat different when using other datasets. Also, the estimation method may not be flawless, especially for the complex ET-P processes. Nevertheless, this study is a step forward by providing a method to quantifying soil moisture-precipitation coupling and its components using observational data, and it will facilitate the comparisons between models and observations.
 We thank an anomalous reviewer for his/her insightful comments, which helped to improve the paper. Qing Liu and Rolf Reichle provided MERRA-land data sets. This research was supported by joint funding from the National Science Foundation (ATM-0830068), National Oceanic and Atmospheric Administration (NA09OAR4310058), and the National Aeronautics and Space Administration (NNX09AN50G, NNX09AI84G).
 The Editor thanks the anonymous reviewer for assisting in the evaluation of this paper.