3.2. Methods Figure 4 shows the scatter plots of May-August daily SM(GW) versus (21-day) Psub in the 10-year period (2004-13) Significant correlations are observed in May-August, in consistency with the common knowledge of observed SM-P feedbacks during late spring to early summer in previous studies [e.g., FE97, Kochendorfer and Ramirez, 2005; Meng et al., 2014; Yin et al., 2014]. Generally, SM(GW)-Psub correlations decrease as SM(GW) dries up. Correlations are positive in May and June (r > 0.5); decrease from July on and turn negative in August. In May-June, SM-Psub correlations at the 20-100cm layers are higher than at other depths (5, 10 and 150cm). The high SM100-Psub correlation is greatly influenced by dry SM outlier. Otherwise, SM at 100-150cm layers are near saturation for most of the time while Psub is greatly varying. The GW reach to 1.5m depth for most of the time in May-June, thus the GW-Psub correlations are similar to SM-Psub correlations at 100-150cm layers. 16/01/2019

4.1. Feedbacks between subsurface water storage and precipitation Figure 5a shows the seasonal variations of the correlations of SM(GW) with (21-day) Pant in inter-annual timescale. The correlations of Pant-SM remain positive for almost all the days in the year with the highest in summer particularly in June and July (with highest r = 0.98 on 18 June at 50cm) and the lowest in winter when the soil is in near saturation. Pant-Psub correlation rarely reach to significant level (with highest r = 0.94 on 29 May). The Pant-SM correlations, in particular for SM layers between 0-50cm, are noticeably higher than Pant-Psub correlation. The influence of Pant to SM is more significant compared to P persistence since Pant affects the SM storage directly through infiltration. On the other hand, the Pant-SM correlations at deep layers (100-150cm) with their peaks at r = 0.93 occurring on 11-16 July are noticeably lower than at the shallow layers. Also, the high Pant-SM correlations (r > 0.63) at the 0-50cm layers start from April, but the correlations at deep layers do not reach r = 0.63 until June-July. The lag of Pant-SM correlations at deep layers mainly reflect the 2-3 month lags in the seasonal cycles of SM, as shown in Figure 3c. While the Pant-SM correlations at 50-150cm layers decrease to become insignificant after August, the correlations remains high (r > 0.63) for surface layers (0-20cm). This coincides in the seasonal cycles of SM in Figure 3c, the SM at deep layers is still drying in August-December, while that at shallow layers has begun to increase after August corresponding to higher P in autumn. 16/01/2019

4.1. Feedbacks between subsurface water storage and precipitation In Figure 5b, in contrast to the Pant-SM correlations, the SM-Psub correlations at all the six layers have similar magnitudes and also follow the similar pattern throughout the year. Significant positive correlations are found only from May to July with the peaks occurring in May and June (highest peak r = 0.94 on 27 May at 50cm). In consistency with the previous findings in Illinois using 1979-02 model-simulated SM data [Wei et al., 2008, Figure 12], the SM-Psub correlations are positive during the warm season and shifts to negative in August. From April-May, the SM50-Psub correlation is slightly higher compared to the SM-Psub correlations of other layers, with their peaks occurring in late June ranging from r = 0.88 (at 150cm) to 0.94 (at 100cm). As seen in the daily SM time series in Figure 2b, SM at shallow layers (0-20cm) has less predictive power because of its high sensitivity to the fluctuations on the surface, thereby decreasing its memory. In contrast, SM at deep layers (100-150cm) are near saturation for most of the time, also decreasing its predictive power to Psub. SM50 has less daily fluctuations but its seasonality is still well-defined. Although the seasonal patterns of the correlations are similar, the magnitude of SM-Psub correlations at 0-100cm layers are larger than that of Pant-Psub from April to July. This suggest the possibility of Pant-Psub correlation being reflected on the SM-Psub correlations [Salvucci et al., 2002]. The amplification of SM-Psub correlations is due to the strong SM memory at these layers [Wei et al., 2008; Meng et al., 2014], as shown in the high Pant-SM correlations in Figure 5a. 16/01/2019

4.1. Feedbacks between subsurface water storage and precipitation The correlations of Pant and Psub with GW, also shown in Figure 5a and 5b respectively, are compared with the SM correlations by taking the r2 between the two correlation time series from April to September. The Pant-GW follows Pant-SM150 the most, with r2 = 0.66. However, from April-August Pant-GW correlation closely follows Pant-SM correlations at shallow layers (0-20cm), then it drops following the correlations at deep layers (50-150cm). This suggest that during wet GW in late spring-early summer period the sensitivity to Pant is high, as reflected by the peak of the seasonal cycles of GW and SM at shallow layers (Figure 3c and 3e). From August until the rest of the year, the interaction between SM at deep layers and GW dominates during the driest period. The GW-Psub correlation follows closely with the SM-Psub correlations at all layers (r2 > 0.87). The peak of Psub-GW correlation (r = 0.92) is second to the peak of Psub-SM50 (r = 0.94), suggesting that GW has more predictive power to Psub than other layers of SM. 16/01/2019

