Land-surface controls on afternoon precipitation diagnosed from observational data: uncertainties and confounding factors

. The feedback between soil moisture and precipitation has long been a topic of interest due to its potential for improving weather and seasonal forecasts. The generally proposed mechanism assumes a control of soil moisture on precipitation via the partitioning of the surface turbulent heat ﬂuxes, as assessed via the evaporative fraction (EF), i.e., the ratio of latent heat to the sum of latent and sensible heat, in particular under convective conditions. Our study investi-gates the poorly understood link between EF and precipitation by relating the before-noon EF to the frequency of afternoon precipitation over the contiguous US, through statistical analyses of multiple EF and precipitation data sets. We analyze remote-sensing data products (Global Land Evaporation: the Amsterdam Methodology (GLEAM) for EF, and radar precipitation from the NEXt generation weather RADar system (NEXRAD)), FLUXNET station data, and the North American Regional Reanalysis (NARR). Data sets agree on a region of positive relationship between EF and precipitation occurrence in the southwestern US. However, a region of strong positive relationship over the eastern US in NARR cannot be conﬁrmed with observation-derived estimates (GLEAM, NEXRAD and FLUXNET). The GLEAM– NEXRAD data set combination indicates a region of positive EF–precipitation relationship in the central US. These dis-agreements emphasize large uncertainties in the EF data. Further analyses highlight that much of these EF–precipitation relationships could be explained by precipitation persistence alone, and it is unclear whether EF has an additional role in triggering afternoon precipitation. This also highlights the difﬁculties in isolating a land impact on precipitation. Regional analyses point to contrasting mechanisms over different regions. Over the eastern US, our analyses suggest that the EF–precipitation relationship in NARR is either at-mospherically controlled (from precipitation persistence and potential evaporation) or driven by vegetation interception rather than soil moisture. Although this aligns well with the high forest cover

Abstract.The feedback between soil moisture and precipitation has long been a topic of interest due to its potential for improving weather and seasonal forecasts.The generally proposed mechanism assumes a control of soil moisture on precipitation via the partitioning of the surface turbulent heat fluxes, as assessed via the evaporative fraction (EF), i.e., the ratio of latent heat to the sum of latent and sensible heat, in particular under convective conditions.Our study investigates the poorly understood link between EF and precipitation by relating the before-noon EF to the frequency of afternoon precipitation over the contiguous US, through statistical analyses of multiple EF and precipitation data sets.We analyze remote-sensing data products (Global Land Evaporation: the Amsterdam Methodology (GLEAM) for EF, and radar precipitation from the NEXt generation weather RADar system (NEXRAD)), FLUXNET station data, and the North American Regional Reanalysis (NARR).Data sets agree on a region of positive relationship between EF and precipitation occurrence in the southwestern US.However, a region of strong positive relationship over the eastern US in NARR cannot be confirmed with observation-derived estimates (GLEAM, NEXRAD and FLUXNET).The GLEAM-NEXRAD data set combination indicates a region of positive EF-precipitation relationship in the central US.These disagreements emphasize large uncertainties in the EF data.Further analyses highlight that much of these EF-precipitation relationships could be explained by precipitation persistence alone, and it is unclear whether EF has an additional role in triggering afternoon precipitation.This also highlights the difficulties in isolating a land impact on precipitation.Regional analyses point to contrasting mechanisms over different regions.Over the eastern US, our analyses suggest that the EF-precipitation relationship in NARR is either atmospherically controlled (from precipitation persistence and potential evaporation) or driven by vegetation interception rather than soil moisture.Although this aligns well with the high forest cover and the wet regime of that region, the role of interception evaporation is likely overestimated because of low nighttime evaporation in NARR.Over the central and southwestern US, the EF-precipitation relationship is 1 Introduction Soil-moisture-precipitation feedback has been investigated for several decades and, despite some progress in recent years, remains a poorly understood process and a large source of uncertainty in climate models (Seneviratne et al., 2010).While studies until the 1990s tended to focus on the concept of moisture recycling (i.e., the fraction of precipitation directly contributed by regional evaporation from the land surface; see Seneviratne et al., 2010), more recent studies have emphasized the importance of indirect feedback mechanisms -that is, an influence of soil moisture on atmospheric stability, boundary layer characteristics, and thereby precipitation formation (e.g., Schär et al., 1999;Pal and Eltahir, 2001;Findell and Eltahir, 2003a;Ek and Holtslag, 2004;Betts, 2004;Santanello et al., 2009;Hohenegger et al., 2009;Taylor et al., 2011;Lintner et al., 2013;Gentine et al., 2013).Such indirect effects can theoretically lead to feedbacks of either sign (Seneviratne et al., 2010).For instance, over wet soils, humidity input into the boundary layer increases, but turbulence and boundary layer height decrease; the interplay of these two effects with the environment can trigger or suppress convective rainfall locally depending on the prevailing conditions (e.g., Ek and Holtslag, 2004;Gentine et al., 2013).Although most studies report a positive feedback, some suggest the existence of a negative feedback in certain regions (Findell and Eltahir, 2003a, b;Cook et al., 2006;Hohenegger et al., 2009;Westra et al., 2012;Gentine et al., 2013).Furthermore, nonlocal processes can also be important (e.g., Taylor and Ellis, 2006).In particular, spatial heterogeneity of soil moisture has been shown to possibly induce mesoscale circulations favoring precipitation over dry soils, for example in the Sahel region (Taylor et al., 2011) but also globally (Taylor et al., 2012).
The entire soil-moisture-precipitation feedback can be decomposed into a chain of processes as follows (Fig. 1, modified from Seneviratne et al., 2010; see also, e.g., Santanello et al., 2011): A. Soil moisture impacts the partitioning of energy at the land surface into sensible and latent heat flux (H and λE, respectively), as quantified by the evaporative fraction EF = λE H +λE .B. The moisture and heat input to the atmosphere corresponding to changes in EF impacts subsequent precipitation.
C. Precipitation impacts soil moisture by replenishing the soil moisture reservoir.
Relationship A (higher soil moisture leading to higher EF) is expected to be most significant in regions that are tran- sitional between wet and dry climates, where soil moisture is the main limiting factor for land evaporation (e.g., Koster et al., 2004;Seneviratne et al., 2006b;Teuling et al., 2009;Hirschi et al., 2011).Note here the potentially negative feedback within relationship A (red arrow in Fig. 1), since increased soil moisture content enabling high evaporation leads to faster depletion of the soil moisture, thus dampening the initial evaporation increase (see also Seneviratne et al., 2010;Boé, 2013).Relationship B, i.e., higher EF leading to higher (or lower) precipitation, is generally the most uncertain part of the soil-moisture-precipitation coupling and feedback and can exhibit positive or negative sign through boundary layer regulation (e.g., Ek and Holtslag, 2004;Santanello et al., 2007;van Heerwaarden et al., 2009).The impact of precipitation on soil moisture (relationship C), on the other hand, can be considered as straightforward, albeit with a dependence on the partitioning of precipitation into interception, runoff, and infiltration.Some studies investigate single relationships (e.g., relationship A; see for instance Dirmeyer, 2011), while A-B has been analyzed as one relationship (e.g., Taylor et al., 2012) as well as by combining metrics from each individual relationship (A and B; e.g., Dirmeyer et al., 2012).The existence, the sign, and the strength of soil-moisture-precipitation coupling, i.e., the impact of soil moisture on precipitation (relationship A-B), and in particular EF-precipitation coupling (B), remain heavily debated in the literature.
Modeling studies yield contrasting results, identifying both positive (Schär et al., 1999;Pal and Eltahir, 2001;Koster et al., 2004) and negative soil-moisture-precipitation relationships in some cases (Findell and Eltahir, 2003a, b;Ek and Holtslag, 2004;Hohenegger et al., 2009;Siqueira et al., 2009;van den Hurk and van Meijgaard, 2010).It has been shown that model-based studies suffer from deficiencies, such as the dependence on the chosen convective parameterization or resolution (e.g., Hohenegger et al., 2009).In particular, Taylor et al. (2013) suggest that current convective parameterizations in models lead to a positive feedback in regions where observations and cloud-resolving simulations indicate negative feedback.Dirmeyer et al. (2006) highlight large biases in global climate models (GCMs) with respect to covariability between key atmospheric and landsurface variables, and Koster et al. (2003) suggest that soilmoisture-precipitation feedbacks may be overestimated in GCMs.
Given the large range of results from modeling studies, observational studies are necessary.However, for a number of reasons, these have been largely inconclusive (Seneviratne et al., 2010).First, the scarcity of soil moisture and EF measurements is a recurrent limitation.In particular, while recent satellite remote-sensing efforts have facilitated global analyses and generated new insights (e.g., Taylor et al., 2012), these only provide data of soil moisture in the top few millimeters of the soil and in regions without dense vegetation cover.This is often not representative of deeper layers and, thus, of EF, especially in vegetated areas.Second, we note that one of the most challenging tasks in assessing soil-moisture-precipitation coupling (i.e., A-B) from observational data is to establish causal rather than mere statistical links between soil moisture (or EF) and precipitation (see also Salvucci et al., 2002;Orlowsky and Seneviratne, 2010).
The difficulty of causal inferences from observational data arises from two main confounding effects.First, given the influence of precipitation on soil moisture (process C) it can be difficult to assess whether a detected relationship between soil moisture and precipitation is due to A-B, C, or both.In particular, persistence in precipitation at various timescales (from synoptic to interannual scales, including seasonal scale) can induce apparent causal links, for which even lagged correlations, such as between soil moisture and subsequent precipitation, may in fact simply reflect relationship C. Second, covariability between two variables (for instance soil moisture and convective precipitation) may be a necessary but not a sufficient condition for a causal link since it does not exclude the possibility that both quantities are governed by a third influencing variable (for instance sea surface temperature; see Orlowsky and Seneviratne, 2010).Ideally, potential confounding variables should be taken into account in observational analyses; this is, however, rarely done in practice, mostly due to difficulties in identifying confounding variables or lack of data availability.
In order to overcome the issue of data scarcity, some studies have used state-of-the-art reanalysis products (e.g., Bisselink and Dolman, 2008;Findell et al., 2011).Soil moisture and associated land-surface fluxes in reanalysis products are, however, ultimately model-based and therefore share the deficiencies of their land-surface models.Some reanalysis products assimilate screen-level variables (temperature, humidity) in order to better constrain the surface energy budget (Mahfouf, 1991;Bouttier et al., 1993a, b;Gentine et al., 2011) and may thus be advantageous over other reanalysis products.Nonetheless, such land data assimilation procedures may introduce biases in surface variables (e.g., Betts et al., 2003;Seneviratne et al., 2004).In addition, reanalyses suffer from other issues such as the lack of mass conservation.Finally, they suffer from the similar difficulties in isolating causal relationships as the studies based on observational data, although they provide a more comprehensive data basis.Therefore, reanalysis-based investigations are a useful complement to, but ultimately cannot replace, observational studies.
In this study, we investigate soil-moisture-EFprecipitation coupling (i.e., processes A and B, with a focus on B) over North America, addressing the aforementioned issues.We use direct observations of EF and precipitation from FLUXNET sites, remote-sensing-derived products (satellite-driven EF estimates from GLEAM and precipitation from the US radar network NEXRAD), and soil moisture, EF, and precipitation from the North American Regional Reanalysis, NARR (see Sect. 2).Specifically, we quantify the relationship between before-noon EF (and soil moisture) and afternoon convective rainfall occurrence via the triggering feedback strength (TFS; see Findell et al., 2011, and Sect. 3).This metric suggests, when applied to NARR, a region of positive coupling over the eastern US (Findell et al., 2011).Here, we first compare TFS estimates derived from observation-driven data sets with those from NARR (Sect.4).We then consider the potentially confounding role of precipitation persistence on TFS (Sect.5), and further investigate the role of soil moisture and vegetation interception storage on land evaporation, as well as the inferred EF-precipitation coupling (Sect.6).Finally, results from these sections and their implications are discussed in Sect.7.

