a. GPCP-1DD

The Global Precipitation Climatology Project one-degree daily (GPCP-1DD) precipitation dataset provides daily, global 1° × 1° gridded fields of precipitation totals from October 1996 to the present (available online at http://precip.gsfc.nasa.gov/gpcp_daily_comb.html; Huffman et al. 2001). It is a combined observation-only dataset, which is based on satellite estimates of rainfall and is scaled to match the monthly accumulation provided by the GPCP satellite–gauge (SG) product, which combines monthly satellite and gauge observations on a 2.5° × 2.5° grid (Huffman et al. 1997; Adler et al. 2003). In this study, we use data from 1997 to 2007.

b. TMPA

The Tropical Rainfall Measuring Mission (TRMM) Multisatellite Precipitation Analysis (TMPA) 3B42 (available online at http://trmm.gsfc.nasa.gov/3b42.html; Huffman et al. 2007) provides a calibration-based scheme for combining precipitation estimates from multiple satellites and gauge analyses where feasible, at fine scales (0.25° × 0.25° and 3 hourly) and over 50°N–50°S. We use the research product, which uses a better calibrator than the real-time product and rescales the monthly sums of the 3-hourly fields to a monthly gauge analysis. The data we used here is from 1998 to 2007.

c. CMORPH

The Climate Prediction Center (CPC) morphing technique (CMORPH; Joyce et al. 2004) produces global precipitation analyses at very high spatial and temporal resolution (half-hourly and 8 km) by using satellite microwave observations only. Instead of using IR brightness temperature algorithms to estimate rainfall rate, as in GPCP-1DD and TMPA, CMORPH uses IR-derived advection vectors to propagate the relatively high-quality precipitation estimates derived from passive microwave data. The shape and intensity of the precipitation features are modified (morphed) during the time between the microwave sensor scans by performing a time-weighted linear interpolation. This process yields spatially and temporally complete microwave-derived precipitation analyses, independent of the IR temperature field. The data are at 0.25° × 0.25° and 3-hourly resolution, ranging from 60°N to 60°S. Data from 2003 to 2008 are used in this study.

Although these datasets are all based on satellites observations, they used different techniques to retrieve precipitation, so intercomparison among these datasets is a kind of verification. Verifications of these datasets have been done by comparing them with gauge- or radar-based estimates (e.g., McPhee and Margulis 2005; Skomorowski et al. 2001; Gebremichael et al. 2005; Su et al. 2008; Zeweldi and Gebremichael 2009). There is generally a good agreement between these datasets and ground-based estimates, especially over large spatial and long temporal scales.

a. Results from GLACE-type experiments

Figure 1 shows the Ω values of total precipitation for ensembles W [16-member control experiment for June–August (JJA)] and S (subsurface soil wetness specified in all ensemble members from an arbitrarily chosen member of W) and their difference Ω(S) − Ω(W) (see the appendix for complete definitions). No matter with which land model the AGCM is coupled, Ω shows similar patterns, with the largest values in the tropical rain belt where the SST forcing has the strongest influence (Shukla 1998). The patterns of Ω(W) and Ω(S) are very similar, with large differences [Ω(S) − Ω(W)] mainly over the regions with high Ω values. This indicates that the land–atmosphere coupling strength may be strongly influenced by the external forcing. By “external,” we mean that the forcing is from outside of the land–atmosphere system, such as that from SST. The patterns of Ω(S) − Ω(W) for different model configurations have much lower similarity than for Ω [spatial correlations are 0.18–0.23 for Ω(S) − Ω(W) and 0.6–0.72 for Ω]. Globally, COLA–SSiB has the strongest land–atmosphere coupling strength, while COLA–Noah has the weakest. The potential contribution of subsurface soil moisture to the total potential predictability {[Ω(S) − Ω(W)]/Ω(S)} is approximately 30%, 28%, and 18% for COLA–SSiB, COLA–CLM, and COLA–Noah, respectively. The differences seen mainly should be from the land models’ different connections between soil moisture and surface fluxes, because they are coupled to the same AGCM.

b. 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 Ω). 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 range to avoid possible problems associated with the initial shock to the model atmosphere, as in calculating Ω, there are 84 days that are 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 because of the length of the time series we refer to the 20–84-day variation as intraseasonal.