4.1. Feedbacks between subsurface water storage and precipitation Figure 6 shows the square of the correlations (r2) in Figure 5, indicating the percentage of Psub that can be explained by SM(GW) or Pant. The 10-year (2004-13) r2 of Pant-Psub is similar to the previous findings in Illinois using 1981-94 P data [FE97, Figure 5], where the peak of predictive power of Pant in mid-June is barely in the 5% level of significance (r2 = 0.40). The difference of the correlations Pant-SM and SM-Psub from Pant-Psub in April-August is larger when the coefficient of determination r2 is considered. The r2 of Pant-SM peaks at 0.96 while that of SM-Psub and Pant-Psub peaks at 0.88. The 21-day smoothing of the original r2 curves further dampens the magnitude of Pant-Psub correlations and its difference to SM-Psub is noticeable. Whether this difference provides evidence of SM having greater predictive power to Psub than Pant will be evaluated in Chapter 6 using analysis of variance (ANOVA) between the two correlation curves. 16/01/2019

4.1. Feedbacks between subsurface water storage and precipitation Figure 7 shows the scatter plots of SM(GW) and (21-day) Pant versus the corresponding (21-day) Psub on 22-26 July, when the r in Figure 5b drops from positive to negative. The scatter plots suggest that the anomalous years of 2012 (dry) and 2010 (wet) may have influence in the direction of r as an outlier. The scatter plot of Pant versus Psub in particular shows that the correlation is sensitive to a single day P event in 24 July 2010. As seen in both figures of Figure 5, the drop of Pant-SM correlations in August lags behind that of SM-Psub correlations by 21-days, with the drop of Pant-Psub correlation occurring in the middle of this period. 16/01/2019

4.1. Feedbacks between subsurface water storage and precipitation Figure 8 shows the 10 data points during the days of highest positive (left) and lowest negative (right) SM(GW)-Psub correlations in Figure 5b. The mean of all the correlations are taken, and the timing of its peak on 25 June and trough on 11 August are taken as the days during which the SM(GW)-Psub correlations are strongest. On June 25, a consistent SM(GW)-Psub positive correlation during the 10-year period can be observed for all layers. On August 11, high Psub is generated during the driest years while the Psub is variable during the other years, and weaker magnitudes (r = 0.61) than the positive r (0.88) are observed at all layers. However, the lack of SM(GW)-Psub correlation during intermediate and wet SM(GW) suggests that from August until early spring, the weak negative correlations in Figures 4 and 5b are caused by the loss of evapotranspiration sensitivity to SM variations [Wei and Dirmeyer, 2012, Meng et al., 2014]. In fact, evapotranspiration in Illinois is dominantly energy-limited, except perhaps in late-spring to early-summer when SM(GW)-Psub correlations are positive. The scatter plots between Pant and Psub for both dates (bottom row) show similar pattern to those with SM(GW)-Psub correlations, suggesting a possibility of P persistence influencing the SM(GW)-Psub correlations. 16/01/2019

4.1. Feedbacks between subsurface water storage and precipitation The correlation analysis between the inter-annual variability of each day’s SM(GW) and P over the 10-year period raise some issues on its statistical robustness due to its 10-pair sampling size per day. While the derived daily r measures the consistency in the relative ranking of SM(GW)-Psub pairs for a certain day, it cannot differentiate among the magnitude of each data point. The correlation using a small sample number (i.e., 10 pairs) makes the analysis sensitive to outliers, in this case the SM(GW) and P conditions during anomalous wet/dry years. Besides, the climatology of a certain day over all the years is not so meaningful, since there is no distinct hydro-climatic condition for each day unlike those for each season. To make the inter-annual correlation more statistically robust, the 5-day pentad SM-, GW- and Pant-Psub correlations are conducted and the results are shown in Figure 9. All the 50 daily data within the same pentad over the 2004-13 period are used to calculate the correlation coefficient. The increase of sampling size from 10 to 50 samples decrease the significant r from 0.63 to 0.28, as indicated by the purple and red solid lines respectively in Figure 9. No considerable difference can be seen when the two correlation timescales are compared. However, the duration of significantly positive SM(GW)-Psub correlations increased (Figure 9a-g) to include April. Significant positive Pant-Psub correlation (Figure 9h) are identified from May to mid-July when pentad correlation analysis is used. 16/01/2019

