## Abstract

An idealized prototype for the location of the margins of tropical land region convection zones is extended to incorporate the effects of soil moisture and associated evaporation. The effect of evaporation, integrated over the inflow trajectory into the convection zone, is realized nonlocally where the atmosphere becomes favorable to deep convection. This integrated effect produces “hot spots” of land surface–atmosphere coupling downstream of soil moisture conditions. Overall, soil moisture increases the variability of the convective margin, although how it does so is nontrivial. In particular, there is an asymmetry in displacements of the convective margin between anomalous inflow and outflow conditions that is absent when soil moisture is not included. Furthermore, the simple cases presented here illustrate how margin sensitivity depends strongly on the interplay of factors, including net top-of-the-atmosphere radiative heating, the statistics of inflow wind, and the convective parameterization.

## 1. Introduction

As transition zones between strong and weak mean precipitation regimes, the margins of tropical land region convection zones experience significant variability. Interannually, some of the most severe droughts occur as localized spatial shifts in the margins of convection zones. Moreover, the tropical hydrologic cycle signatures of greenhouse gas–induced climate change as simulated by models are often strongly localized along particular convective margins, albeit with significant intermodel differences regarding precisely where such changes occur (Williams et al. 2001; Douville et al. 2002; Johns et al. 2003; Soden and Held 2006; Neelin et al. 2006; Solomon et al. 2007; Chou et al. 2009).

Given the variability inherent to convective margins, there is a need for detailed mechanistic understanding of the factors controlling their behavior. In previous work, Lintner and Neelin (2007; hereafter LN07) developed a simple prototype to describe convective margins under idealized conditions of low-level dry air inflow into a land region from an adjacent ocean. The LN07 prototype demonstrates how the characteristics of such inflow convective margins—for example, the location of the transition between nonconvecting and convecting conditions—depend on dynamic and thermodynamic variables, including low-level circulation, inflow moisture, and tropospheric temperature.

For simplicity, the LN07 analysis neglected effects of land surface conditions such as soil moisture on convective margins. Of course, the capacity of the land surface to retain moisture significantly influences the climate system. Soil moisture directly affects surface–atmosphere energy fluxes through evaporation, which modulates the partitioning of the surface energy budget (Charney 1975; Shukla and Mintz 1982; Delworth and Manabe 1988). Soil moisture further constrains vegetation, thereby affecting surface parameters such as albedo and surface roughness that in turn affect surface radiative properties and turbulent exchanges of energy, moisture, and momentum (Xue and Shukla 1993). The persistence of soil moisture on seasonal or longer time scales provides a source of memory to the climate system (Vinnikov et al. 1996), as do slowly varying vegetation characteristics related to soil moisture (Delire et al. 2004; Notaro et al. 2006).

Much interest has focused on the influence of soil moisture on precipitation and its variability, especially the positive feedback through which anomalous precipitation conditions are self-sustained and amplified by the land surface state. The existence of such feedbacks has implications for predictability and long-range forecast skill—for example, land–atmosphere interactions are thought to play a role in the persistence of drought conditions (Hong and Kalnay 2000; d’Odorico and Porporato 2004). Observational studies based on large-scale irrigation projects (Stidd 1975; Barnston and Schickedanz 1984; Moore and Rojstaczer 2002), soil moisture field measurement networks (Findell and Eltahir 1997, 1999), and precipitation persistence statistics (Taylor et al. 1997; Taylor and Lebel 1998; Taylor et al. 2003; Koster and Suarez 2004) point to the operation of the soil moisture–precipitation feedback in nature. General circulation models (GCMs) also manifest the soil moisture–precipitation feedback (Atlas et al. 1993; Beljaars et al. 1996; Zheng and Eltahir 1998; Pal and Eltahir 2001, 2003; D’Odorico and Porporato 2004), although fundamental questions remain regarding the magnitude and sensitivity of the feedback to model parameterizations (Koster et al. 2004; Dirmeyer et al. 2006; Wu et al. 2007; Steiner et al. 2009).

An emergent feature of the simulated soil moisture–precipitation feedback is the occurrence of hot spots, locations of strong land surface–atmosphere coupling (Koster et al. 2004; Guo et al. 2006; Notaro 2008). Within the tropics, such hot spots typically appear in the convective margins. Koster et al. (2004) stressed the role of soil moisture in producing locally intensified soil moisture–precipitation coupling. Within the driest regions, evaporation exhibits significant sensitivity to soil moisture but evaporation rates are small, with limited potential to affect precipitation. Within the wettest regions, soil moisture perturbations cause only small variations in evaporation because the sensitivity of evaporation to soil moisture diminishes as the surface approaches saturation. It is between the wettest and driest extremes that soil moisture perturbations are most conducive to driving variations in precipitation.

Although the role of atmospheric dynamics and convection is inherent in this view of hot spots, the focus of the present study is to elucidate the atmospheric side of land–atmosphere coupling. In particular, we consider circumstances under which the large-scale inflow air mass characteristics into a land region convection zone modulate precipitation along the convective margin, with an emphasis on diagnosing the interplay of margin variability and the underlying surface conditions. Because our principal objective is to develop insights into soil moisture influences on convective margin variability, we develop analytic prototypes that are intended to illustrate some basic mechanisms. We also employ an intermediate level complexity model coupled to a simplified land surface scheme. What this model lacks in terms of realism is leveraged against the ease with which it can be analyzed and interpreted, although even the simple cases considered are nontrivial. We further explore the extent to which the results of this analysis may be applied to more complex models and observations.

