1. Introduction
How precipitation is related to soil moisture is an important issue for the study of land–atmosphere interaction. Large-scale observations are lacking and local observations are very limited, so many processes in the soil moisture–precipitation (S–P) interaction are still not well understood. Findell and Eltahir (1997) assumed that soil moisture may have some influence on subsequent precipitation and found a positive correlation between the observed soil moisture and subsequent precipitation in Illinois during the summer. The feedback is explained by theory and numerical experiments (Eltahir 1998; Zheng and Eltahir 1998; Findell and Eltahir 1999). D’Odorico and Porporato (2004) also analyzed this relationship in Illinois and found soil moisture to be correlated with the occurrence of subsequent precipitation but not with subsequent precipitation amount. They explained their result with an analytical model and supported it with some earlier studies (Eltahir and Pal 1996; Findell and Eltahir 2003a, b). Using Granger causality (e.g., Triacca 2001; Mosedale et al. 2006), Salvucci et al. (2002) studied the same relationship in Illinois and concluded that the soil moisture did not have a significant influence on the subsequent precipitation. They questioned the results of Findell and Eltahir (1997) by arguing that their linear interpolation method introduced artificial correlations between soil moisture and subsequent precipitation. Most importantly, the method of Salvucci et al. (2002) partly excludes the possible influence of the precipitation autocorrelation on the calculated S–P correlation.
Precipitation time series include both random and low-frequency components. The random component is often by itself regarded as a white noise forcing of soil moisture, and soil moisture storage may provide its memory. However, because of internal atmospheric dynamics, the precipitation can have its own intrinsic memory processes, such as the Madden–Julian oscillation (MJO; Madden and Julian 1971, 1972; Madden and Julian 1994; Zhang 2005), that is, the 30–60-day oscillation in the tropics. Thus, the precipitation time series may include low-frequency components from both its own intrinsic variability and land memory. As precipitation has a strong influence on soil moisture (Guo et al. 2006), their lagged correlation may be influenced by the autocorrelation of precipitation and so may not always be an indicator of a causal relationship. How is the S–P correlation influenced by precipitation variability? This will be addressed in the paper.
Modeling can provide more comprehensive data and a better capability to analyze causality than from observations, so it is commonly used to interpret processes. After several decades of development, climate models can now simulate many observed climate phenomena, such as seasonal to decadal climate variability (Randall et al. 2007), but many detailed aspects still cannot be reproduced (e.g., Dirmeyer et al. 2006b). A model for studying the feedback processes of a climate phenomenon should be able to reproduce the climate phenomenon properly. However, for land–atmosphere interaction study, such model evaluation becomes especially difficult because of the paucity of large-scale land observations. In this study, three different reanalysis products and data from the Global Soil Wetness Project, phase 2 (GSWP-2; Dirmeyer et al. 2006a), are used for comparison and model evaluation. Although the land data from these sources are also not observed, they are produced from coupled and offline model simulations that are highly constrained from observations and have a higher credibility than model simulations that are not so constrained.
This study finds a negative S–P relationship that commonly exists in several datasets and tries to understand its causes by using data analysis, model experiments, and theoretical analysis. Section 2 introduces and compares the datasets. Section 3 compares a lagged S–P correlation in the datasets, and their consistency is set as a benchmark to be compared with NCAR Community Atmosphere Model Version 3.1 (CAM3) simulations. Section 4 further investigates the causes of this relationship. Some discussions are given in section 5. Summary and conclusions are given in section 6.