Figure 2 shows the variance percentages of precipitation in these three bands for model simulations and three observational datasets. The three model simulations are highly consistent in their variance distributions, as are the three observational datasets (note that for TMPA and CMORPH the latitudinal extent is limited). However, all of the model simulations underestimate the high-frequency (fast synoptic) variance and overestimate the low-frequency (intraseasonal) variance, especially over the tropics and subtropics. Multiyear simulations of these models, as described Part I, have similar variance percentage distributions as these GLACE-type simulations (not shown). This overestimation of low-frequency variance is also consistent with the overestimation of precipitation persistence shown in Part I. Although these 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 between the 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 lightly in intensity (Trenberth et al. 2003; Sun et al. 2006; Ruane and Roads 2007).

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 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 Ω and the percentage of intraseasonal variance (IV) are very high (right column), but the correlations of Ω with the other two frequency bands are negative (left two columns). Ensemble S (not shown) has similar results as ensemble W. This demonstrates that regions with a larger percentage of IV tend to have a higher value of Ω, 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 Ω) 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 Ω). For ensemble S, the prescribed subsurface 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. 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 effects. 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 a relaxed Arakawa–Schubert formulation of cumulus convection (also used in the COLA AGCM) exhibits a strong bias toward excessive light rain events and too-few heavy rain events.

The above shows that neither the land model nor the 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 Ω(S) − Ω(W) shows the impact of soil moisture. It tries to remove the effects of the same strong external forcing on both S and W and highlights the role of soil moisture, although we understand that the effects of those forcings cannot be completely removed in a nonlinear system (more discussion on this aspect follows in section 3c). The spatial correlations between percentage of IV and Ω(S) − Ω(W) are also shown in Fig. 2 (as the last number in right column). They are generally weaker than the correlation with Ω, indicating that something other than the low-frequency external forcing is playing an important role in Ω(S) − Ω(W). This should be the impact of subsurface soil moisture.

To demonstrate the role of each frequency band in Ω and Ω(S) − Ω(W), we recalculate the variables in Fig. 1 using the decomposed precipitation time series in each ensemble member. The result calculated with only the intraseasonal precipitation (higher frequencies are filtered out) is shown in Fig. 3; the other two frequency bands result in very weak values and are not shown. It can be seen in Fig. 3 that the patterns of Ω and Ω(S) − Ω(W) are very similar to those in Fig. 1. 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. (We do not compare the amplitudes of the two figures because their time series have different degrees of freedom.) It is interesting that the goal of GLACE, as described in Koster et al. (2006), is to examine land surface’s control on precipitation variability on time scales of ∼1 week (synoptic scale), but our results here show that the main impact of the land surface in the models is on intraseasonal time scales.

c. Conceptual relationships

Based on the above analysis, we can build a conceptual relationship between Ω, the impact of low-frequency external forcing F, and the impact of soil moisture α, as

View Expanded

where α₀ is a constant, and α₀ >> α over most regions. Thus, the spatial variation of Ω is largely determined by F, which is consistent with the analysis above. Here, F is similar for both ensemble W and ensemble S, so the coupling strength is

View Expanded

where α(S) − α(W) is the difference of α between the two ensembles, and is the “pure” impact of soil moisture on the coupling strength (i.e., without the influence of external forcing). Note that F and α(S) − α(W) have spatial variations, so both of them can influence the amplitude and spatial distribution of the coupling strength.

In our three model simulations, the atmospheric model is the same, and we have shown that Ω (or F) is similar for all three of the models, but Ω(S) − Ω(W) has larger spatial differences (Fig. 1). From Eq. (2), the differences between the models should be mainly from differences in α(S) − α(W), which appears to be generally smaller when the COLA AGCM is coupled to the Noah model than to the other two land models. However, we must recognize that the impacts of external forcing and local land states may not be explicitly separable as in Eqs. (1) and (2). This simplification is for the conceptual understanding of the relationships.

d. Calibration of the estimated GLACE land–atmosphere coupling strength

To examine whether our results are consistent with those from other models, we look at the GLACE dataset (Koster et al. 2006). Figure 4 shows the percentage of IV for 12 models participating in GLACE, and their respective spatial correlations with Ω and Ω(S) − Ω(W). As for the COLA AGCM above, ensemble S (not shown) shows very similar results to ensemble W. Also, all of the models here have overestimated the percentage of IV. The global average percentages for the three observational datasets are consistently 15% (Fig. 2), while the 12 models show values of 21%–28%. (The COLA AGCM used in the original GLACE experiment is an older version than the one used here for coupling to multiple land schemes, and the versions of SSiB used are also different.) The spatial distributions of the variance percentage differ widely, and the overestimations are not limited to the tropics and subtropics. The spatial correlations of variance percentage and Ω are always high; even the lowest value [0.32 from the University of California, Los Angeles (UCLA)] is well over the 99% confidence level (assuming that the grid points are independent). The correlations with Ω(S) − Ω(W) are always lower than with Ω, and some models even show weak negative correlations, indicating the spatially heterogeneous influence of soil moisture [α(S) − α(W) in Eq. (2)]. Therefore, the GLACE models and our models show similar relationships between Ω, Ω(S) − Ω(W), and the percentage of IV.

