1. Introduction

Soil moisture governs energy and water exchanges at the land–air boundary and so is a key component of the land surface hydrology. The soil moisture reservoir has a memory considerably longer than that of most of the atmospheric processes and hence as a low-pass filter lengthens the time scales of climatic anomalies. Numerous studies have shown that soil moisture acts as feedback on climate in various ways. Coupling to the atmosphere can further lengthen the soil moisture time scales (e.g., Dickinson 2000). Persistence in soil moisture is translated into persistence in near-surface humidity, temperature, and precipitation (Delworth and Manabe 1988, 1989, 1993; Koster and Suarez 1995; Eltahir 1998; Zheng and Eltahir 1998; Findell and Eltahir 1999; Koster et al. 2000; Pal and Eltahir 2001). Hence, it prolongs the effects of drought (Nicholson 2000), enhances the severity and persistence of floods (Bonan and Stillwell-Soller 1998; Hong and Kalnay 2000), and determines the predictability of atmospheric surface climate anomalies (Wang and Kumar 1998; Douville and Chauvin 2000).

Most previous studies have considered soil water as if it were a single reservoir and do not address the dynamics of its vertical profile. The study by Delworth and Manabe (1988), with such a model, shows that the prominent feature of the soil moisture spectra is the “redness,” that is, large amounts of variance are located at periods of 1 yr or more. Liu and Avissar (1999a,b) investigate the persistence of soil moisture, soil temperature, and near-surface atmospheric variables using simulations from the Biosphere–Atmosphere Transfer Scheme (BATS) coupled with the National Center for Atmospheric Research (NCAR) Community Climate Model, version 2 (CCM2). Their results from a 10-yr simulation indicate qualitatively that the persistence increases with soil depth. A study by Oglesby et al. (2002), using coupled NCAR Land Surface Model (LSM) and NCAR Community Climate Model, version 3 (CCM3), suggests that the deep soil zone anomalies exert a more powerful, long-lasting effect than do anomalies in the near-surface soil zone. Water stored at the surface has an immediate response to the atmospheric forcing such as precipitation and evaporation, while soil moisture's longer memory may be carried in the deeper soil layers (Dickinson et al. 2003). Data on soil moisture allow us to examine the site-based soil moisture variability (e.g., Vinnikov et al. 1996; Entin et al. 2000). The low-pass filtered climatology of soil hydrology in terms of amplitude damping, phase shifting, and increasing persistence with soil depth has been quantified using observations over Illinois (Wu et al. 2002), in particular, 1) the amplitude decreases with soil depth, with the dryness signal penetrating more deeply than the wetness signal; 2) the phase shift with soil depth is larger for longer time scales of variation; and 3) the seasonal variation of soil moisture is amplified in the drought years, with an increased phase shift from soil surface to bottom.

What previous studies have not adequately addressed are, for layered soil, how time scales vary geographically with degree of aridity; how the increasing redness with depth seen in Illinois soils is distributed geographically and seasonally; how the time scales of the soil moisture profile depend on 1) the seasonality of forcing by precipitation and radiation, 2) evapotranspiration (ET), 3) runoff, and 4) feedback of soil moisture on precipitation; how well the model agrees with observations; etc. To clarify these issues, we examine variations of layered soil moisture memory and investigate their physical interpretations. A 50-yr climate simulation database from the Common Land Model (CLM) coupled with the NCAR CCM3 is used for the study. Some relevant novel features about CLM are briefly described in section 2. The model reliability for present study is demonstrated in section 3. Section 4 shows the variations of soil moisture memory geographically, vertically, and seasonally. Section 5 examines how the precipitation, ET, and runoff combine to affect the vertical soil moisture memory at different geographical locations with typical vegetations. Discussion and conclusions are presented in sections 6 and 7, respectively.

2. Land model description

The land component of climate models has evolved from the original single soil layer bucket schemes based upon the original work of Budyko (1956) and the early work of Manabe (1969) to comprehensive multilayer diffusion schemes with root and canopy included (e.g., Dickinson et al. 1993; Sellers et al. 1996). The CLM (Dai et al. 2003) has been developed as a state-of-the-art biophysics package and coupled to the NCAR CCM3 (Zeng et al. 2002). This model can address scientific questions which require more realistic simulations of soil moisture profile through its unique uneven soil column discretization and the updated root parameterization as well as other improvements in its physics and parameterizations.