2. Datasets
a. Reanalyses
Three reanalysis products are used for this analysis: the 40-yr European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-40; Uppala et al. 2005), the National Centers for Environmental Prediction–Department of Energy (NCEP–DOE) reanalysis 2 (R-2; Kanamitsu et al. 2002), and the North American Regional Reanalysis (NARR; Mesinger et al. 2006). ERA-40 is a second-generation reanalysis carried out after the successful 15-yr version of the ECMWF Re-Analysis (ERA-15; Gibson et al. 1997). ERA-40 uses a land scheme to model surface exchanges (van den Hurk et al. 2000). The surface fluxes in a grid box are calculated separately for different subgrid fractions (or “tiles”), leading to a separate solution of the surface energy balance equation and skin temperature for each of these tiles. There are 18 vegetation types based on the Biosphere–Atmosphere Transfer Scheme (BATS; Dickinson et al. 1993), and the land surface parameters vary per vegetation type. The R-2 dataset is an update of the widely used NCEP–National Center for Atmospheric Research (NCAR) reanalysis 1 (R-1; Kalnay et al. 1996). The R-2 dataset has newer physics and eliminates several previous errors in R-1. As in R-1, R-2 uses a simple land surface model (Mahrt and Pan 1984; Pan and Mahrt 1987; Pan 1990). Vegetation and surface characteristics are from the Simple Biosphere (SiB) model climatology (Dorman and Sellers 1989). The ERA-40 and R-2 datasets use different nudging techniques to correct soil moisture drift caused by imperfect precipitation and insolation (see Li et al. 2005 for a summary), which makes the soil moisture variability more realistic.
The NARR project is an extension of the NCEP Global Reanalysis for the North American domain. It uses the very high-resolution NCEP Eta Model together with the Regional Data Assimilation System that significantly assimilates high quality and detailed precipitation observations. As a consequence, its forcing to the land model is more accurate than that of previous reanalyses, which leads to a much improved analysis of land hydrology and land–atmosphere interaction. The lateral boundary conditions for NARR are from R-2. The land model is a recent version of the Noah land surface model (Ek et al. 2003).
b. Global Soil Wetness Project, phase 2 (GSWP-2)
The 10 yr (1986–95) of data from GSWP-2 (Dirmeyer et al. 2006a) are also used for comparison. GSWP-2 combines the simulations of 13 land surface models using the same observationally based external forcing and standardized soil and vegetation distributions. The precipitation forcing data of GSWP-2 is a hybrid of reanalysis, observations, and empirical corrections (Zhao and Dirmeyer 2003). The process of averaging across models enhances the quality of the estimates over that of the individual models (Gao and Dirmeyer 2006).
c. Data comparison
The temporal coverage, spatial resolution, and soil-layer thicknesses of the three reanalysis products and GSWP-2 data are shown in Table 1. The top 2-m soil moisture is used for analysis. An exception is GSWP-2, which has only 1.5 m of soil moisture data available. Twenty-four years (1979–2002; 10 yr for GSWP-2) of data are used for analysis. The soil water is used over a depth of 2 m rather than the more commonly used 1 m for two reasons: 1) some products (e.g., R-2) do not have soil moisture for the top 1 m and 2) our study focuses on the S–P interaction on a relatively long time scale, which may be related to soil water in deeper layers. In fact, after removing the seasonal climatology, the soil moisture anomalies at 1 and 2 m differ very little because most of the soil moisture variations are near the surface.
Figure 1 shows the daily soil water of the top 2 m in Illinois from three reanalysis products, GSWP-2, and observational data from the Illinois State Water Survey (Hollinger and Isard 1994; Robock et al. 2000). NARR and GSWP-2 have larger amplitudes of the seasonal variation, and their mean values are closer to the observations (Fig. 1a). ERA-40 and R-2 have lower mean values and smaller amplitudes of the seasonal variation. After removing their respective seasonal climatology, the different time series show more similarity (Fig. 1b). Although NARR and GSWP-2 still have larger amplitudes, the relative differences are less than in the original time series. The 1988 drought and 1993 flood stand out. The anomaly time series is now used. It is more physically relevant as different models and observations can have different values of water storage and unavailable soil moisture [the soil moisture that is not strongly linked to surface evapotranspiration (ET) because of soil properties, vegetation rooting depth etc.].