## 2. Soil moisture effect inferred from an intermediate level complexity model

The model used is the first Quasi-Equilibrium Tropical Circulation Model, version 2.3 (QTCM1; Neelin and Zeng, 2000; Zeng et al. 2000), an intermediate-level complexity model of the tropical troposphere. An advantage of QTCM1 over GCMs is the simplicity of the model framework: the QTCM1’s transparency facilitates diagnosis in ways that are not always feasible or straightforward with GCMs. The simplicity of QTCM1 has proved useful for elucidating many tropical climate phenomena, including tropical ocean–atmosphere coupling (Su et al. 2003), El Niño–Southern Oscillation (ENSO) tropical teleconnections (Neelin and Su 2005), climate sensitivity to global warming (Chou and Neelin 2004), intraseasonal variability (Lin et al. 2000), monsoons (Chou and Neelin 2003), and vegetation–atmosphere interactions (Zeng et al. 1999).

The QTCM1 simulations considered here represent the land surface moisture through a simple bucket model (Zeng et al. 2000), with evaporation *E* linearly proportional to potential evaporation *E _{p}*; that is,

*E*=

*β*(

*w*)

*E*, where the evaporation efficiency

_{p}*β*(

*w*) is a function of the soil wetness

*w*. The latter is a dimensionless quantity obtained by normalizing the soil moisture content by the soil moisture holding capacity

*w*

_{0};

*w*ranges between 0 and 1, with

*w*= 0 (

*w*= 1) representing a completely dessicated (saturated) surface; although,

*w*effectively maximizes at values <1 because of constraints imposed by atmospheric and surface energy balances. In our implementation,

*β*(

*w*) =

*w*and

*w*

_{0}= 150 mm unless otherwise stated. The total surface runoff is modeled as

*w*, where

^{γ}P*P*is precipitation and

*γ*= 4. Although the bucket model neglects many features necessary to provide a fully realistic picture of land–atmosphere coupling (e.g., vegetation, partitioning of evaporation into transpiration and soil evaporation, plant rooting depth, and multiple soil layers), it retains sufficient complexity to produce nontrivial behavior.

We consider first a set of experiments motivated by approaches to investigate soil moisture effects in prior studies (e.g., Koster et al. 2004). In particular, we performed a control simulation (denoted CTL) and a sensitivity simulation in which *β*(*w*) was fixed to a climatology that produces the same mean evaporation as in a CTL, that is, *β*(*w*)* = [ + /]_{CTL}; the latter is denoted “FIXED-*β*.” Here, overbars and primes denote time means and deviations from time means, respectively. Each simulation was forced with imposed climatological monthly-mean sea surface temperatures (SSTs), such that the variability present arises solely from QTCM1’s internal dynamics. The simulations were performed at a horizontal resolution of 1.406 25° × 1°, with output saved as 5-day (pentadal) means for 25 years.

Figure 1a illustrates 3-month seasonal mean precipitation standard deviations of the CTL run for tropical South America (shaded contours). For comparison, the seasonal mean climatologies (line contours) are also shown. In general, the largest variability occurs not at the highest mean rainfall (>14 mm day^{−1}) but rather at somewhat lower values (4–10 mm day^{−1}), that is, along the convective margins. Note that the lack of interannually varying SSTs means that important contributions to observed precipitation variability such as ENSO are absent in the QTCM1 simulations. A further caveat is that QTCM1, like many models, may overemphasize margin variability because the model simulates too little variability in the interior of the convection zone (Lin et al. 2000).

The ratio of to the standard deviation of the FIXED-*β* simulation provides a measure of the importance of interactive soil moisture variations to total precipitation variability in QTCM1 (Fig. 1b, shaded contours). Generally, the largest increases of precipitation variability by interactive soil moisture are localized to the convective margins, although there is considerable spatial variation in the effect. However, the geographic distribution of soil moisture amplification of precipitation variability over tropical South America is broadly consistent with the pattern of soil moisture–precipitation coupling hot spots evident in prior studies [cf. Fig. 1 of Koster et al. (2004) for a comparison to June–August (JJA)]. Other regions of strong soil moisture–precipitation coupling in QTCM1 include the Sahel region of Africa and northern Australia (not shown). QTCM1’s ability to simulate hot spots means that the model has potential utility in diagnosing hot spot genesis, as discussed in section 5. In the following section, we employ an analytic prototype to address modifications to convective margin behavior in the presence of soil moisture and evaporation.

## 3. Incorporating evaporation into the convective margins framework

### a. Setup

As in LN07, we consider 1D steady-state, vertically integrated tropospheric temperature (*T*) and moisture (*q*) equations applied to a land region adjacent to an ocean region, as is the case over northeastern South America (Fig. 2; see section 6 for a discussion of caveats to applicability of the prototype to this region):

Here, *R*_{surf} and *R*_{toa} are the net surface and top-of-the-atmosphere shortwave plus longwave radiative heating, respectively; *E* is latent heat flux (evapotranspiration); *H* is sensible heat flux; and *P* represents convective heating in (1) or drying in (2). For *T* and *q* in units of kelvin (the latter by absorbing the ratio of latent heat of condensation, *L*, to heat capacity at constant pressure, c* _{p}*), the radiative, turbulent heating, and convective fluxes are dimensionalized to K s

^{−1}(normalizing by c

*Δ*

_{p}*pg*

^{−1}, where Δ

*p*is the tropospheric pressure depth and

*g*is acceleration due to gravity, respectively). The terms on the left-hand side of each equation are related to vertical heat and moisture flux convergence, with

**∇**·

**v**(units of s

^{−1}) related to the convergence of the flow (signed positive for conditions of low-level convergence), and

*M*and

_{s}*M*=

_{q}*M*(K) are dry static stability and moisture stratification, respectively (Yu et al. 1998). The first term on the right-hand side of (2) is the horizontal moisture advection, with

_{qp}q*u*(m s

_{q}^{−1}) the projection of the wind field onto the vertical structure of

*q*. A comparable term in the temperature equation is neglected because horizontal temperature gradients are assumed to be weak (Sobel and Bretherton 2000).