Data sets
We provide here a description of the data sets used in this study.The analysis is restricted to North America for consistency with Findell et al. (2011).The data sets include a reanalysis product (the North American Regional Reanalysis, hereafter referred to as NARR), ground-based pointscale observations from FLUXNET, and remote-sensingderived products: the NEXt generation weather RADar system (NEXRAD) and Global Land Evaporation: the Amsterdam Methodology (GLEAM).For 3-hourly data sets (NARR and GLEAM), the 3 h UTC time step closest to each local 3 h time period (in standard local time based on longitude) is www.atmos-chem-phys.net/14/8343/2014/Atmos.Chem.Phys., 14, 8343-8367, 2014 used, as in Findell et al. (2011).Thus, a lead or lag of up to 1 h may occur between the data sets.

NARR
The North American Regional Reanalysis (NARR; see Mesinger et al., 2006) is maintained at the National Center for Environmental Prediction (NCEP) and spans the period from 1979 to present.With its high spatial (about 32 km horizontal) and temporal (3 h) resolution, it allows for analyses focused on the diurnal evolution of land-atmosphere variables, which is an important aspect when analyzing the impact of surface fluxes on convection and precipitation.Its key characteristic is that it successfully assimilates high-quality precipitation observations into the atmospheric analysis, contrary to other reanalyses.This might in principle allow for a more realistic representation of land hydrology and landatmosphere interactions.Humidity observations are also assimilated to constrain the atmospheric state, but they do not directly constrain surface fluxes via soil moisture nudging.Some other variables that affect the land surface, such as screen-level temperature, are not assimilated (Mesinger et al., 2006).Surface radiation fluxes can also be significantly biased in NARR (Kennedy et al., 2011).Moreover, West et al. (2007) identified spurious grid-scale precipitation events and related them to anomalous latent heating in cases of strong mismatch between assimilated and modeled precipitation.Ruane (2010a, b) highlighted that, while the exaggerated model precipitation is reduced by the assimilation of precipitation observations, other components of the water cycle such as evaporation and moisture convergence are not corrected.Indeed, assimilation products do not conserve water.
The land component of NARR is the Noah land-surface model (Ek et al., 2003).The soil includes four layers spanning the following depths: 0-10 cm, 10-40 cm, 40 cm-1 m, and 1-2 m.Bare soil evaporation (plant transpiration) is limited by soil moisture in the top layer (root zone), and evaporation from vegetation interception is accounted for.The root zone is defined for each grid cell as a function of vegetation type -at the analyzed sites, it includes the top three or four layers.
Here, we use NARR data from the years 1995-2007, and most of the analyses are restricted to days when data are available from other data sets (NEXRAD and GLEAM; see Sects. 2.3 and 2.4,respectively).This removes possible impacts of different time periods or time series lengths.Analyses of the longer 1979-2007 period are included in the Supplement (Sects.S1 and S4 in the Supplement) for comparison, yielding similar results.
All data are adjusted to local time by taking the 3 h period closest to the standard local time.Thus, for afternoon values, for instance, (12-6 p.m.), data from 09:00-15:00 UTC are used west from 247.5 • E while 06:00-12:00 UTC data are used for the rest of the continent.

FLUXNET
FLUXNET is a global network of micrometeorological measurement sites (Baldocchi et al., 2001;Baldocchi, 2008), which uses the eddy-covariance technique to measure exchanges of CO 2 , water, and energy between the land surface and the atmosphere.It currently includes over 500 sites worldwide (http://www.fluxnet.ornl.gov/introduction)with a relatively large density over Europe and North America.The density of the network as well as the record lengths in these regions allow for spatial analyses.FLUXNET is the largest available network of "direct" observations of latent and sensible heat fluxes, which, in spite of some known issues (underestimation of the fluxes and lack of energy balance closure, point-scale measurements with relatively small footprint area, possible change in footprint depending on, for example, wind direction), provides largely modelindependent data and is therefore a direct estimate pertinent to our analyses.
In this study, we use data from the FLUXNET LaThuile data set, a global standardized database of eddy-covariance measurements which includes a large number of sites.Measurements of sensible (H ) and latent (λE) heat fluxes are used to compute EF, while global radiation (i.e., incoming shortwave, R g ) and potential global radiation (i.e., extraterrestrial radiation, R pot g ) are used to get a proxy for cloud cover (see Sect. 3.2).One of the main issues with eddy-covariance measurements is that the energy balance is not closed: the sum of H and λE typically underestimates the available energy by 10-30 % (e.g., Wilson et al., 2002;Mauder et al., 2006;Foken, 2008;Hendricks Franssen et al., 2010).However, as we do not use H and λE directly but only their ratio through EF, we note that the commonly used "fixed Bowen ratio" correction for the energy balance closure (i.e., attributing the missing energy to latent and sensible heat fluxes while keeping the Bowen ratio B w = H λE constant; e.g., Blanken et al., 1997) does not affect EF.Hence, we can expect that EF is only marginally affected by the lack of energy closure at the sites.
A total of 39 sites, listed in Table 1, are used in this study, all of them located in the US and Canada.The selection of the sites is based on several criteria: first, coverage by precipitation radars from NEXRAD (see Sect. 2.3) as well as R g measurements are requirements for use in our study.Second, summers with many gaps in any of the required variables are removed, and only sites with a reasonable amount of remaining data are kept for the analysis ( 100 days).1991-2006 1991-1994, 1997, 2000-2005 1997-20061998-2000, 2002-2004 Stylinski et Stylinski et 1998-20062000, 2003, 2005, 2006Waring and McDowell (2002) precipitation product (N1P) from the level 3 data.More details about NEXRAD products can be found at http:// www.ncdc.noaa.gov/oa/radar/radarresources.html(accessed on 20 December 2012).N1P data for summer (June to August, JJA) from 1995 to 2007 were downloaded at NEXRAD stations covering FLUXNET sites and their vicinity.We use 3 hr averages of precipitation within 20 km around each FLUXNET site.Aggregating with different radii and timeaveraging methods leads to similar results (not shown).