The correlations of some hydroclimate variables between ERA-40 and R-2 are shown in Fig. 2. Soil water has a stronger correlation than that of precipitation and ET, and the correlation of downward solar radiation at the surface is even higher, close to 1 with only a few values smaller in the tropics. Similar solar radiation in the two reanalyses forces different hydroclimate variabilities, with soil water having a better correlation than that of precipitation and ET. Two reasons may have contributed to this. First, the slow variation of soil water has a higher predictability than the faster varying precipitation and ET processes. Second, the two reanalysis products both used some kind of nudging techniques to prevent soil moisture from drifting too far away from reality.
3. S–P relationships in different datasets and CAM3
a. Calculation method
There are 92 summer days (1 June–31 August) in each year. For the first 62 days (1 June–1 August), the soil water of the top 2 m in each day is put into a time series, and the accumulated precipitation in each subsequent 30 days (2 June–1 July, 3 June–2 July, . . . , 2–31 August) is calculated and put into another time series. The correlation between the two time series is calculated for each summer. Therefore, there are 24 correlations (10 for GSWP-2) for each grid point. Before calculating their correlations, the seasonal cycle and linear trend in the two time series are removed to eliminate the possible influence of a long-term external forcing, or any influence from the previous period, such as an anomalous wet or dry spring. This calculation method tries to describe the S–P relationship in this period. The variation of soil moisture in the top 2 m can be regarded as a red-noise process (Vinnikov et al. 1996; Wu and Dickinson 2004), and the cumulative precipitation is actually a 30-day running average of the precipitation and is also a red-noise process. Their long-term lagged correlation over a whole season removes the weather-scale processes and reflects a long-term S–P relationship. We focus on the summer of the Northern Hemisphere where most of the earth’s landmass is located.
This calculation method is based on the assumption that the soil moisture on a certain day may have some influence on the precipitation on subsequent days. However, an S–P correlation can also be due to the natural variability of precipitation combined with the direct influence of precipitation on soil moisture. Findell and Eltahir (1997) tried to isolate these two effects by comparing the S–P correlation with the autocorrelation of precipitation. We use model experiments to isolate these effects.
b. Results from datasets
The calculated average S–P correlations for all the years are shown in Fig. 3. The correlations are dominantly negative, although some positive values appear in the dry areas, such as in North and South Africa and western Asia. This negative correlation contrasts with the traditional view that soil moisture has a somewhat positive impact on subsequent precipitation. In calculating the correlations, we have changed the number of subsequent days of cumulative precipitation from 30 to 40 or 20, and changed the total precipitation into convective precipitation or the number of days with convective precipitation. Comparable results were obtained for all such cases. Is this dominantly negative correlation caused by S–P feedbacks or other reasons? We investigate the attribution with a global climate model.
c. CAM3 model and experiments
The model used is the NCAR CAM3–Community Land Model 3.0 (CLM3; Collins et al. 2006) at T42 resolution, a state-of–the-art climate model with sophisticated dynamics and physics. Its land component, CLM3, is a physically based multilayer soil–vegetation–atmosphere transfer model (Oleson et al. 2004). Two simulations are performed. The first simulation (Cnt) is a control run from 1979 to 2002, and is forced by observed interannual-varying SSTs. In the second simulation (Cnt_s), the model restarts the control run from 1 June of each year and integrates for 3 month to 31 August. The difference is that at each time step the soil water in the ET calculation (in fact, soil evaporation and vegetation transpiration) is given as its climatological mean value at that time step from the control run, but soil water in other calculations is not modified. In this way, the soil moisture still responds to precipitation forcing but the wet or dry soil moisture anomaly does not have any influence on ET. Thus, the calculated S–P correlation in the second run (Cnt_s) is an S–P relationship without soil moisture feedback (soil moisture influence on albedo and then precipitation is not considered here). Comparison of the results from the two experiments indicates how much S–P correlation is from soil moisture feedback, and how much would exist even without feedback.