Adding (1) and (2) and invoking a zero net surface flux constraint, *R*_{surf} + *E* + *H* = 0, yields an expression for the convergence, that is,

which upon substitution into the moisture Eq. (2) yields

Here, *M* = *M _{s}* −

*M*denotes the gross moist stability.

_{qp}qFor nonconvecting regions, with *P* = 0, it is instructive to consider instead

The nonconvecting region moisture equation is then as follows:

From (6), it can be seen that *E* has two effects that tend to cancel each other out. On the one hand, *E* > 0 corresponds to a source of tropospheric moisture, while on the other hand *E* > 0 offsets the effect of net energy input at the top of the atmosphere (*R*_{toa} > 0), reducing **∇** · **v*** _{nc}*. Combining the terms in

*E*shows the effective contribution of

*E*is scaled by a factor of .

For the idealized steady-state convective margin solution of LN07, *E* in the nonconvecting portion of the domain was set to zero because *w* = 0 in the absence of recharge by precipitation. However, realistic situations for which *E* is nonzero are encountered on seasonal or subseasonal time scales, as with the annual cycle movements of land region convection zones because the decay time for *w* is of order a few months.

### b. Shift of the convective margin associated with an imposed evaporation in the nonconvecting region

It is notationally convenient to recast (6) as

where

Here, *λ _{E}*(

*x*), which is in units of length

^{−1}, can be interpreted as the local spatial rate of moisture increase along an inflow trajectory associated with moisture convergence.

For arbitrary *R*_{toa}(*x*) and *E*(*x*), integrating (7) between the inflow position (at *x*_{0}) and *x* yields

where . The second term in brackets on the right-hand side of (9) represents the spatially integrated effect of evaporation across the nonconvecting region. For illustrative purposes, taking *R*_{toa}(*x*) and *E*(*x*) as constants in the nonconvecting region, (9) yields (setting *x*_{0} = 0),

where *q*_{0} is the inflow specific humidity and *q _{E}* = (

*u*)

_{q}λ_{E}^{−1}

*E*=

*M*/

_{s}E*M*(

_{qp}*R*

_{toa}−

*E*) is the moisture scale associated with evaporation and convergence. If

*E*>

*R*

_{toa}, leading to divergence in (5), then the moisture scale associated with

*q*(with sign reversed) represents the value of moisture for which evaporation and moisture divergence balance, with the inflow

_{E}*q*

_{0}decaying toward it. However, under conditions with

*E*<

*R*

_{toa}, moisture increases exponentially along the inflow trajectory. We point out that

*q*increases moisture along the inflow trajectory; however,

_{E}*λ*is smaller, relative to no-evaporation conditions, which reduces

_{E}*q*. This behavior reflects the compensation between moistening directly associated with

*E*and lowered convergence indirectly associated with changes to column flux forcing.

For a temperature-dependent convective threshold condition in moisture *q _{c}*(

*T*), the convective margin occurs at

As illustrated in Fig. 3a, for a given *R*_{toa}, *x _{c}^{E}* decreases as

*E*increases; that is, the margin shifts closer to the inflow point. The displacement of the margin toward the inflow point implies that the direct moistening effect associated with

*q*dominates over the convergence reduction in

_{E}*λ*. In terms of the dependence of (11) on top-of-the-atmosphere radiative heating, as

_{E}*R*

_{toa}is increased,

*x*moves closer to the inflow point because larger

_{c}^{E}*R*

_{toa}enhances vertical moisture convergence. Further, Fig. 3b shows stronger sensitivity of

*x*to the inclusion of evaporation with

_{c}^{E}*E*small, with larger sensitivity of

*x*to

_{c}^{E}*E*perturbations for a given value of

*E*when

*R*

_{toa}is small. Note that whereas the value of

*q*becomes large as

_{E}*R*

_{toa}→

*E*, the value of

*x*becomes large as , where

_{c}^{E}*M*=

_{qc}*M*(

_{qp}q_{c}*T*).

Based on these results, convective margin sensitivity to *E* in models or observations should be strongly affected by the relative values of *R*_{toa} and *E.* Moving poleward from the tropics, *R*_{toa} varies as a result of the latitudinal variation in top-of-the-atmosphere insolation; in the winter hemisphere, or during the equinoctial seasons, the meridional decrease of top-of-the-atmosphere insolation causes *R*_{toa} to become small and, at some latitude, to change sign. (Such latitude dependence is roughly analogous to the *x* axis in Fig. 3a.) With the caveats that (11) strictly applies to steady-state conditions and simplified inflow geometries, increased margin sensitivity is anticipated to occur at particular locations dictated by the interplay of the various control factors.

