Impact of Atmospheric Variability on Soil Moisture-Precipitation Coupling

It is now well-established that the chaotic nature of the atmosphere severely limits the predictability of weather, while the slowly varying sea surface temperature (SST) and land surface states can enhance the predictability of atmospheric variations through surfaceatmosphere interactions or by providing a boundary condition (e.g., Shukla 1993, 1998; Shukla et al. 2000; Graham et al. 1994; Koster et al. 2000; Dirmeyer et al. 2003; Quan et al. 2004). Among them, the influence of ocean is more important on a global scale because it covers twice as much surface area as land and is a much larger heat and energy reservoir. But the impact of ocean may not be dominant over land, especially the mid-latitude land (Koster and Suarez 1995). The Global Land-Atmosphere Coupling Experiment (GLACE) (Koster et al., 2004, 2006) builds a framework to objectively estimate the potential contribution of land states to atmospheric predictability (called land-atmosphere coupling strength) in numerical weather and climate models. By averaging the estimated land-atmosphere coupling strength from 12 models participating in GLACE, an ensemble average coupling strength is obtained. However, the coupling strength varies widely among models. The discrepancy is certainly related to differences in the parameterization of processes and their complex interactions, from soil hydrology, vegetation physiology, to boundary layer, cloud and precipitation processes. It is difficult to determine what causes the relatively strong or weak coupling strengths seen in individual models. Some studies have identified the impact of soil moisture on evapotranspiration (ET) (denoted SM→ET) and the impact of ET on precipitation (denoted ET→P) as two key factors for land-atmosphere coupling (Guo et al. 2006 (hereafter GUO06); Dirmeyer et al. 2010). For soil moisture to have a strong impact on precipitation, both SM→ET and ET→P need to be strong. This usually happens in transitional zones between wet and dry climates (Dirmeyer 2006). In addition to the mean climate state, does the climate variability have some impact on land-atmosphere coupling? A theoretical study found that the strength of the external forcing can affect the coupling strength and the location of coupling hot spots (Wei et al. 2006). Even less is known about how the land-atmosphere coupling is related to the


Results from GLACE-type experiments
shows the p  values of total precipitation for ensembles W (16-member control experiment for June-July-August (JJA)) and S (soil wetness specified in all ensemble members from an arbitrarily chosen member of W) and their difference () ( ) pp SW   (see the appendix for complete definitions). The three indexes are generally higher when the LSSs are coupled to the COLA AGCM than to GFS, indicating that the difference in AGCM is the main reason for these differences. The impact of different LSSs, which can be seen from the varying spatial distributions of the indexes when coupled to the same AGCM, is secondary. p  shows largely similar patterns for all the six model configurations, with the largest values in the tropical rain belt where the SST forcing has the strongest influence (Shukla 1998). The patterns of ( ) p W  and ( ) p S  are very similar, with large differences (( ) () pp SW   ) mainly over the regions with common high values. This indicates that the land-atmosphere coupling strength may be strongly influenced by the external forcing. By "external", we mean the forcing is from outside of the land-atmosphere system, such as that from SST. The patterns of ( ) ( ) pp SW   for different model configurations have much lower similarity than those of p  (spatial correlations are 0-0.29 for ( ) ( ) pp SW   and 0.43-0.71 for p  ). For both AGCMs, coupling to SSiB produces the strongest landatmosphere coupling strength globally, while coupling to Noah produces the weakest. The differences seen should be mainly from the land models' different connections between soil moisture and surface fluxes, because they are coupled to the same AGCM.