d. CAM3 results
The S–P correlations from the two CAM3 experiments and their difference are shown in Fig. 4. The general patterns of the correlation from the two experiments are very close, and are also close to that in the above analyzed datasets. The similarity of the patterns from the two experiments indicates that soil moisture feedback is not the main cause of the dominantly negative correlation. There are some regional differences (Fig. 4c) that distinguish the S–P correlation without feedback (Cnt_s) from the total S–P correlation (Cnt), that is, showing the “true” influence of soil moisture feedback on future precipitation. The positive differences in Fig. 4c imply that the soil moisture has a positive influence on future precipitation, and vice versa for the negative differences. Although most of the influence is positive, some regions show negative influences. The negative soil moisture feedback has been inferred in some observational and modeling studies (Giorgi et al. 1996; Findell and Eltahir 2003b; Wu et al. 2006), and some is related to nonlocal feedbacks (Meehl 1994).
Soil moisture feedback may be important for the S–P correlation over the regions with significant differences in Fig. 4c. These regions differ somewhat from those regions of strong S–P coupling obtained from the Global Land–Atmosphere Coupling Experiment (GLACE; Koster et al. 2004, 2006), possibly because this calculation, unlike GLACE, focuses on the impact of current-day soil moisture on subsequent 30-day total precipitation.
4. Causes of the S–P relationship
a. Autocorrelation of precipitation
The above experiments show that the globally widespread negative S–P correlations are not primarily caused by soil moisture feedback. Thus, we would expect some autocorrelations in precipitation. Figure 5 shows the average correlations between past 21-day (including the present day) accumulated precipitation and subsequent 30-day accumulated precipitation. These correlations are also mainly negative, with only a few positive correlations in North Africa. It is likely that the negative S–P correlation is related to this negative correlation. We then calculated the correlation between past 21-day accumulated precipitation and the soil moisture of the current day. Their correlation is predominantly positive in Fig. 6. When the 21-day window is changed to 11 or 5 days in the calculation, no large change in the correlation pattern is found. It is evident that the information about past precipitation is stored in the current soil moisture, depending on its memory, and leading to a negative correlation between soil moisture and subsequent precipitation. Therefore, the negative S–P correlation is caused by the combined effect of the negative autocorrelation of precipitation and the memory of soil moisture. There is no significant S–P correlation in the dry areas like North Africa and Arabia because both of these two effects are weak. The results from the two CAM3 experiments both show similar patterns to those in Figs. 5 and 6 (not shown). This indicates that soil moisture feedback does not play an important role in these two effects, and so the S–P correlation.
The negative correlation between past 21-day accumulated precipitation and subsequent 30-day accumulated precipitation indicates an oscillation in the precipitation time series. Such intraseasonal oscillations are widely recognized for the atmosphere. Besides the MJO over the tropics, a 30–60-day oscillation has also been found to exist in the United States (Ye and Cho 2001), China (Wang et al. 1996a), Europe (Wang et al. 1996b), and even the globe as a whole (Donald et al. 2006; Ghil and Mo 1991; Dickey et al. 1991).
b. Theoretical analysis
The integrations (2)–(4) can be calculated (see the appendix). It is not difficult to find that P30(t), P−21(t), and S(t) all have the same period T as P(t), but with phase shifts. We select λ = 0.02 and 1 (day−1) as two extreme cases of soil moisture memory (Teuling et al. 2006); one is very large (50 days) and one is very small (1 day). Figure 7 shows their respective phase differences with the original precipitation time series P(t). As expected, future precipitation P30(t) leads P(t), while the soil moisture S(t) and past precipitation P−21(t) lag P(t). The case of λ = 0.02 has a larger phase lag than that of λ = 1 because of its longer time scale of soil moisture retention.