4.1. Feedbacks between subsurface water storage and precipitation Although pentad correlation analysis increased the statistical robustness of the SM(GW)-Psub correlations considerably, the climatology of a certain pentad or week over all the years is still not so meaningful compared to the climatology of each month. Thus, the monthly correlations between Pant-Psub, Pant-SM(GW) and SM(GW)-Psub are calculated and plotted in Figure 10. All the ~300 daily data within the same month of a year over the 2004-13 period are used to calculate the correlations. The same patterns of correlations are observed in the daily inter-annual correlations in Figure 5 and the monthly correlations in Figure 10, Significant correlations are observed in April similar to the pentad SM(GW)-Psub correlations (Figure 9). However, the ~21 days lag of the drop in the SM(GW)-Psub correlation (Figure 5b) behind that of Pant-SM(GW) correlation (Figure 5a) cannot be seen in the monthly correlations, where both drops occur in August. The increase of sampling size decrease the significant r from 0.63 to 0.11, with the latter value denoted by the purple solid lines in Figure 10. 16/01/2019

4.2. Sensitivity Analyses Figure 11 shows the comparison between SM-Psub correlations using the complete daily SM data in this study and using bimonthly interpolated SM data similar to FE97 (SM FE97). According to Salvucci et al. [2002], the interpolated daily SM data based on bimonthly observations in Illinois used in FE97 is heavily influenced by the Pant conditions during the next (bimonthly) observational interval. The SM-Psub correlations in FE97 [Figure 7 p. 731] are significantly higher compared to Pant-Psub correlation, leading to their finding that SM-P feedbacks is not a mere consequence of P persistence. Also, a higher SM-Psub correlation at 10cm depth is found [Figure 4 p. 729] where the Pant-SM correlation is stronger than that of the deep layers (50-90cm depths) [Figure 6 p. 730]. In order to test the sensitivity of SM-Psub correlations using interpolated SM, we follow the calculation of SM-Psub correlation in FE97 (r2) by using bimonthly-interpolated SM data. Three sets of SM FE97 are derived in this sensitivity analysis. In SM FE9715-28, only the SM measurements on the 15- and 28-day of each month are used to linearly interpolate SM for the rest of the days of the month. Similarly, SM FE9705-15 and SM FE9710-20 interpolate SM measurements on the 5- and 15-day, and 10- and 20-day of every month. The comparison among the r2 values are shown in Figure 11, An artificial increase in the correlations are found at all soil layers when the interpolated SM data are used (SM FE97-Psub). At shallow layers (0-5 to 0-20cm) (Figure 11a-c), the peak of SM FE97-Psub correlations reach r2 = 0.6 while those of SM-Psub correlations (black lines) reach only r2 = 0.5. At deep layers (0-50 to 0-150cm) (Figure 11d-f), the peak of SM FE97-Psub correlations (r2 = 0.7) differ those of SM-Psub correlations (r2 = 0.6) by 0.1. Assuming the SM-Psub correlations are the true values, the difference between SM FE97-Psub and SM-Psub correlation is larger at the shallow layers (bias 58-75%) than at deep layers (bias 24-36%). 16/01/2019

4.2. Sensitivity Analyses As seen in the daily SM and SM FE97 time series in 2012 in Figure 12, the SM at surface layers (Figure 12a-c) are more dynamic than at deep layers (Figure 12d-f). The correlation (in the years 2004-13) between the daily SM and SM FE97 at shallow layers ranges between 0.91 to 0.95, while it is higher at deep layers with r ~ 0.98. 16/01/2019

4.2. Sensitivity Analyses Despite the higher artificial increase of SM-Psub correlations at shallow layers (Figure 11a-c), the magnitude of correlations (r2 ~ 0.6) are still lower than that at deep layers (r2 > 0.6) (Figure 11d-f). The interpolation of bimonthly SM does not create a bias towards a higher SM-Psub correlation at shallow layers, contrary to the argument of Salvucci et al. [2002]. However, the interpolated SM does create a bias towards SM-Psub correlations over the Pant-Psub correlation (green line), where the SM-Psub correlations at shallow layer are close or even smaller than the P auto-correlation. The SM-Psub correlations at deep layers (Figure 11d-f) is higher compared to that at surface layers (Figure 11a-c), while the inverse was found in FE97 [Figure 4 p. 729]. FE97 found that SM-Psub correlation was damped at greater depths: the peak of SM0-10-Psub correlation ~ 0.7 and ~ 0.5 at 0-50cm layer. However, in this study, the peak of SM0-10-Psub correlation is ~ 0.6 and ~ 0.7 at 0-50cm depth. A potential reason for this discrepancy is likely due to the consistency of SM and P data used in this study, while FE97 used SM data from ICN and daily P from 129 stations of another data source. Additionally, the lagged correlation may be sensitive to the period of analysis chosen: FE97 analysed the 1981-94 period while 2004-13 period was chosen for this study. The sensitivity of the correlation analysis on the chosen period will be discussed later. 16/01/2019

