Editorial Type:
Article
Article Type:
Research Article

A Revised Framework for Analyzing Soil Moisture Memory in Climate Data: Derivation and Interpretation

Sonia I. Seneviratne Institute for Atmospheric and Climate Science, ETH Zurich, Zurich, Switzerland

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Randal D. Koster Global Modeling and Assimilation Office, NASA Goddard Space Flight Center, Greenbelt, Maryland

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Print Publication:
01 Feb 2012
DOI:
https://doi.org/10.1175/JHM-D-11-044.1
Page(s):
404–412
Full access

Abstract

A revised framework for the analysis of soil moisture memory characteristics of climate models and observational data is derived from the approach proposed by Koster and Suarez. The resulting equation allows the expression of the month-to-month soil moisture autocorrelation as a function of 1) the initial soil moisture variability, 2) the (atmospheric) forcing variability over the considered time period, 3) the correlation between initial soil moisture and subsequent forcing, 4) the sensitivity of evaporation to soil moisture, and 5) the sensitivity of runoff to soil moisture. A specific new feature is the disentangling of the roles of initial soil moisture variability and forcing variability, which were both (for the latter indirectly) contributing to the seasonality term of the original formulation. In addition, a version of the framework entirely based on explicit equations for the underlying relationships (i.e., independent of soil moisture statistics at the following time step) is proposed. The validity of the derived equation is exemplified with atmospheric general circulation model (AGCM) simulations from the Global Land–Atmosphere Coupling Experiment (GLACE).

Corresponding author address: Sonia I. Seneviratne, Institute for Atmospheric and Climate Science, Universitätsstrasse 16, ETH Zurich, CH-8092 Zürich, Switzerland. E-mail: sonia.seneviratne@env.ethz.ch

Abstract

A revised framework for the analysis of soil moisture memory characteristics of climate models and observational data is derived from the approach proposed by Koster and Suarez. The resulting equation allows the expression of the month-to-month soil moisture autocorrelation as a function of 1) the initial soil moisture variability, 2) the (atmospheric) forcing variability over the considered time period, 3) the correlation between initial soil moisture and subsequent forcing, 4) the sensitivity of evaporation to soil moisture, and 5) the sensitivity of runoff to soil moisture. A specific new feature is the disentangling of the roles of initial soil moisture variability and forcing variability, which were both (for the latter indirectly) contributing to the seasonality term of the original formulation. In addition, a version of the framework entirely based on explicit equations for the underlying relationships (i.e., independent of soil moisture statistics at the following time step) is proposed. The validity of the derived equation is exemplified with atmospheric general circulation model (AGCM) simulations from the Global Land–Atmosphere Coupling Experiment (GLACE).

Corresponding author address: Sonia I. Seneviratne, Institute for Atmospheric and Climate Science, Universitätsstrasse 16, ETH Zurich, CH-8092 Zürich, Switzerland. E-mail: sonia.seneviratne@env.ethz.ch
Keywords: Biosphere-atmosphere interaction; Climate variability; Hydrometeorology; Soil moisture; Seasonal forecasting; Land surface model

1. Introduction

Recent modeling and observational studies have highlighted the importance of soil moisture for regional climate (e.g., Betts 2004; Koster et al. 2004b; Seneviratne et al. 2006a; Taylor and Ellis 2006; Hirschi et al. 2011; see also Seneviratne et al. 2010 for an overview). Soil moisture “memory” (i.e., persistence) is an important aspect of such land–climate interactions (e.g., Delworth and Manabe 1988; Koster and Suarez 2001, hereafter KS01; Seneviratne et al. 2006b, hereafter S06). In particular, it can contribute to seasonal forecasting of both atmospheric (precipitation and temperature) and land variables (e.g., Schlosser and Milly 2002; Koster et al. 2004a; Lorenz et al. 2010; Koster et al. 2010a,b). It is thus useful to conceptualize the processes that control it.

