1. Introduction
It is now well established that soil moisture (SM) plays an important regulatory role in the land–atmosphere interaction at a range of time scales (Dirmeyer 2001; Koster and Suarez 2001, 2003, Koster et al. 2004). However, most studies have focused on either near-surface or total-column soil moisture. The role of deep-layer moisture dynamics and its influence on the subsurface temperature profile and the surface energy balance for land–atmosphere interaction is not yet well understood. This issue is important as deep-layer processes will have longer memory compared to near-surface anomalies and will perhaps lead to better seasonal to subseasonal predictability (Kumar 2004).
Characteristics of deep-layer memory have been documented through modeling studies. Chen and Kumar (2002) investigated the effect of terrestrial memory on the El Niño–Southern Oscillation signal. They found that terrestrial systems have a delayed response to the ENSO signal due to soil moisture storage, which enhances the persistence of ENSO influence on terrestrial climate. Furthermore, they hypothesized that it is the dynamics of the entire moisture profile, and not just the near surface, that plays an important role in partitioning precipitation into its various moisture reservoirs and radiation into various energy components. In a subsequent study, Chen and Kumar (2004) have explored the influence of ENSO on terrestrial energy profiles and found that there is a correlation between ENSO signal and the soil temperature anomalies at different soil depths and that this correlation does not diminish with increasing depth. They concluded that the signature of ENSO in deeper soil layers may play a key role in explaining the long-term effects of this climate phenomenon on terrestrial hydrologic processes. They have also studied how the variability of soil moisture and temperature affects the impact of ENSO on the terrestrial enthalpy (heat storage) profile and found that the variation of terrestrial enthalpy at shallow layers is dominated by the soil moisture variation, while that of the deep layer is dominated by soil temperature variation. The importance of heat storage in the soil column is not yet well understood. In a recent commentary, Pielke (2003) recommended focus on heat storage, rather than temperature, for monitoring the climate change over the globe.
The present study focuses on understanding the characteristics of hydrologic memory in the deep layers. In addition to soil moisture, we investigate the memory characteristics of soil temperature and heat storage. This comparison is useful to understanding the relative importance of terrestrial heat and moisture processes in land–atmosphere interaction. Our study uses observed soil moisture and simulated soil temperature profiles using the data collected by the Illinois Climate Network (ICN) (Hollinger et al. 1994). The ICN soil moisture data has been used for several studies and its quality is well documented (Findell and Eltahir 1997; Yeh et al. 1998; Rodell and Famiglietti 2001; Wu et al. 2002; Saleem and Salvucci 2002; Niemann and Eltahir 2004; Seneviratne et al. 2004).
2. Data description
This study uses the soil moisture and climate data collected at the ICN stations (Hollinger et al. 1994; Hollinger and Isard 1994; Robock et al. 2000). Established in 1981, the ICN comprises 19 stations distributed across the state of Illinois and is operated by the Illinois State Water Survey. Illinois extends over 36°58′–42°30′N latitude and 87°30′–91°30′W longitude, with a geographical area of 57 918 square miles. Each ICN station provides measurements of soil moisture, soil temperature, precipitation, solar radiation, air temperature, relative humidity, and wind speed and direction. Detailed descriptions of the ICN stations can be found in Hollinger et al. (1994).
Soil moisture measurements are available for 11 soil layers from the surface to 2-m depth at each of the ICN stations. Thickness of the nine intermediate layers is 20 cm each, while that of the top and bottom layers is 10 cm. The frequency of measurement varies from season to season and from station to station. Usually measurements are taken once or twice per month during winter and three or four times per month during summer. The observation days are irregular and vary from station to station. To overcome these sampling artifacts and achieve consistency between stations, the data is aggregated into monthly averages for this study. All of the soil moisture observation sites are located in grass plots, with the exception of the one at Dixon Springs, which is located in bare ground. The soil type at all the stations is predominantly silty loam, except at Kilbourne (Topeka), which is loamy sand. Observations of soil moisture at 16 of the stations began between 1981 and 1982, two began in 1986, and one in 1991. Neutron probes calibrated by the gravimetric technique were used to measure the soil moisture data. Detailed descriptions of the measurement method and the associated uncertainties are given in Hollinger and Isard (1994).
Unlike the soil moisture, the monitoring of other climate variables at ICN stations started in the late 1980s and early 1990s. Furthermore, they are collected routinely through automated systems. Soil temperature is routinely observed for two layers at 10 and 20 cm. Other data of interest in this study are solar radiation, relative humidity, air temperature, and wind speed. These variables are measured at a height of 2 m above the ground surface with the exception of wind speed, which is measured at a height of 10 m. These data are available starting from 1990 to the present. Data on snow depth is not collected at ICN stations but is obtained from other climate stations across Illinois from the Midwestern Regional Climate Center (http://mrcc.sws.uiuc.edu).