For different time series with the same period, their correlations depend on their phase differences. For the same phase, it will be 1. For a phase difference of π, it will be −1. Figure 8 shows the phase difference between P30(t) and S(t) (with λ = 0.02 and λ = 1) and between P30(t) and P−21(t). Phase differences larger than π or smaller than 0 are transformed to 0-π for easy comparison, which shows that the phase differences have strong fluctuations for periods of less than 30 days. As the precipitation time series usually have a wide spectrum, it is useful to look at the running averages of the phase differences. For periods larger than a week, most of the phase differences are between π/2 and π, leading to a negative correlation between P30(t) and S(t) or P30(t) and P−21(t). This explains the negative-dominant correlations obtained from the data analysis. Although the phase differences for λ = 0.02 and λ = 1 are intertwined, for most of the periods λ = 0.02 is closer to π than is λ = 1, indicating that at the same precipitation forcing the areas with longer soil moisture retention time tend to have more significantly negative correlation.
The above theoretical analysis assumes a single period for the oscillations of the precipitation time series. For multiple waves, the theoretical analysis becomes very difficult. It is found through some examples that the waves with larger periods and/or amplitudes are more important for determining the correlations. Small periods more readily cancel when calculating the accumulated precipitation.
c. Test of theory
The above theoretical analysis shows that an oscillation of precipitation can cause a significantly negative S–P correlation. Does such periodicity really exist in the precipitation time series? Figure 9 shows the precipitation power spectrum of a grid point in Russia, where there is a significantly negative S–P correlation of −0.82 in GSWP-2 data (Fig. 3c). Its strongest power is at the 30–60-day period, where the phase difference between P30(t) and S(t) is close to π in Fig. 8, especially for λ = 0.02, the probably more realistic value there.
The theoretical analysis (Fig. 8) shows that there are some spectral intervals that have phase differences closer to π than others, such as the 32–60- and 10–20-day intervals, which indicates more significantly negative S–P correlations. As mentioned, the large periods are more important for determining the correlations. Thus, the 32–60-day period is selected to show the spatial distributions. The spatial distribution of this bandpass spectrum can be compared with the spatial distribution of the S–P correlation to see whether there is some similarity. If there is, our theory is partly supported, although there is a possibility that the period that determines the correlation is in another band, such as 10–20 day.
The spatial distribution of the precipitation spectrum is calculated using the power spectrum analysis, which is based on discrete Fourier transform, and the power is shown at discrete periods: 23, 30.67, 46, and 92 days (Fig. 9). The power at the period of 46 days is selected because it is in the middle of the 32–60-day band. The GSWP-2 data are used as an example. Figure 10 shows that the spatial distributions of the power spectrum are similar to the spatial distributions of the S–P correlations, especially in Mexico, India, parts of Russia and South America, and middle Africa. Note that besides the 32–60-day variability, the precipitation oscillation at other periods may also influence the S–P correlation, and the soil moisture memory also plays a role. Given these factors, the consistency found in Fig. 10 adequately supports the theory.
As this correlation pattern in summer is found to be mainly caused by the precipitation oscillation and not soil moisture feedback, it should also exist in other seasons, as found by further analysis (not shown).
5. Discussion
a. Spatial-scale dependence of the S–P relationship
The S–P correlations have been calculated at each grid point, from 0.3° (NARR) to 2.8° (CAM3). An interesting question is how such correlations change with spatial scales. The average correlation at different spatial scales is calculated using ERA-40 data and for a large region over the Eurasian continent (35°–65°N, 20°–120°E). Figure 11 shows the change of correlation with spatial scale. The correlation is negative at all spatial scales, but is most strongly negative at an intermediate spatial scale. At an intermediate spatial scale, small spatial–temporal variabilities in precipitation and soil moisture time series may cancel with averaging and emphasize the intraseasonal oscillations, leading to stronger S–P correlations. At a too large spatial scale, the intraseasonal oscillations may be weaker because of cancellation, leading to weaker S–P correlations. Similar results are found for other continents.
b. Relation to the study of Findell and Eltahir (1997)
Figure 12 shows the lagged S–P correlation in Illinois as calculated with the method of Findell and Eltahir (1997). Rather than calculating the correlation for each year and then averaging over the years as we did, they calculated the correlation at each day over all the years. Obviously, this calculation method is also affected by the natural variability of the precipitation, but it is interannual variability rather than intraseasonal variability. The correlations for different soil depths differ little because most soil water variability is at the surface. The three reanalyses and CAM3 differ extensively, but most show a positive S–P correlation in the warm season. The main reason for the difference from our analysis is that precipitation has much less autocorrelation at the interannual time scale and so feedbacks may have a higher signal-to-noise ratio.