With this aim, KS01 proposed an analysis framework based on an equation derived assuming a linear dependency of evapotranspiration and runoff on soil moisture and neglecting some higher-order terms. KS01 demonstrated its validity and usefulness, as did subsequent investigations (Mahanama and Koster 2003, 2005; S06). However, the seasonality term—one of the four main terms of the KS01 equation—is not unambiguously linked with soil moisture memory (S06; see also section 2.). Furthermore, in the KS01 version, soil moisture memory over a given time interval is expressed as a function of soil moisture statistics at the following time step. This is a conceptual impediment, as subsequent soil moisture may be viewed as a result rather than a control of soil moisture memory. To address these issues, we present here an extension of the KS01 framework, based on the derivation of an expression for the variability of soil moisture at the following time step. In addition, we propose a version entirely based on explicit equations for the underlying relationships (i.e., independent of soil moisture statistics at the following time step).

2. Equation derivation

a. KS01 equation

KS01 assume that the water balance for the soil column of a typical land surface model, for time period [n, n + 1] of year (or ensemble member) i, can be written (in the absence of snow) as
e1
where Cs is the column’s water holding capacity; wn ,i and wn +1,i are the average degree of saturation in the whole column at the beginning and end, respectively, of time period [n, n + 1]; Pn ,i is precipitation; En ,i is the total evaporation (i.e., transpiration, bare soil evaporation, and interception loss); and Qn ,i is the total runoff (including both surface and subsurface runoff). These latter three variables, Pn ,i , En ,i , and Qn ,i , are accumulated fluxes over the time period [n, n + 1]. Following the approach of Koster and Milly (1997), KS01 approximate the dependence of evaporation and runoff on soil moisture with simple empirically fitted (semi-implicit) linear functions
e2
e3
Here, Rn ,i is the accumulated net radiation over the period [n, n + 1] (normalized by the latent heat of vaporization to have the same units as En ,i ). The empirically derived, model-specific parameters an , bn , cn , and dn are established at each grid point through analysis of the given simulations. The n subscripts indicate that they are derived separately for each time period. Equations (2) and (3) are substituted into (1). Then, by separating w, P, and R into their mean components for the given time of year (indicated by overbars) and corresponding interannual (or intermember) anomalies, subtracting the equation mean and ignoring higher-order terms, the following equation is obtained for the anomalies alone:
e4
where An is a time-invariant factor dependent on the terms and ,1 and Fn is a forcing function dependent on Pn and Rn (for details, see KS01). From Eq. (4), KS01 derive the following equation for the month-to-month autocorrelation of soil moisture:
e5

Equation (5) breaks down soil moisture memory into contributions from four separate terms: 1) , which relates to the seasonality in soil moisture; 2) , which relates to variations of evaporation with soil moisture; 3) , which relates to variations of runoff with soil moisture; and 4) , which depends on the covariance of the atmospheric forcing with antecedent soil moisture, and thus reflects both the memory of external forcing and land–atmosphere feedbacks.

b. Disentangling of seasonality term

One issue with Eq. (5) is the interpretation of the seasonality term for two main reasons:

  • can be both high (strong soil moisture control on evaporation or runoff) or low (strong stochastic forcing) in situations of low soil moisture memory (Fig. 1; see also S06), and

  • the dependency of this term on makes it not easily interpretable, as variability of soil moisture at time step n + 1 is a result rather than a driver of soil moisture memory.

To address this issue, we derive here an analytical expression for , which can then be incorporated in (5). This expression is derived from Eq. (4) by taking its square, then the mean over all years (or ensemble members), and finally the square root of the resulting expression. After rearranging some of the terms, this yields
e6
Replacing with (6) in Eq. (5) leads to the following reformulation of the KS01 equation:
e7
This equation is equivalent to (5), but provides a conceptually more intuitive interpretation of the drivers of soil moisture memory, as discussed in section 3.
Fig. 1.
Fig. 1.

Illustration of contrasting (high and low) values of seasonality term in KS01 equation for cases of low soil moisture memory.