A decomposed view of land-atmosphere coupling strength
As discussed above, the slowly varying boundary forcing may play an important role in the similarity of the precipitation time series in different ensemble members (magnitude of p  ). It is very likely that the "fingerprints" of these slow forcings also exist in the precipitation time series. An effective way to examine this is to decompose the time series by frequency bands. After ignoring the first 8 days of integration of each JJA to avoid possible problems associated with the initial shock to the model atmosphere, as in calculating p  , there remain 84 days left for analysis. We performed a discrete Fourier transform (discussed in detail in Ruane and Roads (2007)) to decompose the daily time series into three frequency bands: fast synoptic (2-6 days), slow synoptic (6-20 days), and intraseasonal (20-84 days). The choice of these frequency bands is arbitrary; other comparable choices give similar results. Note that the time series may contain a portion of the seasonal cycle, but due to the length of the time series we refer the 20-84 days variation as intraseasonal. Fig. 2  have similar variance percentage distributions as these GLACE-type simulations (not shown). For theoretical white noise, the variance at each frequency is the same, so the variance percentages are determined by the widths of the frequency bands. Therefore, the variance percentages of the above three bands (from fast to slow) for white noise are: 69%, 21%, and 10%, respectively. Overall, both the model results and observations follow a red spectrum, with variance percentages less than white noise values at high frequencies and greater than white noise values at low frequencies.
In Fig. 2, the spatial correlations between ( ) p W  and the percentage of intraseasonal variance (IV) are high (right column), but the correlations of ( ) p W  with the other two frequency bands are negative (left two columns). Ensemble S (not shown) shows similar results as ensemble W. This demonstrates that regions with a larger percentage of IV tend to have a higher value of p  , no matter whether soil moisture is interactive (W) or not (S). This is not unexpected because, as we discussed above, most of the precipitation predictability (or p  ) is from the slowly varying boundary forcing. Regions with stronger boundary forcing may be constrained to show more low-frequency variation and the precipitation time series will be more similar in an ensemble (larger p  ). For ensemble S, the prescribed soil moisture is also one of the slow boundary forcings. However, compared to the ensemble without the constraint of this slow forcing (W), ensemble S does not show significant change in the global pattern of variance distribution (ensemble S does show overall less low-frequency variance and more high-frequency variance than ensemble W because of the lack of soil moisture interaction (Delworth and Manabe 1989)). These results show that different land models or land states do not matter much for the global pattern of precipitation variance distribution, which may be determined by other factors such as global climate (SST, radiation etc.) and the convection scheme. Ruane and Roads (2008) obtained similar results from a global assimilation system. They found that two different land models did not produce a noticeable difference in variance distribution of precipitation, but two different convection schemes can have significantly different effect. Wilcox and Donner (2007) also showed that the convection parameterization of a GCM can greatly impact the frequency distribution of rain rate, and their model with relaxed Arakawa-Schubert formulation of cumulus convection (also used in COLA AGCM) exhibit a strong bias toward excessive light rain events and too few heavy rain events. The above shows that neither the land model nor soil moisture has a great impact on the global pattern of precipitation variability and predictability. However, their impact may be strong at regional scales. The difference ( ) ( ) pp SW   shows the impact of soil moisture. It tries to remove the effects of the same strong external forcing on both S and W and highlight the role of soil moisture, although we understand that the effects of those forcing cannot be completely removed in a nonlinear system (more discussion on this aspect follows). The spatial correlations between percentage of IV and ( ) ( ) pp SW   are also shown in Fig. 2 (as the last number in right column). They are generally weaker than the correlation with p  , indicating that something other than the low-frequency external forcing is playing an . This should be the impact of soil moisture. Wei et al. (2010b) demonstrates that the pattern of p  and ( ) ( ) pp SW   in Fig. 1 can be reproduced by using only the time series