GLEAM
GLEAM (Global Land Evaporation: the Amsterdam Methodology; see Miralles et al., 2011b) is a global data set of daily land-surface evaporation (E) based on satellite observations, available at a resolution of 0.25 • .Estimates of E for day i are derived from  Vegetation optical depth NASA-LPRM (Owe et al., 2008) daily (for the S calculation) Precipitation NEXRAD (Sect.2.3) daily (for the S calculation) Net radiation GEWEX SRB 3.0 (Stackhouse et al., 2004) daily (for the S calculations) and 3-hourly frequencies (for the morning E pot ) Air temperature NCEP-1 (Sheffield et al., 2006) daily (for the S calculations) and 3-hourly frequencies (for the morning E pot ) where is the potential evaporation (at day i), derived through the Priestley and Taylor formulation (Priestley and Taylor, 1972) using data of net radiation (R net ) and nearsurface air temperature.S i denotes the evaporative stress (at day i) and is computed combining observations of vegetation water content (microwave vegetation optical depth) and estimates of root-zone soil moisture (θ i ) from a multilayer soil module driven by observations of precipitation (P i ) and surface soil moisture (θ obs i ).The inclusion of vegetation optical depth accounts for the effects of plant phenology; its low day-to-day variability causes minor effects on the short-term dynamics of E i .E I,i denotes the vegetation rainfall interception loss, calculated based on Gash's analytical model of rainfall interception (Gash, 1979) and described in Miralles et al. (2010); β is a constant to account for declines in transpiration when the canopy is wet (see Miralles et al., 2010Miralles et al., , 2011b)).
The satellite-data-driven evaporation model GLEAM is based on a larger array of satellite information than other evaporation products, which often apply algorithms requiring variables that are difficult to retrieve from satellite data (e.g., near-surface humidity and wind speed), and therefore rely on reanalysis forcing.To our knowledge, GLEAM is also the only large-scale satellite-data-driven evaporation product that estimates the temporal dynamics of root-zone soil moisture (based on observations of precipitation and surface soil moisture and a multilayer soil model).This root-zone soil moisture is used to constrain the atmospheric demand for water calculated based on radiation and temperature (note that explicit soil moisture constraints are not directly included in analogous models; e.g., Su, 2002;Mu et al., 2007;Fisher et al., 2008).GLEAM estimates of E have been extensively validated and compared to other methodologies (Miralles et al., 2011a, b;Mueller et al., 2013;Liu et al., 2013;Trambauer et al., 2014;Miralles et al., 2014a, b).In par-ticular, GLEAM was successfully validated using measurements from 163 eddy-covariance stations and 701 soil moisture sensors all across the world and run with a wide range of data sets for the required input variables in Miralles et al. (2014b).λE estimates from GLEAM have been applied to a large number of studies over the past 3 years (e.g., Miralles et al., 2011aMiralles et al., , 2012Miralles et al., , 2014a, b;, b;Reichle et al., 2011;Mueller et al., 2013;Liu et al., 2013;Fersch and Kunstmann, 2014;Jasechko et al., 2013;Trambauer et al., 2014), and the estimates error has been characterized using triple collocation (Miralles et al., 2011a).
We use a version of GLEAM that is driven by the input data sets noted in Table 2. Importantly, precipitation from NEXRAD (see Sect. 2.3) is used as input (to estimate interception loss and drive the soil module).GLEAM estimates using three other precipitation data sets yield similar results (Supplement S2, Fig. S3).GLEAM usually operates at daily time steps; as shown in Eq. ( 1), the computation of E i requires daily estimates of potential evaporation, E pot i ; evaporative stress, S i ; and interception, E I,i .Here, to estimate before-noon EF (9 a.m.-12 p.m., i.e., EF i,9−12 ), several modifications to the original methodology are therefore necessary.
GLEAM is first run with daily input variables aggregated to days beginning/ending at around 9 a.m. standard local time.The resulting estimates of root-zone soil moisture (θ i−1 ) used to derive S i−1 roughly correspond to 9 a.m. on day i, as they are derived using the cumulative precipitation up to 9 a.m. and instantaneous observations of surface soil moisture from the early morning hours (between 1.30 a.m. and 6 a.m.depending on the satellite platform -see Table 2 for details on the soil moisture remote-sensing products).In the assimilation, early morning surface soil moisture observations are combined with the bucket model estimates of soil moisture based on the rainfall until 9 a.m.Although surface Atmos.Chem.Phys., 14, 8343-8367, 2014 www.atmos-chem-phys.net/14/8343/2014/soil moisture might not always be representative of root-zone soil moisture, Miralles et al. (2014b) found mild improvements in the root-zone soil moisture estimates of GLEAM after assimilating the satellite observations.Before-noon EF at day i (i.e., EF i,9−12 ) is then computed using S i−1 estimates as a proxy for the before-noon evaporative stress conditions.Since days with morning-time precipitation are not included in the computations of the TFS, E I,i,9−12 is assumed to be zero.EF i,9−12 is therefore calculated as where R net is net radiation from the GEWEX SRB data set (satellite-based product; see Stackhouse et al., 2004) and G is the ground heat flux, computed as a function of R net and land cover type according to Miralles et al. (2011b).Note that the focus on the inter-day rather than intra-day variability in EF is advantageous since EF is considered most stable around noontime (e.g., Gentine et al., 2007).In addition, EF is rather robust to G given the low day-to-day variability in G relative to its diurnal cycle.
To summarize, EF i,9−12 is computed in two steps: 1. GLEAM is first run as in Miralles et al. (2011b) to derive the daily averages of evaporation (E i ) and evaporative stress (S i ) -see Eq. ( 1).The only difference here is that we compute daily values from about 9 a.m.-9 a.m. for all variables (depending on longitude but always before 9 a.m.).
In this form, S i−1 accounts for evaporative stress due to soil moisture deficits only and does not account for interception.This is done to acknowledge that interception rates are high even at night (see e.g., Pearce et al., 1980) and therefore vegetation only remains wet for a few hours after rainfall (4 ± 1.9 h using values from field studies compiled by Miralles et al., 2010), and because days with morning rainfall are removed, not being the subject of our analyses (Sect.3.2).
Nonetheless, to allow comparison with NARR, we introduce an alternative formulation which accounts for interception evaporation during the before-noon time period by assuming that vegetation stores intercepted water from the previous-day precipitation.To do so, we use a modified stress formulation, S * i−1 , which assumes that water remains on vegetation from the previous-day precipitation.Hence, we can rearrange Eq. ( 1) as Estimates of EF i,9−12 can then be computed using S * i−1 instead of S i−1 in Eq. ( 2) to account for interception evaporation.Nonetheless, this alternative approach is likely unrealistic due to the above-mentioned fast evaporation rates.In addition, findings from field studies highlight that advection and downward sensible heat flux rather than radiation are critical to the evaporation of intercepted water (e.g., Pearce et al., 1980;Asdak et al., 1998;Holwerda et al., 2012), and therefore the contribution of interception evaporation to the (radiation-based) EF is not straightforward.Nonetheless, we use this alternative approach as a sensitivity test of potential interception effects in Sect.6 (see Fig. 11).
Note that the timing of the input data sets for the S and S * computation is crucial to this application, in particular for precipitation.First, we do not want to include any information about afternoon precipitation for the estimated beforenoon EF on the same day.Second, rainfall occurring in the night preceding the estimated EF must be included in order to get an EF reflecting the conditions in the early morning.Unfortunately, the definition of "days" in many standard daily precipitation products varies, as shown in Table S1 in the Supplement, and is sometimes unclear: for instance, the use of data from the Global Precipitation Climatology Project (GPCP; see Huffman et al., 2001) is inappropriate due to the time window of the data set (00:00 to 00:00 UTC, i.e., from 4 p.m. (7 p.m.) to 4 p.m. (7 p.m.) in the US west (east) coast; see Table S1 in the Supplement).Also noteworthy, for the CPC Unified gauge product (Chen et al., 2008) days are defined differently depending on the country.For most of the US, the defined window is 12:00 to 12:00 (UTC, i.e., 4 a.m.-4 a.m. in the west coast/7 a.m.-7 a.m. in the east coast), which in principle suits our requirements, although uncertainties remain due to differing reporting times between contributing rain gauge stations.NEXRAD is not affected by this issue given its higher temporal resolution.
Due to the large diversity of precipitation products and the sensitivity of EF to precipitation, GLEAM has been driven with several precipitation data sets as input (see Supplement Discussion S2).Data sets used for this sensitivity test are NEXRAD, CPC Unified (Chen et al., 2008) and PERSIANN (Hsu et al., 1997).These three data sets either suit the required daily time window (like in the case of CPC Unified) or have a subdaily temporal resolution and therefore allow for appropriate daily aggregates (like in the case of NEXRAD and PERSIANN).Results obtained from these three independent precipitation data sets are qualitatively similar (see Fig. S3 and text in the Supplement).