Figure 12d shows the results from the two CAM3 experiments (described in section 3c). The difference between the two experiments (Cnt-Cnt_s) shows that the influence of soil moisture feedback on the S–P correlation is positive. In addition, both of the two experiments show a positive correlation in the warm season. This indicates that even without soil moisture feedback, the S–P correlation is still mostly positive. This will be very intriguing when analyzing the observational data. Therefore, combining data analysis with model simulations would be more reliable to study a causal relationship.
6. Summary and conclusions
This paper examines a lagged S–P correlation in three reanalysis products, GSWP-2 data, and CAM3 simulations during boreal summer. The S–P correlation patterns are found to be largely negative in all the datasets. Experiments with CAM3 show that soil moisture feedback is not the main reason for this correlation pattern. Further analysis shows that it is caused by the combined effects of the autocorrelation of precipitation and the memory of soil moisture. The precipitation in most land areas tends to have a negative autocorrelation, resulting from the intraseasonal oscillations of the atmosphere. Soil memory integrates the influence of past precipitation and leads to a negative lagged S–P correlation. A theoretical analysis confirms the above results and shows that the S–P correlation depends on both the spectrum of the precipitation oscillation and the time scale of the soil moisture retention. Precipitation oscillations at 32–60-day periods are most likely to induce a significantly negative S–P correlation, which can be enhanced by longer soil water retention time. The observational data support the theory.
Climate processes include complex interactions. Whether a feedback is significant in the system depends on whether it is detectable from the background noise [i.e., other processes and feedbacks; e.g., Wei et al. (2006)]. The lagged S–P correlations in our analysis do not indicate a causal relationship between soil moisture and subsequent precipitation. The effect of soil moisture feedback on the calculated S–P relationship is much weaker than that from other sources and is difficult to distinguish in the observational data. The model experiments in this study allow the feedback effect to be distinguished in a highly interactive climate system. Carefully designed model experiments have been used to study the role of soil moisture on precipitation (e.g., Koster et al. 2003; GLACE). These studies are not limited to correlation analysis and have greatly increased our understanding of their interactions.
Because of the variability in the precipitation time series, the feedback in our analysis has a very low signal-to-noise ratio; other calculation methods or time series may not. Some more complex method, such as Granger causality, may eliminate some noise and enhance the signal. This study cautions against attributing a lagged S–P correlation to the influence of soil moisture on precipitation, or likewise, a lagged vegetation–precipitation correlation to the influence of vegetation on precipitation.
Acknowledgments
ECMWF ERA-40 data used in this study have been obtained from the ECMWF data server. R-2 and NARR data is provided by the NOAA/OAR/ESRL PSD, Boulder, Colorado, USA, from their Web site at http://www.cdc.noaa.gov/. GSWP-2 data is from its website at http://www.iges.org/gswp/. The research was supported by NSF Grant ATM-03433485 while Jiangfeng Wei was a student at Georgia Tech.
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APPENDIX
Theoretical Analysis of the S–P Relationship
Daily soil water of the top 2 m in Illinois from ERA-40, R-2, NARR, GSWP-2, and observational data: (a) soil water and (b) soil water anomaly after removing the seasonal cycles. The GSWP-2 data are multiplied by a factor of 4/3 to normalize its 1.5-m soil water to the 2-m depth of the other datasets.