The CLM is developed primarily based on BATS (Dickinson et al. 1993), NCAR LSM (Bonan 1996), and the snow model from IAP94 (the 1994 version of the Chinese Academy of Sciences Institute of Atmospheric Physics Land Surface Model; Dai and Zeng 1997) to establish a more physically based soil–vegetation–atmosphere transfer scheme for climate studies. Its major characteristics include ten unevenly spaced layers for soil temperature and soil moisture, with free drainage and zero heat flux condition at the bottom; a multilayer parameterization of snow process, with up to five layers depending on the snow depth; an explicit treatment of the mass of liquid water and ice water and their phase change within the snow and soil system; a runoff parameterization following the Topography-based Runoff Prediction Model (TOPMODEL) concept; a canopy photosynthesis–conductance model that describes the simultaneous transfer of CO₂ and water vapor into and out of vegetation; a tiled treatment of subgrid fraction of energy and water balance; a global land cover and vegetation database derived from Advanced Very High Resolution Radiometer (AVHRR) data; and a global database of root vertical distribution. Here we emphasize its unique vertical discretization for the soil column. Additional details about CLM are documented in Dai et al. (2001).

The CCM-like vertical differencing is used, of which the mesh points are specified and interfaces are located halfway between two neighbor layers. For soil layerj ( j = 1, 2, … , 10), its node depth z_j (in m) is defined as

z_jj(1)

then its soil layer thickness Δz_j (in m) is

View Expanded

and the depth at the interface z_h,j is

View Expanded

This discretization is illustrated in Fig. 1. The thermal properties (temperature, thermal conductivity, and volumetric heat capacity) and the hydraulic properties (volumetric soil water content, hydraulic conductivity, and matric potential) are defined at the node of each layer.

The CLM has been tested with comprehensive observational data, including all data in the Project for Intercomparison of Land Surface Parameterization Schemes (Henderson-Sellers et al. 1993), a variety of multiyear point observational data in different land cover type and different climatological regime over the world, regional data over the U.S. Red–Arkansas River basin, and global data from the Global Soil Wetness Project (Dirmeyer et al. 1999). Dai et al. (2003) show that the CLM realistically simulates the state variables, such as soil moisture, soil temperature, and snow water equivalent, and the flux terms, such as net radiation, latent heat flux, sensible heat fluxes, and runoff.

3. Global simulations of soil variability

The model data developed for this study consist of 50-yr monthly mean global values for the ten-layer soil moisture profile, precipitation, ET, and runoff. The seasonal cycle of sea surface temperature has been prescribed at all ocean grid points based upon observed monthly mean fields. The NCAR CCM3 is a spectral atmospheric model with T42 truncation (approximately 2.8° × 2.8° horizontal resolution), 18 vertical levels, and a 20-min time step. It employs comprehensive parameterizations of deep convection, shallow and nonprecipitating convection, shortwave and longwave radiation, and atmospheric boundary layer turbulence. Additional model details are provided in Kiehl et al. (1998).

The simulation of land surface climate by the coupled CLM–CCM3 has been evaluated with LSM–CCM3 and observations by Zeng et al. (2002). It has been found to significantly reduce the summer cold bias of surface air temperature in the LSM, from its higher sensible heat fluxes and lower latent heat fluxes, and the winter warm bias over seasonally snow-covered regions, especially in Eurasia. CLM also significantly improves the simulation of the annual cycle of runoff in LSM. In addition, CLM simulates the snow mass better than LSM during the snow accumulation stage. The comparison of volumetric soil water from CLM and LSM indicated that they both give a similar spatial distribution of soil water but CLM has slightly drier soils. The model simulates the principal spatial and seasonal features of the observed precipitation distribution to within a bias of 0.2 mm day⁻¹ of that observed (Willmott et al. 1998) for most of the months over global land. The results reported by Zeng et al. (2002) appear to indicate that the simulation of land climate in CCM3 has been substantially improved through use of the CLM. Here we present the large-scale features of soil water seasonality simulated by the model.

The model climatology for volumetric soil water content (including only the liquid soil water), that is, averages over the months of June–August (JJA) and the months of December–February (DJF) for the surface layer are displayed in Figs. 2a and 2b, respectively. The blank patches are covered by ice, snow, or water bodies. The model-computed spatial and temporal patterns are consistent with our perceptions. Soils are wet over tropical forests and dry over the arid Sahara and Arabian Desert regions both in summer and winter, as well as dry in most of Australia, and wet around the North Pacific coasts and Asian monsoon region in summer. Generally, surface soil moisture is smaller in summer except for the tropical region and the northern Pacific coasts, while in winter, soils are mostly frozen in North America and northern Europe. Moist areas are strongly connected with the simulated precipitation fields (not shown). While there are few large-scale observations for quantitative evaluation of model soil water, we have examined the simulated climatology against observations from the Illinois Climate Network (http:// www.sws.uiuc.edu/warm; Hollinger and Isard 1994; Robock et al. 2000) and the agreement is reasonable.