To study the interannual variability we used the Southern Oscillation index (SOI) and the sea surface temperature (SST: here Niño-3) datasets, which are available from the NOAA Climate Prediction Center (www.cpc.noaa.gov/data/indices).
3. Variability and memory characteristics of soil moisture
a. Space–time–depth variability of observed soil moisture
Figure 1a shows a box plot that illustrates the spatial variability of soil moisture across the stations. The box plot for each soil layer is constructed based on the temporal average soil moisture over the entire period of the respective layers at each station. Figure 1a reveals two major features. First, there is high spatial variability at each layer that, in general, is higher for deeper layers than the near-surface layers. Second, on average, the soil moisture tends to be drier for the near-surface layers than the deeper layers. This may be partly due to the higher root density, resulting in greater moisture extraction to meet the evapotranspiration demand, near the surface. Despite the spatial variability in magnitude (see Fig. 1a), the temporal and vertical characteristics of soil moisture are similar from station to station, and the spatially averaged data is found to capture these characteristics well. Therefore, we present results based on spatially averaged soil moisture data. These have been compared to the analyses of individual stations and verified to be consistent with the general findingpresented here.
Figure 1b shows time series of spatially averaged soil moisture at selected depths. As one intuitively expects, the temporal variability decreases with depth. In general, minimum (maximum) soil moisture states occur in August (February) for the near-surface layer and in November (May) for the deeper layers. Within the observation period, low moisture years include, 1983, 1988, 1991, 1994, and 1999 (see Fig. 1c). High moisture years are 1985, 1990, 1993, and 1998.
The temporal variability of soil moisture is further explored by analyzing the magnitudes of amplitude and phase variations with depth (see Fig. 2). Figures 2a and 2b, respectively, show plots of spatial mean soil moisture seasonal profiles and box plots of annual variability of spatial mean for each layer. At the seasonal scale, the near-surface layers are dry (wet) during summer (winter), whereas deeper layers are dry (wet) during autumn (spring). The box plot (see Fig. 2b) clearly illustrates how the annual variability in soil moisture decays with depth. Figure 2c shows the cross-correlation curves between soil moistures of the first layer with those of the other layers. Note that (i) the maximal cross-correlation values reduce with depth and (ii) the time lag at which the maximal correlations occur increases with depth. Figure 2d shows the amplitude damping and the phase lag with depth for the annual cycle of soil moisture. The amplitude at each depth is computed as half of the difference between the minimum and the maximum of the annual cycle. The phase lag at each layer is the time lag corresponding to the maximal cross correlation between the first layer and the respective layer. As can be seen, the soil moisture amplitude damps exponentially, while the phase lags linearly. For the top 2-m soil depth, the phase lag for soil moisture is found to be about 95 days (∼3 months). This finding is consistent with that of Wu et al. (2002), who also used Illinois soil moisture data, but provides more specificity about the characteristics of phase lag and decay rate.
b. Persistence in soil moisture
Persistence can be quantified through temporal scale analysis. Temporal scales of observed soil moisture have been examined by Vinnikov et al. (1996) and Entin et al. (2000) following the concept of Delworth and Manabe (1988, 1993) that relates the autocorrelation to the temporal scale. Their findings are in agreement and indicate a soil moisture temporal scale of about 2–3 months. However, these studies have used total column soil moisture, and the memory differences between the near-surface and deep layers were not evident in their analysis. Examination of how the persistence varies with depth is a key to demonstrate the terrestrial memory differences between the near-surface and the deep-layer processes. Here, we investigate how the persistence of soil moisture changes with depth.
Figure 2e shows the profiles of 1-, 2-, and 3-month lag autocorrelations at different depths and Fig. 2f shows the corresponding temporal scales. The temporal scale is computed using Eq. (1) for the given autocorrelation (see Fig. 2e). The result indicates that the temporal scale, which is a measure of persistence, increases with depth. The soil moisture e-folding time varies from less than 2 months at the near surface to more than a year (∼15 months) at the deeper layer. This finding supports the study by Wu and Dickinson (2004), who, using model-generated soil moisture data, also found an increase of soil moisture persistence with depth. The temporal scale for depth-averaged soil moisture is about 4 months. The consistency of the curves in Fig. 2f suggests that the Markovian model provides a good approximation.
c. Dominant temporal modes in soil moisture
We use spectral analysis techniques, such as singular spectrum analysis (SSA) (Broomhead and King 1986; Vautard and Ghil 1989; Vautard et al. 1992; Elsner and Tsonis 1996) and maximum entropy method (MEM) of power spectral analysis (Burg 1978; Ulrych and Bishop 1975; Childers 1978) to identify the dominant temporal modes embedded in the time series of land memory variables (such as soil moisture, soil temperature, and heat storage) at different depths. These two techniques are chosen as they are very effective for analyzing short time series (Vautard et al. 1992; Emery and Thomson 1997), such as the data used in our study.