Citation: Journal of Hydrometeorology 13, 1; 10.1175/JHM-D-11-044.1

c. Expression based on fully explicit equations and alternative definition of forcing term

To make the final equation fully independent of soil moisture at the following time step, we additionally reexpress Eqs. (2) and (3) explicitly rather than semi-implicitly:
e8
e9
Using (8) and (9) and following similar steps as KS01 yields the following equation for the soil moisture anomalies at time n + 1:
e10
Equation (10) can also be reexpressed as follows:
e11
with
e12
e13
The new forcing function Φn ,i [Eq. (12)] is derived using the mean expressions of Eqs. (8) and (9). Using the means of Eqs. (2) and (3), it can also be easily related to the KS01 Fn ,i function (not shown). Based on Eq. (12), the interpretation of the forcing function Φn ,i is fairly straightforward: it represents an estimate of changes in relative soil moisture amounts induced by the atmospheric forcing (Pn ,i , Rn ,i ) in the given time period n and year or simulation member i assuming a constant sensitivity of runoff and evapotranspiration to soil moisture. We introduce Φn ,i here instead of from (10), which would be the equivalent of the KS01 Fn function when using the explicit equations for (8) and (9), as it makes the forcing function fully independent of soil moisture statistics. It also means that it can be more easily assessed from observations, which can be relevant for some applications.
Following similar steps as KS01, and using the approach from section 2b for the derivation of independently of yields lastly the following expression:
e14
This final revised formulation is similar to (7), but is fully independent of information at time step n +1 and uses the newly defined forcing function Φn. It may be considered as entirely “explicit” in the context of the seasonal cycle (though based on multiyear statistics), since it is only based on explicit equations for the underlying relationships. Conceptually, both revised versions of the KS01 equation, (7) and (14), are nonetheless equivalent, as they have the same structure and highlight the same drivers for soil moisture memory (section 3). Indeed, their only distinction lies in the replacement of An and Fn with (1 − αn ) and Φn, respectively. Hence the main conceptual revision in the present framework is the derivation of an expression for (section 2b).

3. Interpretation of new equation

a. Main terms of equation

In this section, we provide an interpretation of the newly derived Eq. (14). Five main terms are found to control soil moisture memory in the new formulation:

  1. the initial soil moisture variability ,

  2. the forcing variability ,

  3. the correlation between the initial soil moisture and the forcing ρ(wn , Φn),

  4. the sensitivity of evaporation to soil moisture , and

  5. the sensitivity of runoff to soil moisture .

As noted in the previous section, the same five terms also control Eq. (7). Thus, this outcome is a result of the inclusion of the new expression for (section 2b), but is not dependent on the choice of semi-implicit versus explicit expressions for Eqs. (2) and (3) [respectively (8) and (9)].

In comparison with the KS01 framework, we find that the revised formulation entails two terms also found in KS01 (items 4 and 5), one term in a modified form (item 3, as correlation instead of the covariance term normalized by the soil moisture variance), and two new terms (items 1 and 2), which were in effect captured jointly in the seasonality term. Nonetheless, because the seasonality term of KS01 uses the subsequent soil moisture variability rather than the forcing variability, it is also affected by the terms 1, 3, 4, and 5, rather than only and is thus less easily interpreted. Hereafter, we discuss the contribution of the expanded set of five terms to soil moisture memory based on Eq. (14), focusing first on the respective roles of versus (terms 1 and 2) and then on the effects induced by soil moisture feedbacks (terms 3, 4, and 5).

b. Effects of initial soil moisture variability and forcing variability on soil moisture memory

In the absence of feedbacks with soil moisture content—that is, if there are no effects of soil moisture on either evapotranspiration, runoff, or the atmospheric forcing—Eq. (14) simplifies to the following expression:
e15
with
e16
In this case, it can be seen from Eqs. (15) and (16) that the critical measure controlling soil moisture memory is the ratio . Hence, one can distinguish three main situations (see also Fig. 2): 1) cases where is much larger than , which have high memory; 2) cases where is much smaller than (by at least one order of magnitude), which have low memory; and 3) cases where the two terms are of similar magnitude, which have moderate memory.
Fig. 2.
Fig. 2.

Illustration of combined effects of the initial soil moisture variability and forcing variability on soil moisture memory, assuming small effects of the correlation of forcing with initial soil moisture ρ(wn , Φn) and of the evaporation and runoff sensitivity to soil moisture .