### c. Asymmetric displacements of the convective margin under anomalous wind field perturbations

Having considered the mean margin shift that occurs with the inclusion of evaporation, we now discuss the related issue of margin variations to imposed wind field perturbations *δu _{q}* in the presence of nonzero

*E*. The starting point is the mean state of LN07, with

*E*(

*x*) = 0 outside of the converting region (

*x*<

*x*

_{c}^{0}) and

*E*(

*x*) =

*E*inside (

*x*>

*x*

_{c}^{0}).

For anomalous outflow (*δu _{q}* < 0), the low-level wind perturbation induces the margin to move toward the inflow point, over a dry surface. The solution is thus identical to LN07, but with

*u*→

_{q}*u*+

_{q}*δu*; thus,

_{q}For anomalous inflow (*δu _{q}* > 0), by contrast, the margin will be shifted away from the inflow point, over a residually wet surface. From (9), it can be shown that

In the limit *δu _{q}*/

*u*→ 0, (13) is, to first order in

_{q}*δu*/

_{q}*u*,

_{q}Equation (14) resembles (12) but is modified by a factor of *κ* = [1 + (*M _{s}* −

*M*)

_{qc}*E*/(

*M*

_{qc}R_{toa})]

^{−1}. Because the second term in

*κ*is positive,

*κ*< 1, which means that for

*δu*of given magnitude, the

_{q}*x*displacements for anomalous inflow conditions are smaller than for anomalous outflow conditions. Such asymmetric displacements arise from the distinct surface states encountered under inflow and outflow perturbations, with the former air masses approaching the convective margin interact with a wet surface near the margin, which enhances the moisture loading of the inflow relative to what it would be upon transiting over a dry surface. The residual moistening allows

_{c}*q*to be met earlier along the inflow trajectory. For typical (QTCMl) values of

_{c}*E*,

*R*

_{toa},

*M*, and

_{qc}*M*,

*κ*≈ 0.5–0.75.

### d. Time scale for margin adjustment

The prototype effectively assumes time-independent surface states; in reality, the surface adjusts to the margin displacement. For example, the initially wet surface encountered under anomalous inflow conditions will begin to dry as evaporative demand diminishes soil wetness. The time scale for margin adjustments *τ*_{margin} is approximately |*δ _{xc}*/

*u*| ≈ |

_{q}*δu*/

_{q}*u*|〈{

_{q}*M*ln[

_{s}*q*(

_{c}*T*)/

*q*

_{0}]}/

*M*(

_{qp}*R*−

*E*)〉, which is of order 30|

*δu*/

_{q}*u*| days for the configuration discussed in the next section. However, the evaporative time scale

_{q}*τ*is approximately

_{e}*Lw*

_{0}/

*E*, assuming constant potential evaporation. For

_{p}*E*of order 100 W m

_{p}^{−2}, and

*w*

_{0}= 150 mm,

*τ*≈ 45 days. For wind perturbations such that 30|

_{e}*δ*/

_{uq}*u*| ≪ 45 days, the margin will effectively adjust before the surface state is substantially altered. At lower (e.g., seasonal) frequencies, the surface evolution may play a role, as considered in section 6. Also, for regions where

_{q}*R*

_{toa}→

*E*,

*τ*

_{margin}becomes large, so that the atmospheric adjustment time scale may become nonnegligible compared to

*τ*.

_{e}## 4. Implications of soil moisture for high-frequency variability of the convective margin

### a. Idealized QTCM1 configuration

In this section, the results of several idealized QTCM1 simulations designed specifically to provide insights into soil moisture effects on convective margins are discussed. The model setup here consists of an equatorial, zonal strip half occupied by a single ocean and land region. For the ocean region, uniform SST was imposed. Top-of-the-atmosphere insolation and surface albedo values were set to equinoctial conditions along the equator. In each simulation discussed below, the tropospheric temperature is a prescribed constant.

Under steady-state conditions, the idealized QTCM1 tropical strip simulation yields a single convection zone symmetric about the midpoint of the land region. To generate variations in the convection zone, spatially uniform, Gaussian-distributed stochastic wind perturbations were imposed in the model’s moisture advection scheme. For computational and diagnostic simplicity, the perturbations were added to the barotropic component of the total wind field over 10-day intervals. The perturbation time scale, although long compared to typical observed tropical transient time scales (such as easterly waves), was chosen to allow the margin in the idealized tropical strip configuration some time to adjust, thereby diminishing the effect of initial conditions on the margin response.

The perturbation precipitation profile, averaged over 500 perturbations, appears in Fig. 4 (solid red line; hereafter, we refer to this simulation as “*δ*CTL”). Note that the *x* coordinate has been normalized relative to the nonperturbed precipitation profile: *x* = 1 corresponds to *x _{c}^{E}* in the steady state, defined relative to the land–ocean interface at

*x*= 0. The principal effect of the imposed perturbations is a smoothing of the precipitation profile; the imposed perturbations essentially displace the edge of the convection zone back and forth, such that a smoothly tapered profile emerges for the mean over a large number of perturbations.

### b. Fixed-β and no wetness memory experiments

To demonstrate how soil moisture affects the variability of the convective margin, two sensitivity experiments were conducted. One sensitivity case (*δ*FIXED-*β*) implemented fixed *β* conditions, with *β* estimated (as in section 2) from *δ*CTL. The other (*δ*NOWETMEM) used *E* estimated functionally from *P* at each land grid point through a sixth-order polynomial fit between the mean *E* and *P* fields obtained from *δ*CTL. This “no wetness memory” simulation suppresses residual soil moisture anomalies associated with prior precipitation conditions and is effectively equivalent to *w*_{0} → 0.

