This paper shows that realistically initialized land surface states enhance atmospheric predictability significantly out to two-to-three months during summer. The spatial structure of the impact of land initialization on atmospheric predictability can be explained by the simultaneous influence of soil moisture memory time and land surface-evapotranspiration coupling strength. A proxy for this impact based on soil moisture and evaporation anomalies is proposed. The results also show that the impact of the land surface on atmospheric predictability varies with season: enhancement of predictability is relatively small during boreal spring and autumn, and reaches a maximum during boreal summer. Remarkably, the predictability of atmospheric temperature and precipitation increases with lead time from spring to summer. This increase is diagnosed as a “transfer” of predictability from land to atmosphere: during spring, the soil moisture predictability is high, but this predictability does not impact the atmosphere due to lack of land-atmosphere coupling; during summer, the coupling increases, thereby transferring the predictability from land to atmosphere.
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 The predictability of the atmosphere has been demonstrated to be no more than three weeks [Lorenz, 1982]. Predictability beyond this limit must rely on the implicit memory or predictability in the boundary components underlying the atmosphere. The ability of sea surface temperature (SST) and soil moisture content to extend atmospheric predictability to subseasonal and seasonal timescales has been explored in many studies. Since a soil moisture anomaly could persist for months [Entin et al., 2000], the implicit predictability of land surface states introduced from long soil moisture memory could be translated into enhanced predictability of the atmospheric system through its strong impacts on atmospheric variability. Accordingly, realistic soil moisture initialization is extensively explored to improve long-range forecasting skill [e.g.,Dirmeyer, 2000; Douville, 2004; Koster et al., 2010, 2011].
 In the most recent internationally coordinated modeling study, the Global Land-Atmosphere Coupling Experiment (GLACE), these ideas are explored with a large number of state-of-the-art global forecasting systems in a comprehensive and systematic manner. While the modulation of soil moisture variations on meteorological variables was examined in the first phase of GLACE (GLACE-1 [Koster et al., 2004; Guo et al., 2006]), the contribution of land surface initialization to subseasonal forecast skill is evaluated in the second phase of GLACE (GLACE-2 [Koster et al., 2010, 2011]). Missing from these studies, however, is an analysis of land surface impacts on atmospheric potential predictability – that is, on the ability of a model to predict its own atmospheric evolution. Recent studies show that the contribution of land surface initialization to atmospheric forecast skill is dependent on the strategy used for the soil moisture initialization and subject to the systematic biases in the initial soil moisture fields [Koster et al., 2009]. In contrast, the contribution of land surface initialization to atmospheric potential predictability does not involve validation against observations and reveals the maximum potential enhancement resulting from land surface initialization (in particular, potential predictability is not influenced by model biases or initialization strategies). Within the framework of GLACE, the present paper employs an Atmospheric General Circulation Model (AGCM) to study land surface impact on the subseasonal and seasonal potential predictability.
 GLACE-2 consists of two parallel sets of retrospective ensemble forecasts driven with the same sea surface temperature observations. In one set of forecasts, the climate noise is maximized in the initial land surface components, and the potential predictability beyond two weeks is presumably derived from the climate signals in SST. In the other set, the climate noise in the initial land surface components is eliminated, and the resultant potential predictability includes the impacts from climate signals in both SST and initial soil moisture anomalies. The same atmospheric initial conditions are used in the two sets of experiments. The comparison of the predictability metrics between these two sets isolates the land surface impacts on atmospheric predictability. We present a method to detect the change in potential predictability between the two sets of runs.Section 2describes the AGCM, our extension of the GLACE-2 forecast experiments, and the metrics used to evaluate potential predictability. The results are presented insection 3, and a summary and discussion are given in section 4.
2. The GLACE-2 Forecast Experiments
 This section describes the Center for Ocean-Land-Atmosphere Studies (COLA) AGCM and the specific details of the GLACE-2 experiments performed.Koster et al. [2010, 2011]provide a detailed description of the GLACE-2 forecast experiments and their basic design.
2.1. COLA AGCM
 A recent version (v3.2) of the COLA AGCM [Misra et al., 2007] is used in this study. The horizontal resolution is T62 (about 1.9° × 1.9°), and the model has 28 vertical levels. The model uses the relaxed Arakawa-Schubert deep convection scheme, the non-local boundary layer vertical diffusion scheme, the longwave radiation scheme of NCAR CAM3 and the cloud radiation scheme of NCAR CCM3. The land surface scheme is an updated version of the Simplified Simple Biosphere Model (SSiB), which has some improvements over the previous version of SSiB: the number of soil layers increases from three to six; a three-layer snow model has been coupled to SSiB to replace the original simple snow parameterization. The Community Land Model (CLM) schemes are used for calculating soil thermal conductivity and soil temperature.