To fully evaluate the global climatic simulation of vertical soil moisture against observations is a complex issue, especially with land–atmosphere interaction involved. Given reliable measurements, how would model output best be compared with observations? What are the more appropriate time and space scales to be examined? Are means or higher order statistics more informative? How do the parameterizations of land cover, root distribution, soil texture, etc., affect soil moisture simulations in a climate model? Although many such questions still need to be addressed, it appears that CLM–CCM3 provides a realistic enough simulation of global soil moisture to warrant the present study.

4. Variations of soil moisture memory

The anomaly time series used to compute the lag-1 autocorrelation coefficients of soil moisture at each gridpoint layer for JJA and DJF are constructed by the monthly value of June, July, August, and December, January, February, respectively, with the climatological mean for that month removed. The results are combined according to their similarities at three levels: (1) top 0.2 m of soil, (2) the rest of the root region down to 1.0-m soil depth, and (3) the deep soil below the root region. Figure 3 shows global distributions of the autocorrelations in JJA and DJF at the 0.2-m level and root region. The autocorrelations are greater than 0.9 almost everywhere in the deep soil below the rooting zone (not shown). Because the time series of soil moisture is similar to red noise (the spectral results not shown), the first-order Markov process assumption provides a plausible comparison of time scales at different latitudes and soil depths as displayed in Fig. 4. The autocorrelations are nonzero and increasing with soil depth; that is, anomalies of soil moisture persist on monthly time scales from approximately 1 month at the surface to more than 10 months at the bottom. These decay time scales of soil moisture profile vary latitudinally and seasonally, qualitatively as expected from the temperature dependence of ET. For the top 0.2 m of soil, smaller values predominate at lower latitudes and greater values at middle and high latitudes of the Northern Hemisphere and portions of the Southern Hemisphere in JJA. The largest values in DJF are mostly in the subtropics and high latitudes of the Northern Hemisphere. Delworth and Manabe (1988, 1989) suggested that potential evaporation, as determined largely by insolation, is the primary factor responsible for such latitudinal dependence of soil moisture memory. Liu and Avissar (1999a,b) also indicated that seasonal-scale damping of soil moisture persistence is very sensitive to solar radiation. The cross-spectral analysis in section 5 shows what are the frequencies at which ET significantly correlates with vertical soil moisture and so affects the vertically varying decay time scales.

To examine how the soil moisture memory changes vertically and horizontally with season, the autocorrelation coefficients at each soil layer were zonally averaged over all land points for JJA and DJF, respectively. The Northern Hemisphere zonally averaged autocorrelation coefficients were further composited into four broad belts within which the profiles were similar. The four belts are geographically defined as equatorial (4°S–14°N), subtropical (14°–33°N), midlatitude (33°– 56°N), and highlatitude (56°–73°N). These belt-averaged autocorrelation coefficient profiles are shown in Fig. 5, representative of the large-scale latitudinal variations of soil moisture decay time characteristics. The autocorrelation coefficients increase from approximately 0.2–0.3 (τ ∼ 0.6–0.8 months) at the surface to about 0.8 (τ ∼ 4.5 months) at 1 m with the exception of the high-latitude belt in JJA, of which the autocorrelation coefficients below the surface are smaller, for example, about 0.6 (τ ∼ 2.0 months) at 1 m, comparing to the others. In the equatorial belt, the decay time is longer for the JJA composite than for DJF through the entire profile, but the opposite in the subtropical belt. In both midlatitude and high-latitude belts, the relative magnitudes of autocorrelation coefficients between JJA and DJF change with soil depth. That is, the soil moisture memory shifts from larger in summer than in winter to larger in winter than in summer, approximately at 1.3 m for the midlatitude belt and at 0.4 m for the high-latitude belt, respectively. Both potential evaporation, or solar radiation, (Delworth and Manabe 1989) and the ratio of evaporation to precipitation (Liu and Avissar 1999a,b) contribute to such a shift. All the factors involved in soil water dynamics, that is, precipitation, ET, and runoff, may contribute to soil moisture memory. Our following analysis in section 5 will explore their relative contributions to various frequencies for the four latitude belts with typical vegetation types selected.