Under fixed *β* conditions, there is little effect on the mean precipitation profile (Fig. 4; solid blue line); however, the standard deviation, (dashed blue line), is reduced by 20%. For *δ*NOWETMEM, the mean precipitation profile (green line) is lowered in the transition to the strongest precipitation values. This mean change can be understood in the context of the prototype results of section 3b: by eliminating residual soil moisture outside of the convection zone—and thus any evaporative moistening from the surface—the mean *δ*NOWETMEM inflow into the convection zone is drier compared to either *δ*CTL or *δ*FIXED-*β*, resulting in reduced mean precipitation values near the convective margin. Here, (dashed green line) is enhanced relative to , especially on the strongly convecting side of the profile.

### c. Anomalous inflow/outflow asymmetry

For the no-wetness memory simulation, nonzero *E* occurs locally during a particular model time step only if *P* is nonzero at the same location during that time step. If *P* ceases—for example, when the wind field perturbation shifts the convective margin—then the soil moisture effect (and hence *E*) is instantaneously removed. Relative to *δ*CTL, an inflow wind field perturbation of a given magnitude results in a greater westward margin displacement in *δ*NOWETMEM because the effect of residual *w* outside of the convecting region is eliminated. Figure 5a, which displays *x _{c}* values bin-averaged by the wind field perturbations

*δu*

_{0}, underscores this behavior because the

*x*values in

_{c}*δ*CTL (red) are below the

*δ*NOWETMEM values (green) for

*δu*

_{0}> 0. For

*δ*FIXED-

*β*, the

*x*values for

_{c}*δu*

_{0}> 0 are also below those of

*δ*NOWETMEM (blue). However, the scatter in the

*δu*

_{0}–

*x*relationship for fixed

_{c}*β*conditions is attenuated relative to

*δ*CTL. The change in

*x*variability points to modulation of the margin location by time-dependent soil moisture perturbations.

_{c}Comparing the idealized QTCM1 results to the analytic prototype of section 3 demonstrates favorable agreement. Assuming no effect from soil moisture (or evaporation) outside of the convection zone, the analytic solution (black) closely matches *δ*NOWETMEM, although the slope of the predicted *δu*_{0}–*x _{c}* relationship is a little too steep. This discrepancy is largely attributed to the nonleading order spatial structure neglected in the analytic solution; for example,

*R*

_{toa}and

*M*are not strictly uniform. When the effect of residual

_{s}*E*is included, the analytic slope (gray) is reduced for anomalous inflow conditions, with the value approximately matching the

*δ*FIXED-

*β*(or

*δ*CTL) results. It is worth reiterating that the analytic solutions are steady-state approximations, whereas the numerical results have some time dependence associated with atmospheric adjustment and, for the

*δ*CTL simulation, the soil moisture.

As was noted in section 3b, *R*_{toa} affects the sensitivity of the convective margin. Repeating the *δ*CTL, *δ*FIXED-*β*, and *δ*NOWETMEM simulations with *R*_{toa} reduced (by lowing net top-of-the-atmosphere insolation) underscores this sensitivity (Fig. 5b). Much of the increased scatter in the *δu*_{0}–*x _{c}* relationship (as evidenced by larger standard errors) is associated with the lengthening of

*τ*

_{margin}from reduced convergence, although the anomalous inflow/outflow asymmetry still emerges. The analytic solutions suggest increased separation of slopes between the zero and residual evaporation results. The increased mismatch between the analytic and numerical results likely reflects the steady-state nature of the analytic solutions, greater sensitivity to the spatial details of the fields, and longer atmospheric adjustment.

## 5. Diagnostic interpretation of convective margin variability

The diagnostic discussed in this section, the precipitation variance budget, represents one that can be readily estimated from GCM outputs and is therefore a useful metric for model intercomparison. Approaches based on budgetary constraints have gained widespread use in studies of tropical precipitation, and example applications include mechanistic analysis of the ENSO tropical teleconnection (Lintner and Chiang 2005; Neelin and Su 2005) and attribution of global warming effects (Chou and Neelin 2004). Many studies of land surface–atmosphere coupling have also employed budgetary analyses, especially the connection between evaporation and precipitation variances as inferred from soil moisture balance (Budyko 1974; Brubaker et al. 1993; Koster et al. 2000, 2001; Wu et al. 2007). Here, we consider a budgetary decomposition of precipitation variance from the atmospheric side to highlight more explicitly the role of atmospheric processes in the generation of hot spots. Of course, although budgets can provide powerful insights into underlying mechanisms, it may be challenging to tease apart (direct) causal agents from (indirect) feedback processes; for example, a large budget term does not imply causality. As will be seen, interpretation of the precipitation variance budget is not completely straightforward, even for the idealized setup considered here; however, viewing the budget in conjunction with margin variations proves instructive.

From the moisture Eq. (2), the precipitation variance budget is

Here, *σ _{A}*

^{2}denotes the variance of

*A*, defined as

*σ*

_{A}^{2}= (

*N*

^{2}−

*N*)

^{−1}Σ(

*A*− 〈

_{i}*A*〉)

^{2}, where 〈

*A*〉 is the average of

*A*. Similarly, cov(

*A*,

*B*) denotes the covariance of

*A*and

*B*, cov(

*A*,

*B*) = (

*N*

^{2}−

*N*)

^{−1}Σ(

*A*− 〈

_{i}*A*〉)(

*Bi*− 〈

*B*〉). We emphasize that, for these simulations, the perturbation forcing is explicitly prescribed and is thus known a priori.