Although we present results based on the MEM method, they were cross-checked and found to be consistent with other techniques, such as the fast Fourier transform (FFT), multitaper method (MTM; Thomson 1982; Percival and Walden 1993), and Blackman–Tukey method (Blackman and Tukey 1958). Linear trends were removed from each time series before applying the spectral techniques.
The choice of the embedding dimension M (also called window length or model order) in SSA and MEM analysis is usually not obvious. Vautard et al. (1992) recommend that the value of M be less than N/3, while Ghil et al. (2002) recommend it to be less than N/2, where N is the number of data points in the time series. As a rule of thumb, M should be chosen to be longer than the number of data points in the oscillatory periods under investigation. Accordingly, in this study, the embedding dimension is set to 60 months (5 yr) in order to resolve scales associated with interannual ENSO signals.
Figure 3 shows the power spectrums of the soil moisture at selected depths. The spectrum is constructed based on the observed monthly data of Illinois soil moisture (spatially averaged), which spans 21 years (1983–2003). The spectra at all layers were normalized by their respective maximum for easy comparison from layers of high variance (i.e., upper layers) to layers of low variance (i.e., lower layers). Two important points can be inferred from Fig. 3. First, the low-frequency modes (interannual and annual modes) are dominant over the high-frequency modes at all soil depths. Second, the significance of interannual modes increases with depth, while that of the annual and high-frequency modes decreases with depth. Though spectra of the spatially averaged soil moisture are presented, similar analyses have been performed for each station as well as 25th, 50th, and 75th quintiles of the soil moisture variability (not shown). They all exhibit patterns consistent with the spatially averaged data.
To extract the dominant modes associated with the interannual and annual time scales, SSA is applied to the average soil moisture time series to filter out the high-frequency modes. Figure 4a shows the singular spectrum [a plot of ordered eigenvalues (variances)] of the space–depth-averaged soil moisture obtained through SSA analysis. The first, second, third, and fourth principal component (PC) pairs account for about 50%, 16%, 11%, and 6%, respectively, of the total variance. In SSA analysis, PC pairs of nearly equal variances (eigenvalues) represent an oscillatory signal (Vautard and Ghil 1989; Elsner and Tsonis 1996). Accordingly, the leading four PC pairs (each with nearly equal eigenvalues) are used to reconstruct a new time series, allowing the power spectrum to be analyzed separately for the reconstructed time series. The power spectrum of the reconstructed time series is shown in Fig. 4b. Clearly, we see three distinct interannual modes along with the annual cycle. We find that the peak frequencies of the three interannual modes correspond to the quasi-quadrennial (QQ) or (4/1), the quasi-biennial (QB) or (4/2), and the 16–18 months or (4/3) ENSO signals. By using the leading five or six PC pairs, still we see the above four principal modes, with minor high-frequency noise, indicating that these four are clearly the dominant modes.
The QQ and QB signals refer to the 4–6-yr and 2–3-yr periodicity of ENSO signals, respectively (e.g., Rasmusson et al. 1990; Jiang et al. 1995; Moron et al. 1998; Ghil et al. 2002). The (4/3) ENSO signal is usually identified as an outcome of the nonlinear interaction between the dominant QQ ENSO signal and the annual cycle (Barnett 1991; Jin et al. 1994, 1996). This phenomenon of interaction is commonly known as “subharmonic frequency locking” (Jin et al. 1994, 1996). It occurs when independent frequencies influence one another in such a way as to produce synchronization of the two oscillations into a periodic oscillation with a common longer period—a subharmonic oscillation. A study by Jin et al. (1994) maps the nonlinear frequency locking between ENSO and annual cycle into a structure similar to the “devil’s staircase”—a structure in which the inherent frequency of the system locks onto a sequence of rational fractions of external frequency.
In our analysis, the QQ signal corresponds to about 60 months (5 yr), the QB signal corresponds to about 34 months (2.8 yr), and the (4/3) signal corresponds to about 17 months (1.5 yr) periodicity (see Fig. 4b). To explore the relative contributions of the interannual and annual modes at different depths, we constructed profiles of these modes (see Fig. 4c). At the near surface the annual cycle is dominant, but the relative contributions of the QQ ENSO signal increases with depth, and at sufficient depth exceeds that of the annual cycle. This indicates that the ENSO influence penetrates deeper than the annual signal. The QB and (4/3) signals are consistently the third and fourth dominant modes throughout the soil profile with maximum contributions from both attained at the midlayers.