Citation: Journal of Hydrometeorology 13, 1; 10.1175/JHM-D-11-044.1

c. Effects of soil moisture feedbacks on soil moisture memory

In this subsection, we address the effects of the terms ρ(wn , Φn), , and on soil moisture memory as implied by Eq. (14). In particular, we assess the extent to which they modulate the aforementioned effects of and . Within the present framework, we can see that the terms and reduce the soil moisture memory associated with because they induce a reduction of the initial soil moisture anomalies (see also discussions in KS01 and S06). This effect is illustrated in the right-hand panels of Fig. 3. On the other hand, the correlation between the initial soil moisture and the forcing ρ(wn , Φn), if positive, leads to an enhancement of soil moisture memory and thereby (partly) counteracts the effect of the forcing variability . This may be either due to positive feedbacks or effects of third variables such as sea surface temperatures (e.g., Orlowsky and Seneviratne 2010). Note that Eq. (14) does not exclude the existence of negative correlations between soil moisture and the forcing (e.g., more precipitation following a negative soil moisture anomaly; see also section 4), which contribute negatively to soil moisture memory. The effect of this term when positive is illustrated in the left-hand panels of Fig. 3.

Fig. 3.
Fig. 3.

Illustration of combined effects of the initial soil moisture variability , of the correlation of the forcing with the initial soil moisture (assumed to be positive) multiplied by forcing variability , and the evaporation and runoff sensitivity to soil moisture on soil moisture memory.

Citation: Journal of Hydrometeorology 13, 1; 10.1175/JHM-D-11-044.1

Limiting cases of the equation can further exemplify these various effects. If ρ(wn , Φn) is close to 0, but the terms and are not negligible, Eq. (14) can be expressed as follows:
e17
with
e18
In analogy to (15), Eq. (17) relates the autocorrelation of soil moisture to the ratio between the initial soil moisture variability, here modified by the and effects, and the forcing variability over the considered time period. The term κ 1 in Eq. (16) can indeed be seen as a special case of Eq. (18).
Another limit of Eq. (14) is when the term is much larger than (e.g., because tends to 0 or αn tends to 1), for which it simplifies to
e19
Hence, in that case, all of the memory comes from the correlation of the initial soil moisture with subsequent forcing. Note also that Eq. (14) implies that when ρ(wn , Φn) tends to 1, soil moisture memory also tends to 1 independently of the values of the other four terms.

4. Application of revised memory equation to GLACE data

In this section, we apply Eq. (14) to AGCM simulations of the Global Land–Atmosphere Coupling Experiment (GLACE). The soil moisture memory characteristics of these simulations were previously analyzed by S06 using the KS01 framework. Therefore, these data provide an ideal test bed for the revised formulation presented here. For a more detailed description of the GLACE project and data, please refer to Koster et al. (2004b, 2006) and Guo et al. (2006). In GLACE, each participating modeling group performed a 16-member ensemble of 3-month (June–August) simulations. Each GLACE simulation was separated into three 27-day periods (delimited at 9, 36, 63, and 90 days) to produce the data utilized in the present analysis. Details regarding data handling are provided in S06. Note that we do not provide analyses here for the Community Atmosphere Model, version 3 (CAM3) model, which was found to have very low soil moisture variability and anomalous soil moisture memory patterns because of a dry bias (S06).

Figure 4 displays maps of the AGCMs’ actual 27-day-lagged soil moisture autocorrelation ρ 27, of their estimation from Eq. (14) , and their differences. The white areas on the plots correspond to regions covered with snow or permanent ice, or to grid points characterized by undefined values (e.g., soil moisture variance equal to zero); note that for the National Aeronautics and Space Administration (NASA) Seasonal-to-Interannual Prediction Project (NSIPP) model, the Andes had not been shaded out in S06. This figure—consistent with the results for the KS01 version (S06)—confirms that for most regions and models, Eq. (14) provides a very good approximation of the AGCMs’ soil moisture memory. The inter- and intramodel variations in soil moisture memory are both clearly captured. The slightly more extended blank areas for compared to ρ 27 (e.g., Sahara for NSIPP model) are due to the larger number of factors that may be undefined in (14), such as Φn when is equal to zero. The few discrepancies, mostly in Southeast Asia [Canadian Centre for Climate Modelling and Analysis (CCCma), Commonwealth Scientific and Industrial Research Organisation Conformal-Cubic 3 (CSIRO-CC3), and the atmospheric component of the third climate configuration of the Met Office Unified Model (HadAM3)] and in the northwestern part of South America [CCCma, CSIRO-CC3, Goddard Earth Observing System (GEOS), and HadAM3], are generally also found with the KS01 formulation (see S06) and overall slightly less pronounced with the revised formulation. A more detailed analysis of the spatial root-mean-square error (RMSE) confirms that the RMSE is generally similar for Eq. (14) and the KS01 version, and overall slightly lower for the revised version with the exception of the CSIRO-CC3 model (not shown).