### a. Moisture convergence and advection

Longitudinal profiles of the terms in (15) for the *δ*CTL and *δ*FIXED-*β* simulations (Figs. 6a and 6b) demonstrate that the variance associated with moisture convergence (orange line) is typically the largest term. The dominance of moisture convergence is especially evident on the strongly convecting side of the profile where constitutes up to 90% of *σ _{P}*

^{2}(black line), whereas the variance associated with horizontal moisture advection (red line) contributes little to the total precipitation variance.

At first glance, the small variance contribution by horizontal moisture advection may appear counterintuitive. After all, it is through moisture advection that the perturbation forcing is applied. However, the apparent smallness of relative to *σ _{P}*

^{2}can be reconciled with the expectation that it should be larger by using the relationship (3) to expand the variance of moisture convergence:

where *γ* = *M _{qp}q*/

*M*(≈ 5). Although fluctuations in

*γ*contribute to , their effect was observed to be sufficiently small to warrant their neglect in (16). The decomposition of moisture convergence reveals that −

*u*∂

_{q}*is the dominant contribution to (Fig. 6c); thus, moisture advection does significantly contribute to*

_{x}q*σ*

_{P}^{2}albeit indirectly.

Moisture advection, like moisture convergence, can be partitioned according to its definition, that is,

where ℛ_{adv} is a residual consisting of higher-order terms:

The largest contribution to arises from . That is, as the margin shifts under *u _{q}* variations, the steepest portion of the humidity profile (which occurs on the weakly convecting side of the margin) is displaced, inducing large variations in

*q*and its horizontal gradient.

### b. Evaporation

Of all terms appearing in (15), the evaporation variance *σ _{E}*

^{2}manifests the largest difference between

*δ*CTL and

*δ*FIXED-

*β*. In the absence of interactive soil moisture perturbations, the contribution of

*E*to

*P*variance is small everywhere. By contrast, for

*δ*CTL, the evaporative contribution approaches and even slightly exceeds the contribution from moisture convergence at low mean

*P.*Here,

*σ*

_{E}^{2}can be decomposed through its definition as follows:

where ℛ_{E} is a residual defined analogously to ℛ_{adv}:

Averaging the terms in the expansion (18) over *x* values close to the maximum of *σ _{E}*

^{2}reveals rather nontrivial behavior in

*δ*CTL (Table 1): although is the largest term, it is largely balanced by the covariance between

*β*and

*E*. The negative covariation of

_{p}*β*′ and

*E*′

*can be understood as follows. For an anomalously wet surface (*

_{p}*β*′ > 0), surface temperature (

*T*

_{s}) decreases. The cooler surface is associated with a lowered saturation specific humidity, which yields negative

*E*′

*because . However, for*

_{p}*δ*FIXED-

*β*, only the variance associated with

*E*is nonzero (since

_{p}*β*′ = 0), but the magnitude of this term (0.2 mm

^{2}day

^{−2}) is considerably reduced relative to its value in

*δ*CTL (9.6 mm

^{2}day

^{−2}). This behavior illustrates a cautionary aspect of budgetary approaches, namely, that they may obfuscate underlying physical mechanisms through covariances and compensation between terms.

The peak value of the ratio *σ _{E}*

^{2}/

*σ*

_{P}^{2}for

*δ*CTL, 0.4, coincides with

*P*≈ 2 mm day

^{−1}, consistent with localization of the strongest soil moisture–precipitation coupling between the most strongly convecting and nonconvecting conditions. [For

*P*< 2 mm day

^{−1}, cov(

*E*,

*M*

_{qp}q**∇**·

**v**) dominates

*σ*

_{p}^{2}.] Considering the variance differences between

*δ*CTL and

*δ*FIXED-

*β*further highlights the importance of interactive soil moisture to precipitation variability (Fig. 7a). Note that the variance differences have been plotted as functions of mean

*P*, which in the idealized QTCM1 configuration is effectively a monotonic function of the distance from the edge of the convection zone. For

*P*< 6 mm day

^{−1}, the difference in

*σ*

_{E}^{2}(Δ

*σ*

_{E}^{2}) accounts for all of the difference in

*σ*

_{P}^{2}(Δ

*σ*

_{P}^{2}) between the two simulations; in fact, because Δ

*σ*

_{E}^{2}> Δ

*σ*

_{P}^{2}for low mean

*P*, the difference in the sum of remaining variance terms is negative. However, at high mean

*P*, Δ

*σ*

_{P}^{2}is accounted for by the remaining terms, which include covariances with

*E*.

One interpretation of the behavior in Fig. 7a is that Δ*σ _{P}*

^{2}− Δ

*σ*

_{E}^{2}represents a downstream, nonlocal feedback to soil moisture perturbations. In this view, a substantial portion of the precipitation change is only realized downstream of where the

*E*contribution to

*P*variance is maximized, that is, at larger mean

*P*values, where dominates

*σ*

_{p}^{2}. Thus, the

*P*changes associated with interactive

*β*occur over a larger range of mean

*P*values (or, here, a larger spatial scale) than do the evaporative changes themselves. The nonlocality implied by Δ

*σ*

_{P}^{2}− Δ

*σ*

_{E}^{2}is qualitatively consistent with the analysis of Schär et al. (1999), which stressed the role of horizontal advection (and nonlocality) to soil moisture–precipitation coupling.