Methods
This section describes the convection triggering metric TFS, including the selection of potentially convective days to which the computations are restricted, and the applied statistical test for assessing the significance of the results.

Triggering feedback strength (TFS)
The TFS, defined by Findell et al. (2011), quantifies the link between before-noon EF and afternoon precipitation occurrence as where EF is the before-noon evaporative fraction (computed between 9 a.m.-12 p.m., where 12 p.m. is noon), σ EF is the standard deviation of EF and (r) is the probability of afternoon rain (> 1 mm, computed between 12 p.m. and 6 p.m.).
The computation is restricted to summer days (June to August, JJA).Only potentially convective days (Sect.3.2) are included in the computation in order to reduce the impact of large-scale synoptic systems.In addition, surface turbulent fluxes of sensible and latent heat are most likely to impact precipitation formation in convective situations (see Sect. 3.2).Note that, like most statistical analyses, a high TFS does not necessarily imply causality between EF and (r) but simply the existence of a statistical correlation between the two variables.Findell et al. (2011) computed TFS in bins of the parameter space of EF, CTP, and HI low (the convective triggering potential and a low-level humidity index, respectively; see Findell and Eltahir, 2003a), which are subsequently aggregated.HI low is an indicator of humidity in the lower atmosphere, while CTP provides information about atmospheric stability.Accounting for these two variables is expected to reduce possible confounding effects from atmospheric conditions.In our study, however, relatively short observational time series preclude extensive sampling of this parameter space and independent observational sources for CTP and HI low , i.e., radio soundings, do not exist in the vicinity of all analyzed FLUXNET sites.
We can therefore only approximate the approach of Findell et al. (2011).Thus, we compute here a simplified version of TFS, where EF QX is the Xth percentile of EF.The variable σ EF and the percentiles of EF are determined for each location and data set independently.The definition of the bins ensures clearly distinct bins (i.e., no possible overlap even if EF Q60 = EF Q40 ) while retaining most of the available data.Considering quantiles also partly accounts for different shapes of the EF distributions when comparing different EF data sets.EF values outside of the 0-1 range are excluded from the analysis.Although TFS * is only an approximation of the original TFS defined by Findell et al. (2011), the two different computations show close agreement when applied to NARR.

Identification of potentially convective days
Midlatitude continental convection tends to occur in the afternoon, as a result of a particular daytime boundary layer evolution (Rio et al., 2009).Potentially convective days are therefore expected to be rain-and cloud-free in the morning.Moreover, convection is usually linked to low atmospheric stability and, therefore, typically positive CTP (Findell et al., 2011).Findell et al. (2011) therefore identify potentially convective days as days with CTP > 0 and no morning precipitation.In the absence of the necessary information for CTP from observations, we alternatively use the following criteria throughout our analyses: -No morning precipitation, as in Findell et al. (2011), and ) in the morning, where R g is the global radiation (i.e., incoming shortwave) at the land surface and R pot g is the potential R g in the absence of atmosphere (i.e., extraterrestrial incoming shortwave).R g is available from NARR and measured at FLUXNET sites.R pot g , being dependent on time and latitude only, is computed for each grid cell used in our analysis for NARR.It is directly available in FLUXNET data.The computation of max(R g /R pot g ), restricted to summer days (JJA), is applied to each site to account for site-specific conditions.R g /R pot g therefore quantifies the fraction of incoming solar radiation reaching the ground, and its maximum value corresponds to clear-sky cases.Requiring R g /R pot g > 0.67max(R g /R pot g ) in the morning is used to remove days with thick, persistent morning clouds from the analysis as they are likely linked to synoptic systems.Cutoff ratios between 0.5 and 0.8 do not lead to different results (not shown).Note that this criterion does not exclude the presence of morning clouds, which could be convective, but prevents cases dominated by morning clouds, likely of stratiform origin.
In this study, the data set combinations use these criteria computed on the following data sets, chosen according to data availability: -NARR: precipitation and R g from NARR, -FLUXNET-NEXRAD: precipitation from NEXRAD and R g from FLUXNET, -GLEAM-NEXRAD: precipitation from NEXRAD and R g from NARR.
The impact of the criteria for the selection of potentially convective days on TFS * , in particular with respect to the NARR analysis and the different set of criteria used in our study compared to Findell et al. (2011), is small, as discussed in the Supplement (Sect.S1 and Fig. S2).

Statistical tests
The statistical significance of TFS * = 0 is tested by bootstrap samples.A TFS * distribution is computed from 1000 bootstrap samples for which the EF data are kept unchanged and precipitation data are shuffled, which simulates the null hypothesis that no relation between EF and precipitation exists.The bootstrap TFS * distribution is approximately symmetrical with respect to 0. For a 90 % significance level, we require a positive (negative) TFS * to be at or above (below) the 95th percentile (5th percentile).We chose a rather low significance level of 90 % to account for the relatively short time series and the noise inherent in the data.

TFS from different data sets
The impact of before-noon EF on precipitation occurrence is quantified using the modified triggering feedback strength, TFS * (see Sect. 3).TFS * is computed at FLUXNET sites from three data set combinations: (i) a reanalysis product (NARR), (ii) direct measurements of surface turbulent heat fluxes at FLUXNET sites for EF in combination with radar precipitation from NEXRAD, and (iii) EF estimates from a satellite-data-driven evaporation product (GLEAM) in combination with NEXRAD precipitation.We compare estimates of TFS * from these data sets (Sect.4.1) and general characteristics of the EF data sets (Sect.4.2).

TFS patterns
Figure 2 displays TFS * for the three analyzed data set combinations.We note that the NARR pattern reproduces the regions of positive TFS * from Findell et al. (2011) over the eastern and southwestern US.This shows that our simplified TFS * computation (Eq.5) reproduces the more sophisticated computation from Findell et al. (2011).Nonetheless, results from Fig. 2 (left) display slightly weaker and less significant values, shown in supplementary analyses to be a result of shorter time series (Fig. S1 in the Supplement).The impact of different sets of criteria for the selection of po-tentially convective days, another source of discrepancy between our analysis and Findell et al. (2011), turns out to be small (Fig. S2 in the Supplement).
To complement the maps shown in Fig. 2, the distribution of TFS * values for the three data sets are compared separately over three regions (western, central and eastern US) using box plots (Fig. 3).The definition of these regions is based on expected coupling regions from previous studies.The central US region represents an expected soil-moisture-precipitation coupling "hot spot" (e.g., Koster et al., 2004), while the eastern US displays a strong positive EF-precipitation relationship in NARR (Findell et al., 2011).The western US, on the other hand, is a dry region (soilmoisture-limited regime; see Thomas et al., 2009;Schwalm et al., 2012) with little soil moisture and EF variability and is therefore usually not considered conducive to strong soilmoisture-precipitation feedbacks.Strong EF-precipitation coupling is a necessary but not sufficient condition for strong soil-moisture-precipitation coupling.
Generally, FLUXNET displays large variations within each region (Fig. 3) and even within smaller climatic regions (e.g., in Florida, Fig. 2).It does not confirm the positive TFS * regional pattern evident in NARR over the eastern US (Fig. 2).The remote-sensing-derived estimate from GLEAM-NEXRAD displays more consistent patterns, but it also does not yield many significant positive TFS * values in that region (3 significant sites out of 23, Fig. 2).Over both the central US and southwestern US, GLEAM-NEXRAD and to some extent FLUXNET show larger TFS * values compared to NARR (Figs. 2 and 3).We note that inspection of the NEXRAD time series reveals suspect features (not shown) for three sites in the middle of the western region; results with NEXRAD (and GLEAM, which is partly based on NEXRAD) are therefore not shown for these sites (empty dots, e.g., in Fig. 3).Results at other sites have been confirmed by analyses with other precipitation data sets (not shown; e.g., with CMORPH; Joyce et al., 2004).
Several reasons might contribute to the observed differences between TFS * estimates from the different data sets, some of which can be discussed with the support of Fig. 4 www.atmos-chem-phys.net/14/8343/2014/Atmos.Chem.Phys., 14, 8343-8367, 2014 (TFS * for the different combinations of EF and precipitation data sets for the same subset of days, namely the potentially convective days according to the NARR selection): i. Spatial scale of the EF data: the footprint of FLUXNET measurements is much smaller than the grid cells of NARR and GLEAM (typically 100-2000 m and 25-30 km, respectively; see Sect.4.2).Since EFprecipitation coupling is expected to occur at scales of about 20-100 km and NEXRAD data are at such a scale, FLUXNET may be less appropriate for this application.
Although different TFS * cannot be clearly attributed to differences in footprints based on Fig. 4, EF uncertainties are shown to play a strong role in controlling the convection triggering metric (see also Sect.4.2).
ii.Time series length and noise: the lengths of the time series considered here range from a few years in FLUXNET to 13 year (with some gaps) in GLEAM-NEXRAD and NARR.Comparing Fig. 2 with the respective panels of Fig. 4 shows that the decreased sample size in Fig. 4   TFS * estimates, although sensitivity tests do not highlight a strong sensitivity of TFS * to the chosen criteria, as shown in the Supplement for NARR (Fig. S2).
iv.Other data set characteristics, such as temporal resolution, uncertainties, and possible errors (e.g., modeling components in NARR): such causes for the observed differences are difficult to disentangle from the three above-mentioned factors as the selection of days and the length of the time series are linked to the data sets.
While the region of strong EF-precipitation relationship in the eastern US in NARR cannot be confirmed with FLUXNET and GLEAM-NEXRAD, it is possible that time series in these observation-derived data sets are simply too short or too noisy to detect a robust TFS * in this region.Nevertheless, NARR generally exhibits a stronger (weaker) link between EF and convection triggering over the eastern (central and southwestern) US compared to the observation-based estimates used here.Hence our results suggest a product dependence of the derived TFS * patterns.
Hereafter, we focus on the disentangling of these various factors, and in particular on possible fundamental differences in the processes underlying the investigated EF-precipitation relationship.Thereby, analysis of the differences in the data sets themselves might shed light on the different TFS * patterns.Since precipitation data from NARR and NEXRAD agree well in terms of precipitation occurrence (not shown), we focus on the differences between EF data sets and analyze these in the next section.