5. Correlation of precipitation, evapotranspiration, and runoff with soil moisture

A cross-spectral analysis (Jenkins and Watts 1968), which measures the correlation between two given time series at each frequency by their coherency spectrum, was applied to obtain cospectra of precipitation (P), ET, and runoff (R) with soil moisture profile (SM), respectively. In addition, the cospectra of transpiration (ETR) and soil moisture profile were also computed for comparison. Four geographical locations, which represent typical vegetation in four latitude belts, respectively, were selected for the cross-spectral analysis based upon similarities in decay time scales and primary vegetation fractions. The locations, their vegetation types and fractions, and rooting zone (Lr) are listed in Table 1. The anomaly time series of P, ET, R, ETR, and SM were constructed as defined in section 4 by subtracting the annual cycle from the original 50-yr monthly mean time series. The cross-spectral results for the four sites are presented in Figs. 6, 7, 8, and 9, respectively. The correlation coefficient for the 95% (99%) confidence level is 0.12 (0.19) and contours range from 0.2 to 1.0, and therefore all spectral contours plotted are above the 99% confidence level. Shaded areas are for values greater than 0.4.

From Fig. 6, large correlation coefficients of P–SM, ET–SM, R–SM, and ETR–SM occur at almost every frequency for the tropical broadleaf forest site, with lower frequencies extending deeper into the soil (i.e., the “redder” feature for deeper-layer spectra). On the time scales of shorter than 4 months (r ≥ 0.25), significant coherencies of ET–SM and ETR–SM are mostly confined to the top 0.5 m of soil, while on longer time scales, ET and runoff are also correlated with deeper-layer soil moisture, for example, down to 2.0-m soil depth for periods of a year or longer. The overall correlation coefficients of P–SM, ET–SM, R–SM, and ETR–SM at the other three sites are smaller than at the tropical site. While precipitation, runoff, and ET at subtropical and midlatitude cropland sites show relatively strong correlations with soil moisture profile at most frequencies, the cospectra of P–SM, R–SM and ET–SM at the high-latitude needle-leaf site are quite weak on shorter than interannual scales. The soil moisture below the rooting zone has a very long time scale and is little correlated with ET and runoff.

6. Discussion

Koster and Suarez (2001) indicate that the autocorrelation of soil moisture—that is, soil moisture memory—is mainly controlled by four distinct factors: (i) nonstationarity (seasonality) in the atmospheric forcing, such as precipitation and net radiation; (ii) the effect of ET in removing soil moisture and hence its memory; (iii) the analogous dependence of runoff; and (iv) feedback of soil moisture on precipitation. The latter depends on how ET and runoff are partitioned between removal from the rooting zone soil column and from smaller stores located at or near the surface (Dickinson et al. 2003). This study quantifies the time scales over which these controls act.

The simulated soil moisture profiles contain notable temporal and spatial variations. Their decay time scales increase with soil depth and vary with season, the latter depending on the latitudinal belt. The analysis of Delworth and Manabe (1989) indicated longer time scales for colder seasons and climates. Such would be expected if it were primarily controlled by ET and its dependence on saturation vapor pressure. Liu and Avissar (1999a,b) indicated that actual, rather than potential, evaporation has an important impact on regional and latitudinal dependence of soil moisture persistence. The analysis of the CLM dynamics suggests that the mechanisms controlling soil moisture time scales may be more complex. In particular, there appear to be important contributions from strong dependences on soil moisture, not only ET but also runoff. These inferences are supported by the compositing of the vertical profile of autocorrelation into four large-scale latitudinal belts (equatorial, subtropical, midlatitude, and high latitude) for the Northern Hemisphere. As seen in Table 2, the tropical belt during its rainy season indicates a 1-month time scale, entirely consistent with that of the bucket model of Delworth and Manabe (1988, 1989), and possible largely controlled by the temperature dependence of the saturation vapor pressure. However, for the JJA drier season, the time scale is extended to 2 months. A bigger contrast is seen in the subtropics where the 1-month time scale for the bucket model is compatible with that of the top 0.5-m soil but the rooting zone has a time scale of 3 months in the relatively wet months to 7 months in the dry season.

Interpreting the soil water time scales in mid and high latitudes is more problematical because of the lagged memory introduced by snowfall and its later melting. In addition, soil water phase changes may contribute since our analysis considers only liquid soil water. Nevertheless, the midlatitude time scales are not unlike that found by Delworth and Manabe (1988, 1989) except that summer time scale is longer, consistent with the impact of drier conditions. High-latitude summer has a short time scale that appears to be connected to snowmelt or soil water phase change since the correlations to ET and runoff are small as suggested by Fig. 9.