Fig. 4.
Fig. 4.

(left) Maps of simulated 27-day-lagged autocorrelation of total profile soil moisture ρ 27 in the seven analyzed AGCMs, (middle) corresponding maps of as estimated with Eq. (14), and (right) differences (i.e., estimated autocorrelations minus simulated autocorrelations).

Citation: Journal of Hydrometeorology 13, 1; 10.1175/JHM-D-11-044.1

To investigate the contribution of the different terms of Eq. (14) to the overall soil moisture memory, we display in Fig. 5 the terms , (1 − αn ), and ρ(wn ,Φn). In case of low values of ρ(wn , Φn), (14) can be expressed from the first two terms alone as shown in (17) and (18). When compared with Fig. 4, Fig. 5 clearly shows a strong relationship between these two terms and the actual soil moisture memory in the models. Interestingly, small values of and (1 − αn ), which both imply low memory, are often found in the same regions [in particular in the Center for Ocean–Land–Atmosphere Studies (COLA) model]. But several regions can be identified where one or the other term dominates the overall response. For its part, ρ(wn , Φn) is overall low, though not inexistent. It generally ranges from about 0.1 to 0.3, and can also be negative in some regions (with particularly large negative values in the GEOS model). This term is generally too small to affect soil moisture memory, with some exceptions: for instance, in the COLA model, it is (positive and) large in Europe, which compensates for a low value of . This results in a high soil moisture memory there—both in the simulation results and as inferred from (14).

Fig. 5.
Fig. 5.

(left) Maps of , (middle) maps of [i.e., (1 − αn )], and (right) maps of ρ(wn , Φn). Values of that are larger than 5 are set to 5 in the left-hand panels for display purposes.

Citation: Journal of Hydrometeorology 13, 1; 10.1175/JHM-D-11-044.1

5. Summary and conclusions

We have presented here a revision of the soil moisture memory equation proposed by KS01. Its main advantage is that it allows the disentangling of the effects of initial soil moisture variability and forcing variability on soil moisture memory, which were previously jointly captured in the seasonality term of the KS01 framework. In addition, the effect of forcing was only implicitly included in the KS01 framework using the soil moisture variability at the following time step, while it is an explicit term of the revised formulation. Finally we also propose a version of the revised equation that is entirely independent of information on soil moisture statistics at the following time step, and we additionally introduce a revised definition of the forcing function, which is independent of any soil moisture information.

The revised framework is useful for assessing the contribution of the different factors controlling soil moisture memory, as illustrated with the analysis of the GLACE simulations and as highlighted by specific limits of the equation. Although the KS01 equation has been so far only applied to model data, both the original formulation and the revised framework presented here could also be applied to observations. While such analyses lie beyond the scope of the present article, this, for example, opens attractive perspectives for model validation. This would be particularly relevant for applications in climate change modeling and seasonal forecasting.

Acknowledgments

We are thankful to Boris Orlowsky, René Orth, and three anonymous reviewers for helpful comments on the manuscript.

REFERENCES

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    • Search Google Scholar
    • Export Citation

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    • Search Google Scholar
    • Export Citation

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    • Search Google Scholar
    • Export Citation

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    • Search Google Scholar
    • Export Citation

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    • Search Google Scholar
    • Export Citation

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    • Search Google Scholar
    • Export Citation

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    • Search Google Scholar
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    • Search Google Scholar
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  • Mahanama, S. P. P., and Koster R. D. , 2003: Intercomparison of soil moisture memory in two land surface models. J. Hydrometeor., 4, 1134–1146.

    • Search Google Scholar
    • Export Citation

  • Mahanama, S. P. P., and Koster R. D. , 2005: AGCM biases in evaporation regime: Impacts on soil moisture memory and land–atmosphere feedback. J. Hydrometeor., 6, 656–669.