EF time series
To analyze the agreement of the spatiotemporal dynamics between the three EF data sets, Fig. 5 displays their respective correlations with one another in summer (JJA) for beforenoon (9 a.m.-12 p.m.) EF.Unlike in the TFS * computation, all days are included in the correlations, but similar results are found for the potentially convective days only.Although positive, correlations are strikingly low at most sites and across all data set combinations.This suggests that the disagreement between the TFS * patterns in the different data set combinations is related to differences in the considered EF data sets (see also Fig. 4).Correlations of 10-day and monthly averages of before-noon EF are higher but remain low over the eastern US (Fig. S4 in the Supplement).Correlations of EF anomalies (i.e., after removing the seasonal cycle within JJA) instead of actual values display similar results (not shown).
Several reasons might explain these differences.First, the spatial scale over which EF is estimated, or footprint, is dataset-specific, as mentioned above (Sect.4.1, point i).Differences might thus arise from contrasting environmental conditions over the respective footprints (e.g., input of water from rainfall in the case of very local precipitation events), but also from differences in land covers.Indeed, while wet vs. dry periods might be similar in all data sets, some studies have shown that different vegetation might respond differently to given conditions (Teuling et al., 2010).Land cover is in fact different at FLUXNET sites compared to the larger scale in NARR, in particular in regions with cultivated land, as FLUXNET sites are often located over natural vegetation.However, we did not find any systematic link between different land covers and resulting TFS * (not shown).Similarly, soil texture impacts soil moisture dynamics and EF (e.g., Guillod et al., 2013) and differences in local vs.larger scale soil texture could also be a reason for the differences in EF.
In order to better characterize the EF time series, Fig. 6 shows the mean, standard deviation, and persistence (quantified by the decorrelation timescale, τ D , which integrates the autocorrelation function; see von Storch and Zwiers, 1999) for the three data sets.While we do not find any clear differences between the data sets that can explain the low temporal correlation and resulting differences in TFS * , the comparison highlights some interesting features.The mean EF is similar in all data sets and exhibits higher values in the eastern US (wetter climate) compared to the drier climate of the western US, although in GLEAM the central US displays even higher mean EF values.The EF standard deviation is noisy, although similar patterns are found across all data sets, with higher EF variability in the central US or in the Southern Great Plains (the exact location depending on the data set).Note, however, that the amplitudes differ widely among the three data sets.This does not necessarily impact TFS * : the change in the probability of afternoon precipitation with respect to EF is scaled by the standard deviation of EF (see Eq. 4 and Berg et al., 2013).Finally, EF persistence is generally lower in the eastern US, suggesting high variability at a scale of one to a few days in this region of strong relationship in NARR (Fig. 2, left).Thus, the regions of strong daily correlation between EF and convection triggering correspond, in NARR, to humid regions with low persistence, while in GLEAM-NEXRAD the drier southwestern region, with higher persistence, displays the strongest relationship.
For the remaining analyses, we exclude FLUXNET data because of the record length of this data set being too limited.

Impact of EF vs. precipitation persistence
Although the TFS metric is a useful tool for investigating the relationship between EF and convective precipitation triggering, precipitation persistence might lead to high TFS even in the absence of an actual impact of EF on precipitation.
Here, precipitation persistence refers to precipitation autocorrelation, which might be induced by atmospheric persistence (e.g., from synoptic weather patterns).Resulting persistent wet conditions cause higher EF and vice versa, potentially leading to high TFS * values simply through externally forced precipitation persistence.Although one cannot exclude the possibility that precipitation days cluster together due to a feedback mechanism, atmospheric forcing is a more likely reason.Precipitation persistence might also arise from seasonality in precipitation.However, this effect is less relevant for our study as only summer is considered, and analyses on individual months do not suggest a strong link to seasonality (not shown).
Ideally, the TFS computation should account for such confounding effects, via the filters for potentially convective days (see Sect. 3.2).In addition, Findell et al. (2011) use bins of CTP and HI low in the computation, which we did not implement (Sect.3.1).Nevertheless, we specifically test for the effect of day-to-day precipitation persistence on TFS * by replacing before-noon EF with precipitation from the previous day in the TFS * computation.With respect to an explanatory variable, X, we denote the change in the probability of afternoon precipitation for high vs. low X as (X) = (r|X > X Q60 ) − (r|X ≤ X Q40 ). Figure 7 (left) shows (EF) for NARR and the GLEAM-NEXRAD combination, and the patterns strongly resemble those of TFS * (Fig. 2).Indeed, (EF) is the term that controls most of the TFS * signal, since σ EF and ∂EF mostly compensate each other in Eq. ( 4), and maps of σ EF (Fig. 6) do not display a pattern similar to that of TFS * (Fig. 2).Using (X) allows for a direct comparison between the impact of EF and that of previous-day precipitation P d,prev , shown on the right of Fig. 7 as (P d,prev ).In fact, previous-day precipitation is a better predictor for afternoon precipitation occurrence than before-noon EF, which holds for both data sets and across all regions.Given these results, one can wonder whether the signal with EF is, in fact, only reflecting precipitation persistence or whether EF conveys additional information that can help explain afternoon precipitation.
In order to disentangle the impact of EF on precipitation from precipitation persistence, we apply a framework similar to Salvucci et al. (2002)  previous-day precipitation.Here, only the occurrence of precipitation is considered and we investigate whether the signal emerging with EF reflects previous-day precipitation occurrence alone and thus may be an artifact of precipitation persistence on a short timescale.Note that Salvucci et al. (2002) also accounted for seasonal-scale persistence, which we omit since our analysis is restricted to summer months and our main interest is on short-term persistence (e.g., due to frontal systems or a sequence of these).Figure 8 shows TFS * independent of previous-day precipitation (i.e., as shown be-fore; left column) as well as conditioned on the occurrence of precipitation the day before: here TFS * is computed for subsets of days with either no precipitation on the previous day or with precipitation on the previous day (center and right columns, respectively).Since the conditioning reduces the number of days available, this analysis is applied to NARR and GLEAM-NEXRAD as well as to the longer set of NARR data, covering 1979-2007 (bottom row) for comparison.
www.atmos-chem-phys.net/14/8343/2014/Atmos.Chem.Phys., 14, 8343-8367, 2014 For both NARR and the GLEAM-NEXRAD combination, the signal over the eastern US strongly weakens when days are conditioned on previous-day rainfall (Fig. 8).This suggests an important role of precipitation persistence on subsequent precipitation and thus on TFS * .Note, however, that the shorter length of the time series after filtering days based on previous-day precipitation might also impact the results: using all available years from NARR (1979-2007, bottom row), TFS * is less sensitive to the conditioning on the previous day's rainfall, where EF might provide information on afternoon precipitation that is additional to previous-day precipitation occurrence.Nonetheless, for days following rainfree days, the weakening of the signal suggests a relevant role of precipitation persistence.Over the southwestern US, the signal appears less sensitive to day-to-day precipitation persistence as TFS * remains significant at most sites for both data sets.
Overall, precipitation persistence plays an important role and thereby affects TFS * in all data sets.Several factors can lead to high precipitation persistence via the atmosphere, such as atmospheric dynamics or SST forcing linked with large-scale teleconnection patterns.That said, we cannot exclude a partial contribution of EF-precipitation coupling to the identified persistence features, although larger with previous-day precipitation than with EF suggests that this is not the dominant mechanism.Finally, the binning in CTP and HI low might already partly account for this effect in Findell et al. (2011).