Care is needed in interpreting Fig. 4c. The plot is based on the relative contribution of the different modes at that particular depth. In an absolute sense, all of the modes decay in amplitude with depth; that is, variance of each of these modes is higher at the near surface and decreases with depth. However, the rate of decay with depth for the interannual and annual modes is not the same (see Fig. 4d). The annual mode decays faster than the interannual modes. This brings an increase (decrease) in the relative contribution of the interannual (annual) modes with depth. In other words, the damping depth for low-frequency modes is deeper than that of the high-frequency modes. This is in agreement with field observations that the daily moisture or temperature signals damps at shallower depth than, for instance, the annual signal (see Jury et al. 1991, their Figs. 5.14 and 5.15).
To investigate the linkage between ENSO and soil moisture signals, the spectra of the soil moisture anomaly (obtained by subtracting the corresponding climatological monthly mean from the individual monthly values) is compared with that of the Southern Oscillation index and Niño-3 index. Figure 5a shows the power spectrum of the SOI, while Fig. 5b shows the power spectrum of the depth-averaged soil moisture anomalies. The power spectrum of Niño-3 (not shown) shows patterns similar to that of the SOI. SSA is used to extract the components associated with the two dominant ENSO signals (QQ and QB) from the three datasets. The singular spectrum of the datasets is shown in Fig. 5c. Both SOI and soil moisture have similar singular spectrums. As is usually the case with nonlinear signals (Elsner and Tsonis 1996), the singular spectrum plots of SOI, Niño-3, and soil moisture anomalies consist of three portions: (i) an initial plateau, representing the dominant signals; (ii) an intermediate steep slope, representing signals that result from the nonlinear interactions of the former; and (iii) the flat floor, representing the noise. For SOI and soil moisture, the leading 4 PCs (modes) account for about 45% of the total variance, while the corresponding variance for Niño-3 is about 70%. A new time series is reconstructed from the leading four PCs, and their power spectra are analyzed for all variables. The power spectrum of the reconstructed time series is shown in Fig. 5d. Clearly, there is an indication of strong linkage between ENSO and soil moisture. This linkage gets much stronger for the deeper layer than the near surface due to the fact that the importance of the interannual modes in soil moisture increases with depth (see Fig. 4c).
4. Variability and memory characteristics of soil temperature
a. Soil temperature profile simulation
To investigate the memory characteristics associated with soil temperature, the soil temperature profile is obtained by a coupled solution of surface energy balance and temperature diffusion equation. These simulations are performed using the station average soil moisture and forcing data. A detailed description of the energy balance and the heat transfer model used in this study is given in the appendix. Modeling is necessary since observation of soil temperature is available only for two layers at 10-cm and 20-cm depth.
Meteorological data (solar radiation, air temperature, relative humidity, and wind speed) is used to drive a surface energy balance model (see the appendix) to obtain the surface temperature using the Newton–Raphson method of iteration. The surface temperature then provides the upper boundary condition for the solution of the heat transfer equation [see Eq. (A15)], which is solved using the Crank–Nicholson finite difference scheme. This provides the soil temperature profile. The observed soil moisture for each layer and the surface snow depth are used to compute the volumetric heat capacity [see Eq. (A16)] and thermal conductivity [see Eq. (A17)] of the soil. Note that, since observed soil moisture is used in the solution, a model for soil moisture transport is not required. Soil temperature is solved for 15 soil layers to a depth of 5 m. The top 11 layers coincide with the soil moisture observation layers, and 4 additional layers are added to extend the lower layer where a no-flux boundary condition can be specified. At the bottom a no-flux boundary condition is specified. Below 2 m no soil moisture variation is assumed and set equal to the mean of the bottom-most observed layer.
The simulation period for temperature covers 13 years (1990–2002) for which meteorological data are available at ICN stations as described in section 2. This shorter time period as compared to the soil moisture data limits the time scales that can be identified. A daily time step is used in the entire simulation. The daily soil moisture data used for computing the soil thermal properties is obtained from its monthly data using a Fourier interpolation technique.