2.2. Forecast Experiments
 All GLACE-2 AGCM integrations consist of two parallel sets of retrospective forecasts, with each forecast comprised of ten ensemble members. The initial land prognostic variables are set to realistic values in the first set of forecasts (denoted by LA\O hereafter since both atmospheric and land realistic initial conditions are used, and observed ocean surface temperature is prescribed) while they are chosen randomly without replacement for each ensemble member from different years in the second set (denoted by A\O hereafter since only realistic atmospheric initial conditions are used and observed ocean surface temperature is prescribed). In COLA GLACE-2 experiments, the realistic land initial conditions are produced by driving an uncoupled implementation of SSiB offline with observationally-derived fields of meteorological forcing for several consecutive decades (extracted fromSheffield et al. ). As explained by Koster et al. [2010, 2011], the offline simulated soil moisture has been scaled to the AGCM soil moisture climatology, so that the local means and variances match. To ensure a reasonable sample size for statistical analysis, both sets of GLACE-2 experiments extend to 250 independent three-month forecasts, one for each of ten start dates (April 1, April 15, … August 15) in each of the 25 years spanning 1982–2006. Sea surface temperatures for both sets are prescribed from a weekly observational dataset [Reynolds et al., 2002]. Atmospheric initial conditions are derived from the NCAR/NCEP reanalysis I, with ensemble members perturbed from each other by being chosen from different days within 5 days of the start date.
 The key feature is the contrast between realistic land surface initialization in the first set of forecasts and random land surface initialization in the second set. In the first set of forecasts, setting the initial land prognostic variables for all the ensemble members to the same realistic values minimizes noise in the land surface components, and maximizes the potential predictability derived from initial land surface and SST climate signals together. In the second set, the initial land prognostic variables for each ensemble member are chosen from the offline simulations with the same start date (day and month), but randomly chosen from different years of the remaining 24 years. This maximizes noise within the ensemble in the land surface component, and minimizes the potential predictability derived from the land surface climate signals. The comparison of the predictability metrics between realistic and random forecast cases isolates the impact of land surface initialization on atmospheric predictability.
2.3. Potential Predictability Metrics
 Potential predictability is the maximum predictability possible within the forecast model system and is model-dependent. One measure of predictability is the correlation between one ensemble member and all other ensemble members. There are several ways this can be defined, but perhaps the most intuitive is to compute the correlation for all possible pairs of ensemble members. It can be shown that the squared correlation defined this way has a one-to-one relation with the signal-to-noise ratio, which means that the predictability can be equivalently measured in terms of correlation and signal-to-noise ratio. In particular, a significance test for one measure is exactly equivalent to a significance test for the other. Letyen represent the ensemble forecast data set, e = 1, …, E and n = 1, …, N. E denotes the number of ensemble members and N denotes the number of verification years. Then, the squared correlation r2can be written in the terms of signal-to-noise ratio SNR by
where y•• = yen and y•n = yen. The numerator VS, called the signal, measures the variability of the ensemble means while the denominator VN, the noise, measures the variability about the ensemble means. For large ensemble size E, r2is approximately equal to the signal-to-total ratio defined bySTR = . Under the null hypothesis that there is no predictability, the critical threshold value of the signal-to-noise ratio for the 95% significance level isSNR95% = FN−1,N(E−1)0.05, where FN−1,N(E−1)0.05denotes the upper 5% threshold value for an F-distribution with N-1 and N(E-1) degrees of freedom.
 In GLACE-2 forecast experiments, we have two distinct ensemble data sets: one ensemble set is based on just atmospheric initial conditions (A\O), and the other is based on both atmospheric and land initial conditions (LA\O). In this study, we want to test not only if there is predictability, but also if the predictability with land initialization greater than the predictability without land initialization. In other words, we want to test whether there is a significant difference in predictability due to land initialization. To measure the difference in predictability due to land surface initialization, we use the signal-to-signal ratio between the two sets of forecast experiments:
Since the two sets of forecast experiments presumably have the same magnitude of total variability, this signal-to-signal ratio is equivalent to the ratio of STR between two sets. Under the hypothesis that the signals in the two sets have equal variances, values of that exceed FN−1,N−10.05 would be evidence that realistic land initial conditions have enhanced predictability.
 This section quantifies the land surface's role in AGCM subseasonal and seasonal predictability.