of intraseasonal precipitation variation (higher frequencies filtered out), and the time series of the other two frequency bands result in very weak values. This is because the intraseasonal component of precipitation, mostly caused by the same low-frequency external forcing, has high consistency among the ensemble members, while the high frequency component of precipitation, mostly from chaotic atmospheric dynamics, is generally incoherent among the ensemble members. This result indicates the importance of IV in the estimation of land-atmosphere coupling. The overestimation of low-frequency variance shown in Fig. 2 is also consistent with the overestimation of precipitation persistence shown in Fig. 3. The lag-2-pentad autocorrelation of precipitation (ACR) shown here is also an indicator of the percentage of low-frequency precipitation variance, and it has similar spatial distributions as the percentage of IV but is much easier to calculate. More importantly, its spatial distributions are more similar to that of ( ) p W  than the percentage of IV, as can be seen from the much higher spatial correlations (Fig. 3). This is probably because the percentage of IV only considers the variation at a certain frequency band (20-84 days here) but ACR considers the general persistence and is not restricted by certain frequencies. It can also be seen in Fig. 3 that the precipitation variability of GFS is overall closer to that of GPCP data (Xie et al. 2003) than the COLA AGCM, which may affect the accuracy of the simulated land-atmosphere coupling. This will be discussed next. This model bias has also been shown in some other studies and by comparing with other observational datasets. Although the observational datasets have uncertainties and errors, Sun et al. (2006) found that no matter what observational dataset is used, this model bias is relatively large compared to the uncertainties among observations. This bias of the models may be related to a well-known problem in AGCM parameterizations: premature triggering of convection so that precipitation falls too frequently but too light in intensity (Trenberth et al. 2003;Sun et al. 2006;Ruane and Roads 2007).  (1987)(1988)(1989)(1990)(1991)(1992)(1993)(1994)(1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002) to match the sample size of the models. Values larger than 0.12 are over 95% confidence level. Seasonal cycles are not removed in this calculation; removing them can lead to results with similar patterns but smaller amplitude.

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Climate Variability -Some Aspects, Challenges and Prospects 24

Respective role of land and atmosphere in soil moisture-precipitation coupling
The above has shown that the low-frequency precipitation variability has an indirect but important connection to the computed land-atmosphere coupling. More low-frequency precipitation variability in the model can lead to higher precipitation predictability ( p  ) and stronger land-atmosphere coupling ( () ( ) pp SW   ). Therefore, there are three different processes involved: SM→ET, ET→P, and precipitation variability. What is the relationship among them? GUO06 separated SM→ET and ET→P based on a post hoc analysis, but they did not explicitly separate the role of soil moisture and atmosphere because ET is strongly affected by precipitation and radiation; the variability of ET is an approximation of low-frequency atmospheric variability. Thus SM→ET inevitably includes some information from atmosphere, including precipitation variability. The multi-model coupling approach provides a unique tool to estimate the respective impacts of the AGCMs and LSSs on the coupling, and only by this approach can the role of atmosphere and land be completely separated. Although the above experiment shows the dominant role of the AGCMs in land-atmosphere coupling, it is still uncertain what are the roles of land and atmosphere in the coupling because the characteristics of the AGCMs may also affect land and its response. How important is the land response compared to the characteristics of the atmosphere (including atmospheric variability, sensitivity of precipitation to ET, etc.)