The model outputs are validated with temperature observations at ICN stations (see Fig. 6). Figure 6a shows the average annual cycles of simulated surface temperature and observed air temperature. As expected, the simulated surface temperature follows the observed air temperature. The difference between the two is found to be significant during the summer season with surface temperature exceeding air temperature by about 2.5°C. The simulated soil temperature at 20 cm is validated with the corresponding observed soil temperature at the same depth (see Figs. 6b–d). There is a good agreement between the observed and simulated soil temperature at 20 cm (see Fig. 6b), with a root-mean-square error of 0.43°C (see Fig. 6c) and a correlation coefficient of 0.986 (see Fig. 6d). The discrepancy between the observed and modeled soil temperature is maximal during winter compared to during summer, attributable to a simpler snow model.
b. Soil temperature memory characteristics
The soil temperature data generated through the solution of the heat transfer equation is used to study its memory characteristics. Figure 7 shows profile plots of variability, phase lag, and persistence features for soil temperature. This is similar to the corresponding analysis in Fig. 2 for soil moisture. As for the soil moisture, the soil temperature portrays more significant variability for the near surface than for the deeper layers. The amplitude damps exponentially and the phase lags linearly with depth (see Fig. 7d). However, the magnitude of soil temperature phase lag is quite different from that of soil moisture. For the top 2-m soil depth, the phase lag for soil temperature is about 53 days (<2 months) as opposed to more than 3 months lag for soil moisture for the same depth. The total phase lag in soil temperature for the 5-m depth is about 130 days (∼4.3 months). Unlike the soil moisture, the annual average soil temperature is nearly constant with depth (see Fig. 7b).
A cross correlation between soil moisture and temperature at different layers (not shown) indicated that soil moisture and soil temperature are out of phase for the topmost layer; the temperature lags the soil moisture by about 6 months. For the bottom layer, the lag between the two is found to be about 7.5 months. This means that, from the surface to 2-m soil depth, the soil moisture lags by about 1.5 months more than the corresponding phase lag by the soil temperature. This agrees well with the phase lag difference between the two, discussed earlier, that is, about 95 days for soil moisture versus about 53 days for soil temperature.
As with the soil moisture, the soil temperature is characterized by increasing persistence with depth (see Figs. 7e and 7f). For a given depth, it is found that the temporal scale for soil temperature is far less than that of the soil moisture. The soil temperature e-folding time varies from about 1 month at the near surface to about 6 months at 2-m soil depth in contrast to 2 and 15 months, respectively, for soil moisture. This indicates that the soil temperature persistence is only half of the soil moisture persistence. The higher persistence of the latter suggests that soil moisture may play a more significant role (compared to soil temperature) in the long-term predictability of climate. In Fig. 7f we see that the temporal scale for the 1-, 2-, and 3-month lag diverges below 2-m depth. This may be due to the lack of variability in the soil moisture forcing for layers below the 2-m depth, which is set to the mean of the 11th layer. The fact that the thickness of the bottom 4 layers (layers 12–15) are larger than the top 11 layers (whose thicknesses are based on the soil moisture measurement levels) might have also had an impact. Overall, the temporal scale for depth-averaged (top 2 m) soil temperature is about 2.5 months, as opposed to 4 months for soil moisture.
A power spectral plot of soil temperature for selected layers is given in Fig. 8. As with the soil moisture, the influence of the interannual modes increases with depth, while that of the annual and other high-frequency modes decreases with depth. However, unlike the soil moisture, which showed four low-frequency dominant modes, the soil temperature spectra reveal only three of the low-frequency modes: QQ ENSO, (4/3) ENSO, and annual cycle. Since the soil temperature simulation is done for a shorter period, we believe that it has resulted in our inability to detect the QB ENSO signal. Unlike for the soil moisture, where the interannual mode takes dominance over the annual cycle at a depth of about 1.5 m, the annual cycle dominates over the interannual modes at a much greater depth for the soil temperature. The dominance of the interannual mode over the annual cycle comes after almost a depth of about 4.5 m. This suggests that the interannual soil temperature signals penetrate deeper into the soil than the interannual soil moisture signals. In other words, the damping depth for the soil moisture signal is shallower than that of the soil temperature signal.
5. Variability and memory characteristics of soil enthalpy
In this study, a 13-yr (1990–2002) enthalpy dataset is generated based on the observed soil moisture and snow datasets, and the simulated soil temperature data. Figure 9 shows profiles of seasonal variations, phase lags, correlations, and temporal scales associated with the soil enthalpy. The seasonal variability in enthalpy (see Figs. 9a and 9b) is governed more by the soil moisture variability than by the soil temperature variability. As for soil moisture and temperature, the phase lags more or less linearly (see Fig. 9d), but the lag (∼7 months) for the 2-m soil depth is larger than the corresponding values for soil moisture and temperature. The correlation (see Fig. 9c) starts to increase after a 6-month lag, as one expects. Also, the decay of amplitude with depth does not seem to follow exponential curve (see Fig. 9d); rather it is nearly constant below 1-m depth with a very high damping rate for the top 1 m. Unlike the soil moisture and temperature, the temporal scale increases with depth for the top 1 m and decreases afterward (see Figs. 9e and 9f). These characteristics of the soil enthalpy have emerged due to the difference in phase lag for soil moisture and temperature. The nonlinear interaction between soil moisture and temperature invalidates the Markovian approximation for soil enthalpy as reflected in Fig. 9f. The temporal scale for the depth-averaged enthalpy is about 2 months.
