An index of the sensitivity of surface fluxes to soil moisture variations is defined that elaborates on the correlation between soil moisture and fluxes to include the magnitude of the forced variations of fluxes across typical ranges of soil moisture variability. This index better represents the strength of the terrestrial segment of the feedback pathway from soil moisture to climate than correlations alone. Maps of this sensitivity index show strong agreement with “hot spots” of land-atmosphere coupling and land-driven predictability enhancement found in other studies. The index is found to be robust across data from land surface models driven by observations and free-running global coupled land-atmosphere models, but is compromised in reanalysis data due to inflated interannual variability in soil moisture caused by non-stationarity in the satellite observing system that is used in data assimilation. The index can be calculated from daily observations or model output of sufficient length to ensure statistical significance of results.
 The land surface has long been recognized as second in importance only to ocean surface temperatures as a driver of climate [National Research Council, 1994]. The land and atmosphere are interlocked by coupled hydrologic and energy cycles that are a major part of the Earth's climate system [Sorooshian et al., 2005]. Recent multi-institutional studies with a combination of operational and research models for global weather prediction and climate simulation have demonstrated the potential for land surface states (predominantly soil moisture) to affect the atmosphere in key regions [Koster et al., 2004, 2006] and for knowledge of the land state to improve the skill of forecasts [Koster et al., 2011].
 There is an obvious and direct response of soil moisture to precipitation, but the feedback via the return path from soil moisture through evapotranspiration (latent heat flux) to precipitation is weaker and subtler [Seneviratne et al., 2010]. Additionally, in a moisture-limited regime, soil moisture variations also affect sensible heat fluxes via partitioning of available energy at the land surface [Santanello et al., 2009]. The effect of soil moisture anomalies on the lower atmosphere results in a direct correlation with near-surface humidity, but an inverse relationship with temperature, and thus the growth of the boundary layer [Betts et al., 1996; Betts, 2004].
 The connection from land surface states to atmospheric response can be considered to have two segments: soil state to surface fluxes, and surface fluxes to atmospheric states and precipitation [Guo et al., 2006; Santanello et al., 2011]. The first or terrestrial segment has been characterized by the correlation in time between variations in soil moisture and evapotranspiration [e.g., Dirmeyer et al., 2009]. A positive contemporaneous correlation between the two indicates variations in soil moisture are the controlling factor and variations in evapotranspiration are the response. This occurs where there is some degree of soil moisture deficit such that it, and not availability of net radiative energy at the surface, determines evapotranspiration [Koster et al., 2009a]. A negative correlation occurs where soil moisture is plentiful but available energy is the limiting factor. In this situation, high net radiation increases evapotranspiration, drawing down soil moisture, whereas low net radiation reduces evapotranspiration. A positive correlation between soil moisture and evapotranspiration is a necessary but not sufficient condition for the land surface state to affect the atmosphere – the linkage could still break down depending on the second or “atmospheric” segment of land-atmosphere coupling.
 Here we present a refinement to the notion of correlation as a marker for the potential of strong land-atmosphere feedback. Specifically, we look beyond correlation to other properties of the relationship between soil moisture and surface fluxes that carry useful physical meaning. Several independent global data sets are investigated for common properties, corroborating results with previous studies.
2. Method and Data
 We examine three independent global datasets of soil moisture and surface fluxes. In each case, we use surface soil moisture taken from the top soil level of each data set, and values from a deeper column, defined according to available data. The multi-model analysis from the Second Global Soil Wetness Project (GSWP-2) [Dirmeyer et al., 2006] provides daily global fields of land surface state variables and surface fluxes for the period 1986–1995 generated by a suite of land surface models driven by the same observationally-based near-surface meteorology. The data are provided on a 1° global grid over land. The surface level soil moisture represents a layer reaching to 10 cm below the surface. For root layer soil moisture, we use values between 0–70 cm depth.