Figure 10 displays the contributions to the surface water budget for the zones analyzed and the resulting residual that represents a net rate of accumulation of water either in the soil or snow. Their numerical comparisons between JJA and DJF are listed in Table 3. It shows in the equatorial belt as much as 0.4 mm day⁻¹ drying out during JJA and as much as 0.2 mm day⁻¹ wetting in the subtropics at the same time. Imbalances of order 1 mm day⁻¹ in mid and high latitudes are largely from snow accumulation and melting since the seasonality of negative values is in phase with maximum runoff, whereas phasing is opposite in the equatorial and subtropical belts. It is indicated again that the time scales of soil moisture memory are longer (shorter) in drier (wet) seasons.

The cross-spectra of soil moisture with the residual of P − ET − R shown in Fig. 11 illustrate further the combined impacts of precipitation, ET, and runoff on the time scales of soil moisture profile for the four latitude belts. Except for the high-latitude belt, soil moisture profiles are strongly correlated with P − ET − R at almost every frequency, with large correlation coefficients extending deeper in Tropics compared to the subtropics and midlatitudes, which is likely caused by the deeper rooting distribution for tropical broadleaf forest. The much weaker correlation shown in Fig. 11d, especially around the periods of 4–6 months, further implies that the freezing and melting processes have a major role in soil moisture memory for the high latitudes.

It should be emphasized that the model variability results presented here must be interpreted in terms of the model's ability to simulate the current climate correctly. Other random factors may act to influence the time scales of soil moisture at the surface, for example, the variation in net surface radiation or temperature because of clouds or frontal passages, soil water phase changes across winter and spring, etc. We cannot quantify these contributions at present.

7. Conclusions

The time scales of layered soil moisture memory show from CLM–CCM3 simulations substantial variations with geography, season, and depth. The major general characteristics are consistent with previous studies (e.g., Delworth and Manabe 1989; Liu and Avissar 1999a; Wu et al. 2002); that is, the time scales are 1) shorter in the Tropics and increasing with latitude, 2) relatively longer in arid regions, and 3) increasing with soil depth. Typically, the seasonal decay time scales increase from approximately less than 1 month at the surface to more than 4 months at 1-m depth and over 10 months at the bottom. While it changes with season, the soil moisture memory is not necessarily longer in wintertime and shorter in summertime and their relative magnitudes are different geographically. For example, in the Tropics and midlatitudes it is longer in JJA and shorter in DJF and opposite in subtropics and high latitudes. The time scales in warm climates can be at least several times longer for drier conditions than while it is sufficiently rainy. This conclusion is significant for assessing the model's predictability and capability for climate prediction. The cross-spectral analysis has shown that precipitation, ET, and runoff are strongly correlated with the soil moisture profile on various time scales. While large significant cross-correlation coefficients occur only in shallow soil layers for shorter time scales, they extend to deeper soil layers for longer time scales. The soil moisture below the rooting zone has a very long time scale and is little correlated with ET and runoff.

Soil moisture decay time scales, cross-spectra of P–SM, ET–SM, R–SM, ETR–SM, and the residual of P − ET − R with SM together with the surface water budget of annual cycle collectively provide physical insights. In particular, 1) cross-correlation with runoff tends to be stronger and deeper than that with ET; 2) in the Tropics and subtropics, the seasonal variations of time scales are inversely proportional to magnitudes of runoff (and soil moisture), and hence 3) the variations of time scales appear to be largely determined by the dependence of runoff on soil moisture, but a similar dependence of ET on soil moisture presumably also contributes; 4) soil moisture in the Tropics during its wet season has the same time scale as found by Delworth and Manabe (1988, 1989) for Tropics and subtropics in general, and hence is presumably controlled by the temperature dependence of ET, the mechanism they identified as a controlling factor for the time scales; 5) in mid and high latitudes, seasonality of snow accumulation and melt as well as freezing and melting of soil water reduces the correlations of soil moisture with runoff and ET; 6) the time scale for high-latitude soil moisture is short comparable to tropical values, this is likely connected to phase changes of water as mentioned above because of the weak connection to runoff and ET; and 7) in midlatitudes, the time scales are not dissimilar to that of Delworth and Manabe (1988, 1989) but the summer values are substantially longer, arguing for slower removal of soil moisture by runoff and ET.