Figure 10 shows the power spectra of the terrestrial enthalpy for different soil layers. Since enthalpy is a function of both soil moisture and temperature, the modes that were detected in soil moisture and temperature were also detected in the enthalpy spectra. However, unlike the case of soil moisture and temperature, the significance of the interannual modes did not increase consistently with depth. Rather, the interannual modes are dominant at the mid soil layers (around 1-m depth), whereas the annual mode dominates at the near surface and deeper layers. This spectral characteristic of the enthalpy is again due to the difference in the phase lags (with depth) between the soil moisture and temperature signals and complements the persistence characteristic discussed above.
Hu and Feng (2004), in their study of land memory, have considered only soil temperature variability in computing the soil enthalpy by setting the heat capacity (which is a function of soil moisture) to a constant value. However, our analysis indicates that the variability of soil enthalpy is governed by both soil moisture and temperature variation. If we neglect the soil moisture variability in computing the enthalpy, then the characteristics of the enthalpy follow that of the soil temperature. Therefore, it is important to consider both soil moisture and temperature variation in analysis of soil enthalpy.
6. Effect of soil moisture variability and root distribution on surface energy fluxes
a. Effect of soil moisture variability
Soil moisture controls the partitioning of energy fluxes at the land surface through its effect on surface temperature (e.g., Entekhabi et al. 1996; Eltahir 1998; Dirmeyer 2000, 2001). Therefore, it is important to study how the surface temperature and energy components are influenced by the variability of soil moisture at different layers. Here, we consider two cases of moisture setup. In the control case (case 1), soil moisture at each layer is set to actual observations. In the second case (case 2), the soil moisture is set to the annual cycle of the respective layer; that is, the interannual variability is neglected.
Figure 11 shows the changes in the simulated surface temperature (see Fig. 11b) and surface energy fluxes (see Figs. 11c–f) between case 1 and case 2. It is obtained by subtracting values of case 2 from case 1. To understand the changes in relation to low and high moisture years, a depth-averaged soil moisture anomaly time series is plotted (see Fig. 11a). As can be seen, removing the interannual variability from the soil moisture has resulted in an increase (a decrease) in surface temperature (see Fig. 11b) and sensible heat flux (see Fig. 11d) during high (low) moisture years. The corresponding change in net radiation (see Fig. 11c) and latent heat flux (see Fig. 11e) is a decrease (an increase) during high (low) moisture years. The changes are higher for the summer than for the winter. The effect on sensible and latent heat flux is dramatic in that during summer the changes are as high as 40 W m−2 for the former and 45 W m−2 for the latter. The maximum change for surface temperature is about 1.5°C and that of net radiation is about 9 W m−2. The effect on ground heat flux (see Fig. 11f) is less significant. The rms of the changes is about 0.3°C for surface temperature and 1.7, 8.9, 10.8, and 0.23 W m−2 for net radiation, sensible heat, latent heat, and ground heat fluxes, respectively.
To quantify the effect of deep-layer moisture on surface fluxes, we studied the cumulative effect of smoothing the soil moisture at different layers. The smoothing is done by setting the soil moisture of the specific layer to its temporal (climatological) mean and starts from the bottom layer and moves upward. Figures 12a and 12b indicate the profiles of the changes in surface temperature and surface fluxes, respectively, due to the changes in soil moisture from variable to climatological mean for the total number of layers shown on the y axis starting from the bottom layer. Plotted in the x axis are the changes in the mean values of the simulated surface variables (temperature and fluxes) between the variable and nonvariable moisture setups. The effect of soil moisture smoothing is consistently pronounced on sensible and latent heat fluxes throughout the depth (see Fig. 12b).
In our case, x represents the surface temperature or the surface fluxes, and y represents the soil moisture at individual layers. The elasticity plot in Fig. 12c shows that the impact of deep-layer processes on surface fluxes is minimal compared to the near-surface processes. However, it can be important depending on the root distribution considered in the model, as will be discussed next. On much longer time scales the deep layers may show an influence on the surface fluxes. Therefore, proper specification of soil moisture (not only the near surface, but also the deep layer) in climate models is important for proper climate prediction.
b. Effect of root distribution
Plants regulate fluxes along the soil–plant–atmosphere continuum (hence, the partitioning of energy fluxes) through their root and stomatal system (Feddes et al. 2001). Fluxes along the soil–plant continuum are controlled partly by the root properties, such as rooting depth and root distribution with depth. Hence, it is important to investigate the role of root distribution in modeling the soil–plant–atmosphere interaction. Most soil–vegetation–atmosphere transfer (SVAT) models (e.g., Noilhan and Planton 1989) represent the rates of water extraction from different soil layers in terms of a root density function. Root distribution is usually assumed as an exponential function of the soil depth (e.g., Jackson et al. 1996; Lai and Katul 2000; Feddes et al. 2001; Zeng 2001).