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  • Schlosser, C. A., and Milly P. C. D. , 2002: A model-based investigation of soil moisture predictability and associated climate predictability. J. Hydrometeor., 3, 483–501.

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  • Seneviratne, S. I., Lüthi D. , Litschi M. , and Schär C. , 2006a: Land–atmosphere coupling and climate change in Europe. Nature, 443, 205–209.

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  • Seneviratne, S. I., and Coauthors, 2006b: Soil moisture memory in AGCM simulations: Analysis of Global Land–Atmosphere Coupling Experiment (GLACE) data. J. Hydrometeor., 7, 1090–1112.

    • Search Google Scholar
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  • Seneviratne, S. I., Corti T. , Davin E. L. , Hirschi M. , Jaeger E. B. , Lehner I. , Orlowsky B. , and Teuling A. J. , 2010: Investigating soil moisture–climate interactions in a changing climate: A review. Earth-Sci. Rev., 99 (3–4), 125–161, doi:10.1016/j.earscirev.2010.02.004.

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Journal of Hydrometeorology

  • Betts, A. K., 2004: Understanding hydrometeorology using global models. Bull. Amer. Meteor. Soc., 85, 1673–1688.

  • Delworth, T. L., and Manabe S. , 1988: The influence of potential evaporation on the variabilities of simulated soil wetness and climate. J. Climate, 1, 523–547.

    • Search Google Scholar
    • Export Citation

  • Guo, Z.-C., and Coauthors, 2006: GLACE: The Global Land–Atmosphere Coupling Experiment. Part II: Analysis. J. Hydrometeor., 7, 590–610.

    • Search Google Scholar
    • Export Citation

  • Hirschi, M., and Coauthors, 2011: Observational evidence for soil-moisture impact on hot extremes in southeastern Europe. Nat. Geosci., 4, 17–21, doi:10.1038/ngeo1032.

    • Search Google Scholar
    • Export Citation

  • Koster, R. D., and Milly P. C. D. , 1997: The interplay between transpiration and runoff formulations in land surface schemes used with atmospheric models. J. Climate, 10, 1578–1591.

    • Search Google Scholar
    • Export Citation

  • Koster, R. D., and Suarez M. J. , 2001: Soil moisture memory in climate models. J. Hydrometeor., 2, 558–570.

  • Koster, R. D., and Coauthors, 2004a: Realistic initialization of land surface states: Impacts on subseasonal forecast skill. J. Hydrometeor., 5, 1049–1063.

    • Search Google Scholar
    • Export Citation

  • Koster, R. D., and Coauthors, 2004b: Regions of strong coupling between soil moisture and precipitation. Science, 305, 1138–1140.

  • Koster, R. D., and Coauthors, 2006: GLACE: The Global Land–Atmosphere Coupling Experiment. Part I: Overview. J. Hydrometeor., 7, 590–610.

    • Search Google Scholar
    • Export Citation

  • Koster, R. D., Mahanama S. P. P. , Livneh B. , Lettenmaier D. P. , and Reichle R. H. , 2010a: Skill in streamflow forecasts derived from large-scale estimates of soil moisture and snow. Nat. Geosci., 3, 613–616.

    • Search Google Scholar
    • Export Citation

  • Koster, R. D., and Coauthors, 2010b: Contribution of land initialization to subseasonal forecast skill: First results from a multi-model experiment. Geophys. Res. Lett., 37, L02402, doi:10.1029/2009GL041677.

    • Search Google Scholar
    • Export Citation

  • Lorenz, R., Jaeger E. B. , and Seneviratne S. I. , 2010: Persistence of heat waves and its link to soil moisture memory. Geophys. Res. Lett., 37, L09703, doi:10.1029/2010GL042764.

    • Search Google Scholar
    • Export Citation

  • Mahanama, S. P. P., and Koster R. D. , 2003: Intercomparison of soil moisture memory in two land surface models. J. Hydrometeor., 4, 1134–1146.

    • Search Google Scholar
    • Export Citation

  • Mahanama, S. P. P., and Koster R. D. , 2005: AGCM biases in evaporation regime: Impacts on soil moisture memory and land–atmosphere feedback. J. Hydrometeor., 6, 656–669.