Citation: Journal of Hydrometeorology 9, 6; 10.1175/2008JHM955.1
The summer (Jun–Aug, JJA) monthly anomaly correlations of (a) soil water of top 2 m, (b) total precipitation, (c) ET, and (d) downward solar radiation between 24 yr of ERA-40 and R-2 data. The R-2 data are interpolated to the same grid as ERA-40.
Citation: Journal of Hydrometeorology 9, 6; 10.1175/2008JHM955.1
The summer average S–P correlations from the (a) ERA-40, (b) R-2, (c) GSWP-2, and (d) NARR datasets. All the data are on their native grids. See text for the calculation method. Only the average correlations over the 95% confidence level are shaded. The 95% confidence level is 0.05 for (a), (b), and (d) but 0.08 for (c), because GSWP-2 only has 10 yr of data while other datasets have 24 yr of data. For simplicity, 0.05 is used for all the datasets. See Wilks (2006, section 5.2) for calculating the confidence level for the mean.
Citation: Journal of Hydrometeorology 9, 6; 10.1175/2008JHM955.1
The average S–P correlations from the CAM3 simulations: (a) Cnt and (b) Cnt_s. Their difference is shown in (c) Cnt − Cnt_s. Only the differences over the 95% confidence level are shown in (c).
Citation: Journal of Hydrometeorology 9, 6; 10.1175/2008JHM955.1
Same as in Fig. 3 but for the correlation between past 21-day accumulated precipitation and subsequent 30-day accumulated precipitation.
Citation: Journal of Hydrometeorology 9, 6; 10.1175/2008JHM955.1
Same as in Fig. 3 but for the correlation between past 21-day accumulated precipitation and soil moisture on the current day.
Citation: Journal of Hydrometeorology 9, 6; 10.1175/2008JHM955.1
The phase differences between the precipitation time series P(t) and future 30-day accumulated precipitation P30(t) (green line), P(t) and soil water S(t) with λ = 0.02 (blue line) and λ = 1 (red line), and P(t) and past 21-day accumulated precipitation P−21(t) (black line) for different periods of T. Positive values denote leading P(t), and vice versa for the negative values.
Citation: Journal of Hydrometeorology 9, 6; 10.1175/2008JHM955.1
The phase differences between P30(t) and S(t) with λ = 0.02 (blue line) and λ = 1 (red line) and between P30(t) and P−21(t) (black line). The thin lines are the calculated values and the thick lines are their respective 15-day running averages. All phase differences are transformed to 0 − π.
Citation: Journal of Hydrometeorology 9, 6; 10.1175/2008JHM955.1
The power spectrum of GSWP-2 JJA daily precipitation for a grid point in Russia (55°N, 50°E). The thin lines are for each year during 1986–95; the thick line with markers is their average. The horizontal dashed line is the 95% confidence level against white noise for each year, not the average.
Citation: Journal of Hydrometeorology 9, 6; 10.1175/2008JHM955.1
(a) Average spectral density of normalized precipitation at a period of 46 days. The 95% confidence level against white noise is 0.06 for each individual year; the average should have a higher confidence level at 0.06. (b) The S–P correlation from Fig. 3c. All the calculations use the 10-yr daily GSWP-2 data in JJA.
Citation: Journal of Hydrometeorology 9, 6; 10.1175/2008JHM955.1
The change of the S–P correlation with the spatial scale. The correlation is calculated as the average of the correlations for all the subregions of a large region over Eurasian continent (35°–65°N, 20°–120°E). The horizontal axis shows the area of a subregion.
Citation: Journal of Hydrometeorology 9, 6; 10.1175/2008JHM955.1
The correlation between soil moisture on each day of a year and precipitation on the subsequent 30 days in IL. The correlation is calculated with the method of Findell and Eltahir (1997). The points are the original correlations, and the lines are their 21-day running averages. Correlations with soil water at different depths are shown. The 95% confidence level for the original correlation (not the smoothed lines) is 0.404.
Citation: Journal of Hydrometeorology 9, 6; 10.1175/2008JHM955.1
The temporal coverages, resolutions, and soil-layer thicknesses of the datasets.