 The global Modern Era Retrospective-analysis for Research and Applications (MERRA) of Rienecker et al.  provides estimates of state and flux variables in a coupled land-atmosphere model employing data assimilation to generate realistic estimates constrained by observations. The Goddard Earth Observing System (GEOS-5) atmospheric model is the basis for this reanalysis. We use the first 30-years of the reanalysis daily fields from 1979–2008 on the native grid resolution of 2/3° longitude by 1/2° latitude. The upper soil layer is 2 cm deep, and root zone soil wetness represents the top 100 cm of soil. Additionally, we use two other sets of land surface data generated uncoupled from the atmospheric model; a “MERRA-Land” product where precipitation biases are corrected and the land surface model is adjusted to reduce canopy interception, and a “MERRA-Fortuna” product which has only the land model adjustment, but retains the original MERRA meteorological fields [Rienecker et al., 2011; Reichle et al., 2011].
 A free-running GCM simulation with specified observed sea surface temperatures is also examined, employing the Integrated Forecast System (IFS) global model of the European Centre for Medium-Range Weather Forecasts (ECMWF) integrated for the period 1961–2007 (J. L. Kinter III et al., Revolutionizing climate modeling – Project Athena: A multi-institutional, international collaboration, submitted to Bulletin of the American Meteorological Society, 2011). Unlike the GEOS-5 model, IFS is used for operational weather prediction and its forecasts are validated daily. It has been run at a spatial resolution of ∼16 km. Soil moisture from the top 7 cm thick layer and the entire column (289 cm) are used in this analysis.
 As mentioned earlier, local temporal correlations between soil moisture and surface fluxes are useful for determining the coupling regime of the terrestrial segment of the land-atmosphere feedback pathway. However, this metric has shortcomings. What if correlations are found to be significant, but surface flux changes are small across the range of soil moisture variations? Conversely, what if surface fluxes are sensitive to changes in soil moisture, but soil moisture itself tends to vary little?
 We address these possibilities by calculating simple additional metrics. To quantify the sensitivity of surface fluxes to soil moisture, we calculate the slope of the linear regression of fluxes against soil moisture. The relationship between latent heat flux and soil moisture, for instance, has been shown to consist of a curve of varying slope, with a range of high sensitivity at low to intermediate soil moisture, and a range of low sensitivity at high values of soil moisture, with details depending on soil and vegetation properties [e.g., Dirmeyer et al., 2000]. However, for this exercise, we are concerned about the relationship across the typical range of soil moisture for the locale, where a simple linear regression captures this property well [Koster and Milly, 1997]. For each grid point, we estimate the slope βϕ by a linear regression of the flux or flux metric (e.g., evaporative fraction) ϕ on the soil moisture w (definitions vary slightly depending on the data set). Slopes are calculated for each of 12 months using deviations from the local climatological annual cycle. A similar calculation determines the correlation with soil moisture rϕ.
 To account for the possibility that soil moisture may be nearly invariant where there otherwise is large correlation and slope, we also estimate the standard deviation of daily soil moisture sw calculated across all dates of a month across all years. The index of surface flux sensitivity to representative soil moisture variability is:
Iϕ has the same units as ϕ, and since forms of the soil moisture variance are in both terms (the denominator of the slope term), the impact of specious differences in soil moisture between data sources is minimized. We mask by the value of the correlation ∣rϕ∣ > rc, where rc is a critical significance threshold of 99% confidence. In all calculations, we use daily data and perform estimates on a monthly basis. Using conservative estimates of the number of degrees of freedom (one fifth the total number of days owing to lagged autocorrelations), rc = 0.30, 0.173 and 0.14 for the GSWP-2, MERRA and IFS data respectively.
 Finally, we break down the variance of soil moisture into intra-seasonal and interannual components. We use 30 years of data from IFS and MERRA, and 10 years from GSWP-2. Interannual deviations for a certain day and month:
and intra-monthly deviations for each month and year:
are used to estimate the interannual standard deviation for each month:
while the intra-seasonal standard deviation is calculated as:
Here y represents the year and d the day of the month; D is chosen to be the same as the number of years Y, sampled at equal intervals throughout the month (e.g., for 30 years data, days 1–30 are used, wrapping into March for February estimates, while we use every third day (1st, 4th, 7th, etc.) for 10 years of GSWP-2 data). For the intra-seasonal estimate, y day-to-day variances are calculated and averaged together. For the interannual standard deviation, the variance is calculated across y years for the 1st day of the month, for the 2nd (or 4th for GSWP-2), and so on, and those d estimates are averaged. Seasonal values for all terms are calculated as the average across each month in the season.