Soil moisture and interception evaporation
In the conceptual framework of a feedback between soil moisture and precipitation via EF (Fig. 1), soil moisture is expected to be the main driver of EF.However, our analysis shows that EF can be highly variable from day to day (as reflected, for example, by the low autocorrelation in the eastern US; see Fig. 6).This feature is inconsistent with an impact of low-frequency soil moisture variations, which is generally the main relevant factor in the context of weather and seasonal forecasting (e.g., Koster and Suarez, 2001;Seneviratne et al., 2006a;Koster et al., 2010).We thus examine the relevance of soil moisture in the analyzed relationships between land conditions and convection triggering.
We recall that λE (and thereby EF) comprises three main components (Fig. 9): plant transpiration (E trans ), bare soil evaporation (E soil ), and evaporation of water intercepted by vegetation (E I ).These evaporate water from different reservoirs that typically evolve at different timescales.Root-zone soil moisture (W roots ), which reflects precipitation over the previous weeks to months and is affected by vegetation, provides a mid-to long-term storage for E trans .Surface soil moisture (W top , top few centimeters of the soil), which reflects precipitation over the preceding days or week, provides a short-term storage for E soil .Finally, intercepted water on vegetation structures (W canopy ), which reflects precipitation over the preceding hours, provides very short storage for E I .Although often neglected in climate studies, evaporation of intercepted rainfall has been estimated to represent more than 10 % of global terrestrial E (Miralles et al., 2011a) and 20-50 % over forests (e.g., Savenije, 2004;McLaren et al., 2008;Gerrits and Savenije, 2011).Typical timescales mentioned here reflect estimates from many studies (see, e.g., Salvucci and Entekhabi, 1994, for soil moisture or Scott et al., 1997, for individual components of evaporation) but may not encompass the entire range of possible interactions.Therefore, a feedback on precipitation through EF can, theoretically, result from any of the three components of λE (or a combination of them), all of them affected by antecedent precipitation itself.
As an extension to Fig. 1, Fig. 9 presents a schematic representation of the soil-moisture-precipitation feedback that distinguishes between the contributions of these three components of λE.Precipitation impacts the three storage terms on different timescales, which might then impact EF and, thereby, precipitation, forming three interlinked feedback loops.The first loop (C 1 -A 1 -B) acts on a short timescale through W canopy and E I , but is likely absent in our analysis due to the removal of days with morning rain.Indeed, field studies indicate high evaporation rates of intercepted water even at night (e.g., Pearce et al., 1980;Asdak et al., 1998;Holwerda et al., 2012), leading to complete evaporation of W canopy within a few hours.Therefore, evening precipitation is unlikely to provide intercepted water available during the before-noon time period (transparent black-green arrow in Fig. 9).Morning rainfall, on the other hand, may provide before-noon W canopy (black-green arrow) but given that such days may be of synoptic origin, they are excluded from our analysis, as noted previously.Moreover, in the few hours following rain, one may expect well-mixed conditions in the atmospheric boundary layer as well as low surface net radiation.Under these conditions, further rain would be more likely due to dynamical forcing from the atmosphere.The second loop (C 2 -A 2 -B) acts on a longer timescale, typically a few days, through W soil and E soil .Finally, a third loop (C 3 -A 3 -B) acts on a midto long timescale, typically weeks to months, via W roots and E trans .Ultimately, all three loops combine and act together on EF, which can impact precipitation.The distinction between these three components has, to our knowledge, rarely been discussed in the literature in the context of EF-precipitation coupling or soil-moisture-precipitation feedback (with exceptions, e.g., Savenije, 1995b, 2004, for moisture recycling and Scott et al., 1995, 1997, for precipitation persistence).However, they may help to better understand some of our results.
In order to investigate the role of these three components, we compute (X) using NARR data, where X is the water storage term controlling each component instead of EF.  1, where "i" indicates the evaporation component of concern (1 for evaporation from vegetation interception, E I ; 2 for bare soil evaporation, E soil ; 3 for plant transpiration, E trans ).The horizontal axis represents time, ending with day i, and precipitation over the past days to months is represented with its persistence timescales and its typical influence on the three water storage terms shown below: canopy or vegetation interception storage W canopy is affected by precipitation over the previous hours only (C 1 ).Surface soil moisture W top is impacted by precipitation in the previous days to weeks (C 2 ).Root-zone soil moisture W roots is mainly impacted by precipitation in the previous weeks to months (C 3 ).These three storages control their respective evaporation components, and thus EF, in different regions.Over vegetated areas for interception (A 1 ), in a transitional soil-moisture-climate regime for soil evaporation (A 2 ), and in regions which are both vegetated and in a transitional climate regime for transpiration (A 3 ).Note that A 2 and A 3 can also occur in other regions in some circumstances (e.g., over wet regions, during dry years), and W roots includes W top .
Note that for loop 1 (through interception), a coupling cannot be distinguished from storm-scale precipitation persistence as before-noon interception is only expected in the presence of morning rain, mainly reflecting precipitation of synoptic origin.Precipitation over the previous evening usually does not affect before-noon W canopy , but a transparent arrow is shown for rare cases where this might happen.
Step B of the feedback remains a single component as the three evaporation components combine and only the total heat fluxes and their partitioning matter to precipitation occurrence.
these are not available from NARR output.Figure 10a-d  Over the eastern US, most of the signal found with EF does not appear to be related to soil moisture (neither for surface nor for root-zone soil moisture, except in Florida).This suggests that the EF variability is not driven by soil moisture variations in this region.On the other hand, computed with morning vegetation interception storage displays a strong signal, suggesting that most of the signal with EF is linked to interception evaporation.However, (EF) is not strongly sensitive to the exclusion of days with vegetation interception storage (Fig. 10e, while Fig. 10f displays the difference to the computation including all days and is rather small), despite the substantial fraction of days they represent in NARR (15-35 %, Fig. 10g).Since the remaining signal (Fig. 10e) cannot be attributed to vegetation interception, it is likely either due to one of the remaining terms of evaporation or to atmospheric controls on EF through potential evaporation.
To test this hypothesis, the third row of Fig. 10 displays (X) computed on days without vegetation interception and where X is (h) surface soil moisture, (i) root-zone soil moisture, and (j ) potential EF (EF pot = λE pot /(R n −G), i.e., the EF that corresponds to potential evaporation from NARR, which is based on Penman-Monteith equation).Since results are noisy due to the low number of included days, Fig. S5 in the Supplement displays the same analysis for the whole NARR time period .For most of the eastern US, (EF pot ) appears to best reproduce the signal with EF on Supplement Fig. S5, suggesting that atmospheric controls on EF (through EF pot ) at least partly induce the apparent  (EF) computation restricted to days without canopy storage, (f) difference between (EF) computed with all days and with days without vegetation interception storage, and (g) percentage of days with interception storage.Bottom row: (X) restricted to days without interception storage, where X is (h) surface soil moisture, (i) root-zone soil moisture, and (j) potential EF (EF pot ).High (low) X refers to values higher (lower) than the 60th (40th) percentile of X, i.e., (X) = (r|X > X Q60 ) − (r|X ≤ X Q40 ).Values significantly different from 0 at the 90 % level are indicated by a black asterisk.Grey dots indicate sites with no rainy days left.
positive coupling.Such a confounding effect could result from the control of temperature and humidity of the air mass on EF pot , which would then simply be a proxy for the likelihood of the air mass to produce rain, independently of surface fluxes.
Over other regions, we identify different key drivers based on Fig. 10 and Supplement Fig. S5.Over the southwestern US, our analysis highlights surface and root-zone soil moisture as important contributors, with interception playing a smaller role.Over the central US, no conclusion can be drawn from NARR as no EF-precipitation relationship is identified (see also Figs. 2 and 3).
As a sensitivity test, we also investigate the potential role of interception using GLEAM, where, in the default version, before-noon interception storage is neglected as it is based on a Gash analytical model (Gash, 1979), and therefore assumes that the vegetation water storage is evaporated within a model time step (Sect.2.4).Here, we relax this assumption to allow comparison to results from NARR. Figure 11 displays TFS * for the GLEAM-NEXRAD combination as shown earlier (standard version, left) and including interception evaporation from previous-day precipitation (right; see Sect.2.4 for details on the computation).Including interception in that way leads to an increase in significant positive TFS * signal, particularly over the eastern US, which is consistent with the results from NARR.However, we recall that this feature is likely not realistic: theoretical considerations do not support the presence of before-noon intercepted water storage in our analysis.Indeed, interception evaporation rates are high even at night (e.g., Pearce et al., 1980), as these are driven by advected energy or negative sensible heat flux rather than radiation (Pearce et al., 1980;Asdak et al., 1998;Holwerda et al., 2012).Thus, intercepted water evaporates within a few hours: for instance, a compilation of numerous studies on interception finds mean evaporation rates of 0.3 ± 0.1 mm h −1 and canopy storage of 1.2 ± 0.4 mm, leading to complete evaporation of the whole canopy reservoir in 4 ± 1.9 h (Miralles et al., 2010).The presence of interception storage during the before-noon time period is therefore largely restricted to days with morning precipitation, which are not included in our analysis as they are indicative of synoptic rainfall (Sect.3.2).Some exceptions might occur under very humid nighttime atmospheric conditions, preventing intercepted water from evaporating, but these cases likely coincide with morning precipitation and are thus more likely to represent the dynamical forcing from the atmosphere.