We have shown that most of the precipitation predictability caused by soil moisture [Ω(S) − Ω(W)] happens at the intraseasonal band, but the models generally overestimated the percentage of variability in this band. If F in Eq. (2) is equivalent to the percentage of IV, it appears to have been overestimated by the models. The influence of F on Ω(S) − Ω(W) is obvious. However, we cannot conclude that the land–atmosphere coupling strength estimated by GLACE is overestimated, because another important factor α(S) − α(W) still cannot be directly observed. Nonetheless, we may assume that α(S) − α(W) from the model ensemble is better than that of most individual models and try to correct F to make Ω(S) − Ω(W) possibly closer to reality. Roughly, we calibrate Ω(S) − Ω(W) for each of the 12 models at each grid point (all of which are interpolated to a common 1° × 1° grid):

View Expanded

where var% is the percentage of IV and var%(obs)/var%(model) is calculated at each grid point. This method tries to correct F by scaling it with a ratio of observed and modeled variance percentages. The GPCP-1DD data are used as ground truth observations. The variance percentage is calculated from ensemble W instead of ensemble S because it corresponds more closely to the real world (soil moisture is interactive). Note that var% also contains a slice of the seasonal cycle during JJA, which is consistent with the 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).

Although the spatial correlations between Ω and the percentage of IV are very significant for all of the models, the correlation coefficients are not necessarily high (e.g., UCLA). This means that the strong connection between Ω and F described in Eq. (1) may not happen over all of the regions. The noise may dampen the connection in some cases. We then calculated the correlation between Ω and the percentage of IV across the 12 GLACE models (a correlation with a sample size of 12; see Fig. 5). It indicates a general connection between Ω and IV for all of the 12 models at each grid point. The regions with strong positive correlations are where Ω and IV have a strong connection for almost all of 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 Ω. We can see in Fig. 5 that over 90% of the land areas show positive correlations, which supports our assumptions of their relationship.

Based on the above analysis, we perform two separate calibrations to the original Ω(S) − Ω(W)—a strong one to calibrate all of the regions where the correction in Fig. 5 is positive, and a weak one to calibrate only the regions where the correlation in Fig. 5 is over 95% confidence level (0.576); both use Eq. (3). The results are shown in Fig. 6. It can be seen that the coupling strength reduces by approximately half after strong calibration, and only a few hot spots survive. The result after weak calibration is similar to the original, but shows weakened coupling strength in the U.S. Great Plains and Mexico, northern India and Pakistan, and Mauritania. Generally, the calibrated coupling strengths are weaker than that from the GLACE, but the pattern does not change much.

In this study, the impact of the model overestimation of low-frequency variance on land–atmosphere coupling is discussed from the perspective of atmosphere, but the effect of this overestimation also shows over land. More low-frequency variance usually means more sustained dry and wet periods and higher evaporation variability, which can lead to a more robust precipitation response (higher predictability). Also, as mentioned, this model bias is manifested as overly frequent rainfall at reduced intensity. This increases infiltration and reduces runoff, enhancing subsequent evapotranspiration and increasing soil moisture memory, which then leads to the overestimation of land–atmosphere coupling.

Because of the changing and heterogeneous nature of the relationship between Ω and F, our calibration method is not flawless. However, the results illustrate how the amplitude and distribution of coupling strength may change after some rectification of the model bias. The unique design of GLACE makes its results difficult to evaluate by directly comparing them with observational variables, even if these large-scale observations exist, because the GLACE metric is based on ensemble statistics, and observations present us with only one “ensemble member.” Some recent studies using observationally based data have cast doubt on the strong coupling strength in the Great Plains (Ruiz-Barradas and Nigam 2005, 2006; Zhang et al. 2008), but whether their results are comparable to the GLACE results need further study. On the other hand, 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.