### c. Effect of changes to the convective parameterization

We also briefly comment on the effect of simulation physics—specifically, the convective parameterization—in determining the locality of the soil moisture–precipitation coupling. Convective parameterizations represent a significant source of divergence among current generation climate models, and a wide range of simulated quantities are known to be sensitive to the details of convective parameterizations (Zhang and McFarlane 1995; Maloney and Hartmann 2001; Gochis et al. 2002; Knutson and Tuleya 2004). To illustrate how convective parameterizations can affect land surface–atmosphere coupling, we performed two additional sets of idealized QTCM1 simulations with lower and higher values of the convective adjustment time scale (*τ _{c}*; =2 h in the standard model version) in the model’s Betts and Miller (1986) convection scheme. The principal effect of decreasing (increasing)

*τ*is a steepening (flattening) of the mean edge of the convection zone. Decreasing

_{c}*τ*further increases precipitation variability under

_{c}*u*perturbations.

_{q}Alterations to *τ _{c}* have a demonstrable effect on the

*P*and

*E*variance differences (Fig. 7b). Overall, the values of Δ

*σ*

_{P}^{2}and Δ

*σ*

_{E}^{2}increase as

*τ*decreases. However, the contribution of Δ

_{c}*σ*

_{E}^{2}to Δ

*σ*

_{P}^{2}is seen to decrease as

*τ*is reduced, while the peak of Δ

_{c}*σ*

_{P}^{2}is shifted deeper into the convection zone, that is, toward higher mean

*P*. These features suggest an increase of the downstream, nonlocal contributions to Δ

*σ*

_{P}^{2}as

*τ*is reduced. A broader implication of such behavior is that the characteristics of land–atmosphere coupling in models—for example, the degree of hot spot behavior expressed by a model—can be affected by parameters in the convection scheme.

_{c}## 6. Example of the soil moisture effect on precipitation seasonality

Over an annual cycle, the location of peak tropical convection varies latitudinally with changes in *R*_{toa}. Other factors may substantially modulate the latitude of peak convection. In the case of monsoon systems, for example, local land–ocean thermal contrasts may exert a leading-order influence on the intensity and duration of monsoonal rainfall (e.g., Steiner et al. 2009). Apart from the meridional seasonality of tropical precipitation, some zonal seasonality is also evident: for tropical South America, the eastern equatorial Amazon experiences its driest conditions during austral spring (Wang and Fu 2002). Such seasonality is driven both by local land–ocean thermal contrasts and interactions of convection with large-scale circulation.

The inflow–evaporative moistening asymmetry described in sections 3 and 4 may potentially contribute to land region seasonality, which we briefly explore here. We limit our focus to the seasonal cycle of *P* at 5°S over the northeastern corner of South America as simulated by QTCM1 configured with realistic geometry, as in section 2. The choice of region is motivated by the straightforward applicability of the LN07 prototype to the convective margin behavior here. Specifically, the circulation geometry is relatively simple, consisting of mostly zonal trade wind inflow from the equatorial Atlantic.

### a. Effect of changing soil moisture holding capacity

To estimate soil moisture effects on the convective margin at 5°S, we consider two experiments in which *w*_{0} is set to either 150 or 15 mm. Varying *w*_{0} corresponds to the alteration of one or more of the surface characteristics, such as vegetation type or fraction of bare soil, that affect the capacity of the surface to retain moisture. A value of 15 mm approximates a bare, “deforested” surface for which the soil moisture holding capacity is severely restricted. From the analysis in section 3d, the characteristic decay time scale of the *w*_{0} = 15 mm surface is of order 5 days.

The convective margin as simulated by QTCM1 for *w*_{0} = 150 mm displays a pronounced seasonal cycle (Fig. 8, black line). From January to July, the convective edge at 5°S lies near or to the east of the Atlantic coast. At the beginning of August, the margin recedes sharply westward, approaching roughly 50°W, or 1300 km from the Atlantic coastline, by the beginning of September. Thereafter, the margin advances eastward through the end of the year. To leading order, such seasonality is consistent with the seasonal evolution of tropical Atlantic SSTs, which are coolest when the margin is close to its maximum westward longitude. In the context of the LN07 prototype, the cool ocean surface is associated with low *q*_{0}, which (for other factors being more-or-less equal) results in *x _{c}* occurring relatively far to the west of the Atlantic coast.

It is important to point out the occurrence of some significant small-scale structure in the observed precipitation field, such as the intense rainfall band along the Atlantic coast, that do not appear in the QTCM1 simulations analyzed here. As discussed in Kousky (1980), this coastal rainfall maximum is associated with diurnally varying land–sea breeze circulations, the physics of which are not represented in the QTCM1 framework. Additional smaller-scale structure associated with topographic forcing and mesoscale circulations is also absent at the resolution of the QTCM1 simulations.

The net effect of reducing *w*_{0} induces a westward shift of the margin of up to 2° relative to the simulation with larger *w*_{0}. As the margin recedes westward from the land–ocean interface, the nonconvecting land surface between the Atlantic and the margin begins to dry. The low *w*_{0} surface loses moisture rapidly once the westward margin displacement begins. Thus, the low-level inflow into the convection zone is relatively drier, so the inflowing air masses must experience further vertical convergence-induced moistening to achieve the same *q _{c}*(

*T*), resulting in lengthening the distance to reach the margin.