 We show results for latent heat flux only. We have examined sensible heat flux and evaporative fraction as well, and the relationships between soil moisture and each of these flux terms vary largely in kind. Figure 1 depicts the annual cycle of ILH calculated from the GSWP-2 surface layer soil moisture. Regions where the correlation between soil moisture and surface latent heat flux are not significant at the 95% confidence level have been masked out. The boreal summer map bears a strong resemblance to the pattern of “hot spots” of land-atmosphere coupling from Koster et al. [2004, 2006]. The seasonal evolution shows that the regions of largest positive values, where there is the greatest soil moisture-driven variance in latent heat flux, are predominantly in the transitions between arid and humid zones and tend to follow the fringes of monsoon regions. Particularly large values are found over the Bengal coast of India, southern Mexico, the Guinea Coast and Horn of Africa during boreal spring, the Great Plains, Sahel and Indus Valley during boreal summer, and much of Australia, southern Africa and the Pampas of South America during austral summer. Negative values are seen in high latitudes after snowmelt, and in some wet low-latitude areas. Eastern China is a particularly persistent area of negative ILH, suggesting that soil moisture here is driven by surface fluxes and it does not typically exert a feedback on the atmosphere.
 Calculations of ILH using soil moisture at varying depths and from independent data sets reveal strong consistencies. Figure 2 shows the JJA values of the index ILH for GSWP-2, IFS and two of the MERRA products using both surface layer and deeper soil moisture values for each. For IFS, the total column soil moisture represents a depth of nearly 3m, well below the reach of roots, so the values are muted compared to the surface soil moisture based index, and differences are greater than for other products. The spatial patterns, however, are quite consistent. More remarkable is the agreement between GSWP-2, an ensemble of land models driven by observed analyzed near-surface meteorology, and IFS, a free-running coupled land-atmosphere model. The regions of large positive values of ILH are strikingly similar. MERRA reproduces high values in the same areas, but also in many other regions where the other two products do not. In the Tropics and Southern Hemisphere, this is due to high values of soil moisture variability sw. In the Northern Hemisphere mid-latitudes and subtropics, both sw and βLH appear to be responsible. MERRA-Replay shows many of these same features, while MERRA-Land resembles GSWP more closely. The auxiliary material shows that the differences between MERRA-Land and MERRA appear to come from both changes to the land model and precipitation forcing.
 We have produced a revised sensitivity index for diagnosing the terrestrial component of land-atmosphere coupling that takes into account not only the correlation between soil moisture and surface heat fluxes, but also the potential for soil moisture fluctuations to result in large surface flux variations. The method depends on a consistent assessment of soil moisture variance at a point, which is found to be difficult using long reanalysis data sets where non-stationarity in the observing system, particularly satellite platforms, strongly perturb the analysis of the hydrologic cycle. Variational bias correction may ameliorate such problems [Dee and Uppala, 2009]. In a free-running global weather model and in offline land surface model runs constrained by observed precipitation, the method appears to produce robust consistent results. The effect of different soil moisture variance characteristics, so problematic in model comparisons [Koster et al., 2009b], is minimized in the construction of the index.
 The sensitivity index reflects quite well the “hot spots” from previous ensemble-based multi-model studies [e.g., Koster et al., 2006], with the advantage that by its construction it can be applied to single-member model simulations or to observations. It also agrees well with locations where realistic land surface initialization may improve forecasts on sub-seasonal to seasonal time scales [Koster et al., 2011]. However, the index isolates the terrestrial segment of land-climate coupling and does not diagnose how strongly perturbed surface fluxes could affect the near-surface atmospheric state, the planetary boundary layer, clouds or precipitation. This sensitivity index points out regions with necessary but not sufficient conditions for strong land-atmosphere coupling. Together with a diagnosis of the planetary boundary layer's ability to convert surface flux anomalies into weather and climate anomalies [e.g., Santanello et al., 2011], a thorough diagnosis of potential land surface impacts on forecast skill and climate variations may be possible.
 Thanks to Qing Liu and Rolf Reichle for providing additional MERRA land surface data sets, and to two reviewers for their helpful comments. 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 Randal Koster and an anonymous reviewer for their assistance in evaluating this paper.