Atmos
Thus, these theoretical considerations based on past field studies suggest an overestimation of the impact of interception in NARR, in line with the results from the validation of other climate reanalysis and land-surface models (e.g., Reichle et al., 2011;Van den Hoof et al., 2013;Davies-Barnard et al., 2014).This could be due to the parameterization of interception as a function of E pot (Chen et al., 1996), with interception unrealistically affected by net radiation (see Shuttleworth and Calder, 1979).Time series in NARR strongly support this hypothesis, showing that before-noon interception storage is most often provided by afternoon or evening precipitation on the previous day which does not evaporate in the night (see Supplement S5 and Fig. S6).
Overall, analyzing the role of individual components of λE in the relationship between EF and subsequent precipitation leads to similar conclusions in NARR and in GLEAM-NEXRAD.In the eastern US, vegetation interception evaporation and atmospheric controls on EF can lead to a likely overestimated relationship, due to, respectively, the fast rates of evaporation of intercepted water (see above) and the atmospheric origin of the signal.In the central and southwestern US, soil moisture (surface and root zone) drives the relationship where it exists, which would be consistent with the existence of a positive soil-moisture-precipitation feedback.These findings fit well with expectations based on climate regimes and vegetation cover: Fig. 12a highlights a wet regime in the eastern US, where land evaporation is controlled by radiation rather than soil moisture, unlike the soilmoisture-limited regime of the central and western US.In addition, vegetation interception is likely more relevant in the eastern US than in the central and southwestern US, as indicated by a high leaf area index in Fig. 12b.Although we recall that the interception-related findings from NARR are not consistent with knowledge from field studies for the above-mentioned reasons, an impact of evening or nighttime interception evaporation via moisture recycling remains possible on longer timescales.

Discussion and conclusions
A recent study (Findell et al., 2011)  (triggering feedback strength), based on data from the North American Regional Reanalysis (NARR), and suggests the existence of an extended region of positive land-surfaceprecipitation coupling over the eastern US.Our study extends that analysis with a systematic cross validation of additional, independent, observation-driven data sources and an in-depth investigation of all components contributing to the identified pattern from Findell et al. (2011).
Comparing the relationship patterns from the different data set combinations, the FLUXNET-NEXRAD and GLEAM-NEXRAD combinations do not reproduce positive TFS * in the eastern US found in NARR.Higher noise levels in these data sets and uneven sampling of different land cover types in the FLUXNET data may contribute to the differences.Nevertheless, our results suggest that land-surface dynamics in NARR and their stronger apparent coupling with precipitation in the eastern US might reflect model artifacts (see also Ferguson et al., 2012, who find that surface soil moisture from NARR correlates poorly with remote-sensing estimates in the eastern US).Conversely, a significant relationship between EF and convection triggering is found for the observation-driven GLEAM-NEXRAD combination in the central US (consistent with, e.g., Koster et al., 2004), although no such signal emerges from NARR in this region.The FLUXNET-NEXRAD combination displays low TFS * values there, possibly due to higher noise levels and short samples.Similarly, NARR might underestimate a possible EF-precipitation coupling in these regions.In the area of the southwestern US close to the Mexican border, all data sets agree on the existence of significant relationships between EF and convective triggering.
We find that the choice of the EF data set has a large impact on the relationship between EF and convection triggering, although the patterns of average EF, EF variability, and persistence in the different data sets do not clearly indicate the sources of this discrepancy.This comparison is further hampered by short observational records, uncertainties, and different spatial scales.
Furthermore, we find that precipitation of the previous day is a better predictor of afternoon precipitation than beforenoon EF, pointing to a short timescale dominance of the atmosphere over land.Although EF seems to provide a small additional predictability to precipitation alone, the confounding effects of precipitation on EF via soil moisture or intercepted water precludes definite conclusions on the existence of a land-precipitation coupling at this stage.Accounting for the individual components of land evaporation (plant transpiration, bare soil evaporation, and evaporation of intercepted water) in the analysis, we find that the coupling, if present, arises from distinct sources in different regions.
Over the eastern US, atmospheric controls on EF (i.e., the atmospheric demand through potential evaporation) and vegetation interception drive the EF-precipitation relationship in NARR.Atmospheric controls on EF might induce an apparent relationship, but identifying these drivers as, for example, in Aires et al. (2013) lies beyond the scope of this study.The unrealistic presence of before-noon intercepted water from previous evening rainfall in NARR, likely due to an underestimation of the rates of evaporation of intercepted water at night, may falsely contribute to the positive TFS * over the eastern US, in line with the GLEAM-NEXRAD experiment (Fig. 11).This questions the reliability of NARR for these applications, despite its real advantage of high-quality precipitation assimilation.Other reanalysis products have issues with the representation of interception, e.g., MERRA (where the MERRA-Land product corrects for interception parameters among others; Reichle et al., 2011).These findings suggest a relatively short timescale of the EF-precipitation relationship in this region in NARR, which is consistent with the role of day-to-day precipitation persistence.Establishing a causal link between atmospheric-and interception-driven EF and precipitation is thus very difficult.Finally, we find that the EF-precipitation relationship found in NARR in the eastern US is not related to soil moisture, which makes sense given the humid climate regime with an expected low control of soil moisture on EF in this region, unlike what has been diagnosed in several studies for the central US (e.g., Koster et al., 2004;Teuling et al., 2009;Seneviratne et al., 2010).
The processes in central and southwestern US are, indeed, different from those in the eastern US.Wherever significant positive relationships between EF and precipitation occurrence are found in GLEAM-NEXRAD or NARR, soil moisture is identified as the primary driver.This is consistent with the soil-moisture-limited evaporation regime in this transitional region (Koster et al., 2004;Seneviratne et al., 2010;Mueller and Seneviratne, 2012) and aligns well with expected regions of soil-moisture-precipitation coupling (e.g., Koster et al., 2004).
A number of processes are not considered in our analysis, such as the dominance of orographic lifting over landatmosphere interactions over the northwestern US where evaporation is soil-moisture-limited (e.g., Schwalm et al., 2012), the effects from different land covers (e.g., young vs. mature forests; see Vickers et al., 2012), or other processes acting at smaller scales than those considered here.Detailed analysis of these local features is, however, beyond the scope and spatial scale of our study.
A small part of the signal in the eastern US in NARR cannot be attributed to vegetation interception, soil moisture, and EF pot .Nonlinear interactions between these variables possibly explain this signal, but the assimilation procedure may also affect it in a way that is difficult to assess.In GLEAM, the adjustments that were made to get estimates of beforenoon EF introduce additional uncertainties that are difficult to quantify.Here we note that the reliability of the estimates is expected to decrease with increasing temporal resolution (Miralles et al., 2011b).
The presence of before-noon vegetation interception storage on days without morning precipitation is unlikely (based on previous field measurements, e.g., Pearce et al., 1980;Asdak et al., 1998;Holwerda et al., 2012).Thus, interception does not likely play a strong role for the triggering of convective storms via morning surface fluxes.Nonetheless, a direct impact via moisture recycling is possible and has already been suggested in the past (e.g., Savenije, 1995a, b).Additional moisture input to the atmosphere may thus provide more rainfall downwind on a longer timescale than the diurnal scale analyzed here.Indeed, evaporation from intercepted water has been estimated to amount to ∼ 11 % of global land evaporation (Miralles et al., 2011a) and to 20-50 % over forests (e.g., Savenije, 2004;McLaren et al., 2008;Gerrits and Savenije, 2011).
The discrepancies between the coupling patterns of precipitation with soil moisture and EF, respectively, as well as the here-proposed explanations through interception evaporation and atmospheric controls on EF, have hardly been addressed in the recent literature on land-precipitation coupling (e.g., Findell and Eltahir, 2003a;Seneviratne et al., 2010;Findell et al., 2011;Taylor et al., 2011;Ferguson et al., 2012;Taylor et al., 2012).This adds to the complexity of this coupling but possibly explains some of the contradictions from recent studies (e.g., Findell et al., 2011;Ferguson et al., 2012;Taylor et al., 2012).We show that not only the individual segments of the soil-moisture-precipitation coupling (Fig. 1; Wei and Dirmeyer, 2010;Dirmeyer, 2011), but also the individual components of λE may be crucial to uncover remaining uncertainties in land-atmosphere coupling.
Given the many unresolved issues in the investigation of land-precipitation coupling, further studies are required to pin down this complicated relationship.Analyses of the feedback accounting for precipitation persistence and confounding variables, applied to different temporal and spatial scales and a wide range of data sets, are urgently needed.Moreover, improvements in models would allow for more realistic sensitivity studies.Finally, soil moisture and EF observations at scales relevant to land-atmosphere coupling (i.e., 10 km) would provide invaluable observational constraints on model results and understanding of land-atmosphere coupling.
The Supplement related to this article is available online at doi:10.5194/acp-14-8343-2014-supplement.