? As the precipitation has more persistence in the COLA AGCM than in GFS, this attribute of precipitation variability is stored in the soil moisture, with more sustained soil states when the LSSs are coupled to the COLA AGCM than coupled to GFS (not shown). In order to investigate the impact of soil moisture variability on the coupling, in experiment (2) we exchange the prescribed soil moistures for COLA-SSiB and GFS-SSiB in ensemble S. This forces the models to see different soil moisture variabilities from their original S ensembles, and there is no change to the W ensembles. The resulting impacts on precipitation predictability (or coupling strengths) are shown in Fig. 4 ). It can be seen that, compared to the original coupling strength in Fig. 1, the modified coupling strength are overall weaker for COLA-SSiB and stronger for GFS-SSiB, but COLA-SSiB still has much stronger coupling strength than GFS-SSiB. This indicates that the impact of soil moisture variability may have some impact on the land-atmosphere coupling, but the characteristics of the atmosphere appear to be more important, at least for the case here. Note that the above action processes may be model dependent and vary spatially, but it is important to know that the atmospheric variability may also impact the coupling strength indirectly through land. Therefore, the precipitation variability impacts soil moisture-precipitation coupling both directly in the atmosphere and indirect through land (Fig. 5). More low-frequency variability of soil moisture usually means more sustained dry and wet periods and stronger low-frequency evaporation variation, which can lead to a more robust precipitation response (higher predictability and coupling strength). The direct impact of precipitation variability on soil moisture-precipitation coupling has been discussed in section 4 and more discussion follows. GUO06 calculated SM→ET as (( )  ). For soil moisture to have a strong impact on ET, both of them need to be sufficiently high. ET→P is simply calculated by GUO06 as the ratio of () ( ) PP SW   to SM→ET. (GUO06 introduced one more method for calculating ET→P, which produces similar results.) As mentioned, this diagnostic of SM→ET should be affected by the variability of precipitation and radiation. The experiment (2) above also demonstrates this indirectly. To verify this in another way, we calculate the inter-model correlation between ACR and SM→ET across the 12 GLACE models ) (a correlation with a sample size of 12). We show results from GLACE models because we do not want our results to be limited to the models we use. It can be seen in Fig. 6a that there is substantial positive correlations between ACR and SM→ET over the globe, supporting our conjecture on the relationship between precipitation variability and SM→ET. The correlations between ACR and ET→P and between SM→ET and ET→P are both very low (Fig. 6b, 6c), suggesting that they are largely independent.

Conceptual relationships
The above analysis shows that the spatial distribution of both () P W  and () P S  are largely consistent with that of the low-frequency variability of the atmosphere, which may come from the slow external forcing or internal atmospheric dynamics. We denote it as F. F can be measured by the percentage of IV or ACR, and we have shown above that ACR is a better metric. The conceptual relationship between p  , F, and the impact of soil moisture  is given as where 0  is a constant, and 0  >>  over most regions. Thus, the spatial variation of  p is largely determined by F, which is consistent with the analysis above. F is similar for both ensemble W and ensemble S, so the coupling strength where () ( ) SW    is the difference of  between the two ensembles and can be further expanded to SM→ET and ET→P. Therefore where SM→ET is a function of F and some other model parameterizations. All the three factorsF, SM→ET, and ET→P may impact the coupling strength. The impact of F is separated from that of SM→ET because the impact of the atmosphere can be independent of the land surface. This multiplicative form of the equation considers the nonlinear combination of the factors. When SST is prescribed, F is mainly a property of the AGCM, especially the convection scheme. SM→ET is affected by both the LSS and the AGCM, and ET→P is mainly determined by the AGCM, especially the convection and boundary layer parameterizations. This decomposition, although is still conceptual, integrates our current understanding on land-atmosphere coupling, and it makes diagnosing land-atmosphere coupling much easier. GUO06 only partly considers the impact of F (through SM→ET) and attributes the rest of the coupling strength to ET→P. They found that, for the 12 GLACE models, SM→ET has stronger correlation with the coupling strength than ET→P, and concluded that SM→ET is the main cause of the differences in the coupling strength. However, we show that the differences in SM→ET can be partly attributed to the impact of atmospheric variability, so it is still hard to say whether the different AGCMs or the different LSSs is the main cause of the differences in coupling strength. In spite of that, for our six model configurations here, the multi-model coupling method has clearly shown that the difference between the AGCMs is the main reason. It remains possible that the differences among the three LSSs are unusually small or the differences between the two AGCMs are unusually large.