The comparison of simulated surface temperature (see Fig. 13b) and surface fluxes (see Figs. 13c–f) for the different root distributions are shown in Fig. 13. These simulations incorporate the observed soil moisture variability. The impact of root distribution on sensible and latent heat fluxes is significant, whereas the influence on surface temperature, net radiation, and ground heat flux is smaller. These influences have important implications in hydrologic and biogeochemical cycles and their parameterizations during model design and/or calibration.
The fact that case 3 (where the root fraction at all depths is assumed equal) resulted in higher latent heat flux than, for example, case 1 (where the root fraction is exponential with depth) suggests that the importance of the deep-layer moisture in regulating the energy partitioning at the land–atmosphere interface depends greatly on the root distribution considered in the model. In case 3 the increased water availability during dry (summer) season that is associated with deep-layer root and soil moisture led to increased latent heat flux.
We may, therefore, conclude that there are inherently two mechanisms by which deep-layer moisture impacts the surface fluxes. First, its temporal variability sets the lower boundary condition for the transfer of moisture and heat fluxes from the surface. Second, this temporal variability influences the uptake of moisture by the plant roots, resulting in the variability of the transpiration and therefore the entire energy balance. Initial results suggest that this second mechanism may be more predominant, indicating that accurate specification of rooting depth in models will play a crucial role in improving the predictability.
7. Summary and conclusions
The soil moisture in the Illinois Climate Network is characterized by high spatial, temporal, and vertical variability. Soil is drier (wetter) during summer (winter) for near-surface layers and during autumn (spring) for deeper layers. The soil moisture spatial variability increases, while the temporal variability decreases with depth. The soil temperature is out of phase with soil moisture. Both soil moisture and temperature are characterized by amplitude decay and phase lag with depth since both the amplitude damps exponentially while the phase lags linearly. The phase lag is about 3 months for the soil moisture and 2 months for soil temperature for the top 2-m soil depth.
Both soil moisture and temperature are characterized by increasing persistence with depth, the persistence for soil moisture at all layers being almost twice that of soil temperature. The e-folding time varies from about 2 months (for 1st layer) to 15 months (for 11th layer) for soil moisture and from about 1 month (for 1st layer) to 6 months (for 11th layer) for soil temperature. This indicates that the memory (modulation effect) of the deeper layer is significantly higher than that of the near-surface layer. For the top 2-m soil depth, the temporal scales for depth-averaged soil moisture, soil temperature, and soil enthalpy are about 4, 2.5, and 2 months, respectively. The temporal scale for SOI is found to be about 5.5 months.
Spectral analysis shows four dominant low-frequency modes that make up the time series. These modes correspond to the quasi-quadrennial (QQ), quasi-biennial (QB), and (4/3) ENSO signals, and the annual cycle. For soil temperature, only three of these modes are identified, with the QB ENSO mode undetected, possibly due to the shorter temperature time series. Modes detected for terrestrial enthalpy agree with that of the soil moisture. For both soil moisture and temperature, the relative significance of the interannual modes increases with depth, while that of the annual mode decreases with depth. For near-surface layers the annual mode dominates over the interannual modes, but for deeper layers the interannual mode tends to dominate over the annual mode. The depth at which the interannual mode takes dominance over the annual mode is shallower for soil moisture than for soil temperature, suggesting that the soil temperature modes penetrate deeper than that of the soil moisture. For terrestrial enthalpy, interannual modes are found to be dominant at middle layers, with the annual mode taking the dominance at near-surface and deep layers. Overall, these analyses suggest that there is a strong influence of ENSO on the land hydrologic memory.
The partitioning between sensible and latent heat fluxes at the surface is highly sensitive to the soil moisture condition and root density at all depths. The interannual variability of soil moisture has a significant impact on the surface energy fluxes. However, it appears that the interannual variability in the near-surface layers plays a more dominant role than that in the deeper layers. The significance of the deep-layer moisture in influencing the energy partitioning for land–atmosphere interaction depends on the root distribution. Vegetation change resulting from anthropogenic impacts can result in the change of root distributions. This can also result in the long-term alteration of land–atmosphere feedback with significant control of the deep-layer moisture variability. Seasonal and interannual variability in moisture stress may also lead to a different root distribution for the same type of vegetation. This suggests that it is important to treat root distribution in hydroclimatic models as a dynamic rather than as a static variable. The latter is typical of current SVAT models.