Figure 1 .
Figure 1.Schematic description of the soil-moisture-precipitation coupling and feedback loop.Positive arrows (blue) indicate processes leading to a positive soil-moisture-precipitation feedback (wetting for positive soil moisture anomaly, drying for negative soil moisture anomaly), the negative arrow (red) indicates a potential negative feedback damping the original soil moisture anomaly, and the red-blue arrow indicates the existence of both positive and negative feedbacks between evaporative fraction (EF) and precipitation anomalies.(A), (B), and (C) refer to the different steps of the feedback loop (see text).Modified from Seneviratne et al. (2010).

Figure 2 .
Figure 2. Triggering feedback strength (TFS * ) in different data sets computed at FLUXNET sites.(left) Evaporative fraction (EF) and precipitation data from NARR, (center) EF from FLUXNET and precipitation from NEXRAD, and (right) EF from GLEAM and precipitation from NEXRAD.TFS * values significantly different from 0 at the 90 % level are indicated by a black asterisk.In case of overlap, points are shifted and the black lines inside the circles indicate the actual location of the station.Empty dots indicate sites with unreliable NEXRAD data.

Figure 3 .Figure 4 .
Figure 3. Quantitative comparison of the triggering feedback strength (TFS * ) in different regions for the three data sets shown in Fig. 2. (top) Definition of the regions.(bottom) Box plot of TFS * in the three regions, where numbers below boxes indicate the fraction of sites with significant TFS * .Central lines denote medians, boxes show interquartile ranges, and whiskers denote minimum and maximum values.Empty dots on the map indicate sites with unreliable NEXRAD data and which are excluded from the box plot.

Figure 5 .
Figure 5. Correlation of daily JJA before-noon EF values between different data sets.The size of the dots indicates the number of days included in the computation according to the legend shown on the bottom right, and significant correlations at a 99 % level are indicated by a black asterisk.Empty dots for GLEAM indicate sites with unreliable NEXRAD (and thus GLEAM) data.

Figure 6 .
Figure 6.Statistical properties of EF data sets (NARR, FLUXNET, GLEAM, from left to right): (top) mean (EF), (middle) standard deviation (σ EF ), and (bottom) decorrelation timescale (τ d Only days with data in all three data sets are included in the computation.The decorrelation timescale τ d is computed following von Storch and Zwiers (1999).Grey dots indicate too many gaps for a reliable quantification of τ d .Empty dots for GLEAM indicate sites with unreliable NEXRAD data.

Figure 7 .Figure 8 .
Figure7.Difference in the probability of afternoon rainfall on days with high vs. low X, (X), where X is the before-noon EF (left panels) or previous-day precipitation (right panels), for NARR (top row) and GLEAM-NEXRAD (bottom row).High (low) X refers to values higher (lower) than the 60th (40th) percentile of X, i.e., (X) = (r|X > X Q60 ) − (r|X ≤ X Q40 ).Values significantly different from 0 at the 90 % level are indicated by a black asterisk.The size of the dots indicates the number of days included in the computation according to the legend shown on the bottom right map.Empty dots indicate sites with unreliable NEXRAD data.

Figure 9 .
Figure9.Different water storage components contributing to λE and their potential relevance for afternoon convective precipitation.The letters (A i , B i , C i ) refer to the steps of the feedback loop shown in Fig.1, where "i" indicates the evaporation component of concern (1 for evaporation from vegetation interception, E I ; 2 for bare soil evaporation, E soil ; 3 for plant transpiration, E trans ).The horizontal axis represents time, ending with day i, and precipitation over the past days to months is represented with its persistence timescales and its typical influence on the three water storage terms shown below: canopy or vegetation interception storage W canopy is affected by precipitation over the previous hours only (C 1 ).Surface soil moisture W top is impacted by precipitation in the previous days to weeks (C 2 ).Root-zone soil moisture W roots is mainly impacted by precipitation in the previous weeks to months (C 3 ).These three storages control their respective evaporation components, and thus EF, in different regions.Over vegetated areas for interception (A 1 ), in a transitional soil-moisture-climate regime for soil evaporation (A 2 ), and in regions which are both vegetated and in a transitional climate regime for transpiration (A 3 ).Note that A 2 and A 3 can also occur in other regions in some circumstances (e.g., over wet regions, during dry years), and W roots includes W top .Note that for loop 1 (through interception), a coupling cannot be distinguished from storm-scale precipitation persistence as before-noon interception is only expected in the presence of morning rain, mainly reflecting precipitation of synoptic origin.Precipitation over the previous evening usually does not affect before-noon W canopy , but a transparent arrow is shown for rare cases where this might happen.Step B of the feedback remains a single component as the three evaporation components combine and only the total heat fluxes and their partitioning matter to precipitation occurrence.
displays in NARR computed with (a) EF, (b) surface soil moisture (for E soil ), (c) root-zone soil moisture (for E trans ), and (d) vegetation interception storage (for E I ).All these variables represent before-noon (9 a.m.-12 p.m.) values.The definition of surface and root-zone soil moisture in NARR is provided in Sect.2.1.

Figure 10 .
Figure10.Identification of the drivers of the EF-precipitation relationship in NARR (see Supplement Fig.S5for the same analysis using the longer NARR time period).Top row: difference in the probability of afternoon rainfall, (X) on days with high vs. low X, where X is the before-noon value of the different drivers.From left to right, X is (a) EF and (b-d) the three water storage terms that control EF: (b) surface soil moisture (W top , controls bare soil evaporation), (c) root-zone soil moisture (W root , controls plant transpiration), and (d) vegetation (canopy) interception storage (W canopy , controls interception evaporation).Middle row: (e)(EF) computation restricted to days without canopy storage, (f) difference between (EF) computed with all days and with days without vegetation interception storage, and (g) percentage of days with interception storage.Bottom row:(X) restricted to days without interception storage, where X is (h) surface soil moisture, (i) root-zone soil moisture, and (j) potential EF (EF pot ).High (low) X refers to values higher (lower) than the 60th (40th) percentile of X, i.e., (X) = (r|X > X Q60 ) − (r|X ≤ X Q40 ).Values significantly different from 0 at the 90 % level are indicated by a black asterisk.Grey dots indicate sites with no rainy days left.

Figure 11 .
Figure 11.Influence of interception evaporation on TFS * in the GLEAM-NEXRAD combination.Left: interception is not included in the EF computation.Right: interception is included in the EF computation and EF is then capped at 1. Values significantly different from 0 at the 90 % level are indicated by a black asterisk.Empty dots indicate sites with unreliable NEXRAD data.

Table 2 .
Data sets used in GLEAM product.Daily aggregates are computed locally to match the before-noon evaporative fraction (EF) estimate (i.e., starting and ending at around 9 a.m.; see Sect.2.4).S and E pot are the evaporative stress and the potential evaporation, respectively.See Sect.2.4 for details.