Calibration of the estimated GLACE land-atmosphere coupling strength
In order to examine whether our results on the overestimation of low-frequency variance and its relationship with p  also apply to other models, we look at the GLACE dataset www.intechopen.com Climate Variability -Some Aspects, Challenges and Prospects 28 Fig. 7. Same as Fig. 3, but for the 12 models participating in GLACE (all from ensemble W; ensemble S has similar results). The first value at the left corner of each panel is the global mean (land only), and the second value (in the parentheses) is the spatial correlation of ACR with ( ) p W  . ). Fig. 7 shows the ACR for 12 models participating in the GLACE, and their respective spatial correlations with p  . Similar to our model simulations above, ensemble S (not shown) shows very similar results to ensemble W. Also, all the models here have overestimated the mean ACR compared to the GPCP results, and their average is about double the ACR of GPCP (Fig. 8). The spatial correlations of ACR and p  are always high; even the lowest value (0.5 from GFS/OSU) is well over the 99% confidence level (assume the grid points are independent). Therefore, the GLACE models and our models show similar relationships between p  and ACR. We have shown that the estimate of precipitation predictability caused by soil moisture ( () ( ) PP SW   ) is closely related to the atmospheric low-frequency variability F but the models generally overestimate it. The influence of F on () ( ) PP SW   is obviously shown in equations (2) and (3). However, we cannot conclude that the land-atmosphere coupling strength estimated by GLACE is overestimated, because other important factors (SM→ET and ET→P) are still not observed at large scale. Nonetheless, we may assume that the other factors from the model ensemble are better than that of most individual models, and try to correct F to make () ( ) PP SW   possibly closer to reality. Roughly, we calibrate the average () ( ) PP SW   for the 12 models at each grid point (all interpolated to a common 2.52.5 grid as GPCP data): (obs) (( ) () ) (( ) () ) (models) where ACR(obs)/ACR(models) is the ratio of ACR for GPCP data and the average ACR for the 12 models. This method tries to correct F by scaling it with a ratio of observed and modeled precipitation ACR. The GPCP-1DD data is used as ground truth observations. The ACR is calculated from ensemble W instead of ensemble S because it corresponds more closely to the real world (soil moisture is interactive). Note that the precipitation time series also contains a slice of the seasonal cycle during JJA, which is consistent with GLACE analysis. The predictability from seasonal variation is also important, because not every model can produce an accurate seasonal cycle. This calibration method considers model biases in both intraseasonal and seasonal variances. If removing the predictability from the seasonal variation, the coupling strength will be weaker but the patterns are similar (not shown). Fig. 8. Same as Fig. 3, but (top) for the average of 12 models participating in GLACE and (bottom) GPCP (same as in Fig. 3).
Although the spatial correlations between p  and the ACR are very significant for all the models, the strong connection between p  and F described in equation (1) may not happen over all the regions. The noise may damp the connection in some cases. We then calculated the correlation between p  and ACR across the 12 GLACE models (a correlation with a sample size of 12; Fig. 9). It indicates a general connection between p  and ACR for all the 12 models at each grid point. The regions with strong positive correlation are where p  and ACR have a strong connection for almost all the models. Over other regions where the correlation is positive but not so strong, their relationship may not be so consistent for the models but larger F can generally lead to larger p  . We can see in Fig. 9 that over 95% of the land areas show positive correlations and more than half land areas show significant correlations (at 95% level), which supports our assumptions on their relationship. Based on the above analysis, we perform a calibration over the regions where the correlation in Fig. 9 is over 95% confidence level (0.576), using equation (4). The results are shown in Fig. 10 Wang et al. (2007) have shown that less restrictive metrics than measuring ensemble coherence, such as the change in overall precipitation variance between S and W cases, reveals even more areas of apparently strong coupling strength. Fig. 9. The correlation between () P W  and ACR across the 12 models participating in GLACE. www.intechopen.com

Conclusions and discussion
Coupling one AGCM to three different land models gives us an unprecedented opportunity to study the role of different components in land-atmosphere interaction. The behavior of the coupled models and their land-atmosphere interaction are investigated by a set of GLACE-type experiments. It is found that the two AGCMs determine the overall spatial distribution and amplitude of precipitation variability, predictability, and land-atmosphere coupling for the six model configurations. The impact of different LSSs is mostly regional. Different LSSs or soil moisture have little influence on the global pattern of precipitation predictability and variance distribution because of the stronger control of other factors. The estimated precipitation predictability and land-atmosphere coupling strength is closely related to the low-frequency variability of atmosphere, which can impact land-atmosphere coupling both directly in the atmosphere and indirectly through soil moisture response to precipitation. Based on these findings, the land-atmosphere coupling strength is conceptually decomposed into the impact of low-frequency precipitation variability, the impact of soil moisture on evapotranspiration (ET), and the impact of ET on precipitation.