4.2. Sensitivity Analyses When r instead of r2 is calculated like in this study (Figure 13), the pattern of Pant-Psub correlation follows those of SM-Psub and SM FE97-Psub. Contrary to the conclusion in FE97, the Pant-Psub correlation is similar to the SM-Psub correlations and it is possible that the SM-Psub correlations reflects the P persistence in Illinois. 16/01/2019

4.2. Sensitivity Analyses The effects of the chosen lag time on the SM(GW)-Psub and Pant-Psub correlations are explored in Figure 14. The sensitivity of the correlations to the different days of cumulative P is evaluated by using 7-, 14- until 63-day Psub(Pant). We focus the comparisons in warm season (April-September) only. In Figure 14a, marginally larger and significant Pant-Psub correlations are found from May to June when more than 21 days of cumulative P are used. The P auto-correlation is not captured in shorter lag times, i.e., 7 and 14 days. Although in a lesser degree, similar results are found in the SM(GW)-Psub correlations (Figure 14b-h) where there are more significant correlations with increasing days of cumulative P. 16/01/2019

4.2. Sensitivity Analyses The difference of Pant-SM(GW), SM(GW)-Psub and Pant-Psub correlations (Figure 15) varies when using different cumulative days. The Pant-SM correlations at shallow layers (0-20cm) remain high for most of the year Those at deep layers (50-150cm) including GW decreases when less cumulative days are used and loses its correlation after the drying of SM(GW). The sensitivity of SM at shallow layers on Pant suggest that their SM-Psub correlations reflects the Pant-Psub (P auto-correlation). The SM at deep layers and GW have more predictive power on Psub since their SM(GW)-Psub are considerably higher than the P auto-correlation. 16/01/2019

4.2. Sensitivity Analyses Figure 16 compares the SM-Psub correlations using direct measurements at six depths (i.e., SM5, SM10, SM20, SM50, SM100, SM150), and using cumulative SM from the top to the depth specified (i.e., SM0-5, SM0-10, SM0-20, SM0-50, SM0-100, SM0-150). Each reading is assumed to represent a layer from previous reading point, that is, SM5 is SM at 0-5cm, SM10 is SM at 5-10cm and SM0-150 is the summation of SM from 5 to 150cm (in mm). As seen in Figure 16, the difference of r using the two SM values is not considerable with the root mean square error (RMSE) from 0.07-0.23 The difference becomes more noticeable in the deep layers (50-150cm). SM0-50-Psub correlation is lower than that using SM50. At 100-150cm, using cumulative SM increase the SM-Psub correlations and become more similar in shape to SM0-50-Psub correlation. This means that the SM-Psub correlation is sensitive to the variability of SM at the top layers. The root zone is within 50-100cm depth, which is the area closely linked to evapotranspiration and thereby to precipitation. The SM at deeper depths (0-50 to 0-150cm) have greater memory than at shallower layers and so yields higher SM-Psub correlations. The SM memory is not captured when using SM measurements at each depths. Thus, the difference between SM-Psub correlations at deep cumulative layers and the Pant-Psub (P auto-correlation) is noticeably higher than using SM readings at each depth alone. 16/01/2019

4.2. Sensitivity Analyses The sensitivity of the correlation analyses on different periods are further explored: the SM-Psub and Pant-Psub correlations derived from a 9-year period, excluding the drought year of 2012, is shown in Figure 17. The dry SM and P conditions in 2012 does not affect the correlations considerably, However the shift from low to high P in August 2012 (Figure 18a) causes the negative SM-Psub correlations at 20-150cm layers (Figure 17c-f). 16/01/2019

4.2. Sensitivity Analyses While the Pant-Psub (P auto-correlation) is not sensitive to an outlier year, the auto-correlation is considerably different when the 1992-01 daily P is used (Figure 18). The April-July P conditions in 2004-13 (Figure18a) are persistently dry (wet) which explains the high P auto-correlation in this 10-year period. However, the April-July P conditions in 1992-01 are not consistent, and the Pant-Psub correlation in this 10-year period is low throughout the year. 16/01/2019