3.1. Geographical Patterns and Controlling Factors
Figures 1a and 1bshow the potential predictability, indicated by the signal-to-total ratio (STR), for the 46–60 day average hindcast air temperature and for LA\O and A\O cases, respectively.Figure 1c shows the land surface impacts on potential predictability, indicated by the index SSR defined in equation (3), for the 46–60 day average air temperature. The model outputs with initial conditions in all five months (from April through August) are used for the calculation. The black dots indicate grid cells for which the land surface impacts are significant at the 95% confidence level. Major regions where land surface has significant impacts on air temperature predictability include central North America, the northern part of South America, midlatitude Eurasia, China, the Sahel, and equatorial Africa. For precipitation predictability (not shown), land surface impacts are weaker, especially over midlatitude Eurasia and China, but still significant over central North America, the northern part of South America, the Sahel, and equatorial Africa. The same quantities have been calculated for all GLACE-2 participating models, and the COLA AGCM largely reproduces the major land-impacted regions revealed by the multi-model average of these quantities (not shown). Most “hotspots” identified from the multi-model analysis and COLA AGCM in the original GLACE-1 experiment [Koster et al., 2004; Guo et al., 2006] show up here except for the southern part of the Great Plains and northern India. This indicates that the realistic land surface initialization tends to have significant impacts on atmospheric predictability over regions with strong land-atmosphere coupling strength. This result is not unexpected: the atmospheric predictability tends to have a large response to soil moisture initialization over the regions where soil moisture variations have strong impacts on atmospheric variability.
 Besides the land-atmosphere coupling strength, soil moisture memory is another critical element underlying soil moisture's ability to influence forecasts. We argue that in order to have significant impacts on atmospheric predictability, the region must have both long soil moisture memory and strong land-atmosphere coupling. We use thee-folding time scale of the soil moisture anomaly as a measure of the soil moisture memory [Entin et al., 2000] and use the correlation between soil moisture and evaporation anomalies as a measure of land-atmosphere coupling strength.Figures 1d and 1e show the correlation between soil moisture and evaporation anomalies (Figure 1d) and the e-folding time scale (units in days) of the soil moisture anomaly (Figure 1e). In fact, the COLA AGCM has a relatively short soil moisture memory over the Great Plains and northern India, and the soil moisture there is highly influenced by weather noise. In these regions, the accuracy in the initial soil moisture anomaly, achieved from the realistic land surface initialization, cannot persist long enough into the forecast period to have a significant impact on atmospheric predictability. This could explain the lack of land surface impact on predictability over these two regions, even though there exists strong land-atmosphere coupling.
Figure 1f presents a proxy for soil moisture's contribution to land surface impacts on atmospheric predictability, represented by the product of soil moisture memory and the correlation between soil moisture and evaporation anomalies (deserts have been masked out), × rET,SM, where τ is the e-folding time scale (units in days) of soil moisture anomaly.τc is an artificial critical value for the e-folding time scale – we arbitrarily setτc = 45 days. rET,SMis the correlation between 15-day mean soil moisture and evaporation anomalies across all ensembles and forecasts. It is observed that neither the land-atmosphere coupling strength nor soil moisture memory separately explains all of the characteristics of the distribution of land surface impacts on atmospheric predictability (SSR;Figure 1c). However, the proxy does reproduce the major features indicated by the index SSR, even though other external factors may influence the impacts, especially in South and East Asia [Xue et al., 2010]. This suggests that land surface initialization has a significant impact on atmospheric predictability only over regions with both strong soil moisture-evaporation coupling and long soil moisture memory. Since bothτand the correlation between soil moisture and evaporation could be derived from observations, this proxy is a promising diagnostic variable for estimating the land surface impacts on predictability once large-scale contemporaneous evaporation and soil moisture data are available.
3.2. Timescales of Land Surface Impacts on Atmospheric Predictability
Figure 2a (left) shows the global average over land areas (Antarctica is excluded) of predictability of air temperature (Figure 2a, top left) and precipitation (Figure 2a, bottom left) as defined by the signal-to-total ratio for LA\O (solid thin lines), A\O (dotted lines) cases, and land surface impacts on the predictability (SSR; solid black lines), respectively. The x-axis indicates the moving window for the 15-day averaging with different lead times from days 1–15 to days 76–90. It is found that the global average of the predictability index STR decreases rapidly from 1–15 days to 16–30 days for both air temperature and precipitation in both cases. This is consistent with the 2–3-week range of deterministic predictability for standard weather forecasts. The predictability index is rather stable thereafter, and it does not degrade to zero due to the SST specification. The results show that the land surface has a significant impact on both air temperature and precipitation predictability, with an extension in time of 10%–50% for a given skill level, depending on the lead time. It is also clear from the SSR index that predictability enhancement persists throughout the 3-month forecast period. This emphasizes that the land surface has significant impact on atmospheric predictability at the subseasonal and seasonal timescales.