Acknowledgments
Support for this research is provided by NOAA under Grant NA03OAR4310070 and NSF under Grant EAR 02-08009.
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APPENDIX
Energy Balance–Heat Transfer Model
(a) Box plot showing spatial variability of the temporally averaged soil moisture data for all 11 observation layers. (b) Time series plot of spatially averaged monthly SM data for selected layers. Li refers to ith layer. (c) Time series plot of space–depth averaged annual SM data.
Citation: Journal of Climate 18, 23; 10.1175/JCLI3590.1
Soil moisture (a) mean seasonal profiles, (b) box plot profile of the annual variability of the spatial mean, (c) cross-correlation curves between the first layer and the other layers, and (d) amplitude decay and phase shift with depth. (e) Depth-wise variations of 1-, 2-, and 3-month lag autocorrelations and (f) the corresponding temporal scales for SM anomaly.
Citation: Journal of Climate 18, 23; 10.1175/JCLI3590.1
Normalized power spectra of spatially averaged SM for selected soil layers for (a) layer 1: 0–10 cm; (b) layer 3: 30–50 cm; (c) layer 5: 70–90 cm; (d) layer 7: 110–130 cm; (e) layer 9: 150–170 cm; and (f) layer 11: 190–200 cm. Only six layers are shown. The spectrum is obtained using the MEM method.
Citation: Journal of Climate 18, 23; 10.1175/JCLI3590.1
(a) Singular spectrum for depth-averaged SM (only leading 20 modes out of 60 are shown), (b) power spectrum of the leading 8 modes (4 PC pairs) and their association to the ENSO signals, (c) profiles of the relative contribution of the dominant modes at different depths, and (d) profiles of the actual (absolute) contribution of the dominant modes at different depths.
Citation: Journal of Climate 18, 23; 10.1175/JCLI3590.1
Power spectra of (a) SOI and (b) depth-averaged soil moisture anomaly; (c) singular spectrum of SOI, Niño-3, and SM anomaly for the leading 20 modes; (d) power spectrum of the four leading principal modes for SOI, Niño-3, and SM.
Citation: Journal of Climate 18, 23; 10.1175/JCLI3590.1
Average annual cycles of (a) surface and air temperature and (b) simulated and observed soil temperature at 20 cm. (c) Difference between simulated and observed soil temperature at 20 cm. (d) Scatterplots of simulated vs observed temperature at 20 cm.
Citation: Journal of Climate 18, 23; 10.1175/JCLI3590.1
Soil temperature (a) mean seasonal profiles, (b) box plot profile of the annual variability of the spatial mean, (c) cross-correlation curves between the first layer and the other layers, and (d) amplitude decay and phase shift with depth. (e) Depthwise variations of 1-, 2-, and 3-month lag autocorrelations and (f) the corresponding temporal scales for the soil temperature anomaly.
Citation: Journal of Climate 18, 23; 10.1175/JCLI3590.1
Normalized power spectra of soil temperature for selected soil layers for (a) layer 1: 0–10 cm; (b) layer 5: 70–90 cm; (c) layer 9: 170–190 cm; (d) layer 13: 220–260 cm; (e) layer 14: 260–340 cm; and (f) layer 15: 340–500 cm.
Citation: Journal of Climate 18, 23; 10.1175/JCLI3590.1
(a) Time series plot of depth-averaged soil moisture anomaly. Time series plot of the changes in (b) surface temperature, (c) net radiation, (d) sensible heat flux, (e) latent heat flux, and (f) ground heat flux between case 1, where SM is set to the actual observation, and case 2, where SM is set to annual cycle (i.e., interannual variability in SM is removed). Positive values indicate that case 2 is greater than case 1.
Citation: Journal of Climate 18, 23; 10.1175/JCLI3590.1
The cumulative effect of SM smoothing at different layers (from bottom up) on (a) surface temperature and (b) surface energy fluxes; (c) the elasticity—the percentage change in surface temperature or fluxes with respect to the percentage change in SM at different layers. The vertical axis in (c) refers to the depth at which the SM is set to constant value to get the corresponding elasticity on the horizontal axis for surface temperature and fluxes.
Citation: Journal of Climate 18, 23; 10.1175/JCLI3590.1
(a) Profiles of root distribution for the different cases. Annual cycles of simulated (b) surface temperature, (c) net radiation, (d) ground heat flux, (e) latent heat flux, and (f) sensible heat flux for the different cases of root distributions.
Citation: Journal of Climate 18, 23; 10.1175/JCLI3590.1
Table A1. Model parameter values. Soil-dependent values are specified for silty loam soil, typical of the soil type at ICN stations.