As most models participating in GLACE have overestimated the low-frequency component of precipitation, a rough calibration to the GLACE-estimated land-atmosphere coupling strength is performed. The calibrated coupling strength shows a similar global pattern, but is significantly weaker over some regions, like US Great Plains and Mexico. We discussed the land-atmosphere coupling strength based on the index defined in GLACE, which emphasizes the temporal coherency of the precipitation time series among the ensemble members. Analysis with another index defined by Wang et al. (2007), which emphasizes the relative divergence of mean precipitation, does not show significant overall differences in the coupling strength between GFS and COLA AGCM configurations. This suggests the important role of atmospheric variability in determining the different GLACE coupling strengths of GFS and COLA AGCM configurations. The integration period of these GLACE-type experiments is JJA, so the longest timescale in this study is intraseasonal. The effect of land may be different for longer timescales. Our judgment on the connections between external forcing, low-frequency precipitation variability, and p  and () ( ) PP SW   is based on model results so may not be absolutely true in reality. Some intraseasonal variations of precipitation may not come from external forcing but from the flow instabilities (especially in midlatitudes; e.g., Charney and Shukla 1981) that are not fully understood nor properly simulated. The observational datasets used in this study are all based on satellite observations, and they may have consistent biases. In spite of these limitations, this study qualitatively separates the role of external forcing and local soil moisture on precipitation variability and predictability, and increases our understanding of land-atmosphere interaction. 9. Appendix 9.1 Global Land-Atmosphere Coupling Experiment (GLACE) GLACE (Koster et al. 2004) is a model inter-comparison study focusing on evaluation of the role of land state in numerical weather and climate predictions. It consists of sets of 16-member ensembles of AGCM experiment (we only discuss two sets here). Ensemble W as a set of free runs with different initial land and atmosphere conditions but forced by the same SST from 1994, and ensemble S is the same as ensemble W except that, at each time step, the soil moisture in all the soil layers is replaced by that from one member chosen from ensemble W (all members of S have the same soil moisture). This is a little different from that of the standard GLACE experiments, where only subsurface soil moisture was replaced in the S ensemble. We design the experiments in this way to make the results from different LSSs more comparable; it has been shown that the upper layer of Noah model is responsible for an unusually large part of evapotranspiration (Zhang et al. 2010). All runs cover the period of 1 June-31 August, 1994. A diagnostic variable Ω was defined in GLACE: where 2 X  is the intraensemble variance of variable X, and 2 X    is the corresponding variance of ensemble mean time series. In calculating the variance, the first 8 days of data of each run is discarded to avoid model initial shock, and the remaining 84 days are aggregated into 14 six-day totals. Therefore, 2 X  is a variance across 224 (1614) six-day totals from all the ensemble members, and 2 X    is a variance across 14 six-day totals from the ensemble mean time series. Theoretically, if the 16 members of an ensemble have identical time series of X, 2 X   will be equal to 2 X  and  will be 1; if the X time series of the 16 members are completely independent, 2 X    will be equal to 2 /16 X  and  will be 0. Without sampling error,  will range between 0 and 1. Ω measures the similarity (or predictability) of the time series in 16 ensemble members. Analyses show that Ω emphasizes the temporal coherency, or the phase relationship, more than the mean and temporal variance of the time series (Wang et al. 2007;Yamada et al. 2007). Mathematically, Ω is equivalent to the percentage of variance caused by the slowly varying oceanic, radiative, and land surface processes Yamada et al. 2007). The difference of Ω from the two ensembles, () ( ) SW   , is then equivalent to the percentage of variance caused by the prescribed soil moisture, and is a measure of land-atmosphere coupling strength in GLACE.