### b. Explicit removal of residual soil moisture outside of the convection zone

To this point, we have not distinguished between the effect of soil moisture anomalies outside of the convection zone (i.e., between the Atlantic coast and *x _{c}^{E}*) relative to those within the convection zone. Although the inflow–evaporation interaction described above only requires nonconvecting region soil moisture, the presence of soil moisture within the convection zone could potentially affect margin behavior. For example, local evaporative recycling increases precipitation, which in turn induces cloud-radiative effects that may alter the temperature profile in the vicinity of the margin, thus affecting

*q*(

_{c}*T*). To demonstrate more conclusively that it is the soil moisture outside of the convection zone that matters most here, we performed an additional simulation, this time explicitly removing the soil moisture from the nonconvecting region after the margin has retreated. Figure 9 shows cross sections of precipitation, evaporation, and soil wetness at 5°S for this simulation as well as the standard setup (in gray and black, respectively), averaged over pentads 50–54. Comparison of the two precipitation profiles reveals a pronounced longitudinal margin displacement, by 2°–3°, which substantiates the role of nonconvecting region moisture in producing the margin shift.

## 7. Summary and conclusions

Straightforward extension of the LN07 convective margins prototype to include the effects of soil moisture acting through evaporation provides some basic intuition about how land surface conditions modulate the transition from nonconvecting to convecting conditions over tropical continents. For the case of low-level oceanic inflow into a land region convection zone, the integrated effect of evaporation along the inflow trajectory moistens air masses approaching the margin; relative to a comparable trajectory over a dry surface, the moisture tends to increase more rapidly along the inflow path, as expected. Given a fixed convective threshold, the integrated evaporation effect induces a shift of the convective margin toward the inflow point. This shift depends on *E* as well as factors determining the large-scale convergence along the trajectory, notably the top-of-the-atmosphere radiative heating *R*_{toa}. In fact, nonzero *E* along the inflow trajectory lowers the large-scale convergence; however, for realistic parameters, the direct evaporative moistening dominates over the convergence reduction.

The analytic prototype further demonstrates how land surface evaporation affects margin variability. In particular, it was shown that the inclusion of *E* yields an asymmetry in the margin displacements to low-level wind perturbations: under anomalous inflow conditions, marginal displacements are smaller than those for anomalous outflow conditions of the same magnitude. That is, for anomalous low-level inflow, the margin moves over a residually wet surface, which moistens the inflow into the convecting region, thereby allowing *q _{c}*(

*T*) to be met earlier along the inflow path. Idealized experiments with an intermediate-level complexity model, QTCM1, subject to imposed high-frequency inflow wind perturbations confirmed the presence of this asymmetry, whereas the asymmetry did not occur under suppression of nonconvecting region soil moisture. On seasonal time scales, it was noted that the inflow–evaporative moistening mechanism may be of relevance to the timing and spatial extent of marginal advances and retreats.

Within QTCM1, behavior reminiscent of the hot spots of strong soil moisture–convective coupling seen in previous studies—for example, Koster et al. (2004)—was also observed. Comparison of simulations with and without interactive soil moisture suggested amplification of precipitation variability via soil moisture by ∼20% in the vicinity of the convective margin. Despite the idealized nature of the simulations in which hot spot behavior was observed, analysis of precipitation variance budgets for these simulations proved challenging because of the multiple terms involved, although the mechanistic understanding provided by the margins framework was useful for interpretating some features of the budget. One aspect of particular note is the nonlocality of soil moisture effects, with a significant portion of the precipitation response realized downstream of where soil moisture and evaporation are most variable.

Alteration of the model’s convection scheme, specifically the time scale for convective adjustment, further demonstrates how the characteristics of hot spots may be affected by model representation of atmospheric processes. Other “atmospheric side” factors that may affect hot spot characteristics, as seen in the prototype, include top-of-the-atmosphere heating and large-scale convergence, the mean and variance of inflow wind, and the convective moisture threshold. These factors interact nonlinearly in setting the convective margin, and they may generate substantial regional variation in margin sensitivity to perturbations. Together, they provide an indication of why the strength of simulated land–atmosphere coupling may vary among models.

## Acknowledgments

The authors thank R. D. Koster, N. Zeng, P. L. Silva Dias, M. Notaro, and an anonymous reviewer for their discussions and comments and J. E. Meyerson for providing graphical assistance. This work was supported partly by National Oceanic and Atmospheric Administration Grants NA08OAR4310882 and NA08OAR4310597 and National Science Foundation Grant ATM-0645200. JDN acknowledges sabbatical support from the J. S. Guggenheim Memorial Foundation.

## REFERENCES

**,**

**,**

**,**

**,**

**,**

**,**

**,**

**,**

**,**

**,**

**,**

**,**

**,**

**,**

**,**

**,**

**,**

**,**

**,**

**,**

_{2}-induced warming on simulated hurricane intensity and precipitation: Sensitivity to the choice of climate model and convective parameterization.

**,**

**,**

**,**

**,**

**,**

**,**

**,**

**,**

**,**

**,**

**,**

**,**

**,**

**,**

**,**

**,**

**,**

**,**

**,**

**,**

**,**

**,**

**,**

**,**

**,**

**,**

**,**

**,**

**,**

**,**

**,**

**,**

**,**

**,**

**,**

**,**

**,**

**,**

## Footnotes

*Corresponding author address:* Benjamin Lintner, Department of Atmospheric and Oceanic Science, UCLA, 7127 Mathematical Sciences Building, Los Angeles, CA 90095-1565. Email: ben@atmos.ucla.edu