    • Search Google Scholar
    • Export Citation

  • Orlowsky, B., and Seneviratne S. I. , 2010: Statistical analyses of land–atmosphere feedbacks and their possible pitfalls. J. Climate, 23, 3918–3932.

    • Search Google Scholar
    • Export Citation

  • Schlosser, C. A., and Milly P. C. D. , 2002: A model-based investigation of soil moisture predictability and associated climate predictability. J. Hydrometeor., 3, 483–501.

    • Search Google Scholar
    • Export Citation

  • Seneviratne, S. I., Lüthi D. , Litschi M. , and Schär C. , 2006a: Land–atmosphere coupling and climate change in Europe. Nature, 443, 205–209.

    • Search Google Scholar
    • Export Citation

  • Seneviratne, S. I., and Coauthors, 2006b: Soil moisture memory in AGCM simulations: Analysis of Global Land–Atmosphere Coupling Experiment (GLACE) data. J. Hydrometeor., 7, 1090–1112.

    • Search Google Scholar
    • Export Citation

  • Seneviratne, S. I., Corti T. , Davin E. L. , Hirschi M. , Jaeger E. B. , Lehner I. , Orlowsky B. , and Teuling A. J. , 2010: Investigating soil moisture–climate interactions in a changing climate: A review. Earth-Sci. Rev., 99 (3–4), 125–161, doi:10.1016/j.earscirev.2010.02.004.

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  • Taylor, C. M., and Ellis R. J. , 2006: Satellite detection of soil moisture impacts on convection at the mesoscale. Geophys. Res. Lett., 33, L03404, doi:10.1029/2005GL025252.

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  • <sc>Fig</sc>. 1.
    View in gallery
    Fig. 1.

    Illustration of contrasting (high and low) values of seasonality term in KS01 equation for cases of low soil moisture memory.

  • <sc>Fig</sc>. 2.
    View in gallery
    Fig. 2.

    Illustration of combined effects of the initial soil moisture variability and forcing variability on soil moisture memory, assuming small effects of the correlation of forcing with initial soil moisture ρ(wn , Φn) and of the evaporation and runoff sensitivity to soil moisture .

  • <sc>Fig</sc>. 3.
    View in gallery
    Fig. 3.

    Illustration of combined effects of the initial soil moisture variability , of the correlation of the forcing with the initial soil moisture (assumed to be positive) multiplied by forcing variability , and the evaporation and runoff sensitivity to soil moisture on soil moisture memory.

  • <sc>Fig</sc>. 4.
    View in gallery
    Fig. 4.

    (left) Maps of simulated 27-day-lagged autocorrelation of total profile soil moisture ρ 27 in the seven analyzed AGCMs, (middle) corresponding maps of as estimated with Eq. (14), and (right) differences (i.e., estimated autocorrelations minus simulated autocorrelations).

  • <sc>Fig</sc>. 5.
    View in gallery
    Fig. 5.

    (left) Maps of , (middle) maps of [i.e., (1 − αn )], and (right) maps of ρ(wn , Φn). Values of that are larger than 5 are set to 5 in the left-hand panels for display purposes.

Fig. 1.

Illustration of contrasting (high and low) values of seasonality term in KS01 equation for cases of low soil moisture memory.
Fig. 2.

Illustration of combined effects of the initial soil moisture variability and forcing variability on soil moisture memory, assuming small effects of the correlation of forcing with initial soil moisture ρ(wn , Φn) and of the evaporation and runoff sensitivity to soil moisture .
Fig. 3.

Illustration of combined effects of the initial soil moisture variability , of the correlation of the forcing with the initial soil moisture (assumed to be positive) multiplied by forcing variability , and the evaporation and runoff sensitivity to soil moisture on soil moisture memory.
Fig. 4.

(left) Maps of simulated 27-day-lagged autocorrelation of total profile soil moisture ρ 27 in the seven analyzed AGCMs, (middle) corresponding maps of as estimated with Eq. (14), and (right) differences (i.e., estimated autocorrelations minus simulated autocorrelations).
Fig. 5.

(left) Maps of , (middle) maps of [i.e., (1 − αn )], and (right) maps of ρ(wn , Φn). Values of that are larger than 5 are set to 5 in the left-hand panels for display purposes.
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