Figure 2a (right) shows the fraction of land area where land surface initialization has had significant impacts on the predictability of air temperature (Figure 2a, top right) and precipitation (Figure 2a, bottom right) as quantified by the fractional area in which SSR is significant at the 95% confidence level. Air temperature predictability significantly benefits from realistic land surface initialization across 30% of the land area early in the forecast period, declining to 10% by the end of the third month. For precipitation, the fraction declines from 12% to 6% over time. The impacted areas are mainly clustered in the aforementioned regions (central North America, northern South America, midlatitude Eurasia, the Sahel, and equatorial Africa).
3.3. Seasonal Variation of Land-Atmosphere Predictability
 In this section, we investigate the seasonal dependence of land-atmosphere predictability in detail in one region over central North America (delineated by the box inFigure 1a). This area is chosen because it has been influenced by major floods and droughts (for example the North American drought in 1988 and the flood of 1993), and it is one of the major regions where the land surface has shown strong impacts on atmospheric predictability. First, the areal average time series of air temperature, precipitation, evaporation, and soil moisture are computed for each ensemble member and start date. Then the 15-day running means are calculated for each time series. The air temperature, precipitation, and soil moisture predictabilities defined by the signal-to-total ratio for LA\O (solid lines) and A\O (dotted lines) cases are computed from the running mean time series, and plotted inFigure 2b. The figure shows a clear contrast in the evolution of atmospheric predictability between the random and realistic land surface initializations for temperature and precipitation. For realistic land surface initializations, the predictability of temperature and precipitation decreases rapidly in early-to-mid spring, rebounds in late spring and early summer, and diminishes from late summer into autumn. Remarkably, this characteristic evolution occurs regardless of the time of forecast initialization. The rebound in predictability also is interesting because predictability is not expected to increase with lead time [Cover and Thomas, 1991, section 2.9]. However, as pointed out by Kleeman , predictability may increase locally due to a transfer between subsystems. To investigate this possibility, we show in Figure 2b (bottom) the predictability of soil moisture (Figure 2b, bottom left) and the correlation between evaporation and soil moisture (Figure 2b, bottom right). As anticipated, soil moisture predictability with realistic land surface initialization is very high from late spring through summer, due to the long soil moisture memory, and there is no increase in soil moisture predictability during summer. However, the coupling between the land-atmosphere, as measured by the correlation between evaporation and soil moisture, is very low in early spring, but rises rapidly by May and peaks in early July, after which it slowly declines until November. Thus, although soil moisture predictability remains high throughout spring and summer, this predictability does not impact the atmosphere in early spring due to the lack of land-atmosphere coupling. In late spring, the coupling increases dramatically, allowing the land predictability to be transferred to the atmosphere. The rebound in atmospheric predictability therefore appears to be due to the fact that the land surface impact on atmospheric predictability is highly dependent on the time of year. The impact seems to be caused by the onset of highly correlated evaporation to persistent soil moisture.
4. Summary and Discussion
 The present study presents a common analysis framework to quantify land surface impact on the subseasonal and seasonal potential predictability of air temperature and precipitation. It is found that air temperature and precipitation predictability over areas with both strong soil moisture-evaporation coupling and long soil moisture memory for our model tend to have large impacts from realistic land surface initialization. These results suggest regions where the establishment of real-time operational networks for monitoring soil moisture would most benefit climate forecasting. It also demonstrates that realistic land surface anomalies could be used to extend the atmospheric predictability in some regions on subseasonal and seasonal scales. A proxy is developed to evaluate the soil moisture's potential contribution to atmospheric predictability, and it could be used to assess the model's estimates since it can be computed from observed soil moisture and evaporation. The results also show that the impacts of the land surface on atmospheric predictability vary with season, with a recovery of predictability over central North America from spring into summer, and a sharp decline into fall. The recovery of predictability could be attributed to the rapid increase of land-atmosphere coupling strength and ongoing long soil moisture memory during that period.
 We are indebted to Randy Koster for his constructive comments on the earlier version of the manuscript, and the backing of the GEWEX Global Land-Atmosphere System Study. This research was supported by joint funding from the National Science Foundation (ATM-0830068), National Oceanic and Atmospheric Administration (NA09OAR4310058), and the National Aeronautics and Space Administration (NNX09AN50G).
 The Editor thanks two anonymous reviewers for their assistance in evaluating this paper.